COLLABORATIVE MULTIPLE INPUT MULTIPLE

OUTPUT AND TURBO EQUALIZATION TECHNIQUES

FOR THE UPLINK OF THE LTE-ADVANCED SYSTEM

A THESIS

Presented to the Graduate School

Faculty of Engineering, Alexandria University

In Partial Fulfillment of the

Requirements for the Degree

Of

Master of Science

In

Electrical Engineering

By

Karim Ahmed Samy Banawan

September 2012

COLLABORATIVE MULTIPLE INPUT MULTIPLE

OUTPUT AND TURBO EQUALIZATION TECHNIQUES

FOR THE UPLINK OF THE LTE-ADVANCED SYSTEM

Presented by

Karim Ahmed Samy Banawan

For The Degree of

Master of Science

In

Electrical Engineering

By

Karim Ahmed Samy Banawan

Examiners' Committee: Approved

Prof. Said Mohamed El-Noubi ………………

Prof. Essam Abdel-Fattah Sourour ………………

Prof. Ayman yehia Ali El-Ezabi ………………

Vice Dean for Graduate Studies and Research

Prof.: Heba Wael Leheta

I

Advisors' Committee:

…………. Prof.Dr. Essam Abdel-Fattah Sourour

II

AACCKKNNOOWWLLEEDDGGEEMMEENNTTSS

All praise be to Allah, the lord of the worlds, most Gracious, most merciful.

Foremost, I would like to express my sincere gratitude to my advisor Prof. Dr. Essam

Sourour for the continuous support of my research, for his patience, motivation,

enthusiasm, and immense knowledge. His guidance helped me in all the time of research

and writing of this thesis. I could not have imagined having a better advisor and mentor for

my Master study.

Besides my advisor, I would like to thank the rest of my thesis committee: Prof. Said El-

Noubi, Prof. Ayman El-Ezabi, for their encouragement, insightful comments, and hard

questions.

My sincere thanks also goes to Dr. Ahmed K. Sultan, and Dr.Karim G. Seddik, for their

continuous support and help.

Special thanks goes to my friends and colleagues specially Mohammed Karmoose ,and

Yasser Yousri.

Last but not the least; I would like to thank my family and my dear fiancée Eman Ahdy

who supports me all the time.

III

AABBSSTTRRAACCTT

In this thesis, we consider the application of the collaborative MIMO and turbo

equalization (TEQ) schemes to the LTE-advanced system. LTE is the evolution of 3GPP‟s

Universal Mobile Telecommunication System (UMTS) towards an all-IP network. LTE is

being developed in Releases 8 and 9 of the 3GPP specifications and enhanced to have the

LTE-advanced in releases 10, 11.The first release of LTE provides peak rates of 300 Mb/s,

a radio-network delay of less than 5 ms, and a significant increase in spectrum efficiency

compared to previous cellular systems. LTE supports Frequency Division Duplex (FDD)

and Time Division Duplex (TDD), as well as a wide range of system bandwidths in order

to operate in a large number of different spectrum allocations. LTE also constitutes a major

step towards 4G requirements.

The MIMO schemes have attracted attention due to its great advantages that

promote it as a key technology for the upcoming 4G mobiles. These advantages include

array gain, spatial diversity gain, spatial multiplexing gain, interference reduction, and

dramatic increase the capacity of wireless channels because of the creation of independent

radio channels. MIMO has become a key component for several broadband wireless

communication standards. However, MIMO systems require complex transceiver circuitry

and signal processing. Moreover, physical implementation of multiple antennas on a small

node specially the uplink (UL) node of the LTE user equipment (UE) may not be realistic

.So single-antenna radio and limited battery power, high network performance and low

energy consumption have been very challenging issues in the design of LTE UL UEs.

Those are the motives for using the concept of the collaborative MIMO spatial schemes

(CSM). CSM works as the two or more users having UEs equipped with single or multiple

antennas, each one of them transmits independent data stream from the others. Those users

are collaboratively transmitting to same resource blocks (RBs), i.e. same frequency/time

grid resource. Now, the eNodeB is receiving combined data from all collaborative users,

eNodeB will then separate the data of each user using multiuser equalization techniques.

The thesis is organized as the following: chapter 1 gives an introduction to the

LTE system, collaborative MIMO system and turbo equalization techniques.

In chapter 2, we provide a detailed literature review about physical uplink shared

channel (PUSCH) processing of the LTE of the UMTS .we will also introduce the SC-

FDMA transmission and its differences from OFDMA transmission, the different

subcarrier mapping schemes and the time domain representation of these schemes. we give

also an overview about the LTE UL in which we consider the FDD frame structure , the

basic transmission parameters , the demodulation reference signals generation and the

PUSCH transmission procedure.

Chapter 3, we start with introducing the collaborative MIMO concept. Then we

proceed to construct the basic system model that will be used all over the context of thesis.

IV

Simulation model is studied in both single input single output case and CSM case for

general number of transmitting and receiving antennas, and then we continue with

describing the used channel model including different channel effects such that shadowing

phenomenon, and flat and frequency selective fading channels in case of slow and fast

fading channels. The chapter is also turning light system on the existent detection schemes

for collaborative MIMO case identifying the pros and cons for each detector. The chapter

ends with illustrative simulation results showing the main characteristics of each equalizer

in different simulation scenarios considering perfect and imperfect channel estimation.

We will then proceed in chapter 4 with our first contribution that include

proposing a novel Initial guess ML (IGML) receiver which dramatically enhances the

performance of the CSM system. The IGML‟s complexity will grow exponentially with

the modulation index only.We also provide a novel simplification for it using the QR

decomposition. Moreover, we present two novel ordering techniques to enhance the

performance of the SIC receiver, especially in the case of shadowing environments. A

comprehensive study of the motivation of each novel scheme with study of channel

imperfections and different channel conditions are also presented.

In chapter 5,we begin with identifying the new MIMO modes introduced in the

LTE-advanced, then we give a brief literature review of the precoding theory .Capitalizing

from advantages of precoding the transmitted streams prior to transmission ,codebook

precoding is discussed for LTE. The chapter thereafter will present system model

modifications over the system model introduced in chapter 3. We propose then a

combination between the collaborative system and the precoded MIMO whether ideally

(Singular value decomposition (SVD) precoding) or suboptimally using codebook

precoding. Then we propose a space frequency block code (SFBC) precoding for the

uplink to achieve space diversity with spatial multiplexing gain achieved before using the

collaborative system. The chapter eventually discusses the effect of these precoding

schemes on the previously presented receiver schemes.

In chapter 6, we introduce the Turbo Equalization (TEQ) technique as multiuser

equalization technique for the CSM system. So, we are getting “softer” ,capitalizing from

the performance gains of turbo codes and the turbo decoding algorithm. The TEQ is a joint

equalization and decoding scheme which are done iteratively by passing the soft outputs

generated by soft input soft output (SISO) equalizer to a SISO decoder and vice versa. This

will enhance the overall link performance at the expense of increasing of receiver‟s

complexity and receiver‟s delay. The chapter discusses the basic components of the TEQ

receiver. Moreover we will extend this TEQ concept to precoded CSM system presented in

chapter 5. We will also generalize the SFBC receiver in chapter 5 to operate in highly

selective channels to maximize the frequency diversity exploited by the TEQ.

Chapter 7 gives a comprehensive conclusion of the discussed work and gives a

glance on the possible research work that can be appended to the presented thesis

V

TTAABBLLEE OOFF CCOONNTTEENNTTSS

ACKNOWLEDGEMENTS ............................................................................................................. II

ABSTRACT ................................................................................................................................... III

TABLE OF CONTENTS ............................................................................................................ V

LIST OF TABLES ..................................................................................................................... IX

LIST OF FIGURES ..................................................................................................................... X

LIST OF ABBREVIATIONS ............................................................................................... XIII

CHAPTER ONE ........................................................................................................................... 1

INTRODUCTION ........................................................................................................................ 1

1.1 Historic view of the evolution of the mobile communications ........................................................ 1

1.2 Introduction to LTE ...................................................................................................................... 3

1.3 Introduction to MIMO technology ................................................................................................ 5

1.4 Introduction to collaborative MIMO (Virtual MIMO systems) ..................................................... 9

1.5 Introduction to Turbo codes ........................................................................................................... 11

1.5 Introduction to Turbo equalization (TEQ) .................................................................................. 12

1.6 Thesis organization and contributions ......................................................................................... 13

CHAPTER TWO ......................................................................................................................... 14

LITERATURE REVIEW OF SC-FDMA AND LTE UPLINK ..................................... 14

2.1 Introduction .................................................................................................................................... 14

2.2 Wide-band single-carrier transmission (SC-FDMA) ....................................................................... 14 2.2.1 Introduction ........................................................................................................................................ 14 2.2.2 SC-FDMA generation ........................................................................................................................ 15 2.2.3 Subcarrier mapping schemes .............................................................................................................. 17 2.2.4 SC-FDMA receiver ............................................................................................................................ 21 2.2.5 Relation between SC-FDMA and OFDMA ....................................................................................... 22 2.2.6 Performance limits for linear frequency equalizers ............................................................................ 23

2.3 Literature review for 3GPP LTE uplink ......................................................................................... 24 2.3.1 Introduction ........................................................................................................................................ 24

VI

2.3.2 Physical resource blocks .................................................................................................................... 25 2.3.3 FDD frame structure .......................................................................................................................... 27 2.3.4 SC-FDMA signal parameters for LTE UL ......................................................................................... 28 2.3.6 Uplink reference signals ..................................................................................................................... 30 2.3.7 Uplink physical data processing (PUSCH processing) ...................................................................... 33

CHAPTER THREE .................................................................................................................. 35

COLLABORATIVE MIMO SYSTEM MODEL AND EXISTENT DETECTION

SCHEMES .................................................................................................................................. 35

3.1 Introduction .................................................................................................................................... 35

3.2 Collaborative MIMO concept ......................................................................................................... 35

3.3 Transmitter description .................................................................................................................. 37 3.3.1Channel coding ................................................................................................................................... 38 3.3.2 Symbol mapping process ................................................................................................................... 39 3.3.3 Summary of the simulation parameters in our model ........................................................................ 40

3.4 Channel modeling ........................................................................................................................... 41 3.4.1 Large scale fading (Shadowing) model .............................................................................................. 41 3.4.2 Flat and frequency selective fading channel modeling ...................................................................... 42 3.4.3 Slow and fast fading channel modeling ............................................................................................. 43 3.4.4 Fading channel for collaborative MIMO channel (Spatial model) ..................................................... 44

3.5 Single user single output (SISO) receiver ........................................................................................ 45 3.5.1 Single user zero forcing equalizer (SISO ZF equalizer) .................................................................... 45 3.5.2 Single user minimum mean square error equalizer (SISO MMSE equalizer) .................................... 46 3.5.3 Channel estimation Schemes .............................................................................................................. 46 3.5.4 Simulation results and discussion ...................................................................................................... 48

3.6 Existent detection schemes for collaborative MIMO schemes ......................................................... 52 3.6.1 Frequency domain multiuser ZF equalizer ......................................................................................... 53 3.6.2 Frequency domain multiuser MMSE equalizer .................................................................................. 53 3.6.3 Frequency domain multiuser SIC equalizer ....................................................................................... 54 3.6.4 Simulation results and discussion ...................................................................................................... 56

CHAPTER FOUR ..................................................................................................................... 65

PROPOSED MULTIUSER EQUALIZATION TECHNIQUES ................................... 65

4.1 Introduction .................................................................................................................................... 65

4.2 Proposed optimal ordering for successive interference cancellation (optimal OSIC) ...................... 65 4.2.1 Motivation .......................................................................................................................................... 65 4.2.2 Optimal OSIC description (per-subcarrier ordering) ......................................................................... 66 4.2.3 Results and discussion........................................................................................................................ 67 4.2.4 Advantages and disadvantages ........................................................................................................... 67

4.3 Proposed suboptimal ordering for SIC (Suboptimal OSIC) ............................................................ 68 4.3.1Motivation ........................................................................................................................................... 68

VII

4.3.2 Suboptimal OSIC description ............................................................................................................ 68 4.3.3 Results and discussions ...................................................................................................................... 69 4.3.4 Advantages and disadvantages ........................................................................................................... 69

4.4 Proposed Initial guess based Maximum likelihood Receiver (IGML receiver) ............................... 70 4.4.1Motivation ........................................................................................................................................... 70 4.3.2 IGML receiver description ................................................................................................................. 70 4.3.3 Results and discussions ...................................................................................................................... 72 4.3.4 Advantages and disadvantages ........................................................................................................... 72

4.5 Proposed simplified Initial guess based Maximum likelihood Receiver (simplified IGML receiver)

.............................................................................................................................................................. 73 4.5.1 Motivation .......................................................................................................................................... 73 4.5.2 Overview of SD ................................................................................................................................. 73 4.5.3 Simplified IGML receiver description (QR-IGML receiver) ............................................................. 75 4.5.3 Results and discussions ...................................................................................................................... 76 4.5.4 Advantages and disadvantages ........................................................................................................... 77

4.6 Conclusions ..................................................................................................................................... 78

CHAPTER FIVE ....................................................................................................................... 79

COMBINED COLLABORATIVE AND PRECODED MIMO FOR THE UPLINK

LTE-ADVANCED ..................................................................................................................... 79

5.1 Introduction .................................................................................................................................... 79

5.2 Overview of the uplink enhancements of the LTE-advanced .......................................................... 79

5.3 Overview of the precoding theory ................................................................................................... 80

5.4 Codebook precoding for uplink of the LTE-advanced .................................................................... 81

5.5 System model modifications for the LTE UL with precoding ......................................................... 84

5.6 Combined collaborative and SVD-precoded MIMO for the uplink of the LTE-advanced .............. 86 5.6.1 Algorithm description ........................................................................................................................ 86 5.6.2 Results and discussions ...................................................................................................................... 87 5.6.3 Advantages and disadvantages ........................................................................................................... 89

5.7 Combined collaborative and Codebook-precoded MIMO for the uplink of the LTE-advanced ... 89 5.7.1 Algorithm description ........................................................................................................................ 89 5.7.2 Results and discussions: ..................................................................................................................... 91 5.7.3 Advantages and disadvantages ........................................................................................................... 94

5.8 Combined collaborative MIMO and space frequency block codes (SFBC) for the uplink of the

LTE-advanced ...................................................................................................................................... 94 5.8.1 Algorithm description ........................................................................................................................ 94 5.8.2 Results and discussions ...................................................................................................................... 96 5.8.3 Advantages and disadvantages ........................................................................................................... 98

5.9 Effect of precoding to other equalization techniques ....................................................................... 99

VIII

5.10 Conclusions ................................................................................................................................... 99

CHAPTER SIX ........................................................................................................................ 101

TURBO EQUALIZATION FOR UPLINK OF LTE-ADVANCED ........................... 101

6.1 Introduction .................................................................................................................................. 101

6.2 Literature review about Turbo Equalization Technique ............................................................... 101 6.2.1 Philosophy of TEQ and Douillard‟s TEQ ....................................................................................... 101 6.2.2 Literature review of TEQ methods ................................................................................................... 102

6.3 System model modifications and Turbo Equalizer main components ........................................... 102 6.3.1 Subblock interleaver and rate matching (RM) ................................................................................. 103 6.3.2 Soft demodulator with priors (SISO demapper) ............................................................................... 104 6.3.3 Soft mapper (SISO mapper) ............................................................................................................. 105 6.3.4 SISO decoder ................................................................................................................................... 105

6.4 TEQ Techniques for CSM of the LTE uplink .............................................................................. 106 6.4.1 Soft -PIC based Turbo Equalization (Soft PIC-TEQ) ...................................................................... 106 6.4.2 Soft initial guess Maximum likelihood receiver (Soft single IGML) extension to PIC-TEQ .......... 110

6.5 TEQ Techniques for Precoded CSM of the LTE-advanced .......................................................... 112 6.5.1 PIC-TEQ for SFBC precoded CSM in highly selective channels .................................................... 112 6.5.2 PIC-TEQ for Codebook and SVD precoded CSM .......................................................................... 118

6.6 Conclusions ................................................................................................................................... 123

CHAPTER SEVEN ................................................................................................................. 124

CONCLUSION AND FUTURE WORK ........................................................................... 124

7.1 Conclusion ..................................................................................................................................... 124

7.2 Future work ................................................................................................................................... 125

APPENDIX 1 ............................................................................................................................ 126

LIST OF PUBLICATIONS .................................................................................................. 126

REFERENCES AND BIBLIOGRAPHY .......................................................................... 127

العربى الولخص ................................................................................................................................. 2

IX

LLIISSTT OOFF TTAABBLLEESS Table 1 LTE system attributes summary ............................................................................... 4

Table 2 LTE uplink transmission parameters ...................................................................... 29

Table 3 Spectrum flexibility parameters in LTE UL ........................................................... 29

Table 4 Optimal connections for rate 1/2 convolutional encoder ........................................ 39

Table 5 Puncturing patterns for rate ½ convolutional encoders .......................................... 39

Table 6 Normalization factors for the LTE modulation schemes ........................................ 40

Table 7 Common simulation parameters ............................................................................. 41

Table 8 adaptive Modulation and V-MIMO configurations for MMSE equalizer .............. 63

Table 9 codebook precoders for two antenna ports ............................................................. 82

Table 10 codebook precoders for four antenna ports rank 1 ............................................... 82

Table 11 codebook precoders for four antenna ports rank 2 ............................................... 83

Table 12 codebook precoders for four antenna ports rank 3 ............................................... 83

Table 13 codebook precoders for four antenna ports rank 4 ............................................... 84

Table 14 signal to noise ratio limits for using the different ranks of the codebook precoded

CSM ..................................................................................................................................... 94

X

LLIISSTT OOFF FFIIGGUURREESS

Figure 1 Time line of Mobile communication Evolution ...................................................... 3

Figure 2 Classification of MIMO techniques ........................................................................ 8

Figure 3 MIMO modes depending on the availability of multiple antennas at the

transmitter and/or the receiver ............................................................................................... 9

Figure 4 Simplified collaborative MIMO system model ..................................................... 10

Figure 5 SC-FDMA frequency domain generation ............................................................. 16

Figure 6 Subcarrier mapping schemes ................................................................................. 18

Figure 7 Subcarrier mapping implementation (a) Disturbed (b) localized .......................... 18

Figure 8 Comparison between time domain and frequency domain structures for different

subcarrier mapping .............................................................................................................. 21

Figure 9 Differences between OFDMA and SC-FDMA detection and equalization

processes .............................................................................................................................. 23

Figure 10 Resource block in LTE ........................................................................................ 26

Figure 11 Basic principles of DFTS-OFDM for LTE uplink transmission ......................... 27

Figure 12 LTE FDD (type 1) frame structure ...................................................................... 28

Figure 13 DRS generation in LTE UL ................................................................................. 31

Figure 14 Transmission of uplink reference signals within a slot in case of PUSCH

transmission ......................................................................................................................... 32

Figure 15 Generation of uplink RS sequence from linear phase rotation of a ..................... 33

Figure 16 PUSCH physical layer processing ....................................................................... 34

Figure 17 LTE user equipments transmitters ...................................................................... 37

Figure 18 LTE Turbo encoder structure .............................................................................. 39

Figure 19 Symbol mapping schemes for LTE UL (gray coded) ......................................... 40

Figure 20 Single user receiver block diagram ..................................................................... 45

Figure 21 Comparison between different modulation and equalization techniques for SISO

LTE uplink ........................................................................................................................... 49

Figure 22 Comparison between coding schemes for SISO LTE uplink .............................. 50

Figure 23 Effect of channel selectivity on LTE uplink ....................................................... 51

Figure 24 Effect of user mobility on the LTE uplink without channel interpolation .......... 52

Figure 25 2x2 SIC equalizer .............................................................................................. 55

Figure 26 Comparison between the existent multiuser equalization techniques for 2x2 V-

MIMO systems .................................................................................................................... 56

Figure 27 Effect of changing number of collaborative users (V-MIMO order) .................. 57

Figure 28 Effect of changing number of receiving antennas ............................................... 58

Figure 29 Effect of different modulation schemes for 2x2 collaborative MIMO system ... 59

Figure 30 Effect of channel selectivity of the multipath channel ........................................ 60

Figure 31 Effect of users‟ mobility ...................................................................................... 60

Figure 32 Effect of channel estimation methods for MMSE and SIC-MMSE receivers .... 61

Figure 33 Effect of the MMSE channel estimation with spline interpolation in case of

different users‟ speeds ......................................................................................................... 62

Figure 34 Comparison between OFDM and SC-FDMA based collaborative MIMO systems

............................................................................................................................................. 62

Figure 35 Spectral Efficiency of different modulation and system configurations for

uncoded V-MIMO system ................................................................................................... 64

XI

Figure 36 performance of the optimal ordering of SIC in presence of shadowing variance

of 12dB ................................................................................................................................ 67

Figure 37 performance of suboptimal ordering SIC with different modulation schemes ... 69

Figure 38proposed IGML receiver ...................................................................................... 71

Figure 39 performance if IGML for different modulation schemes .................................... 72

Figure 40 QR decomposition effect on user separation ....................................................... 74

Figure 41 Tree formation for sphere detection .................................................................... 75

Figure 42 performance of simplified IGML for different modulation schemes .................. 76

Figure 43 Comparison between all presented detection schemes for QPSK modulation ... 77

Figure 44 Overview of uplink physical channel processing for LTE-advanced ................. 80

Figure 45 SVD precoding .................................................................................................... 81

Figure 46 UEs transmitter block diagram ............................................................................ 84

Figure 47 eNodeB receiver .................................................................................................. 84

Figure 48 Comparison between SVD precoded CSM systems and unprecoded schemes .. 88

Figure 49 spectral efficiency achieved upon using the SVD precoded schemes ................. 88

Figure 50 Effect of selectivity on SVD precoded CSM system with 2 userrs , 4 Tx

antennas , 8 Rx antenennas .................................................................................................. 89

Figure 51 Codebook precoded CSM Vs. ordinary CSM ..................................................... 91

Figure 52 Comparison between the selection criteria of the three precoders ...................... 91

Figure 53 Effect of selectivity on the codebook based precoding ....................................... 92

Figure 54 spectral efficiency achieved when using precoded 2 Tx antennas transmission . 92

Figure 55 spectral efficiency of precoded CSM of 4 transmitting antennas for different

ranks ..................................................................................................................................... 93

Figure 56 SFBC precoded CSM Vs. unprecoded CSM ....................................................... 97

Figure 57 Effect of selectivity along SFBC precoding ........................................................ 97

Figure 58 comparison between the presented precoding schemes ...................................... 98

Figure 59 Different Multiuser equalization Techniques for codebook precoding scheme .. 99

Figure 60 Douillard's TEQ ................................................................................................. 101

Figure 61 LTE rate matching ............................................................................................. 103

Figure 62 SISO demapper idea .......................................................................................... 104

Figure 63 SISO mapper idea ............................................................................................. 105

Figure 64 Trellis diagram of one constituent encoder of the 3GPP LTE .......................... 106

Figure 65 proposed eNode B 2 users PIC-TEQ ................................................................. 107

Figure 66 performance of PIC-TEQ for conventional CSM with 2 users using different

MCS ................................................................................................................................... 108

Figure 67 channel selectivity effect on the PIC-TEQ for the conventional CSM with 2

users using 16QAM ¾ ....................................................................................................... 109

Figure 68 performance comparison between MMSE , PIC-TEQ and single user ML-based

TEQ .................................................................................................................................... 111

Figure 69 SFBC precoded 2x2 CSM with different MCS and equalization ..................... 115

Figure 70 performance of SFBC precoding with 4 receiving antennas and corresponding

equalization techniques ...................................................................................................... 116

Figure 71 TEQ iterations effect on SFBC precoded CSM with 2 receiving antennas

Eb/No=11dB ...................................................................................................................... 116

Figure 72 Effect of channel selectivity on TEQ of the SFBC precoded CSM .................. 117

Figure 73 Codebook and SVD precoding for 16QAM ¾ transmission and different

rank/antenna configurations and 1 iteration TEQ .............................................................. 119

XII

Figure 74 Comparison between presented precoding and equalization techniques for

16QAM ¾ rank 1 transmission .......................................................................................... 120

Figure 75 PIC-TEQ of codebook precoded CSM of 2 users of with 2Tx antennas and 2 Rx

antennas with different MCS ............................................................................................. 121

Figure 76 Effect of channel selectivity on the performance of codebook precoded CSM of

rank 1 with 2 transmitting antennas and 2 Rx antennas with 16QAM 3/4 MCS .............. 122

Figure 77 TEQ iterations effect for ordinary, SFBC and rank 1 codebook transmission at

11dB ................................................................................................................................... 122

XIII

LLIISSTT OOFF AABBBBRREEVVIIAATTIIOONNSS

Abbreviation Description 1G First Generation of mobile communication systems

2G Second Generation of mobile communication systems

3G Third Generation of mobile communication systems

3GPP 3G Partnership Projects

4G Forth Generation of mobile communication systems

AMPS Analog Mobile Phone System

AWGN Additive White Gaussian Noise

BER Bit Error Rate

BLAST Bell Labs Layered Space-Time scheme

BLMMSE best linear MMSE estimator

BPSK Binary Phase Shift Keying

CAZAC Constant Amplitude Zero Autocorrelation property

CDM Code Division Multiplexing

CDMA Code Division Multiple Access

CDMA2000-1xEVDO CDMA 2000 Evolution-Data Optimized

CDMA2000-1xEVDV CDMA 2000 Evolution-Data and voice

CDS Channel Dependent Scheduling

CFO Carrier Frequency Offsets

CIR Channel Impulse Response

CP Cyclic Prefix

CRC Cyclic Redundancy Check

CSI Channel State Information

CSM Collaborative Spatial Multiplexing scheme

DFDMA Distributed subcarrier mapping

DFE Decision Feedback Equalizer

DFT Discrete Fourier Transform

DFT-S-OFDM DFT-spread OFDM

DL Downlink

DL-SCH Downlink shared channel

Doppler PSD Doppler power spectral density

DRS Demodulated Reference Signal

DSPs Digital signal processors

EGC Equal Gain Combining

E-MBMS Enhanced- Multimedia Broadcast Multicast Services

eNodeB Evolved NodeB

EPC Evolved Packet Core

EPS Evolved Packet System

ETSI European Telecommunications Standards Institute

E-UTRA Evolved UMTS Terrestrial Radio Access

E-UTRAN Evolved UMTS Terrestrial Radio Access Network

FDD Frequency Division Duplex

FDE Frequency Domain Equalization

FDM Frequency Division Multiplexing

XIV

FDMA Frequency Division Multilpe Access

FER Frame Error Rate

FFT Fast Fourier Transform

GCL Generalized Chirp-Like sequences

GERAN GSM EDGE Radio Access Network

GSM Global System for Mobile Communications

HRPD High Rate Packet Data

HSPA High Speed Packet Access

hybrid-ARQ Hybrid Automatic Repeat Request

IDFT Inverse Discrete Fourier Transform

IFDMA Interleaved subcarrier mapping

IFFT Inverse Fast Fourier Transform

IGML Initial guess ML

IID Identical and Independently Distributed

IMT-2000 International Mobile Telecommunications 2000

Inter-RAT measurements Inter Radio Access Technology measurements

ISI Inter-Symbol Interference

J-TACS Japanese Total Access Communication System

LFDMA Localized subcarrier mapping

LLR Log Likelihood Ratio

LMMSE linear MMSE estimator

LMSC LAN/MAN Standard Committee

LS Least Square

LTE Long Term Evolution

LTE UL Long Term Evolution- Uplink

MAC Medium Access Control layer

MAP Maximum A-Posteriori algorithm

MBMS Multimedia Broadcast Multicast Services

MCS Modulation and Coding Schemes

MIMO Multiple-Input Multiple-Output

MISO Multiple-Input Single-Output

ML Maximum likelihood

MLSE Maximum Likelihood Sequence Estimation

MME Mobility Management Entity

MMSE Minimum Mean Squares Errors

MRC Maximum Ratio Combiner

MSE Mean Square Error

MU-MIMO Multi User MIMO

NMT Nordic Mobile Telephone

OFDM Orthogonal Frequency Division Multiplexing

OFDMA Orthogonal Frequency Division Multiple Access

OSIC Ordered Successive Interference Cancellation

PA Power Amplifier

PAPR Peak to the Average Power Ratio

PCCC Parallel Concatenated Convolutional Code

PDCCH Physical Downlink Control Channel

PDF Probabilty Density Function

PIC Parallel Interference Cancellation

XV

PIC-TEQ Parallel Interference Cancellation based Turbo

Equalization

PMI Precoding Matrix Indicator

PRACH Physical Random Access Channel

PUCCH Physical Uplink Control Channel

QAM Quadrature Amplitude and phase Modulation

QPSK Quadrature Phase Shift Keying

QPP Quadratic permutation polynomial

QR-IGML QR based Initial Guess Maximum Likelihood Detector

RB Resource Block

RI Rank Indicator

RM Rate Matching

RNC Radio Network Controller

RS Reference Signal

RSC Recursive Systematic Convolutional

SAE System Architecture Evolution

SC Selection Combining

SC/FDE Single Carrier/Frequency Domain Equalizer

SC-FDMA Single Carrier Frequency Division Multiple Access

SD Sphere Detection

SDMA Space Division Multiple Access

SER Symbol Error Rate

SFBC Space Frequency Block Codes

SIC Successive Interference Cancellation

SIMO Single-Input Multiple-Output

SINR Signal-to- Interference-plus- Noise Ratio

SISO Single Input Single Output

SISO (in chapter 6 only) Soft Input Soft Output

SNR Signal to Noise Ratio

SRS Sounding Reference Signal

STBCs Space Time Block Codes

STTCs Space-Time Trellis Codes

SU-MIMO Single-User MIMO

SVD Singular Value Decomposition

SAE-GW System Architecture Evolution Gateway

TACS Total Access Communication System

TB Transport Block

TDD Time Division Duplex

TDMA Time Division Multiple Access

TEQ Turbo Equalization

TTI Transmission Time Interval

UE User Equipment

UL Uplink

UL-SCH Uplink Shared Channel

UMB Ultra Mobile Broadband

UMTS Universal Mobile Telecommunication System

UTRA Universal Terrestrial Radio Access

UTRAN Universal Terrestrial Radio Access Network

XVI

V-MIMO Virtual-Multiple Input Multiple Output

VoIP Voice Over Internet Protocol

WCDMA wideband CDMA

WiMAX Worldwide Interoperability for Microwave Access

WSSUS Wide Sense Stationary Uncorrelated Scattering

ZC Zadoff–Chu sequences

ZF Zero Forcing

1

CCHHAAPPTTEERR OONNEE

IINNTTRROODDUUCCTTIIOONN

1.1 Historic view of the evolution of the mobile communications

The cellular wireless communications industry witnessed tremendous growth in the

past decade with over four billion wireless subscribers worldwide [1]. The Long Term

Evolution of UMTS is just one of the latest steps in an advancing series of mobile

telecommunications systems. Arguably, at least for land-based systems, the series began in

1947 with the development of the concept of cells by the famous Bell Labs of the USA.

The use of cells enabled the capacity of a mobile communications network to be increased

substantially, by dividing the coverage area up into small cells each with its own base

station operating on a different frequency [2].

The first mobile communication systems to see large-scale commercial growth

arrived in the 1980s and became known as the „First Generation‟ (1G) systems. The 1G

comprised a number of independently-developed systems worldwide (e.g., Analog Mobile

Phone System (AMPS, used in America), Total Access Communication System (TACS,

used in parts of Europe), Nordic Mobile Telephone (NMT, used in parts of Europe) and

Japanese Total Access Communication System (J-TACS, used in Japan and Hong Kong)),

using analog technology supported voice communication with limited roaming.

Global roaming first became possible with the development of the digital „Second

Generation‟ (2G) system known as Global System for Mobile Communications (GSM).

The success of GSM was due in part to the collaborative spirit in which it was developed.

By harnessing the creative expertise of a number of companies working together under the

auspices of the European Telecommunications Standards Institute (ETSI), GSM became a

robust, interoperable and widely-accepted standard. The 2G digital systems promised

higher capacity and better voice quality than did their analog counterparts. Moreover,

roaming became more prevalent thanks to fewer standards and common spectrum

allocations across countries particularly in Europe. The two widely deployed 2G cellular

systems are GSM and Code Division Multiple Access (CDMA). As for the 1G analog

systems, 2G systems were primarily designed to support voice communication and text

messaging. In later releases of these standards, capabilities were introduced to support data

transmission. However, the data rates were generally lower than that supported by dial-up

connections.

The International Telecommunications Union (ITU-R) initiative on International

Mobile Telecommunications 2000 (IMT-2000) paved the way for evolution to the „Third

Generation‟ (3G). A set of requirements such as a peak data rate of 2 Mb/s and vehicular

mobility support were published under IMT-2000 initiative. Both the GSM and CDMA

camps formed their own separate 3G Partnership Projects (3GPP and 3GPP2, respectively)

to develop IMT-2000 compliant standards based on the CDMA technology. The 3G

standard in 3GPP is referred to as wideband CDMA (WCDMA) because it uses a larger

5MHz bandwidth relative to 1.25MHz bandwidth used in 3GPP2‟s CDMA2000 system.

The 3GPP2 also developed a 5MHz version supporting three 1.25MHz subcarriers referred

to as CDMA2000-3x. In order to differentiate from the 5MHz CDMA2000-3x standard,

the 1.25MHz system is referred to as CDMA2000-1x or simply 3G-1x.

2

The first release of the 3G standards did not fulfill its promise of high-speed data

transmissions as the data rates supported in practice were much lower than that claimed in

the standards. A serious effort was then made to enhance the 3G systems for efficient data

support. The 3GPP2 first introduced the High Rate Packet Data (HRPD) [3] system that

used various advanced techniques optimized for data traffic such as channel sensitive

scheduling, fast link adaptation and hybrid-ARQ, etc. The HRPD system required a

separate 1.25MHz carrier and supported no voice service. This was the reason that HRPD

was initially referred to as CDMA2000-1xEVDO (Evolution Data Only) system. The

3GPP followed a similar path and introduced High Speed Packet Access (HSPA) [4]

enhancement to the WCDMA system. The HSPA standard reused many of the same data-

optimized techniques as the HRPD system. A difference relative to HRPD, however, is that

both voice and data can be carried on the same 5MHz carrier in HSPA. The voice and data

traffic are code multiplexed in the downlink. In parallel to HRPD, 3GPP2 also developed a

joint voice data standard that was referred to as CDMA2000-1xEVDV (evolution data

voice) [5]. Like HSPA, the CDMA2000-1xEVDV system supported both voice and data

on the same carrier but it was never commercialized. In the later release of HRPD, VoIP

(Voice over Internet Protocol) capabilities were introduced to provide both voice and data

service on the same carrier. The two 3G standards namely HSPA and HRPD were finally

able to fulfill the 3G promise and had been widely deployed in major cellular markets to

provide wireless data access.

While HSPA and HRPD systems were being developed and deployed, IEEE 802

LMSC (LAN/MAN Standard Committee) introduced the IEEE 802.16e standard [6] for

mobile broadband wireless access. This standard was introduced as an enhancement to an

earlier IEEE 802.16 standard for fixed broadband wireless access. The 802.16e standard

employed a different access technology named Orthogonal Frequency Division Multiple

Access (OFDMA) and claimed better data rates and spectral efficiency than that provided

by HSPA and HRPD. Although the IEEE 802.16 family of standards is officially called

Wireless MAN in IEEE, it has been dubbed Worldwide Interoperability for Microwave

Access (WiMAX) by an industry group named the WiMAX Forum. The mission of the

WiMAX Forum is to promote and certify the compatibility and interoperability of

broadband wireless access products. The WiMAX system supporting mobility as in IEEE

802.16e standard is referred to as Mobile WiMAX. In addition to the radio technology

advantage, Mobile WiMAX also employed a simpler network architecture based on IP

protocols. The introduction of Mobile WiMAX led both 3GPP and 3GPP2 to develop their

own version of beyond 3G systems based on the OFDMA technology and network

architecture similar to that in Mobile WiMAX. The beyond 3G system in 3GPP is called

evolved Universal Terrestrial Radio Access (evolved UTRA) [7] and is also widely

referred to as Long-Term Evolution (LTE) while 3GPP2‟s version is called Ultra Mobile

Broadband (UMB) [8].

Figure 1 shows an approximate time line for the Mobile communication evolution

from 1G towards the „Forth Generation‟ (4G) [2].

3

Figure 1 Time line of Mobile communication Evolution

1.2 Introduction to LTE

The LTE as defined by the 3GPP is a highly flexible radio interface [9], [2]; its

initial deployment of LTE is in 2010 and 2011. LTE is the evolution of 3GPP‟s Universal

Mobile Telecommunication System (UMTS) towards an all-IP network in order to ensure

the competitiveness of UMTS for the next 10 years and beyond.

LTE was being developed in Releases 8 and 9 of the 3GPP specifications [10] .The

first release of LTE provides peak rates of 300 Mb/s, a radio-network delay of less than 5

ms, a significant increase in spectrum efficiency compared to previous cellular systems,

and a new flat radio-network architecture designed to simplify operation and to reduce

cost. LTE supports both Frequency Division Duplex (FDD) and Time Division Duplex

(TDD), as well as a wide range of system bandwidths in order to operate in a large number

of different spectrum allocations. LTE also constitutes a major step towards IMT-

Advanced. In fact, the first release of LTE already includes many of the features which are

originally considered for future 4G systems.

The multiple access scheme in LTE downlink is the OFDMA and uplink uses

Single Carrier Frequency Division Multiple Access (SC-FDMA) [11]. SC-FDMA

technique for uplink transmission have attracted appreciable attention because of its low

Peak to the Average Power Ratio (PAPR) property compared with competitive OFDMA

technique [12]. SC-FDMA has been adopted for uplink transmission to allow efficient

terminal power amplifier design, which is relevant to the terminal battery life .SC-FDMA

signal can be obtained using Discrete Fourier Transform (DFT) spread OFDMA, where

DFT is applied to convert time domain input data symbols to the frequency domain before

4

feeding them into an OFDMA modulator. These multiple access solutions provide

orthogonality between the users, simple frequency domain equalization in frequency

selective channel, reducing the interference and improving the network capacity. The

resource allocation in the frequency domain takes place with a resolution of 180 kHz

resource blocks both in uplink and in downlink. The uplink user specific allocation is

continuous to enable single carrier transmission while the downlink can use resource

blocks freely from different parts of the spectrum.

LTE offers a 100 Mbps download rate and 86 Mbps upload rate for every 20 MHz

of spectrum. Support is intended for even higher rates, up to 326.4 Mbps in the downlink,

using multiple antenna configurations as Table 1 [1]. To allow the use of both new and

existing frequency bands, LTE provides scalable bandwidth from 1.25 MHz to 20 MHz in

both the downlink and the uplink. LTE is optimized for low speeds (0 - 15 km/h) but will

still provide high performance up to 120 km/h with support for mobility maintained up to

350 km/h. 3GPP is considering support for even higher speeds up to 500 km/h [13].

LTE system Attributes

Bandwidth 1.25-20 MHz

Duplexing FDD, TDD , half-duplex FDD

Mobility Up to 350 Km/hr

Multiple access Downlink: OFDMA

Uplink: SC-FDMA

MIMO Downlink: 2x2 , 4x2 and 4x4

Uplink: 1x2 and 1x4

Peak data rate in

20MHz

Downlink: 173 and 326 Mb/s for 2x2 and 4x4 MIMO respectively

Uplink: 86 Mb/s with 1x2 antenna configuration

Modulation QPSK ,16QAM and 64QAM

Channel coding Turbo code

Other techniques Channel dependant scheduling, link adaptation, power control and

hybrid ARQ

Table 1 LTE system attributes summary

The target in 3GPP Release 8 is to improve the network scalability for traffic

increase and to minimize the end-to-end latency by reducing the number of network

elements. All radio protocols, mobility management, header compression and all packet

retransmissions are located in the base stations called evolved NodeB (eNodeB). eNodeB

includes all those algorithms that are located in Radio Network Controller (RNC) in 3GPP

Release 6 architecture. Also the core network is streamlined by separating the user and the

control planes. The Mobility Management Entity (MME) is just the control plane element

while the user plane bypasses MME directly to System Architecture Evolution (SAE)

Gateway (GW). This Release 8 core network is also often referred to as Evolved Packet

Core (EPC) while for the whole system the term Evolved Packet System (EPS) can also be

used [13].

Discussion of the key requirements for the new LTE system led to the creation of a

formal „Study Item‟ in 3GPP with the specific aim of „evolving‟ the 3GPP radio access

technology to ensure competitiveness over a 10-year time-frame. Under the auspices of

this Study Item, the requirements for LTE were refined and crystallized, being finalized in

June 2005. They can be summarized as follows [2], [14]:

5

Reduced delays, in terms of both connection establishment and transmission

latency;

Increased user data rates: Peak data rates target 100 Mbps (downlink) and 50 Mbps

(uplink) for 20 MHz spectrum allocation, assuming 2 receive antennas and 1

transmit antenna at the terminal. Note: These requirement values are exceeded by

the LTE specification;

Increased cell-edge bit-rate, for uniformity of service provision;

Reduced cost per bit, implying improved spectral efficiency: Downlink target is 3-4

times better than release 6. Uplink target is 2-3 times better than release 6;

Greater flexibility of spectrum usage, in both new and pre-existing bands;

Simplified network architecture: Interworking with existing UTRAN/GERAN

systems and non-3GPP systems shall be ensured. Multimode terminals shall

support handover to and from UTRAN and GERAN as well as inter-RAT

measurements;

Seamless mobility, including between different radio-access technologies. The

system should be optimized for low mobile speed (0-15 km/h), but higher mobile

speeds shall be supported as well including high speed train environment as special

case;

Reasonable power consumption for the mobile terminal;

Multimedia Broadcast Multicast Services (MBMS): MBMS shall be further

enhanced and is then referred to as E-MBMS;

Improved system performance compared to existing systems is one of the main

requirements from network operators, to ensure the competitiveness of LTE and

hence to arouse market interest.

1.3 Introduction to MIMO technology

Wireless system designers are facing a number of challenges. These include the

limited availability of the radio frequency spectrum and a complex space–time varying

wireless environment. In addition, there is an increasing demand for higher data rates,

better quality of service, and higher network capacity. The use of multiple antennas at the

transmitter and receiver popularly known as Multiple-Input Multiple-Output (MIMO)

technology constitutes a breakthrough in the design of wireless communication systems,

and has rapidly gained in popularity over the past decade due to its powerful performance-

enhancing capabilities. The core idea behind MIMO is that signals sampled in the spatial

domain at both ends are combined is such a way that they either create effective multiple

parallel spatial data pipes (therefore increasing the data rate), and/or add diversity to

improve the quality (bit-error rate or BER) of the communication [15], [16], [17].

The benefits of MIMO technology that help to achieve significant performance

gains are array gain, spatial diversity gain, spatial multiplexing gain and interference

reduction [15].

Array gain Array gain is the increase in receive Signal to Noise Ratio (SNR) that results

from a coherent combining effect of the wireless signals at a receiver. The coherent

combining may be realized through spatial processing at the receive antenna array and/or

spatial pre-processing at the transmit antenna array. Array gain improves resistance to

noise, thereby improving the coverage and the range of a wireless network.

6

Spatial diversity gain The signal level at a receiver in a wireless system fluctuates or fades.

Spatial diversity gain mitigates fading and is realized by providing the receiver with

multiple (ideally independent) copies of the transmitted signal in space, frequency or time.

With an increasing number of independent copies (the number of copies is often referred to

as the diversity order), the probability that at least one of the copies is not experiencing a

deep fade increases, thereby improving the quality and reliability of reception. A MIMO

channel with 𝑀𝑇 transmit antennas and 𝑀𝑅 receive antennas potentially offers 𝑀𝑇 × 𝑀𝑅

independently fading links, and hence a spatial diversity order of 𝑀𝑇 × 𝑀𝑅 .

Spatial multiplexing gain MIMO systems offer a linear increase in data rate through

spatial multiplexing [18],[19], i.e., transmitting multiple, independent data streams within

the bandwidth of operation. Under suitable channel conditions, such as rich scattering in

the environment, the receiver can separate the data streams. Furthermore, each data stream

experiences at least the same channel quality that would be experienced by a single-input

single-output system, effectively enhancing the capacity by a multiplicative factor equal to

the number of streams. In general, the number of data streams that can be reliably

supported by a MIMO channel equals the minimum of the number of transmit antennas

and the number of receive antennas, i.e., min(𝑀𝑇 , 𝑀𝑅).

Two key performance metrics associated with any communication system are the

transmission rate and the Frame Error Rate (FER. Intuitively, for a fixed transmission rate,

an increase in SNR will result in reduced FER. Similarly, at a fixed target FER, an increase

in SNR may be leveraged to increase the transmission rate. Hence, a fundamental trade-off

exists in any communication system between the transmission rate and FER. In the context

of MIMO systems, this trade-off is often referred to as the diversity–multiplexing trade-off

[20] with diversity signifying the FER reduction and multiplexing signifying an increase in

transmission rate. The diversity– multiplexing trade-off is central to MIMO

communication theory .

Interference reduction and avoidance Interference may be mitigated in MIMO systems by

exploiting the spatial dimension to increase the separation between users. For instance, in

the presence of interference, array gain increases the tolerance to noise as well as the

interference power, hence improving the Signal-to- Interference-plus- Noise Ratio (SINR).

Additionally, the spatial dimension may be leveraged for the purposes of interference

avoidance, i.e., directing signal energy towards the intended user and minimizing

interference to other users. Interference reduction and avoidance improve the coverage and

range of a wireless network. In general, it may not be possible to exploit simultaneously all

the benefits described above due to conflicting demands on the spatial degrees of freedom.

However, using some combination of the benefits across a wireless network will result in

improved capacity, coverage and reliability.

As a historic view for MIMO schemes, a simple spatial diversity technique, which

does not involve any loss of bandwidth, is constituted by the employment of multiple

antennas at the receiver, where several techniques can be employed for combining the

independently fading signal replicas, including Maximum Ratio Combining (MRC), Equal

Gain Combining (EGC) and Selection Combining (SC) .

Several transmit, rather than receive, diversity techniques have also been proposed

in the literature [21],[22],[23]. In [22], Alamouti proposed a witty transmit diversity

7

technique using two transmit antennas, the key advantage of which was the employment of

low-complexity single-receive-antenna-based detection, which avoids complex joint

detection of multiple symbols. The decoding algorithm proposed in [22] can be generalized

to an arbitrary number of receive antennas using MRC, EGC or SC.The idea can be

extended to the frequency dimension as in space frequency block codes (SFBC).

Alamouti‟s achievement inspired Tarokh et al. [23] to generalize the concept of transmit

diversity schemes to more than two transmit antennas, contriving the generalized concept

of space time block codes (STBCs). The family of STBCs is capable of attaining the same

diversity gain as Space-Time Trellis Codes (STTCs) [21] at a lower decoding complexity,

when employing the same number of transmit antennas. However, a disadvantage of

STBCs when compared with STTCs is that they employ unsophisticated repetition-coding

and hence provide no coding. An alternative idea invoked for constructing full-rate STBCs

for complex-valued modulation schemes and more than two antennas was suggested in

[24]. Here the strict constraint of perfect orthogonality of transmitted symbols was relaxed

in favor of achieving a higher data rate. The resultant STBCs were referred to as quasi-

orthogonal STBCs [24].

The STBC designs offer, at best, the same data rate as an uncoded single antenna

system, but they provide an improved BER performance compared with the family of

single antenna-aided systems by providing diversity gains. In contrast to this, several high

rate MIMO transmission schemes having a normalized rate (which is defined as the ratio

between the number of symbols the encoder takes as its input and the number of space-

time coded symbols transmitted from each antenna) higher than unity have been proposed

in the literature improving the attainable spectral efficiency of the system by transmitting

different signal streams independently over each of the transmit antennas, hence resulting

in a multiplexing gain. This class of MIMO subsumes the Bell Labs Layered Space-Time

(BLAST) scheme and its relatives [25]. The BLAST scheme aims to increase the system

throughput in terms of the number of bits per symbol that can be transmitted in a given

bandwidth at a given integrity.

In contrast to the family of BLAST schemes, where multiple antennas are activated

by a single user to increase the user‟s throughput, Space Division Multiple Access

(SDMA) known also as collaborative MIMO [27] employs multiple antennas for the sake

of supporting multiple users. SDMA exploits the unique user-specific Channel Impulse

Response (CIR) of the different users for separating their received signals.

On the other hand, in beamforming arrangements [27],[28], typically 𝜆/2- spaced

antenna elements are used for the sake of creating a spatially selective transmitter/receiver

beam, where 𝜆 represents the carrier‟s wavelength. Beamforming is employed for

providing a beamforming gain by mitigating the effects of various interfering signals,

provided that they arrive from sufficiently different directions. In addition, beamforming is

capable of suppressing the effects of co-channel interference, hence allowing the system to

support multiple users by angularly separating them. Again, this angular separation

becomes feasible only on condition that the corresponding users are separable in terms of

the angle of arrival of their beams.

Figure 2 shows a classification of MIMO techniques discussed above

8

Figure 2 Classification of MIMO techniques

Figure 3 shows the MIMO modes depending on the availability of multiple

antennas at the transmitter and/or the receiver [2], such techniques are classified as Single-

Input Multiple-Output (SIMO), Multiple-Input Single-Output (MISO) or MIMO. Thus in

the scenario of a multi-antenna enabled base station communicating with a single antenna

User Equipment (UE), the uplink and downlink are referred to as SIMO and MISO

respectively. When a (high-end) multi-antenna terminal is involved, a full MIMO link may

be obtained, although the term MIMO is sometimes also used in its widest sense, thus

including SIMO and MISO as special cases. While a point-to-point multiple-antenna link

between a base station and one UE is referred to as Single-User MIMO (SU-MIMO),

collaborative MIMO (Multiuser (MU-MIMO) or virtual (V-MIMO)) features several UEs

communicating simultaneously with a common base station using the same frequency-

domain and time-domain resources. By extension, considering a multicell context,

neighboring base stations sharing their antennas in virtual MIMO fashion to communicate

with the same set of UEs in different cells will be termed multicell MU-MIMO.

In LTE, MIMO technologies have been widely used to improve downlink peak

rate, cell coverage, as well as average cell throughput [29]. To achieve this diverse set of

objectives, LTE adopted various MIMO technologies including transmit diversity, SU-

MIMO, MU-MIMO, closed loop rank-1 precoding, and dedicated beamforming

[30],[31],[32]. The SU-MIMO scheme is specified for the configuration with two or four

transmit antennas in the downlink, which supports transmission of multiple spatial layers

with up to four layers to a given UE. The transmit diversity scheme is specified for the

configuration with two or four transmit antennas in the downlink, and with two transmit

antennas in the uplink. The MU-MIMO scheme allows allocation of different spatial layers

to different users in the same time-frequency resource, and is supported in both uplink and

MIMO Techniques

Diversity

Techniques

Receive Divesity

*Max. Ratio Combining

(MRC)

*Equal Gain Combining

(EGC)

*Selection Combining (SC)

Transmit Diversity

*STBC

*STTC

*Quasi STBC.

Multplexing

Techniques

BLAST

Multiple access techniques

SDMA , V-MIMO or

collaborative MIMO

Beamforming

*Beamforming designed for interference

reduction

*Beamforming designed for

SNR gain

9

downlink. The closed-loop rank-1 precoding scheme is used to improve data coverage

utilizing SU-MIMO technology based on the cell-specific common reference signal while

introducing a control signal message that has lower overhead. The dedicated beamforming

scheme is used for data coverage extension when the data demodulation based on

dedicated reference signal is supported by the UE.

Figure 3 MIMO modes depending on the availability of multiple antennas at the transmitter and/or the

receiver [2]

1.4 Introduction to collaborative MIMO (Virtual MIMO systems)

The creation of independent radio channels using multiple antennas in the UE is

difficult, so the idea of Collaborative spatial multiplexing (sometimes also referred to as

Spatial Division Multiple Access (SDMA), Uplink MU-MIMO (UL MU-MIMO) or

virtual MIMO (V-MIMO)) is attractive [33], [34], [35].

Collaborative spatial multiplexing (CSM) in

Figure 4 [34] works as the following, two or more users having UEs equipped with single

antenna in the vicinity, each one of them transmits independent data stream from the

others. Those users are collaboratively transmitting to the same resource blocks (RBs), i.e.

same frequency/time grid resource. The above transmission technique creates V-MIMO

link in a sense of imagining that the collaborative users are just antennas for virtual large

UE and at each antenna there is a different stream which works as the conventional spatial

multiplexing idea. Now, the eNodeB is receiving combined data from all collaborative

users, eNodeB will then separate the data of each user using multiuser equalization

techniques.

10

The CSM technique increases the whole throughput of the uplink because the

single RB is now reused among different users , achieves V-MIMO without increasing the

complexity of the UEs ,and is capable of addressing the spatial correlation and complexity

issues inherent in MIMO systems by distributing the antenna used for communication

among a cluster of UEs in the neighborhood. Moreover it achieves a diversity gain from

receiving different and independent replicas of the user data that when the multiuser

interference is perfectly cancelled , the eNodeB can perform combining technique to

benefit from multiuser diversity. In addition to providing higher capacity and better

utilization of the available spectrum, V-MIMO may require less hardware and fewer RF

chains than a MIMO device with the same number of antennas [36].

Traditional multiuser equalization techniques include Zero Forcing (ZF), Minimum

Mean Squares Errors (MMSE) and Maximum likelihood (ML). ZF suffers from noise and

interference enhancement. MMSE accounts for the SNR/SINR value and provides better

performance. However, the optimal receiver is the ML which performs exhaustive search

to find the symbols with minimum detection error. Unfortunately, the full-fledge ML

receiver is abandoned when employing SC-FDMA signals since its complexity increases

exponentially with the DFT-block size as well as the modulation index. To reduce

complexity and maintain performance Successive Interference Cancellation (SIC) is a good

choice. SIC is a Decision Feedback Equalizer (DFE) that sequentially demodulates UE

signals, one at a time, and cancels its contribution from the received signal [25],[26].

Thus it is noted the variant of collaborative MIMO that is included in the WiMAX

specification and has been proposed for 3GPP LTE. In order to support uplink MU-MIMO,

LTE specifically provides orthogonal Demodulated Reference Signal (DRS) using

different cyclic time shifts to enable the eNodeB to derive independent channel estimates

for the uplink from each UE. As a maximum of eight cyclic time shifts can be assigned,

SDMA of up to eight UEs can be supported in a cell. SDMA between cells (i.e. uplink

inter-cell cooperation) is supported in LTE by assigning the same base sequence groups

and/or RS hopping patterns to the different cells [2].

Figure 4 Simplified collaborative MIMO system model

11

1.5 Introduction to Turbo codes

A turbo code can be thought of as a refinement of the parallel concatenated

encoding structure plus an iterative algorithm for decoding the associated code sequence

[37] .In insightful concept of turbo coding was proposed in 1993 in a seminal contribution

by Berrou, Glavieux and Thitimajashima, who reported excellent coding gain results [38],

approaching Shannonian predictions (achieves a bit-error probability of 10-5

using a rate

1/2 code over an additive white Gaussian noise (AWGN) channel and BPSK modulation at

an 𝐸𝑏/𝑁0 of 0.7 dB). The information sequence is encoded twice [39], with an interleaver

between the two encoders serving to make the two encoded data sequences approximately

statistically independent of each other. Often half-rate Recursive Systematic Convolutional

(RSC) encoders are used, with each RSC encoder producing a systematic output which is

equivalent to the original information sequence, as well as a stream of parity information.

The two parity sequences can then be punctured before being transmitted along with the

original information sequence to the decoder. This puncturing of the parity information

allows a wide range of coding rates to be realized, and often half the parity information

from each encoder is sent. Along with the original data sequence, this results in an overall

coding rate of 1/2.

Whereas, for conventional codes, the final step at the decoder yields hard-decision

decoded bits (or, more generally, decoded symbols), for a concatenated scheme such as a

turbo code to work properly, the decoding algorithm should not limit itself to passing hard

decisions among the decoders [37]. To best exploit the information learned from each

decoder, the decoding algorithm must effect an exchange of soft decisions rather than hard

decisions .At the decoder two RSC decoders are used. Special decoding algorithms must

be used which accept soft inputs and give soft outputs for the decoded sequence. These soft

inputs and outputs provide not only an indication of whether a particular bit was a 0 or a 1,

but also a likelihood ratio which gives the probability that the bit has been correctly

decoded. The turbo decoder operates iteratively. In the first iteration the first RSC decoder

provides a soft output giving an estimation of the original data sequence based on the soft

channel inputs alone. It also provides an extrinsic output. The extrinsic output for a given

bit is based not on the channel input for that bit, but on the information for surrounding bits

and the constraints imposed by the code being used. This extrinsic output from the first

decoder is used by the second RSC decoder as a-priori information, and this information

together with the channel inputs are used by the second RSC decoder to give its soft output

and extrinsic information. In the second iteration the extrinsic information from the second

decoder in the first iteration is used as the a-priori information for the first decoder, and

using this a-priori information the decoder can hopefully decode more bits correctly than it

did in the first iteration. This cycle continues, with at each iteration both RSC decoders

producing a soft output and extrinsic information based on the channel inputs and a-priori

information obtained from the extrinsic information provided by the previous decoder.

After each iteration the BER in the decoded sequence drops, but the improvements

obtained with each iteration fall as the number of iterations increases so that for complexity

reasons usually only between 4 and 12 iterations are used. In their pioneering proposal

Berrou, Glavieux and Thitimajashima [38] invoked a modified version of the classic

minimum BER Maximum A-Posteriori (MAP) algorithm due to Bahl et al. [40] in the

above iterative structure for decoding the constituent codes [39].

12

1.5 Introduction to Turbo equalization (TEQ)

Capitalizing on the great performance gains of turbo codes and the turbo decoding

algorithm, turbo equalization is an iterative equalization and decoding technique that can

achieve equally impressive performance gains for communication systems that send digital

data over channels that require equalization, i.e., those which suffer from Inter-Symbol

Interference (ISI) i.e., frequency selective channels [41].

Turbo equalization was first proposed by Douillard et al. in 1995 [42] for a serially

concatenated convolutional-coded Binary Phase Shift Keying (BPSK) system. In this

contribution TEQ was shown to mitigate the effects of ISI, when having perfect channel

impulse response information. Instead of performing the equalization and decoding

independently, in order to overcome the channel‟s frequency selectivity, better

performance can be obtained by the turbo equalizer, which considers the discrete channel‟s

memory and performs both the equalization and decoding iteratively. The basic philosophy

of the original TEQ technique stems from the iterative turbo decoding algorithm consisting

of two Single Input Single Output (SISO) decoders, a structure which was proposed by

Berrou et al. [38].So turbo equalization resembles the case of turbo coding, in which the

channel is assumed to be the other component code connected to the original convolutional

code.

The original turbo equalizer consists of a SISO equalizer and a SISO decoder [39].

The SISO equalizer generates the a-posteriori probability upon receiving the corrupted

transmitted signal sequence and the a-priori probability provided by the SISO decoder.

However, at the first turbo equalization iteration. No a-priori information is supplied by the

channel decoder. Therefore, the a-priori probability is set to 1/2, since the transmitted bits

are assumed to be equiprobable,before passing the a-posteriori information generated by

the SISO equalizer to the SISO decoder. The decoder‟s contribution in the form of the a-

priori information. Accruing from the previous iteration must be removed, in order to yield

the combined channel and extrinsic information. This also minimizes the correlation

between the a-priori information supplied by the decoder and the a-posteriori information

generated by the equalizer. The removal of the a-priori information is necessary, in order to

prevent the decoder from receiving its own information, which would result in the so-

called „positive feedback phenomenon‟, overwhelming the decoder‟s current reliability

estimation of the coded bits, i.e. the extrinsic information. The combined channel and

extrinsic information is channel de-interleaved and directed to the SISO decoder.

Subsequently, the SISO decoder computes the a-posteriori probability of the coded

bits. Note that the latter steps are different from those in turbo decoding. The component

decoder of the turbo equalizer computes the a-posteriori log likelihood ratio (LLR) values

for both the parity and systematic bits. The combined channel and extrinsic information is

then removed from the a-posteriori information provided by the decoder before channel

interleaving. The extrinsic information computed is then employed as the a-priori input

information of the equalizer in the next channel equalization process. This constitutes the

first turbo equalization iteration. The iterative process is repeated until the required

termination criteria are met [43]. At this stage, the a-posteriori information of the source

bits, which has been generated by the decoder, is utilized to estimate the transmitted bits.

13

1.6 Thesis organization and contributions

The thesis is organized in 7 chapters starting with this introduction. In chapter 2, we

provide a detailed literature review about the physical uplink shared channel (PUSCH)

processing of the LTE of the UMTS .we will also introduce the SC-FDMA transmission

and its differences from OFDMA transmission, the different subcarrier mapping schemes

and the time domain representation of these schemes. We give also an overview about the

LTE UL basic transmission

Chapter 3, we start with introducing the collaborative MIMO (CSM) concept. Then

we proceed to construct the basic system model that will be used all over the context of

thesis. Simulation model is studied in both single input single output case and CSM case

for general number of transmitting and receiving antennas, and then we continue with

describing the used channel. The chapter is also turning light system on the existent

detection schemes for collaborative MIMO case identifying the pros and cons for each

detector. The chapter ends with illustrative simulation results showing the main

characteristics of each equalizer in different simulation scenarios considering perfect and

imperfect channel estimation.

We will then proceed in chapter 4 with our first contribution that includes

proposing a novel Initial guess ML (IGML) receiver which dramatically enhances the

performance of the CSM system. The IGML‟s complexity will grow exponentially with

the modulation index only. We also provide a novel simplification for it using the QR

decomposition. Moreover, we present two novel ordering techniques to enhance the

performance of the SIC receiver, especially in the case of shadowing environments. A

comprehensive study of the motivation of each novel scheme with study of channel

imperfections and different channel conditions are also presented.

In chapter 5, we begin with identifying the new MIMO modes introduced in the

LTE-advanced. Capitalizing from advantages of precoding the transmitted streams prior to

transmission, codebook precoding is discussed for LTE. The chapter thereafter will present

system model modifications over the system model introduced in chapter 3. We propose

then a combination between the collaborative system and the precoded MIMO whether

ideally (SVD precoding) or suboptimally using codebook precoding. Then we propose a

SFBC precoding for the uplink to achieve space diversity with spatial multiplexing gain

achieved before using the collaborative system. The chapter eventually discusses the effect

of these precoding schemes on the previously presented receiver schemes.

In chapter 6, we introduce the TEQ technique as multiuser equalization technique

for the CSM system. So, we are getting “softer” capitalizing from the tremendous

performance gains of turbo codes and the turbo decoding algorithm. The chapter discusses

the basic components of the TEQ receiver. Moreover we will extend this TEQ concept to

precoded CSM system presented in chapter 5. We will also generalize the SFBC receiver

in chapter 5 to operate in highly selective channels to maximize the frequency diversity

exploited by the TEQ.

Chapter 7 gives a comprehensive conclusion of the discussed work and gives a

glance on the possible research work that can be appended to the presented thesis. A list of

our publications is presented in appendix 1.

14

CCHHAAPPTTEERR TTWWOO

LLIITTEERRAATTUURREE RREEVVIIEEWW OOFF SSCC--FFDDMMAA AANNDD LLTTEE UUPPLLIINNKK

2.1 Introduction

In this chapter a detailed literature review about PUSCH processing of the LTE of

the UMTS , considering the SC-FDMA transmission, FDD frame structure and reference

signal generation and insertion.

The chapter starts in section 2.2 with introducing the SC-FDMA transmission and

its differences from OFDMA transmission, the different subcarrier mapping schemes and

the time domain representation of these schemes. Then in section 2.3 we give an overview

about the LTE UL in which we consider the FDD frame structure , the basic transmission

parameters , the demodulation reference signals generation and the PUSCH transmission

procedure.

2.2 Wide-band single-carrier transmission (SC-FDMA)

2.2.1 Introduction

OFDMA and SC-FDMA are modified versions of the Orthogonal Frequency

Division Multiplexing (OFDM) and single carrier with frequency domain equalization

(SC/FDE) schemes thus known also as DFT-spread OFDM (DFTS-OFDM) [12]. SC-

FDMA is a promising technique for high data rate uplink communications in future

cellular systems. SC-FDMA has similar throughput performance and essentially the same

overall complexity as OFDMA. A principal advantage of SC-FDMA is PAPR, which is

lower than that of OFDMA.

The design of the LTE uplink physical layer poses some unique Challenges and

requirements which includes [2], [9]:

Orthogonal uplink transmission by different UEs, to minimize intracell interference

and maximize capacity.

Possibility for low-complexity high-quality equalization in the frequency domain.

Flexibility to support a wide range of data rates, and to enable data rate to be

adapted to the SINR.

Sufficiently low PAPR ,i.e., small variations in the instantaneous power of the

transmitted signal, to avoid excessive cost, size and power consumption of the UE

Power Amplifier (PA).

Ability to exploit the frequency diversity afforded by the wideband channel (up to

20 MHz), even when transmitting at low data rates.

Support for frequency-selective scheduling with flexible bandwidth assignment.

Support for advanced multiple antenna techniques, to exploit spatial diversity and

enhance uplink capacity.

SC-FDMA is a transmission scheme that can combine the desired properties

discussed, so SC-FDMA has been selected as the uplink transmission scheme for LTE.

15

However OFDM is abandoned in the LTE UL, OFDM has proven to be an efficient

underlying technology for wireless communication. The major motivation for OFDM

comes from its relatively simple way of handling frequency selective channels which are

normally encountered in wireless mobile systems [44]. The immunity to multipath derives

from the fact that an OFDMA/OFDM system transmits information on 𝑁 orthogonal

frequency carriers, each operating at 1/𝑁 times the bit rate of the information signal. A

major drawback of OFDM transmission, however, is its high PAPR which increases

operational requirements of the Linear Power Amplifier in the transmitting equipment

leading not only to an increased cost but also an increased power consumption which is not

desired especially at the uplink transmitter, the UE besides that the amplifiers have to

operate with a large backoff from their peak power. The result is low power efficiency

(measured by the ratio of transmitted power to DC power dissipated), [45]. An OFDM

signal consists of a number of independently modulated subcarriers, which can give a large

PAPR when added up coherently. When 𝑁 signals are added with the same phase, they

produce a peak power that is 𝑁 times the average power [46]. So in principle, an OFDMA

scheme similar to the LTE downlink could satisfy all the uplink design criteria listed

above, except for low PAPR.

Like OFDM, SC-FDMA divides the transmission bandwidth into multiple parallel

subcarriers, with the orthogonality between the subcarriers being maintained in frequency

selective channels by the use of a Cyclic Prefix (CP) or guard period. The use of a CP

prevents ISI between SC-FDMA information blocks. It transforms the linear convolution

of the multipath channel into a circular convolution, enabling the receiver to equalize the

channel simply by scaling each subcarrier by a complex gain factor [2].

An extra Discrete Fourier Transform (DFT) block prior to the conventional OFDM

transmitter (DFT-S-OFDM), proves to be an effective way of combining the benefits of

OFDM with a low PAPR transmission signal. However, unlike OFDM, where the data

symbols directly modulate each subcarrier independently (such that the amplitude of each

subcarrier at a given time instant is set by the constellation points of the digital modulation

scheme), in SC-FDMA the signal modulated onto a given subcarrier is a linear

combination of all the data symbols transmitted at the same time instant. Thus, in each

symbol period, all the transmitted subcarriers of an SC-FDMA signal carry a component of

each modulated data symbol. This gives SC-FDMA its crucial single-carrier property,

which results in the PAPR being significantly lower than pure multicarrier transmission

schemes such as OFDM [2].

On the other hand, with its high signaling rate, the frequency domain equalizer of a

SC-FDMA link is far more complicated than an OFDMA equalizer. With SC-FDMA

transmission confined to the LTE uplink, complicated equalizers are required only at base

stations and not at UEs [47].

2.2.2 SC-FDMA generation

A SC-FDMA signal can, in theory, is generated in either the time domain or the

frequency domain. Although the two techniques are duals and „functionally‟ equivalent, in

practice, the time domain generation is less bandwidth efficient due to time domain

16

filtering and associated requirements for filter ramp-up and ramp-down times. In this

section, we are considering only frequency domain generation [2].

Figure 5 illustrates the concept of the frequency domain generation for SC-FDMA

signals. It uses a DFT-S-OFDM structure .The input of the transmitter and the output of the

receiver are complex modulation symbols 𝑥(𝑛) where 𝑛 ∈ {0,1,2, … . , 𝑀 − 1}. Practical

systems dynamically adapt the modulation technique to the channel quality, using BPSK in

weak channels and up to 64-level quadrature amplitude modulation (64-QAM) in strong

channels. The data block consists of M complex modulation symbols generated at a rate

𝑅𝑠𝑜𝑢𝑟𝑐𝑒 symbols/second [47].

The second step of DFT-S-OFDM SC-FDMA signal generation is to perform an

𝑀-point DFT operation on each block of 𝑀 QAM data symbols to have 𝑋 𝑚 , 𝑚 ∈{0,1,2, … . , 𝑀 − 1}. Zeros are then inserted among the outputs of the DFT in order to match

the DFT size to an 𝑁-subcarrier OFDM modulator (typically an Inverse Fast Fourier

Transform (IFFT)). The zero-padded DFT output 𝑌 𝑙 , 𝑙𝜖{0,1,2, … . . 𝑁 − 1} is mapped to

the 𝑁 subcarriers, with the positions of the zeros determining to which subcarriers the

DFT-precoded data is mapped.

Usually 𝑁 is larger than the maximum number of occupied subcarriers, thus

providing for efficient oversampling and „sinc‟ (𝑠𝑖𝑛(𝑥)/𝑥) pulse-shaping. The

equivalence of DFT-S- OFDM and a time-domain-generated SC-FDMA transmission can

readily be seen by considering the case of 𝑀 = 𝑁, where the DFT operation cancels the

IFFT of the OFDM modulator resulting in the data symbols being transmitted serially in

the time domain. If 𝑀 is smaller than 𝑁 and the remaining inputs to the IDFT are set to

zero, the output of the IDFT will be a signal with „ single-carrier ‟ properties, i.e. a signal

with low power variations, and with a bandwidth that depends on M .

Figure 5 SC-FDMA frequency domain generation

The difference between the DFT and IFFT size will lead to bandwidth expansion.

The required bandwidth in this case 𝑊𝑐𝑕will be

𝑊𝑐𝑕 = 𝑁. ∆𝑓 (2.1)

17

where ∆𝑓 is the subcarrier spacing, and the channel transmission rate 𝑅𝑐𝑕 would be

𝑅𝑐𝑕 =𝑁

𝑀. 𝑅𝑠𝑜𝑢𝑟𝑐𝑒

(2.2)

where 𝑅𝑠𝑜𝑢𝑟𝑐𝑒 is the source rate .Also the spreading factor 𝑄 which represents also the

maximum number of orthogonal source signals that can be transmitted within the same

𝑊𝑐𝑕 on different 𝑀 set of subcarriers will be

𝑄 =𝑅𝑐𝑕

𝑅𝑠𝑜𝑢𝑟𝑐𝑒=

𝑁

𝑀

(2.3)

The subcarrier mapping block assigns frequency domain modulation symbols to

subcarriers. The mapping process is sometimes referred to as scheduling. Because spatially

dispersed terminals have independently fading channels, SC-FDMA and OFDMA can

benefit from channel dependent scheduling. The IDFT creates a time domain

representation, 𝑦(𝑛), of the 𝑁 subcarrier symbols. The parallel-to-serial converter places

𝑦(0), 𝑦(1), . . . , 𝑦(𝑁 – 1) in a time sequence suitable for modulating a radio frequency

carrier and transmission to the receiver.

The transmitter in Figure 5 performs two other signal processing operations prior to

transmission. It inserts a set of symbols referred to as CP in order to provide a guard time

to prevent ISI due to multipath propagation. The transmitter also performs a linear filtering

operation referred to as pulse shaping in order to reduce out-of-band signal energy.

The cyclic prefix is a copy of the last part of the block. It is inserted at the start of

each block for two reasons. First, the CP acts as a guard time between successive blocks. If

the length of the CP is longer than the maximum delay spread of the channel, or roughly,

the length of the channel impulse response, then, there is no ISI. Second, since the CP is a

copy of the last part of the block, it converts a discrete time linear convolution into a

discrete time circular convolution. Thus, transmitted data propagating through the channel

can be modeled as a circular convolution between the channel impulse response and the

transmitted data block, which in the frequency domain is a point-wise multiplication of the

DFT frequency samples. Then, to remove the channel distortion, the DFT of the received

signal can simply be divided by the DFT of the channel impulse response point-wise.

2.2.3 Subcarrier mapping schemes

Figure 6 basically shows two methods of assigning the 𝑀 frequency domain

modulation symbols to subcarriers: distributed subcarrier mapping and localized subcarrier

mapping. In the localized subcarrier mapping mode, the modulation symbols are assigned

to M adjacent subcarriers. In the distributed mode, the symbols are equally spaced across

the entire channel bandwidth as Figure 6.

18

Figure 6 Subcarrier mapping schemes

Figure 7 Subcarrier mapping implementation (a) Distributed (b) localized

2.2.3.1 Localized subcarrier mapping (LFDMA)

The subcarrier mapping allocates a group of 𝑀 adjacent subcarriers to a user. As

shown in Figure 7 Subcarrier mapping implementation , subcarrier mapping

implementation in which 𝑀 < 𝑁 results in zero being appended to the output of the DFT

spreader resulting in an interpolated version of the original 𝑀 QAM data symbols at the

IFFT output of the OFDM modulator. The transmitted signal is thus similar to a

narrowband single carrier with a CP.

Consecutive subcarriers are occupied by the DFT outputs of the input data in the

localized subcarrier mapping mode resulting in a continuous spectrum that occupies a

fraction of the total available bandwidth.

The time domain samples of localized subcarrier mapping are found in [47] to be

19

𝑦 𝑛 = 𝑦 𝑄. 𝑚 + 𝑞 =

1

𝑄𝑥 𝑛 𝑚𝑜𝑑 𝑀 𝑞 = 0

1

𝑄 1 − 𝑒

𝑗2𝜋𝑞𝑄 .

1

𝑀

𝑥(𝑝)

1 − 𝑒𝑗2𝜋

𝑚−𝑝𝑀

+𝑞

𝑄𝑀

𝑞 ≠ 0

𝑀−1

𝑝=0

(2.4)

where 𝑞 is the remainder of 𝑛/𝑄 .Thus the localized subcarrier mapping transmitted signal

is a scaled version by a factor 1/𝑄 for samples that are placed at integer multiples of 𝑀.

While intermediate samples are a linear combination of all time symbols in the input block.

For example for 𝑀 = 4 , 𝑁 = 12, zeros are appended after the DFT outputs with

input vector of 𝑥 = 5,10,15,20 then the transmitted signal would be

1.667 −0.639 + 3.608𝑖 −2.306 − 3.608𝑖 3.333 −0.64 + 3.608𝑖 −3.526 − 3.608𝑖

5 −1.86 + 3.608𝑖 −3.526 − 3.608𝑖 6.667 −5.19 + 3.608𝑖 1.026 − 3.608𝑖

2.2.3.2 Distributed subcarrier mapping (DFDMA)

The subcarrier mapping allocates 𝑀 equally-spaced subcarriers (e.g. every 𝐿𝑡𝑕

subcarrier). (𝐿 − 1) zeros are inserted between the 𝑀 DFT outputs as shown in Figure 7,

and additional zeros are appended to either side of the DFT output prior to the IFFT

(𝑀𝐿 < 𝑁). The zeros inserted between the DFT outputs produce waveform repetition in

the time domain.

In the distributed subcarrier mapping mode, DFT outputs of the input data are

allocated over the entire bandwidth with zeros occupying the unused subcarriers resulting

in a non-continuous comb-shaped spectrum.

The time domain samples of distributed subcarrier mapping are found in [47] to be

𝑦 𝑛 = 𝑦 𝑄. 𝑚 + 𝑞 =

1

𝑄𝑥 𝑄 . (𝑛 𝑚𝑜𝑑 𝑀) 𝑚𝑜𝑑 𝑀 𝑞 = 0

1

𝑄 1 − 𝑒

𝑗2𝜋𝑄 𝑞𝑄 .

1

𝑀

𝑥(𝑝)

1 − 𝑒𝑗2𝜋

𝑄 𝑚−𝑝𝑀 +

𝑄 𝑞𝑄𝑀

𝑞 ≠ 0

𝑀−1

𝑝=0

(2.5)

where 𝑄 1 ≤ 𝑄 < 𝑄 is the actual spreading factor (i.e., without the overall appended

zeros).

Note that the time domain structure of DFDMA resembles the LFDMA with some

kind of repetition and in case of 𝑄 = 1 the signal is transformed to localized subcarrier

mapping as figure

20

The same example in 2.2.3.1 Localized subcarrier mapping (LFDMA)with 𝑄 = 2 will result in time domain DFDMA signal as

1.67 4.27 - 0.19i 3.44 - 1.25i 5 4.88 - 1.25i 5.72 + 2.69i

1.67 4.27 - 0.19i 3.44 - 1.25i 5 4.88 - 1.25i 5.72 + 2.69i

2.2.3.3 Interleaved subcarrier mapping (IFDMA)

The interleaved subcarrier mapping is a special case of DFDMA with no appended

zeros ,i.e., where the chunk of 𝑀 subcarriers occupy the entire bandwidth with a spacing

of (𝐿 − 1) subcarriers having zero amplitudes.

For IFDMA, time symbols are simply a repetition of the original

input symbols with a systematic phase rotation applied to each symbol in

the time domain. Therefore, their time domain representation is given by

[47]

𝑦 𝑛 =1

𝑄𝑥 𝑛 𝑚𝑜𝑑 𝑀 . 𝑒𝑗2𝜋𝑟𝑛 /𝑁

(2.6)

where 𝑟 is the starting subcarrier index if it isn‟t starting from zero subcarrier. Hence no

need for DFT and IFFT process in this case.

2.2.3.4 Comparison between DFDMA and LFDMA

Figure 8 compares the later subcarrier mapping in time domain and frequency

domain.

These subcarrier mapping schemes differ in PAPR, and frequency diversity.

Subcarrier mapping methods are further divided into static and Channel Dependent

Scheduling (CDS) methods. CDS assigns subcarriers to users according to the channel

frequency response of each user. Localized transmissions are beneficial for supporting

frequency-selective scheduling because it provides significant multi-user diversity, for

example when the eNodeB has knowledge of the uplink channel conditions, or for inter-

cell interference coordination. Localized transmission may also provide frequency

diversity if the set of consecutive subcarriers is hopped in the frequency domain, especially

if the time interval between hops is shorter than the duration of a block of channel-coded

data, while distributed subcarrier mapping provides frequency diversity because the

transmitted signal is spread over the entire bandwidth. With distributed mapping, CDS

incrementally improves performance.

According to PAPR, the IFDMA signal maintains the input time symbols in each sample

whereas LFDMA and DFDMA have more complicated time samples because of the

complex-weighted sum of the input symbols. This implies that higher peak power is

expected for LFDMA and DFDMA [12]

21

Figure 8 Comparison between time domain and frequency domain structures for different subcarrier

mapping

2.2.4 SC-FDMA receiver

Just like the transmitter, the two major computations required to get back the

transmitted symbols in an SC-FDMA receiver are the DFT and IDFT. In an SC-FDMA

receiver, after discarding the cyclic prefix, the DFT block transforms the received time

domain signal into the frequency domain. Afterwards, subcarrier demapping is done

following the same method (distributed, localized or interleaved) in which subcarrier

mapping was done in the transmitter.

Next, an equalizer compensates for the distortion caused by the multipath

propagation channel. After the equalization process, the IDFT block transforms the signal

into the time domain, and finally, a detector recovers the original transmitted symbols.

The equalization process in an SC-FDMA receiver is done in the frequency

domain. Frequency domain equalization is one of the most important properties of SC-

FDMA technology. Conventional time domain equalization approaches for broadband

multipath channels are not advantageous because of the complexity and required digital

signal processing increase with the increase of the length of the channel impulse response.

Frequency domain equalization, on the other hand, is more computationally efficient and

therefore desirable because the DFT size does not grow linearly with the length of the

channel impulse response. Most of the time domain equalization techniques such as

MMSE, DFE and TEQ can be implemented in the frequency domain.

In frequency domain linear equalization, the equalization is carried out block-wise

with block size 𝑁. The sampled received signal is first transformed into the frequency

domain by means of a size- N DFT. The equalization is then carried out as frequency-

domain filtering [9].

With using the CP the channel will, from a receiver point of view, appear as a

circular convolution over a receiver processing block of size 𝑁 . Thus there is no need for

22

overlap-and-discard processing of successive SC-FDMA symbols in the receiver.

Furthermore, the frequency domain filter taps can now be calculated directly from an

estimate of the sampled channel frequency response without first determining the time-

domain equalizer setting, thus the frequency domain coefficient 𝐺𝑍𝐹 𝑙 of the 𝑙𝑡𝑕

subcarrier of the ZF equalizer will be simply as

𝐺𝑍𝐹 𝑙 =1

𝐻(𝑙)

(2.7)

where 𝐻(𝑙) is the frequency response of the channel affecting 𝑙𝑡𝑕 subcarrier and the

frequency domain coefficient 𝐺𝑀𝑀𝑆𝐸 𝑙 of the 𝑙𝑡𝑕 subcarrier of the minimum mean square

error (MMSE) equalizer will be

𝐺𝑀𝑀𝑆𝐸 𝑙 =𝐻∗(𝑙)

𝐻(𝑙) 2 + 𝜍𝑛2

(2.8)

where 𝜍𝑛2 is the noise power.

2.2.5 Relation between SC-FDMA and OFDMA

OFDMA and SC-FDMA transmitters and receivers perform many common signal

processing functions. The two techniques share the following properties [47]

Modulation and transmission of data in blocks consisting of M modulation

symbols;

Division of the transmission bandwidth into sub-bands with information carried on

discrete subcarriers;

Frequency domain channel equalization;

The use of a cyclic prefix to prevent inter-symbol interference;

SC-FDMA has essentially the same overall structure as those of OFDMA system

(so SC-FDMA can be regarded as DFT-precoded or DFT-S-OFDMA).

However, there are distinct differences that lead to different performance

SC-FDMA has a lower PAPR than OFDMA because OFDMA transmits a

multicarrier signal whereas SC-FDMA transmits a single carrier signal.

In the time domain, the duration of the modulated symbols is expanded in the case

of OFDMA by 𝑁 factor. By contrast, SC-FDMA compresses the modulated

symbols in time. The SC-FDMA symbol duration is 𝑇/𝑄 seconds as in a Time

Division Multiple Access (TDMA) system.

OFDMA performs equalization and data detection separately for each subcarrier.

By contrast, SC-FDMA performs equalization across the entire channel bandwidth.

It then uses the IDFT to transform the signal from one terminal to the time domain

prior to detection of the modulated symbols. The IDFT prior to symbol detection is

necessary because the transmitted signal consists of a weighted sum of all symbols

in a block i.e. in the receiver, OFDM performs data detection on a per-subcarrier

basis in the frequency domain whereas SC/FDE performs data detection in the time

domain after the additional IDFT operation as Figure 9.

23

OFDM is more sensitive to a null in the channel spectrum and carrier frequency

offset and it requires channel coding or power/rate control to overcome this

vulnerability

SC-FDMA effectively spreads each modulated symbol across the entire channel

bandwidth; it is less sensitive to frequency-selective fading than OFDMA, which

transmits modulated symbols in narrow sub-bands.

Channel adaptive subcarrier bit and power loading is possible in case of OFDMA.

So by adapting the symbol modulation and power for individual subcarriers,

OFDMA is able to come close to the upper bound of the capacity limit for a given

channel.

Figure 9 Differences between OFDMA and SC-FDMA detection and equalization processes

2.2.6 Performance limits for linear frequency equalizers

In [45] the error probabilities of DFT Spread OFDM systems are analyzed, and

analytical closed form expressions have been derived for the AWGN, fading AWGN,

multipath and fading multipath channel scenarios in case of using ZF and MMSE

frequency domain equalizers.

It was shown that in case of AWGN the Symbol Error Rate (SER) is the same in

case of ZF and MMSE and is equal to the ordinary matched filter probability of error and

found to be

𝑃𝑀𝑍𝐹= 𝑃𝑀𝑀𝑀𝑆𝐸

= 𝑄 2𝐸𝑠

𝑁0

(2.9)

where 𝐸𝑠 is the symbol energy and 𝑁0 is the noise spectral denisty And for the flat

fading Rayleigh channel, the channel frequency response is still flat but the amplitude no

longer remains fixed at 1, rather it varies from one channel realization to other, the symbol

error probabilities for MMSE and ZF are equivalent and found to be

24

𝑃𝑀𝑍𝐹= 𝑃𝑀𝑀𝑀𝑆𝐸

= 𝐸𝐻 𝑄 2𝐸𝑠 𝐻 2

𝑁0

(2.10)

where 𝐸𝐻 is the expectation operator over 𝐻 and 𝐻 is the channel gain In case of

frequency selective channel with deterministic channel gains the performance of ZF and

MMSE will differ. It is worth appreciating here that variance of noise is independent of the

index of symbol, and as such unlike the case of conventional OFDM, all the symbols are

equally likely to be in error. Because of the presence of DFT spreading, the different sub-

channel SNRs in the frequency domain are averaged to a constant SNR in the data-symbol

domain.

The error probability will be in case of ZF as

𝑃𝑀𝑍𝐹= 𝑄

2𝐸𝑠

𝛽𝑍𝐹𝑁0

(2.11)

and 𝛽𝑍𝐹 is the noise enhancement factor of the ZF equalizer and equal to

𝛽𝑍𝐹 =1

𝑀

1

𝐻𝑖 2

𝑀−1

𝑖=0

(2.12)

where 𝐻𝑖 is channel gain over the 𝑖𝑡𝑕 subcarrier and for the MMSE equalizer, the noise

enhancement factor is shown to be much smaller than the ZF equalizer in case of poor

channel conditions. And the symbol error probability is shown to be

𝑃𝑀𝑀𝑀𝑆𝐸= 𝑄

1

1/𝛼𝑀𝑀𝑆𝐸 − 1

(2.13)

Where 𝛼𝑀𝑀𝑆𝐸 =1

𝑀

𝐻𝑖 2

𝐻𝑖 2+𝜍𝑛

2/𝜍𝑠2

𝑀−1𝑖=0 with 𝜍𝑠

2 is the signal power and 𝜍𝑛2 is the noise power.

2.3 Literature review for 3GPP LTE uplink

2.3.1 Introduction

SC-FDMA has been adopted by the 3GPP [47] for uplink transmission in

technology standardized for LTE of cellular systems.

25

LTE offers a smooth evolutionary path to better data speeds and spectral efficiency.

The first version of LTE is documented in Release 8 of the 3GPP specifications. In the

earlier 3GPP releases, the specifications related to this effort were known as E-UTRA

(Evolved UMTS Terrestrial Radio Access) and E-UTRAN (Evolved UMTS Terrestrial

Radio Access Network), but now these are more commonly referred to by the project name

LTE. In addition to LTE, 3GPP is also defining an IP-based, packet-only network

architecture known as Evolved Packet core (EPC). This new architecture is defined as part

of the System Architecture Evolution (SAE) effort and has been developed to provide a

considerably higher level of performance that is in line with the requirements of LTE.

The targets for LTE downlink and uplink peak data-rate requirements are 100 Mb/s and

50 Mb/s, respectively, when operating in 20 MHz spectrum allocation. For narrower

spectrum allocations, the peak data rates are scaled accordingly. Thus, the requirements

can be expressed as 5 bit/s/Hz for the downlink and 2.5 bit/s/Hz for the uplink. As will be

discussed below, LTE supports both FDD and TDD operations (we will focus for the FDD

structure only). An uplink physical channel corresponds to a set of resource elements

carrying information originating from higher layers. The following uplink physical

channels are defined:

Physical Uplink Shared Channel (PUSCH) (we will focus on this channel only

within thesis) ;

Physical Uplink Control Channel (PUCCH);

Physical Random Access Channel (PRACH).

The data processing of the uplink and downlink are nearly identical except for the

usage of the SC-FDMA instead of OFDMA in sake of lowering the PAPR , the structure of

the reference signals and absence of MIMO schemes (spatial multiplexing and transmit

diversity schemes) till release 9.

In this section we will give a brief description of PUSCH taking in consideration

the physical resource block and the whole FDD frame structure, then we will proceed with

the SC-FDMA design parameters of LTE UL showing the reference signal structure and

finally an overview for the data processing of the PUSCH.

2.3.2 Physical resource blocks

LTE specifies signal transmissions in six possible channel bandwidths ranging from

1.4 to 20 MHz. Each channel is divided into frequency bands of 15 kHz, each specified by

a subcarrier frequency. For example, there are 72 subcarriers available in a 1.4 MHz

channel and 1200 subcarriers available in a 20 MHz channel.

All the LTE signals derive their timing from a clock operating at 𝑓𝑠 =30.72 𝑀𝐻𝑧 = 15 𝑘𝐻𝑧 × 2048, where the 15 KHz is the LTE frequency separation. This

is the timing required for the 2048 point DFT specified for 20 MHz channels. Therefore,

the basic time interval in an LTE physical channel is one clock period of duration:

𝑇 𝑠 = 1/(30.72 × 106) ≈ 32.255 𝑛𝑠 𝑝𝑒𝑟 𝑐𝑙𝑜𝑐𝑘 𝑝𝑒𝑟𝑖𝑜𝑑

(2.14)

26

LTE assigns transmission resources to physical channels in time-frequency referred

to as RBs. A RB has duration of 0.5 msec (one slot) and a bandwidth of 180 kHz (12

subcarriers). A physical channel occupies a frequency band containing one or more

contiguous RBs. The bandwidth of a physical channel is a multiple of 180 kHz and the

LTE physical layer performs LFDMA scheduling. Figure 10 [47], [10] illustrates the

uplink RB structure; all the RBs in the available system bandwidth constitute a resource

grid. The number of blocks in the resource grid ranges from 6, for 1.4 MHz channels, to

100, for 20 MHz channels.

Figure 10 Resource block in LTE

The SC-FDMA transmission considered in the LTE UL works as Figure 11. 𝑀-

DFT size being applied to a block of 𝑀 modulation symbols. The output of the DFT is then

mapped to selective inputs of an OFDM modulator, typically implemented as an IFFT. The

DFT size determines the instantaneous bandwidth of the transmitted signal whereas the

exact mapping of the DFT output to the input of the OFDM modulator determines the

position of the transmitted signal within the overall uplink cell bandwidth. A CP is then

inserted for each DFT block. The use of a CP allows for straightforward application of

low-complexity frequency domain equalization at the receiver side. The transmitted signal

corresponding to one DFT block, including the CP, can be referred to as one DFT-S-

OFDM symbol. The remaining subcarriers in the IDFT have zero magnitude and constitute

a guard band in the frequency domain to prevent out-of-band radiation [9].

27

Figure 11 Basic principles of DFTS-OFDM for LTE uplink transmission

From a DFT-implementation point-of-view, the DFT size should preferably be

constrained to a power of two. However, such a constraint is in direct conflict with a desire

to have a high degree of flexibility for the instantaneous transmission bandwidth that can

be dynamically assigned to a mobile terminal for uplink transmission. From a flexibility

point of- view, all possible DFT sizes should rather be allowed. For LTE, a middle way has

been adopted where the DFT size is limited to products of the integers two, three, and five.

For example, DFT size of 84 is not allowed. In this way, the DFT can be implemented as a

combination of relatively low-complex radix-2, radix-3, and radix-5 FFT processing [9].

As described in 2.2.3 Subcarrier mapping schemes, in the general case both

localized and distributed DFTS-OFDM transmissions are possible. However, LTE uplink

transmission is limited to localized transmission that is the output of the DFT is always

mapped to consecutive inputs of the OFDM modulator. This decision was motivated by

the fact that with localized mapping, it is possible to exploit frequency selective gain via

channel dependent scheduling. This simplifies the transmission scheme, and enables the

same RB structure to be used as in the downlink. Frequency-diversity can still be exploited

by means of frequency hopping, which can occur both within one subframe (at the

boundary between the two slots) and between subframes. In the case of frequency hopping

within a subframe, the channel coding spans the two transmission frequencies, and

therefore the frequency diversity gain is maximized through the channel decoding process

Also, similar to the downlink, two CP lengths are defined for the uplink; the normal

CP and an extended CP. LTE uses slots with six symbols in large cells subject to severe

ISI due to a long mulitpath delay spread. These cells require a extended long CP. LTE uses

slots with seven symbols in smaller cells requiring a normal CP. The duration of an

extended CP is 512 clock periods, 512 × 𝑇𝑆 = 16.67 𝜇𝑠𝑒𝑐. In slots with seven symbols,

the duration of a normal cyclic prefix is 160 clock periods, 160 × 𝑇𝑆 = 5.21 𝜇𝑠𝑒𝑐, for

the first symbol and 144 clock periods, 144 × 𝑇𝑆 = 4.69 𝜇𝑠𝑒𝑐, for the other six symbols.

2.3.3 FDD frame structure

Downlink and uplink transmissions are organized into radio frames of 10 ms duration.

𝑇𝑓 = 307200 × 𝑇𝑠 = 10 𝑚𝑠𝑒𝑐 𝑝𝑒𝑟 𝑓𝑟𝑎𝑚𝑒.

(2.15)

28

Each 10 ms frame is divided into 10 equally sized subframes. LTE supports two

types of frame structures; Type 1 is for FDD transmissions and Type 2 is applicable for

TDD transmissions [10].

Frame structure Type 1 is shown in Figure 12. Each subframe consists of 2 equally

sized slots, where each slot has duration of 0.5ms. 20 slots, numbered from 0 to 19,

constitute 1 radio frame. The 1 ms duration of a subframe is an LTE Transmission Time

Interval (TTI) i.e. allows a 1 ms scheduling interval. For FDD, 10 subframes are available

for downlink transmission and 10 subframes are available for uplink transmission in each

radio frame. Uplink and downlink are separated in the frequency domain.

Figure 12 LTE FDD (type 1) frame structure

2.3.4 SC-FDMA signal parameters for LTE UL

Section 2.3.4 summarizes the main parameters of the SC-FDMA signal transmitted

in the LTE uplink [2], [47]. Table 2 LTE uplink transmission parameters clarifies the

PUSCH FDD frame structure taking in consideration the durations of the frame, slot,

subframe and SC-FDMA symbol. Moreover the table shows that the subcarrier spacing is

15KHz as the downlink mode. Two cases of cyclic prefixes are found in the standard and it

is clear that the number of SC-FDMA symbols is dependent on the cyclic prefix length

selected (according to channel maximum delay spread) which are 7 symbols in case of

normal cyclic prefix and 6 in case of extended cyclic prefix. The table also shows that the

number of subcarriers/RB is 12 as downlink structure and the number of assigned

subcarriers for each user is multiples of 12 and multiples of 2, 3, 5 to facilitate the DFT

design.

Table 3 shows the spectrum flexibility capabilities of the LTE UL at which 6

bandwidths are found in the standard. Each bandwidth differs in total number of resource

blocks which scales with the bandwidth selected. The total number of occupied subcarriers

as

𝑂𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑠𝑢𝑏𝑐𝑎𝑟𝑟𝑖𝑒𝑟𝑠 = 𝑁𝑠𝑐𝑅𝐵 ∗ 𝑁𝑅𝐵

𝑈𝐿 (2.16)

The IFFT size is chosen usually to be the nearest power of 2 to the total occupied

subcarriers except for the 15MHz bandwidth. To fix the value of the frequency separation

the sampling rate of the IFFT stage must be increased as that the sampling rates resulting to

be small rational multiples of the UMTS 3.84 MHz chip rate, for ease of implementation in

a multimode UE as

29

𝑓𝑠 = 𝑁. ∆𝑓 (2.17)

LTE refers to the complex numbers produced by the IFFT and the complex numbers in the

cyclic prefix as samples. The size of the IFFT ranges as following

𝑛𝑜. 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒𝑠 = 𝑁𝑠𝑦𝑚𝑏𝑈𝐿 . (𝑁 + 𝐶𝑃) (2.18)

Parameter Description and values

𝑻𝒔 Duration of basic LTE clock period 1/(30.72 ∗ 106) seconds

𝑻𝒇 Duration of one radio frame =10ms

Subframe

duration 1ms

Slot duration 0.5ms

∆𝒇 Frequency separation (spacing) =15 KHz

𝑵𝒔𝒚𝒎𝒃𝑼𝑳

Number of SC-FDMA symbols per resource block (7 for normal cyclic

prefix and 6 for extended cyclic prefix)

𝑵𝒔𝒄𝑹𝑩 Number of subcarriers per resource block =12 subcarriers

𝑵𝑹𝑩𝑼𝑳

Number of resource blocks in the uplink ranges from 6 to 100 resource

blocks

𝑴𝑺𝑪𝑷𝑼𝑺𝑪𝑯

Number of subcarriers allocated to mobile terminal

𝑀𝑆𝐶𝑃𝑈𝑆𝐶𝐻 = 𝑁𝑠𝑐

𝑅𝐵 ∗ 2𝛼2*3𝛼3 ∗ 5𝛼5 where 𝛼2 , 𝛼3, 𝛼5 are nonnegative integers

𝑵 Total number of subcarriers including the guard band area. Also, represents

the IFFT size of the transmitter

CP

Normal: 5.2𝜇𝑠for first symbol (166 modulation symbols) and 4.69 𝜇𝑠(144

modulation symbols) for all other symbols

Extended:16.67𝜇𝑠for all symbols (512 modulation symbols)

SC-FDMA

symbol duration 66.67𝜇𝑠

Table 2 LTE uplink transmission parameters

Characteristic Value

Channel Bandwidth (MHz) 1.4 3 5 10 15 20

Number of resource blocks 𝑵𝑹𝑩𝑼𝑳 6 15 25 50 75 100

Number of occupied subcarriers 72 180 300 600 900 1200

IFFT size (𝑵) 128 256 512 1024 1536 2048

Sampling rate 𝒇𝒔 (MHz) 1.92 3.84 7.68 15.36 23.04 30.72

Samples per slot 960 1920 3840 7680 11520 15360

Table 3 Spectrum flexibility parameters in LTE UL

In contrast to the downlink, no unused DC-subcarrier is defined for the LTE uplink

[2], [9]. The presence of a DC-carrier in the center of the spectrum would have prevented

the assignment of the entire cell bandwidth to a single UE while still retaining the

assumption of mapping to consecutive inputs of the OFDM modulator, something which is

required to keep the low-PAPR property of the uplink transmission. Also, due to the DFT-

30

based pre-coding, the impact of any DC interference will be spread over the block of 𝑀

modulation symbols and will therefore be less harmful compared to normal OFDM

transmission. In order to minimize DC distortion effects on the packet error rate and the

PAPR ,the subcarriers are frequency-shifted by half a subcarrier spacing (±7.5 kHz),

resulting in an offset of 7.5 kHz for subcarriers relative to DC, thus, two subcarriers

straddle the DC location.

2.3.6 Uplink reference signals

As in the downlink [2], the LTE uplink incorporates RSs for data demodulation and

channel sounding. Two types of RS are supported on the uplink:

Demodulation RS (DRS), associated with transmissions of uplink data on the PUSCH

and/or control signaling on the PUCCH. These RSs are primarily used for channel

estimation for coherent demodulation. The DRSs of a given UE occupy the same

bandwidth (i.e. the same RBs) as its PUSCH/PUCCH data transmission (we will

concentrate on this reference signal).

Sounding RS (SRS), not associated with uplink data and/or control transmissions, and

primarily used for channel quality determination to enable frequency-selective scheduling

on the uplink. SRS can occupy a bandwidth different from that used for data transmission.

UEs transmitting SRS in the same subframe can be multiplexed via either Frequency or

Code Division Multiplexing (FDM or CDM respectively),

Desirable characteristics for the uplink RSs include constant amplitude in the

frequency domain for equal excitation of all the allocated subcarriers for unbiased channel

estimates, low PAPR in the time domain, good autocorrelation properties for accurate

channel estimation and good cross-correlation properties between different RSs to reduce

interference from RSs transmitted on the same resources in other cells sufficiently many

reference signal sequences of the same length, that is corresponding to the same

transmission bandwidth, should be available to avoid an unreasonable planning effort.

The uplink reference signals in LTE are mostly based on Zadoff–Chu (ZC) sequences that

satisfy the most of the later requirements as described in the next section

2.3.6.1 ZC sequences

ZC sequences (also known as Generalized Chirp-Like (GCL) sequences) .They are

non-binary unit-amplitude sequences [2], which satisfy a Constant Amplitude Zero

Autocorrelation (CAZAC) property. The ZC sequence of odd-length 𝑁𝑍𝐶 is given in LTE

standard as

𝑎𝑞 𝑛 = 𝑒−𝑗𝜋𝑞𝑛 (𝑛+1)/𝑁𝑍𝐶 (2.19)

where 𝑞 = 1, . . . , 𝑁𝑍𝐶 − 1 is the ZC sequence index (also known as the root index), n

= 0, 1, . . . , 𝑁𝑍𝐶 − 1,

ZC sequences have the following important properties:

31

A ZC sequence has constant amplitude, and its 𝑁𝑍𝐶-point DFT also has constant

amplitude. The constant amplitude property limits PAPR and generates bounded

and time-flat interference to other users. It also simplifies the implementation as

only phases need to be computed and stored, not amplitudes.

ZC sequences of any length have „ideal‟ cyclic autocorrelation (i.e. the correlation

with the circularly shifted version of itself is a delta function) which allows

multiple orthogonal sequences to be generated from the same ZC sequence.

The absolute value of the cyclic cross-correlation function between any two ZC

sequences is constant and equal to 1/ 𝑁𝑍𝐶 , if |𝑞1 − 𝑞2| (where 𝑞1 and 𝑞2 are the

sequence indices) is relatively prime with respect to 𝑁𝑍𝐶 .

2.3.6.2 Basic principles of DRS transmission

When transmitting the DRS, the length-𝑁𝑝 RS sequence is directly applied (without DFT

spreading) to 𝑀 = 𝑁𝑝 reference signal subcarriers at the input of the IFFT [2], [9] as shown

in Figure 13

Figure 13 DRS generation in LTE UL

In LTE the DRS is chosen to be transmitted in the middle of each slot (i.e. the fourth SC-FDMA

symbol) and covers the whole subcarriers assigned to the UE as

Figure 14 Transmission of uplink reference signals within a slot in case of PUSCH

transmission. In LTE, 𝑁𝑍𝐶 is selected to be the largest prime number ≤ 𝑁𝑃 =𝑀𝑆𝐶

𝑃𝑈𝑆𝐶𝐻 (same bandwidth of the data) . The ZC sequence of length 𝑁𝑍𝐶 is then cyclically

extended to the target length 𝑁𝑃 as follows

𝑟𝑞 (𝑛) = 𝑎𝑞(𝑛 𝑚𝑜𝑑 𝑁𝑍𝐶), 𝑛 = 0, 1, . . . , 𝑁𝑝 − 1 (2.20)

The cyclic extension in the frequency domain preserves the constant amplitude

properties (in the frequency domain) and also the zero autocorrelation cyclic shift

orthogonality. Cyclic extension of the ZC sequences is used rather than truncation, as in

general it provides better PAPR characteristics.

32

Figure 14 Transmission of uplink reference signals within a slot in case of PUSCH transmission

(normal CP).

However, for the shortest sequence lengths, suitable for resource allocations of just

one or two RBs, only a small number of low-CM extended ZC sequences is available, so

for sequence lengths equal to 12 and 24, corresponding to transmission bandwidths of one

and two RBs, respectively, special QPSK-based sequences have instead been found from

computer search and are explicitly listed in the LTE specifications. For each of the two

sequence lengths, 30 sequences are then available.

2.3.6.3Phase-rotated reference-signal sequences

In the previous section, it was described how different reference-signal sequences

(a minimum of 30 sequences for each sequence length) can be derived, primarily by

cyclically extending different prime-length ZC sequences [2], [9].

Additional RS sequences can be derived by applying different linear phase rotation

to the same basic RS sequence as illustrated in Figure 15. Applying a linear phase rotation

in the frequency domain is equivalent to applying a cyclic shift in the time domain. Thus,

although being defined as different frequency domain phase rotations, in the LTE

specification this is often referred to as applying different cyclic shifts (or frequency-

domain phase rotation) to the same basic reference-signal sequence as

𝑟𝑞 ,𝛼 𝑛 = 𝑒𝑗𝛼𝑛 . 𝑟𝑞 (𝑛) (2.21)

RSs defined from different RS sequences typically have relatively low but still non-

zero mutual correlation. In contrast, reference signals defined from different phase

rotations of the same basic RS sequence can be made completely orthogonal in case of

frequency non-selective over the span of 12 subcarriers (one resource block), thus causing

no interference to each other, assuming the parameter 𝛼 in

Figure 15 takes a value 𝑚𝜋 /6 where 𝑚 ranges from 0 to 11. Up to 12 orthogonal

RSs can thus be defined from each basic RS sequence. Another prerequisite for

orthogonality between RSs defined from different phase rotations of the same basic RS

sequence is that the RSs should be received relatively time aligned. A timing misalignment

between the RSs will, in the frequency domain, appear as a phase rotation that may

counteract the phase rotation applied to separate the RS sequences. The result may be

substantial interference between the RS transmissions.

33

Figure 15 Generation of uplink RS sequence from linear phase rotation of a

basic RS sequence.

This can be used as UEs can be assigned to transmit on the same set of subcarriers,

for example in the case of uplink multi-user (collaborative MIMO). Using different base

sequences for different UEs transmitting in the same RBs is not ideal due to the non-zero

cross-correlation between the base sequences which can degrade the channel estimation at

the eNodeB. It is preferable that the RS signals from the different UEs are fully orthogonal

2.3.7 Uplink physical data processing (PUSCH processing)

The LTE uplink transport-channel processing, more specifically the processing for

the PUSCH, can be outlined according to Figure 16 . Most steps of the uplink transport-

channel processing are similar to the corresponding steps of the downlink transport-

channel. However, as there is no spatial multiplexing or transmit diversity currently

defined for the LTE uplink, there is no explicit multi-antenna-mapping function as part of

the uplink transport-channel processing. As a consequence, there is also only a single

transport block, of dynamic size, transmitted for each TTI. In more details, the uplink

transport-channel processing consists of the following steps:

CRC insertion per transport block:

A 24-bit CRC is calculated for and appended to each uplink transport block in the

same way as for downlink transport channels.

Code-block segmentation and per-code-block CRC insertion:

In the same way as for the downlink, code-block segmentation is applied for

transport blocks larger than 6144 bits. The code-block segmentation also includes per-

code-block CRC(in case of more than one code block) and possible insertion of filler bits

similar to the downlink.

Turbo coding:

The same rate 1/3 Turbo code with Quadratic permutation polynomial (QPP-based)

internal interleaver as is used for the downlink is also used for the uplink.

Rate-matching and physical-layer hybrid-ARQ functionality:

The uplink physical-layer aspects of the LTE uplink hybrid ARQ are basically the

same as the corresponding downlink functionalities, which are sub-block interleaving and

34

bit collection into a circular buffer, followed by bit selection. It should be noted that, in

some aspects, there are some clear differences between the downlink and uplink hybrid-

Automatic repeat request (ARQ) protocols, such as asynchronous versus synchronous

operation. However, these differences are not really visible in the physical-layer aspects of

the hybrid-ARQ functionality.

Bit-level scrambling:

Similar to the downlink, bit-level scrambling is also applied to the code bits on the

LTE uplink. The aim of uplink scrambling is the same as for the downlink that is to

randomize the interference and thus ensure that the processing gain provided by the

channel code can be fully utilized. To achieve this, the uplink scrambling is UE specific,

which is, different UEs use different scrambling sequences.

Data modulation:

Similar to downlink DL-SCH transmission, QPSK, 16QAM, and 64QAM

modulation can be used for UL-SCH transmission. The block of modulation symbols is

then applied to the DFTS-OFDM processing as outlined in previous sections. The exact

frequency-domain mapping is controlled by the scheduler.

Figure 16 PUSCH physical layer processing

35

CCHHAAPPTTEERR TTHHRREEEE

CCOOLLLLAABBOORRAATTIIVVEE MMIIMMOO SSYYSSTTEEMM MMOODDEELL AANNDD EEXXIISSTTEENNTT

DDEETTEECCTTIIOONN SSCCHHEEMMEESS

3.1 Introduction

In this chapter, we start with introducing the collaborative MIMO concept. Then we

proceed to construct the basic system model that will be used all over the context of thesis.

Simulation model is studied in both Single input single output case and collaborative

MIMO case for general number of transmitting and receiving antennas identifying the

basic components of the uplink transmitters, and then we continue with describing the used

channel model including different channel effects such that shadowing phenomenon, flat

and frequency selective fading channels in case of slow and fast fading channels and

summary of the used simulation conditions.

The Chapter is also turning light on the different equalizers for Single input single

output case considering perfect and imperfect channel estimation. Then, we will proceed

with describing the existent detection schemes for collaborative MIMO case identifying

the pros and cons for each detector. The chapter will end with illustrative simulation results

showing the main characteristics of each equalizer in different simulation scenarios.

3.2 Collaborative MIMO concept

As we have mentioned in section 1.3, MIMO schemes have attracted attention due

to its advantages that promote it as a key technology for the upcoming 4G mobiles. These

advantages include array gain, spatial diversity gain, spatial multiplexing gain, interference

reduction, and increase the capacity of wireless channels since a number of independent

radio channels are generated by placing multiple antennas in the transmitter and the

receiver. MIMO technology has become a key component for several broadband wireless

communication standards, including the 3GPP, LTE and the IEEE 802.16e (also referred to

as mobile worldwide interoperability for microwave access or mobile WiMAX),

IEEE802.11n (new WLAN standard).

On the other hand, MIMO systems require complex transceiver circuitry and signal

processing. Moreover, physical implementation of multiple antennas on a small node

specially the uplink node of the LTE (UE) may not be realistic [48].So single-antenna

radio and limited battery power, high network performance and low energy consumption

have been very challenging issues in the design of LTE UL UEs. Those are the motives for

using the concept of the collaborative MIMO spatial schemes (also known in LTE context

as virtual MIMO) which are one of the MU-MIMO technologies (also introduced as

SDMA)

We will consider the Collaborative Spatial Multiplexing scheme (CSM) which is

distributed single-antenna radio systems cooperate on information transmission and

reception as a multiple-antenna MIMO radio system. CSM works as the following two or

more users having UEs equipped with single antenna, each one of them transmits

independent data stream from the others. Those users are collaboratively transmitting to

same RBs, i.e. same frequency/time grid resource. The above transmission technique

36

creates V-MIMO link in a sense of imagining that the collaborative users are just antennas

for virtual large mobile station and at each antenna there is a different stream which is the

conventional spatial multiplexing idea. Now, the eNodeB is receiving combined data from

all collaborative users, eNodeB will then separate the data of each user using multiuser

equalization techniques [49], i.e. The buzzword V-MIMO denotes a certain class of

spatiotemporal processing techniques in which the classical MIMO transmission schemes

are further developed using some kind of coherent cooperation between distributed radio

nodes [33].

Collaborative MIMO spatial multiplexing offers the following advantages over the

ordinary MIMO schemes:

Increases the whole throughput of the uplink because the single RB is now reused

among different users which in turns provide extremely high spectral efficiencies.

Achieves virtual MIMO without increasing the complexity of the UEs.

Achieves a diversity gain from receiving different and independent replicas of the

user data that when the multiuser interference is perfectly cancelled.

Offers considerable energy savings even after taking into account the additional

circuit power, communications, and training overheads.

Moving the complexity of implementing multiple antennas to the eNodeB.

For practical collaborative MIMO schemes, three issues are required, orthogonal

pilots for the collaborating users, perfect synchronization and collaborating users selection

(namely as user pairing). Different from the SIMO mode based on 1-stream pilot pattern,

each UE involved in the CSM applies one of the two 2-stream orthogonal pilot patterns.

That is, two users transmit the data symbols over the same time-frequency resource but

their pilot tones are non-overlapped. In doing so, the BS can differentiate the channel

responses from each UE. This pilot structure is activated in LTE UL using phase-rotated

reference-signal sequences described in 2.3.6.3Phase-rotated reference-signal

sequences[50]. The remote synchronization needed for virtual MIMO is rarely considered

in the literature. It is shown that timing errors may have similar effects as ISI. The impact

of Carrier Frequency Offsets (CFO) is studied in [51]

User pairing forms a challenging issue in choosing the best collaborating users

Traditional V-MlMO pairing methods consider the orthogonality of the channel matrix.

The users whose channel matrix is more orthogonal are preferred to be chosen for a pair.

Anyway, not only the orthogonality, but also the SNR of each user should be considered

when pairing. This is because that the SNR of each user may affect the V-MlMO channel

capacity. Also the allocation of users should be done in a way that they will cause minimal

disruption to each other. All scheduling schemes need to consider fairness issues, which

typically enforces a tradeoff between network optimality and user optimality [35], [52].

The proposals for multiuser equalization techniques are ZF, MMSE,SIC and ML.

Frequency domain ZF receiver which is a simple linear multiuser equalizer that suffers

from noise enhancement, This problem can be reduced using frequency domain MMSE

receiver which is linear equalizer that counts for the additive noise and SIC receiver which

is a DFE which serially demodulates one user and cancels its effect from the received

signal and so on until the last user [35],[36]. The optimal equalizer is the use of the ML

37

equalizer which performs an exhaustive search in the time domain to find the symbols

combination that results in the minimum detection error.

3.3 Transmitter description

The collaborative spatial multiplexing system is assumed to have 𝐾 users each has

a UE equipped with single antenna as shown in Figure 17. The data of 𝑘𝑡𝑕 user is

independently processed as the following

Figure 17 LTE user equipments transmitters

First, data of the user is encoded to have the encoded data 𝑥𝑘 . The encoded data is

then symbol mapped (baseband modulated) to have the modulation symbols 𝑦𝑘 .The

modulated symbols are then transformed to the frequency representation by the means of

the unitary DFT of size 𝑀 to have 𝑌𝑘 .

𝑌𝑘 𝑚 =1

𝑀 𝑦𝑘

𝑀

𝑛=1

𝑛 exp −𝑗2𝜋

𝑀 𝑛 − 1 𝑚 − 1

(3.1)

where 𝑚: is the subcarrier index and 𝑛:is the symbol index 𝑚, 𝑛𝜖 1,2, … , 𝑀 .

The output of the DFT is then mapped using the subcarrier mapping [12]. The

subcarrier mapping has two versions: Distributed and the localized, the latter is adopted in

the Release 8.With the localized subcarrier mapping which is described in section 2.2.3.1

the user's symbols are mapped into consecutive subcarriers in the center of the overall

allocated band, this is achieved in the presence of frequency selective fading channel the

multiuser diversity.Frequency selective diversity can also be achieved if assigning each

user to subcarriers with favorable transmission characteristics. So localized subcarrier

mapping is applied to have 𝑌 𝑘 .

In this work, we assume full RB usage so 𝑌 𝑘 consists of 𝑌𝑘 appended with zero

guard subcarriers from both sides.

𝑌 𝑘(𝑙) = 𝑌𝑘 𝑚 𝑙𝜖Γ𝑘

0 𝑜𝑡𝑕𝑒𝑟𝑤𝑖𝑠𝑒

38

(3.2)

where: Γ𝑘 is the 𝑁 element mapping set of the 𝑘𝑡𝑕 user Γ𝑘 𝜖

𝑁−𝑀+2

2, … ,

𝑁+𝑀

2 and 𝑁 is the

FFT size.

The output of the subcarrier mapping stage is fed to conventional OFDM transmitter

which consists of Inverse Fourier transform stage (IFFT) with size (𝑁 > 𝑀).

𝑠𝑘 𝑛 =1

𝑁 𝑌 𝑘

𝑀

𝑚=1

𝑚 exp −𝑗2𝜋

𝑁 𝑛 − 1 𝑚 − 1

(3.3)

where 𝑚, 𝑛𝜖 1,2, … , 𝑁 .

Finally, the CP insertion with CP length larger than of the maximum delay spread

of the multipath channel, This will mitigate the ISI occurred due the channel and enable

simple FDE.The above steps will result in DFT-spread-OFDM signal (SC-FDMA signal)

𝑠𝑘 that are described thoroughly in section 2.2. The CP lengths in the LTE are the normal

CP and extended CP defined in section 2.3.4 SC-FDMA signal parameters for LTE UL

according to the frequency selectivity of the multipath channel.

The frame structure used is the FDD (Type 1) described in section 2.3.3 FDD frame

structure in which 20 slots having 6 or 7 SC-FDMA symbols depending on the CP type.

The Demodulation reference signals are inserted in the fourth SC-FDMA symbol as

described in section 2.3.6 Uplink reference signals, the complex Zadoff-Chu (ZC)

sequences described in section 2.3.6.1 ZC sequences.

3.3.1Channel coding

In the context of the thesis, the data bits are encoded by one of the following coding

schemes

Rate 1/2 convolutional coding [53] with different constraint lengths and hence

different connection diagrams. A list of the optimal connection schemes is

summarized in Table 4.

Punctured convolutional coding to support different coding rates. A list of the

coding rates and the puncturing pattern is summarized in Table 5 [54] .

Rate 1/3 compliant turbo code with Parallel Concatenated Convolutional Code

(PCCC) with two 8-state constituent encoders and QPP internal interleaver. The

encoder in this case will have the parameters shown in Table 5.1.3-3 1 [10]and the

transfer function of the 8-state constituent code will be given by as Figure 18 LTE

Turbo encoder structure [31].

G D = 1,g1 D

g0 D where g0 D = 1 + D2 + D3, g1 D = 1 + D + D3 (3.4)

1 3GPP TS 36.212 V8.5.0 (2008-12)

39

Figure 18 LTE Turbo encoder structure

Constraint length Optimal connection (octal)

3 [7 5]

4 [17 13]

5 [27 31]

6 [57 65]

7 [117 345]

8 [237 345]

9 [657 435]

Table 4 Optimal connections for rate 1/2 convolutional encoder

Code rate 1/2 2/3 3/4 5/6

dfree 10 6 5 4

Parity 1 (X) 11 10 101 10101

Parity 2 (Y) 11 11 110 11010

Output X1Y1 X1Y1Y2 X1Y1Y2X3 X1Y1 Y2X3 Y4X5

Table 5 Puncturing patterns for rate ½ convolutional encoders

3.3.2 Symbol mapping process

In our model, we are considering the three symbol mapping schemes defined in the

standard which are QPSK, 16QAM and 64QAM with Gray coding as symbol ordering

scheme to decrease the probability of bit error probability when receiving an erroneous

symbol besides the BPSK [53] , [10]. The constellation diagrams of the lowpass equivalent

(I/Q patterns) showing the Gray coding scheme is described in Figure 19 Symbol mapping

40

schemes for LTE UL (gray coded). Transmitted symbols are normalized for fair

comparison with normalization factors in Table 6.

Modulation

scheme

Normalization

factor

BPSK 1

QPSK 1/ 2

16QAM 1/ 10

64QAM 1/ 42

Table 6 Normalization factors for the LTE modulation schemes

Figure 19 Symbol mapping schemes for LTE UL (gray coded)

3.3.3 Summary of the simulation parameters in our model

For link level simulations of the proposed detection schemes, Type 1 structure FDD

mode of the LTE specifications is assumed. The collaborative users are assumed to be

matched, i.e., have the same transmission parameters, also they are assumed to fully utilize

the full uplink bandwidth, i.e., all the 𝑀 subcarriers Table 7 shows the simulation

parameters of most of simulation cases, other simulation parameters are mentioned

explicitly.

Simulation parameters Values Default

Channel coding

Convolutional coding rate

½ with different constraint

lengths (3,4,5,6,7,8,9)

Punctured rate

convolutional codes

None

41

LTE compliant turbo code

of rate 1/3 with 8-state

constituent encoder

Modulation schemes BPSK ,QPSK , 16QAM and

64QAM QPSK

Frame duration 10ms 10ms

FFT size (𝑵) 128,256 , 512, 1024 ,1536

and 2048 256 subcarriers

Number of resource

blocks

Full utilization of RBs

6, 15 , 25 , 50 , 75, 100 15

Transmission

bandwidth

1.4 MHz, 3 MHz , 5MHz

,10MHz , 15 MHz and

20MHz.

3 MHz

SC-FDMA symbols 6 and 7 6

Cyclic prefix choice Extended and normal extended

Subcarrier separation 15KHz 15KHz

Carrier frequency variable 2GHz

Sampling frequency 𝑓𝑠 = 𝑁. ∆𝑓 3.84MHz

Collaborative system

configuration

Variable

𝐾 𝑢𝑠𝑒𝑟𝑠 x𝑃 𝑎𝑛𝑡𝑒𝑛𝑛𝑎𝑠 2x2 V-MIMO

Delay spread variable 5𝜇s

Delay- power profile Uniform- Exponential Uniform

Users’ speed variable 0 km/hr

Channel estimation

Perfect

Least square estimation

MMSE estimation

Perfect

Table 7 Common simulation parameters

3.4 Channel modeling

In our model, various channel effects are studied in the context of the thesis. In

addition to AWGN, we have modeled all multipath phenomenon such as flat and frequency

selective channels in case of slow and fast fading conditions. In some cases, large scale

fading (shadowing) is considered.

3.4.1 Large scale fading (Shadowing) model

A signal will typically experience random variation due to blockage from objects in

the signal path, giving rise to a random variation about the path loss at a given distance. In

addition, changes in reflecting surfaces and scattering objects can also cause random

variation about the path loss. Since the location, size, and dielectric properties of the

blocking objects as well as the changes in reflecting surfaces and scattering objects that

cause the random attenuation are generally unknown, statistical models are widely used to

characterize this attenuation. The most common model for this additional attenuation is

log-normal shadowing. This model has been confirmed empirically to accurately model the

42

variation in path loss or received power in both outdoor and indoor radio propagation

environments [55].

The log-normal shadowing PDF is given by

𝑝 𝜓𝑑𝐵 =1

2𝜋 𝜍𝜓𝑑𝐵

exp −(𝜓𝑑𝐵 − 𝜇𝜓𝑑𝐵 )2

2𝜍𝜓𝑑𝐵2

(3.5)

where 𝜓𝑑𝐵 is the overall attenuation (shadowing superimposed over the path loss

model), 𝜇𝜓𝑑𝐵 is the mean attenuation in dB scale and in our case we assume 𝜇𝜓𝑑𝐵 = 0 and

𝜍𝜓𝑑𝐵2 is the variance of the shadowing phenomenon.

3.4.2 Flat and frequency selective fading channel modeling

Due to the existence of scatterers and obstacles in the communication channel, the

sent signal takes many paths to go from the transmitter to the receiver as it hits the

scatterers and the obstacles. From here emerge the word multipath transmission. Due to

this, the receiver receives many versions of the same sent signal that come from different

paths, these paths are different in length, so these copies come to the receiver in slightly

different times -come from different directions with different propagation delays- with

different phases. When the receiver combines those copies together which are different in

phases, the combined waves may be in phase so we have a peak and may also be out of phase

so we have a null, this change in the level of the combined signal happens over short time so

we call it small scale fading.

Several modeling techniques are discussed in [55]. In our model we model the

multipath channel as Rayleigh fading channel with 𝐿 taps. This is modeled as baseband

equivalent sample spaced channel impulse response 𝑕(𝑚, 𝜏) where 𝑚 time instant, 𝜏 is the

path number of 𝐿 taps. Each path is assumed to be Wide Sense Stationary Uncorrelated

Scattering (WSSUS) as

𝑕 𝑚, 𝜏 =1

2𝜌 𝑕𝐼 + 𝑗𝑕𝑄

𝑕(𝑚) = 𝑕 𝑚, 𝜏 𝛿(𝑚 − 𝜏)

𝐿

𝜏=0

(3.6)

where 𝑕𝐼 , 𝑕𝑄 are the baseband equivalent inphase and quadrature components of the fading

channel, 𝑕(𝑚) is the overall impulse response of the frequency selective channel and 𝜌 is a

normalization factor is chosen such that

𝜌 =

𝐿 𝑢𝑛𝑖𝑓𝑜𝑟𝑚 𝑝𝑜𝑤𝑒𝑟 − 𝑑𝑒𝑙𝑎𝑦 𝑝𝑟𝑜𝑓𝑖𝑙𝑒

𝑒−𝜏/𝐿𝐿𝜏=0

𝑒−𝜏/𝐿 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡𝑖𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 − 𝑑𝑒𝑙𝑎𝑦 𝑝 𝑟𝑜𝑓𝑖𝑙𝑒

43

(3.7)

The maximum delay spread 𝜏𝑚 is calculated in our model such that

𝐿 = 𝑓𝑙𝑜𝑜𝑟 𝜏𝑚 . 𝑁. ∆𝑓 + 1 (3.8)

In case of flat fading channel, the number of taps is small (𝐿 ≈ 1) and the

selectivity of the fading channel increases with increasing the number of taps which in

turns increases the frequency diversity of the fading channel and requires more complex

equalization schemes.

3.4.3 Slow and fast fading channel modeling

Due to the mobility of users, a Doppler shift would occur [55]. Doppler shift is a

slight change in the signal frequency due to the speed of the receiver and the fading

channel impulse response is no longer time invariant.

The time selectivity experienced when user is moving by velocity 𝑣 is modeled by

Jakes [56]. Jakes proposed a model for Rayleigh fading based on summing sinusoids. Let

the scatterers 𝑁𝑠𝑐𝑎𝑡 be uniformly distributed around a circle which are densely packed with

respect to angle. Then, the modified Jakes model [57] channel gains can be given by

𝑕 𝑡 = 2

𝑁𝑠𝑐𝑎𝑡 𝑊𝜎

𝑛[cos 𝛽𝑛 + 𝑗𝑠𝑖𝑛 𝛽𝑛 ]

𝑁𝑠𝑐𝑎𝑡

𝑛=1

cos(𝜔𝑛𝑡 + 𝜃𝑛 ,𝜎)

(3.9)

where 𝑁𝑠𝑐𝑎𝑡 = 16 (𝑎𝑠 𝑔𝑜𝑜𝑑 𝑐𝑕𝑜𝑖𝑐𝑒) ,𝑊𝜎𝑛 is Walch code chip 𝑛 𝑖𝑛 𝜎𝑡𝑕 code , 𝜃𝑛 ,𝑘 is a

uniform random angle over [0,2𝜋] and 𝛽𝑛 =𝜋𝑛

𝑁𝑠𝑐𝑎𝑡 , and the doppler angular frequency is

given by

𝜔𝑛 = 2𝜋𝑓𝑑𝑐𝑜𝑠 𝛼𝑛 =2𝜋𝑣𝑓𝑐

𝑐cos

𝜋

2 𝑛 − 0.5

𝑁𝑠𝑐𝑎𝑡

(3.10)

Jakes model produces a correlated fading samples which have the autocorrelation

function of

𝐸 𝑕 𝑚, 𝜏 𝑕∗ 𝑛, 𝜏 = 𝜍𝑕2 𝐽0 2𝜋𝑓𝑑𝑇𝑠 𝑚 − 𝑛 (3.11)

and power spectral denisty of

𝑆𝑕 𝑓 =2𝜍𝑕

2

𝜋𝑓𝑑

1

1 − (𝑓/𝑓𝑑)2 𝑓 < 𝑓𝐷

(3.12)

44

where 𝑓𝑑 =𝑣𝑓𝑐

𝑐 is the maximum doppler spread , 𝑇𝑠 = 1/𝑓𝑠 is the sampling time of the LTE

system from Table 3 , 𝜍𝑕2 denotes the power of channel coefficients and 𝑓𝑑𝑇𝑠 is the

normalized Doppler frequency, 𝐽0 . is the zeroth order Bessel function of first kind.

3.4.4 Fading channel for collaborative MIMO channel (Spatial model)

Now, each user's data has been completely processed and transmitted through

multipath Rayleigh channel. This is modeled as baseband equivalent sample spaced

channel impulse response 𝑕𝑘𝑝 (𝑚, 𝑙) ,where 𝑚 time instant , 𝑙 is the path number of 𝐿 taps

and 𝑝 is the receiving antenna index with uniform power delay profile. Each path is

assumed to be WSSUS as section 3.4.2, filtered by Doppler power spectral density

modeled in Jakes as section 3.4.3 Slow and fast fading channel modeling and the sum of

powers of the 𝐿 taps is normalized to 1 as

𝜍𝑕𝑘𝑝 (𝑚 ,𝑙)

2

𝑙

= 1

(3.13)

So, the result of multipath filtering of the 𝑘𝑡𝑕 user to 𝑝𝑡𝑕 receiving antenna channel can be

modeled as

𝑟 𝑘𝑝 𝑚 = 𝑕𝑘𝑝 𝑚, 𝑙 𝑠𝑘(𝑚 − 𝑙)

𝐿

𝑙=0

(3.14)

At eNodeB which is equipped by 𝑃 antennas the collaborative users' signals are

received and added together with contamination of AWGN which is modeled by IID

complex Gaussian noise samples 𝑤(𝑚) with zero mean and total variance of

𝜍𝑤2 = 𝐸{ 𝑤 𝑚 2} = 1/ 𝑁. 𝛾𝑠 (3.15)

where 𝛾𝑠 : is the symbol to noise ratio (𝐸𝑠/𝑁𝑜).

Then, the received signal 𝑟𝑝 at the 𝑝𝑡𝑕 antenna can be written as

𝑟𝑝(𝑚) = 𝑟 𝑘𝑝 𝑚 +

𝐾

𝑘=1

𝑤(𝑚)

(3.16)

The eNodeB starts with taking the FFT of each received stream, this will transform

the input streams into frequency domain again and prepare them for the FDE. The received

signal in the frequency domain at subcarrier 𝑙 can be written as

𝑹 𝑙 = 𝑯 𝑙 𝒀 𝑙 + 𝑾(𝑙) (3.17)

45

where 𝑙: is the subcarrier index , bold face letters denote vectors and matrices and 𝑯 𝑙 is

the channel matrix upon the 𝑙𝑡𝑕 subcarrier

𝑯 𝑙 = 𝐻11

𝑙 ⋯ 𝐻1𝐾𝑙

⋮ ⋱ ⋮𝐻𝑃1 ⋯ 𝐻𝑃𝐾

𝑙

(3.18)

where 𝐻𝑖𝑗𝑙 is the channel frequency gain from user 𝑗 to antenna 𝑖.It should be noted

that in the SC-FDMA transmission and in contrast with the OFDM transmission, the

subcarrier doesn't carry the one symbol directly but a combination of all transmitted

symbols according to the DFT precoding.

3.5 Single user single output (SISO) receiver

In case of single user receiver (𝑘 = 1 , 𝑃 = 1), the eNodeB has to equalize the

received sequence only in order to detect the user bits. Two frequency domain equalization

techniques are studied which are ZF equalizer and MMSE equalizer, as shown in Figure

20.

Figure 20 Single user receiver block diagram

3.5.1 Single user zero forcing equalizer (SISO ZF equalizer)

In this receiver, the distortion introduced to the received signal is compensated by a

simple frequency domain channel inversion. The CP added to the transmitted signal is

responsible for converting the linear convolution of the channel into circular convolution

which in turns is transformed to multiplication via FFT process prior to equalization. The

frequency response of the ZF equalization filter is given by

𝐺𝑍𝐹 𝑙 =1

𝐻 𝑙

(3.19)

Then, the equalized subcarriers are given by 𝑌 𝑙 = 𝑅 𝑙 . 𝐺𝑍𝐹 𝑙

The output of the equalization process is subcarrier demapped i.e. the used portion

of the total bandwidth is extracted; the output of this stage represents the equalized

subcarriers that carry a linear combination of the transmitted symbols to have. These

subcarriers are converted again to the time domain by means of IDFT process as

46

𝑦 𝑍𝐹 𝑛 = 𝑀 𝑌 𝑘 𝑚

𝑀

𝑚=1

exp 𝑗2𝜋

𝑀 𝑛 − 1 𝑚 − 1

(3.20)

The output of the last stage is demodulated and decoded to detect the received bits. The ZF

equalizer suffers from noise enhancement of the low quality subcarriers. This noise

enhancement is spread along all the received symbols which in turns increase the BER .

3.5.2 Single user minimum mean square error equalizer (SISO MMSE

equalizer)

In this equalizer, the noise enhancement problem of low quality subcarriers is

considered. The MMSE equalizer will take into account noise effect to decrease the errors

resulting from noise and channel distortion jointly. The CP extraction step is the same as

section 3.5.1 Single user zero forcing equalizer (SISO ZF equalizer).

At this point, we are able to compute the equalizer 𝐺𝑀𝑀𝑆𝐸 𝑙 . Our aim is to minimize the

BER, so we compute 𝐺𝑀𝑀𝑆𝐸 𝑙 to minimize the Mean Square Error (MSE), since this

solution maximizes the decision SNR, which is inversely proportional to the BER. The

optimum solution (MMSE) is then given by the Wiener solution which is simplified in [58]

to have the MMSE frequency domain equalizer as

𝐺𝑀𝑀𝑆𝐸 𝑙 =𝐻∗(𝑙)

𝐻(𝑙) 2 + 𝜍𝑤2

(3.21)

Then, the equalized subcarriers are given by 𝑌 𝑙 = 𝑅 𝑙 . 𝐺𝑀𝑀𝑆𝐸 𝑙 . The remaining steps

of the receiver are still as section 3.5.1 Single user zero forcing equalizer (SISO ZF

equalizer). The MMSE equalizer takes in account noise so it outperforms ZF.

3.5.3 Channel estimation Schemes

In this section, we give an overview about channel estimation techniques employed

in our model besides the perfect channel estimation. Least square (LS) and MMSE channel

estimation methods are discussed briefly. The channel estimation methods for the SC-

FDMA discussed in this section are the same methods used accompanying the OFDM-

based systems [59],[60] .Channel interpolation is also discussed in presence of high time

selectivity i.e. in case of high Doppler shift. The channel estimation for single user system

will be directly extended in case of collaborative MIMO system by ensuring non-

overlapping ZC pilots for each user or using the orthogonality feature of different phase-

rotated ZC sequences as shown in section 2.3.6. DRS of the LTE uplink and the ZC

sequences parameters are discussed in section 2.3.6

47

3.5.3.1 Least square channel estimation (LS estimation)

The LS estimator minimizes the metric 𝒀𝑫𝑹𝑺 − 𝑯 𝑿𝑫𝑹𝑺 2 where 𝒀𝑫𝑹𝑺 is the

received DRS, 𝑋𝐷𝑅𝑆 is the transmitted DRS and 𝐻 is the estimated version of the channel.

The LS estimator 𝐻𝐿𝑆 is given in [60] as

𝑯𝑳𝑺 = 𝑿𝑫𝑹𝑺

−𝟏𝒀𝑫𝑹𝑺

𝐻𝐿𝑆 𝑙 =

𝑌𝐷𝑅𝑆(𝑙)

𝑋𝐷𝑅𝑆(𝑙)

(3.22)

So the LS estimator is equivalent to what is also referred to as the ZF estimator.

The LS channel estimator is calculated with very low complexity (only subcarrier-wise

division) without using any knowledge of the statistics of the channel. But they suffer from

high MSE between the actual channel gain and estimated version.

3.5.3.2 Minimum mean square error channel estimation (MMSE estimation)

The MMSE estimator employs the second order statistics of channel conditions to

minimize the MSE. Denoting that 𝑹𝒉𝒉,𝑹𝑯𝑯 and 𝑹𝒀𝒀 are the autocovariance matrix of

𝒉, 𝑯, 𝒀𝑫𝑹𝑺 and 𝑹𝒉𝒀 is the crosscovariance matrix between 𝑕 , 𝑌𝐷𝑅𝑆 . Also 𝑭 is the DFT

orthonormal matrix of size 𝑁 as

𝑭 = 𝑊𝑁

00 ⋯ 𝑊𝑁0(𝑁−1)

⋮ ⋱ ⋮

𝑊𝑁(𝑁−1)0

⋯ 𝑊𝑁 𝑁−1 (𝑁−1)

(3.23)

And 𝑊𝑁𝑛𝑘 =

1

𝑁𝑒−𝑗

2𝜋𝑛𝑘

𝑁 .

Assuming channel vector and noise are uncorrelated then

𝑹𝑯𝑯 = 𝐸 𝑯𝑯𝑯 = 𝐸 𝑭𝒉𝒉𝑯𝑭𝑯 = 𝑭 𝑹𝒉𝒉𝑭𝑯 (3.24)

𝑹𝒉𝒀 = 𝐸 𝒉𝒀𝑯 = 𝐸 𝒉(𝑿𝑭𝒉 + 𝑾)𝑯 = 𝑹𝒉𝒉𝑭𝑯𝑿𝑯 (3.25)

𝑹𝒀𝒀 = 𝐸 𝒀𝒀𝑯 = 𝑿𝑭 𝑹𝒉𝒉𝑭𝑯𝑿𝑯 + 𝜍𝑤2 𝐈 (3.26)

In our case 𝑹𝒉𝒉 is known at the receiver via a training process to identify the

second order characteristics of the channel i.e. its autocovariance , also 𝜍𝑤2 is known in

advance. In this case, the best linear MMSE estimator (BLMMSE) is discussed in [60] and

is given by

𝒉 𝑀𝑀𝑆𝐸 = 𝑹𝒉𝒀𝑹𝒀𝒀−𝟏𝒀 (3.27)

Using equations (3.24) through (3.27) the MMSE estimate of the channel 𝑯 𝑀𝑀𝑆𝐸 will be

𝑯 𝑀𝑀𝑆𝐸 = 𝑭𝒉 𝑀𝑀𝑆𝐸

48

= 𝑭 (𝑭𝑯𝑿𝑯)−𝟏𝑹𝒉𝒉−𝟏𝜍𝑤

2 + 𝑿𝑭 −𝟏

𝒀

= 𝑹𝑯𝑯 𝑹𝑯𝑯 + 𝜍𝑤2 (𝑿𝑿𝑯)𝐻 −𝟏𝑯𝑳𝑺

(3.28)

The MMSE estimator yields much better performance than LS estimators,

especially under the low SNR scenarios. A major drawback of the MMSE estimator is its

high computational complexity, especially if matrix inversions are needed each time the

data in changes.

3.5.3.3 Channel interpolation

In case of the LTE uplink, the demodulation reference signals occupy the whole

transmitted bandwidth of the middle SC-FDMA symbol. So, there is no need for frequency

domain interpolation and the channel gains can be assumed constant during slot.

But in case of high speed mobile users i.e. high time selectivity, the channel gains

cannot be constant anymore across the slot and hence an error floor is experienced, so time

domain interpolation is needed.

Different types of interpolation filters are present such as linear interpolation, spline

interpolation and low pass interpolation [59]. In this work we assume the time domain

spline interpolation. The Spline interpolation method produces a smooth and continuous

polynomial fitted to given data points (the spline function in MATLAB) [61].

3.5.4 Simulation results and discussion

In this section we will present and discuss the results of simulation obtained for the

LTE uplink in case of SISO system. The simulation parameters follow Table 7 unless

explicitly stated.

49

3.5.4.1 Effect of different modulation, coding and equalization schemes

Figure 21 Comparison between different modulation and equalization techniques for SISO LTE uplink

Figure 21 shows that the MMSE equalization for LTE uplink outperforms the ZF

equalizer by almost 18dB at a target BER of 10−4 for QPSK modulation, 14dB for the

16QAM modulation and 16dB for 64QAM modulation. Thus the results recommend that

the LTE uplink receiver should use MMSE equalizers instead of ZF.

-10 0 10 20 30 40 5010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Comparison between MMSE and ZF equalizers for SISO LTE uplink system

for different modulation schemes

SISO , MMSE, QPSK

SISO , MMSE, 16QAM

SISO , MMSE, 64QAM

SISO , ZF, QPSK

SISO , ZF, 16QAM

SISO ,ZF, 64QAM

-10 0 10 20 30 40 5010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Comparison between MMSE and ZF equalizers for SISO LTE uplink system

for different modulation schemes

SISO , MMSE, QPSK

SISO , MMSE, 16QAM

SISO , MMSE, 64QAM

SISO , ZF, QPSK

SISO , ZF, 16QAM

SISO ,ZF, 64QAM

50

Figure 22 Comparison between coding schemes for SISO LTE uplink

Figure 22 shows the effect of different coding schemes on the LTE uplink . The

figure shows the tremendous performance enhancement due to addition of coding. For

convolutional coding rate ½ with constraint length 7 with connections shown in Table 4

Optimal connections for rate 1/2 convolutional encoder, the coding gain in order of 3dB.

While for the compliant turbo code stated in standard the coding gainin order of 9dB at

target BER of 10−4.

-5 0 5 10 15 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/No

BE

R

Comparison between coding schemes

SISO , MMSE, QPSK uncoded

SISO,MMSE , Turbo coding rate 1/3

SISO ,MMSE , conv. coding rate 1/2

51

3.5.4.2 Effect of channel selectivity

Figure 23 Effect of channel selectivity on LTE uplink

The delay spread of the frequency selective channel affects the performance of the

LTE uplink due to the main property of SC-FDMA of spreading the deep fade subcarriers

effect along all the subcarriers which in turns affect the performance of the LTE uplink.

Figure 23 shows that increasing the delay spread of the channel i.e. the frequency

selectivity increase the frequency diversity of the multipath channel and hence some

subcarriers is in deep fade and others are not and because each symbol is carried over all

subcarriers , these symbols benefit from the frequency selectivity and hence BER

decreases.

-10 -5 0 5 10 15 20 25 30 35 4010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

RDelay spread effect on

delay spread=5us

delay spread=10us

delay spread=15us

delay spread=3us

delay spread=1us

52

3.5.4.3 Effect of user mobility

Figure 24 Effect of user mobility on the LTE uplink without channel interpolation

Figure 24 shows the effect of user mobility on LTE uplink assuming zero order

interpolation i.e. fixing the channel gains over the whole slot. The figure shows that the

system is degraded slightly in low mobility users from fixed users to 20Km/hr. As the

mobility of users increases, the gain is changing faster than the slot time, so the channel

will have a faulty estimates which in turns lead to faulty channel equalization and hence

we will have an error floor i.e., irreducible error although of excessive increase in 𝐸𝑏/𝑁0 .

As the speed of users increases, the BER floor is increased to have irreducible error of

10−3 at 40 Km/hr and 10−2 at 60 Km/hr which is unacceptable and instructs to use

interpolation for high mobility users which will be discussed in section 3.6.4.7

3.6 Existent detection schemes for collaborative MIMO schemes

After transforming the received signal to frequency domain the eNodeB must separate

the collaborative users' signals using multiuser equalization technique. In this section

frequency domain multiuser ZF equalizer, Frequency domain multiuser MMSE equalizer

and Frequency domain multiuser SIC equalizer are presented.

-10 -5 0 5 10 15 20 25 30 35 4010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

REffect of user mobility of the LTE UL

user speed=0km/hr

user speed=10km/hr

user speed=20km/hr

user speed=40km/hr

user speed=60km/hr

53

3.6.1 Frequency domain multiuser ZF equalizer

The ZF receiver is a suboptimal linear receiver [62]. It behaves like a linear filter

and separates the data streams and thereafter independently decodes each stream. The ZF

receiver neglects the effect of the noise. We assume that the channel matrix on the 𝑙𝑡𝑕

subcarrier 𝑯 𝑙 (simply written 𝑯𝒍 ) is invertible and the estimate the equalized subcarrier

as

𝒀 𝑙 = 𝑯𝒍†𝑹 𝑙 = (𝑯𝒍

𝐻𝑯𝒍)−1𝑯𝒍

𝐻𝑹 𝑙 (3.29)

where 𝑯𝒍† = (𝑯𝒍

𝐻𝑯𝒍)−1𝑯𝒍

𝐻 is the pseudo inverse (Moore-Penrose pseudo-inverse) of a

non square channel matrix and (. )𝐻 is Hermitian operator (complex conjugate).

Afterwards the equalized symbols are symbol demapped (simply picking the 𝑀-

data loaded subcarriers) and then IDFT the equalized subcarriers. The output will be hard

demodulated.

The ZF receiver suffers from noise enhancement of poorly conditioned subcarriers.

Also, the noise in the separated streams is correlated and consequently the SNRs are not

independent. The diversity order of each stream is 𝑃 − 𝐾 + 1. The ZF receiver

decomposes the link into 𝑃 parallel streams, each with diversity gain and array gain

proportional to 𝑃 − 𝐾 + 1. Hence, it is suboptimum.

Note that unlike ordinary OFDM systems, this noise enhancement will be averaged

all over the received symbols [45] ruining the entire data symbols frame, and hence doesn‟t

achieve neither the full diversity gain nor the antenna gain.

3.6.2 Frequency domain multiuser MMSE equalizer

To solve the problem of noise enhancement that occurs in the ZF receiver in case of

relatively low-determinant channel matrix, a common approach is to regularize the inverse

of the ZF filter.

To elaborate, it is required to find the regularized equalizing filter of the 𝑙𝑡𝑕

subcarrier 𝑩𝒍 which minimizes the MSE, i.e., this is a linear detection algorithm to the

problem of estimating a random vector 𝒀 𝑙 on the basis of observations 𝒀 𝑙 is to choose

a matrix 𝑩𝒍 that minimizes the MSE

𝜖2𝑀𝑀𝑆𝐸 = 𝐸 𝒀 𝑙 − 𝒀 𝑙

𝐻 𝒀 𝑙 − 𝒀 𝑙

= 𝐸 𝒀 𝑙 − 𝑩𝒍𝑹 𝑙 𝐻 𝒀 𝑙 − 𝑩𝒍𝑹 𝑙

(3.30)

where 𝜖2 is the mean square error. This will lead to the LMMSE solution as [62]

𝒀 𝑙 = 𝑩𝒍𝑹 𝑙 = (𝑯𝒍𝐻𝑯𝒍 + 1/𝛾𝑠𝑰𝑲)−1𝑯𝒍

𝐻𝑹 𝑙

54

(3.31)

Linear MMSE equalization of SC-FDMA signals has a low complexity and can be

easily implemented in frequency domain [35] .Then the receiver continues with the other

detection steps (subcarrier demapping, IDFT and hard demodulating).

Note that because of the factor 1/𝛾𝑠 the MMSE equalizer doesn‟t perfectly

eliminate the “mixing” of the channel, but on the other hand can minimize the overall error

caused by noise and mutual interference between the co-channel signals, thus outperforms

the ZF equalizer.

3.6.3 Frequency domain multiuser SIC equalizer

To benefit from the inherent spatial diversity of the collaborative system with slight

increase in the computational complexity, SIC can be a promising technique.

SIC equalizer is decision-feedback receiver which makes a decision on one of the

user‟s 𝑀 points DFT frame and subtract its interference effect on the other users based on

that decision, after “simulating” the transmission stages of this user at the receiver side

[63], i.e., the SIC approach can take advantage of the channel code of a user to generate

feedback. Doing so, the interference created by the stronger user can be more efficiently

suppressed before the detection of the weaker user [35].

Then the SIC will generally do the following steps [62]

Nulling: Estimate the strongest received signal by nulling out all the weaker

transmit signals.

Slicing: Detect the value of the strongest received signal by slicing to the nearest

signal constellation value.

Cancellation: Cancel the effect of the detected signal from the received signal

vector to reduce the FER for the remaining signals.

55

Figure 25 2x2 SIC equalizer

To elaborate, the algorithm works as explained in Figure 25 assuming that 𝐾𝑡𝑕user is

the desired user:

First , begin detection by user 1 using ZF or MMSE algorithms as shown in

equations (3.30),(3.31) this will lead to 𝑌1 𝑙 .

Second, IDFT the 𝑀 points DFT frame followed by ordinary symbol

demodulation and bit level decoding, this will lead to 𝑥1 (𝑛).

Third , simulate the transmission procedure of user 1 i.e. repeat the encoding,

symbol mapping ,DFT spreading ,subcarrier mapping to have 𝑌 𝑜𝑢𝑡 𝑇𝑥1(𝑙)

Fourth, remove the interference obtained from first user as

𝑹𝒊+𝟏 𝑙 = 𝑹𝒊 𝑙 − 𝑌 𝑜𝑢𝑡 𝑇𝑥𝑖(𝑙)𝑯𝒍

(𝒊)

(3.32)

where 𝑖: cancellation stage (initially 𝑖 =1)

𝑯𝒍(𝒊)

: is 𝑖𝑡𝑕 user channel vector on the 𝑙𝑡𝑕 subcarrier i.e.,

𝑯𝒍(𝟏)

= 𝐻11𝑙 𝐻21

𝑙 … 𝐻𝑃1𝑙

𝑇 where . 𝑇 is the transpose operator.

Repeat the previous steps for the first (𝐾 − 1) users till we have the

𝑹𝑲 𝑙 =

𝐻1𝐾

𝑙 𝑌𝐾(𝑙)

𝐻2𝐾𝑙 𝑌𝐾(𝑙)

⋮𝐻𝑃𝐾

𝑙 𝑌𝐾(𝑙)

+ 𝑾(𝑙)

56

(3.34)

By inspection of last equation , it is obvious that after completely subtract the

whole interference on the 𝐾𝑡𝑕user the spatial diversity now exists which

instructs us to combine using Maximum Ratio Combiner (MRC) as

𝑌 𝐾𝑀𝑅𝐶 𝑙 =

1

𝑯𝒍(𝑲)

2 𝑹𝑲

𝐻 𝑙 𝑯𝒍(𝑲)

(3.35)

where . is the Euclidean norm.

3.6.4 Simulation results and discussion

In this section, the results of the collaborative MIMO for the LTE uplink are

considered. A comparison between the existing detection schemes is discussed thoroughly.

Different system configurations are discussed whether changing the number of

collaborative users or even the number of receiving antennas. Different channel conditions

are studied to find the best collaborating conditions.

3.6.4.1 Comparison between the existent detection methods

In figure 26 a comparison between the previously presented detection schemes is

shown. Assuming 2 users by 2 receiving antennas system as baseline for comparison. The

transmission is considered uncoded, QPSK modulated in uniform gain-delay profile

multipath channel with 𝟓𝝁𝒔 delay spread.

Figure 26 Comparison between the existent multiuser equalization techniques for 2x2 V-MIMO

systems

-5 0 5 10 15 20 25 3010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Comparison between detection techniques of

2x2 VMIMO systems

SIC-MMSE 2x2

MMSE 2x2

ZF 2x2

SIC-ZF 2x2

full diversity 1x2(reference)

57

The reference curve presents the full diversity system i.e., the case of one user and

2 receiving antennas and the equalizer is doing a MRC for the received streams. The

simulation results reveal that using the ZF or even the ZF based SIC will result in power

loss of almost 16dB at a 10−4 target BER from the full diversity curve which excludes ZF

receiver as choice for the collaborative MIMO system for the LTE uplink due to the noise

enhancement problem for poorly conditioned subcarriers. The MMSE equalizer offers only

a 5dB loss from the full diversity curve with almost same computational complexity of the

ZF equalizer. With incremental computational complexity MMSE based SIC decreases the

gap to only 2.5dB which makes it good candidate as multiuser equalization technique the

collaborative MIMO system.

3.6.4.2 Effect of changing number of users

Figure 27 assumes same simulation parameters of the previous section shows the effect

of increasing the V-MIMO order ,i.e., increasing number of users along with increasing the

receiving antennas in case of MMSE and MMSE based SIC receivers, the simulation

results reveal that the SIC receiver exploit the increase of V-MIMO order more efficiently

than the ordinary MIMO spatial multiplexing receiver, the MMSE is enhanced slightly

(~1.5dB) when increasing the system order to 4x4 system, while SIC is clearly enhanced

(~4.5dB) . So increasing the V-MIMO order increases the order of spatial diversity of the

collaborative system which in turns decreases the BER.

Figure 27 Effect of changing number of collaborative users (V-MIMO order)

3.6.4.3 Effect of changing number of receiving antennas

To enhance the diversity order of the collaborative system, it is proposed to equip

the eNodeB by a number of receiving antennas much more than the collaborative users

-5 0 5 10 15 20 2510

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

effect of changing the V-MIMO order to MMSE

and MMSE based SIC equalizers

MMSE 2x2

MMSE 4x4

MMSE 6x6

SIC-MMSE 2x2

SIC-MMSE 4x4

SIC-MMSE 6x6

58

𝑃 > 𝐾 , this will lead to receive the users‟ data from different scatter paths and hence the

combined signal would dramatically have higher SNR.

Figure 28 Effect of changing number of receiving antennas shows the dramatic

enhancement of the MMSE equalized V-MIMO system while increasing the receiving

antennas. The diversity benefit decreases from almost of 10dB when increasing antennas to

4 antennas, 3dB from to 4 to 6 antennas and 2dB from 6 to 8 antennas. These results advise

us to use at least 4 antennas at the receiver side when using V-MIMO system.

Figure 28 Effect of changing number of receiving antennas reveals that the MMSE-

based SIC exploits the spatial diversity enhancement of increasing the receiving antennas

more efficiently than the traditional MMSE by almost (2.5dB) for 2x2 system and the

diversity benefit is also decreased with increasing the receiving antennas reaching a

(0.6dB) for the 2x8 system.

Figure 28 Effect of changing number of receiving antennas

3.6.4.4 Effect of different modulation

In Figure 29, different modulation schemes are discussed for the uncoded 2x2 V-

MIMO system. The figure shows that increasing the modulation index of the QAM

modulator will increase whole throughput of the system in the cost of increasing the BER

-5 0 5 10 15 20 2510

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Effect of increasing number of receiving antennas

to V-MIMO system of 2 users

MMSE 2x2

MMSE 2x4

MMSE 2x6

MMSE 2x8

MMSE-SIC 2x2

MMSE-SIC 2x8

MMSE-SIC 2x6

MMSE-SIC 2x4

59

i.e. decreasing the power efficiency of the system . Also the MMSE based SIC power

efficiency bonus is decreased while using higher order modulation schemes.

Figure 29 Effect of different modulation schemes for 2x2 collaborative MIMO system

3.6.4.5 Effect of channel selectivity

Figure 30 shows the effect of changing the delay spread of the multipath channel

i.e. the frequency selectivity of the channel. The simulation results reveal that for a CP

length ≥ delay spread of multipath channel, increasing the delay spread leads to more

frequency selectivity and hence better output SNR because of the inherent frequency

diversity property of the SC-FDMA.

The simulation results show that using MMSE receiver in flat fading is almost

identical to use the ZF receiver, The result also instructs us to use the collaborative system

in highly selective channels i.e. outdoor environments rather than flat fading channel.

-10 -5 0 5 10 15 20 25 30 35 4010

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Effect of different modulation schemes for the 2x2 V-MIMO system

MMSE 2x2 QPSK uncoded

MMSE-SIC 2x2 QPSK uncoded

MMSE-SIC 2x2 16QAM uncoded

MMSE-SIC 2x2 64QAM uncoded

MMSE 2x2 16QAM uncoded

MMSE 2x2 64QAM uncoded

60

Figure 30 Effect of channel selectivity of the multipath channel

3.6.4.6 Effect of user mobility

In this section users‟ mobility is studied. Figure 31 shows that the V-MIMO system

with non overlapping demodulation reference signals in case of zero order interpolation is

optimized for low speeds up to 10Km/hr. The system will have error floor when the users‟

velocity exceeds 15Km/hr. the system is severely degraded when velocity exceeds

20Km/hr.

Figure 31 Effect of users’ mobility

-5 0 5 10 15 20 25 3010

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Effect of changing the delay spread of the MUltipath channel

MMSE 2x2 flat fading channel

MMSE 2x2 delay spread=1us

MMSE 2x2 delay spread=3us

MMSE 2x2 delay spread=5us

MMSE 2x2 delay spread=15us

-5 0 5 10 15 20 25 3010

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Effect of users' mobility

users' velocity = 0,10Km/hr

users' velocity=15km/hr

users' velocity=20km/hr

users' velocity=30km/hr

users' velocity=60km/hr

61

3.6.4.7 Effect of Channel estimation methods

In this section, the effect of imperfect channel estimation is examined. Figure 32

shows that in case of no Doppler shift, i.e., fixed users, the MMSE channel estimation

almost coincide with the perfect channel estimation (≈0.5dB penalty) in expense of the

increasing complexity, while the LS channel estimation is far by almost 5dB than the

perfect one. Figure 33 reveals that using MMSE channel estimation with spline

interpolation along SC-FDMA symbols leads to decrease the susceptibility of collaborative

system to Doppler shift , the system in this case will operate efficiently to almost 60km/hr

and then slightly degrade when reaching 80km/hr. The system will have an error floor at

almost 100 km/hr.

Figure 32 Effect of channel estimation methods for MMSE and SIC-MMSE receivers

-5 0 5 10 15 20 25 3010

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Effect of imperfect channel estimation for MMSE receivers and

SIC-MMSE receivers

perfect channel est.,MMSE equaliz.

LS channel est.,MMSE equaliz.

MMSE channel est.,MMSE equaliz.

LS channel est.,SIC-MMSE equaliz.

MMSE channel est.,SIC-MMSE equaliz.

perfect channel est.,SIC-MMSE equaliz.

62

Figure 33 Effect of the MMSE channel estimation with spline interpolation in case of different users’

speeds

3.6.4.8 Comparison to equivalent OFDM system

Figure 34 Comparison between OFDM and SC-FDMA based collaborative MIMO systems

Assuming 2x2 collaborative MIMO system and QPSK modulation, it is obvious

that the uncoded OFDM system is more sensitive to spectral nulls than SC-FDMA system

due to inherent frequency diversity and hence better performance in terms of lower BER.

-5 0 5 10 15 20 25 3010

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Effect of MMSE channel estimation with spline time interpolation

in presence of doppler shift effect

perfect channel estimation, no doppler

MMSE est. ,velocity=20km/hr,spline interp.

MMSE est. ,velocity=40km/hr,spline interp.

MMSE est.,velocity=60km/hr,spline interp.

MMSE est.,velocity=80km/hr,spline interp.

MMSE est.,velocity=100km/hr,spline interp.

MMSE est.,velocity=120km/hr,spline interp.

-5 0 5 10 15 20 25 30 35 4010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Comparison between OFDM and SC-FDMA based collaborative MIMO systems

2x2 OFDM-based ,QPSK system

2x2 OFDM-based ,QPSK system2x2 SC-FDMA-based , QPSK system

63

We also note that the OFDM-based system performance resembles the SC-FDMA using

ZF equalizer.

3.6.4.9 Overall Spectral efficiency

Figure 35 shows the overall spectral efficiency curve at the receiving eNodeB of

different modulation and system configurations i.e. changing number of users and different

receiving antennas.

The spectral efficiency is defined as the information rate that can be transmitted

over a given bandwidth in a specific communication system. It is a measure of how

efficiently a limited frequency spectrum is utilized by the physical layer protocol. And

given by

𝜂 =𝑅𝑏

𝐵𝑊= 𝐾. (1 − 𝑃𝑒)𝑛 . 𝑙𝑜𝑔2 ℳ . 𝑅𝑐

(3.36)

where 𝑛 is the number of bits/block , ℳ is the size of the constellation set and 𝑅𝑐 is the

coding rate. Figure 35 shows that increasing the order of the modulation scheme increases

the overall spectral efficiency for 2x2 V-MIMO system to have 4,8,12 bits/s/Hz at

17dB,26dB,34dB for QPSK ,16QAM and 64QAM respectively.

The Figure shows also that increasing V-MIMO order increases throughput of the

system to have 8,16 and 24 bits/s/Hz at 17,26 and 32dB for QPSK , 16QAM and 64QAM

respectively and also 16,32 and 48bits/s/Hz at 15,24 and 32dB for the same modulation

schemes.

So increasing the V-MIMO order also reaches the full spectral efficiency with

smaller power consumption with tradeoff of higher complexity to have maximum

throughput of 960Mb/s for 8 users by 8 receiving antennas system using uncoded 64QAM

modulation and occupying the whole 20MHz bandwidth stating from 𝐸𝑏/𝑁𝑜 =32dB

The Figure also instructs using an adaptive V-MIMO configurations and

modulation schemes to satisfy the complexity, throughput and BER constraints according

to Table 8

QPSK 16QAM 64QAM

2x2 17dB, 4b/s/Hz 26dB , 8b/s/Hz 34dB, 12b/s/Hz

4x4 17dB ,8b/s/Hz 26dB, 16b/s/Hz 32dB, 24b/s/Hz

8x8 15dB, 16b/s/Hz 24dB, 32b/s/Hz 32dB, 48b/s/Hz

Table 8 adaptive Modulation and V-MIMO configurations for MMSE equalizer

64

Figure 35 Spectral Efficiency of different modulation and system configurations for uncoded V-MIMO

system

3.6.4.10 Conclusions

From the sample simulation results shown previously we conclude to the following

ZF based equalizers suffer from severe noise enhancement for poorly

conditioned subcarriers so it is not advised to use it in the context of V-MIMO

for LTE uplink.

MMSE-SIC outperforms MMSE but the cost of incremental complexity.

Increasing number of receiving antennas increases the spatial diversity and

hence leads lower BER.

Increasing V-MIMO order enhances output SNR and increases system spectral

efficiency simultaneously due to the increase of spatial diversity and reusing

system resources more efficiently at the cost of increasing complexity, so

increasing the V-MIMO order is promoted for LTE uplink.

Collaborative MIMO system for LTE uplink is optimized for low speed users

and for high mobility users channel interpolation is required.

Collaborative MIMO system for LTE uplink is optimized for highly selective

channels due to the inherent frequency diversity of SC-FDMA systems.

MMSE channel estimation schemes outperform LS channel estimation in the

cost of increasing system complexity

SC-FDMA based system is more immune to spectral nulls due to the

distribution of the noise enhancement of poorly conditioned subcarriers along

all subcarriers in contrast of OFDM that will ruin this symbol directly.

-10 0 10 20 30 40 500

5

10

15

20

25

30

35

40

45

50

Eb/N

o

spectr

al eff

icie

ncy (

bits/s

/Hz)

spectral efficiency for different modulation and order of V-MIMO system with MMSE equalizer

2x2 QPSK

2x2 16QAM

2x2 64QAM

4x4 QPSK

4x4 16QAM

4x4 64QAM

8x8 QPSK

8x8 16QAM

8x8 64QAM

65

CCHHAAPPTTEERR FFOOUURR

PPRROOPPOOSSEEDD MMUULLTTIIUUSSEERR EEQQUUAALLIIZZAATTIIOONN TTEECCHHNNIIQQUUEESS

4.1 Introduction

In chapter three, the existent and the well known multiuser detectors for

collaborative MIMO systems were presented in the context of the LTE uplink. Traditional

multiuser equalization techniques include ZF, MMSE and ML. ZF suffers from noise and

interference enhancement. MMSE accounts for the SNR/SIR value and provides better

performance. However, the optimal receiver is the ML which performs exhaustive search

to find the symbols with minimum detection error. Unfortunately the full-fledge ML

receiver is abandoned when employing SC-FDMA signals since its complexity increases

exponentially with the DFT-block size as well as the modulation index. To reduce

complexity and maintain performance SIC is a good choice. SIC is a DFE that sequentially

demodulates UE signals, one at a time, and cancels the contribution from the received

signal [49].

In this chapter, we first present two novel ordering techniques to enhance the

performance of the SIC receiver, especially in the case of shadowing environments.

Moreover, we propose a novel initial guess ML (IGML) receiver which enhances the

performance of the collaborative LTE SC-FDMA system. Its complexity grows

exponentially with the modulation index only. A comprehensive study of the motivation of

each novel scheme with study of channel imperfections and different channel conditions.

4.2 Proposed optimal ordering for successive interference cancellation

(optimal OSIC)

4.2.1 Motivation

In chapter three, section 3.6.3, SIC was discussed. The SIC performance is

dominated by the weakest stream which is the first stream to be decoded. Hence, the

improved diversity performance of the succeeding layers does not help. To get around this

problem the ordered successive cancellation (OSIC) receiver was introduced. In this case,

the signal with the strongest SINR ratio is selected for processing. This improves the

quality of the decision and reduces the chances of error propagation. This is like an

inherent form of selection diversity where the signal with the strongest SNR is selected

[62].

So optimal ordering for SIC seems to be interesting. The optimal SIC receiver

relies on ordering the users‟ powers in a descending order so that the highest user which

corresponds to the highest detection SNR is detected first, this will decrease the effect of

error propagation and increase the reliability of the detected user‟s data. On the other hand

the user with highest power has the largest interference contribution in the received signal,

this will decrease the overall interference after each cancellation.

66

4.2.2 Optimal OSIC description (per-subcarrier ordering)

A main characteristic of SC-FDMA systems, that each symbol is spread over the

entire assigned bandwidth. So the idea of ordering seems to be tricky, to tackle this

problem, the ordering must be done along all the subcarriers. To perform this ordering

must be done in subcarrier by subcarrier basis i.e. users must be ordered along all the

loaded subcarriers (the 𝑀-length DFT subcarriers) and each time the larger user will be

cancelled along this subcarrier

The algorithm is described as the following [49]:

First, begin by linear frequency domain equalization such as ZF equalization or

MMSE equalization as in equation (3.30), (3.31), this will lead to initial guess

of all subcarriers.

For the first subcarrier, determine the highest power user to be detected first

𝑖 = argmax𝑖∈{1,2,..,𝐾}

𝑯𝒍(𝒊)

𝟐

(4.1)

Then the 𝑖𝑡𝑕 user will be cancelled first , so we will detect the user‟s data and

simulate the transmission procedure of 𝑖𝑡𝑕 user

Remove the interference of 𝑖𝑡𝑕 user as equation (3.32) on the first subcarrier

only, this will ensure that the maximum interference to the collaborative MIMO

system is removed within the first subcarrier only as

𝑹𝒊+𝟏 1 = 𝑹𝒊 1 − 𝑌 𝑜𝑢𝑡 𝑇𝑥𝑖(1)𝑯𝟏

(𝒊)

(4.2)

where 𝑯𝒍(𝒊)

: is 𝑖𝑡𝑕 user channel vector on the 𝑙𝑡𝑕 subcarrier, i.e., 𝑯𝒍(𝟏)

=

𝐻11𝑙 𝐻21

𝑙 … 𝐻𝑃1𝑙

𝑇 where . 𝑇 is the transpose operator.

Repeat the previous steps for the first (𝐾 − 1) users till we will have the

𝑹𝑲 𝑙 =

𝐻1𝐾

𝑙 𝑌𝐾(𝑙)

𝐻2𝐾𝑙 𝑌𝐾(𝑙)

⋮𝐻𝑃𝐾

𝑙 𝑌𝐾(𝑙)

+ 𝑾(𝑙)

(4.3)

By inspection of last equation , it is obvious that after completely subtracting

the whole interference on the 𝐾𝑡𝑕user the spatial diversity now exists which

instructs us to combine using MRC as

𝑌 𝐾𝑀𝑅𝐶 𝑙 =

1

𝑯𝒍(𝑲)

2 𝑹𝑲

𝐻 𝑙 𝑯𝒍(𝑲)

(4.4)

Fix the result of cancelling of first subcarrier i.e.

𝑹𝒊 1 ……… 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑔𝑢𝑒𝑠𝑠

𝑹𝒊+𝟏 1 ……… 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑔𝑢𝑒𝑠𝑠 (4.5)

Repeat the previous steps along all subcarriers with fixing the result of

cancelling of all previous subcarriers.

67

4.2.3 Results and discussion

Figure 36 performance of the optimal ordering of SIC in presence of shadowing variance of 12dB

Figure 36 performance of the optimal ordering of SIC shows considerable performance

gains with respect the MMSE equalization. The scheme benefits from the power difference

between the users in the expense of excessive complexity.

4.2.4 Advantages and disadvantages

Advantages

Reduced error propagation due to excluding the largest interference first.

Decreased multiuser interference.

Disadvantages

The scheme is highly complex and requires extensive ordering along all

subcarriers which means that the scheme do SIC as complex as 𝑀 times and left

for reference only. Note that this excessive complexity can be justified that the

equalization would be done at the eNodeB that can be supplied by powerful

DSPs.

The enhancement in performance i.e. power efficiency over ordinary SIC is

only 0.6dB and this in case of shadowing environments only , while the

enhancement is almost negligible in case of equal-average-power users i.e.

users experiencing power control schemes.

-10 -5 0 5 10 15 20 25 3010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

Rperformance of optimal ordering for SIC-MMSE for different modulation schemes

MMSE 2x2 QPSK

MMSE 2x2 16QAM

optimal ordering QPSK

optimal ordering 16QAM

68

4.3 Proposed suboptimal ordering for SIC (Suboptimal OSIC)

4.3.1Motivation

The discussion of section 4.2.1 reveals that the ordering of users‟ powers is

essential to decrease the error propagation effects; however the complexity of the optimal

ordering scheme seems to be enormous due to performing the SIC process along the whole

loaded subcarriers. So the need of suboptimal ordering scheme with small little loss in

performance seems to be necessary.

4.3.2 Suboptimal OSIC description

To decrease the complexity of the optimal ordering, a suboptimal ordering scheme

is proposed the new scheme orders the cancellation procedure based on the average

norm of user‟s channel along all subcarriers and choose the largest user to be cancelled

first [49] i.e.

𝑖 = argmax𝑖∈{1,2,..,𝐾}

𝑯𝒍(𝑲)

2

𝑀

𝑙=1

(4.6)

The suboptimal OSIC works as the previous algorithm i.e., first we start with initial

guess of all subcarriers, then we order all users according to the average powers of all

loaded subcarriers, then we continue with the remaining cancellation procedure as

equations (4.2) to (4.5)

This will lead to execute the SIC once only instead of doing SIC 𝑀 times along all

subcarriers as the optimal case. Note that this scheme is very useful in case of different

channel conditions of collaborative users e.g. if one of the users experiences deep

shadow with respect to other.

69

4.3.3 Results and discussions

Figure 37 performance of suboptimal ordering SIC with different modulation schemes

Figure 37 performance of suboptimal ordering SIC with different modulation schemes

shows that the suboptimal ordering scheme achieves a similar performance of the optimal

ordering with decrease of the receiver complexity of 1 SIC operation instead of M

iterations.

4.3.4 Advantages and disadvantages

Advantages

The complexity of the suboptimal ordering scheme is very reasonable with respect

to optimal ordering scheme, almost less than 1/𝑀 of its complexity with almost

same performance.

The suboptimal ordering scheme benefits from shadowing environments without

need for power control which can decrease the complexity of eNodeB with better

performance than the ordinary successive cancellation scheme.

Reduced error propagation due to excluding the largest interference first and

decreased multiuser interference with less complex receiver than the optimal case

Disadvantages

The scheme doesn‟t exploit the full diversity of the virtual MIMO link.

The scheme is almost useless in case of power controlled users i.e. if the average

power of all users along all loaded subcarriers is the same; in this case the ordering

gain seems to be negligible.

-10 -5 0 5 10 15 20 25 30 3510

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

Rperformance of suboptimal ordering for SIC-MMSE for different modulation schemes

MMSE 2x2 QPSK

MMSE 2x2 16QAM

MMSE 2x2 64QAM

suboptimal ordering 2x2 QPSK

suboptimal ordering 2x2 16QAM

suboptimal ordering 2x2 64QAM

70

4.4 Proposed Initial guess based Maximum likelihood Receiver (IGML

receiver)

4.4.1Motivation

The ML receiver is the optimal receiver, the ML receiver solves

𝑠 = argmin𝑠 𝑟 − 𝐻𝑠 2 (4.7)

where 𝑠 is the estimated symbol vector. The ML receiver searches through the entire vector

constellation for the most probable transmitted signal vector. These receivers are difficult

to implement, but provide full 𝑃 diversity and zero power losses as a consequence of the

detection process. In this sense it is optimal [62].

In this section a ML receiver is proposed. ML is an optimal receiver which

performs exhaustive search along all time domain symbol combinations to find which one

minimizes the Euclidean distance to the received symbol.

For this two issues are discussed:

First, the exhaustive search domain i.e. the domain at which symbols have discrete

values is the time domain which differs from the equalization domain which is the

frequency domain.

Second, Trying to directly apply exhaustive search in the equalization domain i.e.

frequency domain is not applicable because in this case the search will be applied

along all possible permutations of the whole 𝑀-length DFT precoded symbols, i.e.

the complexity of the ML receiver in this case will increase exponentially not only

with the modulation order but also will increase exponentially with the DFT length

,i.e. for 𝐾 users , 𝑀 points DFT frame and constellation set ℂ of size of ℳ the

complexity will be in the order of 𝑂(ℳ𝐾𝑀), e.g. for the minimum throughput of

the collaborative system assuming 𝑀 = 180, 𝐾 = 2 and QPSK constellation the

complexity would be 5.5157*10216

tests for each symbol which is not feasible.

To jointly address the two problems, a simple algorithm is proposed. The algorithm

relies on guessing all the values of time domain symbols using one of the previously

presented equalization schemes whether ZF, MMSE or SIC (MMSE is preferred because it

tradeoffs between complexity and initial quality of time domain symbols), then find the

error metric along all subcarriers based on the fact that the error in SC-FDMA signal

spread over all subcarriers.

4.3.2 IGML receiver description

The IGML [49] will firstly guess all the time domain symbols using one of the previous

equalization schemes , then tests the time domain symbols with fixing the previous

combinations along all the loaded subcarriers in the frequency domain.

To elaborate the novel algorithm works as following as shown in Figure 38:

71

Figure 38proposed IGML receiver

First, perform frequency domain equalization such as ZF or MMSE multiuser

FDE as in equation (3.30), (3.31), this will lead to initial guess of all

subcarriers. This will lead to 𝒀 𝑙

Second , find the initial guess of all time domain symbols by 𝑀- size IDFT

process followed by slicing process as following

𝑦 𝑘𝐼𝐺(𝑛) = ℚ 𝑀 𝑌 𝑘 𝑚

𝑀

𝑚=1

exp 𝑗2𝜋

𝑀 𝑛 − 1 𝑚 − 1

(4.8)

where ℚ{. } is the slicing to nearest constellation point operator i.e. hard

decision detection.

Third, start performing a symbol-by-symbol exhaustive search

o Begin by testing all constellation values for the first symbol only

while fixing other symbols to their initial guess.

o DFT the new SC-FDMA symbols 𝒀 𝑴𝑳 .

o Find the ML solution that corresponds to the minimum error metric

along all subcarriers as following

𝒚 𝐼𝐺𝑀𝐿(𝑛) = argmin𝒚∈ℂ𝐾

𝑹 𝑙 − 𝑯𝒍 𝒀 𝑴𝑳(𝑙) 2

𝑀

𝑙=1

(4.9)

o By this the first symbol is optimally detected, so, fix the value of first

symbol to 𝒚 𝐼𝐺𝑀𝐿(𝑛) .

o Repeat last two steps to all other symbols

The ML receiver achieves full diversity of the collaborative system which equals

to the number of receiving antennas 𝑃 on the complexity of only 𝑂(ℳ𝐾).

72

4.3.3 Results and discussions

Figure 39 performance if IGML for different modulation schemes

Figure 39reveals tremendous power efficiency gains with respect to the MMSE

equalization technique. The figure shows a 5dB gains for both QPSK and 16QAM

modulation. The 64QAM modulation is not shown due to its intractable exponential

complexity

4.3.4 Advantages and disadvantages

Advantages

Exploits the full diversity of the V-MIMO system.

Minimum achievable BER.

The power efficiency is increased by almost 4.5dB from the ordinary MMSE.

The scheme is far by only 0.4dB than the 1x2 receiving diversity.

The complexity of the IGML system is in the same order 𝑂 ℳ𝐾 of the OFDM-

ML system with negligible loss of performance compared to 𝑂 ℳ𝑀𝐾 of brute

force scheme.

Disadvantages

The investigations of all constellation points in higher order modulation schemes

and increased number of collaborative users seems to be intractable due to the

exponential complexity 𝑂 ℳ𝐾 .

-10 -5 0 5 10 15 20 25 3010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

performance of IGML for different modulation schemes

IGML-MMSE2x2 QPSK

IGML-MMSE 2x2 16QAM

MMSE 2x2 QPSK

MMSE 2x2 16QAM

73

4.5 Proposed simplified Initial guess based Maximum likelihood Receiver

(simplified IGML receiver)

4.5.1 Motivation

The main challenge of receiver design for MIMO systems lies in the non-

orthogonality of the transmission channel i.e. the superposition of the signals from all

transmit antennas at the receiver side. Optimum ML detection requires finding the signal

point 𝑠 of the transmitter vector signal set that minimizes the Euclidean distance with

respect to the received signal vector 𝑟 when transmitted over the channel, i.e., the closest

lattice point in a transformed vector space [64].

Unfortunately this problem is exponential in the number of possible constellation

points, making ML unsuitable for practical purposes when aiming at high spectral

efficiencies. Other sub-optimum receivers ZF, MMSE and SIC of low to moderate

complexity have been devised, yet all suffer from rather limited performance and none of

them achieves diversity in the number of receive antennas, in contrast to ML.

The concept of Sphere Detection (SD) was introduced in [65] and has been further

discussed in various publications [66], [67]. To avoid the exponential complexity of the

ML problem, the search for the closest lattice point is restricted to include only vector

constellation points that fall within a certain search sphere. This approach allows for

finding the ML solution with only polynomial complexity, for sufficiently high SNR.

SD algorithm has a nondeterministic instantaneous throughput; its average

complexity was shown to be polynomial in the rate [67]. In most practical cases is still

significantly lower than an exhaustive search. The algorithm is thus widely considered the

most promising approach towards the realization of ML detection in high-rate MIMO

systems [68].

So a suboptimal ML receiver that rely on the basic concepts of SD seems to be

attractive to exploit the full diversity of the collaborative MIMO system with polynomial

complexity instead of the exponential complexity of the IGML receiver presented in the

previous section.

4.5.2 Overview of SD

In this section, we briefly review the basics of sphere detection as our motivation

for the simplified IGML receiver.

The main idea in SD is to reduce the number of candidate vector symbols to be

considered in the search that solves the ML detection problem, without accidentally

excluding the ML solution. This goal is achieved by constraining the search to only those

points 𝑯𝒔 where 𝒔 is the transmitted vector that lie inside a hypersphere with radius 𝑟

around the received point 𝒚. The corresponding inequality is referred to as the Sphere

Constraint (SC) [64], [68]:

𝒚 − 𝑯𝒔 2 < 𝑟2 (4.10)

74

Obviously, the selection of 𝑟 is a critical issue largely influencing the complexity of

any SD algorithm. Choosing 𝑟 too large leads to a sphere containing a very high number of

hypotheses (also referred to as candidates) and hence to high detection complexity.

Choosing 𝑟 too small will result in an empty sphere and the search has to be restarted with

an increased radius.

The search for candidates fulfilling (4.10) is done by back-substitution algorithms.

Towards this aim, Cholesky or QR decompositions of the channel matrix 𝐻 may be

equivalently used.

In the following, we concentrate on the symmetric case i.e. 𝐾 = 𝑃 and use the 𝒬ℛ-

decomposition of 𝑯 . With 𝑯 = 𝓠𝓡 , where 𝓡 is upper triangular and 𝒬 is unitary, the

sphere detection in (4.19) criterion can be expressed as:

𝒚 − 𝑯𝒔 2 < 𝑟𝑠𝑝𝑕2

𝓠𝑯𝒚 − 𝓠𝑯𝑯𝒔 2 < 𝑟𝑠𝑝𝑕2

𝓠𝑯𝒚 − 𝓡𝒔 2 < 𝑟𝑠𝑝𝑕2

(4.11)

Due to the upper triangular nature of the 𝓡 matrix then (4.11) can be rewritten as

𝑦𝑖 − 𝑟𝑖 ,𝑗 𝑠𝑗

𝐾

𝑗 =𝑖

2𝐾

𝑖=𝑙

< 𝑟𝑠𝑝𝑕2 𝑙 = 1, …… . , 𝐾

(4.12)

This will lead to layer-by-layer separation as shown in Figure 40. That works its

way up until the first layer is detected. This process is quite similar to SIC techniques – the

signals from previously detected layers are subtracted from the received signal before

detection within the current layer is performed.

Figure 40 QR decomposition effect on user separation

The above inequality implies that not only a single, but several constellation points

may be selected. The SD receiver hence performs its search in a tree like structure, we

build a tree such that the leaves at the bottom correspond to all possible vector symbols 𝑠

and the possible values of the entry 𝑠𝐾 define its top level, we can uniquely describe each

75

node at level 𝑖 (𝑖 = 1,2, … . . 𝐾) by the partial vector symbols 𝒔 = 𝑠𝑖 𝑠𝑖+1 ⋯ 𝑠𝐾 ,as

illustrated in Figure 41 for 3x3 system with BPSK modulation , then the error metric in

(4.12) can be recursively calculated by traversing down the tree and accumulating error

metric in descending order of the users.

Figure 41 Tree formation for sphere detection

The partial error metrics of all its children will also violate the sphere condition.

Consequently, the tree can be pruned above this node. This approach effectively reduces

the number of vector symbols

4.5.3 Simplified IGML receiver description (QR-IGML receiver)

The IGML receiver presented in section 4.4 can be performed sequentially by

means of Cholesky or 𝒬ℛ-decomposition of channel matrix [69] which decomposes the

channel matrix into an orthogonal matrix 𝓠(𝑙) and an upper triangular matrix 𝓡(𝑙) , this

will lead to a layer-by-layer (user-by-user) separation of the received symbols. This will

lead to exhaustive search computation complexity of only 𝑂(𝐾ℳ).

The algorithm works as previous scheme for step 1,2 and then:

Apply 𝒬ℛ decomposition of the channel matrix along all subcarriers. note that this

step is done for limited number of times only assuming slow fading channel

𝑯 𝑙 = 𝓠 𝑙 𝓡 𝑙

= | | |

𝒒𝟏 𝒒𝟐 𝒒𝟑

| | |

𝓡𝟏𝟏 𝓡𝟏𝟐 𝓡𝟏𝟑

0 𝓡𝟐𝟐 𝓡𝟐𝟑

0 0 𝓡𝟑𝟑

(4.13)

where 𝒒𝟏, 𝒒𝟐,…. are orthonormal vectors

Filter the frequency domain components 𝑹 𝑙 with the Hermitian of the orthogonal

matrix 𝓠𝑯(𝑙).

To find the filtered frequency domain components

𝑹′ 𝑙 = 𝓠𝑯 𝑙 𝑹 𝑙

76

(4.14)

Save the values of non zero values of 𝓡 matrix along all subcarriers e.g. in case of

2x2 collaborative system 𝓡𝟏𝟏 = [ℛ11 1 ℛ11 2 … ℛ11 𝑀 ] and also 𝓡𝟏𝟐, 𝓡𝟐𝟐.

Begin with last layer i.e. 𝐾𝑡𝑕 user exhaustive search to find the minimum error

metric along all subcarriers with fixing all other symbols to their initial values taking

in account the upper triangular property of 𝓡(𝑙) as following:

𝑦 𝐾 𝑛 = argmin𝒚∈ℂ

𝑅𝐾′ 𝑙 − ℛ𝐾𝐾(𝑙) 𝑌𝐾

𝑴𝑳

(𝑙) 2

𝑀

𝑙=1

(4.15)

Proceed to (𝐾 − 1)𝑡𝑕 user after fixing the 𝐾𝑡𝑕 user symbol to 𝑦 𝐾 𝑛 to find

𝑦 𝐾−1 𝑛 = argmin𝒚∈ℂ

𝑅𝐾−1′ 𝑙 − ℛ 𝐾−1 𝐾 𝑙 𝑌𝐾

𝑴𝑳

𝑙

𝑀

𝑙=1

− ℛ 𝐾−1 (𝐾−1) 𝑙 𝑌𝐾−1

𝑴𝑳 𝑙

2

(4.16)

Then repeat for the whole 𝐾-users, this will lead to maximum likelihood solution

obtained using IGML with less number of exhaustive search combinations. Note that this

proposed scheme is similar to sphere detection except for not doing the step of tree

pruning, because the error is averaged along all subcarriers so it is unlikely to move away

from the ML solution.

4.5.3 Results and discussions

Figure 42 performance of simplified IGML for different modulation schemes

-10 -5 0 5 10 15 20 25 30 3510

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

performance of simplified IGML for different modulation schemes

MMSE 2x2 QPSK

MMSE 2x2 16QAM

MMSE 2x2 64QAM

simplified IGML QPSK

simplified IGML 16QAM

simplified IGML 64QAM

77

Figure 43 Comparison between all presented detection schemes for QPSK modulation

Figure 42 performance of simplified IGML for different modulation schemes

shows considerable performance gains with respect MMSE equalization technique. Note

that the performance gains decrease with increasing the order of modulation to reach 2.5dB

for 64QAM modulation, which will result in tractable complexity with considerable

degradation in performance gains .

Figure 43 Comparison between all presented detection schemes for QPSK

modulation shows a comparison between all detection techniques presented above for the

V-MIMO 2x2 system. The figure shows that the ZF receiver is not suitable for separating

the collaborative users (BER=10-3

at almost 25dB) ,also the figure reveals that using ZF

receiver as initial detection step in SIC or IGML receiver leads to severe degradation in

performance.

The figure also instructs using the other practical equalizers like MMSE (BER=10-4

at almost 14.5dB),MMSE based SIC(BER=10-4

at 12dB),proposed suboptimal OSIC-

MMSE (based on the channel average norm) in case of shadowing variance of 12dB

(BER=10-4

at 11.3dB),note that in case of no shadowing i.e. small difference between the

average norms no enhancement is achieved ,the proposed IGML-MMSE (BER=10-4

at

10.1dB) which is almost 0.4 dB only away from the full receive diversity 1x2 system

which confirms the claim of considering the IGML receiver as optimal receiver , On the

other hand the simplified IGML scheme is almost 0.2dB inferior to the IGML receiver

4.5.4 Advantages and disadvantages

Advantages

Exploits the full diversity of the virtual MIMO system as IGML.

-5 0 5 10 15 20 25 3010

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

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o

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R

Comparison between detection techniques of

2x2 VMIMO systems

proposed IGML-MMSE2x2

simplified ML 2x2

SIC-MMSE 2x2

MMSE 2x2

Suboptimal OSIC-MMSE

ZF 2x2

proposed IGML-ZF2x2

SIC-ZF 2x2

full diversity 1x2(reference)

78

Near optimal reception and separation of each user.

Near the minimum BER.

The power efficiency is increased by almost 4.3dB from the ordinary MMSE.

The scheme is far by only 0.6dB than the 1x2 receiving diversity.

The power efficiency loss to the latter IGML receiver is only 0.2dB

The complexity of the QR-IGML system is in the order 𝑂(𝐾ℳ) which

corresponds to polynomial complexity rather than the exponential complexity of

the IGML with negligible loss in performance.

Deterministic throughput unlike the standard sphere detection which rely on tree

pruning and incremental sphere radius because in QR-IGML ,no tree pruning is

required due to the inherent frequency diversity of the SC-FDMA virtual MIMO

links which averages the error over the whole loaded subcarriers and make it

unlikely to shift from the optimal ML solution.

Disadvantages

The investigations of all constellation points in higher order modulation schemes

and increased number of collaborative users are still complex although of the

polynomial complexity 𝑂(𝐾ℳ) .

4.6 Conclusions

In this chapter, we have presented 2 novel techniques for SIC.

Results show a considerable enhancement of power efficiency in case of

shadowing environments and negligible performance gains in case of power

controlled systems

Moreover we have presented a novel IGML receiver that exploits the full diversity

of the inherent frequency and spatial diversity of the V-MIMO links.

The scheme achieves almost 5dB power efficiency gains over the multiuser MMSE

equalization technique in expense of exponential complexity which leads to

intractable complexity in case 64QAM.

We also have presented a simplified IGML scheme which solves the ML problem

in linear complexity scheme with negligible power efficiency loss in case of QPSK

and 16QAM.

79

CCHHAAPPTTEERR FFIIVVEE

CCOOMMBBIINNEEDD CCOOLLLLAABBOORRAATTIIVVEE AANNDD PPRREECCOODDEEDD MMIIMMOO FFOORR TTHHEE

UUPPLLIINNKK LLTTEE--AADDVVAANNCCEEDD

5.1 Introduction

In this chapter we discuss the multiple antennas enhancement introduced to the

LTE uplink of the LTE-advanced. In LTE-advanced the LTE uplink mode is equipped by

2-4 antennas which can be used with the collaborative MIMO system to increase data rate,

enhance system performance and match channel conditions to achieve the channel capacity

assuming full or partial channel knowledge at the transmitter end.

The chapter begins with identifying the new MIMO modes introduced in the LTE-

advanced, then gives a brief literature review of the precoding theory .Capitalizing from

advantages of precoding the transmitted streams prior to transmission ,codebook precoding

is discussed for LTE. The chapter thereafter will present system model modifications over

the system model introduced in chapter 3. We propose then a combination between the

collaborative system and the precoded MIMO whether ideally (Sigular Value

Decomposition (SVD) precoding) or suboptimally using codebook precoding. Then we

propose a Space Frequency Block code (SFBC) precoding for the uplink to achieve space

diversity with spatial multiplexing gain achieved before using the collaborative system.

The chapter eventually discusses the effect of these precoding schemes on the previously

presented receiver schemes.

5.2 Overview of the uplink enhancements of the LTE-advanced

The LTE-advanced agreed to evolve the LTE-UL transmission capabilities toward

MIMO. MIMO helps to achieve the LTE-advanced, which include UL peak spectrum

efficiency of 15bits/s/Hz and average spectrum efficiency of 2bits/s/Hz [70]. The LTE-

advanced introduced in release 10 [71] supports up to four-layer transmission using multi-

rank precoded spatial multiplexing as well as transmit diversity for control channel to

provide robust signaling and improve cell coverage techniques .In this section we present

an overview of these schemes for the uplink of LTE-advanced.

The uplink of the LTE-advanced supports 1 or 2 codewords where codeword is an

independently encoded data block, corresponding to a single Transport Block (TB)

delivered from the Medium Access Control (MAC) layer in the transmitter to the physical

layer, and protected with a CRC. These codewords will be mapped using a layer mapper

into 1 to 4 layers where the layer is one of the different streams generated by spatial

multiplexing. A layer can be described as a mapping of symbols onto the transmit antenna

ports. Each layer is identified by a precoding vector of size equal to the number of transmit

antenna ports and can be associated with a radiation pattern. The number of layers is called

the rank .These layers will be further precoded to fit the antenna ports which are 2 or 4 in

LTE-advanced [70],[2].Note that number of codewords is smaller than or equal to number

of layers which in turns is smaller than or equal to the number of antenna ports as Figure

44.

80

Figure 44 Overview of uplink physical channel processing for LTE-advanced

The precoder is defined by rank and precoding matrix, which are selected by an

eNodeB based on uplink channel measurements and conveyed to UE through the Rank

Indicator (RI) and the Precoding Matrix Indicator (PMI) fields in an uplink grant via the

PDCCH. The rank and precoding matrix is chosen to maximize throughput adaptively

based on the SINR measured, higher link quality will result in higher rank chosen and

hence higher spectral efficiency. Link quality measurements are conveyed via SRS.

5.3 Overview of the precoding theory

The main motivation of precoding the spatial substreams is to match channel conditions

by increasing the received signal power in case of perfect or partial channel state

information (CSI) ,also decrease the interstream interference from other antennas and

maximize the channel capacity of the wireless channel [70].So, optimal communication

over 𝑁𝑅 × 𝑁𝑇 MIMO channel uses channel-dependent precoder, which achieves the roles

of both transmit beamforming and power allocation across the transmitted streams, and a

matching receive beamforming structure [2].

The well-known optimal (capacity-maximizing) precoder in literature for exploiting the

channel knowledge at the transmitter is to send data over the strongest eigenmodes of the

channel. A common way to express the channel matrix in 𝑙𝑡𝑕 subcarrier is through its

Singular Value Decomposition (SVD) [55], [72] as

𝑯 𝑙 = 𝑼 𝑙 𝜮 𝑙 𝑽𝐻(𝑙) (5.1)

where 𝑼 𝑙 is 𝑁𝑅 × 𝑁𝑅 orthonormal matrix , 𝑽 𝑙 is 𝑁𝑇 × 𝑁𝑇 orthonormal matrix and

𝜮 𝑙 = 𝑑𝑖𝑎𝑔(𝜆1, 𝜆2, … . . ) is eigenmodes‟ diagonal matrix. The matrix 𝑽 𝑙 is used to

precode the input data stream in the frequency domain to have 𝒁(𝑙) as

𝒁(𝑙) = 𝑽 𝑙 𝒀 (𝑙) (5.2)

In the eNodeB frequency domain equalizer, the precoding process leads to orthogonal

streams if the channel is further filtered by 𝑼𝐻(𝑙) (channel matched filter) as

𝒀 (𝑙) = 𝜮−𝟏 𝑙 𝑼𝐻(𝑙)𝑹 𝑙 (5.3)

Or using the MMSE linear equalizer for the equivalent channel 𝑯𝒆𝒒 𝑙 = 𝑯 𝑙 𝑽(𝑙)

81

𝒀 𝑙 = (𝑯𝑒𝑞𝐻 (𝑙)𝑯𝒆𝒒(𝑙) + 1/𝛾𝑠𝑰𝑲)−1𝑯𝑒𝑞

𝐻 (𝑙)𝑹 𝑙 (5.4)

The SVD precoding which is called also Transmit Precoding and Receiver Shaping shown

in Figure 45, allows to decompose channel matrix into SISO channels, whose gains are

𝜆12, 𝜆2

2 , … to increase the capacity of the MIMO system, since the interstream interference is

apriori removed , however the scheme requires perfect CSI and can enhance PAPR.

Figure 45 SVD precoding

5.4 Codebook precoding for uplink of the LTE-advanced

In practice the feedback messages cannot provide full CSI at UE, also the selection

of precoder in LTE-advanced is signaled via eNodeB, so a limited number of codebook-

based precoders 𝑭𝒊(𝑙) should be available.

In uplink of LTE-advanced, there is a finite set 𝔽 of 𝑁𝑇 × 𝜌 precoders where 𝜌 is

the rank of the transmission schemes. These precoders are chosen to be confined to QPSK

alpha{±1, ±𝑗} as in the tables 9 through table 13 [71] to ease the precoding process

implementation, and have constant modulus property for maximizing power efficiency of

the power amplifier .The UL precoders differ from the DL ones of having one nonzero

element in each row which ensures that no linear combination between different layers is

allowed to decrease the resulting PAPR which is considered a major issue in UL

transmission. On the other hand, these precoding matrices suffer from degradation in

precoding gain.

The precoder is chosen so that it maximizes the received signal power i.e.

𝑭𝒊 𝑙 = argmax𝑭𝒊 ∈𝔽

𝑯𝒆𝒒 𝑙 2

= argmax𝑭𝒊∈𝔽

𝑯(𝑙)𝑭𝒊(𝑙) 2

(5.5)

This is equivalent to maximizing the post-MMSE channel power matrix metric which

corresponds to the sum of the equivalent channel gains for the 𝜌 layers defined in [72]

𝑴𝐹𝑖(𝑙) = (𝑯𝑒𝑞

𝐻 (𝑙)𝑯𝒆𝒒(𝑙) + 1/𝛾𝑠𝑰𝑲)−1𝑯𝑒𝑞𝐻 (𝑙)𝑯𝒆𝒒(𝑙) (5.6)

82

𝑭𝒊 𝑙 = argmax𝑭𝒊∈𝔽

𝑚𝐹𝑖

𝑘 . 𝜍𝑤2

1 − 𝑚𝐹𝑖(𝑘)

𝜌

𝑘=1

(5.7)

where 𝑚𝐹𝑖 𝑘 = 𝑑𝑖𝑎𝑔(𝑴𝐹𝑖

(𝑙)).

Codebook index 𝝆 = 𝟏 𝝆 = 𝟐

0 1

2 11

1

2 10

01

1 1

2

1−1

-

2 1

2 1𝑗 -

3 1

2

1−𝑗

-

4 1

2 10 -

5 1

2 01 -

Table 9 codebook precoders for two antenna ports

Codebook index 4 Antenna ports , 𝝆 = 𝟏

0 ~7

1

2

111

−1

1

2

11𝑗𝑗

1

2

11

−11

1

2

11−𝑗−𝑗

1

2

111𝑗

1

2

1𝑗𝑗1

1

2

1𝑗

−1−𝑗

1

2

1𝑗

−𝑗−1

8 ~15

1

2

1−111

1

2

1−1𝑗

−𝑗

1

2

1−1−1−1

1

2

1−1−𝑗𝑗

1

2

1−𝑗1−𝑗

1

2

1−𝑗𝑗

−1

1

2

1−𝑗−1𝑗

1

2

1−𝑗−𝑗1

16 ~23

1

2

1010

1

2

10

−10

1

2

10𝑗0

1

2

10−𝑗0

1

2

010

−1

1

2

010

−1

1

2

010𝑗

1

2

010−𝑗

Table 10 codebook precoders for four antenna ports rank 1

83

Codebook index 4 Antenna ports , 𝝆 = 𝟐

0 ~ 3 1

2

1 01 00 1

0 −𝑗

1

2

1 01 00 10 𝑗

1

2

1 0−𝑗 00 1

0 1

1

2

1 0−𝑗 00 1

0 −1

4 ~ 7 1

2

1 0−1 00 1

0 −𝑗

1

2

1 0−1 00 10 𝑗

1

2

1 0𝑗 00 10 1

1

2

1 0𝑗 0

0 10 −1

8 ~ 11 1

2

1 00 11 00 1

1

2

1 00 11 1

0 −1

1

2

1 00 1

−1 00 1

1

2

1 00 1

−1 10 −1

12 ~ 15 𝟏

𝟐

𝟏 𝟎𝟎 𝟏𝟎 𝟏𝟏 𝟎

𝟏

𝟐

𝟏 𝟎𝟎 𝟏𝟎 −𝟏𝟏 𝟎

𝟏

𝟐

𝟏 𝟎𝟎 𝟏𝟎 𝟏

−𝟏 𝟎

𝟏

𝟐

𝟏 𝟎𝟎 𝟏𝟎 −𝟏−𝟏 𝟎

Table 11 codebook precoders for four antenna ports rank 2

Codebook index 4 Antenna ports , 𝝆 = 𝟑

0 ~ 3 1

2

1 0 01 0 00 1 00 0 1

1

2

1 0 0−1 0 00 1 00 0 1

1

2

1 0 00 1 01 0 00 0 1

1

2

1 0 00 1 0

−1 0 00 0 1

4 ~ 7 1

2

1 0 00 1 00 0 11 0 0

1

2

1 0 00 1 00 0 1

−1 0 1

1

2

0 1 01 0 01 0 00 0 1

1

2

0 1 01 0 0

−1 0 00 0 1

8 ~ 11 1

2

0 1 01 0 00 0 11 0 0

1

2

0 1 01 0 00 0 1

−1 0 0

1

2

0 1 00 0 11 0 01 0 0

1

2

0 1 00 0 11 0 0

−1 0 1

Table 12 codebook precoders for four antenna ports rank 3

84

Codebook index 4 Antenna ports , 𝝆 = 𝟒

0 1

2

1 0 00 1 00 0 10 0 0

0001

Table 13 codebook precoders for four antenna ports rank 4

5.5 System model modifications for the LTE UL with precoding

Figure 46 UEs transmitter block diagram

Figure 47 eNodeB receiver

The CSM system shown in Figure 46 has 𝐾 users each has an UE equipped with

multiple antennas 𝑁𝑇 . The data of 𝑘𝑡𝑕user is independently processed, first each user

having 𝜌 independent data streams (called rank of transmission), 𝜌 ≤ 𝑁𝑇 ,these data

streams are symbol mapped to have the modulated symbols in 𝑖𝑡𝑕 layer 𝑦𝑘𝑖 .The modulation

𝑠𝜌 𝑠𝑁𝑇 𝑌𝜌

𝑥𝜌

𝑥1

𝑌𝜌 𝑦𝜌

𝑦1 𝑌1 𝑌1

Channel

coding

Symbol

mapping

(base band

modulation)

DFT

with size

"M"

Subcarrier

mapping

and DRS

insertion

IFFT

with size

"N"

CP

insertion

Channel

coding

Symbol

mapping

(base band

modulation)

DFT

with size

"M"

Subcarrier

mapping

and DRS

insertion

IFFT

with size

"N"

CP

insertion

Frequency

domain

precoding

𝑽 𝑙

𝑠1 𝑠1

UE 1

𝑠𝜌 𝑠𝑁𝑇 𝑌𝜌

𝑥𝜌

𝑥1

𝑌𝜌 𝑦𝜌

𝑦1 𝑌1 𝑌1

Channel

coding

Symbol

mapping

(base band

modulation)

DFT

with size

"M"

Subcarrier

mapping

and DRS

insertion

IFFT

with size

"N"

CP

insertion

Channel

coding

Symbol

mapping

(base band

modulation)

DFT

with size

"M"

Subcarrier

mapping

and DRS

insertion

IFFT

with size

"N"

CP

insertion

Frequency

domain

precoding

𝑽 𝑙

𝑠1 𝑠1

UE K

Frequency

Domain

Multiuser

equalizer

CP

extraction

FFT

CP

extraction FFT

Subcarrier

demapping IDFT

Subcarrier

demapping IDFT

Symbol

Demodulation

Channel

Decoding

Symbol

Demodulation

Channel

Decoding 𝑟𝑝

𝑟1

𝑅𝑝

𝑅1

𝑌1

𝑌𝑝

85

symbols are then transformed to the frequency representation by the means of the unitary

DFT of size 𝑀 to have 𝑌𝑘𝑖

𝑌𝑘𝑖 𝑚 =

1

𝑀 𝑦𝑘

𝑖

𝑀

𝑛=1

𝑛 exp −𝑗2𝜋

𝑀 𝑛 − 1 𝑚 − 1

(5.8)

where 𝑚: is the subcarrier index and 𝑛:is the symbol index , 𝑚, 𝑛𝜖 1,2, … , 𝑀

The output of the DFT is then mapped using the subcarrier mapping, which has two

versions: the Distributed and the localized, the later is adopted in Release 10, at which the

user's symbols are mapped into consecutive subcarriers. So, localized subcarrier mapping

is applied to have 𝑌 𝑘 . In this work, we assume full RB usage so

𝑌𝑘

𝑖 (𝑙) = 𝑌𝑘𝑖 𝑙 𝑙𝜖Γ𝑘

0 𝑜𝑡𝑕𝑒𝑟𝑤𝑖𝑠𝑒

(5.9)

where: Γ𝑘 is the 𝑁 element mapping set of the 𝑘𝑡𝑕 user Γ𝑘 𝜖 𝑁−𝑀+2

2, … ,

𝑁+𝑀

2 and 𝑁 is the

FFT size. The output of the subcarrier mapping is then precoded in the frequency domain

to map the 𝜌 streams to 𝑁𝑇 streams by one of the precoding schemes that will be presented

in next sections. The output of the precoding stage is fed to a conventional OFDM

transmitter which consists of IFFT stage with size(𝑁 > 𝑀) , 𝑚, 𝑛𝜖 1,2, … , 𝑁

𝑠𝑘𝑖 𝑛 =

1

𝑁 𝑌𝑘

𝑖 𝑁

𝑛=1

𝑚 exp 𝑗2𝜋

𝑁 𝑛 − 1 𝑚 − 1

(5.10)

Finally, the CP is inserted with length larger than the maximum delay spread of the

multipath channel, to mitigate the intersymbol interference (ISI) and enable simple

frequency domain equalization (FDE). The above steps will result in SC-FDMA signal.

Now, each user's data streams have been transmitted through multipath Rayleigh channel

which is modeled as normalized baseband equivalent sample spaced channel impulse

response 𝑕𝑘𝑝 (𝑚, 𝑙) where m is the time instant , 𝑙 is the path number of 𝐿 taps and 𝑝 is the

receiving antenna index with uniform power delay profile. Each path is assumed to be

WSSUS filtered by Doppler PSD modeled in Jakes as explained in chapter (3). In this

work we assume perfect channel knowledge at the transmitter. So, the result of multipath

filtering of the kth user to pth receiving antenna channel can be modeled as

𝑟 𝑘𝑝 𝑚 = 𝑕𝑘𝑝 𝑚, 𝑙 𝑠𝑘(𝑚 − 𝑙)

𝐿

𝑙=0

(5.11)

86

At eNodeB as Figure 47 , which is equipped by 𝑁𝑟 antennas (𝑁𝑟 ≥ 𝐾. 𝜌), the

collaborative users' signals are added together with contamination of AWGN , which is

modeled by i.i.d complex Gaussian noise samples 𝑤(𝑚) with zero mean and variance

𝜍𝑤2 = 1/ 𝑁. 𝛾𝑠 , where 𝛾𝑠 is the symbol to noise ratio (𝐸𝑠/𝑁𝑜) Then, the received signal 𝑟𝑝

at the 𝑝𝑡𝑕 antenna is written as

𝑟𝑝(𝑚) = 𝑟 𝑘𝑝 𝑚 +

𝐾

𝑘=1

𝑤(𝑚)

(5.12)

After CP removal, the eNodeB takes the FFT of each received stream to transform the

input streams back into frequency domain and prepares them for the FDE. The received

signal in the frequency domain at any subcarrier can be written as

𝑹 𝑙 = 𝑯 𝑙 𝒀 𝑙 + 𝑾(𝑙) (5.13)

where 𝑙: is the subcarrier index and 𝑯 𝑙 : is the channel matrix upon the 𝑙𝑡𝑕 subcarrier

𝑯 𝑙 = 𝐻11

𝑙 ⋯ 𝐻1𝐾𝑙

⋮ ⋱ ⋮𝐻𝑃1

𝑙 ⋯ 𝐻𝑃𝐾𝑙

(5.14)

5.6 Combined collaborative and SVD-precoded MIMO for the uplink of

the LTE-advanced

5.6.1 Algorithm description

To optimally exploit the extra antennas introduced to the uplink of the LTE-

advanced in the context of collaborative MIMO system, the precoding of all streams of the

collaborative users seems to be attractive. However, the optimal SVD-precoding requires

the knowledge of the other user‟s data to use the precoding matrix resulting from SVD

decomposition of channel matrix 𝑯 𝑙 as equations (5.1), (5.2).

A novel suboptimal SVD-precoding is introduced in this section, consider the

channel matrix at the 𝑙𝑡𝑕 subcarrier assuming perfect CSI at UE [73]

𝑯 𝑙 =

𝐻11

𝑙 𝐻12𝑙

𝐻21𝑙 𝐻22

𝑙 … 𝐻1 𝐾𝑁𝑇−1

𝑙 𝐻1 𝐾𝑁𝑇

𝑙

𝐻2 𝐾𝑁𝑇−1 𝑙 𝐻2 𝐾𝑁𝑇

𝑙

⋮𝐻 𝑁𝑅−1 1

𝑙 𝐻 𝑁𝑅−1 2𝑙

𝐻 𝑁𝑅 1𝑙 𝐻 𝑁𝑅 2

𝑙 … 𝐻 𝑁𝑅−1 𝐾𝑁𝑇−1

𝑙 𝐻 𝑁𝑅−1 𝐾𝑁𝑇

𝑙

𝐻 𝑁𝑅 𝐾𝑁𝑇−1 𝑙 𝐻𝑁𝑅 𝐾𝑁𝑇

𝑙

87

(5.15)

where 𝑯 𝑙 is 𝑁𝑅 × 𝐾𝑁𝑇 channel matrix. To tackle the problem of joint precoding, we

will suboptimally precode the data streams of each user individually i.e. we will precode

each 𝑁𝑅 × 𝑁𝑇 submatrix independently as

𝑯𝑢𝑠𝑒𝑟 1 𝑙 =

𝐻11

𝑙 𝐻12𝑙

𝐻21𝑙 𝐻22

𝑙

𝐻 𝑁𝑅−1 1𝑙 𝐻 𝑁𝑅−1 2

𝑙

𝐻 𝑁𝑅 1𝑙 𝐻 𝑁𝑅 2

𝑙

…

𝐻1 𝑁𝑇

𝑙

𝐻2 𝑁𝑇

𝑙

𝐻 𝑁𝑅−1 𝑁𝑇

𝑙

𝐻𝑁𝑅 𝑁𝑇 𝑙

(5.16)

This submatrix will be SVD decomposed according to (5.1),(5.2) as

𝑯𝒖𝒔𝒆𝒓 𝟏 𝑙 = 𝑼𝟏 𝑙 𝜮𝟏 𝑙 𝑽𝟏𝐻(𝑙) (5.17)

The process will continue to the remaining 𝐾 − 1 users to have 𝐾 precoding matrices, then

the transmitted signals of all users will be

𝒁 𝑙 =

𝑽𝟏 𝑙 𝒀𝟏

𝑙

𝑽𝟐 𝑙 𝒀𝟐 𝑙 ⋮

𝑽𝑲 𝑙 𝒀𝑲 (𝑙)

(5.18)

And the equivalent channel matrix will be

𝑯𝒆𝒒 𝑙 = [𝑯𝒖𝒔𝒆𝒓 𝟏 𝑙 𝑽𝟏 𝑙 … 𝑯𝒖𝒔𝒆𝒓 𝑲 𝑙 𝑽𝑲 𝑙 ] (5.19)

Then, the equalization methods discussed in equation (5.3),(5.4) can be used. Note

that this scheme is suboptimal which means it ensures removal of all interstream

interference for each user alone, while the multiuser interference still exists, however it

doesn‟t need knowledge of other users‟ data . The performance of this scheme will be

worse than perfectly precoded scheme which corresponds to 𝐾𝑁𝑇 orthogonal streams at the

receiver and better than unprecoded one which suffers from interstream and multiuser

interferences.

5.6.2 Results and discussions

For the simulation results in this section 16QAM modulation is used, delay spread

is 5𝜇𝑠. The result is compared with reference curves of the unprecoded scheme. Figure 48

shows that the SVD precoded CSM system schemes outperforms the unprecoded ones by

almost 2.5dB for rank 4 transmission and 1dB for rank 2 transmission . Note that the

precoded rank2 with 2 transmitting antenna CSM coincides with precoded rank 4 with 4

transmitting antennas CSM, because the increase of the diversity order according to the

increase of the degrees of freedom of the channel in the same time of decreasing the

interstream interference according to precoding. Therefore the interuser interference will

dominate the overall performance. Figure 49 shows the spectral efficiency achieved when

88

using the SVD precoded scheme. Figure 50shows the effect of selectivity on the presented

scheme , it shows that SVD precoded CSM is enhanced in highly selective channels.

Figure 48 Comparison between SVD precoded CSM systems and unprecoded schemes

Figure 49 spectral efficiency achieved upon using the SVD precoded schemes

-10 -5 0 5 10 15 20 25 3010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

RComparison between SVD precoding and unprecoded schemes

SVD precoded 2users,2 Tx ant. , 4 Rx ant.

SVD precoded,2users,4 Tx ant. ,8 Rx ant.

unprecoded 2 users , 4 Tx ant., 8 Rx ant.

unprecoded 2 users , 2 Tx ant. , 4 Rx ant.

-10 0 10 20 30 40 500

5

10

15

20

25

30

35

Eb/N

o

spectr

al eff

icie

ncy b

/s/H

z

spectral efficiency of the SVD precoded CSM system

89

Figure 50 Effect of selectivity on SVD precoded CSM system with 2 userrs , 4 Tx antennas , 8 Rx

antenennas

5.6.3 Advantages and disadvantages

Advantages:

Achieves the capacity of the MIMO channel.

Exploits the whole degrees of freedom of the CSM system

Performance enhancement by 2.5dB.

Disadvantages

Requires full knowledge of the channel matrix at each frequency.

High feedback overhead.

Increased complexity

5.7 Combined collaborative and Codebook-precoded MIMO for the

uplink of the LTE-advanced

5.7.1 Algorithm description

To make use of the new spatial dimension introduced in LTE-advanced with

limited feedback signaling in case of collaborative MIMO system, codebook-based

-10 0 10 20 30 40 5010

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Effect of selectivity on SVD precoded CSM system with

2 userrs , 4 Tx antennas , 8 Rx antenennas

90

precoding should be taken into consideration. Three different precoder selection techniques

are presented in comparison [73].

5.7.1.1 Submatrix precoding

This selection method is the same as the previous scheme ,the channel matrix is

divided into 𝐾 submatrices and each of them is precoded independently by metric

identified in equations (5.5),(5.6),(5.7) thus precoding matrix of 𝑘𝑡𝑕 user is

𝑭𝒖𝒔𝒆𝒓𝒌 𝑙 = argmax𝑭𝒊∈𝔽

𝑯𝒖𝒔𝒆𝒓 𝒌(𝑙)𝑭𝒊(𝑙) 2 (5.20)

𝑯𝒖𝒔𝒆𝒓 𝒌(𝑙) is the channel columns corresponds to the 𝑘𝑡𝑕 user.The equivalent channel

would be

𝑯𝒆𝒒 𝑙 = [𝑯𝒖𝒔𝒆𝒓 𝟏 𝑙 𝑭𝒖𝒔𝒆𝒓𝟏 𝑙 … 𝑯𝒖𝒔𝒆𝒓 𝑲 𝑙 𝑭𝒖𝒔𝒆𝒓𝑲 𝑙 ] (5.21)

5.7.1.2 Joint maximization precoding

In this selection method the MIMO channel is divided into 𝐾x𝐾 submatrices , for example

for rank 1 , 2 users equipped by 2 antennas and 4 receiving antennas , we will have 4

submatrices 2x2 each.

𝑯 𝑙 = 𝑯𝑢𝑠𝑒𝑟 1

12 (𝑙) 𝑯𝑢𝑠𝑒𝑟 212 (𝑙)

𝑯𝑢𝑠𝑒𝑟 134 (𝑙) 𝑯𝑢𝑠𝑒𝑟 2

34 (𝑙) (5.22)

where 𝑯𝑢𝑠𝑒𝑟 112 (𝑙) is 2x2 MIMO channel between user 1 and receiving antennas 1,2. Here

we will choose the precoder so as to it jointly maximizes the norm of these subchannels as

𝑭𝒖𝒔𝒆𝒓𝒌 𝑙 = argmax𝑭𝒊∈𝔽

( 𝑯𝑢𝑠𝑒𝑟 112 𝑙 𝑭𝒊

2 + 𝑯𝑢𝑠𝑒 𝑟 134 𝑙 𝑭𝒊

2) (5.23)

And the equivalent channel would be as equation (5.14)

5.7.1.3 Linear combination precoding

In this selection criteria, the precoder is chosen as a linear combination of the precoders

which maximize the metric of 𝑯𝑢𝑠𝑒𝑟 112 (𝑙), 𝑯𝑢𝑠𝑒𝑟 1

34 (𝑙) independently as

𝑭𝒖𝒔𝒆𝒓𝒌 𝑙 = argmax𝑭𝒊∈𝔽

𝑯𝑢𝑠𝑒𝑟 112 𝑙 𝑭𝒊

2 + argmax𝑭𝒊∈𝔽

𝑯𝑢𝑠𝑒𝑟 134 𝑙 𝑭𝒊

2

(5.24)

The chosen precoder must be normalized. The drawback of this selection method is that

the resultant precoder doesn‟t have a constant modulus and probably can enhance PAPR.

91

5.7.2 Results and discussions:

Figure 51 Codebook precoded CSM Vs. ordinary CSM

Figure 52 Comparison between the selection criteria of the three precoders

-10 -5 0 5 10 15 20 25 30 35 4010

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codebook precoding Vs. ordinary CSM

precoding 2x4 rank 1

unprecoded 2x4rank 1

precoding 2x4rank 2 (asunprecoding)

precoding 2x8 rank 1

unprecoded 2 usersx8 ant.

precoding 2x 8 rank 2

unprecoded 2 usersx8ant. rank 2

precoding 2 usersx8 ant. rank 3

unprecoded 2 users x 8 ant. rank 3

precoding 2x8 rank4 (asunprecoded)

SVD precoding rank 4

-8 -6 -4 -2 0 2 4 6 8 10 1210

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Comparison between selection methods of precoders for2usersx8 receive ant.

rank 1

Submatrix precoding

joint maximization

linear combination

best channel metric precoding

92

Figure 53 Effect of selectivity on the codebook based precoding

Figure 54 spectral efficiency achieved when using precoded 2 Tx antennas transmission

-8 -6 -4 -2 0 2 4 6 8 10 1210

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Effect of selectivity along codebook precoding

codebook flat fading channel

codebook delay spread=2us

codebook delay spread=5us

codebook delay spread=15us

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2

4

6

8

10

12

14

16

Eb/N

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/s/H

z

Spectral efficiency of codebook precoded 2usersxreceiving antennas

and UE having 2 transmitting antennas

rank 1

rank 2

93

Figure 55 spectral efficiency of precoded CSM of 4 transmitting antennas for different ranks

Same simulation conditions of the previous section are examined. Figure 51 shows

a comparison between codebook precoded CSM for 2 and 4 transmitting antennas and

unprecoded CSM system using joint maximization method. The figure demonstrates a

power efficiency enhancement of almost 2dB than the equivalent unprecoded system.

Figure 52 shows a comparison between the three selection criterias presented in this

section. The figure reveals that the submatrix precoding exploits the full channel

knowledge and hence better interstream and interuser interference cancellation. For the

joint maximization method, the performance is degraded by 1dB because the scheme

searches for the precoder which jointly maximizes the channel metric of the sub MIMO

channels, so more interstream interference will exist. Choosing to maximize the best sub

MIMO channel only will degrade the performance by another 0.5dB.

Figure 53 shows that the codebook precoding performance is enhanced for the

increased selectivity due to the increase of the inherent frequency diversity of SC-FDMA

system. Figure 54 and Figure 55 illustrate the achieved spectral efficiency upon using the

codebook precoding CSM which are summarized in Table 14 signal to noise ratio limits

for using the different ranks of the codebook precoded CSM.

-10 0 10 20 30 40 500

5

10

15

20

25

30

35

Eb/N

o

spectr

al eff

icie

ncy b

/s/H

z

Codebook precoded collaborative spatial multiplexing

for 4 transmitting antennas

rank 1 2usersx8ant.

rank 2 2usersx8ant.

rank 3 2users x8ant.

rank 4 2userx8ant.

94

Rank 1 Rank 2 Rank 3 Rank 4

Tranmitting

antennas=2 <22.5dB ≥ 22.5 dB - -

Tranmitting

antennas=4 <7.8dB 7.8-15dB 15-25.5dB ≥ 25.5dB

Table 14 signal to noise ratio limits for using the different ranks of the codebook precoded CSM

5.7.3 Advantages and disadvantages

Advantages

Different ranks can be supported which instruct of adaptive rank selection.

limited feedback signaling.

Precoder can be selected by the eNodeB.

Disadvantages

Suboptimal precoding.

Requires partial channel knowledge.

Interuser and interstream interference are still present.

5.8 Combined collaborative MIMO and space frequency block codes

(SFBC) for the uplink of the LTE-advanced

5.8.1 Algorithm description

To achieve spatial diversity and spatial multiplexing jointly without a need of any

feedback signaling, a novel combined scheme of SFBC and collaborative spatial

multiplexing is proposed [73].

In this scheme, each user equipped by 2 antennas will precode its signal by the well

known frequency domain version of the orthogonal Alamouti‟s matrix [74], [75] , which

will result in encoding each two successive subcarriers for the 𝑘𝑡𝑕 user as

𝐴𝑛𝑡 1𝐴𝑛𝑡 2

𝑠𝑢𝑏𝑐𝑎𝑟𝑟𝑖𝑒𝑟 (𝑙) 𝑠𝑢𝑏𝑐𝑎𝑟𝑟𝑖𝑒𝑟 (𝑙 + 1)

𝑌 𝑘(𝑙)/ 2 −𝑌 𝑘∗(𝑙 + 1)/ 2

𝑌 𝑘(𝑙 + 1)/ 2 𝑌 𝑘∗(𝑙)/ 2

(5.25)

The result of SFBC precoding of each user will achieve transmit spatial diversity

and orthogonal substream transmission. The result of SFBC will be transmitted

collaboratively across same time and frequency grid which corresponds to spatial

multiplexing. Considering the case of 2 users x 2 receiving antennas, then the received

signal at the 𝑙𝑡𝑕 subcarrier would be

95

𝑹 𝑙 = 𝐻11

𝑙 𝐻12𝑙

𝐻21𝑙 𝐻22

𝑙 𝐻13

𝑙 𝐻14𝑙

𝐻23𝑙 𝐻24

𝑙

𝑯 𝑙

𝑌 1(𝑙)

𝑌 1(𝑙 + 1)

𝑌 2(𝑙)

𝑌 2(𝑙 + 1)

+ 𝑾(𝑙) (5.26)

Where 𝑯 𝑙 is 2x4 MIMO channel which will be assumed to be quasi static over every two

successive subcarriers, similarly the received signal at the (𝑙 + 1)𝑡𝑕 would be

𝑹 𝑙 + 1 = 𝑯 𝑙

−𝑌 1

∗(𝑙 + 1)

𝑌 1∗(𝑙)

−𝑌 2∗(𝑙 + 1)

𝑌 2∗(𝑙)

+ 𝑾(𝑙 + 1) (5.27)

Then the receiver will now exploit the inherent orthogonality of the SFBC encoding

,the receiver will do the following multiplication, conjugate and Hermitian processes to

have 𝑿 𝑙

𝑿 𝑙 =

𝐻11𝑙 … 𝐻14

𝑙 𝐻𝑅1 𝑙

𝐻21𝑙 … 𝐻24

𝑙 𝐻𝑅2 𝑙

𝐻11𝑙 … 𝐻14

𝑙 𝑅1∗ 𝑙 + 1

𝐻21𝑙 … 𝐻24

𝑙 𝑅2∗ 𝑙 + 1

(5.28)

where 𝑅1 𝑙 , 𝑅2 𝑙 are the received signals along the 𝑙𝑡𝑕 subcarrier on antenna 1 and

antenna 2 respectively. Apparently we can exploit the full diversity of the collaborative

system per user and also exclude the interstream interference as we make a specific linear

combination of the rows of 𝑿 𝑙 . To maximize the diversity of 𝑌 1 𝑙 , add the following

𝜃1 𝑙 = 𝑋1 𝑙 + 𝑋5 𝑙 + 𝑋10 𝑙 + 𝑋14 𝑙

= 𝐻11𝑙

2+ 𝐻12

𝑙 2 𝐻21

𝑙 2

+ 𝐻22𝑙

2 𝑌 1 𝑙

+ 𝐻11𝑙 ∗

𝐻13𝑙 + 𝐻21

𝑙 ∗𝐻23

𝑙 + 𝐻12𝑙 𝐻14

𝑙 ∗+ 𝐻22

𝑙 𝐻24𝑙 ∗

𝑌 2 𝑙

+ 𝐻11𝑙 ∗

𝐻14𝑙 + 𝐻21

𝑙 ∗𝐻24

𝑙 − 𝐻12𝑙 𝐻13

𝑙 ∗− 𝐻22

𝑙 𝐻23𝑙 ∗

𝑌 2

= 𝛼1𝑌 1 𝑙 + 𝛽𝑌 2 𝑙 + 𝛾𝑌 2 𝑙 + 1 (5.29)

Equation (5.29) shows the exclusion of interstream interference 𝑌 1(𝑙 + 1) and

exploiting all the spatial channels experienced by 𝑌 1 𝑙 .Similarly, To maximize 𝑌 1 𝑙 +1 , 𝑌 2 𝑙 , 𝑌 2(𝑙 + 1) to have 𝜃2 𝑙 , 𝜃3 𝑙 , 𝜃4 𝑙 respectively as

𝜃2 𝑙 = 𝑋2 𝑙 + 𝑋6 𝑙 − 𝑋9 𝑙 − 𝑋13 𝑙

𝜃3 𝑙 = 𝑋3 𝑙 + 𝑋7 𝑙 + 𝑋12 𝑙 + 𝑋16 𝑙

𝜃4 𝑙 = 𝑋4 𝑙 + 𝑋8 𝑙 − 𝑋11 𝑙 − 𝑋15 𝑙 (5.30)

96

Then the equivalent transmission scheme can be written as quasi-orthogonal system of

equations as

𝛼1 00 𝛼1

𝛽 𝛾

−𝛾∗ 𝛽∗

𝛽∗ −𝛾𝛾∗ 𝛽

𝛼2 00 𝛼2

𝑯𝒆𝒒(𝑙)

𝑌 1(𝑙)

𝑌 1(𝑙 + 1)

𝑌 2(𝑙)

𝑌 2(𝑙 + 1)

=

𝜃1 𝑙

𝜃2 𝑙

𝜃3 𝑙

𝜃4 𝑙

𝚯(𝑙)

(5.31)

where 𝛼2 = 𝐻13𝑙

2+ 𝐻14

𝑙 2

+ 𝐻23𝑙

2+ 𝐻24

𝑙 2

Then the estimate of the received subcarriers will be

𝒀 𝑙 = 𝑯𝒆𝒒−𝟏(𝑙) 𝚯(𝑙) (5.32)

The scheme makes use of inherent spatial diversity shown in 𝛼1 , 𝛼2 , doubles the

spectral efficiency (4 symbols x2 subcarriers) with no CSI at the transmitting end. Note

that the selectivity of channel is a main issue in this scheme because the channel gains are

assumed to be constant over two successive subcarriers, so highly selective channel will

degrade the whole performance of the scheme. It is worth saying that extending the scheme

for 2 users x 4 receiving antennas at eNodeB to achieve higher diversity order is quite

simple with only extensions of 𝑿 𝑙 , 𝚯 𝑙 , 𝛼1 , 𝛼2 , 𝛼, 𝛽 to acquire the extra channels.

To prevent system from severe degradation in performance in case of highly

selective channels simple averaging of channel gains over 𝑙𝑡𝑕 and (𝑙 + 1)𝑡𝑕 subcarriers as

𝑯 𝑙 = 12 𝑯 𝑙 + 𝑯 𝑙 + 1 (5.33)

5.8.2 Results and discussions

To show the ideal performance of SFBC precoded CSM, we will work on channel

delay spread=1𝜇𝑠 with the same 16QAM modulation to ensure flat channel gains over each

2 successive subcarriers.

97

Figure 56 SFBC precoded CSM Vs. unprecoded CSM

Figure 56 shows a comparison between unprecoded CSM and SFBC precoded

CSM , results reveal that the SFBC precoding outperforms the ordinary CSM by 5dB for

target BER of 10-5

for eNodeB having 4 receiving antennas and 7dB for eNodeB having 2

receiving antennas.

Figure 57 Effect of selectivity along SFBC precoding

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SFBC precoded CSM Vs. unprecoded CSM

SFBC 2 users , 2 Tx ant. , 2Rx ant.

SFBC 2 users , 2 Tx ant. , 4Rx ant.

unprecoded 2 users , 4Rx ant.

unprecoded 2 users , 2Rx ant.

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Effect of selectivity along SFBC precoding

SFBC flat fading

SFBC delay spread 1uS

SFBC delay spread=3.5us

SFBC delay spread=2uS

SFBC delay spread=5us

98

Figure 57 shows the effect of selectivity on the SFBC precoded CSM system. Two

factors are controlling the performance, the frequency diversity and the flat frequency gain

over each two successive subcarriers. So the performance is improved when the selectivity

is increased till 1𝜇𝑠 (medium selectivity) and then the subcarriers gains will become

different, so an error floor will be introduced for channels have selectivity more than

3.5𝜇𝑠.

Figure 58 comparison between the presented precoding schemes

Figure 58 shows comparison between the presented precoding schemes , simulation

results reveals that for rank 1 transmission in flat fading channel , SFBC precoding and

codebook precoding are almost identical , and outperforms the unprecoded system by more

than 3dB at a target BER=10-5

, so SFBC in this case is preferred due to the no CSI needed

at the transmitter. For rank 2 the SVD precoding outperforms the codebook precoding by

2.5dB.

5.8.3 Advantages and disadvantages

Advantages

Outperforms the ordinary CSM.

No need for channel knowledge at the transmitter (blind precoding)

Make use of the MIMO enhancements of the LTE-advanced.

Simple inversion receiver.

Disadvantages

Performance enhancement is limited to low and medium selective channels only.

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Comparison between presented precoding schemes

ref erence curv e f lat f ading without precoding 2x4 antennas

SFBC precoding 2 users x 4 receiv e antennas

Codebook precoding 2 user x 4 ant. rank 1

SVD precoding 2 users x 4 ant. rank 2

unprecoded rank 2 and codebook precoded rank 2

99

Fixed rank transmission .

5.9 Effect of precoding to other equalization techniques

In this section other multiuser equalization techniques which are previously

presented in chapter (3) and chapter (4) are studied when accompanying the precoding

schemes presented in this chapter.

Figure 59 Different Multiuser equalization Techniques for codebook precoding scheme

Simplified IGML solutions presented in chapter 4 will be in the order of 𝑂(𝐾𝜌ℳ).

Simplified IGML is a user by user separation by means of or 𝒬ℛ-decomposition of the

equivalent channel matrix 𝑯𝒆𝒒 𝑙 obtained in equations (5.21) and (5.31). SIC based

system will be the same as presented in chapter (3) but the interference will be regenerated

assuming the channel matrix is the equivalent channel matrix presented in also equations

(5.21) and (5.31).

Figure 59 shows that SIC-based equalizer coincides with the MMSE base equalizer.

Because the SIC performance is dependent on the SINR, and for precoded system most of

the interference components are excluded and hence slight enhancement in performance

can be expected. The QR based IGML receiver outperforms the MMSE equalizer by 1dB.

The cost is the increased complexity of checking the error metric of all possible

constellation points.

5.10 Conclusions

In this chapter, we studied the new MIMO enhancements introduced to the uplink

of LTE-advanced standard.

-8 -6 -4 -2 0 2 4 610

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Effect of different equalization techniques accompanying

codebook precoding 2users , 4Tx ant. , rank 1 , 8 receiving antennas

SIC equalization

simplified IGML equalization

MMSE equalization

100

Three precoding schemes are proposed to the CSM system

The SVD precoding based CSM is the optimal precoding scheme and achieves the

capacity of the resulting system; however it requires full channel knowledge at the

transmitter. It excludes the interstream interference but cannot count for the

interuser interference. Its performance is enhanced by increasing of the selectivity

of the channel.

The codebook precoded CSM is a suboptimal precoding which can limit the

feedback information to the transmitter and enables eNodeB to select the proper

precoder.

Three precoder selectors are presented in this chapter and we conclude that a

submatrix precoding outperforms the others by 1dB at minimum.

The codebook precoded CSM supports adaptive rank transmission

The SFBC precoded CSM performance is the same order of the codebook precoded

CSM in case of low and medium selective channels with no need for the channel

knowledge at the transmitter.

The results instruct using adaptive precoding scheme, that works as follows

o For low and medium selective channel use SFBC based precoding.

o As selectivity increases , use the adaptive rank codebook transmission using

the submatrix selection method.

o As SNR is sufficiently high to use the full rank of the MIMO channel you

can use the SVD-based precoding .

101

CCHHAAPPTTEERR SSIIXX

TTUURRBBOO EEQQUUAALLIIZZAATTIIOONN FFOORR UUPPLLIINNKK OOFF LLTTEE--AADDVVAANNCCEEDD

6.1 Introduction

In this chapter, we introduce the TEQ technique as multiuser equalization technique

for the collaborative MIMO system. So, we are getting “softer” capitalizing from the

performance gains of turbo codes and the turbo decoding algorithm. The turbo equalization

works as joint equalization and decoding which are done iteratively by passing the soft

outputs generated by soft input soft output (SISO) equalizer to a SISO decoder and vice

versa. This will enhance the overall link performance in expense of increasing of receiver‟s

complexity and receiver‟s delay.

The chapter is organized as the following, first we will give a short literature

review about the TEQ technique, and then we will discuss the basic components of the

TEQ receiver. The chapter will continue with presenting different multiuser equalization

for the CSM system. Moreover we will extend this TEQ concept to precoded CSM

system presented in chapter 5. We will also generalize the SFBC receiver in chapter 5 to

operate in highly selective channels to maximize the frequency diversity exploited by the

TEQ.

6.2 Literature review about Turbo Equalization Technique

6.2.1 Philosophy of TEQ and Douillard‟s TEQ

The philosophy of TEQ relies on iteratively exchanging soft outputs between the SISO

frequency domain equalizer and the SISO decoder, i.e., the TEQ relates the ISI channel as

random serial concatenated channel coder. Turbo equalization was first proposed by

Douillard et al. in 1995 in [42] for a serially concatenated convolutional-coded BPSK

system, as shown in Figure 60. In this contribution, turbo equalization was shown to

mitigate the effects of ISI, when having perfect channel impulse response information.

Instead of performing the equalization and decoding independently, in order to overcome

the channel‟s frequency selectivity, better performance can be obtained by the turbo

equalizer, which considers the discrete channel‟s memory and performs both the

equalization and decoding iteratively

Figure 60 Douillard's TEQ

102

The basic philosophy of the original turbo equalization technique stems from the

iterative turbo decoding algorithm consisting of two SISO decoders, a structure which was

proposed by Berrou et al. [38].As mentioned previously, the original turbo equalizer

consists of a SISO equalizer and a SISO decoder. The SISO equalizer in Figure 60)

generates the a-posteriori probability upon receiving the corrupted transmitted signal

sequence and the a-priori probability provided by the SISO decoder. However, at the initial

iteration stages . i.e. at the first turbo equalization iteration . No a-priori information is

supplied by the channel decoder. Therefore, the a-priori probability is set to 1/2, since the

transmitted bits are assumed to be equiprobable.

Before passing the a-posteriori information generated by the SISO equalizer to the

SISO decoder of Figure 14.2, the contribution of the decoder. In the form of the a-priori

information. The removal of the a-priori information is necessary, in order to prevent the

decoder from receiving its own information, which would result in the so-called “positive

feedback” phenomenon.Overwhelming the decoder‟s current reliability estimation of the

coded bits, i.e. the extrinsic information which will prevent the channel equalizer from

receiving information based on its own decisions, which was generated in the previous

turbo equalization iteration. The combined channel and extrinsic information is channel de-

interleaved and directed to the SISO decoder. The iterative process is repeated until the

required termination criterias are met. At this stage, the a-posteriori information of the

source bits, which has been generated by the decoder, is utilized to estimate the transmitted

bits.

6.2.2 Literature review of TEQ methods

In this section, we present a brief review about previous work on TEQ. TEQ was

originally proposed by Douillard et al. [42] with the purpose of mitigating the effects of

inter-symbol interference using an MLSE (Maximum Likelihood Sequence Estimation)

equalizer. Tuchler [76] proposed the turbo equalization based on both MMSE and DFE

equalizer with the advantage of reducing the receiver complexity.

Combined turbo coding equalization and decoding has been studied in [77],

whereas in [78], turbo equalization has been extended for multi-level modulation schemes.

In all of these papers, the equalization is performed in the time domain. Tuchler et al.

proposed a frequency domain equalizer with fixed coefficients solution, and with lower

complexity [79]. The proposed turbo equalization in this chapter follows the principles

explained in [80], but the equalization is performed through a frequency domain soft

interference cancellation (SIC) equalizer as [81].

6.3 System model modifications and Turbo Equalizer main components

In this chapter, we will work generally with the system model presented in section

5.5 (Figure 46 UEs transmitter block diagram). However, we will assume coded operation for this

CSM system. i.e. The data of the kth user is independently processed as the following ,

first each user will have ρ independent data streams (called rank of transmission), ρ ≤ NT ,

the ith layer data stream is encoded by turbo encoder to have cki (n) .The output systematic

and parity bits are interleaved by random interleaver, then punctured to desired rate R to

103

have cki (n) .A group of m interleaved coded bits are symbol mapped to have the modulated

symbols yki . Then, the rest of the system model of section 5.5 is reused.

Moreover, The TEQ principle relies on exchanging the soft decisions back and

forth between the equalizer and the decoder. This requires some modifications for both

demodulator and decoder to accept and provide this soft information, because the process

of making hard decisions on the channel symbols destroys the information pertaining to

how likely each of the possible channel symbols might have been [80].

6.3.1 Subblock interleaver and rate matching (RM)

In order to improve the performance of the error correction coding, by spreading

out any burst errors that might occur in the channel, an interleaver is used to scramble the

data, in order to ensure that such errors appear random and to avoid long error bursts. The

interleaver is used to randomize the order of the code bits prior to transmission. This

process is completely reversible, and is simply mirrored in the receiver.

In our model, the rate 1/3 turbo code generates a stream of systematic bits, a stream

of parity bits from the first constituent convolutional code (parity 1 bits), and a stream of

parity bits from the second constituent convolutional code (parity 2 bits). Each of these

three streams is interleaved separately by random subblock interleavers.

The LTE standard [31],[1] as shown in Figure 61 performs rate matching by using

circular buffer to offer different and adaptive Modulation and Coding Schemes

(MCS).This can be done by interlacing parity 1 and parity 2 streams, each transmission

reads bits from the buffer, starting from an offset position and increasing the bit index. If

the bit index reaches a certain maximum number, the bit index is reset to the first bit in the

buffer. In other words, the buffer is circular.

Figure 61 LTE rate matching

104

6.3.2 Soft demodulator with priors (SISO demapper)

To provide SISO demodulator as shown in Figure 62 , the demodulator should be fed by

the output of the equalizer 𝑦 𝑒𝑞 .𝑖 (𝑛) and the a priori LLRs 𝑳𝒂

𝒅𝒆𝒄 of previous decoding stages.

The demodulator will then calculate the a posteriori LLRs 𝐿𝑎𝑒𝑞

(𝑐𝑘𝑗 ,𝑖

(𝑛)) which corresponds

to the LLR of 𝑗𝑡𝑕 bit of the 𝑛𝑡𝑕symbol of the 𝑖𝑡𝑕 layer of 𝑘𝑡𝑕user (simply written

as 𝐿𝑎𝑒𝑞

𝑐𝑛𝑗 ) shown in [39]

𝐿𝑎𝑒𝑞

𝑐𝑛𝑗 = 𝑙𝑜𝑔

exp − 𝑦 𝑒𝑞 .𝑖 (𝑛) − 𝑦𝑘

𝑖 2

𝜍𝑤2 Pr 𝑐𝑛

𝑗= 𝑐𝑗 |𝑳𝒂

𝒅𝒆𝒄 𝑚𝑗 =1 𝑦𝑘

𝑖 :𝑐 𝑗 =0

exp − 𝑦 𝑒𝑞 .𝑖 (𝑛) − 𝑦𝑘

𝑖 2

𝜍𝑤2 Pr 𝑐𝑛

𝑗= 𝑐𝑗 |𝑳𝒂

𝒅𝒆𝒄 𝑚𝑗 =1 𝑦𝑘

𝑖 :𝑐 𝑗 =1

(6.1)

where 𝑦𝑘𝑖 𝜖ℳ .

The correspondence between the decoder LLRs and the a priori probability can be

calculated as

Pr 𝑐𝑛𝑗

= 𝑐𝑗 |𝑳𝒂𝒅𝒆𝒄 =

1

2 1 + 1 − 2𝑐𝑗 tanh

𝑳𝒂𝒅𝒆𝒄

2

(6.2)

where 𝑐𝑗 ∈ {0,1}.

The previous demodulator can be approximated by converting (6.1) into logarithmic scale

and finding the dominant term in both summations as

𝐿𝑎𝑒𝑞

𝑐𝑛𝑗 = max

𝑦𝑘𝑖 :𝑐 𝑗 =0

− 𝑦 𝑒𝑞 .𝑖 (𝑛) − 𝑦𝑘

𝑖 2

𝜍𝑤2

+ logPr

𝑚

𝑗 =1

𝑐𝑛𝑗

= 𝑐𝑗 |𝑳𝒂𝒅𝒆𝒄

− max 𝑦𝑘

𝑖 :𝑐 𝑗 =1

− 𝑦 𝑒𝑞 .𝑖 (𝑛) − 𝑦𝑘

𝑖 2

𝜍𝑤2

+ logPr

m

j=1

𝑐𝑛𝑗

= 𝑐𝑗 |𝑳𝒂𝒅𝒆𝒄

(6.3)

where logPr . is the logarithmic probability metric of the corresponding a priori LLRs

calculated as

logPr 𝑐𝑛𝑗

= 𝑐𝑗 |𝑳𝒂𝒅𝒆𝒄 = − log 1 + exp( 2𝑐𝑗 − 1 . 𝑳𝒂

𝒅𝒆𝒄) (6.4)

Figure 62 SISO demapper idea

𝑳𝒂𝒅𝒆𝒄

𝑦 𝑒𝑞 .𝑖 (𝑛)

SISO demapper

𝐿𝑎𝑒𝑞

𝑐𝑛𝑗

105

6.3.3 Soft mapper (SISO mapper)

The SISO mapper in Figure 63 SISO mapper idea outputs the mean constellation

symbol based on the a priori LLRs given by the turbo decoder. This will provide a slight

cancellation gains with respect to hard mapping. The output of the SISO mapper is

calculated in [81]

𝑦𝑘𝑖 𝑛 = 𝐸 𝑦𝑘

𝑖 |𝑳𝒂𝒅𝒆𝒄 = 𝑦𝑘

𝑖 Pr 𝑐𝑛𝑗

= 𝑐𝑗 |𝑳𝒂𝒅𝒆𝒄

𝑚

𝑗 =1 𝑦𝑘𝑖 ∈ℳ

(6.5)

where the summation is carried out over all the possible modulation symbols of the signal

set ℳ.i.e. the SISO mapper will generate the conditional probability density distribution of

the transmitted symbols given the decoder LLRs and outputs the statistical average.

The SISO mapper should also give a statistical insight about the reliability of its

output, that is provided by calculating the variance of the soft symbols for a given time slot

having 𝑁𝑠𝑦𝑚𝑏𝑈𝐿 symbols as

𝜍𝑦 2 ≈

1

𝑁𝑠𝑦𝑚𝑏𝑈𝐿 . 𝑀

𝑦𝑘𝑖 𝑛

2

𝑁𝑠𝑦𝑚𝑏𝑈𝐿 .𝑀

𝑛=1

(6.6)

Figure 63 SISO mapper idea

6.3.4 SISO decoder

In turbo equalization the SISO decoder block accepts soft inputs from the SISO

equalizer and gives LLRs of systematic and parity bits 𝐿𝑎𝑑𝑒𝑐 𝑐𝑛

𝑗 𝐿𝑎

𝑒𝑞 𝑐𝑛

𝑗 [39]. This can be

done by modifying the turbo decoder to have three soft outputs based on the transitions of

the trellis of the constituent encoder in Figure 64 Trellis diagram of one constituent

encoder of the 3GPP LTE [82] .The LLR of each coded bit individually can be calculated

as

𝐿𝑎𝑑𝑒𝑐 𝑐𝑛

𝑗 𝐿𝑎

𝑒𝑞 𝑐𝑛

𝑗 = 𝑙𝑜𝑔

exp(𝐴𝑛−1 ℇ′ + Γn ℇ′ , ℇ + 𝐵𝑛 ℇ )

ℇ′ ,ℇ ∶𝑐𝑛𝑗

=+1

exp(𝐴𝑛−1 ℇ′ + Γn ℇ′ , ℇ + 𝐵𝑛 ℇ )

ℇ′ ,ℇ :𝑐𝑛𝑗

=−1

(6.7)

Where𝐴𝑛 ℇ , 𝐵𝑛 ℇ are forward and backward recursion values respectively and Γn ℇ′ , ℇ

is transition metric between ℇ′ , ℇ states.

SISO mapper 𝑳𝒂

𝒅𝒆𝒄 𝑦𝑘

𝑖 𝑛

𝜍𝑦 2

106

Figure 64 Trellis diagram of one constituent encoder of the 3GPP LTE

6.4 TEQ Techniques for CSM of the LTE uplink

6.4.1 Soft -PIC based Turbo Equalization (Soft PIC-TEQ)

6.4.1.1 Motivation

The philosophy of TEQ relies on iteratively exchanging soft outputs between the

SISO frequency domain equalizer and the SISO decoder, i.e. the TEQ relates the ISI

channel as random serial concatenated channel coder. The problem in CSM is that users‟

data are mixed together in the channel, so soft parallel interference cancellation (PIC-TEQ)

seems to be attractive [83].

107

6.4.1.2 Algorithm description

Figure 65 proposed eNode B 2 users PIC-TEQ

The PIC-TEQ in Figure 65 proposed eNode B 2 users PIC-TEQ works as the following:

1. First, Separate the users‟ data using MMSE equalization as (3.31)

2. These decisions would be fed to the SISO demapper shown in (6.4) with zero

initialized 𝑳𝒂𝒅𝒆𝒄 corresponding to absence of a priori information in the first

iteration. This will result in to have the demodulator soft outputs 𝐿𝑎𝑒𝑞

(𝑐𝑘𝑗 ,𝑖

(𝑛))

3. The output of the demapper is rate dematched (not shown explicitly in figure) by

inserting zeros corresponding to lack of a priori information in the positions of

punctured bits.

4. The output of the rate dematcher is decoded by SISO turbo decoder defined in (6.7)

to have 𝑳𝒂𝒅𝒆𝒄 which will be further soft mapped using soft mapper as (6.5) , (6.6) to

have the soft symbols 𝑦𝑘𝑖 𝑛 and statistical variance 𝜍𝑦

2.

5. DFT the output soft symbols to have 𝒀 𝑑𝑒𝑐 (𝑙) which corresponds to soft estimate of

all users‟ data carried on the 𝑙𝑡𝑕 subcarrier and start the soft PIC stage by

reconstructing the interference and subtract it from the channel symbols 𝑹 𝑙 to

have the 𝑚𝑡𝑕 layer‟s data on 𝑙𝑡𝑕 subcarrier during the 𝑛𝑡𝑕 equalizing iteration

𝒀𝑃𝐼𝐶𝑚 ,𝑛 𝑙 = 𝑹 𝑙 − 𝑯𝑒𝑞

𝑍−{𝑚}(𝑙)𝒀 𝑑𝑒𝑐

𝑍−{𝑚}(𝑙) (6.8)

where 𝑍 = {1,2, . . , 𝐾} , 𝑯𝑒𝑞𝑍−{𝑚}

are the columns of 𝑯𝑒𝑞 (𝑙) except 𝑚𝑡𝑕 column of

equivalent channel corresponding to 𝑚𝑡𝑕 user‟s channel.

108

6. Two issues concerned about the output of the soft PIC . First, the output of the

canceller should be combined together from all antennas. Second, residual error after

cancellation should be taken into account, this can be done by filtering the output of

PIC by soft combiner filter

𝒀𝑒𝑞𝑢𝑙 .𝑚 ,𝑛 𝑙 = 𝑯𝑒𝑞

𝑚 𝑯 𝑙 (𝑯𝑒𝑞𝐻 (𝑙)𝚿𝑛𝑯𝑒𝑞 (𝑙) + 1/𝛾𝑠𝑰𝑲)−1𝒀𝑃𝐼𝐶

𝑚 ,𝑛 𝑙 (6.9)

where 𝚿𝑛 denotes the residual interference power matrix of the 𝑛𝑡𝑕 iteration 𝚿𝑛 =𝑑𝑖𝑎𝑔(𝜓1, 𝜓2, … ) where the 𝑗𝑡𝑕 is given by

𝜓𝑗 = 1 𝑖𝑓 𝑗 = 𝑚

1 − 𝜍𝑦 𝑍− 𝑚 ,𝑛−1

2 𝑖𝑓 𝑗 ≠ 𝑚 (6.10)

7. The output of the soft PIC are fed to SISO demapper with the knowledge of 𝑳𝒂𝒅𝒆𝒄 of the

zeroth iteration

8. Steps 2 to 5 are repeated iteratively for specific number of iterations or till the cyclic

redundancy check (CRC) has been successful to minimize the complexity of PIC-TEQ

6.4.1.3 Results and discussion

Figure 66 performance of PIC-TEQ for conventional CSM with 2 users using different MCS

Figure 66 shows that the PIC-TEQ achieves a 1dB gain for the MCS QPSK ½ . The

power efficiency will be enhanced for 16QAM ¾ modulation to have 2.5dB gain over the

conventional MMSE equalization. The gain will be decreased for weaker channel coding

rates like 5/6 in accompany with the 64QAM 4/5to be 1.5dB gain.

-10 -5 0 5 10 15 20 25 3010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

PIC-TEQ of 3 iterations of CSM system with 2 users

with different MCS

QPSK 1/2 MMSE

16QAM 3/4 MMSE

64QAM MMSE

QPSK 1/2 PIC-TEQ 3 iterations

16QAM 3/4 PIC-TEQ 3 iterations

64QAM 4/5 PIC-TEQ 3 iterations

109

Figure 67 channel selectivity effect on the PIC-TEQ for the conventional CSM with 2 users using

16QAM ¾

Figure 67 channel selectivity effect on the PIC-TEQ for the conventional CSM with

2 users using 16QAM ¾. The figure reveals the dependency of SC-FDMA systems on the

frequency diversity attained from higher channel selectivity. The results reveal that the

TEQ gain increases gradually upon increasing selectivity to have 5dB gain at delay spread

of 1𝜇s compared with 1dB for flat fading channels. The TEQ gains will be then decreased

for higher delay spread due to exploiting the full fledge of the frequency diversity through

the channel code.

6.4.1.4 Advantages and disadvantages

Advantages

Achieves 2.5dB gain over the ordinary CSM for moderate MCS.

Achieves 1.2dB gain over the initial guess ML proposed in chapter 4.

Exploits the frequency diversity of the moderate selective channels more efficiently

than ordinary MMSE equalization

Disadvantages

Excessive eNodeB receiver‟s complexity due to the need of DFT, and turbo

decoding the stream in each iteration.

Performance is sensitive to high order MCS (ex.64QAM 4/5) and optimized for

moderate rates.

-5 0 5 10 15 20 25 30 35 4010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Effect of channel selectivity on PIC-TEQ of CSM system

of 2 users with 16QAM 3/4

flat fading MMSE

1us MMSE

5us MMSE

15us MMSE

flat fading TEQ 3 iterations

1 us TEQ 3 iterations

5 us TEQ 3 iterations

15us TEQ 3 iterations

110

6.4.2 Soft initial guess Maximum likelihood receiver (Soft single IGML)

extension to PIC-TEQ

6.4.2.1 Motivation

The PIC-TEQ scheme presented in the previous section will be performed till

ensuring that the CRC of one of the user‟s data is correct. In this case we still have the

opportunity to decrease the erroneous symbols of the other user by means of simpler

version of the IGML receiver presented in chapter 4 .The scheme here will take advantage

of separating the correct user‟s data which result in IGML complexity relaxation and better

initial guess for the input symbols obtained by PIC-TEQ as initial guess equalizers‟

performance is closely related to the quality of the guess. Moreover, a priori information

from PIC-TEQ will be used in the final soft demodulation as (6.4) [85].

6.4.2.2 Algorithm description

The scheme works as extension of PIC-TEQ presented in previous section. The

scheme will accept the soft symbols from the output of the PIC-TEQ 𝑦𝑘 𝑛 and consider it

the initial guess of the receiver, cancels the correct user‟s data from the channel symbols

according to (6.8) to have 𝒀𝑃𝐼𝐶𝑚 ,𝑛 𝑙 . Then, perform a symbol-by-symbol exhaustive search

as:

Test all constellation values for the first symbol only while fixing other symbols to

their initial guess, and DFT the new SC-FDMA symbol to obtain 𝒀 𝑴𝑳.

Find the ML solution that corresponds to the minimum error metric along all

subcarriers as follows

𝒚 𝐼𝐺𝑀𝐿(𝑛) = argmin𝒚∈ℳ 𝒀𝑃𝐼𝐶𝑚 ,𝑛 𝑙 − 𝑯𝒍 𝒀 𝑴𝑳(𝑙)

2𝑀𝑙=1 (6.11)

By this, the first symbol is optimally detected, so fix the value of first symbol to

𝒚 𝐼𝐺𝑀𝐿(𝑛) and repeat the last two steps to all other symbols.

The output is soft demodulated using (6.4).

111

6.4.2.3 Results and discussion

Figure 68 performance comparison between MMSE , PIC-TEQ and single user ML-based TEQ

Figure 68 performance comparison between MMSE , PIC-TEQ and single user

ML-based TEQ shows performance comparison between MMSE , PIC-TEQ and single

user ML-based TEQ for QPSK ½ as MCS. The results show that the two users based

IGML presented in chapter 4 is better by 0.5dB from the ordinary MMSE. For the PIC-

TEQ, it achieves 1dB from MMSE when using 5 iterations. Better performance can be

attained by using one iteration TEQ and providing the single user ML presented in this

section. That will boost the performance by extra 0.5 with less number of iterations.

6.4.2.4 Advantages and disadvantages

Advantages

Achieves 1.5dB gain over ordinary MMSE and 0.5dB for 5 iterations PIC-TEQ

Works as performance booster of the PIC-TEQ.

Benefits from the higher quality initial guess from the TEQ-PIC instead of ordinary

MMSE initial guess in chapter 4.

Can possibly decrease the number of iteration required by the PIC-TEQ (one

iteration is almost sufficient , if the PIC-TEQ is preceded by the single IGML)

Disadvantages

The increase of receiver‟s complexity due to the Brute-force search along all

constellation symbols which could be difficult for higher modulation orders

-1 0 1 2 3 4 5 610

-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

SIC 1 +ML with half priors

SIC 1 +ML no priors

SIC 5 iterations

ordinary MMSE

ML with prior

112

6.5 TEQ Techniques for Precoded CSM of the LTE-advanced

6.5.1 PIC-TEQ for SFBC precoded CSM in highly selective channels

6.5.1.1 Motivation

In this section, we will generalize the scheme presented in section 5.8 to propose a

novel MMSE receiver for SFBC that works in highly selective channels and then apply the

PIC-TEQ presented in 6.4.2 as power efficient multiuser equalization technique. That will

provide full spatial and frequency diversities that can be exploited by means of TEQ

instead of operating the scheme in flat fading channel as 5.8 and misses the frequency

diversity [85]

6.5.1.2 Algorithm description

In this scheme, each user equipped by 2 antennas will precode its signal by the

well-known frequency domain version of the orthogonal Alamouti‟s matrix [13] .This will

result in encoding each two successive subcarriers for the 𝑘𝑡𝑕 user as

𝐴𝑛𝑡 1𝐴𝑛𝑡 2

𝑌 𝑘(𝑙) 2 −𝑌 𝑘

∗(𝑙 + 1) 2

𝑌 𝑘(𝑙 + 1) 2 𝑌 𝑘∗(𝑙) 2

(6.12)

The result of SFBC precoding of each user will achieve transmit spatial diversity.

The result of SFBC will be transmitted collaboratively across same time and frequency

resource block, which corresponds to spatial multiplexing. Considering the case of 2 users

x 2 receiving antennas, then the received signal at the 𝑙𝑡𝑕 subcarrier would be

𝑹 𝑙 = 𝐻11

𝑙 𝐻12𝑙

𝐻21𝑙 𝐻22

𝑙 𝐻13

𝑙 𝐻14𝑙

𝐻23𝑙 𝐻24

𝑙

𝑯 𝑙

𝑌 1(𝑙)

𝑌 1(𝑙 + 1)

𝑌 2(𝑙)

𝑌 2(𝑙 + 1)

+ 𝑾(𝑙) (6.13)

where 𝑯 𝑙 is 2x4 MIMO channel. Similarly the received signal at the (𝑙 + 1)𝑡𝑕 would be

𝑹 𝑙 + 1 = 𝐻11

𝑙+1 𝐻12𝑙+1

𝐻21𝑙+1 𝐻22

𝑙+1 𝐻13

𝑙+1 𝐻14𝑙+1

𝐻23𝑙+1 𝐻24

𝑙+1

𝑯 𝑙+1 −𝑌 1

∗(𝑙 + 1)

𝑌 1∗(𝑙)

−𝑌 2∗(𝑙 + 1)

𝑌 2∗(𝑙)

+ 𝑾(𝑙 + 1)

(6.14)

Then, the receiver will utilize the inherent diversity of the SFBC by performing the

following multiplication, conjugate and Hermitian processes to have 𝑿 𝑙

113

𝑿 𝑙 =

𝐻11𝑙 … 𝐻14

𝑙 𝐻𝑅1 𝑙

𝐻21𝑙 … 𝐻24

𝑙 𝐻𝑅2 𝑙

𝐻11𝑙+1 … 𝐻14

𝑙+1 𝑅1∗ 𝑙 + 1

𝐻21𝑙+1 … 𝐻24

𝑙+1 𝑅2∗ 𝑙 + 1

(6.15)

where 𝑅1 𝑙 , 𝑅2 𝑙 are the received signals along the 𝑙𝑡𝑕 subcarrier on antenna 1 and

antenna 2 respectively. To maximize the diversity order of 𝑌 1 𝑙 , the rows of 𝑿 𝑙 are

combined in the following order

𝜃1 𝑙 = 𝑋1 𝑙 + 𝑋5 𝑙 + 𝑋10 𝑙 + 𝑋14 𝑙

= 𝐻11𝑙

2+ 𝐻21

𝑙 2

+ 𝐻12𝑙+1

2+ 𝐻22

𝑙+1 2 𝑌 1 𝑙

+ 𝐻11𝑙 ∗

𝐻12𝑙 + 𝐻21

𝑙 ∗𝐻22

𝑙 − 𝐻12𝑙+1𝐻11

𝑙+1∗− 𝐻22

𝑙+1𝐻21𝑙+1∗

𝑌 1 𝑙 + 1

+ 𝐻11𝑙 ∗

𝐻13𝑙 + 𝐻21

𝑙 ∗𝐻23

𝑙 + 𝐻12𝑙+1𝐻14

𝑙+1∗+ 𝐻22

𝑙+1𝐻24𝑙+1∗

𝑌 2 𝑙

+ 𝐻11𝑙 ∗

𝐻14𝑙 + 𝐻21

𝑙 ∗𝐻24

𝑙 − 𝐻12𝑙+1𝐻13

𝑙+1∗− 𝐻22

𝑙+1𝐻23𝑙+1∗

𝑌 2 𝑙 + 1

= 𝛼1𝑌 1 𝑙 + 𝜂1𝑌 1 𝑙 + 1 + 𝛽1𝑌 2 𝑙 + 𝛾1𝑌 2 𝑙 + 1 (6.16)

Similarly, the diversity order of the preceding symbols 𝑌 1 𝑙 + 1 , 𝑌 2 𝑙 , 𝑌 2(𝑙 + 1)is

maximized to have 𝜃2 𝑙 , 𝜃3 𝑙 , 𝜃4 𝑙 respectively by the following linear combinations

𝜃2 𝑙 = 𝑋2 𝑙 + 𝑋6 𝑙 − 𝑋9 𝑙 − 𝑋13 𝑙

𝜃3 𝑙 = 𝑋3 𝑙 + 𝑋7 𝑙 + 𝑋12 𝑙 + 𝑋16 𝑙

𝜃4 𝑙 = 𝑋4 𝑙 + 𝑋8 𝑙 − 𝑋11 𝑙 − 𝑋15 𝑙 (6.17)

Then, the equivalent transmission scheme can be written as symmetric system of

equations as

𝛼1 𝜂1

𝜂1∗ 𝛼2

𝛽1 𝛾1

𝛾2 𝛽2

𝛽1∗ 𝛾2

∗

𝛾1∗ 𝛽2

∗ 𝛼3 𝜂2

𝜂2∗ 𝛼4

𝑯𝒆𝒒(𝑙)

𝑌 1(𝑙)

𝑌 1(𝑙 + 1)

𝑌 2(𝑙)

𝑌 2(𝑙 + 1)

=

𝜃1 𝑙

𝜃2 𝑙

𝜃3 𝑙

𝜃4 𝑙

𝚯(𝑙)

(6.18)

where 𝛼2 = 𝐻12𝑙

2+ 𝐻21

𝑙 2

+ 𝐻12𝑙+1

2+ 𝐻22

𝑙+1 2

𝛼3 = 𝐻13𝑙

2+ 𝐻23

𝑙 2

+ 𝐻14𝑙+1

2+ 𝐻24

𝑙+1 2 ,

114

𝛼4 = 𝐻14𝑙

2+ 𝐻24

𝑙 2

+ 𝐻13𝑙+1

2+ 𝐻23

𝑙+1 2 , 𝛼′𝑠 correspond to exploiting the resultant full

diversity branches over space and frequency. The 𝛽′𝑠 , 𝛾′𝑠 and 𝜂′𝑠 represent multiuser and

multistream interferences respectively as

𝛽2 = 𝐻12𝑙 ∗

𝐻14𝑙 + 𝐻22

𝑙 ∗𝐻24

𝑙 + 𝐻11𝑙+1𝐻13

𝑙+1∗+ 𝐻21

𝑙+1𝐻23𝑙+1∗

𝛾2 = 𝐻12𝑙 ∗

𝐻13𝑙 + 𝐻22

𝑙 ∗𝐻23

𝑙 − 𝐻11𝑙+1𝐻14

𝑙+1∗− 𝐻21

𝑙+1𝐻24𝑙+1∗

𝜂2 = 𝐻13𝑙 ∗

𝐻14𝑙 + 𝐻23

𝑙 ∗𝐻24

𝑙 − 𝐻14𝑙+1𝐻13

𝑙+1∗− 𝐻24

𝑙+1𝐻23𝑙+1∗

The estimate of the received subcarriers can be readily obtained by frequency

domain MMSE equalization as

𝒀 𝑀𝑀𝑆𝐸 𝑙 = (𝑯𝑒𝑞𝐻 (𝑙)𝑯𝑒𝑞 (𝑙) + 1/𝛾𝑠𝑰𝑲)−1𝑯𝒍

𝐻𝚯(𝑙) (6.19)

For flat fading channels and quasi static channels over every two successive

subcarriers 𝑯 𝑙 ≈ 𝑯 𝑙 + 1 , then the above scheme can apparently exploit the full

diversity of the CSM per user and also exclude the interstream interference. i.e. 𝜂1 = 𝜂2 =0 and the transmission matrix (6.18) can be relaxed to be a quasi orthogonal channel with

𝛽2 = 𝛽1∗, 𝛾2 = −𝛾1

∗ as scheme presented in 5.8

To apply the PIC-TEQ to the SFBC precoding presented in 6.4.2 then we will do

the first four steps of getting the 𝑦𝑘𝑖 𝑛 and statistical variance 𝜍𝑦

2 then DFT the output soft

symbols to have 𝒀 𝑑𝑒𝑐 (𝑙) which corresponds to soft estimate of all users‟ data carried on the

𝑙𝑡𝑕 subcarrier and start the soft PIC stage by reconstructing the interference and subtract it

from the channel symbols 𝚯(𝑙) in case of SFBC

𝒀𝑃𝐼𝐶𝑚 ,𝑛 𝑙 = 𝚯(𝑙) − 𝑯𝑒𝑞

𝑍−{𝑚}(𝑙)𝒀 𝑑𝑒𝑐

𝑍−{𝑚}(𝑙) (6.20)

where 𝑍 = 1, … ,4 are the set of symbols‟ indices and 𝑯𝑒𝑞𝑍−{𝑚}

are the columns of 𝑯𝑒𝑞 (𝑙)

except 𝑚𝑡𝑕 column of equivalent channel corresponding to 𝑚𝑡𝑕 user‟s channel. Then we

will perform filtering the output of PIC by soft combiner filter in (6.9),(6.10) .The output

of the soft PIC is fed to SISO demapper with the knowledge of 𝑳𝒂𝒅𝒆𝒄 of the zeroth

iteration.Steps are repeated iteratively for specific number of iterations or till the CRC has

been successful to minimize the complexity of PIC-TEQ

We can also provide the extension of IGML in section 6.4.2 to achieve better performance.

115

6.5.1.3 Results and discussions

Figure 69SFBC precoded 2x2 CSM with different MCS and equalization

Figure 69SFBC precoded 2x2 CSM with different MCS and equalization shows the

performance enhancement gains obtained upon using SFBC precoding of 2 users CSM

system and 2 receiving antennas for different MCS and the corresponding equalization

techniques. The results reveal that at target BER of 10-4

,the proposed PIC-TEQ with 3

iterations accompanied with SFBC precoding provides an impressive gains of 3,4.5 and

5dB over the ordinary 2x2 CSM system (dotted line) for QPSK 1/2 ,16QAM 3/4 and

64QAM 4/5 respectively. The figure also shows that the performance of the SFBC receiver

that uses the average channel gains, and ignores the multistream interference will have

slight degradation in performance when working along QPSK modulation (0.5dB) , while

the scheme will be more sensitive when working with 16QAM modulation (inferior by

2.5dB). Proposed TEQ outperforms the proposed MMSE receiver for SFBC precoding in

case of highly selective channels as (6.18) by 1, 1.8 and 2dB for QPSK, 16QAM and

64QAM respectively in expense of increasing the receiver complexity of the eNodeB.

Figure 70 shows the performance of turbo equalization based receiver while suiting

the receiver by 4 receiving antennas. The results show slight enhancements with respect to

the case of two antennas, because the SINR in case of 4 antennas is increased according to

the higher diversity order which will result in less possible interference cancellation gains.

-15 -10 -5 0 5 10 15 20 25

10-6

10-5

10-4

10-3

10-2

10-1

Eb/N

o

BE

R

spce frequency block code precoding with 2 users CSM

and 2 Tx antennas for each user , 2 antennas at the receiver

unprec. 1Tx 2Rx QPSK 1/2

unprec. 1Tx 2Rx 16QAM 3/4

unprec. 1Tx 2Rx 64QAM 4/5

SFBC 2Tx 2Rx QPSK 1/2 av eraging

SFBC 2Tx 2Rx QPSK 1/2 MMSE

SFBC 2Tx 2Rx QPSK 1/2 TEQ 3 iterat.

SFBC 2Tx 2Rx 16QAM 3/4 av erag.

SFBC 2Tx 2Rx 16QAM 3/4 MMSE

SFBC 2Tx 2Rx 16QAM 3/4 TEQ 3 iterat.

SFBC 2Tx 2Rx 64QAM 4/5 MMSE

SFBC 2Tx 2Rx 64QAM 4/5 TEQ 3 iterat.

64QAM 4/516QAM 3/4QPSK 1/2

116

Figure 70performance of SFBC precoding with 4 receiving antennas and corresponding equalization

techniques

Figure 71 TEQ iterations effect on SFBC precoded CSM with 2 receiving antennas Eb/No=11dB

-15 -10 -5 0 5 1010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

performance of SFBC precoding with 4 receiving antennas and corresponding equalization techniques

QPSK 1/2 TEQ 3 iterations

16QAM 3/4 MMSE averaging

16QAM 3/4 TEQ 3 iterations

16QAM 3/4 MMSE selective

64QAM 4/5 MMSE selective

64QAM 4/5 TEQ 3 itartions

0 1 2 3 410

-5

10-4

10-3

iterations

BE

R

TEQ iterations effect on SFBC with 2 receiving antennas

117

Figure 71 TEQ iterations effect on SFBC precoded CSM with 2 receiving antennas

Eb/No=11dB shows considerable BER enhancement while moving from MMSE

equalization (0 iterations) to TEQ with1 iteration. The enhancement gain decreases until it

becomes zero at 4 iterations.

Figure 72 Effect of channel selectivity on TEQ of the SFBC precoded CSM

Figure 72 Effect of channel selectivity on TEQ of the SFBC precoded CSM .It

shows that the modified MMSE equalizer presented here benefits from the channel

selectivity in contrast of the SFBC receiver presented in the previous chapter , However as

the selectivity increases , the multistream interference also increases and hence slightly

degrades the performance (as we moved from 5𝜇s to 15𝜇s selectivity). Results also show

that as the selectivity of the channel increases the TEQ gains compared with the MMSE

equalization become larger (0.8dB in case of flat fading in comparison with 1.8dB in case

of 5,15 𝜇s).

6.5.1.4 Advantages and disadvantages

Advantages

Tremendous precoding gain without need of CSI at the transmitter (5dB for 2

receiving antennas and 12dB for 4 receiving antennas)

Enhanced equalization gains using TEQ.

Enhancement in performance for moderate number of iterations (3 for example)

Less susceptible to channel selectivity with respect to the scheme in chapter 5.

-5 0 5 10 15 20 25 3010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Effect of channel selectivity on TEQ of SFBC precoded CSM

MMSE equalization flat fading

1 us MMSE

5 us MMSE

15 us MMSE

TEQ 3 iterations flat fading

5 us TEQ 3 iterations

15 us TEQ 3 iterations

118

Disadvantages

Excessive complexity of eNodeB receiver.

Increase complexity of the UE by employing 2 transmitting antennas

Degradation in performance in very high selectivity.

6.5.2 PIC-TEQ for Codebook and SVD precoded CSM

6.5.2.1 Motivation

To achieve the capacity maximizing precoding scheme, SVD precoding presented

in section 5.6 provides transmitting users‟ layers on the strongest eigenmodes provided full

CSI of the MIMO channel. In the case of limited CSI is only available or in case of

signaling the precoder from eNodeB, SVD precoding cannot be used and codebook

precoding presented section 5.7 is preferred. However, in CSM we can only provide an

individual precoding for each user alone which result in multiuser interference. Then, the

PIC-TEQ can be efficient multiuser equalization technique for separating users‟ data. So in

this section we will present how PIC-TEQ can be used as multiuser equalizer for precoded

CSM [85].

6.5.2.2 Algorithm description

Same PIC-TEQ can be used accompanied with the SVD and codebook precoding

with noting the following

First, the equivalent channel will be modified according the used precoding scheme

as in SVD precoding

𝑯𝒆𝒒 𝑙 = [𝑯𝒖𝒔𝒆𝒓 𝟏 𝑙 𝑽𝟏 𝑙 … 𝑯𝒖𝒔𝒆𝒓 𝑲 𝑙 𝑽𝑲 𝑙 ] (6.21)

And in case of codebook precoding the equivalent channel would be

𝑯𝒆𝒒 𝑙 = [𝑯𝒖𝒔𝒆𝒓 𝟏 𝑙 𝑭𝒖𝒔𝒆𝒓𝟏 𝑙 … 𝑯𝒖𝒔𝒆𝒓 𝑲 𝑙 𝑭𝒖𝒔𝒆𝒓𝑲 𝑙 ] (6.22)

Second , the cancellation procedure will be applied on channel symbols 𝑹 𝑙 in

case of having 𝑚𝑡𝑕 layer‟s data on 𝑙𝑡𝑕 subcarrier during the 𝑛𝑡𝑕 iteration in case of

codebook and SVD precoding as

𝒀𝑃𝐼𝐶𝑚 ,𝑛 𝑙 = 𝑹 𝑙 − 𝑯𝑒𝑞

𝑍−{𝑚}(𝑙)𝒀 𝑑𝑒𝑐

𝑍−{𝑚}(𝑙) (6.23)

where 𝑍 = {1,2, . . , 𝜌𝐾}. Then the rest of PIC-TEQ can be reused again.

119

6.5.2.3 Results and discussions

Figure 73 Codebook and SVD precoding for 16QAM ¾ transmission and different rank/antenna

configurations and 1 iteration TEQ

-15 -10 -5 0 5 10 15

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Eb/N

o

BE

R

codebook and SVD submatrix precoding

16QAM 3/4 for 2 users CSM

unprec. 1Tx 2Rx

unprec.rank 1 2Tx 4Rx

prec./unprec. rank 2 2Tx 4Rx

unprec. rank 1 4Tx 8Rx

unprec. rank 2 4Tx 8Rx

unprec. rank 3 4Tx 8Rx

prec./unprec. rank 4 4Tx 8Rx

codebook rank 1 2Tx 4Rx

codebook rank1 4Tx 8Rx

codebook rank 2 4Tx 8Rx

codebook rank 3 4Tx 8Rx

SVD rank 2 2Tx 4Rx

SVD rank 4 4Tx 8Rx

120

Figure 74 Comparison between presented precoding and equalization techniques for 16QAM ¾ rank 1

transmission

Figure 73 shows the performance of codebook and SVD precoded 2 users CSM

system when operating on fixed MCS (16QAM 3/4) with different rank and antenna

configurations and using MMSE receiver equipped by 4 receiving antennas and 1 iteration

PIC-TEQ. When users are equipped by 2 antennas, rank 1 codebook precoding achieves

2.5dB gain over the unprecoded (dotted line) system. For rank 2, transmission is equivalent

to unprecoded system, so no performance gain is achieved, however SVD precoding will

remarkably achieve a 9dB gain in expense of excessive CSI required at the transmitter

which requires unlimited feedback channel. Moreover , for users equipped by 4

transmitting antennas and 8 receiving antennas, rank 1 transmission will now having a

BER=10-4

at extremely low Eb/No (-2.5dB) and outperforms the unprecoded system by

3dB. For rank 2 codebook transmission the performance coincides with rank1 with 2

transmitting antennas. Rank 3codebook precoded system will achieve a 5dB gain over the

equivalent unprecoded system. SVD precoding for rank 4 transmissions will provide a

substantial precoding gain of 16dB.

Figure 74 demonstrates a comparison between all presented precoding and

equalization techniques for 16QAM ¾ rank1 transmission. The red dotted curve

corresponds to basic 2 users CSM system, the solid curves denote SFBC precoding

presented before in fig.1. The figure reveals that rank 1 codebook transmission

outperforms the SFBC precoding by 1, 1.2dB gains for MMSE and TEQ receivers

respectively. The gain achieved here in expense of the feedback channel required for the

codebook precoding in comparison with zero CSI required in case of SFBC. The leftmost

curves correspond to same results with 4 receiving antennas. The figure shows that because

of high diversity order of the channel the TEQ performance gains will be decreased to

-5 0 5 10 15 20

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Eb/N

o

BE

R

Comparison between differenr rank 1 precoding for

16QAM 3/4 transmission 2 users CSM system and their corresponding receivers

reference CSM 1Tx 2Rx

SFBC 2Tx 2Rx averaging

SFBC 2Tx 2Rx MMSE

SFBC 2Tx 2Rx TEQ 3 iterat.

SFBC 2Tx 4Rx averaging

SFBC 2Tx 4Rx TEQ 3 itera.

SFBC 2Tx 4Rx MMSE

codebook 2Tx 2Rx MMSE

codebook 2Tx 2Rx TEQ 3 iterat.

codebook 2Tx 2Rx TEQ+ML

codebook 2Tx 4Rx MMSE

codebook 2Tx 2Rx TEQ+ML

121

0.3dB. The purple curves show the IGML gain boost. The IGML gives a 0.7dB boost over

the TEQ in expense of excessive receiver complexity

Figure 75 PIC-TEQ of codebook precoded CSM of 2 users of with 2Tx antennas and 2 Rx antennas

with different MCS

Figure 75 shows the performance of PIC-TEQ of codebook precoded CSM of 2 users of

with 2 transmitting antennas and 2 receiving antennas with different MCS. The figure

shows 1.2dB, 2.5dB and 2dB for QPSK, 16QAM and 64QAM respectively.

Figure 76 shows the effect of channel selectivity on the performance of codebook

precoded CSM of rank 1 with 2 transmitting antennas and 2 Rx antennas with 16QAM 3/4

MCS. The figure shows the same effect of selectivity on PIC-TEQ of unprecoded CSM.

Figure 77 shows the TEQ iterations effect for ordinary, SFBC and rank 1 codebook

transmission at 11dB. The results show that the TEQ performance will saturate after few

iterations (3 or 4), this occurs due to positive feedback phenomenon. The figure also

shows that in case of unprecoded system, the 11dB is not sufficient to produce reliable a

posteriori decisions, so the system will saturate from the first iteration (0 iteration means

MMSE only).

-10 -5 0 5 10 15 20 2510

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

RPIC-TEQ for rank 1 codebook transmission with 2 Tx ant. and 2 Rx ant

CSM system with 2 users working with different MCS

QPSK 1/2 MMSE

16QAM 3/4 MMSE

64QAM 4/5 MMSE

QPSK 1/2 TEQ 3 iterations

16QAM 3/4 TEQ 3 iterations

64QAM 4/5 TEQ 3 iterations

122

Figure 76 Effect of channel selectivity on the performance of codebook precoded CSM of rank 1 with 2

transmitting antennas and 2 Rx antennas with 16QAM 3/4 MCS

Figure 77 TEQ iterations effect for ordinary, SFBC and rank 1 codebook transmission at 11dB

-5 0 5 10 15 20 25 30 35 4010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

o

BE

R

Effect of channel selectivity on the performance of codebook precoded CSM of rank 1

2 Tx ant. and 2 Rx ant,

flat fading MMSE

1us MMSE

15us MMSE

flat fading TEQ 3 iterations

1 us TEQ 3iterations

15us TEQ 3 iterations

0 1 2 3 410

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Eb/N

o

BE

R

Effect of changing numebr of iterations for TEQaccomapnyingthe presented precoding schems for 16QAM 3/4 transmission at E

b/N

0=11dB

unprecoded 1Tx 2Rx CSM

SFBC 2Tx 2Rx CSM

codebook 2Tx 2Rx rank 1

Iterations

123

6.5.2.4 Advantages and disadvantages

Advantages

Different ranks can be supported which instructs of adaptive rank selection.

Limited feedback signaling.

Precoder can be selected by the eNodeB

Tremendous equalization gains by using TEQ.

Disadvantages

Needs CSI at the transmitter

Excessive receiver complexity

6.6 Conclusions

In this chapter, we have presented TEQ as promising technique of separating

combined users‟ data in CSM system.

We focused on the soft parallel successive interference cancellation (PIC-TEQ) to

exploit the soft information attained by MMSE equalization.

The PIC-TEQ achieves a better power efficiency upto 5dB for moderate selective

channels and moderate MCS.

We also provide novel single user ML extension to be added after the PIC-TEQ as

performance booster. It will achieve a performance gain by extra 0.5dB over the

PIC-TEQ with just straight path PIC (one iteration)

Better performance gains can be achieved if precoded CSM is used, so we have

discussed the application of PIC-TEQ and its ML add-on to the precoded CSM

system.

The chapter also presents a detailed derivation for MMSE receiver of SFBC in

highly selective channels.

It was shown that PIC-TEQ assisted SFBC precoded CSM system is slightly

inferior from same order codebook precoding in the expense of no CSI is needed.

124

CCHHAAPPTTEERR SSEEVVEENN

CCOONNCCLLUUSSIIOONN AANNDD FFUUTTUURREE WWOORRKK

7.1 Conclusion

In this thesis, the CSM system is proposed to increase the capacity of the LTE UL.

We have proposed a near-ML receiver (IGML) which exploits the full diversity of the

inherent frequency and spatial diversity of the virtual MIMO links. The scheme achieves

almost 5dB power efficiency gains over the multiuser MMSE equalization technique in

expense of exponential complexity which leads to intractable complexity in case 64QAM.

We have also presented a simplified version of it based on the QR decomposition of the

channel matrix which solves the ML problem in linear complexity scheme with negligible

power efficiency loss in case of QPSK and 16QAM.We also proposed two ordering

techniques to enhance the SIC receiver. Results show a considerable enhancement of

power efficiency in case of shadowing environments and negligible performance gains in

case of power controlled systems when using these ordering techniques. The results

suggests to using IGML receiver or its simplification in a sense of reliable transmission

.On the other hand, the thesis results advise to use the collaborative system in low speed,

MMSE channel estimation, highly selective channels with equipping the eNodeB by

number of receiving antennas exceeds the number of collaborative users.

We have also exploited the multiple transmitting antennas in the uplink of the LTE-

advanced. We have introduced a blind SFBC-based precoding which doesn‟t need any

channel knowledge at the transmitter and derived a suitable receiver for it. We concluded

that SFBC precoding performance almost coincides with codebook precoding for flat

fading channel, the performance of the SFBC precoding degrades in case of moderate and

high selective channels because of the assumption of flat channel gains over each two

successive subcarriers. On the contrary, we compared three selection methods for suitable

precoders and we found that the submatrix precoding technique outperforms the others

because it exploits the full diversity of the MIMO channel. The performance of the

codebook precoding is enhanced in case of high selective channel because an extra

diversity source (frequency) exists. Also we introduce suboptimal SVD precoding for each

of the collaborative users. Also the resultant spectral efficiencies are shown to exceed the

target spectral efficiency of the LTE-advanced (15bits/s/Hz). The results instruct using

adaptive precoding scheme that uses SFBC based precoding for low and medium selective

channel. As selectivity increases, use the adaptive rank codebook transmission using the

submatrix selection method. Finally as SNR is sufficiently high to use the full rank of the

MIMO channel you can use the SVD-based precoding.

Moreover, we have presented the turbo equalization technique (TEQ) as promising

technique of separating combined users‟ data in CSM system. We focused on the soft

parallel successive interference cancellation (PIC TEQ) to exploit the soft information

attained by MMSE equalization. The PIC-TEQ achieves a better power efficiency upto

5dB for moderate selective channels and moderate MCS. We also provide novel single

user ML extension to be added after the PIC-TEQ as performance booster. It will achieve a

performance gain by extra 0.5dB over the PIC-TEQ with just straight path PIC (one

iteration) .Better performance gains can be achieved if precoded CSM is used, so we have

discussed the application of PIC-TEQ and its ML add-on to the precoded CSM system.

125

The chapter also presents a detailed derivation for MMSE receiver of SFBC in highly

selective channels. It was shown that PIC-TEQ assisted SFBC precoded CSM system is

slightly inferior from same order codebook precoding in the expense of no CSI is needed.

7.2 Future work

Detailed mathematical analysis of the proposed detection schemes (IGML QR-

IGML and PIC-TEQ).

Study of the effect of the frequency hopping technique on the CSM system.

Exploiting the orthogonal characteristics of the Zad-off Chu sequences in case of

the imperfect channel estimation of the CSM system.

Proposing and studying other detection schemes like belief propagation, greedy

search and ML sequence estimators.

Derivation of conditions of optimal power allocations of users and optimal

reference signal arrangements.

Proposing a joint technique that combine collaborative MIMO system with

cooperative algorithms like (Amplify and forward, decode and forward …etc.)

Proposing a blind precoding scheme that don‟t need the knowledge of the other

user data and still exploiting the full channel matrix knowledge in case CSM

system.

Discussing the imperfections of the CSM receiver like frequency offset error, phase

shift error, users‟ channel correlation …. Etc.

Studying the user pairing choice of the collaborative users.

126

AAPPPPEENNDDIIXX 11

LLIISSTT OOFF PPUUBBLLIICCAATTIIOONNSS

[1] Karim A. Banawan, Essam Sourour “Enhanced SIC and Initial guess ML receivers

for collaborative MIMO of the LTE Uplink”, Vehicular Technology Conference

(VTC2011-Fall), Sept. 2011.

[2] Karim A. Banawan, Essam Sourour “Combined Collaborative and Precoded

MIMO for Uplink of the LTE-Advanced”, The 29th

National Radio Science

Conference (NRSC 2012), pp.523-531, April 2012.

[3] Karim A. Banawan, Essam Sourour “Turbo Equalization of Precoded Collaborative

MIMO for the Uplink of LTE-advanced”, International Conference on Computing,

Networking and Communications (ICNC 2013), submitted.

127

RREEFFEERREENNCCEESS AANNDD BBIIBBLLIIOOGGRRAAPPHHYY

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لقى الفصل الضوء على أنواع الكواشف . الترددات االنتقائة والمسطحة سواء فى حالة الخبو السرع او البطئ

مع عقد مقارنات للمزاا والعوب الخاصة بكل كاشف فى مختلف الحالة للنظم متعددة المداخل والمخارج التشاركة

.سناروهات المحاكاة مع األخذ فى االعتبار حالتى تقدر القناة المكتمل وغر المكتمل

نقدم أول إسهاماتنا التى تتلخص فى إبتكار كاشف جدد عتمد على التخمن األولى لإلحتمالة : الفصل الرابع

وتناسب تعقد . متعددة المداخل والمخارج التشاركة نظمالأداء بشكل كبر من الذي عزز (IGML)القصوى

. (QR) لهذا الكاشف باستخدام تحلل اعرض الفصل أضا تبسط.الكاشف ذو التخمن االولى مع مؤشر التعدل فقط

خصوصا عند (SIC)زادة على ذلك سوف نقدم نوعن جددن لطرق الترتب فى لكاشف اإللغاء المتعاقب للتداخل

ونعرض فى هذا الفصل دراسة وافة لدوافع ابتكار كل كاشف ودراسة تأثر عوب القناة و .حدوث ظاهرة التظلل

.ها المختلفةتحاال

بدأ الفصل بدراسة التطورات الجددة للنظم متعددة المداخل والمخارج فى الوصلة الصاعدة لنظام الفصل الخامس

و ناقش الفصل استخدام . (precoding)المطورونقدم فى بداته عرض موجز لنظرة التكود السابق " ال تى اى"

من ثم . المطورلإلستفادة من مزاا التكود السابق لإلرسال" ال تى اى"كتب التكود السابق فى الوصلة الصاعدة لنظام

ثم نقدم ابتكارا جددا لمزج النظم .نقدم التعدالت على نموذج النظام الرئسى الذى تم عرضه فى الفصل الثالث

او (SVD precoding)المتعددة المداخل والمخارج التشاركة مع تقنة التكود السابق سواء فى الحالة المثالة

زادة على اقتراح مزج الترمز الفراغى الترددى مع النظم متعددةالمداخل والمخارج . بإسخدام كتب التكود السابق

التشاركة للحصول على مزاا التنوع الفراغى الناتج من الترمز باالضافة لمزاا النظم التشاركة و نتهى الفصل

بدراسة تأثر التكود السابق على الكواشف السابق ذكرها

كتقنة معادلة للنظم متعددة المستخدمن فى النظم متعددة (TEQ) قدم الفصل نظام معادلة التربوالفصل السادس

فى هذه التقنة سوف نستخدم القرارات اللنة للحصول على مكاسب األداء الهائل . المداخل والمخارج التشاركة

حث تقوم تقنة معادلة التربو على أساس خوارزمة مشتركة للمعادلة وفك التكود بطرقة .للتكود بترمز التربو

بهذه . تكرارةحث تم فها تمرر القرارات اللنة الناتجة من المعادل اللن الى جهاز فك التكود اللن والعكس بالعكس

التقنة من شأنها تحسن االداء العام للنظم متعددة المداخل والمخارج التشاركة على حساب زاد تعقد وتأخر جهاز

و تناول الفصل االجزاء الرئسة فى تقنة معادلة التربو ثم درس كفة تطبق هذا المفهوم فى النظم متعدد . اإلستقبال

المداخل والمخارج سابقة التكودالمعروضة فى الفصل الخامس وتعمم نظام معادلة التربو للترمز الفراغى الترددى

. للنظم التشاركة فى قنوات الخبو ذات الترددات االنتقائة

. المستقبل ف ستأنف أن مكن الذي للعمل تقدم و للرسالة خالصة هوالفصل السابع

العربىالعربى الولخصالولخص

فى هذه الرسالة تمت دراسة تطبق النظم متعددة المداخل والمخارج التشاركة وتقنة معادلة التربو على الوصلة

هو تطورللنظام العالمى لإلتصاالت المتنقلة (LTE) "ال تى اى" نظام عتبر.المطور" ال تى اى"الصاعدة لنظام

(UMTS) فى اإلصدار الثامن " ال تى اى"وقد تم تطور نظام . بإتجاه الشبكات المستخدمة لبروتوكول اإلنترنت

المطور فى " ال تى اى"والتاسع من مشروع الشراكة لشركات الجل الثالث ثم جرى تحسنه للحصول على نظام

ملون رمز 300تحقق معدالت نقل بانات " ال تى اى"اإلصدارات األولى لنظام . اإلصدارن العاشر والحادى عشر

مللى ثانة و زادة ملحوظة فى كفاءة استخدام الطف الترددى مقارنة بنظم 5 فى الثانة وتأخر للشبكة اقل من ثنائى

والتقسم FDD))كال من نظام التقسم الترددى للوصلتن " ال تى اى"دعم نظام . اإلتصاالت الخلوة االخرى

باالضافة لمختلف الحزات الترددة المتاحة وعتبر هذا النظام خطوة مهمة بإتجاه متطلبات (TDD)الزمنى للوصلتن

.الجل الرابع لشبكات المحمول

لقد لفتت النظم متعددة المداخل والمخارج النظر نتجة المزاا الهائلة التى تزكها كتقنة محورة فى شبكات الجل

الرابع وتشمل هذه المزاا مكسب المجموعة و مكسب التنوع الفراغى والدمج الفراغى الى جانب إنقاص التداخل و

وعلى الرغم من ذلك فالنظم . الزاده الهائلة فى السعة اإلستعابة للقنوت الالسلكة نتجة تكون قنوات السلكة مستقلة

متعددة المداخل والمخارج تحتاج ألجهزة إرسال وإستقبال ذات نظم معالجة اشارات معقدة باإلضافة إلى صعوبة

" ال تى اى"التنفذ الواقعى لهوائات متعددة داخل جهاز صغرفى الوصلة الصاعدة ألجهزة المستخدمن فى نظام

ولذلك ظل التحدى فى استخدام هوائى واحد و بطارة محدودة القدرة وتحقق أداء مرتفع عند تصمم الوصلة

(CSM)هذه كانت الدوافع وراء التفكر فى النظم متعددة المداخل والمخارج التشاركة " . ال تى اى"الصاعدة لنظام

وعمل هذا النظام بمعاونة اثنن او اكثر من المستخدمن كالهما مزود بهوائى واحد او أكثر وكل منهما رسل دفقة .

. (نفس التردد ونفس الوقت)هذه الدفقات ستم إرسالها تشاركا على نفس الموارد المتاحة .بانات مستقلة عن األخرن

بإستقبال كل البانات من كل المستخدمن المشاركن و فك البانات الخاصة (eNodeB)وتقوم العقدة ب المطورة

.بكل مستخدم بإستخدام أسالب معادلة متعددة المستخدمن

:وفيما يلى ملخص عما تم فى كل باب

والنظم متعددة المداخل والمخارج التشاركة و نظام " ال تى اى"وتقدم لنظام ال للرسالة مقدمة عرض األول الفصل

.معادلة التربو

" ال تى اى"وقدم مراجعة تفصلة حول خطوات معالجة القناة المشتركة للوصلة الصاعدة لنظام ال الثاني الفصل

وإختالفتها (SC-FDMA)ستخدام التردد الناقل األوحدإونتناول اضا مراجعة تفصلة لتقنة تعدد طرق الوصول ب

باالضافة الى تقدم مقارنات بن الطرق المختلفة لرسم خرائط (OFDMA)عن النظم متعددة الحوامل المتعامدة

الفصل قدم اضا دراسة موجزة عن خصائص نقل البانات و شكل . الترددات الناقلة والتمثل الزمنى لكل منها

.اإلشارات المستخدمة فى إستخالص البانات

نموذج بناء نشرع ف ثم .شاركةالتالنظم متعددة المداخل والمخارج إدخال مفهوم مع نبدأ : الفصل الثالث

النظم حالة من ف كل نموذج المحاكاة تم دراسة . الرسالةساق ف جمع أنحاء ستخدامهإي ستم ذال األساس النظام

اإلرسال هوائاتمن شاركةألى عدد الت النظم متعددة االدخال واالخراج ذات المدخل والمخرج الوحد وحالة

المستخدم بما شمله من أثار ظاهرة التظلل وقنوات الخبو ذات قناةال نموذج وصف مع واصلنا ومن ثم ستقبال،واإل

: لجنت االشراف

.……………...…عصام عبد الفتاح سرور / د.ا

تطبيقات النظم متعددة المداخل والمخارج التشاركية وتقنية معادلة التربو فى المطور " ال تى اى"الوصلة الصاعدة لنظام

هقذهت هي

كرين أحوذ ساهى عبذ الوحسي أحوذ بنواى

الواجستير فى العلوم الهنذسيت

فى

الهنذست الكهربيت

لجنة المناقشة والحكم على الرسـالـة موافقون

. سعيد محمد النوبى /د.أ .1 .......................

.عصام عبد الفتاح سرور/د.أ .2 .......................

. أيمن يحيى على العزبى/ د.أ .3 .......................

وكل الكلة للدراسات العلا والبحوث

جامعة االسكندرة – كلة الهندسة

هبة وائل لهطة .د.أ

تطبيقات النظم متعددة المداخل والمخارج التشاركية وتقنية معادلة التربو فى المطور" ال تى اى"الوصلة الصاعدة لنظام

رسالت علويت

جاهعه االسكنذريت– الى الذرساث العليا بكليت الهنذست هقذهت

استيفاء للذراساث الوقررة للحصول على درجت

الواجستير فى العلوم الهنذسيت

فى

الهنذست الكهربيت

هقذهت هي

كرين أحوذ ساهى عبذ الوحسي أحوذ بنواى

2012سبتوبر