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REDUCTION OF PEAK-TO-AVERAGE POWER RATIO
IN ORTHOGONAL FREQUENCY DIVISION
MULTIPLEXING
Farzana Rauf
Doctor of Philosophy
In
Electronic Engineering
MEHRAN UNIVERSITY OF ENGINEERING & TECHNOLOGY
JAMSHORO
October, 2016
i
REDUCTION OF PEAK-TO-AVERAGE POWER RATIO IN
ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING
A thesis submitted by
Farzana Rauf
In fulfillment of the requirements for the degree of
Doctor of Philosophy
In
Electronic Engineering
Department of Electronic Engineering
Institute of Information and Communication Technologies
Faculty of Electrical, Electronic and Computer System Engineering
Mehran University of Engineering and Technology
Jamshoro
October, 2016
ii
Dedicated to
my loving parents
who brought me on this earth,
my respected teachers, and
Worthy Vice Chancellor Dr. Usman Ali. G. Issani,
Iqra University Karachi,
who raised me up to sky.
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MEHRAN UNIVERSITY OF ENGINEERING & TECHNOLOGY
JAMSHORO
This thesis, written by Ms. Farzana Rauf Abro under the direction of her supervisors,
and approved by all the members of the thesis committee, has been presented to and
accepted by the Dean, Faculty of Electrical, Electronic and Computer Systems
Engineering, in fulfillment of the requirements of the degree of Doctor of Philosophy
in Electronic Engineering.
________________________ ___________________
Supervisor Co-supervisor
Prof. Dr. Manzoor Ahmed Hashmani Prof. Dr. Mukhtiar Ali Unar
____________________ ___________________
Internal Examiner External Examiner
____________________ ___________________
Co-Director IICT Director IICT
Prof. Dr. Zubair Ahmed Memon Prof. Dr. Mukhtiar Ali Unar
Mehran UET, Jamshoro Mehran UET, Jamshoro
__________________________________
Prof. Dr. Bhawani Shankar Chowdhury
(Dean Faculty of Electrical, Electronic and
Computer Systems Engineering)
Date: ______________________
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ACKNOWLEDGEMENTS
First of all I would like to thank Almighty Allah for giving me understanding,
intelligence and everything. I needed to finish up my research work with full
concentration and motivation.
Initially, with great respect, I would like to thank my supervisor Prof. Dr. Manzoor
Ahmed Hashmani, Director (Research and Publication), Faculty of Engineering,
Sciences, and Technology, Iqra University, Main Campus, Karachi who is first of all a
great man, a great engineer and a great team leader. I would have never dreamt of being
successful in this Ph.D. research work without his visionary guidance and mentoring.
He has been a continuous contributor of innovative ideas and knowledge throughout
my research work. He is no doubt the best resource; MUET has provided me for the
Ph.D. research.
I am also grateful to my respected co-supervisor, Prof. Dr. Mukhtiar Ali Unar,
Director Institute of Information and Communication Technologies, MUET, who has
always been a source of inspiration and who has critically judged and guided me during
my research. His expertise in this field and valuable observations has been very useful.
I have been fortunate to do Ph.D. in his kind Co-supervision.
I appreciate open heartedly cooperation and facilities provided by the Faculty of
Electrical, Electronic, and Computer Systems Engineering (FEECE) and the Institute
of Information and Communication Technologies (IICT). I am thankful heartedly to
Prof. Dr. Bhawani Shankar Chowdhry, Dean FEECE, Prof. Dr. Mukhtiar Ali
Unar, Director IICT and Prof. Dr. Zubair Ahmed Memon, Co-director IICT for their
phenomenal encouragement and immense cooperation. I would like to express sincere
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gratitude to my beloved father Abdul Rauf Abro for his selfless support and guidance
during my Ph.D. research. His advices and guidelines had assisted me in many difficult
situation faced for completion of the thesis.
I especially appreciate the support and guidance provided by the Worthy Vice
Chancellor Dr. Usman Ali. G. Issani, Iqra University Karachi and Prof. Dr. Imtiaz
Hussain Kalwar for their special attention towards me during my Ph.D. Their
encouragement and guidance had always been source of motivation for me to complete
this Ph.D. research.
This research work is carried out at Mehran University of Engineering and Technology
(MUET) and I gratefully acknowledge MUET for providing me the opportunity to
study in a very interesting and challenging research area of security issues in wireless
sensor networks.
A portion of my research work has been carried out at University of Limerick, Ireland,
where I did my Ph.D. research for twelve months under the scholarship of Erasmus
Mundus Mobility for Life from 10th August 2013 to 11th September 2014. I am grateful
to my professors at University of Limerick, Ireland, Prof. Dr. Sean McGrath and
Prof. Dr. Elfed Lewis, Department of Electronic and Computer Systems Engineering,
for their guidance and support during this research.
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TABLE OF CONTENTS
Description Page
Acknowledgements (iv)
Table of Contents (vi)
List of Abbreviation (x)
List of Tables (xiii)
List of Figures (xiv)
Abstract (xvii
Chapter 1 INTRODUCTION 01
1.1 Rationale and Motivation 01
1.2 Research goal and Objectives 02
1.3 Structure of Dissertation 03
Chapter 2 ORTHOGONAL FREQUENCY DIVISION
MULTIPLEXING
06
2.1 Introduction to OFDM 06
2.2 Applications and Usage 07
2.2.1 ADSL 07
2.2.2 Wireless Local Area Networks (LAN), Metropolitan
Area Networks (MAN), and Personal Area Network (PAN)
07
2.2.3 Digital Video Broadcasting (DVB) 08
2.2.4 Digital Radio 08
2.2.5 Flash-OFDM (FOFDM) 09
2.3 Advantages and Disadvantages 09
2.3.1 Advantages 09
2.3.2 Disadvantages 10
2.4 Principles of Operation 10
2.4.1 Orthogonality 10
2.4.2 Implementation using FFT Algorithm 11
2.4.3 Guard Interval 12
2.4.4 Channel Coding and Time/Frequency Interleaving 13
2.4.5 Adaptive Transmission 14
2.4.6 OFDM with Multiple Access 14
2.4.7 Linear Transmitter Power Amplifier 15
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2.5 Efficiency Comparison between Single Carrier and Multi-
carrier OFDM Systems
16
2.6 System Model 18
2.6.1 Transmitter 18
2.6.2 Receiver 19
2.7 Mathematical Description 20
Chapter 3 REDUCTION OF PEAK-TO-AVERAGE POWER RATIO 22
3.1 Introduction 22
3.2 High Power Amplifier 23
3.2.1 Soft Limiter Power Amplifier 23
3.2.2 Solid State Power Amplifier 24
3.2.3 Travelling wave tube 24
3.3 PAPR Defined 24
3.4 Well Known PAPR Reduction Schemes 26
3.4.1 Signal Scrambling Schemes 26
3.4.1.1 Selective Mapping (SLM) 26
3.4.1.2 Partial Transmit Sequence (PTS) 28
3.4.1.3 Tone Reservation (TR) 29
3.4.1.4 Tone Injection (TI) 29
3.4.1.5 Interleaving Technique 30
3.4.2 Signal Distortion Schemes 31
3.4.2.1 Clipping and Filtering 31
3.4.2.2 Peak Reduction Carrier 32
3.5 Summary 33
Chapter 4 PERFORMANCE EVALUATION AND ANALYSIS
OF PAPR REDUCTION SCHEMES
35
4.1 Analysis of PAPR Reduction Schemes Through
Literature Survey
35
4.1.1 Clipping and Filtering Scheme 36
4.1.2 Coding Scheme 37
4.1.3 Peak Reduction Carriers Scheme 38
4.1.4 Envelope Scaling Scheme 39
4.1.5 PTS and SLM Schemes 39
4.1.6 Interleaving scheme 45
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4.1.7 Tone Reservation and Tone Injection Schemes 45
4.1.8 Active Constellation Extension Scheme 47
4.1.9 Comparison of PAPR Reduction Scheme 49
4.2 Performance Evaluation and Analysis of Selected
Mapping PAPR Reduction Schemes through Simulation
49
4.2.1 Motivation for Using Tone Reservation (TR) 51
4.2.2 Simulation Results on Performance of TR 52
4.2.3 PAPR Reduction Using Selective Mapping (SLM) 62
4.2.3.1 Motivation for Using Selective Mapping (SLM) 62
4.2.3.2 Selective Mapping (SLM) 62
4.2.3.3 Simulation Results and Discussion 64
4.2.3.4 Performance Analysis of SLM 65
4.3 Chapter Summary and Conclusion 69
Chapter 5 PROPOSAL OF A NOVEL PAPR REDUCTION
SCHEME BASED ON MNKB-RBF
70
5.1 Issue of SLM (Optimization Problem) 70
5.2 ANN (Artificial Neural Networks) and RBF (Radial Basis
Function)
70
5.3 Conventional RBF 73
5.4 A Recently Proposed “Novel Kernel Based RBF
(NKB-RBF)”
75
5.5 Issues of NKB-RBF 76
5.6 Proposed Solution: Modified NKB-RBF (MNKB-RBF) 78
5.7 Proposal of a Novel PAPR Reduction Scheme Based on
MNKB-RBF
79
5.8 Chapter Summary and conclusion 81
Chapter 6 PERFORMANCE EVALUATION OF PROPOSED PAPR
REDUCTION SCHEME
82
6.1 Performance Evaluation Environment 83
6.2 Simulation Environment and Test Cases 83
6.2.1 Regarding Datasets 83
6.2.2 Regarding Test Cases 84
6.3 Core Code of the Proposed Algorithm 84
6.4 Training Results 86
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6.4.1 Evaluation, Analysis, and Deductions 87
6.5 Testing Results 93
6.5.1 Evaluation, Analysis, and Deductions 94
6.5.2 Probability of Selecting Carrier of Low PAPR 100
6.6 Chapter Summary and Conclusion 102
Chapter 7 SUMMARY AND CONCLUSION 103
7.1 Summary 103
7.2 Conclusion 104
7.3 Future Work/Research Guideline 105
References 107
x
LIST OF ABRIVIATIONS
ACE = Active Constellation Extension
ADC = Analog to Digital Converter
ADSL = Advanced Digital Subscriber’s Line
AM = Amplitude Modulation
ANN = Artificial Neural Networks
BER = Bit Error Rate
BPSK = Binary Phase Shift Keying
BRAN = Broadcast Radio Access Network
CBC = Complement Block Coding
CC = Cyclic Coding
CCDF = Complementary Cumulative Distribution Function
CCI = Co-Channel Interference
CD = Cosine Distance
CDF = Cumulative Distribution Function
CDMA = Code Division Multiple Access
CF = Clipping and Filtering
CP = Cyclic prefix
COFDM = Coded Orthogonal Frequency Division Multiplexing
DAC = Digital-to-Analogue Converter
DMT = Discrete Multi-tone
DRM = Digital Radio Mondiale
DSL = Digital Subscriber’s Line
DVB = Digital Video Broadcasting
DS = Doppler Shift
ED = Euclidean Distance
ETSI = European Telecommunications Standards Institute
FEC = Forward Error Correction
FFT = Fast Fourier Transform
FOFDM = Flash Orthogonal Frequency Division Multiplexing
FPGA = Field Programmable Gate Array
FVs = Feature Vectors
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Giga Hertz = GHz
Hz = Hertz
IBO = Input Back-off
ICI = Inter Channel Interference
HPA = High Power Amplifier
IEEE = Institute of Electrical and Electronic Engineers
IFFT = Inverse Fast Fourier Transform
ISI = Inter-Symbol Interference
LAN = Local Area Network
LDPC = Low Density Parity Check
LTE = Long Term Evolution
MAN = Metropolitan Area Networks
MCBC = Modified Complementary Block Coding
MHz = Mega Hertz
MIPS = Million Instructions Per Second
MNKB-RBF = Modified Novel Kernel Based Radial Basis Function
NKB-RBF = Novel Kernel Based – Radial Basis Function
OFDM = Orthogonal Frequency Division Multiplexing
OFDMA = Orthogonal Frequency Division Multiple Access
PAN = Personal Area Networks
PAPR = Peak-to-Average Power Ratio
P/S = Parallel-to-Serial Conversion
PM = Phase Modulation
PRC = Peak Reduction Carrier
PSK = Phase-Shift Keying
PTS = Partial Transmit Sequence
QAM = Quadrature Amplitude Modulation
QoS = Quality of Service
QPSK = Quadrature Phase Shift Keying
RBF = Radial Basis Function
S/P = Serial-to-Parallel Conversion
SBC = Simple Block Coding
SII = Side Information Index
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SNDR = Signal-to-Noise-plus-Distortion Ratio
SLM = Selective Mapping
SNR = Signal-to-Noise Ratio
SL = Soft Limiter
SSPA = Solid State Power Amplifier
SVM = Support Vector Machine
TR = Tone Reservation
TWT = Travelling Wave Tube
UMB = Ultra-Mobile Broadband
UWB = Ultra-Wideband
VHF = Very High Frequency
VDSL = Very-high-speed Digital Subscriber Line
WRAN = Wireless Regional Area Network
WiMAX = Worldwide interoperability for Microwave Access
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LIST OF TABLES
Description Page
Table 2.1 Performance Comparison between Single and Multicarrier 17
Table 3.1 Classification of Major PAPR Reduction Schemes 26
Table 3.2 Performance of PAPR Reduction Techniques 33
Table 4.1 Comparison of Different PAPR Reduction Schemes 49
Table 4.2 Different PRC Sum Variable Combinations 53
Table 4.3 PAPR Levels in dBs for OFDM Symbol Candidate Combination 65
Table 5.1 Criteria for Selection (Manual) of Mining Parameters α1 and α2 77
Table 6.1 Final Mean Square Error (MSE) Comparison 88
Table 6.2 Probability of Selecting Carrier of Low PAPR 101
xiv
LIST OF FIGURES
Description Page
Figure 2.1 OFDM Transmitter Model 18
Figure 2.2 OFDM Receiver Model 19
Figure 3.1 Block Diagram of SLM Scheme 27
Figure 3.2 Block Diagram of PTS Scheme 28
Figure 3.3 Block Diagram of Interleaving Scheme 31
Figure 4.1 PAPR distribution when “Clipping and Filtering Scheme” is
used
37
Figure 4.2 PTS Scheme Block Diagram 40
Figure 4.3(a) CCDF for PAPR of OFDM with and without PTS 41
Figure 4.3(b) CCDF for PAPR of OFDM with and without PTS 42
Figure 4.4 Block Diagram of SLM Scheme 43
Figure 4.5(a) CCDF for PAPR of OFDM with and without SLM 44
Figure 4.5(b) CCDF for PAPR of OFDM with and without SLM 44
Figure 4.6(a) PAPR of Tone Reservation, 12 Sub-Carriers, and 4 Peak
Cancellation Sub-Carriers
46
Figure 4.6(b) PAPR of Tone Reservation, 12 Sub-Carriers, and 4 Peak
Cancellation Sub-Carriers
47
Figure 4.7 The ACE Scheme for QPSK Modulation 48
Figure 4.8 TR-OFDM signal for -r1-r2-r3-r4 combination 54
Figure 4.9 TR-OFDM signal for -r1-r2-r3-r4 combination 54
Figure 4.10 TR-OFDM signal for +r1+r2-r3-r4 combination 55
Figure 4.11 TR-OFDM signal for -r1-r2+r3+r4 combination 55
Figure 4.12 TR-OFDM signal for -r1-r2-r3+r4 combination 56
Figure 4.13 TR-OFDM signal for -r1+r2+r3+r4 combination 56
Figure 4.14 TR-OFDM signal for +r1-r2-r3-r4 combination 57
Figure 4.15 TR-OFDM signal for +r1-r2-r3+r4 combination 57
Figure 4.16 TR-OFDM signal for +r1+r2+r3-r4 combination 58
Figure 4.17 TR-OFDM signal for -r1+r2-r3+r4 combination 58
Figure 4.18 TR-OFDM signal for +r1+r2+r3-r4 combination 59
Figure 4.19 TR-OFDM signal for +r1-r2+r3+r4 combination 59
Figure 4.20 TR-OFDM signal for +r1+r2-r3+r4 combination 60
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Figure 4.21 TR-OFDM signal for -r1+r2-r3-r4 combination 60
Figure 4.22 TR-OFDM signal for -r1-r2+r3-r4 combination 61
Figure 4.23 TR-OFDM signal for -r1+r2+r3-r4 combination 61
Figure 4.24 Block Diagram for SLM Scheme for OFDM System 63
Figure 4.25 CCDF graph for PAPR of OFDM with and without SLM 66
Figure 4.26 CCDF graph for PAPR of OFDM with and without SLM 66
Figure 4.27 CCDF graph for PAPR of OFDM with and without SLM 67
Figure 4.28 CCDF graph for PAPR of OFDM with and without SLM 67
Figure 4.29 CCDF graph for PAPR of OFDM with and without SLM 68
Figure 4.30 CCDF graph for PAPR of OFDM with and without SLM 68
Figure 5.1 Architecture of the RBF based Neural Network 74
Figure 5.2 Block Diagram of the Proposed PAPR Reduction Scheme
Using MNKB-RBF
80
Figure 6.1 Core MatLab Code of the Proposed RBF (MNKB-RBF) 85
Figure 6.2 Training Cost Comparison between Novel RBF and Proposed
RBF (Phase-Rotated Sequences = 64, Modulation = 8-QAM)
89
Figure 6.3 Training Cost Comparison between Novel RBF and Proposed
RBF(Phase-Rotated Sequences = 64, Modulation = 16-QAM)
89
Figure 6.4 Training Cost Comparison between Novel RBF and Proposed
RBF (Phase-Rotated Sequences = 64, Modulation = 32-QAM)
90
Figure 6.5 Training Cost Comparison between Novel RBF and Proposed
RBF (Phase-Rotated Sequences = 128, Modulation = 18-QAM)
90
Figure 6.6 Training Cost Comparison between Novel RBF and Proposed
RBF (Phase-Rotated Sequences = 128, Modulation = 16-QAM)
91
Figure 6.7 Training Cost Comparison between Novel RBF and Proposed
RBF (Phase-Rotated Sequences = 128, Modulation = 32-QAM)
91
Figure 6.8 Training Cost Comparison between Novel RBF and Proposed
RBF(Phase-Rotated Sequences = 256, Modulation = 8-QAM)
92
Figure 6.9 Training Cost Comparison between Novel RBF and Proposed
RBF (Phase-Rotated Sequences = 256, Modulation = 16-QAM)
92
Figure 6.10 Training Cost Comparison between Novel RBF and Proposed
RBF(Phase-Rotated Sequences = 256, Modulation = 32-QAM)
93
Figure 6.11 Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 64, Modulation = 8-QAM)
96
Figure 6.12 Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 64, Modulation = 16-QAM)
96
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Figure 6.13 Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 64, Modulation = 32-QAM)
97
Figure 6.14 Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 128, Modulation = 8-QAM)
97
Figure 6.15 Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 128, Modulation = 16-QAM)
98
Figure 6.16 Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 128, Modulation = 32-QAM)
98
Figure 6.17 Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 256, Modulation = 8-QAM)
99
Figure 6.18 Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 256, Modulation = 16-QAM)
99
Figure 6.19 Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 256, Modulation = 32-QAM)
100
xvii
ABSRACT
It has been observed over the last several decades that greediness of applications in
terms of their demand for bandwidth never gets fulfilled. Hence, scientists, researchers,
and engineers keep working on new ways and means of providing higher bandwidth.
Not in the much distant past, a new modulation technique called Orthogonal Frequency
Division Multiplexing (OFDM) has been introduced which provides very high data
rates. The key feature of OFDM is the orthogonality of its carrier frequencies. Note that
in OFDM the high frequency input signal is modulated over a large number of low
frequency sub-carrier signals which are orthogonal to each other. This feature makes it
very robust against efficiency degradation at higher frequencies. That is the reason for
the OFDM to be a choice technology for modern high and ultra-high data rate
communication systems. However, it suffers from high levels of the peak power to the
average power also called Peak-to-Average Power Ratio (PAPR). Reducing PAPR in
OFDM is a hot research area. There are many schemes available which attempt to
reduce PAPR. Some are in fact able to reduce PAPR but not sufficient enough to make
these feasible. Others do reduce it but increase its complexity to an extent that these
become unfeasible to realize.
The main motivation behind this research effort is to find a mechanism which results
in minimum PAPR for OFDM based communication systems and has a reasonable level
of complexity so that it may be realizable.
This thesis has investigated and analyzed a number of PAPR reduction schemes
available in the literature. It has been identified that the Selective Mapping (SLM) is
xviii
better than others methods in terms of computational complexity for reduction of the
PAPR.
As an outcome of this research activity, a novel framework based on Artificial Neural
Networks (ANN) and SLM is proposed. The kernel being used by the ANN of the
proposed framework is called Modified Novel Kernel Based Radial Basis Function
(MNKB-RBF) and is a modified version of an already available kernel (NKB-RBF) in
the literature and is shown to be highly efficient. It has been shown through simulations
that the proposed kernel is more efficient than NKB-RBF and thus produces better
results in selection of low frequency sub-carrier with the lowest PAPR.
Keywords: Orthogonal Frequency Division Multiplexing, Peak-to-Average Power
Ratio, Selected Mapping, Artificial Neural Networks, Novel Kernel Base Radial Basis
Function, Modified Novel Kernel Base Radial Basis Function.
1
CHAPTER 1
INTRODUCTION
1.1 RATIONALE AND MOTIVATION
It has been seen over the years that as the data rates of communication systems increase
so does the demand by the applications. It has been observed that the current
applications demand very high data rates from the communication networks. Some
examples of these applications are; high definition TV, good quality video, on-line
gaming, vehicle navigation systems, etc.
One more demand of modern applications is an ability of the communication system to
sustain high data rates (without service disruption) to devices present in vehicles
moving at very high speed, i.e., fact moving cars, electric trains, airplanes, etc.
These demands of high date rates with seamless service require new and ingenious
techniques to be employed in new communication systems to provide ultra-high data
rates. One area of focus is the modulation techniques. It has been observed that efficient
modulation techniques can multiply the data rates that are made available by the
networks.
Not in distant past, a new modulation technique called Orthogonal Frequency Division
Multiplexing (OFDM) has been introduced which provides very high data rates and is
based on multiplexing of frequencies. The key feature of OFDM is the orthogonality of
its carrier frequencies. This feature makes it very robust against efficiency degradation
at higher frequencies (which results in higher data rates) unlike other modulation
techniques which suffer from substantial degradation of service at higher frequencies.
2
This is the reason for the OFDM to be the choice technology for the modern high and
ultra-high data rate communication systems.
However, like many of its contemporary modulation technologies, it has its share of
demerits. In particular, it suffers from high levels of the peak power to the average
power ratio also called Peak-to-Average Power Ratio (PAPR). In OFDM, PAPR is high
mainly due to the reason that the summation of peaks of many sub-carriers may result
in very high value. Note that in OFDM the high frequency input signal is modulated
over a large number of low frequency sub-carrier signals which are orthogonal to each
other. Though the average of these sub-carriers would be quite low, the peak power
which is the summation of all peak values may become very high in some cases.
Reducing PAPR in OFDM is a hot research area. There are many schemes available
which attempt to reduce PAPR. Some are in fact able to reduce PAPR but not sufficient
enough to make these feasible. Others do reduce it but increase its complexity to an
extent that these become unfeasible to realize. Sufficient details of these schemes, their
merits and demerits are provided in Chapter 3. To say it in brief, the issue is not settled
yet.
The motivation and rationale behind this research work is to study various PAPR
reduction techniques, for study their limitations and propose a novel approach to
overcome those limitations.
1.2 RESEARCH GOAL AND OBJECTIVES
The goal of the attempted research is:
To address and resolve (in a better way) the PAPR issue to improve the Quality
of Service (QOS) in OFDM based broadband communication systems.
3
In order to achieve the above stated goal, it is natural to fulfill/accomplish the
following objectives:
1. Literature Survey to Devise Strategy for PAPR Reduction
Literature survey has been conducted to comprehend already available
Methods/ scheme to reduce high PAPR.
2. Identify the Most Promising PAPR Reduction Scheme
Using means like literature survey and/or performance evaluation of
existing schemes, identify a scheme that has the most promise in order to
be used as a candidate for PAPR reduction.
3. Propose a Novel PAPR Reduction Scheme
Depending upon the outcome of 2nd objective, to propose a modified
scheme to achieve our stated goal of reducing PAPR.
4. Validation of Effectiveness of the Proposed Scheme
The last objective in order to fulfill our goal is to validate and verify the
effectiveness of the proposed scheme (outcome of the 3rd objective). The
proposed scheme has been validated through extensive simulations
studies.
1.3 STRUCTURE OF DISSERTATION
This dissertation consists of seven chapters in total.
Chapter 2: Provides the detailed technical knowhow about OFDM, its application,
usage, mathematical background, and its demerit (namely, high PAPR).
However, the detailed description of PAPR, its impact on system design
4
and performance, and an introduction of these schemes to handle PAPR
is given in Chapter 3.
Chapter 3: Chapter 3 provides an introduction to the schemes which are available in
the literature to reduce PAPR. A detailed account of a few prominent
schemes as per published literature as well as our own evaluation
(simulation based) is given in Chapter 4.
Chapter 4: This chapter focuses upon the following PAPR reduction schemes and
provides a critical review of these schemes based on the information
available in the literature. The schemes under focus are Clipping and
Filtering (CF), Tone Reservation (TR), Partial Transmit Sequence
(PTS), and Selective Mapping (SLM). Note that Chapter 2, Chapter 3,
and Chapter 4 are based primarily on the survey of the available
literature.
On the other hand, the subsequent chapters, i.e., Chapter 4 to Chapter 6 are based on
original work as part of this research activity and reflect upon the contribution of this
research work. Though performance evaluation of above stated PAPR reduction
schemes is available in literature, a comprehensive evaluation of these schemes under
uniform evaluation criteria is not available in the literature. Hence, such comprehensive
evaluation has been done and is reported in the later part of Chapter 4. This chapter
concludes that the most promising of all these PAPR reduction schemes as per our
evaluation is the SLM.
5
Chapter 5: In the first part of Chapter 5, a new Artificial Neural Network (ANN)
kernel is proposed called Modified Novel Kernel Base Radial Basis
Function (MNKB-RBF), which is a modified version of one of the most
efficient ANN kernels available to be used in optimization applications.
The later part of this chapter proposes a new framework/scheme based
primarily on the proposed MNKB-RBF to select for SLM a sequence of
sub-carriers from candidate sequences with minimum expected PAPR.
Chapter 6: Reports on the comprehensive performance evaluation of proposed kernel
(MNKB-RBF) and the proposed framework to minimize PAPR. The
results indicate that new proposed kernel and the framework both work as
anticipated, i.e., help SLM selects the sub-carriers sequence with
minimum PAPR in most cases.
Chapter 7: Provides a summary of this research work, states the contributions of this
activity, and also sums up the guidelines for those who would like to
continue from the point where this research activity reached.
6
CHAPTER 2
ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING
(OFDM)
2.1 INTRODUCTION TO OFDM
OFDM is a modulation technique which uses multiple low frequency sub-carrier
frequencies instead of a single high frequency carrier and is very popular these days to
transmit digital data. In particular, it is the most widely used encoding scheme for
wideband digital communication [1]. In a wideband system, the message bandwidth is
much greater than the channel’s coherence bandwidth. On the other hand, the
broadband communication system is a wideband data transmission system having
multiple transmissions simultaneously [2]. Applications of wideband systems are
numerous, for example, wireless networks, Digital Subscriber’s Line (DSL), digital
TV, and 4G mobile communications systems. As stated earlier, OFDM uses many sub-
carrier frequencies to modulate the original signal. The sub-carriers frequencies are
always spatially orthogonal to one other. The important fact is that the modulation used
on each sub-carrier is at a low symbol rate. However, overall symbol rate is quite high
because multiple sub-carriers are used. Note that for modulation, any of the
conventional modulation techniques methods such as QAM or Phase-Shift Keying
(PSK) is used.
We know that higher symbol rate over single carrier results in severe channel conditions
(attenuation, interference, fading, etc.). These conditions are reduced substantially due
to low symbol rate on each sub-carrier in OFDM. Nevertheless, to acquire high symbol
rate due to accumulation of low symbol rates of all sub-carriers. Moreover, due to low
7
symbol rate we do not need to use a large guard interval between symbols. This results
in elimination of Inter-Symbol Interference (ISI) and achievement of better Signal-to-
Noise Ratio (SNR).
2.2 APPLICATIONS AND USAGE
The OFDM based multiple access technology is being used in cable, wireless, many
4G cellular networks, and mobile broadband networks. Some of the main applications
and usage of OFDMA are given below.
2.2.1 ADSL
The Asymmetric Digital Subscriber’s Line (ADSL) connections use OFDM for
modulation. ADSL uses ANSI T1.413 and G.992.1 standards. DSL and ADSL provide
high speed data transmission over existing copper wires. The subsequent versions of
ADSL, i.e., ADSL2, ADSL2+, VDSL, and VDSL2, also use OFDM [3].
It is known that on copper wires in particular, the higher the frequency the higher the
attenuation. It means that the data rate is directly proportional to the frequency. Hence,
in order to achieve high data rate we need to use higher frequencies at the cost of higher
attenuation. But since OFDM uses many low frequency sub-carriers instead of a single
high frequency carrier, it is robust against attenuation. And thus it is a favorable choice
for use in DSL based technologies [3].
2.2.2 Wireless Local Area Networks (WLAN), Metropolitan Area Networks
(MAN) and Personal Area Networks (PAN)
Besides wired networks, OFDM is also widely used in all types of Wireless Local Area
Networks (LAN) and worldwide interoperability for Microwave Access (WiMAX).
8
Latest broadband wireless LANs (IEEE 802.11a/g/n) operate in very high frequency
bands, from around 2.4 GHz to around 5 GHz. Each stream in these standards may
provide data rates from 6 to 54 Mbps. In "HT mode" (with 802.11n), the data rate of
each stream is increased up 150 Mbps. These standards use four different modulation
schemes (BPSK, QPSK, 16-QAM, 64-QAM).
Similarly, PANs in the 3.1–10.6 GHz ultra-wideband spectrum are also using OFDM.
2.2.3 Digital Video Broadcasting (DVB)
Digital Video Broadcasting (DVB) is a well-known project of European Commission
for transmission of high quality digital video over large distances [4]. It is compulsory
for all television services in the whole European Community to use this standard. DVB
standard requires that Coded OFDM (COFDM) be used for modulation of television
data over carrier frequencies. The word “Coded” refers to the use of Forward Error
Correction (FEC), i.e., for error detection and correction.
2.2.4 Digital Radio
Like television transmission, COFDM is used in high quality radio transmission
standards as well. For example, COFDM is used in a European digital audio
broadcasting standard referred to as Digital Radio Mondiale (DRM) at VHF frequencies
[4]. The similar American standard, iBiquity also uses COFDM as lower layer
technology to broadcast audio signals in various frequency spectra [5].
Similarly wireless personal area network technology of ultra-wideband also utilizes
OFDM.
9
2.2.5 Flash-OFDM (FOFDM)
Flarion [6] developed a new standard based on OFDM and is called Fast Low Latency
Access with Seamless Handoff Orthogonal Frequency Division Multiplexing
(FOFDM) or Flash OFDM. It was later purchased by Qualcomm in January 2006 [7].
FOFDM was supposed to compete with GSM and 3G networks. For example, 450 MHz
spectrum previously used by NMT450 and CNetC450 is now being to FOFDM
operators.
USA based wireless carrier Nextel Communications also started using FOFDM based
wireless broadband networks in 2005. Sprint has deployed mobile version of WiMAX
which uses another variation of OFDM, namely Scalable Orthogonal Frequency
Division Multiple Access (SOFDMA) technology [8].
2.3 ADVANTAGES AND DISADVANTAGES
Listed below are the advantages and disadvantages of OFDM. These are discussed in
further detail in section 2.4 (Principles of Operation).
2.3.1 Advantages
Here are some of the main advantages of OFDM [14, 15].
Spectral efficiency of OFDM is much higher than the other advanced
modulation schemes such as spread spectrum, etc.[17]
OFDM does not need complex time domain equalization in order to handle
severe channel conditions.
It is highly robust against Co-Channel Interference (CCI).
At the same time OFDMA is robust against ISI and multipath related fading.
OFDM is not sensitive to time synchronization problems.
10
Fast Fourier Transform (FFT) is used to efficiently implemented OFDM.
2.3.2 Disadvantages
The disadvantages are listed below [9, 11].
High PAPR is one of the major disadvantages of OFDM based systems. A lot
of research is being conducted to find ways and means to reduce PAPR. This is
also the main focus of this research.
OFDM is sensitive to problems related to frequency synchronization.
It is also sensitive to Doppler shift (DS) which is caused due to motion of
communicating entities [9].
Some loss of efficiency caused due to guard interval.
2.4 PRINCIPLES OF OPERATION
The following sub-sections describe the main characteristics and principles of
operation of OFDM.
2.4.1 Orthogonality
As stated earlier, OFDM is a frequency division multiplexing scheme with an additional
requirement that the sub-carrier frequencies must be orthogonal to one another.
Because of the orthogonality of sub-carriers, crosstalk between sub-carriers is
eliminated. Moreover, inter-carrier guard-bands are not required. This results in great
amplification in designs of both the transmitter and the receiver. Note that a separate
filter for each subcarrier is not required in OFDM which would not be the case if
conventional FDM were used [10, 11, 12, 13].
11
The condition of orthogonality makes it mandatory to separate sub-carriers in frequency
by a factor of ∆f = k
TU Hertz. Here TU is the size in seconds of the receiver’s window,
and k is a positive integer generally equal to 1. Hence, if N sub-carriers are used in an
OFDM based communication, the total bandwidth will be B ≈ N ∆f Hertz.
Because of orthogonality, we can utilize almost all of the allocated bandwidth resulting
in very high spectral efficiency. OFDM generally gives benign electromagnetic
properties which result in very low interference between co-channel users.
However, retaining orthogonality requires careful frequency synchronization between
the transmitter and the receiver. If a frequency deviation occurs, the sub-carriers will
not remain orthogonal which consequently result in Inter Channel Interference (ICI),
ISI and other severe channel conditions. Frequency deviations usually occur due to
reasons such as Doppler Shift or mismatched transmitter and receiver oscillators.
DS is caused by the relative movement of the transmitter and/or receiver. DS can easily
be handled by the adjustment (addition or subtraction) of frequency at the receiver’s
end, however, when this gets combined with multipath phenomenon, it becomes very
difficult to correct. And as the speed increases so does its worsening effect. This factor
limits the usage of OFDM in high-speed vehicles [9].
2.4.2 Implementation using FFT Algorithm
The implementation of modulation and demodulation can be efficiently done at both
the sender and the receiver side due to the orthogonality feature of sub-carriers. Note
that inverse FFT algorithm is applied on the transmitter side and forward FFT algorithm
on the receiver side. The recent substantial cost reduction in the digital signal
12
processing components that can efficiently calculate the FFT has boosted the use of
OFDM in wideband communication systems.
In order to be used, the time required to compute the FFT (or inverse FFT) has to be
less than the time for each symbol. For example for Digital Video Broadcast which
uses FFT 8k puts a compulsion on computation time to be less than or equal to 896 μs.
For an 8192-point FFT the computational requirement can be calculated to be 428 MIPS
as shown below:
MIPS = Computational Complexity
TSymbolx 1.3 x10−6 (2.1)
= 147456 x 2
896 x10−6x 1.3 x10−6 = 428
The computational demand increases approximately linearly (not exponentially) with
respect to FFT which implies that if the size of FFT is doubled, the amount of time
would be approximately double. This feature is very important for OFDM to be used in
all cases. If it were an exponential increase, the use of OFDM in higher frequency
communication would have been cost ineffective.
2.4.3 Guard Interval
In OFDM, many low frequency sub-carrier signals are used instead of one high
frequency signal. Note that both would provide the same high data rate because data
rates of all sub-carriers have to be added. However, having many low frequency sub-
carriers is very advantageous (some were described in preceding sub-sections).
The rate at which symbols are modulated over each sub-carrier is kept low. Hence, each
modulated symbol in terms of time is relatively long as compared to time characteristics
13
of the channel. Longer symbols suffer less from ISI caused by multipath phenomena.
Note that when the duration of each symbol is long, it becomes feasible to insert guard
interval between the OFDM symbols which eliminates ISI. The guard intervals reduce
the sensitivity of OFDM to time synchronization issues and simultaneously eliminates
the requirement of pulse-shaping filter.
For an illustration consider the following example. On a conventional single carrier
wireless channel one million symbols are modulated in one second which implies that
each symbol is approximately one microsecond long. Shorter symbols (in time) make
it very difficult to synchronize in time and hence a mechanism to handle the multipath
problem has to be put in place. If the same symbol rate, i.e., one million symbols per
second is distributed evenly among one thousand sub-carriers, the symbol rate on each
sub-carrier would be one thousand symbols per second. This implies that the duration
of each symbol on each carrier would be approximately one thousand times longer, i.e.,
one millisecond. Assume that we insert a guard interval of 1/8 of the symbol length,
i.e., 125 microseconds after each symbol. It has been seen that ISI can be eliminated if
the multipath time-spread is shorter than the guard interval indicating that a maximum
difference of 37.5 kilometers between all paths can be tolerated which is generally more
than enough.
2.4.4 Channel Coding and Time/Frequency Interleaving
Generally speaking, OFDM is used together with FEC also called channel coding as
well as time and/or frequency interleaving.
The benefit of frequency interleaving of sub-carriers is that it increases robustness
against channel fading. Frequency interleaving ensures that when one part of the
14
bandwidth being used fades, then the bit errors of that part are distributed into the
unaffected part of the bandwidth. Similarly, time interleaving distributes bit errors far
away in time. As evident, the purpose of frequency and time interleaving is to eliminate
concentration of errors. This attribute is very important because FEC’s ability of error
detection and correction becomes highly reduced or in some cases impossible to detect
and correct errors when errors are concentrated. Hence, interleaving is almost always
used on OFDM systems, so that FEC decoders could detect and correct more evenly
distributed bit errors.
2.4.5 Adaptive Transmission
In order to mitigate severe channel conditions, OFDM uses the technique of “Adaptive
Transmission”. In adaptive transmission, information about the channel condition is
sent over a return channel. This information is then used to adapt modulation, coding
scheme and power allocation for all or some sub-carriers as the need may be to optimize
transmission. Some sub-carriers can even be disabled if these are suffering from high
interference or attenuation.
For example, ADSL and VDSL uses Discrete Multi-tone (DMT) modulation which is
an adaptive OFDM based communication system. The granularity of the adaptation is
a single subcarrier.
2.4.6 OFDM with Multiple Access
As stated in previous sections, OFDM is a digital modulation technique which is
primarily used to modulate one original stream of data on a single communication
channel. However, it can be used to provide multiple access (access to multiple users
15
over a channel) using well known techniques of dividing time, frequency, or code. In
this form it is termed Orthogonal Frequency Division Multiple Access (OFDMA).
In OFDMA, multiple access is provided by assigning different sub-channels to different
users. Different Quality of services (QOS) for different users is achieved by assigning
different number of sub-channels effectively by increasing or decreasing the assigned
bandwidth to a user.
OFDMA is used in a variety of modern high-speed communication systems. Some are
mentioned below:
WiMAX IEEE 802.16 based Mobile Wireless MAN standard.
MWBA – IEEE 802.20 based Mobile Wireless MAN standard
Long Term Evolution (LTE) – Fourth generation mobile broadband standard.
Ultra-Mobile Broadband (UMB) – Qualcomm/3GPP2 project, intended as a
successor of CDMA2000, but replaced by LTE.
Wireless Regional Area Networks (WRAN) – IEEE 802.22 based network
which will potentially use OFDMA.
2.4.7 Linear Transmitter Power Amplifier
One of the main demerits of OFDM is a high PAPR. The average power of each sub-
carrier is quite low. However, because of the independent phases of sub-carriers of
OFDM, the peak power is determined by accumulation of powers of sub-carriers and
may become quite high. Handling high PAPR is a hot research area. Some ways to
handle PAPR are given below.
A high resolution Digital-to-Analogue (DAC) Converter is placed in the
transmitter.
16
A high resolution Analogue-to-Digital (ADC) Converter in the receiver.
Ensuring a linear signal chain.
If linearity in the signal chain is not ensured, it will cause inter-modulation distortion
which in turn may cause the following.
Raise the noise floor.
Produce Inter-Carrier Interference (ICI).
Generate out-of-band radiation.
Ensuring linearity is a very complex issue. In particular it is very demanding for the
transmitter because the amplifiers used in the transmitter are deliberately made non-
linear so as to minimize power consumption. One way to handle this is to allow a small
amount of clipping to limit PAPR. However, the transmitter output filter has the effect
of restoring peak levels which were previously clipped. Hence, clipping indeed is not a
suitable solution to reduce PAPR.
Since PAPR is in fact the main area of focus of this research activity, a detailed report
and discussion on PAPR and the schemes that attempt to reduce PAPR are given in
subsequent chapters.
2.5 EFFICIENCY COMPARISON BETWEEN SINGLE CARRIER AND
MULTI-CARRIER OFDM SYSTEMS
A communication system’s performance is generally measured using two very
important parameters, i.e., the power efficiency and the bandwidth efficiency. Power
efficiency is defined as the ability of a communication system to transmit signal with
low Bit Error Rate (BER) at low power levels. On the other hand bandwidth efficiency
of a communication system is its ability to utilize the available bandwidth to the
17
maximum, i.e., to achieve highest possible date rate per Hertz. For example, the
bandwidth efficiency of an OFDM system on fiber using multiple sub-carriers can be
calculated from the following formula.
η = 2 RS
BOFDM (2.2)
Here, RS is the symbol rate in giga symbols per second (Gsps),
and BOFDM is the bandwidth of OFDM signal.
The bandwidth efficiency of a multicarrier system such as OFDM is higher as compared
to a single carrier system. Table 2.1 shows comparison of performance of OFDM
systems having single carrier and multi-carrier modulation. The last column in this table
(titled “Bandwidth Efficiency”) indicates a performance gain of 76.7% at the cost of 1
dBm increase in receiver power as indicated in the 2nd last column (titled “Power at
Receiver”).
Table 2.1: Performance Comparison between Single Carrier and
Multicarrier OFDM [10]
S. No. Type of
Transmission QAM
Sub
carriers Bit Rate
Fiber
Length
Power
at
Receiver
Bandwidth
Efficiency
1 Single Carrier 64 1 10 Gbps 20 km -37.3
dBm 6.0000
2 Multi Carrier 64 128 10 Gbps 20 km -36.3
dBm 10.6022
18
2.6 SYSTEM MODEL
The subsequent sub-sections describe OFDM system models for the transmitter and the
receiver side.
2.6.1 Transmitter
In OFDM, the carrier signal is the summation of multiple sub-carriers which are
orthogonal to one another. Some conventional modulation scheme, such as QAM,
Phase Shift Keying (PSK), etc., is used to modulate given data on each sub-carrier.
As shown in Figure 2.1, s[n] is a stream of digital data. This digital data stream is first
of all de-multiplexed into N parallel streams. Using a set of symbols, now each sub-
stream of digital data is modulated using a conventional modulation scheme (QAM,
PSK, etc.). Since each stream is modulated independently of the other, some streams
may have higher symbol/data rate than the others.
Figure 2.1: OFDM Transmitter model
Source: Wikipedia, the free encyclopedia
X
X
X0
s[n]
FFT-1
X1
XN-2
XN-1
DAC
DAC
Constellation Mapping
𝕽𝒆
fe
𝟗𝟎𝒐 Serial to Parallel
s(t)
𝕽𝒎
19
After modulation, inverse FFT is applied on each sub-stream which produces a set of
complex time-domain samples for that sub-stream. As shown in Figure 2.1, the next
stage which consists of DACs converts real and imaginary components into analogue
domain. The analogue signals are then used to modulate at the carrier frequency, fc,
respectively. These modulated signals are then summed up to give the signal s(t) which
is to be transmitted.
2.6.2 Receiver
The corresponding receiver model of an OFDM system is shown in Figure 2.2. It can
observe in this figure that the receiver receives the signal r(t) and quadrature-mixes it
to baseband frequency. The resultant baseband analogue signal is converted into digital
stream in the next stage which consists of ADCs. Note that this signal is still in time
domain. FFT is applied on this signal to convert it into frequency domain. This produces
N parallel sub-stream of modulated symbols. Each stream is demodulated to produce
sub-streams of digital data. These sub-streams are combined into one stream of digital
stream S[n] which is approximately equal to the stream of digital data s[n] transmitted
by the transmitter.
Figure 2.2: OFDM Receiver model. Source: Wikipedia, the free encyclopedia
FFT
X Y0
Y1
YN-2
YN-1
Symbol Detection
fc
𝟗𝟎𝒐
Parallel to Serial
r(t)
X ADC
ADC
𝕽𝒎
𝕽𝒆
𝐬∧[𝐧]
20
2.7 MATHEMATICAL DESCRIPTION
In an OFDM system, if N sub-carriers are used, and each sub-carrier is modulated using
M symbols, then the set symbol of this OFDM system consists of MN elements.
Mathematically, low-pass OFDM signal is expressed as:
v(t) = ∑ Xkej2πkt/T , 0 ≤ t < T
N−1
k=0
(2.3)
Where, Xk denotes the set of data symbols used, N is the number of sub-carriers and T
is the time of an OFDM symbol. The orthogonality of the sub-carrier is ensured by
spacing them by a 1/T. This property is expressed as:
1
T∫(ej2πk1t/T)
∗(ej2πk2t/T) dt
T
0
(2.4)
= 1
T∫(ej2π(k2−k1)t/T) dt = δk1k2
T
0
(2.5)
Where * operates returns the complex conjugate and δ is the Kronecker delta.
A guard interval of length Tg is inserted before each OFDM block in order to eliminate
Inter Symbol Interference (ISI). During this interval, a cyclic prefix is transmitted so
that the signal in the interval −Tg ≤ t < 0 is the same as the signal in the interval
(T − Tg) ≤ t < T. Therefore, the OFDM signal with cyclic prefix can be represented
by the following equation.
v(t) = ∑ Xkej2πkt/T , −Tg ≤ t < T
N−1
k=0
(2.6)
21
The above stated signals can be either real or complex. Real valued signals are generally
transmitted at baseband wired applications such as DSL use this approach. The complex
valued signals are generally transmitted after conversion to a carrier frequency, wireless
application use this approach.
In general, the transmitted signal is represented as:
s(t) = ℜ{v(t)ej2πfct} = ∑ |Xk|cos(2π[fc + k/T]t + arg[Xk])
N−1
k=0
(2.7)
22
CHAPTER 3
REDUCTION OF PEAK-TO-AVERAGE POWER RATIO
As put forward in chapter 2, OFDM is a choice technology for high speed multi-user
communication systems. However, one major problem with OFDM hinders its
widespread use. The problem is that of “high level of PAPR”. This chapter presents an
introduction and explanation of this problem besides a brief of the schemes/methods
used to palliate this problem up to a degree of success. Note that “Reduction of PAPR”
is still a hot research area which is evident from the fact that a lot of research papers are
being published on this topic currently.
3.1 INTRODUCTION
One of the emerging technologies in the field of communications is the wireless
technology. It offers effective data transmission and a growing concept of 4G and 5G
communications. The concept of OFDM system states that it is a kind of modulation
scheme which accommodate multiple users simultaneously. As stated earlier, OFDM
suffers from the drawback of high PAPR [14, 15]. Numerous techniques, for example,
Selective Mapping [16], Partial Transmit Sequence [17], Clipping and Filtering [18, 19,
20], Tone Reservation [21], Companding [22], etc. are available which can be
employed to reduce PAPR effect in OFDM systems [14, 15, 16]. Different parameters
such as distortion rate, data rate, power, etc. are analyzed by the study of different PAPR
reduction schemes. OFDM communication systems find its applications in digital
television and audio broadcasting, DSL internet access, wireless networks, and 4G
mobile communications [23].
23
3.2 HIGH-POWER AMPLIFIERS
The purpose of PAPR reduction is to counteract the nonlinear effect of the High
Power Amplifier (HPA). Usually, HPAs are characterized as memory-less nonlinear
amplifiers in accordance with
g(x(t)) = F(|x(t)|)ej(∅(t)+Ф(|x(t)|)) (3.1)
Where g(x(t)) is the output of the HPA; x(t) = |x(t)|ej∅(t) is the time domain signal
input to the HPA; F(|x(t)|) and Ф(|x(t)|) are, respectively, the AM/AM and the
AM/PM distortion functions respectively, where AM denotes the Amplitude
Modulation, and PM denotes the Phase Modulation. Usually HPAs can be partitioned
into three categories: the Soft Limiter (SL), the Solid State Power Amplifier (SSPA),
and the Traveling-Wave Tube (TWT). Their characteristics can be described as follows.
3.2.1 Soft Limiter Power Amplifier
The Soft Limiter (SL) [24] is the simplest model of the HPA. It introduces no distortion
in the phase of the input signal and simply clips the signal magnitude when it exceeds
a threshold.
Therefore, the output of the SL can be written as
g(x(t)) = {Aej∅(t), |x(t)|A,
x(t), other wise ( 3.2)
Where A > 0 represents the threshold of the Soft Limiter.
24
3.2.2 Solid State Power Amplifier
The Solid State Power Amplifier is the most commonly used amplifier in wireless
communications. The output of SSPA can be written as [3].
g(x(t)) =|x(t)|
(1 +|x(t)|
A
2p
)
12p
ej∅(t); (3.3)
i.e., it introduces no distortion in the signal phase. When p → ∞, the SSPA becomes
the SL. Usually, p = 3 for a practical SSPA.
3.2.3 Traveling-Wave Tube
Travelling Wave Tubes (TWTs) are wideband amplifiers widely used in satellite
communications [25, 26]. The AM/AM and AM/PM functions of TWT can be written
as [27].
F(|x(t)|) =|x(t)|
1 + ( |x(t)|
2A )2 ,
or ∅(|x(t)|) =π
3
|x(t)|2
3|x(t)2| + 4A2 . (3.4)
3.3 PAPR DEFINED
In OFDM System Model, it can be noticed that the input channel signals are modulated
first using either Phase Shift Keying (PSK) or QAM and then undergo Inverse Fast
Fourier Transform (IFFT) operation at the transmitter end [28, 29]. This creates low-
frequency sub-carriers (orthogonal to one another) at the transmitter side [30]. These
transmitted signals can deliver high peak values in the time domain and these high peak
values when get summed up due to alignment produce high ratio of peak power to the
average power. The high PAPR is a consequence of the summing up of sonic waves
25
and non-constant envelope [31]. The injurious effect of high PAPR is that it brings
down the performance of power amplifier. Therefore, RF power amplifiers need to be
controlled in a very large linear region, otherwise the signal peaks will enter into a non-
linear region and will cause deformation. Though there are many schemes which reduce
PAPR, the efficiency of any PAPR reduction scheme is measured through Cumulative
Distribution Function (CDF). PAPR of a signal is calculated by the following equation
[14].
PAPR[x(t)] =Pmax
Pav=
max0≤t≤NT
[|x(t)|2]
E{|x(t)2|} (3.5)
Where Pav is the average power of signal x(t) and is calculated in the frequency
domain, since IDFT is a (scaled) unitary transform and E{⋅} represents the value
operator. The nonlinear distortion in the HPA occurs in the analog domain. But, the
majority of the signal processing to reduce PAPR OFDM signal is used in the digital
domain. In general, the PAPR in the digital domain is not necessarily the same as PAPR
in the analog domain.
The PAPR (in dB) of the transmitted OFDM signal can be written as in equation (3.6)
CFRmax = 10log(N)dB (3.6)
It is a random variable, because PAPR is a function of input data. The crest factor is
generally characterized by the square root of the PAPR.
Crest Factor, C. F = √PAPR or PAPR = (C. F)2 (3.7)
The clipping ratio (CR) is define as follows:
CR =Amax
Aave (3.8)
26
Where Amax is the maximum amplitude of the output signal after clipping, and Aave is
the average amplitude of input signal before clipping.
3.4 WELL KNOWN PAPR REDUCTION SCHEMES
This section describes various PAPR reduction schemes and discusses their
performance as given in the literature.
As shown in Table 3.1, the schemes to reduce PAPR are primarily divided into two
classes, i.e., Signal Scrambling Schemes and Signal Distortion Schemes.
In section, 3.4.1, described some popular signal scrambling schemes, and in section
3.4.2, similarly some major signal distortion schemes for PAPR reduction are
elaborated.
Table 3.1: Classification of Major PAPR Reduction Schemes [17]
Signal Scrambling Schemes Signal Distortion Schemes
Selective Mapping (SLM) Clipping and Filtering (C and F)
Partial Transmit Sequence (PTS) Peak Windowing
Tone Reservation (TR) Peak Reduction Carrier
Tone Injection (TI) Companding
Interleaving
3.4.1 Signal Scrambling Schemes
3.4.1.1 Selective Mapping (SLM)
The research that introduced the “Selective Mapping Technique” was penned down by
Bamul, Fischer and Huber in 1996. SLM [16, 32, 33] is one of the favorable PAPR
27
reduction techniques as it does not introduce distortion and effectively reduces PAPR.
In this technique the input data blocks are multiplied by each of the given phase-rotated
sequences to generate alternative input symbol sequences. Part of the alternative
sequences is processed further under IFFT and their PAPR is determined. Then the
signal with lowest PAPR is selected for transmission [16, 32, 33]. SLM is a technique
which is utilized to lessen the PAPR effect in OFDM Systems. It is a type of Phase
Rotation Method. As shown in the block diagram of SLM (Figure 3.1), the Side
information index (SII) should be transferred to appropriate retrieval of data cube at the
recipient position [34, 35].
Figure 3.1: Block diagram of SLM scheme [17]
In SLM, input data is partitioned into smaller data blocks of length N (Figure 3.1).
These smaller data blocks result into the parallel data streams obtained through serial
Serial- to-
Parallel
Converter
Choose the
one with
minimum
PAPR
IDFT
IDFT
IDFT
X
X
X
S
S(1)
S(2)
S(U)
s(1)
s(2)
s(U)
SK
Side
Information
S
B(1)
B(U)
B(2)
28
to parallel converter. Each element in each data bock of parallel streams is multiplied
with a phase-rotated sequence [15], [52].
After data block is phase rotated, the rotated OFDM data blocks represent similar
information, multiplied with known phase sequence. The fundamental idea that lies in
this technique is that it helps to select the signal with lowest PAPR value from a pool
of phase-rotated sequences.
3.4.1.2 Partial Transmit Sequence (PTS)
Partial Transmit Sequence technique [17] is popularly used technique for PAPR
reduction and the concept of PTS Scheme can be clearly seen in its block diagram as
shown in Figure 3.2. PTS is based on the concept of addition of phase rotation to
develop a candidate signal and to select one signal with low PAPR [29, 30, 36, 37]. The
statistics of a multicarrier signal gets enhanced by practicing this technique.
Figure 3.2: Block diagram of PTS scheme [17]
Data
Source
Serial to
Parallel
Partition
in to
Clusters
Selection optimal
combination with
lowest PARP
Parallel
To Serial
X
X
X
b1
U
N-point
IFFT
N-point
IFFT
N-point
IFFT
u(1)
u(2)
u(Z-1)
b2
b(Z-1)
Phase OptimizationSide Information
If necessary
29
The important idea that lies behind PTS scheme is to divide the original OFDM carrier
sequence into several sequences. Distinct weights are multiplied with each sequence
until the best solution is accomplished. This idea is visible in block diagram of PTS
(Figure 3.2) [17]. The portioning into sub-carriers of a single carrier is a major drag on
performance and must be taken into consideration. The three ways of sub-block
portioning schemes are adjacent, interleaved and pseudo-random portioning [29]. PTS
scheme has high level of computational complexity and it also needs to handle SII as
that in SLM scheme.
3.4.1.3 Tone Reservation (TR)
In this scheme, N sub-carriers (tones) are divided into two parts, i.e., data tones and
peak reduction tones. The central thought behind this scheme is that a humble set of
sub-carrier frequencies (tones) are created for PAPR reduction. This method is applied
to minimize the high peak values. At the transmitter side, the computation of time
domain signal can be made. The effectiveness for PAPR reduction in tone reservation
approach depends on the tones that are reserved. TR is a low complexity scheme [15].
This technique demonstrates that by reserving even a modest fraction of tones leads to
big reductions in PAPR value. Moreover, no additional data is required to be handled
at the recipient side. However, reserving tones is not only an optimization issue but
leads to inefficient use of spectrum.
3.4.1.4 Tone Injection (TI)
The Tone Injection (TI) approach was given by Seung. H., and Jae. H. Lee in [15]. The
basis of the tone injection scheme is a general additive method which provides a desired
PAPR reduction. By the execution of the additive method of the multicarrier signal, the
30
PAPR reduction is accomplished. A circle of equivalent constellation points is being
used by TI scheme for original constellation points to minimize the effect of PAPR.
The demerits of the TI are that this access requires additional information for
deciphering the signal at the receiver and causes extra IFFT operations which results in
complex circuitry.
3.4.1.5 Interleaving Technique
This is a technique which utilizes a set of Interleavers for PAPR reduction and is thus
called Interleaving technique. In this scheme, the high value of PAPR is reduced by
applying a set of Interleavers, but not by using the set of phase sequences as was the
case with both PTS and SLM techniques. A long correlation pattern is worn down to
melt off the elevated values of correlated data structures [15]. By the use of this
Interleaving technique, higher code rate without expansion in bandwidth is obtained as
compared to conventional OFDM systems, without an increased number of sub-
carriers. The Interleaving technique is moderately complex in nature.
As shown in Figure 3.3, Interleavers are used to produce permuted data blocks from the
original data block. PAPR is then computed for the original and the permuted data
blocks. The data block with the lowest PAPR is then selected for transmission. These
computations are comprehensive in nature and make this scheme moderate complex in
terms of computational complexity. The block diagram of interleaving scheme is shown
in Figure 3.3.
The performance (in terms of reduction in PAPR) of the Interleaving scheme depends
on the number and design of the Interleavers.
31
Figure 3.3: Block diagram of Interleaving scheme
3.4.2 Signal Distortion Schemes
3.4.2.1 Clipping and Filtering
The technique is one of the simplest techniques and is being mostly used for getting
reduced value of PAPR. The functioning of clipping and filtering technique is clear
from its name itself, i.e., it clips the part of the signals which are not allowed to enter
the specified region. The operation of clipping and filtering technique can be realized
by using the HPA with the saturation region below the signal span will automatically
induce the signal to be clipped [18.19,20]. The amplitude clipping is mathematically
defined as follows:
C(x) = {x, x ≤ AA, x > A
(3.9)
Clipping is generally speaking at the transmitter side. The receiver is supposed to
estimate the clipping performed by the sender and compensates accordingly. Since, at
Select One
With
Minimum
PAPR
32
most one clipping is done by the sender per OFDM symbol, thus the receiver has to
estimate two parameters, i.e., location and size of the clip. It is difficult for the receiver
to estimate this data. Hence, clipping introduces both in-band distortion and out-of-
band radiation into OFDM signals. This degrades system performance including bit-
error-rate and effective use of the available spectrum. Though filtering (pruning) can
reduce out-of-band radiation, it can not reduce in-band distortion. However, on the
other hand filtering may cause regrowth of some peaks so that the signal after clipping
and filtering will go past the clipping level at some stages [18].
3.4.2.2 Peak Reduction Carrier
Peak Reduction Carrier technique was proposed by Muller and Huber [38]. This
technique is demonstrated to have the capability to reduce the elevated value of PAPR
by using data bearing Peak Reduction Carrier in OFDM systems. This technique is
associated with the use of higher order modulation scheme to represent a lower order
modulation symbol [15]. The phase shift keying modulation scheme is suited for Peak
Reduction Carrier as in this envelope of all the sub-carriers are the same. The
implementation of QAM scheme will result in serious BER degradation. When the
higher order modulation schemes are used by this technique to represent lower order
modulation scheme data then, there is increased probability of error and hence the
overall BER performance gets degraded.
33
Table 3.2: Performance of PAPR Reduction Techniques [17]
S. No. PAPR Reduction
Techniques Performance
1. Selective Mapping
(SLM) Reduces Distortion
No Power Raise
Selects sub-carriers with the lowest
PAPR value
2. Partial Transmit
Sequence (PTS) Reduces Distortion
No Power Raise
High Computational Complexity
3. Tone Reservation (TR) Reduces Distortion
Power Gets Raised
Less Complex as Compared with PTS
4. Tone Injection (TI) Reduces Distortion
Power Gets Raised
PAPR Reduction without Data Rate
Reduction
5. Clipping and Filtering Introduces Distortion
No Power Raise
One of the Simplest
3.5 SUMMARY
OFDM is a kind of multicarrier and multiuser modulation technique. Wireless
communication is emerging technology in the present times and OFDM systems are in
use because of its advantages such as providing High Spectral Efficiency, Increased
Bandwidth Power and its Robustness against Multipath Interference. But the OFDM
system suffers from the demerit of high values of PAPR. In this chapter, several
techniques for PAPR reduction are reviewed and discussed. These techniques are
separated into two classes. 1. Signal Scrambling Techniques and 2. Signal Distortion
Techniques.
34
A number of techniques such as Selective Mapping, Partial Transmit Sequence, Tone
Reservation, Tone Injection, Interleaving, Clipping and Filtering and Peak Reduction
Carrier techniques are talked about in this chapter. The analysis of PAPR reduction
techniques as given in the literature on various parameters is done. It can be said that
different PAPR reduction techniques are able to reduce the PAPR effectively but each
having its own demerits. Hence, the jury is still out and the research work is still being
done to optimize these schemes.
35
CHAPTER 4
PERFORMANCE EVALUATION AND ANALYSIS OF PAPR
REDUCTION SCHEME
This chapter consists of two major parts. First part is given in section 4.1 and its sub-
sections which produce a detailed account of various PAPR reduction schemes based
on the analysis done on the documents available on these schemes in the literature.
Based on this analysis of various schemes, two PAPR reduction schemes are selected
as the schemes having more promise and are to be considered for further improvement.
Second part of this chapter (section 4.2 and its sub-sections), describe the performance
evaluation done by us of the selected schemes. The objective of this performance
evaluation is two-fold, i.e., to verify the performance of these schemes against the
performance given in the literature, and to understand their workings for the purpose of
further enhancement.
4.1 ANALYSIS OF PAPR REDUCTION SCHEMES THROUGH
LITERATURE SURVEY
This section provides a detailed account of the following PAPR reduction schemes
based on the analysis done on the documents available in the literature related to these
schemes. The details on each scheme are given in the subsequent sub-sections of this
section.
Clipping and Filtering Scheme
Coding Scheme
Peak Reduction Carriers Scheme
36
Envelope Scaling Scheme
PTS and SLM Scheme
Tone Reservation and Tone Injection Schemes
Active Constellation Extension(ACE) Scheme
4.1.1 Clipping and Filtering Scheme
This is one of the simplest schemes to reduce PAPR. This scheme can be implemented
without any significant computational overhead to the OFDM modulator [39, 40]. In
this scheme, a power threshold is first of all fixed. The signal power is compared with
the threshold power. If the power of the signal is less than the threshold then it is
transmitted as it is but if the power of the signal power is greater, then instead of the
signal power, the threshold power is used to send the signal. This simplicity, however,
has a cost involved. Since, a part of OFDM signal is clipped altogether, it causes loss
of information. This loss of information in turn increases the BER. Higher BER
severely affects some critical application like real-time video transmission etc. [41].
The results shown in Figure 4.1, illustrate that as we increase the number of clips done
on the data, so does the reduction in PAPR. For example, it can be seen that the
Complementary Cumulative Distribution Function (CCDF) is the highest for the
original signal (without clipping). CCDF after first clipping is lower than the original
clipping. Same pattern can be seen in Figure 4.1 as the number of clips are further
increased. However, it may increase BER, which may cause distortion.
37
Figure 4.1: PAPR distribution when “Clipping and Filtering Scheme” is used
4.1.2 Coding Scheme
In this method FEC codes are used for PAPR reduction. The FEC codes help scramble
the data so that the OFDM symbol created has a smaller PAPR. The advantage of PAPR
reduction using Coding is that this method not only provides error correction but also
PAPR reduction. The disadvantage is that coding reduces the information rate (bit rate)
since redundant information needs to be transmitted. However, since FEC are typically
used in communication systems, therefore the idea of using FEC for PAPR reduction
is quite attractive. To develop a Complement Block Coding (CBC) scheme, this helps
to reduce the PAPR of the OFDM signal. A reduction of about 3dBs is achieved using
this method. The convolutional codes are also used to reduce the PAPR of OFDM
signals. The motivation is that convolutional codes are already used for various
38
communication systems such as UMTS, LTE, WiMAX etc., so using this scheme for
PAPR reduction will be efficient. The use of Low Density Parity Check (LDPC) codes
for PAPR reduction show that the use of LDPC can reduce the PAPR of OFDM by
about 60%. Also, the combination of LDPC codes and PTS for PAPR reduction of
OFDM shows that such schemes can reduce the PAPR by about 3.7 dBs for 8 partitions.
In [14], the authors have compared the PAPR reduction capabilities of Cyclic Coding
(CC), Simple Block Coding (SBC), Complement Blocking Coding (CBC) and
Modified Complementary Block Coding (MCBC). They propose the use of CBC and
MCBC codes since they offer high coding rates and provide flexibility between coding
rate choices and complexity.
4.1.3 Peak Reduction Carriers Scheme
This scheme uses bearings to reduce the Peak Reduction Carriers (PRCs) data to reduce
the effective PAPR [15]. It includes the use of a higher order modulation scheme to
represent a lower order modulation symbol. The amplitude and phase of the PRC is
positioned within the constellation region symbolizing the data symbol to be
transmitted. This scheme is suitable for PSK modulation. Note that in PSK the
envelopes of all sub-carriers are the same. When QAM modulation is implemented in
the OFDM systems, the carrier envelope scaling will result in serious BER degradation.
BER degradation can be reduced but at the cost of substantial increase in the side
information to be transmitted by the sender.
39
4.1.4 Envelope Scaling Scheme
Envelope scaling technology is proposed in [42]. Based on this technique, many
algorithms are available to reduce the peak signal before the expected input envelope
by scaling some part of the subcarriers after these are sent to the IFFT [42]. Generally,
256 subcarriers are used with Quadratic Phase Shift Keying (QPSK) modulation
schemes to make the envelope subcarriers equivalent. The core of this scheme states
that a bundle of only some sub-carriers is to be made which reduces PAPR. Hence, the
receiver does not require further additional information to decode the sequence. A
reduction of 4dB has been reported in literature for this scheme [42].
4.1.5 PTS and SLM Schemes
PTS and SLM which use multiple signal representation represent another class of PAPR
reduction schemes. Both PTS and SLM are shown not to degrade BER performance.
However, their computational cost is much higher [43, 44, 45].
PTS is one of the most popular distortion less PAPR reduction schemes in that it does
not increase the BER [44, 45]. However PTS is computationally complex and is thus
comparatively slow. This is a serious disadvantage when compared to other available
techniques. During OFDM transmission, it is critical that the side information is
received without errors. The performance of PTS depends upon two factors, i.e., (1) the
phase factors and (2) the segmentation method. In practice the computational load of
PTS is reduced by fixing the phase factors, segmentation method, and the number of
segments [36, 37].
For PTS, the data is divided into non-overlapping parts and the subcarriers within each
part are applied a phase shift so as to reduce the overall PAPR as much as possible as
40
shown in Figure 4.2. This figure is same as figure 3.2 in Chapter 3(section 3.4, and its
sub-sections 3. 4.1.4).
Figure 4.2: PTS scheme block diagram [17]
The above block diagram shows the functional steps of PTS [36, 37].
First start with a serial sequence of incoming data.
In the next step, the incoming data having N subcarriers is divided into non-
overlapping parts by the serial to parallel converter.
This is followed by IFFT being performed on the data blocks.
The individual signals now need to be assigned phase factors having a complex
value. This is achieved by means of the PTS method to determine the best
possible phase shifts for each data part so as to reduce the overall PAPR to the
minimum value.
On the receiver end, the reverse operation is performed.
41
Figures 4.3(a) and 4.3(b) compare the performance of PTS with the Original signal
(without PTS) in terms of their PAPR reduction capability.
Figure 4.3(a) shows the performance of PTS which uses 4 different phase rotations and
16 different segmentations (number of sub-band is 64, the oversampling factor L is 8).
We can see in this figure that the above stated combination of parameters reduces PAPR
by about 2dB.
Similarly Figure 4.3(b) shows the performance of PTS when the number of different
phase sequences is 4 and the number of different segmentation combinations is 256.
This figure shows that this combination can reduce PAPR of an OFDM signal by about
5.8 dB.
Figure 4.3(a): CCDF for PAPR of OFDM with and without PTS [17]
42
Figure 4.3(b): CCDF for PAPR of OFDM with and without PTS [17]
Out of many PAPR reduction schemes, it can be found SLM is one of the most
promising schemes. In SLM statistically independent data blocks are generated from
the given OFDM data blocks. These data blocks are generated using a set of phase-
rotated sequences and one with the lowest PAPR is selected for transmission. The goal
is to perform a change of phase on the modulated symbols (before IFFT) in order to
reduce the probability of constructive interference between the subcarriers (after IFFT)
has been computed. The block diagram of SLM is shown in Figure 4.4, in this figure it
is cleared that each block of data is multiplied with a phase rotator Z for different length
N.
Bz = [bz, 0, bZ, 1, … , bZ, N − 1]T, Z = 1,2, … , Z − 1
43
Resulting in 𝑍 different data blocks, so the zth phase sequence after multiplying is given
as:
Figure 4.4: Block diagram of SLM scheme [17]
UZ = [U1bZ,1, U2bZ,2, … , UN−1bZ,N−1]2
, (z = 1, 2, … , Z − 1). (4.1)
Therefore, OFDM signal becomes as given in equation 4.2.
uz(t) =1
√N∑ Unb
z,nej2πfnt
N−1
n=0
where 0 ≤ t ≤ NT, = 1,2, … , U (4.2)
From the data blocks U(z)(z = 0, 1, … , Z − 1)the one with smallest PAPR is selected
for transmission. After that the data is transmitted along with the phase sequences as
side information. At the receiver, reverse operation is performed to recover the original
data. This methodology is calculable with a wide range of modulation and with a
number of sub-carriers.
Data
Source
Partition
In to
Clusters
Serial to
Parallel
Select
one
With
Minimum
PAPR
Parallel
To Serial
N-point
IFFT
N-point
IFFT
N-point
IFFT
X
X
X
U
U(1)
U(2)
U(Z-1)
u(1)
u(2)
u(Z-1)
B(1)
B(2)
B(Z-1)
44
Figure 4.5(a): CCDF for PAPR of OFDM with and without SLM
Figure 4.5(b): CCDF for PAPR of OFDM with and without SLM
45
By analysing the graph shown in Figure 4.5(a), it is deducted that SLM reduces PAPR
by as much as 3dB (quite significant) when 04 different phase-rotated sequences are
used.
Similarly, Figure 4.5(b) shows that when in SLM, the number of OFDM symbol
candidates C=8, different phase sequences is 4, number of sub bands is 64, and the
oversampling factor L= 4, PAPR of an OFDM signal is reduced by about 3.7dB.
Under the above observation, it is clear that both SLM and PTS schemes are very
similar in nature. The only difference is the provision of phase-rotated sub-sequences
in SLM before the IFFT operation and in PTS scheme after the IFFT operation.
4.1.6 Interleaving Scheme
The interleaving scheme is very similar in its nature to SLM scheme. As we have seen
that the sub-sequences are separated by doing phase-rotation in SLM, however in
Interleaving, intervals are used to separate sub-sequences. The interleaver generates the
modified data blocks which are actually permuted to the data blocks of the original one.
Finally, the data black with the least PAPR is selected for transmission. The
performance of this scheme in terms of PAPR reduction heavily depends on the amount
and design of intervals [14].
4.1.7 Tone Reservation and Tone Injection Schemes
After thorough literature survey it is found that like some other schemes, both Tone
Reservation and Tone Injection are categorized as efficient schemes too (in terms of
PAPR reduction).
In contrast to the other PAPR reduction methods discussed above, TR seems to be
efficient in terms of both complexity and BER requirements [46, 47]. Since TR does
46
not manipulate data subcarriers therefore it does not cause any errors to it. TR utilizes
a set of reserved subcarriers for PAPR reduction. The task is to optimize the signal of
non-data bearing subcarriers, while keeping the data subcarriers unchanged [48].
In TR, the receiver does not need to share the complexity of this PAPR reduction
algorithm. That is the processing load for the selection of TR carriers needs to be
performed by the transmitter only [21, 49].
It can be observed from Figure 4.6 (a) and 4.6 (b) that the PAPR reduction is inversely
related to the number of PRCs. Therefore, the lower the PRC sum, the more the
reduction in the PAPR.
Figure 4.6(a): PAPR of Tone Reservation, 12 sub-carriers, and 4 Peak
Cancellation sub-carriers
47
Figure 4.6(b): PAPR of Tone Reservation, 12 sub-carriers, and 4 Peak
Cancellation sub-carriers
TR has many advantages. In TR the data rate does not get reduced substantially.
Moreover, side information is also not needed to be transmitted. However, TI suffers
from some disadvantages too. The most important disadvantage is that exhaustive
search for the best constellation from a large number of constellations is required. This
implies that the computational complexity of TI is quite high.
TI is more complex than TR [50]. This is because in TI both the injected signal and
information signal occupy the same frequency bands.
4.1.8 Active Constellation Extension Scheme
The method of Active Constellation Extension is also used to minimize the PAPR and
falls in to the same line of methods as TI. This is a non-linear method utilized for
reduction of the PAPR of OFDM signal in addition to using Companding and
48
Clipping. ACE has a major edge over other techniques in that it improves the BER
without affecting the rate of data exchange which is a very important requirement for
wireless communication. Nevertheless, the advantage of good BER comes at the cost
of computational complexity as it is intensive to determine the best possible
constellation which is an iterative process [50, 51].
Figure 4.7: The ACE scheme for QPSK modulation [17], [36]
lm
Re
49
4.1.9 Comparison of PAPR Reduction Schemes
Table 4.1: Comparison of Different PAPR Reduction Schemes [15], [17]
PAPR
Reduction
Schemes
Metric
Power
Increase
Implementation
Complexity
Bandwidth
Expansion
BER
Degradation
Required
Processing
Clipping /
Filtering No Low No Yes
Tx: Amplitude Clipping
Rx: None
Coding No Low Yes No Tx: Encoding
Rx: Decoding
TR Yes High Yes No
Tx: IDFTs, Final value
PRCs
Rx: Ignore non-data
carriers
ACE Yes High Yes No
Tx: IDFTs, projection on
“shaded area”
Rx: None
PTS No High Yes No
Tx: M IDFT, Wm-1
complex vector sums
Rx: Side information
extraction, Inverse PTS
SLM No High Yes No
Tx: U-IDFTs
Rx: Side information
extraction, Inverse SLM
Interleaving No Low Yes No
Tx: K-IDFTs, K-1
interleavings
Rx: Side information
extraction, Inverse
interleaving
TI Yes High Yes No
Tx: IDFT, search for
maximum point in time,
tones to be modified
Rx: Modulo-D operation
4.2 PERFORMANCE EVALUATION AND ANALYSIS OF SELECTED
PAPR REDUCTION SCHEMES THROUGH SIMULATIONS
Wireless digital communications is an ever increasing phenomenon thereby requiring
structures that are dependable and extremely efficient. OFDM allows efficient use of
the available spectrum, tolerance in multipath delay, and robustness to fading. It has
50
therefore been used for high speed communication as well as it is a part of several
standards.
As a result it has been chosen for high data rate communications, DVB, Digital Video
Broadcasting Terrestrial (DVB-T) and mobile Worldwide interoperability for
Microwave Access (WiMAX) based on OFDM access technology (Jiang., et al., 2007)
Digital Signal Processing has helped develop recent interest in this technique and it has
found use in many international standards such as IEEE 802.11, IEEE 802.16, IEEE
802.20, European Telecommunications Standards Institute (ETSI) Broadcast Radio
Access Network (BRAN) committees, and high-speed digital subscriber lines (HDSL,
ADSL, and VDSL) [52].
Even with its many advantages, OFDM suffers from power issues i.e. the largest power
value during an OFDM transmission can be equal N times the average power of the
signal (N being the number of carriers used in the signal). This is a major drawback for
its use as it results in distortions in the output. To circumvent this, one solution is to
reduce the power being transmitted thus reducing the PAPR of the signal. Having a
lower PAPR allows for a higher average power to be sent for a fixed value of peak
signal power. This increases the signal to noise ratio.
To achieve this, a number of methods have been proposed [52]. These techniques are
Clipping [53] Clipping and Filtering [40, 41, 54], coding [55, 56] Tone Reservation
[47, 48] and Active Constellation Extension [50]. Other methods having discrete
solutions such as Tone Injection [49] and multiple signal representation techniques such
as Partial Transmit Sequence [57, 58, 59] Selected Mapping [44, 45, 60], and Inter
Leaving [50] have also been proposed.
51
4.2.1 Motivation for Using Tone Reservation (TR)
There have been many methods proposed for decreasing the PAPR values during an
OFDM transmission. Of all the presented techniques, TR is considered to be an
effective technique to achieve this task. Each method of TR has its own benefit and
suitable for use in a certain scenario.
All the approaches used here to apply the tone reservation technique have their own
benefits, so that each can be used in different condition. If the complexity is not an
issue then Signal to Clipping Noise Ratio (SCR) Gradient TR iterative algorithm or
Adaptive Scaling TR algorithm can be used that give reasonable PAPR reduction. On
other hand if system cannot be offered much complexity, then other algorithm like
Gaussian pulse based TR is suitable. Active set TR Algorithm can be used where there
is a need to attack only high peaks, the complexity is bit higher but techniques is
reasonable as not all the symbols samples are checking.
The simplest of the methods for the reduction of PAPR are Clipping and Companding,
which rely on literally clipping the amplitude of the multicarrier signal. These
procedures have a number of shortfalls such as in-band distortions and noise
amplification which result in BER degradation. Another class of PAPR reduction
techniques includes multiple signal representation methods such as PTS and SLM.
These techniques do not degrade the BER performance but are computationally quite
expensive. BER performance is improved due to TR. Some subsets of subcarriers are
exploited by the TR for controlling PAPR.
No internal separation method is applied in TR to eventually calculate effective
PAPR. All of the measurements are computed at Transmitter side without
involvement of the receiver. Recent counterpart communication systems comprising
52
3G and 4G standards like LTE-Advanced its predecessor, and Wireless
Interoperability for Microwave Access (WiMAX) utilize TR for this purpose.
Distinguished sided quality of TR is industrious BER enhancement i.e. since TR does
not control information subcarriers accordingly it doesn't outcome in any omission to
it.
4.2.2 Simulation Results on Performance of TR
In order to validate the proposed scheme in this research few simulation experiments
are conducted having different no of carriers for PRC observations. To check flat
signal observation 12 subcarriers are considered, consequently. we decide +r1-r2+r3
and+r4 as a PRC and transmit on x1: x2, that results x1: x2 summation to create a peak,
while r4 creates an anti- peak, which concludes that the exact ant peak or results output
to be a flat signal from which data cannot be retrieved.
Similarly (Figure 4.8 through 4.23) compares the TR OFDM signal with 12 subcarrier
and 4 peak cancellation simulation results. The blue line represents the original value
of PAPR in dB, whereas red line indicates the result after PAPR reduction in dB.
Table 4.2 presents the summary of the results presented in Figures 4.8 to 4.23,
depicting the significant reduction in PAPR.
Table 4.2 eventually provides use of TR method results to accomplish that PRC-4
with combination +r1+r2+r3 and r4 provides the greatest reduction of PAPR to be
2.45 dB, from all experimented combinations.
53
Table 4.2: Different PRC Sum Variable Combinations [46]
Figures. Nos
Peak
Cancellation
Sum
Variable
Carrier Sum
Calculation
PAPR
Level (dB)
Figure 4.8 sum1 -r1-r2-r3-r4 2.45
Figure 4.9 sum2 -r1-r2-r3-r4 1.4
Figure 4.10 sum3 +r1+r2-r3-r4 1.1
Figure 4.11 sum4 -r1-r2+r3+r4 0.7
Figure 4.12 sum5 -r1-r2-r3+r4 0.7
Figure 4.13 sum6 -r1+r2+r3+r4 0.8
Figure 4.14 sum7 +r1-r2-r3-r4 0.4
Figure 4.15 sum8 +r1-r2-r3+r4 0.7
Figure 4.16 sum9 +r1+r2+r3-r4 1.1
Figure 4.17 sum10 -r1+r2-r3+r4 0.9
Figure 4.18 sum11 +r1+r2+r3-r4 1.1
Figure 4.19 sum12 +r1+r2+r3-r4 1.3
Figure 4.20 sum13 +r1+r2-r3+r4 1.0
Figure 4.21 sum14 -r1+r2-r3-r4 0.25
Figure 4.22 sum15 -r1-r2+r3-r4 0.2
Figure 4.23 sum16 -r1+r2+r3-r4 0.3
54
Figure 4.8: TR-OFDM signal for -r1-r2-r3-r4 combination
Figure 4.9: TR-OFDM signal for -r1-r2-r3-r4combination
55
Figure 4.10: TR-OFDM signal for +r1+r2-r3-r4 combination
Figure 4.11: TR-OFDM signal for -r1-r2+r3+r4 combination
56
Figure 4.12: TR-OFDM signal for -r1-r2-r3+r4 combination
Figure 4.13: TR-OFDM signal for -r1+r2+r3+r4 combination
57
Figure 4.14: TR-OFDM signal for +r1-r2-r3-r4 combination
Figure 4.15: TR-OFDM signal for +r1-r2-r3+r4 combination
58
Figure 4.16: TR-OFDM signal for +r1+r2+r3-r4 combination
Figure 4.17: TR-OFDM signal for -r1+r2-r3+r4 combination
59
Figure 4.18: TR-OFDM signal for +r1+r2+r3-r4 combination
Figure 4.19: TR-OFDM signal for +r1-r2+r3+r4 combination
60
Figure 4.20: TR-OFDM signal for +r1+r2-r3+r4 combination
Figure 4.21: TR-OFDM signal for -r1+r2-r3-r4 combination
61
Figure 4.22: TR-OFDM signal for -r1-r2+r3-r4 combination
Figure 4.23: TR-OFDM signal for -r1+r2+r3-r4 combination
62
4.2.3 PAPR Reduction Using Selective Mapping (SLM)
4.2.3.1 Motivation for Using Selective Mapping (SLM)
SLM is arguably the most popular PAPR reduction scheme which can be used for
OFDM. The main benefit of SLM is the guarantee of achieving a smaller PAPR
providing that the mapping sequences were pre-selected in an optimal manner. Another
important motivation for using SLM is that it does not cause distortion, which means
that the SNR of the transmitted signal remains the same. It must be mentioned here that
SLM does require the knowledge of scrambling sequences at the receiver end, but this
can be communicated via log2(Z) bits, where Z represents the number of SLM
sequences used.
4.2.3.2 Selective Mapping (SLM)
A promising scheme for reducing PAPR in OFDM is selected mapping. Within this
scheme, data blocks which are statistically independent are generated by means of
different phase sequences with the lower one being utilized and transmitted. This
scheme has the potential to reduce the probability of a major PMEPR (Peak-to-Mean
Envelope Power Ratio) for multicarrier transmission scheme. The goal is to perform a
change of phase on the modulated symbols (before IFFT) in order to reduce the
probability of constructive interference between the subcarriers (after IFFT) has been
computed. A block diagram of SLM is represented in (Figure. 4.24).
63
Figure 4.24: Block Diagram for SLM Scheme for OFDM System [15] [17]
Each block of data is multiplied with phase rotator Z for different length N.
Bz = [bz, 0, bZ, 1, … , bZ, N − 1]T, Z = 1,2, … , Z − 1
Resulting in 𝑍 different data blocks, so the zth phase sequence after multiplying is given
as:
UZ = [U1bZ,1, U2bZ,2, … , UN−1bZ,N−1]2
, (z = 1, 2, … , Z − 1).
Therefore, OFDM signal becomes as given in equation (4.3).
uz(t) =1
√N∑ Unb
z,nej2πfnt
N−1
n=0
where 0 ≤ t ≤ NT, = 1,2, … , U. (4.3)
Among the data blocks U(z)(z = 0, 1, … , Z − 1) only one of the modified data block,
that has the lowest PAPR value is chosen to be sent. After that the data is transmitted
Data
Source
Partition
In to
Clusters
Serial to
Parallel
Select
one
With
Minimum
PAPR
Parallel
To Serial
N-point
IFFT
N-point
IFFT
N-point
IFFT
X
X
X
U
U(1)
U(2)
U(Z-1)
u(1)
u(2)
u(Z-1)
B(1)
B(2)
B(Z-1)
64
along with the phase sequences as side information. The opposite operation is
performed at the receiver to recover the original signal. The SLM technique requires Z
IFFT operations to be performed to use it in OFDM signals and the quantity of bits used
as side data is ⌈log2(Z)⌉ for each block of information. This methodology is calculable
with a wide range of modulation and the number of sub carriers. It is cleared that the
performance of SLM in terms of PAPR reduction is dependent on the number of phase
factors Z and the design of the phase components.
4.2.3.3 Simulation Results and Discussion
By closely observing the graphical analysis, it is inferred that the PAPR reduction in
terms of dB in the CCDF for OFDM system is shown with dotted (- - - -) line and
without SLM solid (______) line. The graphical analysis and simulation results of PAPR
reduction SLM methodology can be utilized for OFDM based system. From Figure
4.25 to Figure 4.30. SLM technique uses different number of OFDM Symbol candidates
(C), with 4 phase sequences, 64 number of sub-band, and L = 4 (Oversampling factor).
This combination can reduce the PAPR of an OFDM signal at different level in dB.
But, Figure 4.30 shows the reduction approximately about 5.5 dB by using number of
OFDM symbol candidates C=256, 4 different phase sequences, 64 number of sub band,
L=4 (Oversampling factor). Table 4.3 summarizes the results presented in figures 4.25
to 4.30.
It is observed that SLM with increasing number of OFDM symbol candidate improves
the PAPR performance and no BER increases. This also decreases the system
complexity.
65
4.2.3.4 Performance Analysis of SLM
The major aim of this sub-section is to conduct a performance analysis of SLM
technique for PAPR reduction. The proposed methodology can be utilized for the
OFDM based system. One workable solution is SLM which is an easy way to mitigate
the effect of PAPR by means of undistorted processing. This is done by increase the
number of OFDM symbol candidate with 4 different phase sequences, 64 number of
sub band, L=4 (Oversampling factor), combinations can reduce the PAPR of an OFDM
signal by about 5.5 dB. This is quite enough. Furthermore it makes no BER degradation,
no interference to different subcarriers and does not require any extra processing at the
receiver. The potential of the research is quite evident from the simulation results
presented. Further work can be carried out to reduce the complexity. It can be seen that
the SLM scheme is very useful and offers advantages over the other techniques to
reduce the PAPR efficiently.
Table 4.3: PAPR Levels in dBs for OFDM Symbol Candidate Combinations [34]
Figure Nos
OFDM
Symbol
Candidates
Phase
Sequences
Over
Sampling
Factors
Sub-band
PAPR
Level
(dB)
Figure. 4.25 C=8 4 4 64 3.7
Figure. 4.26 C=16 4 4 64 4.3
Figure. 4.27 C=32 4 4 64 4.7
Figure. 4.28 C=64 4 4 64 5.0
Figure. 4.29 C=128 4 4 64 5.3
Figure.4.30 C=256 4 4 64 5.5
66
Figure 4.25: CCDF graph for PAPR of OFDM with and without SLM
Figure 4.26: CCDF graph for PAPR of OFDM with and without SLM
4 5 6 7 8 9 10 11 1210
-4
10-3
10-2
10-1
100
number of OFDM symbol candidates=8
PAPRa[dB]
CC
DF (Pr(
PA
PR
>PA
PR
a))
Original
SLM
4 5 6 7 8 9 10 11 1210
-4
10-3
10-2
10-1
100
number of OFDM symbol candidates=16
PAPRa[dB]
CC
DF (Pr(
PA
PR
>PA
PR
a))
Original
SLM
67
Figure 4.27: CCDF graph for PAPR of OFDM with and without SLM
Figure 4.28: CCDF graph for PAPR of OFDM with and without SLM
4 5 6 7 8 9 10 11 1210
-4
10-3
10-2
10-1
100
number of OFDM symbol candidates=32
PAPRa[dB]
CC
DF (Pr(
PA
PR
>PA
PR
a))
Original
SLM
4 5 6 7 8 9 10 11 1210
-4
10-3
10-2
10-1
100
number of OFDM symbol candidates=64
PAPRa[dB]
CC
DF (Pr(
PA
PR
>PA
PR
a))
Original
SLM
68
Figure 4.29: CCDF graph for PAPR of OFDM with and without SLM
Figure 4.30: CCDF graph for PAPR of OFDM with and without SLM
4 5 6 7 8 9 10 11 1210
-4
10-3
10-2
10-1
100
number of OFDM symbol candidates=128
PAPRa[dB]
CC
DF (Pr(
PA
PR
>PA
PR
a))
Original
SLM
4 5 6 7 8 9 10 11 1210
-4
10-3
10-2
10-1
100
number of OFDM symbol candidates=256
PAPRa[dB]
CC
DF (Pr(
PA
PR
>PA
PR
a))
Original
SLM
69
4.3 CHAPTER SUMMARY AND CONCLUSION
This chapter consists of two parts, i.e., section 4.1 and section 4.2. Section 4.1 provides
details and performance analysis of various PAPR reduction schemes as seen in the
literature. It is concluded from the analysis presented in section 4.1 is learnt that though
there are many schemes available to reduce PAPR, two are the most promising and can
be focused for further optimization. These are (1) Tone Reservation, and (2) Selective
Mapping.
In order for us to fully understand their functionality and to do an independent
evaluation, simulation-based performance evaluation of both of these schemes is given
in section 4.2. The results agree with the results already available in the literature and
show that both the schemes can substantially reduce PAPR without distortion.
However, SLM performs marginally better than TR. It is also noted that the
performance of SLM mainly depends upon the selection of appropriate sequence of
sub-carriers from a set of sub-carrier sequences. If selected appropriately, we can have
a large gain in PAPR reduction in SLM. However, if an optimal sequence of sub-
carriers is not selected, it may even lead to worsening of performance.
In short, SLM has great promise but needs further investigation and tuning to perform
optimal selection of sub-carrier sequences from a set of available sub-carrier sequences.
70
CHAPTER 5
PROPOSAL OF A NOVEL PAPR REDUCTION SCHEME
BASED ON MNKB-RBF
5.1 ISSUE OF SLM (OPTIMIZATION PROBLEM)
As stated in the conclusion of Chapter 04, SLM is an efficient, distortion-less PAPR
reduction scheme. It reduces PAPR substantially and has good promise for further
improvement as well.
SLM scheme is based on the core principle of selecting one sequence of sub-carriers
from a set of available sequences of phase-rotated sub-carriers. Selection of a particular
sequence is a major issue and determines the performance of SLM in terms of the
magnitude by which the PAPR is reduced. Hence, selection of an appropriate phase-
rotated sequence of sub-carriers is essentially an optimization problem.
In order to enhance performance of SLM, we intend to solve the above stated problem
by using a framework which would use ANN which is one of the best ways to solve
optimization problems.
5.2 ARTIFICIAL NEURAL NETWORKS (ANNs) AND RADIAL BASIS
FUNCTION (RBF)
Computational model for ANNs was first proposed by McCulloch and Pitts [62]. Since
then, ANNs have been recognized as a decision making tool by many researches [63,
64, 65]. ANN is particularly very useful in solving optimization problems. Optimization
problem is either difficult or almost impossible to solve with the help of conventional
rule-based programming [66].
71
Simple but yet powerful generalization capability of ANN had drawn the attention of
numerous past and present researchers [63, 64, 66, 67]. It all started with Rosenblatt
when he created the perceptron [68], a pattern recognition algorithm for supervised
classification. However, Rosenblatt’s idea could not be translated into a computer
program until the development of back propagation algorithm which has so far been the
most popularly used algorithm in ANN paradigm [70]. Thereafter, immense research
was done in this field, and in last 50 years or so there has been extraordinary growth in
this domain and the result is invention of several sophisticated algorithms [67, 71, 72].
An RBF network [73] is an ANN and whose activation functions are radial basis
functions. It was first introduced by Broom head and Lowe [71] and since then it has
become a very popular methodology to solve optimization problems that suit ANN
paradigm [72, 73, 74, 75]. The main advantage of RBF when compared with other
algorithms based on ANN paradigm is the simplicity of the computation of network
parameters [73]. Another very important feature of RBF based ANNs is to be able to
perform complex nonlinear mappings that allow a fast linear and robust learning
mechanism [66]. Originally, RBF networks were developed for data interpolation in
high dimensional space [73]. Nonetheless, RBF networks have been used in diverse
optimization domains, including pattern classification [68], time series prediction [74],
systems and control [75], and function approximation [76].
Some of the most commonly used basis functions are Gaussian functions [73],
multiquadrics functions [73], thin plate spline function [73], inverse multiquadrics
functions [73], and so forth. There is no general rule, but the choice of a radial basis
function is highly problem specific. Also, most applications using RBF make use of a
free shape parameter that plays pivotal role in the accuracy of the method and is
72
commonly chosen with the help of cross-validation [77] technique. It is a standard
practice [73] to learn three sets of parameters for RBF network: locations, widths, and
weight factors of RBF kernel. Enormous amount of work [78, 79, 80] has already been
done to select those parameters optimally.
In the conventional RBF kernel, mostly Gaussian of the Euclidean distance (ED)
between feature vector and neuron’s center is used [78]. However, there can be
scenarios where Euclidean distance is not the dominant measure to find separation
among the features, for example, if two feature vectors are separated by equal distance
from a center but separated from the center via unequal angles. In that case, the cosine
of the angle can play a vital role in differentiating the feature vectors.
There are some existing works in the literature that had discussed usage of cosine
measure with RBF kernels [81, 82, 83, 84, 85, 86, 87]. Karayiannis and Randolph-Gips
[88] have proposed a novel RBF which is a normalized version of the multiquadratic
radial basis function, where the cosine represents the angle between the transformed
vectors rather than the original vectors. Liu et al. [89] have used cosine similarity
measure to achieve high performance of classification by selecting meaningful features.
They compute the cosine similarity among the kernels rather than the original vectors.
By doing so, they transformed all the vectors to the same length, whereas we do not
perturb the feature space. Moreover, these cosine kernels are developed for Support
Vector Machine (SVM). Cho and Saul [90] have used arc cosine of the angles between
inputs in their kernel.
73
5.3 CONVENTIONAL RADIAL BASIS FUNCTION (RBF)
RBF networks in their general form consist of three layers. These layers are called an
input layer, a hidden layer, and a linear output layer. The hidden layer is one where
nonlinear activation functions operate. The layout is shown in Figure 5.1. Generally,
the input is a real vector, x ∈ Rn. The network output maps the input vector to a
scalar, y: Rn → R, which is achieved by employing the following equation:
yi = ∑ ωiφi(‖x − ci‖) +
N
i=1
bj ∀j = 1,2 … , No (5.1)
Where N and No are the number of hidden and output layer neurons, respectively, ci ∈
Rn is the center for ith neuron, ωi is output layer weight for ithneuron, bj is the bias
term for the jth output neuron, and φi is the basis function associated with ith hidden
neuron.
RBF solves a problem by mapping it into a high dimensional space in a nonlinear
manner and then applies linear decision boundary. The concept of transformation to
high dimensional space is justified by Cover’s theorem, according to which
classification via linear separation becomes easier by translating the features from low
dimension to high dimension [91].
The significance of adding bias to the output is to improve the approximation quality
by shifting the decision boundary. The weights of the network govern the position of
the decision boundary in the feature space. However, during the adaptive weight update,
if bias is not used, then the hyper-plane is forced to pass through the origin of the feature
space defined by the inputs or feature vectors. Although it is valid for some problems,
in many others this separation boundary is desired to be located somewhere else.
74
Figure 5.1: Architecture of the RBF based Neural Network [66]
As a general rule, all inputs are connected to each hidden neuron. The domain of
activation function is a norm which is typically taken to be the Euclidean distance
between input and the centers of every neuron. Most commonly used RBF kernels are
as follows [66].
Multiquadrics are given as:
φi(‖x − ci‖) = (‖x − ci‖2 + τ2)1/2 (5.2)
Inverse multiquadrics are given as:
φi(‖x − ci‖) = 1
(‖x − ci‖2 + τ2)1/2 (5.3)
And Gaussian as:
φi(‖x − ci‖) = e−‖x−ci‖2/β2 (5.4)
ϕ1
Σ ϕ2
ϕn
ωi
X1
X2
Xn
y
Bias
Input layer Hidden layer Output layer
75
Where τ > 0 a constant and β is spread parameter. The sensitivity of a hidden neuron
towards a data point varies in proportion with the distance of the data point from its
center. For example, in case of a conventional ED based RBF network that uses
Gaussian in its kernel, this sensitivity can be fine-tuned by adjusting β; if β is large, it
implies less sensitivity and vice versa.
5.4 A RECENTLY PROPOSED “NOVEL KERNEL BASED RBF (NKB-
RBF)”
Motivated by the observation that “in many scenarios Euclidean distance is not the
dominant measure to find the separation among features”, Aftab et.al, propose in [92]
a novel RBF kernel which consists of a linear combination of Gaussian and cosine RBF
kernels. The cosine RBF kernel computes the cosine of the angle between supplied
feature vector and the center vector associated with that neuron.
Aftab et.al, in [92] state that intuition suggests that ED is not the only measure to
contrast the FVs. For example, in the case when FVs are equally separated in distance,
then the ED will be no more effective. To deal with this issue, they proposed a
generalized RBF kernel by linearly combining the conventional ED based RBF kernel
and a cosine based RBF kernel which is formulated as follows:
φi(x, ci) = α1φi1(x. ci) + α2φi2(‖x − ci‖) (5.5)
Where α1, α2 are weightage parameters for cosine and Euclidean kernels, respectively,
which can acquire values in this range: 0 ≤ α1, α2 ≤ 1. Moreover, φi1(x. ci) and
φi2(‖x − ci‖) are the cosine and the Euclidean kernels, respectively, for 𝑖𝑡ℎ neuron.
These are further defined as follows:
76
φi1(x. ci) ≜ cos(θi) = x. ci
‖x‖. ‖ci‖ (5.6)
φi2(‖x − ci‖) = e−‖x−ci‖2/β2 (5.7)
Where x. c𝑖 represent the dot product between the two vectors.
By observing Equation (5.6), we can notice that the kernel φi1(x. ci) computes the
cosine of angle between x and ci. Hence, φi1(x. ci) may attain the values in the range
[−1, +1]. If it returns to 1, it implies that the x is aligned with ci, whereas its 0 return
value corresponds to the scenario when x is perfectly orthogonal to ci: and the return
value of −1 indicates that x and ci are aligned in opposite directions.
5.5 ISSUES OF NKB-RBF
Recently proposed Novel Kernel Based RBF (NKB-RBF) is shown in [92] to perform
well with different problems as it utilizes the complimentary property of two kernels
that are based on the Euclidean (distance) and Cosine (angle) or correlation measure.
However the NKB- RBF suffers from the manual selection of the mixing parameter.
We can see in Equation (5.5) that α1 and α2 are the mixing parameters of Cosine and
Euclidean kernels. The manual selection (as suggested by MNKB-RBF) of the mixing
parameters α1 and α2 is a critical issue particularly in the situations with no
generalization of the problem. For the selection of these mixing parameters one needs
prior information about the problem. In cases where cosine is the good measure of
similarity or in other words the angle is the discriminating element we will have to
choose higher value for α1 (close to 1) and lower value for α2 (close to 0) to have
optimal performance. The reserve must be selected for these mixing parameters, i.e.,
α1 (close to 0) and lower value for α2 (close to 1), for the problem where angle is not
77
the optimal discriminating element. If this guide line is not followed, we will face
degradation in performance instead of improvement. Table 5.1 shows the criteria for
the manual selection of mixing parameters α1 and α2.
Table 5.1: Criteria for Selection (Manual) of Mining Parameters 𝛂𝟏 and 𝛂𝟐 [92]
α1 α2
Weightage to the Cosine
Distance (CD) should be high
in case where CD is the
distinguishing element.
Should be low if the CD is the
confusion factor
NKB-RBF allows to choose
α1 manually which is not
possible in the dynamic
scenario of SLM
Weightage to the Euclidean
Distance (ED) should be high
in case where ED is the
distinguishing element.
Should be low if the ED is the
confusion factor
NKB-RBF allows to choose α2
manually which is not possible
in the dynamic scenario of
SLM
To get the best performance from the NKB-RBF one needs to select the optimal values
of the mixing parameters. The manual selection of mixing parameters as suggested by
NKB-RBF requires prior knowledge of the system. This restricts the application of
NKB-RBF to only the problems where prior information about the system is known. In
the case of SLM, we need as adaptive optimization algorithm that can select the optimal
weights of the individual kernels to harness the complimentary properties of the two
kernels without the prior knowledge of the incoming signal type.
78
5.6 PROPOSED SOLUTION: MODIFIED NKB-RBF (MNKB-RBF)
The critical issue of NKB-RBF is the manual tuning of the mixing parameters α1
and α2. In order to use it for optimization of selection of one phase rotated sub-
sequence of signals among many candidate in SLM (with minimum PAPR), we need
to make the tuning of α1 and α2 dynamically adaptive. Since the core objective of the
proposed adaptive algorithm is to minimize the overall error of the system, we propose
to use the error energy besides distance for tuning of α1 and α2. We call our new
algorithm as Modified NKB-RBF or MNKB-RBF in short.
In order to incorporate the error energy, we replace α1 and α2 with the η(n) and 1-η(n)
in Eq. (5.5), to make them time varying. We can rewrite the kernel equation as:
φi(x, ci) = η(n)φi1(x. ci) + (1 − η(n))φi2(‖x − ci‖) (5.8)
Where,
η(n) = weight of Cosine Distance (CD)
1- η(n) = weight of Euclidean Distance (ED)
The MNKB-RBF algorithm uses the update rule of a Robust Variable Step-Size Least
Mean Square (RVS-SLMS) algorithm [93] for its learning rate where the update is
obtained by an estimate of the autocorrelation between current error e(n) and past error
e(n-1).
If ρ(n) is the final output error, the error energy of the MNKB-RBF algorithm is defined
as follows:
ρ(n) = β ρ(n) + (1 − β)e(n)e(n − 1) where 0 < β < 1 (5.9)
Note that ρ(n) is the error energy at nth instant.
79
In the proposed method the weight of the cosine kernel can be calculated as follows:
η(n + 1) = τ ∗ η(n) + σρ(n) where 0 < τ < 1, 0 < σ < 1 (5.10)
Here η(n+1) is the weight of the Cosine Distance for next iteration and τ, σ and β are
the momentum coefficients.
η(n + 1) = {
1, η(n + 1) > 1
η(n + 1), 0 < η(n + 1) < 1
0, η(n + 1) < 0
(5.11)
5.7 PROPOSAL OF A NOVEL PAPR REDUCTION SCHEME BASED ON
MNKB-RBF
In section 5.6, we proposed a novel technique for the autonomous selection of weights
of mixing parameters of the NKB-RBF algorithm and named it MNKB-RBF. The
proposed kernel can be used in the dynamic environments where little or no prior
information about the discriminating measure in known. As in the case of Selective
Mapping we want to make our system adaptive and suitable for dynamically selecting
an optimal sub-sequence (with lowest PAPR) from a set of available sub-sequences of
the frequencies with unknown effects on PAPR. The proposed kernel is expected to
perform well in this scenario because it autonomously selects weights based on the error
energy.
80
Figure 5.2: Block diagram of the Proposed PAPR Reduction Scheme
Using MNKB-RBF
The framework of the proposed technique (based on MNKB-RBF and SLM) has been
shown in Figure 5.2, which selects the sub-sequence with the lowest PAPR from the
given sequences. From this figure it can be seen that the selection of the optimal phase
rotation is performed by advanced technique of optimized weighted kernel. In the
proposed system the signal will first pass through the frequency transformation block
and then the SLM block, which will select the appropriate carrier signal for the given
signal.
The SLM block in modified to indicate the selection of the best carrier sub-sequence
based on the intelligent decision of the dynamic method of MNKB-RBF to minimize
S/P IFFT
SLM Encoder
MNKB-RBF phase rotation selector
Input Data
.
.
.
.
.
.
MNKB-RBF based SLM Module
Modified Novel Kernel Based-Radial Basis Function Neural Network Phase Rotation Selection System
utilizes the intelligence of Artificial Neural Networks to select the optimal sequence set for PAPR reduction
81
the chances of the rise in PAPR. The argument is supported by extensive
simulations/experiments performed and discussed in Chapter 6.
5.8 CHAPTER SUMMARY AND CONCLUSION
In this chapter, we stated that in SLM, the selection of an appropriate phase-rotated
sequence of sub-carriers with minimum PAPR is essentially an optimization problem.
And that the issue can be optimally addressed by using ANNs. We showed that the
performance of ANN largely depends upon the kernel (Radial Basis Function) being
used. We introduced an RBF most recently proposed (NKB-RBF) and is shown to
perform well in many optimization applications. The performance of NKB-RBF largely
depends upon the tuning parameters α1 and α2. Moreover, NKB-RBF suggests manual
selection of weights of these tuning parameters. In many applications in general and in
our case in particular manual selection of weights of these parameters is simply not
possible due to dynamic nature (real-time selection) of our application.
Hence, we proposed in this chapter a modified version of NKB-RBF and termed it
MNKB-RBF. The key feature of MNKB-RBF is its ability to automatically adjust the
weights of the tuning parameters taking into account the error energy.
Also described in this chapter is the framework proposed by us for reduction of PAPR
which is based on SLM and our proposed MNKB-RBF.
82
CHAPTER 6
PERFORMANCE EVALUATION OF PROPOSED PAPR
REDUCTION SCHEME
In chapter 5, it is stated that selection of a phase-rotated sequence of signals with the
lowest PAPR from a set of given sequences is an optimization issue. And that the
problem can be solved using Artificial Neural Networks. However, the performance of
an ANN depends upon the RBF kernel being used. Though many conventional kernels
exist but a recently introduced kernel that is referred to as NKB-RBF has shown better
performance. It is also described in Chapter 5, that the performance of NKB-RBF in
turn depends upon careful manual selection of two tuning parameters α1 and α2. Since,
in proposed case manual selection of these parameters is not possible, so a modified
kernel is proposed and referred to as MNKB-RBF. MNKB-RBF selects optimal values
of α1 and α2 automatically instead of manually (for details please refer to chapter 5).
The performance of the proposed scheme (chapter 5) for selection of a phase-rotated
sequence of signals from a set of available sequences depends on MNKB-RBF and
SLM. Since SLM is already a known and evaluated scheme, hence the performance of
the proposed scheme solely depends upon the performance of MNKB-RBF. In this
chapter, the MNKB-RBF is presented with thorough evaluation, which shows that
MNKB-RBF performs better than NKB-RBF.
83
6.1 PERFORMANCE EVALUATION ENVIRONMENT
We have performed a comprehensive evaluation of Modified Novel Kernel Based RBF
(MNKB-RBF) against Novel Kernel Based RBF (NKB-RBF) by using simulations in
MATLAB of ANNs which use these kernels.
In order to have a good level of confidence in the deduction that we make after
comparison of these two kernels. Nine different datasets have been generated on which
the performance of both of these kernels is tested and compared. The details of the
simulation environment, test cases, and the nature of the datasets are being given in the
following section.
6.2 SIMULATION ENVIRONMENT AND TEST CASES
In order to train and test the ANNs which use the Novel RBF and the proposed RBF
(MNKB-RBF), first of all nine different datasets of one hundred randomly generated
messages are generated. In each dataset, the initial fifty messages are for the purpose of
training the ANN and the later fifty messages are to be used for testing the performance
of the ANN.
6.2.1 Regarding Datasets
Regarding dataset 1, 2, and 3, the carrier is to be selected from a pool of 64 sequences
of phase-rotated carriers. However, 8- QAM, 16-QAM, and 32-QAM are used to
modulate each message in dataset 1, dataset2, and dataset 3 respectively. This is done
in order to see whether or not changing modulation changes the pattern of results or
leads to the same conclusion. In our graphic or numeric results it indicates the nature of
dataset by the following scheme [64 x 8]. In this scheme, the first numeric value
indicates the number of phase-rotated sequences in the pool and the second numeric
84
value representing the number of symbols used in QAM for modulation. For example
in [64 x 8], the pool has 64 sequences and 8 symbols are used to modulate the messages.
Similarly, in dataset 4, 5, and 6, the pool has 128 phase-rotated sequences with
messages modulated using 8-QAM, 16-QAM, and 32-QAM respectively.
Lastly, in dataset 7, 8, and 9, there are 256 phase rotated sequences and messages are
modulated using 8-QAM, 16-QAM, and 32-QAM respectively.
6.2.2 Regarding Test Cases
Multiple iterations of simulations are performed for both “Training Phase” as well as
“Testing Phase” on all of the datasets as specified in the above section. Since, a large
number of iterations are performed, the deductions derived from the analysis of these
results (in section 6.4 and 6.5) have higher level of confidence and their reliability is
thought to be better too.
6.3 CORE CODE OF THE PROPOSED ALGORITHM
The proposed kernel has been implemented in MATLAB. Produced below is the core
portion of the code representing the main part of the proposed algorithm. The phase-
rotated sequence of the carrier selected by this code is fed to the “SLM Encoder” for
encoding and later transmission to the destination. The performance of new proposed
algorithm is decided by the fact that it should select a carrier with minimum PAPR.
The code given in Figure 6.1 implements the proposed MNKB-RBF algorithm. It is
clear from lines 1, 5, and 6 that many iterations are done in order for the error energy
to become minimum. In line number 7 and 8, Euclidean Distance (φi1) and Cosine
Distance (φi2) are calculated for the ith iteration (refer to Equation 5.8). In line number
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9, overall Distance (φi) is calculated for the ith iteration incorporating both φi1 and φi2
weighted by the error energy e(n) (Equation 5.8).
Figure 6.1: Core MATLAB code of the Proposed RBF (MNKB-RBF)
The loop from line number 6 to 10 determines final output error energy ρ(n) for the nth
instant (Equation 5.9) incorporating the momentum controlling coefficient β. Finally,
the weighted sum of the error energy e(n) and the final error energy ρ(n) is calculated
in line number 16, which in turn becomes error energy for the next instant, i.e., (n+1)th
instant (Equation 5.10).
1. for k=1:epoch 2. I(k)=0; 3. ind=randperm(m); 4. 5. for n=1:m 6. for i=1:n1 7. ED(i)=exp((-(norm(P(ind(n),:)-c(i,:))^2)))/beeta^2; 8. CD(i)=abs(P(ind(n),:)*c(i,:)')/(norm(P(ind(n),:))*norm(c(i,:))+1e-50); 9. phi(n,i)=eta(n)*ED(i)+(1-eta(n))*CD(i); 10. end 11. y(n,:)=w*phi(n,:)'; 12. d(n,:)=f(ind(n),:); 13. e(n+1,:)=d(n,:)-y(n,:); 14. 15. p(n+1)=(p(n)*beeta)+((1-beeta)*(e(n,:)*e(n+1,:)')); 16. eta(n+1)=(tau*eta(n))+(sigma*p(n)); 17. 18. I(k)=I(k)+e(n+1,:)*e(n+1,:)'; %%% Objective Function 19. 20. w=(w+eta*e(n+1,:)'*phi(n,:)); 21. end 22. e(1,:)=e(end,:); 23. End
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6.4 TRAINING RESULTS
The training of both kernels, i.e., NKB-RBF and MNKB-RBF is done using three
different training cases. Each test case consists of tests done on three datasets of similar
nature as listed below.
Training Case I: Dataset having 64 sequences of phase-rotated carriers.
Dataset 1 – [ 64 x 8]
Dataset 2 – [ 64 x 16]
Dataset 3 – [ 64 x 32]
Training Case II: Dataset having 128 sequences of phase-rotated carriers.
Dataset 4 – [128 x 8]
Dataset 5 – [128 x 16]
Dataset 6 – [128 x 32]
Training Case III: Dataset having 256 sequences of phase-rotated carriers.
Dataset 7 – [256 x 8]
Dataset 8 – [256 x 16]
Dataset 9 – [256 x 32]
The results of the training phase in graphical form are shown in Figures 6.2 to 6.10.
The results shown in Figure 6.2, 6.3, and 6.4 correspond to “Training Case I”. Similarly
Figure 6.5, 6.6, and 6.7 to “Training Case II” and Figure 6.8, 6.9, and 6.10 relate to
“Training Case III”.
Evaluation and analysis of training phase results are given in the following sub-section.
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6.4.1 Evaluation, Analysis, and Deductions
The x-axis in these graphs (Figures 6.2 to 6.10) represents the number of epochs for
which the simulation was run. The y-axis gives the magnitude of the Mean of the
Squared Error (MSE). Each graph has two curves, i.e., the dashed-line curve (red
colored curve) for the Novel RBF (NKB-RBF) and the solid-line curve (blue curve) for
the Proposed RBF (MNKB-RBF).
Let us first of all analyze graphs of the “Training Case I” (64 sequences of carriers),
i.e., graphs shown in Figure 6.2, 6.3, and 6.4. It can be seen that in Figure 6.2, 8 symbols
are used for modulation, that for only the first epoch, the MSE is higher for MNKB-
RBF. Whereas, from 2nd epoch and onwards, MSE for MNKB-RBF is lower than NKB-
RBF. This indicates much early successful training of ANN which uses the proposed
kernel. After around only 7th epoch, MSE for MNKB-RBF reaches its minimum which
is 2 and is an excellent result showing that less time is needed to train MNKB-RBF
based ANN.
It can be seen that curves in Figure 6.2, 6.3, and 6.4 do not show substantial change in
their pattern even after increase in modulation symbols from 8 to 64. This leads us to
deduce that MNKB-RBF is robust against variation in modulation symbol rate. This is
important for MNKB-RBF to be indeed practically used in not only PAPR reduction
schemes but also in other optimization applications.
The results of “Training Case II and III” which are shown in Figures 6.5 to 6.10 are
focused now, some interesting observations can be made. For one, the performance of
MNKB-RBF does not change even though the pool of candidate phase-rotated
sequences is increased from 64 to 256. In all of these graphs it can be seen that MSE
exponentially reduces (solid blue curve) and minimizes after around 7 epochs. This
88
analysis leads us to the deduction that MNKB-RBF is robust against variation in the
size of the pool of phase-rotated carrier sequences as well.
On the other hand the performance of NKB-RBF has degraded with increase in the pool
size of carrier sequences. MSE for NKB-RBF is not reducing fast enough which is
evident from the less steepness of the dashed-line red curves for NKB-RBF in Figures
6.2 to 6.10.
Now look at the final value of MSE for which both NKB-RBF and MNKB-RBF
stabilize. It is visible in these graphs that the final MSE value for NKB-RBF is around
5, whereas for MNKB-RBF, MSE keeps on decreasing as we increase the size of the
pool of sequences and becomes almost zero. The final MSE values (approximated) are
summarized against size of pool of sequences in the following table for MNKB-RBF.
Hence, it is concluded that MNKB-RBF performs much better than NKB-RBF in terms
of training of ANN.
Table 6.1: Final Mean Square Error (MSE) Comparison
Size of Pool of
Carrier Sequences
MSE for
Novel RBF
MSE for
Proposed RBF
64 4.0 2.0
128 3.5 1.0
256 3.0 0.1
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Figure 6.2: Training cost comparison between Novel RBF and Proposed RBF
(Phase-rotated sequences = 64, Modulation = 8-QAM)
Figure 6.3: Training Cost Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 64, Modulation = 16-QAM)
90
Figure 6.4: Training cost comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 64, Modulation = 32-QAM)
Figure 6.5: Training cost comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 128, Modulation = 8-QAM)
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Figure 6.6: Training cost comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 128, Modulation = 16-QAM)
Figure 6.7: Training cost comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 128, Modulation = 32-QAM)
92
Figure 6.8: Training cost comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 256, Modulation = 8-QAM)
Figure 6.9: Training cost comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 256, Modulation = 16-QAM)
93
Figure 6.10: Training cost comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 256, Modulation = 32-QAM)
6.5 TESTING RESULTS
The second most important phase of performance evaluation of primarily MNKB-RBF
is done and is generally termed as “Testing Phase” in the ANN community. However,
in order to evaluate MNKB-RBF, we need to do its comparison with other similar
algorithm. Hence, like the “Training Phase” performance of MNKB-RBF is compared
with NKB-RBF and additionally with simple SLM as well.
Like the “Training Phase”, in the “Testing Phase” too three basic test cases are
performed. Each testing case in turn consists of tests done on three datasets of similar
nature as listed below:
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Testing Case I: Dataset having 64 sequences of phase-rotated carriers.
Dataset 1 – [ 64 x 8]
Dataset 2 – [ 64 x 16]
Dataset 3 – [ 64 x 32]
Testing Case II: Dataset having 128 sequences of phase-rotated carriers.
Dataset 4 – [128 x 8]
Dataset 5 – [128 x 16]
Dataset 6 – [128 x 32]
Testing Case III: Dataset having 256 sequences of phase-rotated carriers.
Dataset 7 – [256 x 8]
Dataset 8 – [256 x 16]
Dataset 9 – [256 x 32]
The results of the testing phase in graphical form are shown in Figures 6.11 to 6.19.
The results shown in Figure 6.11, 6.12, and 6.13 correspond to “Testing Case I”.
Similarly Figure 6.14, 6.15, and 6.16 to “Testing Case II” and Figure 6.17, 6.18, and
6.19 relate to “Testing Case III” respectively.
Evaluation and analysis of training phase results are given in the following sub-section.
6.5.1 Evaluation, Analysis, and Deductions
The x-axis in these graphs (Figures 6.11 to 6.19) represents the “Message Number”
under focus. Recall that a total of 50 messages are to be sent as separate transmissions
95
selecting a phase-rotated sequence from a pool of given sequences. The sequence is to
be selected in a manner to minimize PAPR for that message. Hence, it can be seen that
there are 50 messages on x-axis with PAPR for each message shown on y-axis.
Each graph has three curves black solid-line curve representing our proposed RBF
(MNKB-RBF), blue dashed-line curve for the Novel RBF (NKB-RBF) and red solid-
line curve for simple SLM.
First of all let us analyze the graphs for the “Testing Case I” shown in Figures 6.11,
6.12, and 6.13. At first glance it seems that the results are random. But a careful look at
these graphs reveals the following.
For majority of the messages, the red solid-live curve is below the other
two curves indicating high values of PAPR for simple SLM and thus it
is knocked out of the competition with NKB-RBF and MNKB-RBF
Comparing and carefully analyzing the solid-line black curve (MNKB-
RBF) with the dashed-line blue curve (NKB-RBF). It can be seen that
for majority of the messages PAPR for MNKB-RBF is lower than NKB-
RBF. For only a few messages, PAPR for MNKB-RBF is higher than
NKB-RBF.
As a whole it is concluded that MNKB-RBF outperforms both Simple
SLM and NKB-RBF in terms of reduction in PAPR levels.
The same pattern, i.e., curve for MNKB-RBF is below other two curves for most of the
messages, is observable in results of Test Case II and III as shown in the graphs of
Figures 6.14 to 6.19. Hence, these results concur with the conclusion we drove from
the results of Test Case I.
96
Figure 6.11: Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 64, Modulation = 8-QAM)
Figure 6.12: Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 64, Modulation = 16-QAM)
97
Figure 6.13: Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 64, Modulation = 32-QAM)
Figure 6.14: Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 128, Modulation = 8-QAM)
98
Figure 6.15: Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 128, Modulation = 16-QAM)
Figure 6.16: Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 128, Modulation = 32-QAM)
99
Figure 6.17: Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 256, Modulation = 8-QAM)
Figure 6.18: Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 256, Modulation = 16-QAM)
100
Figure 6.19: Testing Comparison between Novel RBF and Proposed RBF
(Phase-Rotated Sequences = 256, Modulation = 32-QAM)
6.5.2 Probability of Selecting Carrier of Low PAPR
In order to be clearer about the deduction drawn in the previous sub-section, the results
of the previous sub-section are reprocessed to find the probability of selection of a
phase-rotated carrier sequence with the lowest PAPR from a given pool of phase-
rotated sequence. The probability is calculated for all three schemes, i.e., Simple SLM,
Novel RBF, and Proposed RBF is shown in Table 6.2.
The 1st column of this table (from left) gives the test number. The details regarding the
size of the pool of sequences and the number of symbols used for modulation are given
in the 2nd column. Whereas, the 3rd, 4th, and 5th column show the probability calculated
for the Simple SLM, Novel RBF, and the Proposed RBF. Now note the values in these
columns give the probability of the selection of the lowest PAPR which implies that the
101
scheme with the highest probability is the best one. Hence, for each row the highest
values are underlined and produced in bold font.
One can easily notice that except for Test Case 1-3 and 3-2, the performance of the
Proposed RBF is the best of the three. Therefore, it is concluded with a higher level of
confidence that the performance of the Proposed RBF is better than the other two
contenders.
Table 6.2: Probability of Selecting Carrier of Low PAPR
Test Case
Number
Test Case Details
(Carriers x Symbols) SLM
Novel
RBF
Proposed
RBF
Test Case 1-1 256 x 32 0.54 0.82 0.88
Test Case 1-2 256 x 16 0.48 0.74 0.80
Test Case 1-3 256 x 8 0.44 0.80 0.76
Test Case 2-1 128 x 32 0.46 0.58 0.60
Test Case 2-2 128 x 16 0.40 0.52 0.66
Test Case 2-3 128 x 8 0.40 0.66 0.68
Test Case 3-1 64 x 32 0.58 0.58 0.62
Test Case 3-2 64 x 16 0.42 0.60 0.40
Test Case 3-3 64 x 8 0.40 0.56 0.58
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6.6 CHAPTER SUMMARY AND CONCLUSION
This chapter has elaborated upon the extensive performance evaluation of the proposed
PAPR reduction framework which is based upon SLM and the proposed MNKB-RBF.
Both the training and the testing results indicate that the proposed framework performs
better than simple SLM and when SLM is used in conjunction with NKB-RBF.
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CHAPTER 7
SUMMARY AND CONCLUSION
7.1 SUMMARY
In this dissertation, first of all described the reasons for conducting this research
activity. The argument goes like this. Lately most of the broadband systems use OFDM
as the main modulation technique. ODFM is used due to its main feature of using a
large number of low frequency sub-carrier signals (orthogonal to each other) instead of
one high-frequency carrier to achieve high data rate. The orthogonality of the sub-
carriers and being of low frequency ensure robustness against many kinds of
interferences. However, OFDM also suffers from high level of PAPR. A lot of research
activity is being done by the research community in this area to device frameworks and
algorithms which may ensure low PAPR values.
Many schemes and frameworks do exist in the literature which claim to produce low
PAPR values, for example, Clipping and Filtering, Peak Reduction Carriers, Envelop
Scaling, Coding, Partial Transmit Sequence, Selective Mapping, Tone Reservation,
Tone Injection, etc. A literature-survey has been performed based performance of
evaluation of some of the promising among these in order for us to select one to two
schemes to focus upon for performance improvement. However, it was felt to conduct
our own simulation-based performance evaluation for two reasons, i.e., firstly, to
understand in a better way the working of these schemes, and secondly to be absolutely
sure which scheme has the potential for further improvement. It was found that SLM
fulfills research criteria.
104
Since the core idea of SLM scheme is to choose one sequence of low frequency sub-
carriers from a pool of given sub-carriers in such a way that PAPR gets reduced, hence
it effectively is an optimization issue. Therefore, a new framework is proposed which
uses Artificial Neural Networks (ANN) in conjunction with SLM. The job of the ANN
is to optimize the selection of sub-carrier sequence such that the PAPR is the lowest for
that sequence. Because this scheme is to be used in real life and real time environments,
the performance of the ANN is critical issue. The performance of the ANN in turn
depends upon the RBF Kernel used in the ANN.
Recently, a new kernel has been proposed and termed to as Novel Kernel Based RBF
(NKB-RBF) and is shown to have better performance. However, the performance of
NKB-RBF depends upon values selected for the weightage parameters α1 and α2. In
NKB-RBF, the weights of α1 and α2 are selected manually which is not feasible in our
case of usage in real time environment. Hence, proposed a modified version of this
kernel and call it as Modified NKB-RBF (MNKB-RBF). The proposed framework is
evaluated which uses SLM and MNKB-RBF based ANN, which optimally selects a
sequence of phase-rotated sub-carriers to be better and more efficient than Simple SLM
and NKB-RBF based SLM as well.
7.2 CONCLUSION
As stated in the previous section, the focus of this research activity is to propose a
mechanism/framework which minimizes PAPR in majority of transmissions. Such a
mechanism is indeed proposed and described in this dissertation. The core of the
proposed scheme consists of both SLM scheme and ANN which uses a modified
105
version (MNKB-RBF) of already available kernel. The conclusions of this research
activity are enumerated below.
SLM, one of the PAPR reduction schemes, has the potential for further
improvement in performance and can lead to optimal selection a sequence of
phase-rotated sub-carrier from a pool of available sequences such that its PAPR
is the lowest.
SLM used in conjunction with ANN has the potential to lead to optimal
selection.
A recently proposed ANN kernel (NKB-RBF) is shown to perform better but
suffer from the manual selection of weights of the tuning parameters α1 and α2.
The proposed kernel (MNKB-RBF) which uses error-energy to automatically
adjust weights of α1 and α2 is shown in this dissertation through simulation
results to perform better than NKB-RBF.
From analysis of simulation results (comprehensive set of scenarios) it is
concluded that the probability of selection of a sequence of phase-rotated sub-
carriers from a pool of given sequences in the proposed framework is the highest
among all contenders (Simple SLM, NKB-RBF based SLM).
7.3 FUTURE WORK/RESEARCH GUIDELINE
There are multiple ways in which this research activity can be taken to the next level.
A few of these ways are listed below.
Though simulation based evaluation does provide a pretty good idea on
performance, hardware based implementation and experimentation may open
up new issue and avenues regarding realizability of MNKB-RBF. It would be
106
interesting to implement MNKB-RBF in the hardware and study its usability in
the real environment.
It would be very interesting to compare the performance of the Proposed RBF
when it is implemented in both ordinary hardware and in Field Programmable
Gate Array (FPGA). In this aspect the selection the performance comparison
parameters may require a lot of brain storming. Note that FPGA provides a lot
of flexibility in terms of change management. However, the time taken by both
implementations to decide the phase-rotated sequence of sub-carrier may or
may not be substantially different.
In this project error energy has been used to automatically adjust the weights of
the tuning parameters α1 and α2. There may be other and better choices
available. It is worth exploring these choices.
107
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