Spatial Multiplexing System with OrthogonalData Streams

IKhawaja Tauseef Tasneem, 2Adnan Ahmed Khan, 2Sajid Bashir, 'Syed Ismail Shah, Sr. MIEEElIqra University Islamabad Campus, Islamabad, Pakistan2Centre for Advanced Studies in Engineering, Pakistan

Email of the corresponding author: tauseefwiqraisb.edu.pk

Abstract- A new orthogonal coded Multi-Input-Multi-Output (MIMO) system using Walsh codes ispresented in this paper. The proposed SpatialMultiplexing system offers equivalent Bit ErrorRate (BER) performance as compared to theconventional uncoded MIMO system whileincreasing data transmission rate by two folds. Theoptimum Maximum Likelihood (ML) detector isused in the proposed system. As ML detector offershigh computational complexity, therefore we alsopresent the linear zero forcing (ZF) and minimummean square error (MMSE) detectors. Aperformance comparison between the proposed andconventional MIMO system is also discussed.

Index Terms Multi-Input Multi-Output systems(MIMO), Walsh, ML detection.

I. INTRODUCTION

The demand for higher data rate communications formultimedia-based bandwidth intensive applications is onincrease. Multiple transmitter and receiver basedcommunication systems (MIMO) have shown promise tomeet these challenges [1-3]. MIMO systems are a naturalevolution of the so-called Smart antennas, a populartechnology using antennas arrays for improving wirelesstransmissions couple of decades back. A MIMO systemhas the ability to deal with multi-path propagation, byturning it into a benefit for the user. It effectively takesadvantage of random fading [1-4] and multipath delayspread [5-6].A number of architectures have been developed for

MIMO systems in the last couple of years. The VerticalBell-laboratories Layered Space-Time (V-BLAST)system is one promising implementation of MIMOsystems [1-2]. However, the performance of the V-BLAST detection scheme [7-8], is limited due toimperfect interference cancellation and insufficientreceive diversity. Maximum Likelihood (ML) detectionscheme performs the best, but its complexity increasesexponentially when numbers of transmit antennasincrease and complex modulation schemes are used.

The ML detection of the signals transmitted over theMIMO channel is a known NP-complete communications

problem. A number of MIMO detectors have beenproposed [9-11] to reduce its complexity. Anotherpotential solution is Sphere Decoder (SD) [12-16] withhas polynomial computational cost on the average [13].However, when problem dimensions are high itscomplexity coefficients and variance of computationaltime becomes large. These drawbacks of SD were tackledin Ordered Sphere Decoding (OSD) [17]. In [18] QRdecomposition with sort and Dijkstra's algorithm is usedto decrease the complexity of Sphere Decoder. Anotherdetector based on multistage likelihood scheme isproposed in [19] where the Euclidean distance of thancandidate symbols combinations instead of all possiblecombinations is calculated. The group detection schemes[9] give better performance but their complexity increasewhen the number of sub streams in a group is large. Softinterference cancellation mitigates error propagationeffect; however complexity is again a problem [11].

In this contribution we present a Walsh coded MIMOsystem. The proposed architecture enhances the data ratewhile keeping having lower computational complexity ascompared to the conventional uncoded MIMO systems.Rest of the paper is organized as follows. The WalshCoded MIMO (WC-MIMO) system model is explainedin section II. Section-III presents the proposed lineardetection techniques for the proposed system. In section-IV performance analysis and simulation results are given,finally last section concludes the paper.

II. SYSTEM MODEL

A Walsh coded multiple-input multiple-output (MIMO)system consists of two transmit and two receive antennasas shown in fig-1. The demultiplexer in the transmittersplits the input data di into two sub-streams. Each sub-stream is then further demultiplexed into two. Theindividual bits are then spread using Walsh code andadded to form the transmitted signal Xk where

2

XkZ=EdkWiil for k = 0, 1i=l

(1)

Grouping all the transmitted and received signals intovectors, the system can be viewed as transmitting anvector signal x through a 2x2 Raleigh fading channel

1-4244-1494-6/07/$25.00 C 2007 IEEE

0

W i1Fig. 1 : Orthogonal coded MIMO system transmitter and receiver

matrix channel H, with Nr x 1 Gaussian noise vector nadded at the input of the receiver.The received signal at the first and second receivingantenna can be expressed as

Y1 h 1XI +h82X2 +n,

Y2 = h2IXI +h22X2+n2

(2)

(3)

The received signals are despreaded separately usingcorresponding Walsh codes as follows

1 T 1 1r5 = yi Wo =0 idl + 42d2 + 7

2 T1 2 2r5 = WI = kdl2 + 42A2 +771

r2 = Y21W = h21 1+ h22 2 + 7722 Ti,

2

~ 2 2r2 =Y2WIu= h2A + h22d2 +72

Using (4) and (6) we can write

r, = Hdl + il

whererIIIIrT1;1 = [1 71 aT nd

d=[di d2]

Similarly, combining (5) and (7) we can write

r2=Hd2 + 112

(4)

(5)

(6)

The results in (8) and (9) can be more generallyexpressed as

r1 =Hdi +Ii for i = 1,2 (10)which can be used to decode the data vectors di and d2.

III. DETECTION TECHNIQUES

A number of detection schemes can be used for theproposed transmission system. We start with the OptimalMaximum Likelihood (ML) Detection method fordecoding the transmitted data.

A. ML DETECTION:Considering equiprobable symbol transmissionMaximum Aposteriori Probability (MAP) rule on (10)simplifies to Maximum Likelihood (ML) detection andcan be expressed as:

d, = arg min I|ri - Hd, 11di es

(7)

(8)

(1 1)

Which is in fact the minimization of squared Euclideandistance to a target vector r, .

B. LINEAR DETECTORS1) Zero Forcing Detector:

Assuming perfect channel state information (CSI), a low-complexity linear Zero-Forcing (ZF) detection algorithmcan also be applied that outputs

(9)

h r=[2 r2 T } g2 52 T dwhere r2 = Irl r22IT; 112 =I1;7472 1 and

di = [dj d2 ]T

Also H LZ:1 h221

di= Q(H- rl) for i =1,2 (12)

where Q is a quantizer that maps its argument to nearestsignal point in the constellation.

2) MMSE Detector:

The MMSE detector minimizes the mean square errorbetween the desired symbols and the output of the lineardetector and leads to the result

di= Q(Wr) for i =1, 2 (13)

where W is chosen to minimize the mean square error

J= E[Wr -d1] (14)

IV. PERFORMANCE ANALYSIS ANDSIMULATION RESULTS

We evaluate the performance of the proposed MIMO-Walsh system and compare it with an equivalent uncodedMIMO system using BPSK modulation. The SNR (Eb/No)is the average signal to noise ratio per antenna (PlUV2)where P is the average power per antenna and ov2 is thenoise variance. The simulation environment assumes

Rayleigh fading channel. The channel is assumed to bequasi-static for each symbol, but independent among

different symbols. Perfect channel state information(CSI) is assumed. Walsh codes of length two are

generated using Hadamard function.Fig. 2 presents the performance of the proposed WC-MIMO systems. The ML detector performs optimal,however its complexity increase exponentionally with theincrease in transmitters. Linear detectors ZF and MMSEgive sub-optimal BER performance but their complexityis very low as compared to ML.Fig. 3 compares the performance of the proposed WC-MIMO system with the conventional uncoded MIMOsystem. The BER performance of the proposed detectorsis approximately same as that of the conventional MIMOdetectors.These results suggest that the proposed SpatialMultiplexing technique offers same BER performance as

that of the conventional uncoded MIMO, however thegain in the proposed system is twice increase in the datatransmission rate while keeping the BER same as that ofthe existing uncoded MIMO system.

V. CONCLUSIONS

In this paper a spatial multiplexing system with orthogonaldata streams is proposed. The system offers promisingresults as compared to the conventional MIMO system.Optimal ML and Linear ZF and MMSE detectors for theproposed WC-MIMO system are compared with theuncoded MIMO detectors. The data rate of the proposedWC-MIMO system increase while keeping the BER at parwith the existing MIMO system. The proposed transmitterand receiver architecture possess capability and promise tobe used for future high-speed data intensive applications.

REFERENCES

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[18] Kakayuki Furkatani, Ryutaroh Matsumoto, andTomohiko Uyematsu. " Two Methods for Decreasingthe Computational Complexity of the MIMO MLDecoder". International Symposium on InformationTheory and its Applications, ISITA2004, Parma,October 10-13, 2004.

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[19] Jee Woong Kang and Kwang Bok (Ed) Lee. ASimplified Maximum Likely hood Detection". IEEEVehicular Technology conference, September 2004.

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