Heuristics Assisted Detection in High Speed

Wireless Communication Systems

*lAdnan Ahmed Khan, *Sajid Bashir, **Muhammad Naeem, **Syed Ismail Shah, Sr. MIEEE* CASE, University of Engineering and Technology, Taxila, Pakistan.

**lqra University Islamabad Campus, H-9, Islamabad, Pakistan.

Iadkhanl0OO(gmail.com

Abstract- Swarm Intelligence assisted Multi-Input-Multi-Output (MIMO) system is presented in this paper.Efficient symbol detection of MIMO system is performedusing Swarm-Intelligence inspired iterative robuststochastic algorithm. Optimized detection based on"Memetic" (Local Search) Particle Swarm Optimization(MPSO) is also proposed. These PSO-MIMO and MPSO-MIMO system detectors significantly reduce thecomputational complexity as compared to the conventionalMaximum Likelihood (ML) detection technique. Thesimulation results achieved with these detectors show nearML performance. These new heuristic based symboldetection techniques are efficient for systems using high-order modulation schemes and large number of antennaswhere conventional ML detector becomes computationallynon-practical to use. These proposed detectors are bestsuited for high- speed wireless communication systems.

Index Terms Multi-Input Multi-Output systems(MIMO), heuristic, optimization, memetic, ML detection.

I. INTRODUCTION

MIMO based communication systems have shownpromise to meet the high bandwidth requirements ofmultimedia based applications [1],[2]. ML detection inMIMO systems is a NP-hard problem. ML detectorperforms optimal, but its complexity increasesexponentially with the increase in number of transmitantennas and as modulation schemes become morecomplex. Number of MIMO detectors has been proposedto solve this problem. Recent literature includes two mainstreams of high performance MIMO detectors: onesphere decoding based (SD) [3] and the other semi-definite relaxation (SDR) based [4]. SD performsoptimum with low complexity at a relative high signal-to-noise ratio (SNR). However, when problem dimensionsare high its complexity coefficients and variance ofcomputational time becomes large. These drawbacks ofSD were tackled in Ordered Sphere Decoding (OSD)[5],[6]. SDR approaches polynomial worst-casecomplexity, with high performance [7],[8].Heuristic based optimization techniques are fast growingtools that can be employed in efficient lookup of searchspaces for optimal solutions. PSO heuristic is a

population-based search algorithm, inspired by the socialbehavior of animals like birds flocking, bacteria moldingand fish schooling. Kennedy and Eberhart firstintroduced PSO algorithm [9]. PSO advances arepresented in [10],[1 1]. Numerous variants were proposedbut global (Gbest) version is most standard PSOtechnique [12]. PSO has been used successfully in thefield of Electromagnetism [13] and Electric PowerSystems [14], however its applications in wirelesscommunications are relatively new. It has been usedeffectively in code division multiple access (CDMA)multiuser detection (MUD)[1 5].

In this contribution we present a simple efficientMIMO systems detector optimized by continuous PSOand MPSO techniques. The paper is organized as follows.The MIMO system model and ML detection is presentedin section-Il. In section-Ill, PSO and MPSO heuristics areexplained. The computational complexity is given insection-IV. Followed by Section-V showing simulationresults and comparison of the computational complexityvis-'a-vis the systems performance, finally last sectionconcludes the paper.

II. MIMO SYSTEMS DETECTION

A. MIMO System ModelThe Multi-Input Multi-Output system model consists of

N transmit antennas and M ( >N ) receive antennas asshown in fig. 1. The demultiplexer in the transmitterdivides the input data stream into N sub-streams,transmitted using N transmit antennas with equal transmitpower. The N radiated sub-streams after passing througha scattering wireless channel are collected by M receiveantennas. The MIMO model of the received signal vectorat each sampling instant can be represented as:

r = H.x + nN

(1)

where r = [r1 ... rm ... rM]T is an Mx 1 received signalvector, X = [X1 ... Xn ... XN] T is an Nx 1 sub-stream vector,n = [n1 ... nn .nM] Tis an Mx I white complex Gaussiannoise vector with elements having zero mean andvariance of G 2. P is the total transmitted energy. Thechannel impulse response matrix is:

1-4244-0794-X/06/$20.00 ©2006 IEEE 1

x H

~~~. ..

P ~~~~~~~~nI

P .. >.

:N *.- . -

* g *-.-- --. - nm

N

Fig. 1. Model of a MIMO system withN transmit antennas and Mreceive antennas.

Fh11 hl2 ... hlN

H h2 1 h22 ... h2N... ... ...

-hMI hM2 ... hMAN_-

(2)

Where hm,n denotes the channel impulse response fromthe n-th transmit antenna to the m-th receive antenna andis assumed to be an independent and identicallydistributed complex Gaussian random variable with zero-

mean and unit-variance. In MIMO the data is transmittedover a matrix rather than a vector channel. Each elementof x has unit power and is determined from the same set Scomprised of C constellation points. Perfect channelestimation is assumed at the receiver.

B. ML Detector Complexity Problem

The optimal ML detector estimates sub-streams x1, x2,

,XN by choosing the symbol combination associatedwith the minimal distance metric among all possiblesymbol combinations in the constellation:

mixAIL arg r- HX

N(3)

As shown in (3), the conventional ML detectionscheme needs to examine all CW symbol combinations.Therefore, the computational complexity increasesrapidly with C and N. The high speed processingrequirements of real time applications and the advancedcommunication systems demand a comparativelysimplified detection scheme. The proposed PSO andMPSO based detection scheme clearly avoids this hugecomplexity at an affordable performance loss.

III. PSO AND MPSO ALGORITHMS

A. PSO Heuristic Algorithm

Gbest model [12] where the complete population isconsidered as a single neighborhood is the most generic

PSO algorithm implementation. Significance of PSO liesin its simple mathematical model consisting of twoequations (4) and (5). Steps shown in fig. 2 are acted on

all particles. The coordinates of each particle depict thepossible solution.

vij (t + 1) = wvij (t) + clrlj (t)[yij (t) - xij (t)] +

(4)

(5)Where 'yij(t)' is the personal best (Pbest,) for particle 'i' indimension 'j', '5i(t)' is the global best (gbest). 'Vij(t)' is thevelocity of particle 'i' in dimension 'j'. 'xij(t)' is theposition of particle 'i' in dimension 'j' at a particular time't'. 'cl' and 'c2' are positive acceleration constants usedto scale contribution of 'cognitive' and 'social' elements.'rl' and 'r2' are the independent random numbers between'0' and '1' used to stochastically vary the relative pull ofgbest and Pbest- 'w' is the inertial weight. The particlemotion is based on (5). The farthest partials experiencegreater 'pull' from gbest orpbest. The particles accelerate inthe direction of the place of greatest fitness until they run

over them. The velocity consists of three componentsfirst is the 'previous velocity' which is the memory of theprevious flight direction (inertia). Secondly a 'cognitivecomponent' it is the Pbest for a particle, and last is the'social component' that is the influence on particle basedon gbest. x(t) is the present and x(t+1) is the new positionof particle in the parameter space. A particle at itspresent position experiences these cognitive, inertial andsocial velocities and moves in the resultant direction ofnew velocity to jump to next location.

B. Memetic PSO Algorithm

Hybridization of pure PSO with local search is MPSO.The pseudo-code of the heuristic is shown in table- 1.

C. Parameter control

The algorithm parameters are required to be tuned toachieve optimal system performance. The particles size istypically in the range of 10 to 40. For our simulations it is

2

INPUTDATA

STREAMDEMULTIPLEXER DETECTOR

DETECTOROUTPUTI >0

I

c2r2j (Olyj (t) xij (01

xi(t+l) = xi (t) + vi(t + 1)

gbest in the

solution spacey

Fig. 2: Flow Chart ofPSO Technique

Table-1: PSO and MPSO (italic) algorithm

kept at 16 and 32. The range of particles 'Vmax'determines the maximum change one particle can takeduring iteration. Eberhart and Shi [18] found that withoutinertial weight (w= 1), this maximum allowed velocity'Vmax' is best set around 10-20% of the dynamic range ofeach dimension. We choose this Vmax range between -10to +10, to avoid particles flying out of meaningfulsolution space. Inertial weight 'w' is also introduced in[18]. Larger value of this parameter encourages more

global search and is lesser influenced by Pbest and gbest,

analogous to the phenomenon that it is difficult to diverge

heavier objects in their flight trajectory than the lighterones. Smaller inertial weight encourages the localexploration as the particles are attracted towards Pbest andgbest more. We assume w=1 in our case. The stoppingcriteria can be the maximum number of iterations(velocity changes allowed for each particle) or reachingthe minimum error threshold. For MPSO the degree oflocal search 'b,' shows the least significant bits (LSBs) ofthe best solution to be searched-for further refining thesolution. Keeping search degree as two would mean fourneighbors would be searched for better fitness. In our

local search algorithm 'b,' is kept as 1 and 2 respectively.

IV. COMPUTATIONAL COMPLEXITY OF MIMO-PSO AND MIMO-MPSO ALGORITHMS

The computational complexity of the PSO basedMIMO systems detection scheme compared with that ofML detection is discussed here. The computationalcomplexity is taken in terms of the number of transmit,receive antennas and the number of bits per symbol 'b'.In case of ML detector the Euclidean distance metriccalculation for a candidate symbols possiblecombinations require M(N+1) multiplications. The searchspace for ML detector given by (2) is CN where C is thetotal number of constellation points given by 2b. Thecomputational complexity for ML detector comes out tobe [6].

(6)7ML 2bxN (M(N + 1))

For the proposed PSO detector, first the fitness of eachparticle in the complete swarm (Np) is calculatedaccording to:

7pso = Np (M(N + 1)) (7)Incorporating the velocity and position updating (3) ofeach particle requires (utve) multiplications. Therefore,

(8)

3

Phase-i. Initialize particle size= Np; Randomly getparticle position; Set boundaries for velocities; Initializeparameters;Phase-2 :For i= 1: Np

%Get velocity for next position updatingvij(t+l)= vij+ cirij(t)[yij(t)- xij(t)]+ C2r2j(t)[yj(t)-ij(t)]

If velocity < boundary%Update particle position;x1(t+1) = xi(t) + vi(t)

Else%Velocity = Cyclic velocity;

End% Apply neighborhood searchInitialize lower bits to searchFor J = L-Number ofneighbors

%Iterative search in neighborhoodEvaluateo;IfFitness(xi(t+1)) < Fitness(xi(t))%Update Local Best;pbesti = xi(t+1),;

End%Update Global Best;Gbest = min(pbest);End

7pso::::::::Np (M(N +1)) + Pvel)

Keeping the weight of each multiple operation as unity

and repeating Nitr time, PS0 computational complexity

comes out to be.

Nitr

The computational complexity for MPSO becomes.

Y"mpso :::::16 xN xXN tr2b

(9)

(1 U)

V. SIMULATION RESULTS

MIMO system simulated consists of two transmit

antennas (N=2) and four receive antennas (M=4). 4-

QAM, 1 6-QAM, 32-QAM and 64-QAM schemes are

used with the proposed algorithm. The particle size is 16

and 32. The simulation results in Fig.3 demonstrate that

the proposed MIMO-PSO and MIMO-MPSO detector

generally achieves near-optimum performance. The

acceleration constants cl andc2 are one. For 10-2 bit error

rate (BER) the former detector requires 4 db Eb/No,whereas the later requires 2 db more Eb/No

(approximately) in comparison with ML detector. The

degree of local search is four for this result.

Fig.4 presents the bit error rate (BER) pertormance with

increase in number of iterations. In 25 iterations MIMO-

PSO detector with 1 6-QAM reaches optimal

performance, whereas 32-QAM systems takes 32

iterations. Similarly MIMO-MPSO system with 1 6-QAM

converges to ML performance in 18 iterations and 32-

QAM systems requires 25 iterations.

The computational complexity is computed using

equations (6), (9) and (10). Complexity comparison with

different modulation techniques is plotted in Fig.5. The

complexity of ML has exponential increase with the

increase of constellation alphabet size. MIMO-MPSO

detector is less computationally efficient than MIMO-

PSO detector since it performs additional local search

operations.

These results show that the proposed swarm intelligence

optimized detectors result in drastic improvement in

terms of computational efficiency as compared to ML

detection especially with higher order modulation

schemes. This efficiency improvement with higher order

modulation techniques make these especially useful for

high data rate transmission systems employing higher

order modulation techniques and more transmitting

antennas. With 32-QAM, Iterative MIMO-PSO detectors

improve by 420o and this efficiency improvement reach

83 using 64-QAM constellations. Similarly MPSO

based detector improves by 700o with 64-QAM in a

MIMO communication system.

VI. CONCLUSIONS

MIMO-PSO and MIMO-MPSO detection algorithms

show promising results when compared with the

traditional ML detector. The proposed simple detection

mechanisms approaches near optimal performance with

reduced complexity especially for higher order

modulation schemes and when greater numbers of

antennas are used in MIMO system. The results depict

that with two transmitters and four receivers, these

iterative detectors achieves near optimal performance at a

much lower computational complexity. Proposed

algorithms have resulted in 830 increase in the system

efficiency when compared with ML detection technique.

The performance enhancement increase exponentially

with the increase in number of antennas and complexity

of modulation schemes where conventional detector is

not practical to use due to complexity burden. This makes

this proposed detection algorithms suitable for high-

speed wireless communication systems.

1 00

LU

6 10 12 14 16-2 0

Fig. 3. BER versus Eb/No: At T=2, R 4.

DI 6

12

0.i~ ~ ~ ~

ITERATIONS

Fig. 4. BER versus iterations: Particle size= 16.

1- 2t

.,0 3 40 9I I5

Fig. 5. Complexity versus Modulation Schemes.

4

-e- ML Detector ------- -------PSO DetectorMPSO Detector --------r-------I--------I--------I--------I---------

------------------------------ !!l] s ZAC ----------------------------------------------------- - -------

---------------- ------- ------- ------- -------------

----------------- ------- ---------------- ------- ------- -------------------------------------- ------- ------- ------- i---------------------------------------------------------------------- t ------- -----------

-4- ML DUE RMMQ.PSQ DETUTORMMOmNPSO DE7Ef-'Tf--jR

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