Iterative multi user detection for OFDM using biased mutation assisted genetic algorithms

Iterative Multi-User Detection for OFDM Using Biased Mutation Assisted Genetic Algorithms

M.

Jiang and L.

Hanzo1

School of ECS, Univ. of Southampton,

S017 1BJ, UK.

Tel:

+44-703-593 125, Fax: +44-703-593 045

Email: [email protected], http://www-mobile.ecs.soton.ac.uk

Abstract- Space Division Multiple Access (SDMA) aided Or- also been employed in OFDM systems [7, 8] for achieving a near-thogonal Frequency Division Multiplexing(OFDM) systems assisted optimum performance. Against this background, the novel contri-by efficient Multi-User Detection (MUD)techniques have recently bution of this paper is that we propose a MMSE-assisted Itera-attractedintensive research interests. Asexpected, Maximum Like- tive GA (IGA) MUD invoking a technique referred to here as the lihood (ML) detection was found to attain the best performance, Biased Q-function Based Mutation (BQM) designed for improv-although this was achieved at the cost of a high computational com- ing the performance of a TTCM-aided multi-userSDMA-OFDM plexity. Forward Error Correction (FEC)schemes such as Turbo system. Our simulation results show that the proposed MMSE-Trellis CodedModulation (TTCM) can be efficiently amalgamated IGA assisted TTCM-SDMA-OFDM system is capable of achiev-with SDMA-OFDM systems for the sake ofimproving the achiev- ing an Eb/No gain of about 6dB in comparison to the TTCM-able performance without bandwidth expansion. In this contri- assistedMMSE-SDMA-OFDMbenchmarker systemboth in low-bution, a MMSE-aided Iterative GA (IGA) MUD is proposed for and high-throughput modem scenarios, such as 4QAMand 16QAM, employment in a TTCM-assisted SDMA-OFDM system, which is respectively, while maintaining a substantially lower complexity capable ofachieving a similar performance to that attained by its than that imposed by theoptimum ML MUD.

optimum ML-aided counterpart at a significantly lower complex- The structure of this paper is as follows. TheSDMA MIMO chan-ity, especially at high user loads. Moreover, when the proposed nel model is described inSection 2.1, while the overview of the pro-novel Biased Q-function Based Mutation (BQM) scheme is em- posed TTCM-aided SDMA-OFDM system using the MMSE-IGA MUD ployed, the IGA-aided system's performance can be further im- isgiven in Section 2.2, followed by the introduction of the novel BQM proved by achieving an

Eb/No

gain of about 6dB in comparison scheme of Section 3. Our simulation results are provided in Section 4, to the TTCM-aided MMSE-SDMA-OFDM benchmarker system while Section 5 concludes our findings.

both in low- and high-throughput modem scenarios, respectively,

while stillmaintaining a modest complexity. 2. SYSTEM MODEL

1. INTRODUCTION 2.1. SDMA MIMO Channel Model

SpaceDivisionMultipleAccess(SDMA) based Orthogonal Frequency In SDMAuplink systems, each of the L simultaneousmobile users

Division Multiplexing (OFDM) [1] communication invoking Multi- employsasingletransmit antenna, while the BS's receiver exploits P UserDetection(MUD) techniqueshasrecentlyattracted intensive re- antennas. At the kth subcarrier of the nfth OFDM symbolreceived search interests. InSDMAMulti-Input-Multi-Output (MIMO)systems bythe P-element receiver antenna array we have the received com-the transmittedsignals of L simultaneousuplinkmobile users- each plexsignal vectorx[n,

k],

which is constituted bythe superposition equippedwith asingletransmit antenna-arereceivedbythe P differ- oftheindependentlyfadedsignalsassociated with the L mobile users entreceiver antennas ofthe Base Station(BS).Atthe BS the individual and contaminatedbythe Additive White Gaussian Noise(AWGN), ex-users'signalsareseparated byMulti-User Detectors(MUDs)with the pressedas:

aid of theuser-specific spatial signature constituted bytheir channel

transfer functions or,equivalently,ChannelImpulseResponses(CIRs). x Hs+ n, (1)

Intheliterature,Maximum Likelihood(ML)detection [1, 2] was found

togive the bestperformance, although this was achieved at the cost where the

(P

x

1)-dimensional

vectorx, the

(L

x

1)-dimensional

vec-of a dramatically increased computational complexity, especially in torsand the

(P

x

1)-dimensional

vectorn arethereceived,transmitted the context of a high number of users and higher-order modulation and noise

signals, respectively.

Herewehave omitted the indices[n, k]

schemes. By contrast, MinimumMean-Square Error(MMSE) [1, 2] for each vector for the sake of notational convenience. Specifically,the detection exhibits a low complexity, while suffering from a perfor- vectorsx,sandn are

given

by:

manceloss.

Furthermore, the achievable performance canbesignificantlyim- X (XI,X2, .

XP)

, (2)

proved, ifForward Error Correction(FEC) schemes are incorporated s = (

8(2)

(L))T

into the SDMA system. Various Coded Modulation (CM) [3] schemes ' ' 4

have attracted intensive research interests, since they are capable of (ni,?2,**P) (4)

achieving a substantialcoding gainwithout bandwidthexpansion. It

was shown in [4] that Turbo

Trellis Coded

Modulation

(TTCM)

[3]

T

generally provides

thebest performance in the family of CM schemes channel transfer functions

(FD-CCHTF)

of the L users and isgiven by:

in the specific context ofthe SDMA-OFDM system investigated. HH1 () HL

Genetic Algorithms (GAs) [5] have been applied to a number of H = (H : H

:,.

H()), (5)

problems, such as machine learning and modelling adaptive processes.

Furthermore, GA-based multiuser detection has been proposed for Code where

H(1)

(1 - 1,... .,L) is the vector of the FD-CHTFs associated Division Multiple Access (CDMA) systems [6]. Recently, GAs have withthe transmission paths from the 1th user's transmit antenna to each

__________________________

~~~~~of

the P-element receiver antenna array, which is expressed: Acknowledgements: The work reported in this paperhas formed part ofthe

Wireless Enabling Techniques work area of the Core 3 Research Programme H(1) - (H(1l, H( ,H(l))T, 1 {1, L},...(6)

of the Virtual Centre of Excellence in Mobile andPersonalCommunications,' ' ' ' ' '

Mobile VCE, www.mobilevce.com, whose funding support, including thatof

order tofurtherimprovethesignal's quality, invokinganumber of it-erations. Following the last iteration, the final GA solution will be decodedby the TTCMdecoders,and the hard-decision version of the estimated information bits of the Lindependentusersis forwarded to the output, which isonly enabled at the final iterationbythe switch seeninFigure 2.

Figure 1: Schematic of the MMSE-IGA MUD assisted multi-user Figure 3: The 2Doptimizationprovided by the MMSE-IGA MUD of SDMA-OFDMuplink system. Figure 2. The squarebrackets [.] denote the subcarrier indices in the

TTCM-coded frame of length N.

2.2. System Overview Therefore, two improvements have been achieved by the

MMSE-IGA MUD. Firstly, a more accurate initial knowledgeof the

transmit-InFigure 1, we present the schematic of the proposed MMSE-IGA ted signals, namely the output ofthe TTCMdecoders rather than that of MUDaided SDMA-OFDM uplink system. At the transmitter end, as theMMSE MUD, is supplied for the GA MUD. This reliable improve-seen atthe top ofFigure 1, theinformation bit sequences of the ge- menttherefore offers a better starting point for theGA'ssearch.

Sec-ographically separated L simultaneous mobile users are forwarded to ondly, the iterative processing ensures that the detected L-user symbol the TTCM

[3]

encoders, where they are encoded into symbols. The vectorcan be optimized in two dimensions, as demonstrated in Fig-encodedsignalss(l) (I= 1, ...IL) arethen forwarded to the OFDM- ure 3. During every iteration, on one hand, each L-symbol vector at

related Inverse Fast Fourier Transform (IFFT) based modulator, which a specified subcarrier slot is optimized by the GA in the context of convertsthe frequency-domain signals to the time-domain modulated the user domain. On theother hand, the entire TTCM-coded frame OFDM

symbols.

The OFDM

symbols

arethentransmitted

by

the in- ofeachuseris

optimized by

the TTCM decoder in thecontextof the dependentMobile Stations (MSs) to the BS over theSDMAMIMO TTCM-related codeworddomain, or more specificallythe

frequency

channel. Then each element of the receiver antenna array shown at the domain. Therefore, as the iterative processing continues, an informa-bottom ofFigure 1 receives the superpositionof the transmitted sig- tionexchange takes place between the two domains and thus an im-nals faded and contaminated by the channel and performs Fast Fourier proved system performance may be expected.

Transform (FFT) based OFDMdemodulation. The demodulated

out-putsxp

(p

= 1, ... FP)seen inFigure 1 are forwarded to the proposed 3. IMPROVED MUTATION SCHEME

MMSE-assisted IGA MUD for separating the different users' signals.

The separatedsignals

0(l)

(I

1,...IL),namely the estimated ver- The GA-based MUDs[6-8] invoke anintelligentnaturalevolution-like

sions of the transmittedsignals,arethen independently decoded by the processto find theoptimum ML solution bysearchingthroughasmall TTCMdecoders of Figure 1. subset of thetypicallyexcessiveML search space. At the

commence-mentofthe GA-based search, aninitialGApopulationconsistingof X number ofso-calledindividualsiscreated. One of these initial individ-uals isgenerated bymaking a hard decision at the output ofthe MMSE MUD,while the other(X- 1)individuals aregenerated by mutating the MMSE solution. An individual is represented by a symbol vector

containingL complex-valuedsymbols, each of which belongs to one of the L number of users at the specific subcarrier considered. More

specifically,theith individual of theyth generation isexpressed as:

i1,

Ii,2 Ii,LJ, i={1- .,X}, (7)

where

9(y)

denotes the1th

(I

1,... L)gene of the ith individual.

i,l

Figure2: Structureof the MMSE-initialized IGA MUD used at the BS Each gene can be represented by anyelement of Mc,where

MA

is the

shown inFigure 1. set containing the

2'

number of legitimatemodulated symbols, while

the entire evolutionprocedure,since itprovidesachance for the indi-viduals of the currentpopulationtoinfluence theforthcomingones,so

that new areas of the total search space may beexplored,thus increas-ingthe chances offindingtheoptimumsolution.

3.1. Conventional Uniform Mutation

Theso-called Uniform Mutation(UM)[6-8] has beenwidelyused in the GA-based MUD literature. Accordingtothe UM, whenageneis

subjectedtomutation, it will be substituted bya differentsymbolin

MA basedon auniform mutation-inducedtransitionprobability

p(i),

whichquantifiestheprobabilityof the ithlegitimate symbolbecoming Figure5: Illustration of the 2D transition

probability

p($g)

for4QAM,

thejth.Forthe sake ofbrevity,from now on we refer to thisprobabil- which is theproductofthe relevant ID transitionprobabilities. SRiand ity asthe transitionprobability. However,this fixed uniform transition sli

(i

= 1,

2)

denote theIDconstellationsymbolsinthe context ofthe probabilityfails to reflect the realistic channel conditions that the sys- real andimaginary components of the4QAMconstellation symbols,

tem is subjected to. More specifically, whenconsidering a specific respectively.

receivedsymbol,theadjacentconstellationsymbolsare morelikelyto be the transmittedsymbol, than the more distantones. Hence,it may

be more reasonable to consideronlytheneighbouring symbolsasthe have a certain probability for the original gene to remain unchanged,

potentialmutationcandidates, andassignamodified biased transition which can also be expressed

as:

p(1l)

=

p(22)

= 1-Q(d°

).

Hence,

probability, whichis dependentonboth the Euclidean distance from thecorresponding two-dimensional (2D) symbol transition probability theoriginal symboland on the Signal-to-NoiseRatio(SNR). Inother

_P(mi)

(i )

canbederived

by combining

the ID real and

imaginary

transition

words,

the GA's search space may be

substantially

reducedwiththe Pt

aid ofabiased

mutation,

which pays less attentiontothe constellation probabilities. For the

specific

ID-based

4QAM

example

of

Figure

4,

'

. . .

~~~we

plotthecorres

onding

2D constellation in

Figure

5. In

Figure 5,

for

pointsthat are far from thereceived

symbol,

and thus

increasing

the p

plg

g g

GA'sefficiency.

instance,

the 2D

transition

probability of mutating from the

constella-tionsymbol

8(l)

to

(l),

namely

p(I

2),

canbe calculatedby

multiplying

3.2. Biased

Q-function

BasedMutation thetworelevant

ID

transition

probabilities according

to:

Inthis section, anovel mutation scheme will bepresented, whichwe P(t2) P(1) (12)

(=

(

Q(°))Q(°

(l)

shall refer to as Biased

Q-function

Based Mutation(BQM). According 0 0

toBQM, for an original geneto bemutated, an SNR-related biased while the associated 2D probability of remaining in the current state is transitionprobability

p($f)

will beassignedtoeach of the target candi-

(ll)

= (11) (11) =

(1_

Q(do))2 Note thatwhen amutationtakes

Mt (ii)

Pm~~~~~~~Pit

P Ptin d0 2 oeta hnamtto ae

date symbolsinMA. The calculation of

pmt)

maybe carriedoutwith place,themutatinggene shouldnotbe allowedtobe mutatedtoitself. the aid of thewidely-knownQ-function [9]: Inorder to remove the effect of theprobabilityof

mutating

a

symbol

to

1 °° 2 itself, the 2D transition probability

p(ii)

(i

7?

j)

should be normalized

Q(x)

_{2w Jx}f

et2dt

x > 0.

(8)

with_ory[10].

p($i

_Notebyfollowing_{that the proposed BQM scheme can be readily extended}theprinciples of conditional probability the-toM-dimensional(MD)constellations,since the MD transition prob-abilityassociated with aspecificMD symbol canbe

readily

derived uponmultiplyingthe M number ofcorrespondingIDtransition

prob-abilities. It is worthpointingoutthat theproposed BQMscheme

only

requiresamodest "once-for-all" calculation, since we canderive the associated transitionprobabilitiesbyoffline

precomputation

for

typical

SNRlevels,whichcanthen be stored in the BS's memory forreuse.

3.3. Simplified BQM

Furthermore,theproposed BQMschemecanbeeffectively

simplified,

when only a subset of all the

theoretically-possible

mutation target

symbols are considered. More precisely, for the

original

gene

sub-Figure4: Illustration of theIDtransitionprobabilityp for4QAM. jectedto

mutation,

wemay

only

consider its

adjacent neighbouring

constellation symbols as mutation target

candidates,

since the

origi-nal transmitted

symbol

is less

unlikely

to be

corrupted

to a

relatively

For the sake of easy

explanation,

_dimensionalletusfirst

_(,D)

consider_{scenario. In}a

simple

one-_{F e 4}

_wdistant

tanteymy

_{constellation}

_symbol.

_An

_example

_{of the}

_simplified

_BQM

_de-y

dimnsinal(ID

scnaro. n

Fgur

4 e

pottd

te I relcm-

signed

for

16QAM

is

provided

in

Figure

6. As shown in

Figure 6,

ponentof the constellation

symbols

<)

inthecontextof the

4QAM

_{srhforexample,we assumethat}

_(s

_the

_original

_gene

_subjected

_to mu-modem constellation. The horizontal axis is then divided into two i

zones, each of which represents one

specific

ID constellation sym- tation, and ( (i

2,...

, 9) represents the adjacent neighbours of bol

sRi

(i = 1,. . ,

2),

as separated by the vertical dashed line of

8l.

Moreover,

the

GA's

search spacecanbe further

reduced,

when

Figure 4. If

8R1

is the original gene to be mutated, theGaussian distri- we only consider the nearest neighbours of 8(l as the legitimate mu-bution

N(O, v)

may be centered at theposition of

SRi,

where o is the tation candidates, namely the symbols 8(l (i - 3, 5, 6, 8), which are noisevariance at a given SNR level. In this specific example,

8R2

is printed in grey in Figure 6. Each of these symbols is then assigned an the only mutation target and the

lD

transition probability of mutating equal 2D transition probability

p(lQ)

- 1/4 (j

=3,

5, 6, 8), whileall from

SRi

to SR2, i.e. (12)

iS characterized

by the shadow area shown other constellation symbols printed in white are neglected. In this case, in Figure 4, which isgiven by: the BQM scheme is simplified to a new scheme similar to UM, which (12) do ~~~~~wemay refer toas the Closest-Neighbour Unform Mutation ('CNUM)

scheme or the CNUM arrangement, the computational

complexity

of BQM canbesignificantlyreduced.

Figure6: Anexampleof thesimplified BQMfor 16QAM. Figure 7: BER versus

Eb/No

performance comparison ofthe iterative ornon-iterative TTCM-assistedMMSE-GA-SDMA-OFDM system

usingUM orBQM, whileemployinga4QAMscheme for transmis-Modem Transitionprobabilityvalue set sion over the SWATMchannel, where L=6 users are supported with

4QAM 1/2 the aid of P=6 receiver antenna elements, respectively.

16QAM

1/2,1/3,

1/4

64QAM 1/2, 1/3, 1/4

pable of

achieving

a

virtually indistinguishable

performance

from that

Table 1: Possible transitionprobabilityvalues for the CNUM scheme. of the optimum ML-aided system, despite its significantly lower

com-plexity

of 200 metricevaluations.

4. SIMULATION RESULTS

Inthissection,wecharacterize theperformanceofthe

proposed

TTCM-aidedSDMA-OFDMsystemusingtheBQM-aidedMMSE-IGA MUD. The simulation results were obtained using a 4QAM scheme com-municatingover achannel characterizedbythe3-pathShort Wireless

AsynchronousTransfer Mode(SWATM)CIRgivenonpage 78of[1], assumingthat the channels' transfer functionswere

perfectly

known. The maximumpathdelay Tmaxis48.9ns, while each of thepaths ex-periences independent Rayleigh fading

having

the same normalized

Dopplerfrequencyof

fd

= 1.235 x

10-5.

The OFDM modem em-ployedK = 512subcarriers and 64 samplesasthe

cyclic prefix.

For

the iterative TTCM scheme

[3]

used,

the code memoryvwasfixedto

3,the generatorpolynomialexpressedinoctal formatwas

[13

6],

and the TTCM codewordlengthaswellaschannel interleaver

depth

were fixed to 1024symbols. Foreach of the various schemes

evaluated,

a

similar total number of TTCM

decoding

iterationswas

maintained,

so

that the total TTCM-related

complexity

remained

approximately

the Figure8: BERversus

Eb/No

performance comparison ofthe iterative

samefor all systems. ornon-iterativeTTCM-assisted

MMSE-GA-SDMA-OFDM

system

Figure7comparesthe Bit Error Rate(BER) performanceachieved usingUM orBQM,whileemployinga16QAMscheme for

transmis-bythe non-iterative GA aided schemes of[7,

8]

tothat of the

proposed

sionoverthe SWATM

channel,

where L=6users are

supported

with

IGA-aided systems. Theperformanceof the TTCM-assisted MMSE- the aid of P=6 receiver antenna elements,respectively.

SDMA-OFDM system,the TTCM-assisted

optimum

ML-detected

sys-temand the uncoded

single-user

scheme

employing

a

single

receiver Moreover, when ahigh-throughputmodem such as 16QAM is em-whencommunicating over anAWGN channel are also

provided

for ployed,BQM may significantly outperform UM. Figure 8 shows that

reference,respectively. The numbers in the round bracketsseeninthe theUM-aided scheme yielded a high error floor, even when the IGA

legendsofFigure7 denote the associated number of IGA MUD iter- wasemployed. By contrast, BQMsignificantly improved the perfor-ations and the total GAorML

complexity',

respectively.

As shown

mance by

lowering the error floor

by

at

leasttwo orders of

magnitude.

in Figure 7, at the same GA complexity, the IGA MUD assisted sys- Furthermore, when the number of IGA MUD iterations was

increased,

tems outperformed their non-iterative GA MUD aided counterparts, theperformance of the BQM-aided system was dramatically

improved,

regardless of the different mutation schemes used. This is because the while theUM-aided scheme still suffered from an error floor. This sug-proposed IGA MUD's initial population was generated from the output geststhat the BQM-aided scheme is capable of exploiting the benefits of theTTCM decoders, which is more reliable than that of the MMSE arising from both a better initial GA population and from a higher num-MUDof [7, 8]. On the other hand, the BQM-aided systems achieved a ber of IGA MUD iterations.

betterperformance than the UM-aided schemes, since BQM is more

ef-ficientin guiding the GA towards the optimum solution. Furthermore The left-hand side ofFigure 9 shows the Eb/NO gain achieved thesystem employing the BQM-aided two-iteration IGA MUD was ca-_{______________________}

_{~~~~~~ploying}

by the BQM-IGA assisted_{16QAM at the BER of}TTCM-MMSE-SDMA-OFDM

_1io-,

_{while usingdifferent number of}systems

em-Heethecomplexity is quantifiedin terms of the number of optimization IGA MUD iterations. Inthis

scenario,

six

usersweespotdbsi

dif-Figure 9: Eb/No Gain atthe BER of

i0-5

versus the number of IGA MUD iterations(left)and the number of users (right)

perfor-mance of the TTCM-assisted MMSE-IGA-SDMA-OFDM system

usingBQM, whileemployinga16QAM scheme for transmission over

the SWATM

channel,

where L=6(left)and

L=4,

5,6(right)users are

Figure

10: BER versus

Eb/NO

performance comparison

of the

supportedwith the aid of P=6 receiver antennaelements,

respectively.

TTCM-assisted MMSE-GA-SDMA-OFDMsystem using CNUM or BQM,whileemployinga4QAM or 16QAMscheme for transmission overthe SWATMchannel,where L=6 users aresupportedwith the aid ference measured at the BER of

10-5

between the systemsemploying of P=6 receiver antenna

elements,

respectively.

theBQM-IGAMUD ordispensingwith itsemployment.Asexpected,

when we had ahighernumber of IGA MUDiterations,ahigher Eb/No

gainwasobserved. Furthermore,ahigher gaincanbe attainedbyem- optimum GA solution in high-SNR and/orhigh-throughput scenarios.

ployingahigherGApopulationsize. Our simulation results show that the scheme that combines BQM with Theright-handside ofFigure9exhibits thecorresponding Eb/No the IGA MUD yields the best performance in allthe scenarios

consid-gains achieved bythe SDMA-OFDM system exploiting P = 6 re- ered. For example, as evidenced by Figures 7 and 8, anEb/No gainof

ceiver antenna elements at the BER of

10-5,

inthe scenarios where about 6dB was achievedbytheproposed BQM-IGA-aidedscheme in the number of users varies from four to six. It is shown that when the comparisontothe MMSE-SDMA-OFDM benchmarkerscheme,both userload becomes higher, ahigher gaincanbe attained. For exam- inthe scenarios where 4QAM and 16QAM wasemployed.

ple,for the single-iterationIGA-aided system, a furthergainof about

3.5dB isachieved,when the number ofusers increases from fourtosix. 6. REFERENCES

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