Iterative Joint Channel Estimation and Symbol Detection for Multi-User MIMO OFDM M. Jiang, J. Akhtman, F. Guo and L. Hanzo 1

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1 Iterative Joint Cannel Etimation and Symbol Detection for Multi-Uer MIMO OFDM M. Jiang, J. Aktman, F. Guo and L. anzo Scool of ECS, Univ. of Soutampton, SO7 BJ, UK. Tel: , Fax: ttp://www-mobile.ec.oton.ac.uk Abtract Multiple-Input-Multiple-Output (MIMO) Ortogonal Frequency Diviion Multiplexing (OFDM) ytem ave recently attracted ubtantial reearc interet. owever, compared to Single-Input-Single-Output (SISO) ytem, cannel etimation in te MIMO cenario become more callenging, owing to te increaed number of independent tranmitter-receiver link to be etimated. In te context of te Bell LAyered Space-Time arcitecture (BLAST) or Space Diviion Multiple Acce (SDMA) multi-uer MIMO OFDM literature, no cannel etimation tecnique allow te number of uer to be iger tan te number of receiver antenna, wic i often referred to a an overloaded cenario. In ti contribution we propoe a new Genetic Algoritm (GA) aited iterative joint cannel etimation and multiuer detection approac for MIMO SDMA-OFDM ytem, wic exibit a robut performance in te above-mentioned overloaded cenario. Furtermore, GA-aided Multi-Uer Detection (MUD) tecnique found in te literature can only provide a ard-deciion output, wile te propoed GA i capable of providing oft output, ence acieving an improved performance wit te aid of cannel decoder. Finally, a range of imulation reult are provided to demontrate te uperiority of te propoed ceme.. INTRODUCTION Multiple-Input-Multiple-Output (MIMO) Ortogonal Frequency Diviion Multiplexing (OFDM) ytem ave recently attracted ubtantial reearc interet, becaue te employment of multiple antenna offer an opportunity to exploit bot tranmitter and receiver diverity, ence ignificantly increaing te ytem tranmiion integrity. Specifically, intenive reearc effort ave been inveted bot in Bell Lab Layered Space-Time arcitecture (BLAST) and in Space Diviion Multiple Acce (SDMA) baed MIMO OFDM []. More pecifically, in SDMA-OFDM ytem te tranmitted ignal of L imultaneou uplink mobile uer - eac equipped wit a ingle tranmit antenna - are received by te P different receiver antenna of te Bae Station (BS). At te BS Multi-Uer Detection (MUD) tecnique are invoked for detecting te different uer tranmitted ignal wit te aid of teir unique, uer-pecific patial ignature contituted by teir Frequency-Domain Cannel Tranfer Function (FD- CTF) or, equivalently, Cannel Impule Repone (CIR). Since te ame time-frequency reource i ared by imultaneou uer, a ig bandwidt efficiency can be acieved. owever, in tee ytem accurate cannel etimation i required at te receiver for te ake of invoking bot coerent demodulation and interference cancellation. Compared to Single-Input-Single-Output (SISO) ytem, cannel etimation in te MIMO cenario become more callenging, ince a ignificantly increaed number of inde- Acknowledgement: Te financial upport of te Mobile VCE i gratefully acknowledged. pendent tranmitter-receiver cannel link ave to be etimated imultaneouly for eac ubcarrier. Moreover, te interfering ignal of te oter tranmit antenna ave to be uppreed. In te literature, numerou cannel etimation tecnique ave been propoed for MIMO-OFDM ytem, uing blind etimation [], tranmitter diverity [3], Contrained Leat Square (CLS) [4], Second-Order Statitic (SOS) baed SubSpace (SS) [5] algoritm a well a te QR Decompoition combined wit te M-algoritm (QRD-M) [6], etc. owever, in te context of te BLAST or SDMA type multi-uer MIMO OFDM ytem, no cannel etimation tecnique in te literature allow te number of uer L to be iger tan te number of receiver antenna P, wic we refer to a an overloaded cenario, were te cannel matrix become ingular and tu rendering te degree of freedom of te detector inufficient. In te literature, a number of Genetic Algoritm (GA) aided cannel etimation ceme ave been propoed for Code Diviion Multiple Acce (CDMA) ytem [7 9]. owever, to our bet knowledge, no tecnique employing GA for joint cannel and data optimization can be found in te literature in te context of multi-uer MIMO OFDM. Furtermore, te GA found in te literature, for example toe of [7, 9, 0] can only provide a ard-deciion output for te Forward Error Correction (FEC) decoder, wic inevitably limit te ytem acievable performance. Againt ti background, in ti paper we propoe a new GA-aited iterative Joint Cannel Etimation and Multi-Uer Detection (GA-JCEMUD) approac for multi-uer MIMO SDMA-OFDM ytem, wic provide an effective olution to te multi-uer MIMO cannel etimation problem in te above-mentioned overloaded cenario. Moreover, our propoed GA i capable of providing oft output and ence acieving an improved performance over conventional GA. Te tructure of ti paper i a follow. A detailed analyi of te propoed ceme i given in Section, followed by te numerical reult of Section 3. Our final concluion are offered in Section 4.. GA-ASSISTED ITERATIVE JOINT CANNEL ESTIMATION AND MULTI-USER DETECTION Te propoed iterative GA-JCEMUD i illutrated in Figure. We aume tat eac OFDM ymbol conit of K ubcarrier. Te firt tranmitted OFDM ymbol of all te L uer i completely filled by known pilot Quadrature Amplitude Modulation (QAM) ymbol. Witin te firt OFDM ymbol duration (n =0), te BS pilot controller een in te middle of Figure feed te pilot to te GA- JCEMUD printed in grey, wic imultaneouly procee te received ignal x p[0,k](p =,,P; k =,,K) at te P receiver antenna element. In order to implify te analyi, we now focu our attention on te p t receiver. Baed on te pilot and te correponding received ignal, te initial etimate of te FD-CTF p [0,k](l =,,L; k =,,K) can be generated, followed by te time-domain filtering invoking at te p t receiver, a plotted on /06/$0.00 (c) 006 IEEE

2 Detected oft bit b [, ] n+ k b ˆ [ n+, k ] () bˆ [ n+ ) ˆ () l Final-iteration Trigger () p () p [, n k] () l Time-domain filtering at oter receiver antenna ˆ () l Time-domain filtering at te p t receiver antenna CIR-related tap () () p [,] n p [,] n () p [,] n () p [,] n () p [ n, K0] Cannel Tranfer Function Buffer On/Off Control GA-aided Joint Cannel Etimator and MUD () p [, n K] ) p [ n,] ) p [ n,] ) p [ n, K] IFFT IFFT 0 ) p [,] n ) p [,] n ) p [, n K0] 0 Working mode witcing: pilot mode / data mode Pilot ymbol FFT FFT () ˆ p [,] n [,] n [, n K] ˆ ) [ n,] ˆ ) [ n,] Pilot Controller () [ n+ () [ n+ ) [ n+ ˆ ) [ n, K] Cannel Tranfer Function Buffer ORSA MUD On/Off Control ˆ () [, n k] ˆ ) Received ignal x [0, k] x [ n+ Rx x [0, k] x [ n+ Rx xp k Rx P [0, ] x [ P n+, k ] Figure : Te tructure of te propoed iterative GA-JCEMUD. te top of Figure. Te time-domain filtering i conducted for eac of te L uer on an OFDM ymbol bai. More generally, for te l t uer, te K initial FD-CTF etimate p [n, k] (k =,,K) aociated wit te current, i.e. te n t OFDM ymbol are proceed by a K-lengt Invere Fat Fourier Tranform (IFFT), reulting in te et of K uncorrelated CIR-related tap p [n, k]. Ten, only te firt K 0 CIR tap coefficient are retained wit te ret et to zero. Te value of K 0 depend on te delay profile of te cannel, wic i not known aprioriat te receiver. owever, in many application cenario it i poible to appropriately over-etimate K 0 on te bai of previou field experiment. ence, in our ytem te value of K 0 i et to a ufficiently large number o tat it ignificantly exceed te actual maximum delay pread of te cannel. Nonetele, we point out tat te ignificant-tap catcing approace of [3] can be employed for improving te cannel etimator performance by furter removing te low-power tap witin te range of [,,K 0] according to a pre-defined treold. Te retained CIR-related coefficient p [n, k] (k =,,K 0) are ten converted to te improved a potepriori FD-CTF etimate Ĥ p [n, k] (k =,,K) by te Fat Fourier Tranform (FFT). If in te (n +) t OFDM ymbol duration a data ymbol rater tan a pilot ymbol wa tranmitted, te pilot controller will enable a firt-tage MUD for generating reference ymbol etimate. Specifically, te Optimized ierarcy Reduced Searc Algoritm (ORSA) aided MUD of [] i employed. Wit te aid of te a potepriori FD-CTF etimate Ĥ p [n, k] aociated wit te previou OFDM ymbol, a ubcarrier-by-ubcarrier baed detection i invoked by te ORSA MUD for generating an initial gue of te L uer tranmitted ymbol [n +,k](l =,,L; k =,,K). Moredetail of te ORSA MUD are provided in Section.. Te reultant ymbol etimate [n +,k], te FD-CTF etimate Ĥ p [n, k] a well a te correponding received ignal x p[n +,k](p =,,P; k =,,K) are ten forwarded to te GA-JCEMUD, were te FD-CTF and data ymbol aociated wit te (n +) t OFDM ymbol are jointly optimized on a ubcarrier-by-ubcarrier bai, a to be dicued in Section.3. Te GA-optimized FD-CTF etimate p [n +,k] are ten forwarded to te time-domain filter for furter enancement. Baed on te improved cannel etimate, te ORSA MUD i now capable of providing a better initial gue of te tranmitted ymbol for te GA-JCEMUD. Ti deciion-directed proce can be invoked for a number of iteration for furter performance enancement. After te final iteration, te L uer detected ˆb oft bit [n +,k](l =,,L; k =,,K) correponding to te (n +) t OFDM ymbol are generated... Pilot-aided Initial Cannel Etimation In order to obtain an initial etimate of te FD-CTF, eac uer pilot OFDM ymbol i multiplied by a uer-pecific preading code before it i tranmitted. Note tat a ame unpread pilot QAM ymbol can be ued by all uer, wic i known at te receiver. Wit te aid of te pread pilot OFDM ymbol, an initial FD-CTF etimate i attainable at te receiver, were te Multi-Uer Interference (MUI) i effectively reduced proportionately to te preading factor. Note tat no preading i applied to te data OFDM ymbol. Depending on te pecific performance-veru-trougput deign tradeoff targeted, ti proce of generating initial cannel etimate can be invoked at pre-defined time interval. ere we denote te pilot overead a ɛ, wic i defined by te ratio of te number of pilot OFDM ymbol to te total number of tranmitted OFDM ymbol. We will ow in Section 3 tat a good performance i acievable by te propoed ceme wit a mall value of ɛ... Generating Initial Symbol Etimate In te propoed ceme te ORSA MUD [] own in Figure i employed a te firt-tage MUD for obtaining initial ymbol etimate, wit te aid of te a potepriori FD-CTF etimate generated witin te previou OFDM ymbol duration. Due to te pace limitation, ere only a very uccinct introduction on te ORSA MUD i provided. Briefly peaking, te ORSA MUD employ a bit-baed dendritic recurive earc algoritm to find te L uer optimum Maximum Likeliood (ML) etimate. More pecifically, two legitimate ypotee of and are tipulated at eac recurive tep i of te earc algoritm, concerning one of te bit of te trial bitwie vector ˇb i. Te recurive earc algoritm i carried on by evaluating a et of inverely ordered Cumulative Sub-Cot (CSC) function wic are derived from te ML metric. For eac tentatively aumed value of ˇb i a ucceive recurive earc tep (i ) i invoked, wic i conditioned on te ypotee made in all preceding recurive tep j = i,,l b = ml, werem denote bit per ymbol. Upon eac arrival at te index i =of te recurive proce, a complete bit-baed candidate vector ˇb aociated wit a certain ymbol vector š i ypoteized and te correponding value of te cot function i evaluated. Wit te aid of ome carefully-deigned earc rule, te ORSA MUD i capable of acieving at a near-optimum performance at a ignificantly-reduced computational complexity. For more detail on te ORSA MUD, te intereted reader i referred to [].

3 .3. GA-aided Joint FD-CTF and Data Optimization Providing Soft Output.3.. Genetic Evolution Te baic idea of te GA-baed optimization i to find te optimum or a near-optimum olution according to a pre-defined objective function (OF). In te context of joint detection aided SDMA-OFDM ytem, te GA OF aociated wit te k t ubcarrier in te n t OFDM ymbol can be formulated a: ( ) Ω [n, k], [n, k] = x[n, k] [n, k] [n, k], () were x[n, k] i te received ignal vector, wile [n, k] and [n, k] are te trial FD-CTF matrix and te trial multi-uer ymbol vector, repectively. Eac combination of [n, k] and [n, k] contitute a GA individual, wic i initialized by te tentative FD-CTF etimate of Section. and te initial ymbol etimate of Section., repectively. Te GA ultimate aim i ten to find an individual tat minimize te OF of Equation. In comparion to te pure GAbaed MUD [9, 0, ], wic optimize te multi-uer data ymbol only, te joint optimization work require te FD-CTF to be imultaneouly optimized along wit te data ymbol. Since te FD- CTF and data ymbol are jointly optimized witin te ame genetic proce, te individual aving better FD-CTF etimate will ave a iger probability of producing better ymbol etimate and vice vera. Tu, ti joint optimization i a elf-adaptive proce wit it native intuition leading toward te optimum olution. Furtermore, comparing to oter tecnique, for example tat of [8], were te cannel etimation and ymbol detection are completed by te GA and te Viterbi Algoritm (VA) eparately, te propoed joint ceme i capable of reducing te aociated complexity, ince te cannel etimation i imultaneouly acieved wit te aid of te ame GA proce, tu incurring no additional complexity. For more detail on te principle of genetic optimization proce, we refer to[7,9,]. owever, by te time of writing te GA-aided detection ceme found in te literature, for example toe of [7, 9, 0, ] can only provide ingle-individual baed ard-decoded ymbol etimate, wic inevitably limit te GA-aided ytem attainable performance. In Section.3., we will introduce a metod, wic enable te GA to provide oft output baed on te entire population..3.. Generating te GA Soft Output At te k t ubcarrier of te n t OFDM ymbol received by te P - element receiver antenna array we ave te received complex ignal vector x[n, k], wic i contituted by te uperpoition of te independently faded ignal aociated wit te L mobile uer and contaminated by te Additive Wite Gauian Noie (AWGN), expreed a: x[n, k] = [n, k][n, k]+n[n, k], () were [n, k] and n[n, k] are te tranmitted and noie ignal vector, repectively, wile [n, k] i te FD-CTF matrix. For te ake of notational convenience, te index of [n, k] i omitted in te ret of ti ection. Te oft-bit value or Log-Likeliood Ratio (LLR) aociated wit te (m B) t bit poition of te l t (l =,,L) uer tranmitted ymbol can be formulated a: L l,mb =ln P (b l,m B = x, ) P (b l,mb =0 x, ), (3) wic i te natural logaritm of te quotient of probabilitie tat te bit conidered a a value of b l,mb =or b l,mb =0. Note tat te probability P (b l,mb = b x, ) tat te ymbol tranmitted by te l t uer a te (m B) t bit value of b l,mb = b 0,, igivenbyte um of all te probabilitie of te ymbol combination wic aume tat b l,mb = b. ence, Equation 3 can be equivalently rewritten a: š M L P (š x, ) l,m L l,mb =ln B, P (š x, ), (4) were M L l,m B,b denote te pecific ubet aociated wit te l t uer, wic i contituted by toe pecific trial vector, woe l t element (m B) t bit a a value of b, wic i expreed a: M L l,m B,b = š =[š (), š (),, š (L) ] T š (), š (),, š (L) M c b l,mb = b Wit te aid of Baye teorem, we ave:. (5) P (š x, ) =P (x š, ) P (š) P (x). (6) Upon ubtituting Equation 6 into Equation 4, we arrive at: š M L P (x š, ) l,m L l,mb =ln B, P (x š, ). (7) Note tat ere we ave aumed tat te different ( m )-ary ymbol combination vector š ave te ame probability, namely tat P (š), š M c i a contant. On te oter and, it can be oberved from Equation tat x i a random ample of te L-dimenional multi-variate complex Gauian ditribution, were te mean vector i, wile te (P P )-dimenional covariance matrix R n i given by: R n = Enn = σni, (8) and te noie encountered at te P number of receiver antenna i aumed to be uncorrelated. ence, te above-mentioned multi-variate complex Gauian ditribution can be decribed by: f(x, ) = π P R exp n (x ) R n (x ). (9) Wen ubtituting Equation 8 into Equation 9, we ave: f(x, ) = exp x. (0) π P σn σn Note tat f(x, ) =P (x, ) i te aprioriprobability tat te vector x a been received under te condition tat te vector wa tranmitted over te MIMO cannel caracterized by te FD-CTF matrix. Tu, Equation 7 can be furter developed wit te aid of Equation 0, yielding: L l,mb =ln š M L l,m B, exp π P σn exp π P σn x š σn. () x š σ n In order to avoid te exponential computation impoed by Equation, te maximum-approximation [] can be applied, yielding: L l,mb [ x š σn l,mb, x š l,mb,0 ], ()

4 were š l,mb,b =arg min š M L l,m B,b [ x š ], b =0,. (3) Furtermore, concerning te fact tat te true FD-CTF matrix i unknown and uing Equation, Equation can be repreented a: L l,mb [ ] Ω σn l,mb, Ω l,mb,0, (4) were Ω l,mb,b =min [ ( ) ] Ω, š l,mb,b,ω, b =0,, (5) and ω = P L i a normalization factor. Equation 4 ugget tat te LLR can be obtained by evaluating te GA OF. More explicitly, in order to calculate te LLR of te (m B) t bit of te l t (l =,,L) uer at te pecific ubcarrier conidered, te X number of individual in te GA final generation are divided into two group, were te firt (or econd) group i contituted by toe individual tat ave a value of one (or zero) at te (m B) t bit of te l t uer etimated tranmitted ymbol. Te reultant lowet OS calculated in eac of te two group i ten compared to ω, and te maller of te two will be ued in Equation 4 for calculating te correponding LLR, wic can terefore ait te cannel decoder in improving te SDMA-OFDM ytem performance. It i wort pointing out tat te propoed GA generating te abovementioned population-baed oft output only impoe a modet complexity increae in comparion to te conventional ard-deciion aided individual-baed GA [7, 9, 0, ]. Ti i becaue te only additional operation required by te propoed ceme i to compare ω to te reult of te OF evaluation carried out by te conventional GA. 3. SIMULATION RESULTS In ti ection, we will quantify te performance of te MIMO SDMA- OFDM ytem uing te propoed iterative GA-JCEMUD tecnique. Due to pace limitation, ere we only provide te reult acieved in an overloaded cenario aociated wit L =4uer and P = receiver antenna element. owever, we point out tat te propoed ceme alo perform well in te cenario aociated wit L P. An OFDM modem employing K =64ubcarrier and a cyclic prefix of eigt ample wa ued. A two-pat Rayleig fading cannel model wa employed, were eac pat experienced independent fading aving te ame Doppler frequency of F D normalized to te OFDM ymbol rate. Te delay profile of te cannel wa ( z z ). Te value of te parameter K 0 wa et to 8, wic i potentially capable of tolerating an increae of te actual diperion up to eigt CIR tap. Te complex-valued cannel envelope wa aumed to remain uncanged witin an OFDM ymbol duration. Te fading envelope of te P L number of uer-receiver cannel link were aumed to be uncorrelated. Eac uer aociated tranmit power or ignal variance wa aumed to be unity. Bot cenario wit and witout FEC coding were invetigated. In te FEC-coded cenario, a an example, a alf-rate binary Low Denity Parity Ceck (LDPC) [3] code wa employed, wic aumed a block lengt of 640 input bit, a column weigt of.5 and a maximum of 0 decoding iteration. It i wort pointing out tat oter FEC code, for example turbo code are alo applicable to te propoed ytem. Furtermore, te GA configuration wa imilar to tat of [], except tat te metod of [7] wa ued for FD-CTF mutation. LDPC-GA-JCEMUD-SDMA-OFDM, L4/P, 4QAM, -pat Rayleig GA-JCEMUD, F D=0.00 GA-JCEMUD, F D=0.003 GA-JCEMUD, F D=0.005 Uncoded LDPC-coded paper_d_fdx-and-fftitx_u4r_jga_ldpc_4qam_mul.gle Tu Sep :9:30 F D=0.003 GA-JCEMUD, Itr.=0 GA-JCEMUD, Itr.= GA-JCEMUD, Itr.= Uncoded LDPC-coded Figure : veru SNR performance of te uncoded and LDPCcoded iterative GA-JCEMUD/SDMA-OFDM ytem at different F D (left) and different GA-JCEMUD iteration (rigt). Te Bit Error Ratio () veru Signal-to-Noie Ratio (SNR) performance of bot te uncoded and LDPC-coded GA-JCEMUD aited SDMA-OFDM ytem recorded at different value of F D and different number of GA-JCEMUD iteration are provided at te left-and and rigt-and ide of Figure, repectively. Te performance of te ytem employing te linear MMSE MUD or te optimum ML MUD are alo provided a reference, bot auming perfect Cannel State Information (CSI). A pilot overead of ɛ wa aumed and te GA-JCEMUD ued a ingle iteration. A een at te left-and ide of Figure, te performance of te GA-JCEMUD aided ytem degraded, wen F D wa increaed, ince cannel etimation become more callenging wen te cannel fade more rapidly. Ti i epecially true for MIMO ytem, even more o for overloaded MIMO ytem, a dicued in Section. Nonetele, wit only a.5% pilot overead, te propoed GA-JCEMUD/SDMA- OFDM ytem wa capable of acieving a performance cloe to te perfect-csi aided optimum ML MUD at F D =0.00. By contrat, te ytem employing te MMSE MUD completely failed even wit te aid of perfect CSI, owing to te inufficient degree of detection freedom experienced in overloaded cenario. On te oter and, a ignificant iteration gain wa acievable, wen te GA-JCEMUD invoked more iteration, a revealed by te rigt-and ide of Figure, were we ad ɛ and F D = In Figure 3 te performance of te propoed ytem uing different pilot overead i invetigated. In mot cae, te GA- JCEMUD wa capable of acieving a good performance uing a pilot overead a low a ɛ =.5.5%. Furtermore, te increae of pilot OFDM ymbol overead bring about more ubtantial benefit at te iger Doppler frequencie tan at te lower one, epecially in te cenario aociated wit iger SNR, were an increaing fraction of te reidual detection error wa inflicted by inaccurate cannel etimation. In order to furter caracterize te advantage of te propoed joint optimization ceme, on te left-and ide of Figure 4 we compare te performance of te GA-JCEMUD and it counterpart, referred to a te GA-baed cannel etimator aited ORSA MUD (GACE-ORSA-MUD), were te ORSA MUD i erially concatenated wit te tand-alone GA-aided cannel etimator. More pecifically, in te GACE-ORSA-MUD arrangement te ymbol etimate offered by te ORSA MUD are fixed during te GA-aided optimization proce of te FD-CTF etimate. Explicitly, in ti cae te effect of error propagation due to inaccurate ymbol and/or

5 LDPC-GA-JCEMUD-SDMA-OFDM, L4/P, 4QAM, -pat Rayleig paper_pilot-v-ber_u4r_jga_ldpc_4qam_mul.txt Fri Sep :56:5 GA-JCEMUD, F D =0.00 GA-JCEMUD, F D =0.003 GA-JCEMUD, F D =0.005 capable of exibiting a robut performance in overloaded cenario, were te number of uer i iger tan te number of receiver antenna element, eiter wit or witout FEC coding. Ti attractive property enable te SDMA-OFDM ytem to potentially upport an increaed number of uer. SNR=0dB SNR=5dB Pilot Overead (%) Figure 3: veru pilot overead performance of te LDPC-coded iterative GA-JCEMUD/SDMA-OFDM ytem at different F D. LDPC-GA-JCEMUD-SDMA-OFDM, L4/P, 4QAM, -pat Rayleig GA., F D=0.00 GA., F D=0.003 GA., F D=0.005 GACE-ORSA-MUD GA-JCEMUD paper_d_jnt-v-rl_bpo-v-bid_u4r_jga_ldpc_4qam_mul.gle Tu Sep :47:6 GA-JCEMUD, F D=0.00 GA-JCEMUD, F D=0.003 GA-JCEMUD, F D=0.005 Indvidual-baed Population-baed Figure 4: Performance comparion of te LDPC-coded SDMA- OFDM ytem uing eiter te iterative GA-JCEMUD or te GACE- ORSA-MUD (left) and uing eiter te conventional individualbaed or te propoed population-baed GA-JCEMUD (rigt) at different F D. cannel etimate will become more evere, tu reulting in a dramatic performance degradation in comparion to te propoed joint optimization ceme. Lat but not leat, we preent te performance comparion of te GA-JCEMUD providing eiter te conventional individual-baed ard output [7, 9, 0, ] or te propoed population-baed oft output, a own on te rigt-and ide of Figure 4. A expected, wit te advent of FEC code, te propoed oft GA i capable of ignificantly outperforming te conventional arrangement, epecially wen te cannel fade more rapidly. Ti reult implie te propoed GA i more robut againt fat fading cannel tan te conventional GA. 4. CONCLUSIONS From te invetigation and dicuion conducted, we conclude tat te propoed iterative GA-JCEMUD tecnique generating oft output contitute an effective olution to te cannel etimation problem in multi-uer MIMO SDMA-OFDM ytem. Furtermore, it i 5. REFERENCES [] L. anzo, M. Münter, B. J. Coi, and T. Keller, OFDM and MC-CDMA for Broadband Multi-uer Communication, WLAN and Broadcating. IEEE Pre - Jon Wiley & Son Ltd., 003. [] M. C. Necker and G. L. Stüber, Totally blind cannel etimation for OFDM on fat varying mobile radio cannel, IEEE Tranaction on Wirele Communication, vol. 3, pp , September 004. [3] Y. Li, N. Seadri, and S. Ariyaviitakul, Cannel Etimation for OFDM Sytem Wit Tranmitter Diverity in Mobile Wirele Cannel, IEEE Journal on Selected Area in Communication, vol. 7, pp , Marc 999. [4] S. Toen, L. Deneire, L. V. der Perre, M. Engel, and. D. Man, Contrained Leat Square Detector for OFDM/SDMA-baed Wirele Network, IEEE Tranaction on Wirele Communication, vol., pp. 9 40, January 003. [5] Y. Zeng and T. S. Ng, A Semi-blind Cannel Etimation Metod for Multiuer Multiantenna OFDM Sytem, IEEE Tranaction on Signal Proceing, vol. 5, pp , May 004. [6] K. J. Kim, J. Yue, R. A. Ilti, and J. D. Gibon, A QRD- M/Kalman Filter-baed Detection and Cannel Etimation Algoritm for MIMO-OFDM Sytem, IEEE Tranaction on Wirele Communication, vol. 4, pp. 70 7, Marc 005. [7] K. Yen and L. anzo, Genetic algoritm aited joint multiuer ymbol detection and fading cannel etimation for yncronou CDMA Sytem, IEEE Journal on Selected Area in Communication, vol. 9, pp , June 00. [8] S. Cen and Y. Wu, Maximum likeliood joint cannel and data etimation uing genetic algoritm, IEEE Tranaction on Signal Proceing, vol. 46, pp , May 998. [9] L. anzo, L.-L. Yang, E.-L. Kuan, and K. Yen, Single- and Multi-Carrier DS-CDMA: Multi-Uer Detection, Space-Time Spreading, Syncroniation and Standard. IEEE Pre - Jon Wiley & Son Ltd., 003. [0] C. Ergün and K. acioglu, Multiuer Detection Uing a Genetic Algoritm in CDMA Communication Sytem, IEEE Tranaction on Communication, vol. 48, pp , Augut 000. [] J. Aktman and L. anzo, Reduced-Complexity Maximum- Likeliood Detection in Multiple-Antenna-Aided Multicarrier Sytem, in Proceeding of te 5t International Workop on Multi-Carrier Spread Spectrum Communication, (Oberpfaffenofen, Germany), 4-6 September 005. Available at ttp:// mj0r/t/mc-05.pdf. [] M. Jiang and L. anzo, Improved ybrid MMSE Detection for Turbo Trelli Coded Modulation Aited Multi-Uer OFDM Sytem, IEE Electronic Letter, vol. 40, pp , Augut 004. [3] R. Gallager, Low Denity Parity Ceck Code, IEEE Tranaction on Information Teory, vol. 8, pp. 8, January 96.