EFFICIENT TRANSMITTER-RECEIVER OPTIMIZATION FOR MULTI-USER SPATIAL MULTIPLEXING MIMO SYSTEM WITH ANTENNA SELECTION

Transcription

1 INTERNATIONAL JOURNAL JOURNAL OF OF INFORMATION AND AND SYSTEMS SYSTEMS SCIENCES Volume Volume 5, Number, Number, Page, Page Intitute for Scientific Computing and Information EFFICIENT TRANSMITTER-RECEIVER OPTIMIZATION FOR MULTI-U SPATIAL MULTIPLEXING MIMO SYSTEM WIT ANTENNA SELECTION ZIBIN XIE, JINUAN WANG, JING GAO, YUN WANG Abtract Spatial multiplexing Multi-uer multiple-input multiple-output (MU-MIMO) communication i an effective cheme to provide a ubtantial gain in ytem throughput. In MU-MIMO downlin communication ytem, it i a challenge to pre-cancel multi-uer interference (MUI) and inter-ymbol interference (ISI) effectively. owever, traditional bloc diagonalization (BD) algorithm i deficient of avoiding noie enhancement, and it complexity of optimal preproceing i high. Therefore, auming channel tate information (SCI) i full available in the bae tation (BS), we propoe a novel linear precoder and a low cot tranmitting optimal preproceing cheme for the MU-MIMO downlin channel. For economic purpoe, correponding to optimal preproceing, thi paper propoe an alternative multi-uer antenna election algorithm which minimize the bit error rate for each uer. In addition, for avoiding reidual MUI effect and noie enhancement, we deign a decorder to minimize the mean quare error (MSE) by an extended ZF approach. Compared with traditional algorithm, the propoed cheme can get good performance, reduce the effect of channel etimation error, and ha lower complexity. Simulation reult how the performance of the propoed cheme. ey Word, Multi-uer MIMO ytem, Precoding, Antenna election, bit error (BER), multi-uer equalizer. Introduction Over the lat year, the demand for high data rate in wirele tranmiion ha increaed ignificantly. Communication ytem with multiple tranmit and receive antenna have drawn ignificant interet. So-called multiple-input multiple-output (MIMO) cheme i extenively invetigated a a promiing technology of providing high pectral efficiency for future wirele communication ytem [] []. Previou wor wa focued on point-to-point ingle uer MIMO ytem, more recently the ubtantial capacity offered by the ingle uer multiple-input multiple-output (MIMO) ytem motivate the ue of multiple antenna a a mean to provide multiple acce capabilitie or improve the multiple acce capabilitie of exiting multi-acce cheme. And in the point-to-multipoint multi-uer cae, a bae tation (BS) tranmit to multiple mobile tation (MS) imultaneouly over the ame frequency band, thereby greatly increaing the channel capacity. Received by the editor June 3, 8 57

2 58 Z. XIE, J. WANG, J. GAO AND Y. WANG Several wor have propoed cheme to maximize capacity and power control of MU-MIMO ytem. Cota dirty paper coding (DPC) technique i utilized to achieve the um rate capacity of the Gauian broadcat channel for a MIMO ytem, and it wa proved to achieve the capacity region of the multi-uer multiple antenna broadcat channel [3] [4] [5]. owever, implementation of DPC require ignificant complexity at both tranmitter and receiver, and the problem of finding practical dirty paper code cloe to the capacity limit i till open [6]. Motivated by the conideration of DPC [3], much more ytem capacity can be achieved by uing nonlinear proceing, uch a Tomlinon arahima precoding (TP) [7] [8]. The TP i an ISI mitigation tructure coniting of a feedbac filter in the tranmitter and a feed forward filter in the receiver. Initial reearch on TP in multi-uer MIMO ytem ha mainly focued on the cenario with perfect channel tate information (CSI) aumed at the tranmitter, applying both the zero forcing (ZF) and the minimum mean-quare-error (MMSE) criterion. In thi cae, compared with the linear precoding cheme, the nonlinear mechanim help TP obtain more power gain and larger ytem capacity. owever, the linear precoding, uch a the bloc diagonalization (BD), i a low complexity technique for the multi-uer MIMO ytem [9] [] []. Thee method reult in uperior performance by completely canceling the CCI at every receiver. But they tend to impoe a retriction on the ytem configuration in term of the number of antenna. For thi reaon, the paper [] [3] gave out the ignal-to-leaage ratio (SLR) and ignal-to-leaage-plu-noie ratio (SLNR) approache to get the uboptimal ignal-to-interference-plu-noie ratio (SINR). The tranmit beamforming approache are baed on the concept of ignal leaage and avoid olving the coupled problem of maximizing SINR in [4] [5]. Though the SLR/SLNR relaxe the condition on the number of tranmit-receive antenna, the maximum SLR method i uitable for ingle tream and can degrade the ytem performance when the number of tranmit antenna increae. The SLNR method improved the performance of the SLR, but it i only uitable for multiple tream for orthogonal pace time code MU-MIMO ytem. In thi paper, we conider the downlin of an uncoded multi-uer wirele MIMO ytem where each uer i equipped with multiple receive antenna. The firt, we purue an alternative low complexity linear precoding technique to achieve unitary tranmit precoder in the downlin of multi-uer MIMO ytem. In thi cheme, the propoed optimal tranmitting preproceing approach i imple and effective to improve ytem performance. Moreover, an efficient and financial tranmit antenna election algorithm i propoed to minimize BER for each MS. In addition, to improve the BER of MU-MIMO ytem, we propoe a computationally efficient match filter algorithm for MU-MIMO ytem. Thi algorithm extend the ZF to the olution which can minimize the mean quare error (MSE), and decreae the effect of reidual MUI and channel etimation error. Compared with traditional algorithm, the propoed cheme attain good performance, ha low computational complexity, and i uitable for practical communication ytem. Thi paper i organized a follow. The next ection, we preent the MU-MIMO ytem under conideration. In ection III, we give a hort overview of the main precoder technique propoed in previou wor, the preproceing cheme i propoed and the

3 EFFICIENT- RANSIMITTER-RECEIVER OPTIMIZATIONS 59 antenna election algorithm i determined. Section IV deign the matched filter for MU-MIMO ytem. In ection V, we tudy the effect of channel etimation error on ytem BER performance, and give out the complexity analyi. In ection VI, Simulation reult are preented to demontrate the effectivene of the propoed algorithm. Sytem model Conider a downlin multi-uer MIMO ytem with N t tranmit antenna at the bae tation (BS), and Nr, antenna are located at the th mobile tation (MS). The BS i communicating with uer imultaneouly in the downlin tranmiion. Aume MIMO channel i flat-fading, and let x repreent the l tranmit data ymbol vector for uer, the received ignal y at the th receiver i y = F + n, =,, () = where the i the channel matrix from the bae to the th uer, the precoding matrix of uer i denoted by F, the n i the AWGN noie in the th uer receiver. In addition, we aume that the channel are independent between all uer. The tranmitted vector at time t i x ( t) = F ( t) () The compoite channel matrix i = = = (3) If he tranmit ignal for all uer i X, the MU-MIMO ytem model i Y = X + n (4) where the noie n= n n n, the precoding matrix F = [ FF F ]. RF Nr, Uer S Tranmitting Optimal proce D Precoder F RF Nt Antenna Selection Swichter Nr, Uer S Tranmitting Optimal proce D Precoder F Nt RF Nt Nr, Uer Fig. The diagram of MU-MIMO ytem with antenna election

4 6 Z. XIE, J. WANG, J. GAO AND Y. WANG 3 The propoed preproceing cheme and antenna election 3. Overview In the MU-MIMO ytem, the coordination i lac among the MS. ow to deign the weight of the precoder and decoder i very important. Generally peaing, due to low complexity, the linear precoder ha attracted coniderable interet. The BD method i a imple linear precoding approach which cancel the MUI efficient. One major category of the precoder deign i Fx j j = j=, j Fx j j = F, F,, F = arg j=, j (5) < trace ( FF ) P, =,, Fx j j = j=, j where trace ( ) repreent the trace operation and P i the tranmit power of uer. In [9][], the author give out a BD precoding approache by utilizing ingular value decompoe (SVD). Σ = = U ( )( V V ) (6) + where the column ofv pan the null pace of. In [], the author ue tandard QR decompoition or the Gram-Schmidt orthogonalization (GSO) to cancel the interference. Note that for an n mmatrix Φ, where n m, it can be ( ) ΦIΦΦ = (7) Let the Φ =, the QR decompoition of I i written a R I = QR = ( Q Q) where the Q contain the bai of ubpace of null pace. Thee approache can achieve uperior performance. owever, perfect MUI cancellation require more tranmit antenna. The other one i to chooe the precoder for maximizing the output SINR. The SINR at the input of receiver i given by (8)

5 EFFICIENT- RANSIMITTER-RECEIVER OPTIMIZATIONS 6 SINR = N w r, σ + w j j=, j (9) where w i the precoding matrix th column vector, and theσ i the noie variance. Baed on the SINR criterion, the [] [3] conider an alternative approach baed on maximizing the SLR/SLNR for deigning tranmit beamforming vector in a multi-uer ytem. w o w = arg max N w C w j j=, j () and W SLR for uer κ { } ubject to w =, =,, o W r, σ + W j j=, j = arg max N w C N SLNR for uer i { } ubject to w =, =,, o The optimal w i the eigenvector that correpond to the larget generalized eigenvalue of and, = +. Thee two cheme avoid olving the coupled problem and do not need dimenion condition on the number of tranceiver antenna. o Oberve that the SLR (vector w in ()) i not optimal relative to the SINR criterion (9) and i uitable for ingle ubchannel l =. The SLNR criterion improve the performance by conidering the noie. And in [3], the author applie the leaage-baed olution to the cae of multiple tream per uer for the orthogonal pace-time coding. owever, the improved performance i limited baed on SLNR algorithm. For the ingle tream, firtly, when the tranmit antenna i le than the um of all uer antenna except uer, the BER performance of SLNR algorithm i wore than SLR. And increaing the number of antenna at ome uer can degrade the SLNR performance at other uer. Secondly, for the multiple tream, the SLNR i uitable for orthogonal coding. For the uncoded MU-MIMO ytem, the approach i not to prevent inter-tream-interference well. To olve thee problem, we propoe a novel BD precoder deign cheme for uncoded MU-MIMO ytem in thi paper. 3. The propoed tranmitting proceing cheme In [], the author gave out a precoding algorithm for a multi-uer MIMO ytem, and every uer equipped a ingle antenna. owever, in the ZFDPC method, the channel inverion cheme can not be eaily generalized to the cae of uer with multiple receive antenna. In thi paper, we propoe an algorithm for the multi-uer MIMO ytem baed on channel invere, and there are multiple antenna in each receiver. We can ee that the ()

6 6 Z. XIE, J. WANG, J. GAO AND Y. WANG propoed algorithm i a general method. At the ame time, compared with the approach in [], the preproceing method i alo different. For the uer, the primary objective of BD i to find the nonzero precoding matrix F uch that Fx j j =. The precoding matrix contraint can be expreed a j F = F = F = arg =,, () < trace( FF ) P + F = F = where trace ( ) repreent the trace operation and P i the tranmit power of uer. Aume the channel matrix i independent and row full ran between MS and BS. Thu, the compoite channel matrix i (3). For the uer, the precoding matrix contraint () can be rewritten a F = A =,, F j =, j =,, j (3) ubject to F = Baed on thi deign, the multiuer MIMO ytem can get perfect interference cancellation. According to the contraint (3), we propoed a low complexity bloc diagonalization cheme different traditional method. Becaue of the row full ran of the compoite channel, baed on the characteritic of partitioned matrix, we can ue the right peudo-invere of to get a Nt Nr, preproceing matrix a follow = F = FF F where, ( =,, ) ( ) = = i Nt Nr, matrix, correponding to the th partition of right peudo-invere of. And then, we can get the expectant precoding matrix utilize Gram-Schmidt orthogonalization (GSO) a [ ] (4) F= FF F = (5) F = GSO F, = GSO, =,,. where ( ) ( ) Thi deign can get expected precoder which cancel the MUI well. To guarantee the exitence of a nonzero precoding matrix, from (4) we can ee that the dimenion of the ufficient condition i that the number of tranmit antenna i t r,,,,, (6) = N N =

7 EFFICIENT- RANSIMITTER-RECEIVER OPTIMIZATIONS 63 And the dimenion of tranmitting tream of the uer i the ame a the receive antenna number l = Nr,, =,,, (7) It i different from BD traditional precoding algorithm, the tranmitting ignal tream i decided by the receive antenna in the propoed precoder. In thi cae, it reduce the burden of BS and can atify the variou requirement of different uer. At the ame time, by ome criteria or the tructure of the receiver, a tranmitting proceing matrix can be deigned for the parallel independent ingle-uer MIMO downlin channel. In thi paper, we propoe a optimal preproceing nonzero Nr, l matrix D, =,,, which can be deigned alone by a permutation matrix. Briefly peaing, we can let the D = I, where I i the lat l column of identity matrix. Thi imple deigned cheme can get better F and i eay to implement. The whole tranmitting preproceing can be expreed a follow x Nr, y lx D G lx x lx D Nr, G y lx F F y x lx D Nt Nr, G lx F Gˆ F Gˆ FD FD F G ˆ Fig. The tranmitting preproceing of the propoed cheme 3.3 Antenna election approach The MU-MIMO ytem can achieve great capacity through patial multiplexing. owever, the major limiting factor in the deployment of MU-MIMO ytem are the increae of hardware cot and ignal proceing complexity. To olve thi problem, we propoe an antenna election algorithm for the MU-MIMO ytem baed on minimizing BER. Since the error probability i the function of ignal-to-noie ratio (SNR), the error probability i obtained by the receive SNR [6]. For example M-ary PS, an approximation to the error probability for large value of M and for large SNR can be expreed a

8 64 Z. XIE, J. WANG, J. GAO AND Y. WANG γ P e d π π π = Q γ in M π / M γ in θr im, coθ π / M r θ r u e du (8) γ in ( π / M ) where γ i the ymbol SNR and θr i the phae of tranmitting ignal. If the M i fixed, the probability of error i decided by the SNR. For the linear receiver (for example zero forcing, ZF), the SNR of ub-tream at receiver i SNR ( ZF) E = N Baed on the above equation, the approximate equivalent probability of error can be written a E min P min SNR min (:, ), M Nt Mt N t N E ( ) min min M, t N N R e R R e E r where R i the R matrix of QR decompoe of channel. From the above analyi, we now that the minimum ub-tream SNR of receiver i gotten by the diagonal element of R. That i to ay that the bound of error probability can be obtained by r. Therefore, ii, we propoe an antenna election algorithm baed on minimizing BER criterion a follow ( N N N r r t ii, ) { N } (6) for i = Fat AntSel,,, () S: =,,, N t () for j = to N (7) r = diag Sorted-QR (3) = N { CN } t t (8) end (4) end (9) J = arg max r ii ( ( A) ) i=,, N ii, min { h h } (5) A = () Η =,, J J (9) () Where S:i the tranmit antenna et, i the antenna ubet, i the elected channel, Sorted - QR ( ) repreent the decending order QR decompoition, and J orrepond to the index of the column of elected. Compared with the propoed preproceing cheme in ection 3., the antenna election can reduce the cot of the radio frequency (RF) in ignal tranmiion. The imulation reult are hown in ection VI. 4 The optimal deign for multi-uer receiver

9 EFFICIENT- RANSIMITTER-RECEIVER OPTIMIZATIONS 65 In the MS, the uer doen t now other uer CSI and i lac of cooperation. For the patial multiplexing MU-MIMO ytem, the imple linear of ingle-uer can not get good performance. In [7], the author propoed a MMSE-SQRD algorithm which had a low complexity. Unfortunately, it i not directly ued to the MU-MIMO ytem. In thi ection, we contruct a matched filter baed on the MMSE olution, and extend the decoder to the MU-MIMO ytem. Becaue of the compoite channel i nown in BS and the uer only now itelf, we can definite a extended channel matrix and the receive vector y for the uer a y = and y = () l, where the ( ) = F. Thu, the MMSE olution of the th uer can be get through a matched filter a follow where the ( ) expreed a G F = Il, l () i the left peudo invere. The output of the extended MMSE filter can be ˆ,MMSE = x G y (3) Thi configuration of the propoed matched filter i important for getting a good BER performance and the complexity i temperate. At the ame time, it can further incorporate the olution into the multi-uer BLAST ytem for a SQRD detected algorithm. 5 The channel etimation error and complexity analyi 5. The channel etimation error In actual ytem, the perfect channel tate information i not alway true, and the channel etimation error can influence the performance of the MU-MIMO ytem. Baed on the paper [9], we analyi the performance of the propoed matched filter in the preence of channel uncertaintie. Firt, the channel etimation error model can be expreed a = Η + (4) ' E, where i the perfect channel etimation and i the etimating error of the uer. E, Aume the element of matrix are independent identically ditributed (i.i.d.) E, zero-mean complex Gauian with variance σ. Therefore, the ' E ' ' F ' = and ' G = I (5) l, l Following the analyi of (4) and (5), the reult i imulated in ection VI to illutrate the effect of channel etimation error.

10 66 Z. XIE, J. WANG, J. GAO AND Y. WANG 5. The complexity analyi In the traditional algorithm, the [9] [] ue SVD method to get the precoder and have imilar computational complexity. Conidering the tranmitter and received ignal a well a the channel matrix are complex, the cot of the traditional algorithm i 3 about O 4 Nr, Nt+ N t. The [] ha lower computational complexity j=, j than [9] []. When all proceing i conducted on complex value, the complexity of [] i O 8 Nr, Nt + 8 Nr, Nt j=, j j=, j by ignoring the flop of addition and ubtraction [8]. The complexity of the propoed algorithm i mainly determined by the Moore-Penroe peudo-invere ( ), and the GSO of. Becaue of the modified Gram-Schmidt (M-GSO) ha a much ounder computational procedure than GSO, thi paper adopt the M-GSO a well a [6]. Therefore, the complexity of finding the peudo-invere and M-GSO i about O 8 N ( r, Nt + 8 Nr, Nt ). = The propoed D matrix doe not need to calculate and i given baed on the number of multiple tream. The traditional algorithm utilize the SVD to get the optimal eigenvector, and it computational complexity i about O Nt N = j, j= 3 r,. Compared with the traditional algorithm, the propoed preproceing deign cheme ha lower computational complexity than traditional BD approache. 6 Simulation reult and analyi In thi ection, imulation reult for the above propoed tranmiion proceing and decoder cheme are provided. Aume the MIMO channel i quai-tatic, and it element are i.i.d. complex Gauian random variable in the imulation. All tranmitting ignal of imulation are conducted uing QPS contellation. The performance i meaured by ymbol error rate (). Throughout the imulation, we conider a MU-MIMO ytem with uer. There are N tranmit antenna at the BS and N r, receive antenna at each MS. t

11 EFFICIENT- RANSIMITTER-RECEIVER OPTIMIZATIONS 67 nt=9 nr=3 3 3 l=3 traditional algorithm traditional algorithm propoed algorithm nt=6 nr= l= Propoed algorithm Traditional algorithm Traditional algorithm (a) (b) Fig 3. of MU-MIMO ytem with three uer. Figure 3 compare the average of traditional precoding algorithm and propoed algorithm. In (a), there are nine antenna in BS and three uer where each uer ha three antenna and receive three ub-tream. The BS ha nine tranmit antenna. When the SNR i low, the propoed algorithm ha good. A SNR increae, the of propoed algorithm i lightly inferior. In (b), the number of uer i three, and there are ix tranmit antenna and two receive antenna per uer. The ub-tream i two. The performance ha little difference in variou precoding algorithm. The figure 3 how that the propoed precoder can get imilar performance compared with the traditional algorithm. - nt=9 nr=3 3 3 l=3 nt= nr= l= nt=9 nr=3 3 3 l= D nt= nr= l= D nt=9 nr=3 3 3 l= D Fig 4. Performance comparion of different number of tranmit antenna with preproceing In figure 4, a plot of the performance veru the SNR i provided for the propoed preproceing algorithm. The number of tranmit antenna i nine and ten. Correpondingly, the receive antenna i three and two in each uer. The firt ytem there i three uer and the econd ytem ha five uer. It can be een in figure 4, the i cloe in two ytem which do not adopt preproceing algorithm and are full ub-tream. When the number of ub-tream i le than the number of receive antenna, the MU-MIMO ytem adopt the optimal preproceing matrix D. In thi cae, the performance i different in each ytem. The one who ha more tranmitting lin, ha better performance.

12 68 Z. XIE, J. WANG, J. GAO AND Y. WANG - =3 l= [9n6 ] l= [ ] D l= [6 ] no D - = l=3 [8n6 3 3] l=3 [6 3 3] no D l=3 [8 4 4] D (a) (b) Fig 5. comparion between the propoed preproceing and antenna election cheme A we can ee from figure 5, there are three uer where each uer ha two and three antenna and receive two ub-tream in (a). When the ytem adopt the antenna election (AS) algorithm, the BS ha nine antenna element and ix RF chain. At the ame time, the optimal preproceing (OP) approach need nine RF chain. When the ytem doe not adopt AS and OP, there are i RF in BS. In the above algorithm, the ytem ha poor without AS and OP. The preproceing algorithm can get better performance than antenna election cheme. owever, the OP algorithm need more RF and i not financial. In (b), we give out the comparion of ytem which have more ub-tream and fewer uer. The antenna election ytem ha two uer where each uer ha three antenna and l i three, and the BS ha eight antenna element and ix RF chain. The ytem, which adopt the preproceing algorithm, ha eight RF and four receive antenna in every MS. The ytem without adopting AS and OP ha ix tranmit antenna and two uer where there are three antenna and receive three ub-tream. The (b) ha imilar performance curve with (a). owever, a the number of uer i fewer, the gap of the become large. Thi indicate that, when the ytem ha more uer, the antenna election cheme can attain good hardware cot with little performance lo than optimal preproceing algorithm. - - nt=5 nr=5 5 5 l=5 MMSE nt=5 nr=5 5 5 l= nt=9 nr=3 3 3 l=3 nt= -4 nt= nt=9 nr=3 3 3 l=3 MMSE nt= nt= (db) (a) (b) Fig 6. performance of the propoed matched filter

13 EFFICIENT- RANSIMITTER-RECEIVER OPTIMIZATIONS 69 In figure 6, the performance of propoed matched filter i given out. The tranmit antenna i nine ten and eleven repectively in (a). There are three uer and the ub-tream are three. From (a) we can ee that the performance of the MU-MIMO ytem i improved by increaing the tranmit antenna with general linear equalizer. Correpondingly, the ytem with propoed decoder can attain much better performance. When the tranmit antenna increae, the i almot ame in the ytem adopting the equalizer. In (b), we give out the ytem which ha large antenna array and ub-tream. In thi imulation condition, the performance of the propoed algorithm i alo imilar with (a). nt=9 nt= no ESE σ = - σ = -.5 σ = - σ = -.5 σ = (a) -3-4 no ESE σ = - σ = -.5 σ = - σ = -.5 σ = (b) nt= nt= no ESE σ = - σ = -.5 σ = - σ = -.5 σ = no ESE σ = - σ = -.5 σ = - σ =-.5 σ = (c) (d) Fig 7. The performance of ytem with channel etimation error Plotted in figure 7 are the curve of veru channel etimation error for a three-uer ytem where each uer ha three antenna and receive three ub-tream. And the tranmit antenna Nt i nine and ten in BS. The element of error matrix are i.i.d. complex Gauian random variable with zero mean and variance σ. In (a) and (c), for the CSI etimation error, becaue the tranmit antenna increae, the performance of ytem i improved ignificantly. In (b) and (d), the MU-MIMO ytem adopt the propoed matched filter. At thi time, the propoed decoder ha better robutne for the mall etimation error.

14 7 Z. XIE, J. WANG, J. GAO AND Y. WANG 6 nt= nr= nt=5 nr= Average capacity 4 3 = =3 =4 = Average capacity = 3 =3 =4 =5 =6 = (a) (b) Fig 8. The average um capacity of the propoed MU-MIMO ytem Figure 8 provide the um capacity of our MU-MIMO ytem veru the SNR with variou number of uer. In the two ytem, there are four and even uer where each uer ha two receive antenna. In the BS, the tranmit antenna i ten and fifteen repectively. From the db to the 5 db, we can ee that the capacity of ytem increae rapidly in figure 8. In 5dB~5dB, the average capacity grow lowly. Another cloe obervation to figure (a) and (b) i that the um capacity i decided by the number of the tranmit antenna and uer. When the number of uer i cloe to the upper bound of the ytem, it i notable that the capacity performance i difficult to improve. 7 Concluion In thi paper, the MU-MIMO ytem wa conidered. Auming the full channel tate information i nown at the BS, a novel low complexity tranmitting proceing cheme i propoed. The cheme can eliminate the multi-uer interference of downlin MIMO channel and achieve good performance. At the ame time, for the financial purpoe, we propoe a tranmit antenna election algorithm for the tranmiion cheme. Thi algorithm can obtain good tradeoff between the hardware cot and ytem performance. And then, we give out a configuration of decoder for the MU-MIMO ytem. The equalizer improve the performance greatly, and it i robut when the error occur during the channel etimation. The imulation reult illutrate the performance of the cheme. REFERENCES [] Telatar, E. (999) Capacity of multi-antenna Gauian channel, European Tranaction on Telecommunication, Nov./Dec., pp [] Fochini, G. J., Gan, M.J. (998) On limit of wirele communication in fading environment when uing multiple antenna, Wirele Peronal Communication, Vol. 6, No. 3, pp [3] Cota, M. (983) Writing on dirty paper, IEEE Tranaction on Information Theory, Vol.9, No. 3 pp [4] Caire, G., Shamai, S., (3) On the achievable throughput of a multi-antenna Gauian broadcat channel, IEEE Tranaction Information Theory, Vol. 49, No. 7, pp [5] Weingarten,., Steinberg, Y., and Shamai, S. (4) The capacity region of the Gauian MIMO broadcat channel, International Sympoium on Information Theory, June 7-July,

15 EFFICIENT- RANSIMITTER-RECEIVER OPTIMIZATIONS 7 pp. 74. [6] Erez, U., Brin, S. T. (5) A cloe-to-capacity dirty paper coding cheme, IEEE Tranaction on Information Theory, Vol. 5, No., pp [7] arahima,., Miyaawa,. (97) Matched-tranmiion technique for channel with interymbol interference, IEEE Tranaction On Communication, Vol., No. 4, pp [8] Tomlinon, M. (97) New automatic equalier employing modulo arithmetic, Electronic Letter, Vol. 7, No.5-6, pp [9] Spencer, Q.., Swindlehurt, A. L., and aardt, M. (4) Zero-forcing method for downlin patial multiplexing in multiuer MIMO channel, IEEE Tranaction on Signal Proceing, Vol. 5, No., pp [] Choi, L., Murch, R. D. (4) A tranmit proceing technique for multiuer MIMO ytem uing a decompoition approach, IEEE Tranaction Wirele Communication, Vol. 3, No., pp. 4. [] Chen, R., Andrew, J. G., and eath, Jr., R. W. (4) Multiuer pace-time bloc coded MIMO ytem with unitary downlin preceding, IEEE International Conference Communication, Pari, France, June, pp [] Tarighat, A., Sade, M., and Sayed, A.. (5) A multi uer beamforming cheme for downlin MIMO channel baed on maximizing ignal-to-leaage ratio, IEEE International Conference on Acoutic, Speech, and Signal Proceing, Philadelphia, USA, pp. iii/9 iii/ 3. [3] Sade, M., Tarighat, A., and Sayed, A.. (7) A Leaage-Baed Precoding Scheme for Downlin Multi-Uer MIMO Channel, IEEE Tranaction on Communication, Vol. 6, No. 5, pp [4] Wong,., Cheng, R., Letaeif,. B. and Murch, R. D. () Adaptive antenna at the mobile and bae tation in an OFDM/TDMA ytem, IEEE Tranaction on Communication, Vol. 49, No., pp [5] Schubert, M., Boche,. (4) Solution of the multiuer downlin beamforming problem with individual SINR contraint, IEEE Tranaction on Vehicular Technology, Vol. 53, No., pp.8-8. [6] Proai, J. G. (6) Digital Communication, Fourth Edition Publihing oue of Electronic Indutry. [7] Wübben, D., Böhne, R., uhn, V. and ammeyer,. D. (3) MMSE extenion of V-BLAST baed on orted QR decompoition, Vehicular Technology Conference, October 6-9, pp [8] Golub, G.., Van Loan, C. F. (996) Matrix computation, The John opin Univerity Pre. [9] utter, A. A., de Carvalho, E., and Cioffi, J. M. () On the impact of channel etimation for multiple antenna diverity reception in mobile OFDM ytem, Conference Record of the Thirty-Fourth Ailomar Conference on Signal, Sytem and Computer, Pacific Grove, CA, USA, pp