Multiuser Detection in Large-Dimension Multicode MIMO-CDMA Systems with Higher-Order Modulation

Transcription

1 The 2011 Militay Communications Confeence - Tack 1 - Wavefoms and Signal Pocessing Multiuse Detection in Lage-Dimension Multicode MIMO-CDMA Systems with Highe-Ode Modulation Pitam Som and A. Chockalingam Depatment of ECE, Indian Institute of Science, Bangaloe , India Abstact In this pape, we ae inteested in high spectal efficiency multicode CDMA systems with lage numbe of uses employing single/multiple tansmit antennas and highe-ode modulation. In paticula, we conside a local neighbohood seach based multiuse detection algoithm which offes vey good pefomance and complexity, suited fo systems with lage numbe of uses employing M-QAM/M-PSK. We apply the algoithm on the chip matched filte output vecto. We demonstate nea-single use (SU) pefomance of the algoithm in CDMA systems with lage numbe of uses using 4- QAM/16-QAM/64-QAM/8-PSK on AWGN, fequency-flat, and fequency-selective fading channels. We futhe show that the algoithm pefoms vey well in multicode multiple-input multiple-output(mimo) CDMA systems as well, outpefoming othe linea detectos and intefeence canceles epoted in the liteatue fo such systems. The pe-symbol complexity of the seach algoithm is O(K 2 n 2 tn 2 cm), K: numbe of uses, n t: numbe of tansmit antennas at each use, n c: numbe of speading codes multiplexed on each tansmit antenna, M: modulation alphabet size, making the algoithm attactive fo multiuse detection in lage-dimension multicode MIMO- CDMA systems with M-QAM. Keywods Multicode MIMO, DS-CDMA, highe-ode modulation, nea-optimal pefomance, local neighbohood seach. I. INTRODUCTION MIMO techniques ae attactive to achieve high-spectal efficiency wieless tansmissions, and they have been widely adopted in cuent wieless standads including LTE-A and WiFi. Diect-sequence code division multiple access (CDMA) has been attactive in both militay as well as non-militay (2G/3G cellula) communication scenaios. It is of inteest to incease the spectal efficiencies achieved in CDMA systems. This can be achieved though the use of i) highe-ode modulation, ii) multicode opeation, and iii) MIMO techniques. Multicode scheme divides a high ate data steam into multiple low ate substeams, and tansmits these substeams in paallel using multiple speading codes. Fo example, in CDMA based wieless communication standads, e.g., HSDPA and HSUPA [1-[3, M-QAM modulated multicode opeation has been intoduced in the physical laye in ode to povide enhanced data ates. In fequencyselective channels, multipath induced code-domain intefeence in such systems can seiously degade pefomance. In addition to code-domain intefeence, spatial intefeence will esult if MIMO tansmission is adopted. Conventional matched filte (MF) detection esults in poo pefomance in such cases. It has been shown that in ode to achieve high spectal efficiencies using highe-ode modulation in CDMA, multiuse detection [4 is essential [5. Achieving optimal/nea-optimal multiuse detection pefomance, when the dimensionality of the detection poblem is lage, is challenging. Paticulaly, the size of maximumlikelihood (ML) solution space in multicode MIMO-CDMA is M Kntnc (M: modulation alphabet size, K: numbe of uses, n t : numbe of tansmit antennas at each use, n c : numbe of codes multiplexed on each tansmit antenna), which makes ML detection impactical fo lage Kn t n c log 2 M. In this pape, ou focus is on achieving nea-ml pefomance in lage-dimension multicode MIMO-CDMA with highe-ode modulation at low complexities. Seveal papes on multiuse detection in CDMA with higheode modulation (without o with multicode MIMO) mainly conside linea detectos including MF, decoelating/zeofocing (ZF), and minimum mean squae eo (MMSE) detectos. Fo example, in [5, the spectal efficiency analysis in lage CDMA systems with highe-ode modulation is fo MF and MMSE detectos. Ealy pefomance analysis woks on MMSE detection in CDMA with highe ode modulation is due to Milstein et al [6-[9. In [10, van Houtum analyzed the BER pefomance of quasi-synchonous CDMA with M- QAM/M-PSK and Walsh-Hadamad codes in the pesence of synchonization eos smalle than the chip time fo MF detection. In [11, Rhee et al poposed a multicaie 16- QAM CDMA tansceive system, which used a combination of decoelato and RAKE eceive. In [12,[13, Yu et al developed appoximations fo the symbol/bit eo ate of LMMSE eceives fo M-QAM in Rayleigh faded CDMA channels. In [14, it has been shown that chip-level LMMSE equalize with eceive divesity povides a significant pefomance enhancement in HSDPA system. Chip-level LMMSE has been extended to MIMO multicode CDMA in [15. Intefeence canceling detectos with highe ode modulation have also been widely studied [16,[17. In [18, Huang et al poposed a goup detection scheme fo multicode MIMO. In [19, Meue and Webe studied an iteative multiuse detection scheme, which is closely elated to paallel intefeence cancellation (PIC), fo TD-CDMA with higheode modulation. Pefomance of multicode CDMA with successive intefeence cancellation (SIC) in Nakagami-m channel channels is pesented in [20. In [21, Xia and Wang deived analytical BER expessions fo multicode CDMA with M-QAM using a PIC eceive. Recently, this wok has been extended fo bit-inteleaved coded M-QAM (BIC-MQAM) [22. A fequency-domain PIC scheme fo multicode MIMO-CDMA is studied in [23. In [24, Change and Lee pesented a two stage intefeence cancelling scheme fo detection in multicode MIMO. This pape also poposed powe allocation stategies at the tansmitte based on the feedback fom eceive in ode to balance signal-to-noise /11/$ IEEE 364

2 atio in all substeams of data, and theeby impoving the pefomance futhe. In [25, eceives that cancel codedomain and space-domain intefeences in multicode MIMO in adhoc netwok settings ae pesented. In [26, Yang et al showed that with usage of LCZ and ZCZ sequences as speading codes the BER pefomance of SIC schemes in multicode schemes can be impoved significantly. Highe-ode QAM detection in CDMA using othe techniques including semi-definite pogamming (SDP) have been studied [27. Howeve, most of the above mentioned detectos eithe scale well in complexity but pefom pooly (e.g., MF, ZF, MMSE), o pefom well but do not scale well in complexity (e.g., intefeence canceles), making them inadequate fo use in communication systems with lage dimensions. Achieving high spectal efficiencies needs signaling to be done in lage dimensions (e.g., in hundeds), i.e., lage K, n t, n c, M in multicode MIMO-CDMA. Recently, algoithms ooted in atificial intelligence/machine leaning have been shown to be attactive to achieve nea-optimal pefomance in communication poblems in lage dimensions [28-[32. In this pape, we conside a low complexity algoithm based on local neighbohood seach fo multiuse detection in multicode MIMO-CDMA systems using M-QAM/M- PSK, and demonstate its nea-optimal pefomance in lage (hundeds of) dimensions. The algoithm stats fom an initial solution vecto, which can be the output fom any known lowcomplexity detecto such as ZF, MMSE detectos. This initial solution is efined (in tems of ML cost) though an iteative low-complexity seach in the neighbohood to get the final solution vecto. We apply the algoithm on the chip-matched filte output vecto in multicode MIMO-CDMA. Simulation esults fo 16-QAM/64-QAM/8-PSK show that the algoithm achieves nea-single use BER pefomance in multiuse multicode MIMO CDMA. The pe-symbol complexity of the algoithm is O(K 2 n 2 tn 2 cm). A key advantage is that the algoithm offes both scalability to lage dimensions as well as nea-optimal pefomance in lage dimensions. II. SYSTEM MODEL We conside K-use DS-CDMA on the uplink. Without loss of geneality, we conside synchonous CDMA whee each use employs n t tansmit antennas and multiplexes n c substeams of data in the code domain using n c speading codes on each tansmit antenna with N chips pe symbol. The base station (BS) eceives the signal using n eceive antennas. Figue 1 shows the system model consideed. Let x k denote the kth use s tansmit data symbol vecto of size n t n c 1, which is given by x k = [ x T k,1,x T k,2,,x T k,n t T, (1) whee x k,j is the sub-vecto of size n c 1 on jth antenna of kth use, given by x k,j = [ x k,j,1,x k,j,2,,x k,j,nc T, (2) whee x k,j,i A is the complex data symbol mounted on ith code on jth antenna of kth use, and A is the modulation alphabet (e.g., M-QAM/M-PSK). Stacking the tansmit vectos fom all the K uses, the oveall Kn t n c 1 sized tansmit vecto is given by x = [ x T 1,x T 2,,x T K T. (3) The speading wavefom on kth use s ith code, denoted by c k,i (t), is given by c k,i (t) = N 1 n=0 c n k,iφ(t nt c ), k = 1,,K, (4) whee T c is one chip duation, c n k,i {±1} is the nth chip of kth use s ith code, φ(t) is the chip wavefom, which is assumed to be ectangula, i.e., unity fo 0 t T c and zeo othewise, N = T s /T c is the pocessing gain, and T s is one data symbol duation. Thee ae n c diffeent speading codes assigned to each use. So thee ae a total of Kn c diffeent speading codes. Each use euses its assigned codes on all its n t tansmit antennas. The ith code sequence of kth use, denoted by c k,i, is given by c k,i = [ c 0 k,i,c 1 k,i,,c N 1 T. k,i (5) Putting all n c codes on jth antenna of use k in a N n c matix fom, we wite C k,j = [ c k,1,c k,2,,c k,nc. (6) Because of code euse, same codes ae used in all tansmit antennas in a given use. We theefoe wite kth use s full code matix of size N n t n c as C k = [ C k,j,c k,j, n t times. (7) Putting the code matices of all uses togethe, the oveall system code matix C of size N Kn t n c is witten as C = [ C 1,C 2,,C K. (8) So, the oveall input to the channel in N chip intevals is given by Cx, whee nth ow denotes the tansmit vecto at the nth chip inteval. Conside fequency-selective fading channel model, whee multiple esolvable paths exist between each use and the BS. Without loss of geneality, let L denote the numbe of esolvable paths between any pai of tansmit and eceive antennas. Let h l k,p,j CN(0,Ω l) denote the complex channel gain on the lth path between jth tansmit antenna of kth use and the pth eceive antenna at the BS. We assume that the channel coefficients emain constant ove one symbol duation. Exponential powe-delay pofile with Ω l = E[ h l k,p,j 2 = Ω 0 e βl, l = 0,,L 1, (9) is assumed, whee β is the ate of exponential decay of aveage path powe. It is also assumed that the delay spead is small compaed to the symbol duation (i.e., L << N), so that thee is inte-chip intefeence but no inte-symbol intefeence. The eceived sample at nth chip of pth eceive antenna is y p (n) = K L 1 n t n c k=1 l=0 j=1 i=1 h l k,p,jc n,l k,i x k,j,i + w p (n) (10) 365

3 x k,j,i k j i : data symbol : use index : Tx antenna index : code index x 1,1,1 Reuse of codes acoss antennas c 1,1 c k,i k i Use 1 Tx : speading code : use index : code index x 1,1,nc c 1,nc Tx Antenna 1 Receive at BS Input data 1 : n cn t seial to paallel convesion x 1,2,1 x 1,2,nc c 1,1 c 1,nc c 1,1 Tx Antenna 2 Channel Rx Antenna 1 Rx Antenna 2 Chip matched filteing y Detection Detected data x 1,nt,1 x 1,nt,nc c 1,nc Tx Antenna n t Rx Antenna n Use 2 Tx Use K Tx Fig. 1. Multicode MIMO-CDMA System Model. whee c n,l k,i is the nth enty of the l chip delayed code sequence vecto c l k,i = [0,0, l times,c 0 k,i,c1 k,i,,cn l 1 k,i T, and w p (n) is the complex Gaussian noise sample with zeo mean and vaiance σ 2. Note that c 0 k,i in the above is the same as c k,i defined in (5). We want to develop a linea vecto channel model compising the eceived samples fo eceive pocessing at the BS. Let us take the N 1 eceived vecto at pth x antenna y p as y p = [y p (0),y p (1),,y p (N 1) T, (11) and the oveall n N 1 eceived vecto ove all eceive antennas as y = [ y T 1,y T 2,,y T n T. (12) We poceed to detemine the equivalent code matix (S) and channel matix (H) at the eceive side, such that the linea vecto channel equation with tansmit vecto x can be witten in the fom y = SHx + w, (13) whee w is n N 1 noise vecto, given by w = [ w T 1,w T 2,,w T n T, (14) whee w p is the noise vecto at the pth x antenna, given by w p = [w p (0),w p (1),,w p (N 1) T. (15) Let h k,p,j denote the L 1 multipath channel coefficient vecto coesponding to kth use s jth tansmit and BS s pth eceive antennas, which is given by h k,p,j = [ h 0 k,p,j,h 1 k,p,j,,h L 1 k,p,j. (16) Since the fades emain same fo all the n c codes fo a given tx-x antenna pai, we define a n c L n c channel matix H k,p,j = diag { h k,p,j,h k,p,j, n c times }. (17) Putting togethe the above matices fo all n t tansmit antennas fom use k to eceive antenna p, define the n t n c L n t nc channel matix H k,p = diag { H k,p,1,h k,p,2,,h k,p,nt }. (18) Likewise, the channel matix of size Kn t n c L Kn t n c at the pth x antenna fom all the K uses can be witten as H p = diag { H 1,p,H 2,p,,H K,p }. (19) The oveall channel matix between all the uses and the BS eceive is of size n Kn t n c L Kn t n c, and is given by H = [ H T 1,H T 2,,H T n T. (20) The eceive side code matix S becomes diffeent fom tansmit side code matix C because of the fact that at the eceive side additional effect of multipath channel gains on the tansmit symbols have to be consideed. The data steam coesponding to ith code on jth tansmit antenna of use k (c k,i ) is eceived at the pth eceive antenna though L esolvable paths. Combining the delayed code sequences coesponding to L paths, we wite the N L matix S p,k,j,i = [ c 0 k,i,c 1 k,i,,c L 1 k,i. (21) Putting togethe the code matices coesponding to all n c codes on jth tx antenna of use k, we wite N n c L matix S p,k,j = [ S p,k,j,1,s p,k,j,2,,s p,k,j,nc. (22) 366

4 The N n t n c L code matix coesponding all tansmit antennas of use k can be obtained by concatenating S p,k,j n t times as codes ae eused acoss all tx antennas, i.e., S p,k = [ S p,k,j,s p,k,j, n t times. (23) The oveall code matix of size N Kn t n c L coesponding to pth x antenna can be obtained by combining all S p,k s as S p = [ S p,1,s p,2,,s p,k. (24) The code matices acoss the eceive antennas emain same. Theefoe, the oveall eceive side code matix S of size n N n Kn t n c L is given by S = diag { S p,s p, n times }. (25) With the above definitions of channel and code matices H and S, we will cay out eceive pocessing on the linea vecto channel model in (13). III. DETECTION ALGORITHM Conside the complex system model (13) y = }{{} SH x + w, (26) =A whee y C d, d = n N, A C d dt, d t = Kn t n c x A Kntnc and w C d. We convet the complex system model in (26) to a eal system model, given by y = A x + w, (27) whee, defining y = y I + jy Q, A = A I + ja Q, x = x I + jx Q, w = w I + jw Q, ( ) y = [yi T yq T T AI A, A = Q, A Q A I x = [x T I x T Q T, w = [w T I w T Q T, (28) so that A R 2d 2dt, y R 2d 1, x S 2dt 1, and w R 2d 1. With this eal system model, when x takes values fom squae M-QAM alphabet, each enty of x can be thought of as an element fom M-PAM signal set S such that, S {(2m 1 M) : m = 1,2,, M}. Assuming channel state infomation to be available at the eceive, the optimal maximal likelihood (ML) solution vecto, x,ml, is x,ml = = ag min x S 2d t ag min x S 2d t y A x 2 x T A T A x 2y T A x. (29) }{{} ψ(x ) The detection poblem in (29) is exponentially complex in d t. We conside a low-complexity algoithm, temed as likelihood ascent seach (LAS) algoithm [28,[29,[30. Details of the algoithm ae developed below. The algoithm attempts to each the global minima of the objective function in (29) an iteative fashion, stating fom an initial solution vecto. This initial solution vecto, x (0), can be the output of a low-complexity linea detecto, e.g., MF, ZF, MMSE detectos. Let x (t) denote the solution vecto afte tth iteation of the algoithm. In each iteation, the solution vecto updates one of its enty such that the cost function undegoes maximum eduction. The iteative pocedue teminates when none of the possible updates educes the cost function any futhe. The update ule at tth iteation, assuming the symbol update happens at the qth enty of the solution vecto, can be witten as x (t) = x (t 1) + θ (t) q e q, (30) whee e q is unit vecto with its qth enty as one, and all othe enties as zeo, and θ q (t) is change in the value of qth enty of x (t 1). The task at each iteation is to find out q and θ q (t) that minimizes the ML cost in that iteation. The change in cost function in the tth iteation is given by (t) q = ψ ( x (t) ) ( ψ x (t 1) ) = θ (t) 2 q G (q,q) 2θ q (t) z q (t), (31) whee G (q,q) is the (q,q)th enty of G = A T A, z q (t) is the qth enty of the z (t) = A T (y A x (t 1) ). If (t) q is negative fo some q, then eduction of the cost function at tth iteation is possible. Let us assume that qth enty of x (t 1) has taken the value s q (t 1) S. Then, θ q (t) can take values only fom the set S q (t) {(2m 1 M s q (t 1) ) : m = 1,, M}, so that the qth enty of x (t) can also be an element of S. We find out the cost function diffeence coesponding to each possible value of θ q (t) S q (t) using (31) and detemine the minimum among the negative cost diffeence values thus obtained. Let (t) q,min be the minimum cost diffeence value fo symbol update at the qth enty of x (t 1). We compae the minimum cost diffeence value (t) q,min s fo q = 1,2,,2d t, and detemine the least among them. Let us call the least cost diffeence value thus obtained as (t) min, which is given by (t) min = min{ (t) q,min : q = 1,,2d t}. (32) Let the values of q and θ q (t) coesponding to (t) min be q(t) min and θ (t) min, espectively. The symbol update at ith iteation then becomes x (t) = x (t 1) + θ (t) min e. (33) q (t) min We also obseve that z (t+1) can be obtained fom z (t) as z (t+1) = A T (y A x (t) ) = A T ( y A x (t 1) ) (t) θ min Ge q (t) min = z (t) θ (t) min Ge. (34) q (t) min The algoithm teminates when (t) q 0, q {1,,2d t } and fo all possible values of θ q (t), i.e., thee is no negative cost diffeence, and hence futhe eduction of cost of the objective function is not possible. Since the seach is only based on local neighbohood (i.e., 1-symbol neighbohood) athe than exhaustive seach, the final solution vecto fom the algoithm can be a local minima. Howeve, the pefomance of this simple algoithm is found to get inceasingly close to optimal pefomance fo inceasing values of d t. 367

5 A. Computational Complexity The algoithm is compised of the following main components: i) computation of G, ii) computation of initial solution vecto x (0), iii) computation of z (1), and iv) seach opeations. The complexity of calculating G is O(d 2 td ). Computation of initial vecto using ZF/MMSE involves taking invese of a matix of size d t d t, whose complexity is O(d 3 t). The computation of z (1) compises of two components: multiplication of G and x (0), and subtaction of A T y fom Gx (0). The complexity involved in this is O(d 2 t). Fom simulations, the aveage complexity involved in one seach iteation and aveage numbe of iteations equied ae found to be clealy sub-cubic in d t and linea in M. So the oveall complexity ode is dominated by the cubic tem in the MMSE matix invesion. Combining all the above complexities, the total complexity is O(d 3 tm). Since d t symbols ae detected, the aveage pe-symbol complexity of the algoithm is O(d 2 tm), i.e., O(K 2 n 2 tn 2 cm). IV. SIMULATION RESULTS AND DISCUSSIONS We evaluated the BER pefomance of LAS detection algoithm though simulations in uplink DS-CDMA with 4- QAM, 16-QAM, 64-QAM and 8 PSK, as a function of aveage SNR unde diffeent channel conditions (AWGN, fequency-flat fading, and fequency-selective fading) fo diffeent values of n c, n t, and n. Simulations ae caied out fo systems with lage dimensions, i.e., lage Kn t n c, to illustate the scalability of the algoithm to lage dimensions as well as achievability of nea-single use pefomance in lage dimensions. We also pesent the compaison of BER pefomance of MMSE-LAS algoithm with those of few othe algoithms available in the liteatue fo both single use as well as multiuse multicode MIMO. The aveage SNR fo kth use is P k /σ 2, whee P k = n t E s n c N is the total tansmit powe of kth use in one symbol duation, and E s is aveage symbol enegy. The output of MMSE detecto is used as the initial solution vecto fo LAS algoithm in all simulations; consequently, the algoithm is efeed to as MMSE-LAS in all the BER pefomance figues. Pefomance on AWGN channel: In Fig. 2, we plot the BER pefomance of MMSE-LAS detecto fo DS-CDMA with 4-QAM, 16-QAM and 64-QAM on AWGN channels with n c = n t = n = 1 (i.e., system with single tansmit antenna pe use, single code pe tansmit antenna, and single eceive antenna at the BS). The numbe of uses and pocessing gain ae kept at K = 128 and N = 256, espectively. The pefomance of MMSE detecto as well as the single use (SU) pefomance ae also plotted fo compaison. Note that obtaining the tue ML pefomance fo such a lage dimension system with K = 128 though exhaustive seach o sphee decoding is pohibitively complex. Hence, we have used SU pefomance (i.e., pefomance with no multiuse intefeence) as a lowe bound on the ML pefomance in ode to assess the neaness of MMSE-LAS pefomance to ML pefomance. Fom Fig. 2, we see that the pefomance of MMSE-LAS detecto is close to SU pefomance, wheeas K=128, N=256 AWGN Channel 4 QAM 16 QAM Single Use, 4 QAM Single Use, 16 QAM Single Use, 64 QAM MMSE, 4 QAM MMSE, 16 QAM MMSE, 64 QAM MMSE LAS, 4 QAM MMSE LAS, 16 QAM MMSE LAS, 64 QAM 64 QAM Fig. 2. BER pefomance of MMSE-LAS detecto as a function of aveage SNR in AWGN channel fo 4-QAM/16-QAM/64-QAM with K = 128, N = 256, n t = n = n c = 1. K=192,N=256, Flat Fading Channel 16 QAM 4 QAM 64 QAM Single Use, 4 QAM Single Use, 16 QAM Single Use, 64 QAM MMSE, 4 QAM MMSE, 16 QAM MMSE, 64 QAM MMSE LAS, 4 QAM MMSE LAS, 16 QAM MMSE LAS, 64 QAM Fig. 3. BER pefomance of MMSE-LAS detecto as a function of aveage SNR in flat Rayleigh fading fo 4-QAM/16-QAM/64-QAM with K = 192, N = 256, n t = n = n c = 1. MMSE pefomance is fa fom SU pefomance. This shows the effectiveness of the seach opeation caied out in MMSE-LAS to impove the MMSE pefomance towads SU pefomance. Pefomance on flat Rayleigh fading: Figue 3 shows a simila set of BER pefomance plots fo flat Rayleigh fading with 4-QAM, 16-QAM, 64-QAM and n c = n t = n = 1. The numbe of uses and pocessing gain used ae K = 192 and N = 256. Hee again, MMSE-LAS achieves nea-su pefomance fo all the modulations consideed, maintaining significant SNR advantage ove the MMSE detecto (about 5 db at BER). Multicode CDMA in fequency-selective fading: In Fig. 4, we pesent the MMSE-LAS detecto s BER pefomance fo multicode CDMA with 4-QAM, 16-QAM, 64-QAM in fequency-selective fading with n c = 4, n t = 1, K = 32, N = 128, L = 3, β = 0, and n = 2. The vaiance of the channel coefficients ae nomalized, i.e. L 1 l=0 Ω l is set to 1. Multicode MIMO-CDMA in fequency-selective fading: In Fig. 5, multicode MIMO-CDMA is consideed in fequency- 368

6 K=32, N=128, n t =1,n c =4,=n =2, L=3, β=0 MMSE, 4 QAM MMSE, 16 QAM MMSE, 64 QAM MMSE LAS, 4 QAM MMSE LAS, 16 QAM MMSE LAS, 64 QAM Single Use, 4 QAM Single Use, 16 QAM Single Use, 64 QAM 1 Stage SIC [27 2 Stage SIC [27 Goup Detecto [21 MMSE LAS 4 QAM, n t =n =4, n c =8, L=3, β =0.5, N= Fig. 4. BER pefomance of MMSE-LAS detecto as a function of aveage SNR fo multicode CDMA in fequency-selective fading with n c = 4, n t = 1, n = 2, K = 32, N = 128, L = 3. Unifom powe delay pofile. 4 QAM K=64, n t =n c =n =2, L=3, N=256, β=0 16 QAM 4 QAM, MMSE 16 QAM, MMSE 64 QAM, MMSE 4 QAM, MMSE LAS 16 QAM, MMSE LAS 64 QAM, MMSE LAS 4 QAM, Single Use 16 QAM, Single Use 64 QAM, Single Use 64 QAM Fig. 6. Compaison of MMSE-LAS detecto pefomance with the pefomance of intefeence cancele in [27 and goup detecto in [21 fo 4-QAM in single use multicode MIMO with n c = 8, n t = 4, n = 4, K = 1, N = 32, L = 3, β = 0.5. Intefeence Cancelle [28 MMSE LAS 4 QAM, n t =2, n =4, n c =8, K=2, L=3, β =0.5, N= Fig. 5. BER pefomance of MMSE-LAS detecto as a function of aveage SNR fo multicode MIMO-CDMA in fequency-selective fading with n c = 2, n t = n = 2, K = 64, N = 256, L = 3. Unifom powe delay pofile. selective fading with n c = 2, n t = 2, K = 64, N = 256, L = 3, β = 0, n = 2. BER plots ae shown fo 4-QAM, 16-QAM and 64-QAM. In multicode CDMA (Fig. 4) and multicode MIMO-CDMA (Fig. 5), MMSE-LAS outpefoms MMSE detecto, and pefoms close to SU pefomance. Compaison with othe IC detectos: Figue 6 compaes the BER pefomance of MMSE-LAS detecto fo single use multicode MIMO with those of the multi-stage SIC eceive poposed in [24, and the goup detecto poposed in [18. The numbe of antennas both at tansmitte and eceive side is kept at n t = n = 4. The othe simulation paametes ae taken as in [24, i.e., N = 32, L = 3, n c = 8, β = 0.5 and 4-QAM. It can be seen that at BER, MMSE-LAS BER cuve is bette than the goup detecto [18 by about 3 db. The SIC in [24 exhibits eo floos. [24 also poposed a tansmit powe allocation scheme to bette the pefomance of the SIC. But powe allocation equies feedback fom eceive and also esults in additional pocessing ovehead at the tansmitte. The pefomance achieved by 2-stage SIC with powe allocation scheme in [24 could not bette the Fig. 7. Compaison of MMSE-LAS detecto pefomance with the pefomance of the IC in [28 fo 4-QAM in multicode MIMO-CDMA with n c = 8, n t = 2, n = 4, K = 2, N = 32, L = 3, β = 0.5. pefomance of the goup detecto in [18, wheeas MMSE- LAS outpefoms even the goup detecto. Figue 7 pesents the compaison of MMSE-LAS BER pefomance as a function of aveage SNR fo multiuse multicode MIMO with that of the IC detecto poposed in [25. The simulation paametes, consideed as in [25, ae N = 32, n c = 2, K = 2, n t = 2, n = 4, n c = 8, L = 3, β = 0.5. At BER MMSE-LAS is nealy 10 db bette than the IC algoithm pesented in [25. The IC eceive in [25 suffes fom eo floo while MMSE-LAS does not. It is to be noted that [18, [24 and [25 divide the data steams into multiple segments and fomulates detection poblem individually fo each goup teating othe segments contibution to eceived signal powe as noise. Wheeas we have fomulated the poblem at the chip matched filte output as joint detection poblem ove all the data steams. This esults in the impoved pefomance obseved in Figs. 6, 7. BER Pefomance fo M-PSK: Finally, in Fig. 8, we pesent the MMSE-LAS detecto s BER pefomance fo 8-PSK with 369

7 8 PSK, K=128, N=256, n c =n t =n =1, L=3, β=0(fo Multipath Fading) MMSE, AWGN MMSE, Flat fading MMSE, Multipath fading MMSE LAS, AWGN MMSE LAS, Flat fading MMSE LAS, Multipath fading Single Use, AWGN Single Use, Flat fading Single Use, Multipath fading Fig. 8. BER pefomance of MMSE-LAS detecto as a function of aveage SNR fo DS-CDMA with 8-PSK in AWGN, flat fading, and fequencyselective fading channels. K = 128, N = 256, n t = n = n c = 1. K = 128, N = 256, n t = n c = n = 1, in AWGN, flat fading and fequency-selective fading channels. Fo fequencyselective fading, L is taken to be 3 with unifom powe delay pofile. Fo convenience in handling M-PSK symbols, we did not decompose the vecto channel model into in-phase and quadatue pats, and applied the detection algoithm diectly on the complex system model. The esults in Fig. 8 establishes the suitability of LAS algoithm fo M-PSK and its ability to achieve nea SU pefomance. V. CONCLUSIONS We pesented a low complexity detection scheme based on local neighbohood seach fo multicode multi-antenna uplink DS-CDMA systems with highe-ode modulation. The detecto was shown to scale well fo lage dimensions and give nea SU BER pefomance. Simulation esults showed that the consideed MMSE-LAS detecto exhibits significant pefomance advantage ove the othe detection algoithms epoted in the liteatue fo multicode MIMO-CDMA. With its attactive featues like low complexity/scalability and nea optimal pefomance, the LAS detecto pesented in this pape can addess the challenge of achieving highe data ates in the next geneation MIMO-CDMA wieless systems. REFERENCES [1 H. Holma and A. Toskala, HSDPA/HSUPA fo UMTS, John Wiley & Sons, [2 3GPP TS v7.8.0, Multiplexing and channel coding (FDD), Release 7, May [3 3GPP TS v7.5.0, Speading and modulation (FDD), Release 7, May [4 S. Vedu, Multiuse Detection, Cambidge Univesity Pess, [5 O. Pato and G. P. 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