Research Article BitErrorRatePerformanceofaMIMO-CDMA System Employing Parity-Bit-Selected Spreading in Frequency Nonselective Rayleigh Fading

Antennas and Propagation Volume 0, Article ID 5699, pages doi:055/0/5699 Research Article BitErrorRatePerformanceofaMIMO-CDMA System Employing Parity-Bit-Selected Spreading in Frequency Nonselective Rayleigh Fading Claude D Amours and Adel Omar Dahmane School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Canada KN 6N5 Département de génie électrique et génie informatique, UniversitéduQuéec àtroisrivières, Trois Rivières, Canada G9A 5H7 Correspondence should e addressed to Claude D Amours, damours@siteuottawaca Received Feruary 0; Revised 5 May 0; Accepted 7 June 0 Academic Editor: Athanasios Panagopoulos Copyright 0 C D Amours and A O Dahmane This is an open access article distriuted under the Creative Commons Attriution License, which permits unrestricted use, distriution, and reproduction in any medium, provided the original work is properly cited We analytically derive the upper ound for the it error rate BER performance of a single user multiple input multiple output code division multiple access MIMO-CDMA system employing parity-it-selected spreading in slowly varying, flat Rayleigh fading The analysis is done for spatially uncorrelated links The analysis presented demonstrates that parity-it-selected spreading provides an asymptotic gain of 0 logn t db over conventional MIMO-CDMA when the receiver has perfect channel estimates This analytical result concurs with previous works where the BER is determined y simulation methods and provides insight into why the different techniques provide improvement over conventional MIMO-CDMA systems Introduction The oject of much research in wireless communications is to enale users to transmit and receive at high and variale data rates to support the growing numer of applications that involve such transfer of data [] Code Division Multiple Access CDMA systems employ spread spectrum SS technology and were developed for second and third generation G, 3G wireless communications For example, IS-95 and Wideand CDMA WCDMA systems are ased on direct sequence SS techniques Multiple access interference MAI is present in CDMA systems due to the nonzero cross-correlation etween the different users spreading codes []The MAI that each user s signal creates in all other users signals results in increased it error rate BER The overall system capacity is determined y the numer of simultaneous transmitters that can e supported efore the BER increases to an unacceptale level [3] Much research presented in the literature has concentrated on making systems more power efficient as a means to increase the overallspectralefficiency of the CDMA system [4 6] Other techniques, such as multiuser detection, have also een considered to increase the capacity of CDMA systems [, 7, ] Recent research has shown that comining DS-CDMA systems with Multiple Input Multiple Output MIMO techniques can achieve high gains in capacity, reliaility and data transmission speed [9 4] This is achieved y exploiting the spatial diversity made possile y multiple antennas at the transmitter and the receiver, allowing more degrees of freedom when the complex channel gains etween different transmit and receive antenna pairs are sufficiently uncorrelated MIMO-CDMA systems are also more roust to multiple access interference MAI than their single input single output SISO DS-CDMA counterparts Currently, MIMO-CDMA is considered for many eyond 3G B3G applications [3, 4] In [5], the concept of parity-it-selected spreading for direct sequence spread spectrum DS-SS is introduced In [6], the parity-it-selected spreading technique is extended to code division multiple access CDMA systems using multiple input multiple output MIMO techniques Also in [6], the parity-it-selected spreading technique is modified to create the so-called permutation spreading technique The

Antennas and Propagation permutation spreading technique comines spreading and space time coding to produce the effect of transmit diversity without retransmitting data from different antennas Compared to a conventional MIMO-CDMA system, which assigns a unique spreading waveform from a set of mutually orthogonal waveforms to each antenna, the MIMO-CDMA system employing either parity-it-selected or permutation spreading provides significant power gains This is demonstrated in [6] through the use of Monte Carlo simulations The BER performance of the aforementioned spreading techniques for MIMO-CDMA is also determined for systems encountering multiple access interference MAI, spatial correlation, and/or channel estimation errors [7, ] What is lacking in [6 ] is an analysis of the BER performance of MIMO-CDMA systems, employing these techniques Such an analysis permits us to etter understand why the new spreading techniques provide improvements over conventional MIMO-CDMA systems and this can, in turn, permit us to improve upon the new spreading techniques In this paper, we provide, for the first time, an analytical expression for the upper ound of the BER for a MIMO- CDMA system employing parity-it-selected or permutation spreading MIMO-CDMA System A MIMO-CDMA system has N t transmit and receive antennas The serial data, whose it rate is R,isconverted into N t parallel data streams, each with it rate R /N t The ith data stream of user m is spread y spreading waveform w mi t, which is an antipodal signal with chip rate R c and is selected from a set of mutually orthogonal spreading waveforms C m ={c m t, c m t, c mn t} In other words, T, i = j, c mi tc mj tdt = T 0 0, i j, where T = N t /R is the signaling interval In this paper, we consider the use of short spreading waveforms A short spreading waveform is one whose duration is equal to one signaling interval Thus on the interval 0 t T, the ith spreading waveform from the set C m can e descried mathematically y L c mi t = c j mi p t jt c, j= where c j mi =± is the jth ipolar chip of the mth user s ith spreading waveform, T c = /R c is the chip interval, L is the numer of chips in the spreading waveform and is given y L = T/T c = R c N t /R,andpt is the rectangular chip pulse shape given y, 0 t T c, pt = 0, otherwise 3 Data in Serial-toparallel converter n n n N t w n mt w n mt w n mn t t transmit antennas α n α n N t α n α n α n α n N t α n α n N t α n receive antennas Figure : MIMO-CDMA transmitter and link gains Different users are assigned unique sets of spreading waveforms Therefore, C m C l = for m l The transmitter, receive antennas and link gains are shown in Figure On interval n T t nt signaling interval n, the data to e transmitted is m n = [m n, m n,, m n N t ], where m n k is either 0 or with equal proaility and they are independent of one another In this paper, we assume that inary phase shift keying BPSK modulation is used Therefore, we define n = m n = [ n, n,, n N t ], where n k for our aseand model is ± with equal proaility and E[ n k n g ] = 0, if k g, where E[ ] is the expectation operator Each independent identically distriuted iid it to e transmitted on the nth signaling interval is assigned to a different transmit antenna, therefore, n k is transmitted on transmit antenna kthemth user s data it, transmitted y transmit antenna k on the nth signaling interval, is multiplied y spreading waveform w n mk t The complex channel gain etween transmit antenna k and receive antenna j on the nth signaling interval is α n ij The receiver for MIMO-CDMA is shown in Figure Here, the signal received y each receive antenna is correlated with each spreading waveform, and the contriutions from the different antennas are comined according to the spreading technique used The kth matched filter output on receive antenna j and signaling interval n is u n jk The expressions for these decision variales and how they are comined depend on the spreading method used y the transmitter 3 Parity-Bit-Selected Spreading Parity-it-selected spreading for spread spectrum systems is introducedin[] The technique therein is modified slightly for MIMO-CDMA the vector m n is input to a parity-it generator The parity-it generator produces a vector p n = [p n, p n,, p n N ], where N is the numer of spreading codes used and is given y N = lengthp There are as many parity

Antennas and Propagation 3 receive antennas Filter matched to c t Filter matched to c t Filter matched to c N t Bank of matched filters Bank of matched filters u n u n u n N u n u n u n N u n u n u n N Cominer and decision device Figure : MIMO-CDMA receiver it patterns as there are spreading waveforms in each user s set Each spreading waveform is assigned to one of the parity it vectors Therefore, if p n = p x, then ˆ n ˆ n ˆ n N t w n mi t = c mx t nt for i =,,, N t 4 For the spreading strategy descried y 4, the decision variales of Figure are given y N t E u n jk = n i i= n n α n ij + n n jk, k = x, jk, k x, where E is the received energy per it Let u n = [u n, u n,, u n N, u n,, u n N,, u n N] which is a N vector The xth channel gain matrix, H n x is an N t N matrix, is defined as [ H n x = 0Nt,x h n 0 Nt,N h n 0 Nt,N, h n 3 h n ] 6 0 Nt,N x, where 0 a, is an a all zero matrix and h n i = [α n i, α n i,, α n N ti] T The channel matrix used on signaling interval n depends on the spreading waveform used during that interval For example, if the transmitter employs c m t nt, then H n is the appropriate channel gain matrix to use We can now express u n as u n = E n H n + n n, 7 5 Tale : The allocation of spreading waveforms in parity it selected spreading technique for N t = 4 Messages Spreading waveform Channel gain matrix m n used used in 7 and 0000 000 0 000 0 00 00 000 0 00 00 00 00 0 000 where H n n and n n c m t nt c m t nt c m3 t nt c m4 t nt c m5 t nt c m6 t nt c m7 t nt c m t nt H n H n H n 3 H n 4 H n 5 H n 6 H n 7 H n is the channel matrix associated with data vector = [n n, n n,, n n,, n n N] isa N noise vector The elements of n n are uncorrelated zero mean complex Gaussian random variales with variance σ n In [5], a suoptimum detection scheme is presented in which the detector determines which spreading code has een used and then detects the data only y oserving the outputs matched to that code and comparing them to the possile messages associated with that code In this paper, maximum likelihood ML detection is considered The receiver does not try to determine which code has een used It compares u n to all possile receive vectors E i H n i, where H i is the channel matrix associated with transmitted message i The receiver selects n as the message vector that minimizes the square of the Euclidean distance as shown in: n = min u n E i H n i, i B whereb is the set of all possile transmitted data vectors We consider the four transmit antenna case of [] Tale shows the allocation of spreading waveforms to message vectors as well as the corresponding channel gain matrix that is used in 7and From Tale, we see that the two message vectors m = 0000 and m = which correspond to = and = form a suset of all possile inary messagevectorsoflength4thissusetisspreadusing spreading waveform c m t nt The messages associated with other spreading waveforms are simply cosets of the suset {0000, } Therefore, we can state that each coset is assigned a unique spreading waveform As previously mentioned, ML detection is used in this paper Therefore, the squared Euclidean distance etween

4 Antennas and Propagation u n and each of the vectors in Tale is computed, and the message vector corresponding to the smallest squared distance is selected as the most likely transmitted message In terms of BER performance, this is equivalent to correlating u n to each of the vectors in Tale and selecting the one with the highest correlation value The correlation technique is in fact the least computationally complex method as manytermsinthevectorsintale are 0 However, if additional coding is used, the Euclidean distances are useful for calculating log likelihood ratios for the decoder 4BERPerformanceofMIMO-CDMAUsing Parity-Bit-Selected Spreading In CDMA systems, it error rate BER performance is a very important parameter Not only does BER determine the quality of transmission, ut also does it determine the amount of data that can e transmitted per unit of andwidth As every user contriutes to the interference levels at the receiver, the BER of each user increases as more users access the channel Thus, the maximum numer of users is determined y the amount of interference that can e tolerated We will determine the BER performance of MIMO- CDMA employing parity-it-selected spreading analytically using the following assumptions The MIMO-CDMA system under consideration uses four transmit antennas and eight spreading waveforms as in [] and as detailed in Tale The fading process is assumed to e frequency nonselective In other words, the multipath spread is zero and there is no channel induced intersymol interference ISI 3 The channel gains are independent slowly varying circularly-symmetric complex Gaussian random variales with zero mean and unit variance 4 The channel gains are known to the receiver, thus coherent detection is performed When determining the BER of communication systems operating in Rayleigh fading channel with diversity order L, typically we are required to integrate a Q-function multiplied y the proaility density function pdf of the energy per it to noise spectral density ratio E /N o The pdf of E /N o is a chi-square distriution with L degrees of freedom The result of this integral takes to form of pl, x [9] whichis shown in: pl, x = μ where μ = x/x + L L k=0 L +k +μ k, 9 k 4 Single Receive Antenna, = We start y assuming that there is only one receive antenna Thus, the received vector is [ u n = u n, u n,, u n ] N 0 Tale : The received vectors for the parity-it-selected spreading technique for N t = 4and = Messages m n Received vector u n 0 : 0000 [ E α n + α n 4, 0, 0, 0, 0, 0, 0, 0] 5 : [ E α n + α n 4, 0, 0, 0, 0, 0, 0, 0] : 000 [0, E α n + α n 3 α n 4, 0, 0, 0, 0, 0, 0] 4 : 0 [0, E α n + α n 3 α n 4, 0, 0, 0, 0, 0, 0] : 000 [0, 0, E α n + α n α n 4, 0, 0, 0, 0, 0] 3 : 0 [0, 0, E α n + α n α n 4, 0, 0, 0, 0, 0] 3 : 00 [0, 0, 0, E α n + α n α n 3 α n 4, 0, 0, 0, 0] : 00 [0, 0, 0, E α n + α n α n 3 α n 4, 0, 0, 0, 0] 4 : 000 [0, 0, 0, 0, E α n α n 4, 0, 0, 0] : 0 [0, 0, 0, 0, E α n α n 4, 0, 0, 0] 5 : 00 [0, 0, 0, 0, 0, E α n α n 3 α n 4, 0, 0] 0 : 00 [0, 0, 0, 0, 0, E α n α n 3 α n 4, 0, 0] 6 : 00 [0, 0, 0, 0, 0, 0, E α n α n α n 4, 0] 9 : 00 [0, 0, 0, 0, 0, 0, E α n α n α n 4, 0] 7 : 0 [0, 0, 0, 0, 0, 0, 0, E α n α n α n 3 α n 4 ] : 000 [0, 0, 0, 0, 0, 0, 0, E α n α n α n 3 α n 4 ] In the asence of noise, the set of all received vectors form an dimensional constellation The points of the constellation are given in Tale The variale E is the average energy per it For ML detection, the proaility of symol error, as well as the BER, can e determined y the Euclidean distance etween the constellation points Let us assume that the transmitted message is message 0 0000 The proaility that message 5 is detected, given that message 0 is transmitted, is a function of the distance etween their constellation points, d 5,0 This distance is given y d5,0 = u u 0000 α n = 4E + α n 4 We let X = α n + α n 4 and Z = X Because of assumption 3 aove, X is a zero mean complex Gaussian random variale with variance 4 Thus, Z has a chi-square proaility density function pdf with degrees of freedom [9] It has a mean of 4 Thus, the pdf of Z is given y f Z z = 4 e z/4, 0<z< The proaility of incorrectly detecting message 5 when message 0 is transmitted is P5 0 = erfc d 5,0 = 4N o erfc E Z, 3 N o where N o is the single-sided noise spectral density We see that P5 0 is a function of the random variale Z Thus, E[P5 0] = p 5 0 is found y multiplying P5 0 y

Antennas and Propagation 5 the pdf of Z and integrating from 0 to This is shown in [9]toe p 5 0 = 0 erfc E Z e z/4 dz N o = [ ] 4 4γ = p, 4γ, +4γ where γ = E /N o is the average energy per it to noise spectral density ratio Next we consider the proaility that message 000 is detected when message 0 is transmitted The distance d,0 is given y d,0 = u 000 u 0000 α n = E + α n 4 α n + E + α n 3 α n 4 5 It can e shown that A + B + A B = A + B, thus d,0 ecomes d,0 α n = E + α n 3 + α n 4 6 Let Y A = α n + α n 3 and Y B = α n 4 Also, let W A = Y A and W B = Y B Finally, let W = W A + W B Although W has the same mean as Z, it does not have the same higher order statistics, nor does it have the same pdf The pdfs of W A and W B are f WA w = 3 e w/3, f WB w = e w, 0<w<, 0<w< 7 Since the channel gains are iid, W A and W B are independent Thus the pdf of W = W A + W B is given y f W w = f WA w f WB w = e w/3 e w, 0<w<, where denotes convolution It can e seen that f W w is a weighted sum of chi-square distriutions with two degrees of freedom Therefore, the expected proaility of detecting message when message 0 is transmitted is [9] p 0 = 0 erfc E W f W wdw N o = 3 [ ] 3γ [ ] γ 9 4 +3γ 4 +γ = 3, p 3 γ p, γ We can show that distances etween messages, 4, 7,,, 3, and 4 and message 0 all have the same statistics as the distance etween message and message 0 Therefore p 0 = p 0 = p 4 0 = p 7 0 = p 0 = p 0 = p 3 0 = p 4 0 The distance etween message 3 and message 0 is given y d3,0 = u 00 u 0000 α n = E + α n 4 α n + E + α n α n 3 α n 4 α n = E + α n + α n 4 0 Here, we let V = V A + V B,whereV A = α n + α n and V B = α n 4 are independent chi-square distriuted random variales The pdfs of V A and V B are f VA v = f VB v = e v/, 0<v< The pdf of V is f V v = f VA v f VB v, which is f V v = 4 ve v/, 0<v<, which is a chi-square distriution with 4 degrees of freedom The expected proaility of detecting message 3 when message 0 is transmitted is [9] p 3 0 = 0 erfc γ V f V v dv = p, γ 3 It can e shown that the distance etween messages 5, 6, 9, 0, and and message 0 have the same statistics as the distance etween message 3 and message 0 Thus, p 3 0 = p 5 0 = p 6 0 = p 9 0 = p 0 0 = p 0 Using a union ound, we can estimate the proaility of detection error when message 0 is transmitted as 5 p i 0 i= PE 0 < <p, 4γ +p, 3 γ 4p, γ +6p, γ 4 We can show that the proaility of detection error is independent of which message was transmitted; therefore, PE 0 = PE Similarly, the proaility of it error is independent of the transmitted message; therefore, we can use the conditional expressions that we derived previously to determine an upper ound It is given y P <p, 4γ +4p, 3 γ p, γ +3p, γ 5

6 Antennas and Propagation 4 Multiple Receive Antennas, > In the single user case, the use of multiple receive antennas provides BER improvement through receive diversity The received vector is a vector As an example, u 0000 is [ ] u 0000 = u0000 u 0000 u 0000Nr, 6 where u 0000i = [ E / α n i + α n i + α n 3i + α n 4i, 0,,0] The proaility that message 5 is detected when message 0issentisgiveny p 5 0 = 0 erfc γ Z Nr f Z Nr zdz, 7 where Z Nr = Z + Z + + Z Nr Each of the Z i s has a pdf that is given y Assuming no spatial correlation, the Z i s are mutually independent; therefore f Z Nr z is the convolution of with itself times Thus, as shown in [9], f Nr Z zis f Z Nr z =!4 e z/4, 0<z<, Nr znr which is a chi-square distriution with degrees of freedom Therefore, from [9], we can show that p 5 0 is p 5 0 = p, 4γ 9 The proaility of detecting message 3 when message 0 is transmitted is given y p 3 0 = 0 erfc γ V Nr f V Nr vdv, 30 where V Nr = V + V + + V Nr,andeachV i has distriution f Vi v that is given y Therefore, f V Nr v is the convolution of with itself timeswecan show that f V Nr visgiveny f V Nr z = e v/, 0<v<,! Nr vnr 3 which is a chi-square distriution with 4 degrees of freedom Therefore, p 3 0 is p 3 0 = p, γ 3 Lastly, the proaility p 0 is given y p 0 = 0 erfc γ W Nr f N W Nr wdw, 33 r where W Nr = W + W + + W Nr Each W i has distriution f Wi w giveny To find the pdf of W Nr we must convolve with itself times Therefore: f W Nr w = 4 we w/3 + 4 we w 3 4 e w/3 + 3 4 e w, 0<w< 34 for = For = 3itisgiveny: f W Nr w = e w/3 e w 6 w + 7 6 35 9 6 w e w/3 + e w, 0<w< For = 4 the pdf is given y: f W Nr w = e w/3 + e w 96 w3 + 45 3 w e w/3 e w 3 6 w + 35 3, 0<w< 36 Using these pdfs and the results in [9], we can find p 0 For =, p 0 is given y: p 0 = 9 4 p, 3γ + 4 4 p, γ 9 4 4 p, 3γ 4 + 3 4 p, γ 37 4 For = 3, p 0 is given y: p 0 = 7 p 3, γ p 3, γ 6 9 6 p, γ + 6 6 p, γ 6 p, γ 7 6 p, γ 6 For = 4, p 0 is given y: p 0 = 6 p 4, 3γ + 6 p 4, γ p 3, 3γ + 3 p 3, γ + 405 3 p, 3γ + 405 3 p, 3γ + 45 3 p, γ 35 3 p, γ 3 39 As is the case for =, the proaility of it error is given y: P <p 5 0 +4p 0 +3p 3 0 40 43 BER Performance of MIMO-CDMA Using Parity-Bit- Selected Spreading The upper ounds on the BER performance of MIMO-CDMA employing parity-it-selected spreading that were derived in the previous susections are shown in Figure 3 We have also simulated the BER performance using the same assumptions that were made in the derivation of the equations We see from Figure 3 that the upper ound is tight as E /N o increases as we would expect This is due to the proaility of the intersection of events the distance etween the received vector and desired vector is greater than two or more incorrect vectors tends towards zero as E /N o increases

Antennas and Propagation 7 BER E+00 E 0 E 0 E 03 E 04 E 05 0 4 6 0 4 6 0 E /N o db = ound = simulated = ound = simulated = 3 ound = 3 simulated = 4 ound = 4 simulated Figure 3: Comparison of BER upper ound to simulated performance of MIMO-CDMA employing parity-it-selected spreading for N t = 4and =,, 3, and 4 We also noticed that as E /N o increases, P of 5 and 40 tends towards p 5 0 of 4 and9, respectively This means that as E /N o increases, the message eing inverted is the most likely detection error In other words, the most likely error is to detect the other message from the same coset Let us consider the coset {0000, } Ifwewereto place in a different coset, for =, the distance squared d5,0 would decrease to E α +α +α 3 +α 4,thus increasing the proaility of this error If we were to include other messages in this coset, for example, 00, then the distance squared etween 0000 and 00 would e 4E α 3 + α 4 whichislessthand5,0, making it the dominant error Thus, the pairing of a message with its one s complement is the optimum coset pairing with respect to the BER for this scheme It can e shown that the BER of a conventional singleuser MIMO-CDMA system operating in frequency nonselective Rayleigh fading has a proaility of it error given y: P = p, E N o, 4 when the fading on the different links is independent and the receiver has perfect knowledge of the channel gains The conventional system assigns each antenna a unique spreading waveform, and the set of Nt waveforms are mutually orthogonal From the aove discussion, we know that as E /N o tends towards infinity, the proaility of it error for a single-user MIMO-CDMA system using the parity-it-selected spreading technique has a it error rate of P = p, N t E N o 4 Therefore, the MIMO-CDMA system employing the parityit-selected spreading technique provides an asymptotic gain of 0 logn t over the conventional MIMO-CDMA system under the conditions discussed in this paper As E /N o increases, the actual gain approaches ut is less than 0 logn t This gain can e traded off against additional users accessing the common channel 5 Conclusion In this paper, we derived an analytical expression for the BER of a single user MIMO-CDMA system employing the parityit-selected spreading technique in frequency nonselective Rayleigh fading under the assumptions of independently fading links and known channel gains The results otained from the analytical expression were compared against the simulated BER performance of the same system The comparison shows that the derived upper ound is very tight to the simulated performance for moderate to high levels of signal to noise ratio The expression also allows us to determine that for MIMO-CDMA employing parityit-selected spreading, the most likely error results in an inversion of the message This then further allowed us to determine that parity-it-selected spreading provides an asymptotic gain of 0 logn t compared to conventional MIMO-CDMA This gain can e traded off against additional users, thus increasing the spectralefficiency of MIMO- CDMA systems at an expense of increased transmitter and receiver complexity References [] I Koutsopoulos, U C Kozat, and L Tassiulas, Dynamic resource allocation in CDMA systems with deterministic codes and multirate provisioning, IEEE Transactions on Moile Computing, vol 5, no, pp 70 79, 006 [] S Verd, Multiuser Detection, Camridge University Press, Camridge, UK, 99 [3] A J Viteri, When not to spread spectrum a sequel, IEEE Communications Magazine, vol 3, no 4, pp 7, 95 [4] D Haccoun, S Lefrancois, and E Mehn, An Analysis of the CDMA capacity using a comination of low rate convolutional codes and PN sequence, in Proceedings of the Canadian Conference on Electrical and Computer Engineering CCECE 96, vol, pp 3 35, Calgary, Canada, May 996 [5] Y F M Wong and K B Letaief, Concatenated coding for DS/CDMA transmission in wireless communications, IEEE Transactions on Communications, vol 4, no, pp 965 969, 000 [6] R D Cideciyan, Concatenated reed-solomon/convolutional coding for data transmission in CDMA-ased cellular systems, IEEE Transactions on Communications, vol 45, no 0, pp 9 303, 997 [7] Z Guo and K B Letaief, Performance of multiuser detection in multirate DS-CDMA systems, IEEE Transactions on Communications, vol 5, no, pp 979 93, 003 [] A Duel-Hallen, J Holtzman, and Z Zvonar, Multiuser detection for CDMA systems, IEEE Personal Communications, vol, no, pp 46 5, 995 [9] K Deng, Q Yin, L Ding, and Z Zhao, Blind channel estimator for V-BLAST coded DS-CDMA system in frequencyselective fading environment, in Proceedings of the 5th IEEE

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