adaptive randomized dstc

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Adaptive Randomized Distributed Space-TimeCoding for Cooperative MIMO Relaying Systems

Tong Peng, Rodrigo C. de LamareCommunications Reasearch Group, Department of Electronics

University of York, York YO10 5DD, UKEmail: [email protected]; [email protected]

Anke Schmeink UMIC Research Centre

RWTH Aachen University, D-52056 Aachen, GermanyEmail: [email protected]

Abstract —An adaptive randomized matrix optimization algo-rithm for cooperative MIMO networks with linear minimummean square error (MMSE) receivers which employ an amplify-and-forward (AF) strategy and space-time coding schemes atthe relay nodes is proposed. The randomized matrix multipliesthe space-time coded matrix at the relay node and can beregarded as a part of the space-time coding scheme. We derivethe upper bound of the error probability of a cooperative MIMOsystem employing the randomized space-time coding schemerst, and then, present an optimization algorithm based on theMMSE criterion. A stochastic gradient algorithm is derived

in the calculation of the adaptive optimization in order torelease the receiver from the massive calculation complexity. Thesimulation results indicate that the proposed algorithm obtainsgains compared to the existing schemes.

I. INTRODUCTION

Multiple-input and multiple-output (MIMO) communicationsystems employ multiple collocated antennas at both thesource node and the destination node in order to obtain thediversity gain and combat multi-path fading in wireless links.The different methods of space-time coding (STC) schemes,which can provide a higher diversity gain and coding gaincompared to an uncoded system, are also utilized in MIMOwireless systems for different numbers of antennas at thetransmitter and different conditions of the channel. Coop-

erative MIMO systems, which employ multiple relay nodeswith antennas between the source node and the destinationnode as a distributed antenna array, apply distributed diversitygain and provide copies of the transmitted signals to improvethe reliability of wireless communication systems [1]. Amongthe links between the relay nodes and the destination node,cooperation strategies, such as Amplify-and-Forward (AF),Decode-and-Forward (DF), and Compress-and-Forward (CF)[2] and various distributed STC (DSTC) schemes in [5], [6]and [19] can be employed.

The utilization of a distributed STC (DSTC) at the relaynode in a cooperative network, providing more copies of thedesired symbols at the destination node, can offer the systemdiversity gains and coding gains to combat the interference.The recent focus on the DSTC technique lies in the delay-toleration code design and the full-diversity schemes designwith the minimum outage probability. In [7], the distributeddelay-tolerant version of the Golden code [8] is proposed,which can provide full-diversity gain with a full codingrate. An opportunistic DSTC scheme with the minimumoutage probability is designed for a DF cooperative network and compared with the xed DSTC schemes in [9]. Anadaptive distributed-Alamouti (D-Alamouti) STBC design isproposed in [10] for the non-regenerative dual-hop wirelesssystem which achieves the minimum outage probability. DSTCschemes for the AF protocol are discussed in [11]-[12]. In [11],

the GABBA STC scheme is extended to a distributed MIMOnetwork with full-diversity and full-rate, while an optimalalgorithm for design of the DSTC scheme based on achievingthe optimal diversity and multiplexing tradeoff is derived in[12].

The performance of cooperative networks using differentstrategies has been widely discussed in the literature. In [13],an exact pairwise error probability of the D-Alamouti STBCscheme is derived according to the position of the relay node.In [14], a bit error rate (BER) analysis of the distributed-Alamouti STBC scheme is proposed. The difference betweenthese two works lies in the different cooperative schemes theyconsider. A maximum likelihood (ML) detection algorithmfor a MIMO relay system with DF protocol is derived in[15] with its performance analysis as well. The symbol errorrate and diversity order upper bound for the scalar xed-gainAF cooperative protocol are given in [16]. The utilization of single-antenna relay nodes and the DF cooperative protocolconstitute the main differences between their works and ours.The most similar works compared with our work are [17] and[18]. However, an STC encoding process is implemented at thesource node in [17], which decrease the output of the systemand increase the calculation complexity at the destination nodeto decode. In [18], the BER upper bound is given without the

STC scheme utilization at the relay node.In this paper, we propose an adaptive randomized distributedspace-time coding scheme and algorithms for cooperativeMIMO relaying systems. The upper bound pairwise errorprobability of the randomized-STC schemes (RSTC) in acooperative MIMO system which employs multi-antenna relaynodes with the AF protocol is analyzed. We focus on howthe randomized matrix affects the DSTC during the encodingand how to optimize the parameters in the matrix, and it isshown that the utilization of a randomized matrix benetsthe performance of the system by lowering the upper boundcompared to using traditional STC schemes. Then an adaptiveoptimization algorithm is derived based on the MSE criterion,with the utilization of the Stochastic Gradient (SG) algorithmin order to release the destination node from the high com-puting complexity of the optimization process. The updatedrandomized matrix is transmitted to the relay node through afeedback channel that is assumed in this work error free anddelay free.

The paper is organized as follows. Section II introducesa two-hop cooperative MIMO system with multiple relaysapplying the AF strategy and the randomized DSTC scheme.In Section III the proposed optimization algorithm for therandomized matrix is derived, and the analysis of the upperbound of pairwise error probability using the randomized D-STC is shown in Section IV. Section V focus on the results



N

F SR 1

F SR n r

Destination

NodeNode

RelayNode

NN 1st

Relay

Node

N

N

n r thN

G R 1 D

G R n rD

H SDSource

Fig. 1. Cooperative MIMO System Model with n r Relay nodes

of the simulations and Section VI leads to the conclusion.

I I . C OOPERATIVE S YSTEM M ODEL

The communication system under consideration, shownin Fig.1, is a cooperative communication system employingmulti-antenna relay nodes transmitting through a MIMO chan-nel from the source node to the destination node. The 4-QAMmodulation scheme is used in our system to generate the

transmitted symbol vector s

[i] at the source node. There aren r relay nodes with N antennas for transmitting and receiving,applying an AF cooperative strategy as well as a DSTCscheme, between the source node and the destination node. Atwo-hop communication system that broadcasts symbols fromthe source to n r relay nodes as well as to the destination nodein the rst phase, followed by transmitting the amplied andre-encoded symbols from each relay node to the destinationnode in the next phase. We consider only one user at the sourcenode in our system that has N Spatial Multiplexing (SM)-organized data symbols contained in each packet. The receivedsymbols at the k −th relay node and the destination node aredenoted as r SR k and r SD , respectively, where k = 1 , 2,...,n r .The received symbols r SR k will be amplied before mappedinto an STC matrix. We assume that the synchronization ateach node is perfect. The received symbols at the destinationnode and each relay node can be described as follows

r SR k [i] = F k [i]s [i] + n SR k [i], (1)

r SD [i] = H [i]s [i] + n SD [i], (2)

i = 1 , 2, ... ,N , k = 1 , 2, ... n r ,

where the N ×1 vector n SR k [i] and n SD [i] denote the zeromean complex circular symmetric additive white Gaussiannoise (AWGN) vector generated at each relay and the destina-tion node with variance σ2 . The transmitted symbol vector s [i]contains N parameters, s [i] = [s 1[i], s 2[i],...,s N [i]], whichhas a covariance matrix E s [i]s H [i] = σ2

s I , where E [·]stands for expected value, (

·)H denotes the Hermitian operator,

σ 2s is the signal power which we assume to be equal to 1 andI is the identity matrix. F k [i] and H [i] are the N ×N channelgain matrices between the source node and the k −th relaynode, and between the source node and the destination node,respectively.

After processing and amplifying the received vector r SR k [i]at the k − th relay node, the signal vector s̃ SR k [i] =A R k D [i](F k [i]s [i] + n SR k [i]) can be obtained and will beforwarded to the destination node. The amplied symbols ins̃ SR k [i] will be re-encoded by a N ×T DSTC scheme M ( s̃ [i])and then multiplied an N × N randomized matrix R [i] in

[22], then forwarded to the destination node. The relationshipbetween the k − th relay and the destination node can bedescribed as

R R k D [i] = G k [i]R [i]M R k D [i] + N R k D [i], (3)

k = 1 , 2,...,n r ,

where the N × T matrix M R k D [i] is the DSTC matrix

employed at the relay nodes whose elements are the ampliedsymbols in s̃ SR k [i]. The N × T received symbol matrixR R k D [i] in (3) can be written as an NT ×1 vector r R k D [i]given by

r R k D [i] = R eq k [i]G eq k [i]s̃ SR k [i] + n R k D [i], (4)

where the block diagonal NT ×NT matrix R eq k [i] denotesthe equivalent randomized matrix and the NT × N matrixG eq k [i] stands for the equivalent channel matrix which is theDSTC scheme M ( s̃ [i]) combined with the channel matrixG R k D [i]. The NT ×1 equivalent noise vector n R k D [i] gen-erated at the destination node contains the noise parametersin N R k D [i]. After rewriting R R k D [i] we can consider thereceived symbol vector at the destination node as a N (n r +1)vector with 2 parts, one is from the source node and anotherone is the superposition of the received vectors from each relaynode, therefore the received symbol vector for the cooperativeMIMO network we considered can be written as

r [i] = H [i]s [i]

∑n r

k =1 R eq k [i]G eq k [i]s̃ SR k [i] + n SD [i]n RD [i]

= D D [i]s̃ D [i] + n D [i],(5)

where the (T +1) N ×(n r +1) N block diagonal matrix D D [i]denotes the channel gain matrix of all the links in the network which contains the N ×N channel coefcients matrix H [i]between the source node and the destination node, the N T ×N equivalent channel matrix G eq k [i] for k = 1 , 2,...,n r betweeneach relay node and the destination node. The (n r + 1) N

×1

noise vector n D [i] contains the received noise vector at thedestination node and the amplied noise vectors from eachrelay node, which can be derived as an AWGN with zero meanand covariance matrix σ2(1+ ∥

R eq k [i]G eq k [i]A R k D [i]∥2F )I ,

where ∥X ∥F = √ Tr( X H ·X ) = √ Tr( X ·X H ) stands for

the Frobenius norm.

III . A DAPTIVE R ANDOMIZED STC O PTIMIZATIONA LGORITHM

As derived in the previous section, the DSTC schemeused at the relay node will be multiplied by a randomizedmatrix before being forwarded to the destination node. In thissection, we design an adaptive optimization algorithm basedon the stochastic gradient (SG) estimation algorithm [20] fordetermining the optimal randomized matrix.

A. Optimization Method Based on the MSE CriterionFrom (5) we propose the MSE based optimization at the

destination node as

[W [i], R eq [i]] = arg minW [i ],R eq [i ]

E ∥s [i]−W H [i]r [i]∥

2 ,

where r [i] is the received symbol vector at the destination nodewhich contains the randomized matrix to be optimized. If weonly consider the received symbols from the relay node, the



received symbol vector at the destination node can be derivedas

r [i] = D D [i]s̃ D [i] + n D [i]= R eq [i]G eq [i]A [i]F [i]s [i] + R eq [i]G eq [i]A [i]n SR [i]

+ n RD [i]= R eq [i]C [i]s [i] + n D [i],

(6)

where C

[i] is an NT × N matrix that contains all thecomplex channel gains and the amplied matrix assignedto the received vectors at the relay node, and the noisevector n D is a Gaussian noise with zero mean and varianceσ 2(1+ ∥

R eq [i]G eq [i]A [i]∥2F ). Therefore, we can rewrite the

MSE cost function as[W [i], R eq [i]] =

arg minW [i ], R eq [i ]

E ∥s [i]−W H [i](R eq [i]C [i]s [i] + n D [i])∥

2 .

(7)By expanding the righthand side of (7) and taking the

gradient with respect to W ∗ [i] and equaling the terms to zero,we can obtain the MMSE lter vector equalling

W [i] =

E r[i]r H

[i]

− 1E r

[i]s H

[i]

, (8)

where the rst term denotes the inverse of the auto-correlationmatrix and the second one is the cross-correlation matrix.Dene r̃ = C [i]s [i] + C [i]n SR , then the randomized matrixcan be calculated by taking the gradient with respect to R ∗ [i]and equating the term to zero, resulting in

R [i] = W H [i](E r̃ [i]r̃ H [i] )W [i]− 1

E s [i]r̃ H [i] W [i],(9)

where E r̃ [i]r̃ H [i] is the auto-correlation of the space-time coded received symbol vector at the relay node,and E s [i]r̃ H [i] is the cross-correlation. The optimizationmethod requires an inversion calculation with a high compu-tational complexity.

B. Adaptive Randomized Matrix Optimization AlgorithmIn order to reduce the computational complexity and achieve

the optimal performance, an adaptive randomized matrix opti-mization (ARMO) algorithm based on an estimation algorithmis designed. The MMSE problem is derived in (7), and theMMSE lter matrix can be calculated by (8) rst during theoptimization process. The simple ARMO algorithm can beachieved by taking the instantaneous gradient term of (7) withrespect to the randomized matrix R eq

∗ [i], which is

∇LR eq∗ [i ]

= ∇E ∥s [i]−W H [i](R eq [i]C [i]s [i] + n D [i])∥

2R eq

∗ [i ]

= −(s [i]−W H

[i]r [i])sH

[i]C H

[i]W [i]= −e [i]s H [i]C H [i]W [i],

(10)where e [i] stands for the detected error vector. After we obtain(10) the ARMO algorithm can be obtained by introducing astep size into a gradient optimization algorithm to update theresult until the convergence is reached, and it is given by

R [i + 1] = R [i] + µ(e [i]s H [i]C H [i]W [i]), (11)

where µ stands for the estimation step size. The complexity of calculating the randomized matrix is O(2N ), which is much

less than that of the calculation method derived in (9). Asmentioned in Section I, the randomized matrix will be sentback to the relay nodes via a feedback channel which isassumed to be error-free in the simulation, however in thepractical circumstances, the errors caused by the broadcastingand the diversication of the feedback channel with timechanges will affect the accuracy of the received randomizedmatrix at the relay node.

IV. P ROBABILITY OF E RROR A NALYSIS

In this section, the upper bound of the pairwise errorprobability of the system employing the randomized DSTCwill be derived. As we mentioned in the rst section, therandomized matrix will be considered in the derivation andit affects the performance by reducing the upper bound of the pairwise error probability. For the sake of simplicity, weconsider a 2 by 2 MIMO system with 1 relay node, and thedirect link is ignored in order to prominent the effect of therandomized matrix. The expression of the upper bound is alsostable for the increase of the system size and the number of relay nodes.

Consider an N × N STC scheme we use at the relaynode with L codewords. The codeword C 1 is transmitted

and decoded to another codeword C i

at the destination node,where i = 1 , 2,...,L . According to [23], the probability of error can be upper bounded by the sum of all the probabilitiesof incorrect decoding, which is given by

P e ≤L

i =2

P( C 1 →C i ). (12)

Assuming the codeword C 2 is decoded at the destinationnode and we know the channel information perfectly at thedestination node, we can derive the pairwise error probabilityas

P( C 1 →C 2 | R )

= P( ∥R

1

−G R C 1

∥

2F − ∥R

1

−G R C 2

∥

2F > 0 | R eq )

= P( ∥r 1 −R eq G eq F s 1

∥2F

− ∥r 1 −R eq G eq F s 2∥

2F > 0 | R eq ),

(13)where F and G eq stand for the channel coefcient matrixbetween the source node and the relay node, and betweenthe relay node and the destination node, respectively. Therandomized matrix is denoted by R eq . Dene H = G eq F ,which stands for the total channel coefcients matrix. Afterthe calculation, we can transfer the pairwise error probabilityexpression in (13) to

P( C 1 →C 2 | R eq ) = P( ∥R eq H (s 1 −s 2) ∥

2F < Y ), (14)

where Y = Tr(

n 1HR

eqH

(s 1

−s 2

)+(R

eqH

(s 1

−s 2

))H n 1

),

and n 1 denotes the noise vector at the destination node withzero mean and covariance matrix σ2(1+ ∥ R eq G eq ∥2F )I .By making use of the Q function, we can derive the errorprobability function as

P( C 1 →C 2 | R eq ) = Q γ 2 ∥R eq H (s 1 −s 2) ∥F ,

(15)where

Q = 1√ 2π ∫

∞

xexp −

u 2

2du, (16)



and γ is the received SNR at the destination node assumingthe transmit power is equal to 1.

In order to obtain the upper bound of P( C 1 →C 2 | R eq )we expand the formula

∥R eq H (s 1−s 2) ∥

2F . Let U H Λ s U be

the eigenvalue decomposition of (s 1 −s 2)H (s 1 −s 2), whereU is a Hermitian matrix and Λ s contains all the eigenvaluesof the difference between two different codewords s 1 ands 2 . Let V H Λ R V stand for the eigenvalue decomposition of

(R eq HU )H

R eq HU , where V is a random Hermitian matrixand Λ R is the ordered diagonal eigenvalue matrix. Therefore,the probability of error can be written as

P( C 1 →C 2 | R eq ) = Q γ 2

NT

m =1

N

n =1

λ R m λ s n |ξ n,m |2 ,

(17)where ξ n,m is the (n, m ) −th element in V , and λR m andλ s n are eigenvalues in Λ R and Λ s , respectively. Accordingto [23], a good upper bound assumption of the Q function isgiven by

Q(x ) ≤ 12

e− x 2

2 . (18)

Thus, we can derive the upper bound of pairwise error prob-ability for a randomized STC scheme as

P( C 1 →C 2 | R eq ) ≤ 12

exp −γ 4

NT

m =1

N

n =1

λ R m λ s n |ξ n,m |2 ,

(19)while the upper bound of the error probability expression fora traditional STC is given by

P( C 1 →C 2 | H eq ) ≤ 12

exp −γ 4

NT

m =1

N

n =1

λ s n |ξ n,m |2 .

(20)With comparison of (19) and (20), it is obvious to note thatthe eigenvalue of the randomized matrix is the difference,

which suggests that employing a randomized matrix for a STCscheme at the relay node can provide an improvement in BERperformance.

V. S IMULATIONS

The simulation results are provided in this section to assessthe proposed scheme and algorithm. The system we consideredis an AF cooperative MIMO system with the Alamouti STBCscheme [23] using QPSK modulation in quasi-static block fading channel with AWGN, as derived in Section II. Thebit error ratio (BER) performance of the ARMO algorithm isassessed. The simulation system with 1 relay node and eachtransmitting and receiving node employs 2 antennas. In thesimulation we dene both the symbol power at the sourcenode and the noise variance σ 2 for each link to be equal to 1.

The upper bound of the D-Alamouti and the randomizedD-Alamouti we derived in the pervious section are shown inFig. 2. The theoretical pairwise error probabilities provide thelargest decoding errors of the two different coding schemesand as shown in the gure, by employing a randomized matrixat the relay node decreases the decoding error upper bound.The comparison of the simulation results in BER performanceof the R-Alamouti and the D-Alamouti indicates the advantageof using the randomized matrix.

The proposed ARMO algorithm is compared with theSM scheme and the traditional RSTC algorithm using the

Fig. 2. BER performance v.s. E b /N 0 for the upper bound of the R-Alamoutischeme without the Direct Link

Fig. 3. BER performance v.s. E b /N 0 for ARMO Algorithm with and withoutthe Direct Link

distributed-Alamouti (D-Alamouti) STBC scheme in [19] withn r = 1 relay nodes in Fig. 3. The number of antennasN = 2 at each node and the effect of the direct link isconsidered. The results illustrate that without the direct link,by making use of the STC or the RSTC technique, a signi-cant performance improvement can be achieved compared tothe spatial multiplexing system, and the RSTC algorithm isoutperforms the STC-AF system, while the ARMO algorithmcan improve the performance by about 3dB as compared tothe RSTC algorithm. With the consideration of the direct link,the results indicate that the cooperative diversity order canbe increased, and using the ARMO algorithm achieves theoptimal performance with 2dB gains compared to employingthe RSTC algorithm and 3dB gains compared to employingthe traditional STC-AF algorithm.

The simulation results shown in Fig. 4 illustrate the con-vergence property of the ARMO algorithm. The SM, D-



Fig. 4. BER performance v.s. Number of Samples for ARMO Algorithmwithout the Direct Link

Alamouti and the randomized D-Alamouti algorithms obtainnearly at performance in BER as the utilization of xedSTC scheme and the randomized matrix. The SM schemehas the worst performance due to the lack of coding gains,while the D-Alamouti scheme can provide a signicant perfor-mance improvement in terms of the BER improvement, andby employing the randomized matrix at the relay node theBER performance can decrease further when the transmissioncircumstances are the same as that of the D-Alamouti. TheARMO algorithm shows its advantage in a fast convergenceand a lower BER achievement. At the beginning of theoptimization process with a small number of samples, theARMO algorithm achieves the BER level of the D-Alamoutione, but with the increase of the received symbols, the ARMOalgorithm achieves a better BER performance.

VI . C ONCLUSION

We have proposed an adaptive randomized matrix optimiza-tion (ARMO) algorithm for the randomized DSTC using alinear MMSE receive lter at the destination node. The pair-wise error probability of introducing the randomized DSTCin a cooperative MIMO network with the AF protocol isderived. The simulation results illustrate the advantage of theproposed ARMO algorithm by comparing it with the coopera-tive network employing the traditional DSTC scheme and thexed randomized STC scheme. The proposed algorithm can beutilized with different distributed STC schemes using the AFstrategy, extended to DF cooperation protocols and non-lineardetectors.

REFERENCES

[1] A. Scaglione, D. L. Goeckel, and J. N. Laneman, ”CooperativeCommunications in Mobile Ad Hoc Networks”, IEEE Signal Process.Magazine, pp. 1829, September 2006.

[2] J. N. Laneman and G. W. Wornell, ”Cooperative Diversity in WirelessNetworks: Efcient Protocols and Outage Behaviour”, IEEE Trans. Inf.Theory , vol. 50, no. 12, pp. 3062-3080, Dec. 2004.

[3] P. Clarke, R. C. de Lamare, ”Joint Transmit Diversity Optimization andRelay Selection for Multi-Relay Cooperative MIMO Systems UsingDiscrete Stochastic Algorithms”,IEEE Communications Letters, vol.15, no. 10, 2011 , pp. 1035 - 1037.

[4] P. Clarke, R. C. de Lamare, ”Transmit Diversity and Relay SelectionAlgorithms for Multirelay Cooperative MIMO Systems”, IEEE Trans.on Vehicular Technology , vol. 61 , no. 3, 2012, pp. 1084 - 1098.

[5] J. N. Laneman and G. W. Wornell, ”Distributed Space-Time-CodedProtocols for Exploiting Cooperative Diversity in Wireless Networks”, IEEE Trans. Inf. Theory , vol. 49, no. 10, pp. 2415-2425, Oct. 2003.

[6] S. Yiu, R. Schober, L. Lampe, ”Distributed Space-Time Block Coding”, IEEE Trans. on Wireless Commun. , vol. 54, no. 7, pp. 1195-1206, Jul.2006

[7] M. Sarkiss, G.R.-B. Othman, M.O. Damen, J.-C. Belore, ”Construc-tion of New Delay-Tolerant Space-Time Codes”, IEEE Transactions on

Information Theory, vol. 57, Issue: 6, pp. 3567 - 3581, June 2011.[8] J.-C. Belore, G. Rekaya, E. Viterbo, ”The Golden Code: A 22Full-Rate Space-Time Code with Nonvanishing Determinants”, IEEETransactions on Information Theory, vol. 51 , Issue: 4, April 2005.

[9] Yulong Zou, Yu-Dong Yao, Baoyu Zheng, ”Opportunistic DistributedSpace-Time Coding for Decode-and-Forward Cooperation Systems”,IEEE Transactions on Signal Processing, vol. 60, pp. 1766 - 1781,April 2012.

[10] J. Abouei, H. Bagheri, A. Khandani, ”An Efcient Adaptive DistributedSpace-Time Coding Scheme for Cooperative Relaying”, IEEE Trans.on Wireless Commun. , vol. 8, Issue: 10, pp. 4957-4962, October 2009.

[11] B. Maham, A. Hjorungnes, G. Abreu, ”Distributed GABBA Space-Time Codes in Amplify-and-Forward Relay Networks”, IEEE Trans.on Wireless Commun., vol.8, Issuse: 4, pp. 2036 - 2045, April 2009.

[12] Sheng Yang, J.-C. Belore, ”Optimal Space-Time Codes for the MIMOAmplify-and-Forward Cooperative Channel”, IEEE Transactions onInformation Theory, vol. 53, Issue: 2, pp. 647-663, Feb. 2007.

[13] T.Q. Duong, Ngoc-Tien Nguyen, Viet-Kinh Nguyen, ”Exact PairwiseError Probability of Distributed Space-Time Coding in Wireless RelaysNetworks”, International Symposium on Communications and Informa-tion Technologies 2007, pp. 279 - 283, 17-19 Oct. 2007.

[14] Minchul Ju, Hyoung-Kyu Song, Il-Min Kim, ”Exact BER Analysisof Distributed Alamouti’s Code for Cooperative Diversity Networks”,IEEE Trans. on Commun., vol. 57, Issue: 8, pp. 2380 - 2390, Aug.2009.

[15] G.V.V. Sharma, V. Ganwani, U.B. Desai, S.N. Merchant, ”PerformanceAnalysis of Maximum Likelihood Detection for Decode and ForwardMIMO Relay Channels in Rayleigh Fading”, IEEE Trans. on WirelessCommun., vol. 9, Issue: 9, pp. 2880 - 2889, September 2010.

[16] Youngpil Song, Hyundong Shin, Een-Kee Hong, ”MIMO CooperativeDiversity with Scalar-Gain Amplify-and-Forward Relaying”, IEEETransactions on Communications, vol. 57, Issue: 7, pp. 1932 - 1938,July 2009.

[17] Liang Yang, Q.T. Zhang, ”Performance Analysis of MIMO RelayWireless Networks With Orthogonal STBC”, IEEE Transactions onVehicular Technology, vol. 59, Issue: 7, pp. 3668 - 3674, Sept. 2010.

[18] T. Unger,A. Klein, ”On the Performance of Distributed Space-TimeBlock Codes in Cooperative Relay Networks”, IEEE CommunicationsLetters, vol. 11, Issue: 5, pp. 411 - 413, May 2007.

[19] R.C. de Lamare, R. Sampaio-Neto, ”Blind Adaptive MIMO Receiversfor Space-Time Block-Coded DS-CDMA Systems in Multipath Chan-nels Using the Constant Modulus Criterion”, IEEE Trans. on Commun.,vol. 58, no. 1, Jan. 2010

[20] S. Haykin, ”Adaptive Filter Theory”, 4 th ed. Englewood Cliffs, NJ:Prentice- Hall, 2002.

[21] R. C. de Lamare and R. Sampaio-Neto, “Adaptive Reduced-Rank Processing Based on Joint and Iterative Interpolation, Decimation andFiltering”, IEEE Transactions on Signal Processing , vol. 57, no. 7, July2009, pp. 2503 - 2514.

[22] B. Sirkeci-Mergen, A. Scaglione, ”Randomized Space-Time Codingfor Distributed Cooperative Communication”, IEEE Transactions onSignal Processing, vol. 55, no. 10, Oct. 2007.

[23] H. Jafarkhani, ”Space-Time Coding Theory and Practice”, CambridgeUniversity Press, 2005.

[24] R.C. de Lamare, R. Sampaio-Neto, “Minimum Mean-Squared ErrorIterative Successive Parallel Arbitrated Decision Feedback Detectorsfor DS-CDMA Systems”, IEEE Transactions on Communications, vol.56, no. 5, May 2008, pp. 778 - 789.

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