Source Transmit Antenna Selection for MIMO Decode-and-Forward Relay Networks

Transcription

1 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 7, APRIL 1, Source Transmit Antenna Selection for MIMO Decode--Forward Relay Networks Xianglan Jin, Jong-Seon No, Dong-Joon Shin Abstract Transmit antenna selection (TAS) is usually applied to multiple-input multiple-output (MIMO) systems because it does not require additional radio frequency (RF) chains which are quite expensive. In MIMO decode--forward (DF) relay networks, both source-destination source-relay-destination paths should be simultaneously considered to find an effective source TAS (STAS). In this paper, a new STAS is proposed based on both channel state information transmission scheme for the MIMO DF relay networks. It is also shown that the proposed STAS which selects antennas among transmit antennas at the source can achieve full diversity regardless of the value of. Simulation results show that the proposed STAS has better average bit error probability (BEP) performance than other STASs. Also, the proposed STAS with has lower cost, complexity, overhead, BEP than the STAS with using full-rate full-diversity space-time block codes with the same total transmit power. Index Terms Decode--forward (DF), diversity, multiple-input multiple-output (MIMO), relay network, transmit antenna selection (TAS). I. INTRODUCTION When multiple antennas are used at the source, transmit diversity can be achieved by using space-time block codes (STBCs). However, STBCs require multiple antennas associated with radio frequency (RF) chains which are costly in terms of size, power, hardware [1]. To solve this problem, low-cost low-complexity antenna selection schemes have been studied [1] [5], transmit antenna selections (TASs) with STBCs have also been considered [6] [8]. Unlike point-to-point MIMO systems, cooperative relay systems utilize two independent source-destination (SD) source-relay-destination (SRD) paths. To select good transmit antennas at the source, we have to consider both the SD SRD paths simultaneously. For amplify--forward (AF) relay networks, the optimal suboptimal TASs at the source were investigated basedonmaximizingsignal-tonoise ratio (SNR) at the destination [9], [10]. Unfortunately, contrary to the AF relaying case, the exact SNR for the decode--forward (DF) relaying is very difficult to derive. For the DF relay networks, a joint relay--antenna selection scheme which selects the best relay the best antenna at both source the selected relay was studied without considering the SD link in [11]. In [12], a suboptimal TAS of selecting two antennas at the source was proposed such that one maximizes the Manuscript received October 31, 2011; revised June 14, 2012 October 13, 2012; accepted December 31, Date of publication January 18, 2013; date of current version March 08, The associate editor coordinating the review of this manuscript approving it for publication was Dr. Josep Vidal. This work was partly supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science Technology( ) the Korea Communications Commission (KCC), Korea, under the R&D program supervised by the Korea Communications Agency(KCA) (KCA ). X. Jin is with the Department of Information Communication Engineering, Dongguk University-Seoul, Seoul , Korea ( jinxl77@gmail.com). J.-S. No is with the Department of Electrical Engineering Computer Science, INMC, Seoul National University, Seoul , Korea ( jsno@snu.ac.kr). D.-J. Shin is with the Department of Electronic Engineering, Hanyang University, Seoul , Korea ( djshin@hanyang.ac.kr). Digital Object Identifier /TSP SNR of source-relay (SR) link, the other maximizes the SNR of the SD link. Also, the maximum diversity was achieved by using Alamouti code [13]. However, this scheme can be used only for two-antenna selection has not been extended to general multiple-relay networks. In this paper, we consider DF relay networks of one source, one destination, relays with,, antennas, respectively. We assume that the relay-destination (RD) channels are orthogonal, which decreases the data transmission rate. The reason for this assumption is that if the relays transmit signals via the same channel, the potential maximum diversity may be difficult to achieve. To achieve such maximum diversity, joint coding for multiple relays should be investigated it is far from the scope of this paper. In this paper, we propose a criterion of source TAS (STAS) of selecting antennas among transmit antennas at the source based on the upper bound on the pairwise error probability (PEP) derived in [14]. The proposed STAS can be performed at the destination, then the information on the selected transmit antennas is fed back to the source. In the first phase, the source transmits an uncoded single symbol ( ) or a codeword of a full-diversity STBC with transmit antennas. During the second phase, the relays decode, re-encode, re-transmit signals from antennas, so the relays may transmit erroneous signals. Finally, the destination decodes the received signals from the source the relays by using the near-maximum-likelihood (near-ml) decoding scheme [15]. antennas transmit antennas achieves the maximum diversity in the DF relay networks. We also We prove that the proposed STAS which selects among compare the average bit error probability (BEP) of the proposed STAS with those of other STASs through Monte Carlo simulation. The simulation results show that the proposed STAS has better average BEP than other STASs [12]. Moreover, with the same total transmit power, the proposed STAS with has lower cost, complexity, overhead, BEP than the STAS with using full-rate full-diversity STBCs. The following notations are used in this paper: the capital letter denotes a matrix; denotes the identity matrix; denotes a set of complex matrices; represents the Frobenius norm of amatrix; denotes the expectation; the superscript denotes the complex conjugate transpose. For, denotes that the elements of are independent identically distributed (i.i.d.) circularly symmetric Gaussian rom variables with zero mean variance. II. SYSTEM MODEL AND SOURCE TRANSMIT ANTENNA SELECTION A. System Model A cooperative DF relay network with one source, one destination, relays with,, antennas, respectively, is considered as shown in Fig. 1. The half-duplex transmission frequency-flat quasi-static fading channels are assumed. It is also assumed that the relay knows the channel state information (CSI) of the corresponding SR link the destination knows the CSIs of all SR, SD, RD links. Let be the numbers of transmitted symbols at the source the relay during the first the second phases, respectively, be a set of message symbols from the -ary signal constellation. Let be the channel coefficient matrices of the SR link the SD link, respectively, where are channel vectors from the transmit antenna X/$ IEEE

2 1658 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 7, APRIL 1, 2013 B. Source Transmit Antenna Selection To select good source transmit antennas, we should consider both the SD SRD paths simultaneously. Unlike AF relay networks, it is difficult to find the optimal solution for the STAS in the DF relay networks due to the difficulty in deriving their error probabilities. Instead, the union bound on BEP can be used as a criterion of selecting good source antennas by deriving PEPs. However, it is still difficult to derive the exact PEP. Therefore, for the MIMO relay networks with the source antenna subset, we can use the following upper bound on PEP for,, Fig. 1. A DF relay network with multiple relays. The solid line denotes the first phase transmission the dashed line denotes the second phase transmission. (4) at the source to antennas in the relay antennas in the destination, respectively. In the first phase, the source broadcasts a codeword encoded from a full-diversity code with -tuple message vector to the relays the destination by using the selected antennas. Thus, possible source antenna subsets can be selected. We define them as,. We assume that the antennas in the source antenna subset are selected. Then, the column vectors compose the channels matrix, respectively. Hence, the received signal at the relay the destination can be written as by adopting the result of Theorem 2 in [14], where means. As proved in [14], the expectation of the upper bound in (4) taken over the rom variables denoting CSIs is proportional to,where is the diversity of MIMO DF relay networks. Therefore, the union bound on BEP derived from the upper bounds for all pairs of in (4) can be used as a performance criterion. Let (5) (1) (2) Then, selecting the antennas in the subset which satisfies (6) respectively, where is the average transmit power at the source, is the noise matrix at the relay with distribution, represents the noise matrix at the destination with distribution. In the second phase, relays transmit the codewords reencoded from their decoded symbols through orthogonal RD channels. Thus, the received signal at the destination through the orthogonal channel is given as the union bound on BEP derived from the upper bounds on PEPs in (4) can be minimized. The performance of this proposed STAS is analyzed in the following sections. III. DIVERSITY ANALYSISOFTHEPROPOSED STAS In this section, we show that the proposed STAS achieves full diversity. Using (4), the upper bound on the average PEP of the proposed STAS based on (6) can be written as (3) where is the codeword constructed from -tuple message vector decoded by the relayinthefirst phase. A relay may decode correctly or incorrectly, therefore may be different from. is the average transmit power of each relay, is the channel coefficient matrix of the RD channel distributed as, is the noise matrix at the destination for the orthogonal channel with. Let be the minimum rank among the ranks of for all, be the unitary matrices whose columns are the eigenvectors of for any, respectively. We define an matrix with,where (7)

3 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 7, APRIL 1, means the column of a matrix. Since the multiplication of the unitary matrix does not change the statistical distribution of the matrix with circularly symmetric complex Gaussian entries, the entries of,, have the same distribution as the entries of,, respectively. Let be the minimum values among nonzero eigenvalues of for all, respectively. Since is a full-diversity code, we have Proof: Let,,. Then, by using the upper bound in Lemma 1, the expectation in (9) can be upper bounded as By from the Appendix D in [14], the expectation can also be upper bounded as Finally, an upper bound on the average PEP for the DF relay networks with the proposed STAS is derived as (8) (10) where is due to Fact 1 in Appendix A, is from. Let Therefore, the DF relay networks with the proposed STAS can achieve the diversity,when, the maximum diversity is achieved. The PDF of is very difficult to derive for general multiple-antenna cases. However, by doing integration by parts, we can rewrite the last part of (8) as Then, an upper bound on the average PEP can be derived by calculating an upper bound on cumulative density function (CDF) of, which is derived in the following lemma. Lemma 1: The CDF of can be upper bounded as where,,. Proof: See the Appendix B. Using Lemma 1, the following theorem for the achievable diversity can be established. Theorem 1: The proposed STAS which selects antennas among transmit antennas at the source can achieve the maximum diversity in the MIMO DF relay networks of one source, one destination, relays with,, antennas, respectively. (9) IV. SIMULATION RESULTS AND DISCUSSION In this section, we compare the average BEPs of MIMO DF relay networks with the proposed STAS other STASs, also compare the performance of the proposed STAS for various. For other STAS of selecting antennas among transmit antennas at the source, the following schemes are considered. The first one selects antennas with largest SNRs of the SR link, called MAX-SR, another one selects antennas with largest SNRs of the SD link, called MAX-SD as shown in [12]. Also, the rom selection which selects antennas romly is considered. For the case of, the STAS which selects one antenna with the maximum SNR of the SR link the other antenna with the maximum SNR of the SD link [12] is also considered, which will be called MAX-SR-SD. For the simulation, quadrature phase shift keying (QPSK) is used under the channel condition of, total transmit powers at the source ateachrelayare1, respectively. Furthermore, the ML decoder is used at each relay the near-ml decoder [15] is used at the destination. To begin with, we consider the case of,,,. Fig. 2 compares the average BEPs of various STASs in the DF relay network. It is easy to find that the proposed STAS has better average BEP performance than MAX-SD by about 1.5 db at BEP= much better performance than rom selection MAX-SR for both cases of. In Fig. 3, we compare the average BEP of the proposed STAS with those of other STASs for,,, in the Alamouti-coded DF relay network with,where The proposed STAS also shows better average BEP than MAX-SD MAX-SR-SD, much better average BEP than rom selection MAX-SR.

4 1660 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 7, APRIL 1, 2013 Fig. 2. Comparison of average BEPs of various STASs with,, in DF relay networks with one relay. Fig. 4. Comparison of average BEPs of the proposed STAS with various in MIMO DF relay networks with. Fig. 3. Comparison of average BEPs of various STASs with,, in Alamouti-coded DF relay networks with one relay. Fig. 5. Comparison of average BEPs of the proposed STAS with various in MIMO DF relay networks with. Next, we discuss compare the proposed STAS for various. The proposed STAS with requires one RF chain, feedback bits, calculations of the metric in (5). Therefore, without considering the error correction performance, the proposed STAS with is the most beneficial case. To fairly compare the error probabilities on similar decoding complexity level, we consider the proposed STAS with various by using single-symbol-decodable full-rate full-diversity STBCs at the source. First, we consider the case of with. While the uncoded single symbol is used for the case of, Alamouti code is used for the case of. Fig. 4 shows that the BEP curves of the proposed STAS with with have the same slope for the same even though the case of has better average BEP performance than the case of with the same total transmit power. Additionally, we consider the case of with in Fig. 5. For the same symbol rate diversity, an uncoded single symbol is used for, the Alamouti code is used for the case of, the coordinate interleaved STBC (CISTBC) [16], is used for the case of,where with the optimal rotation angle.the BEP curves of the proposed STAS for various also show the same slope, the case of shows the better average BEP performance than the cases of with the same total transmit power. Therefore, the proposed STAS with can be a good STAS scheme at the source.

5 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 7, APRIL 1, V. CONCLUSION In this paper, a new STAS for MIMO DF relay networks was proposed by considering the SD SRD paths. It was also proved that the proposed STAS can achieve the maximum diversity regardless of the number of the selected antennas. The simulation results showed that the proposed STAS has better average BEP performance than other existing STASs ( ). Surprisingly, the proposed STAS with has lower cost, lower complexity, lower overhead, better BEP performance than the cases of with full-rate full-diversity STBCs. Therefore, the proposed STAS with can be a good STAS scheme. Since where means the element of row column of a matrix, we have APPENDIX A FACT 1 Fact 1: [15]: For an matrix, there exists a unitary matrix a real diagonal matrix such that,where, are the eigenvalues of, the columns of are the corresponding eigenvectors. Suppose that are nonzero the remaining eigenvalues are all zero, is the minimum nonzero eigenvalue. Then, for any matrix, the inequality always holds where is an matrix constructed by using the column of as its column,. where is due to (13) The CDF of APPENDIX B PROOF OF LEMMA 1 canbewrittenas the fact that are i.i.d., is due to the exponential distribution of rom variable with the rate parameter.for the last term in (12), we have Since the rom variables, are not statistically independent, the CDF of is very difficult to derive. However, we have Since (14) thus, the CDF can be upper bounded as by the similar derivation in (13), we have (11) (15) where the row vectors are statically independent the row vectors are i.i.d. Therefore, we can rewrite the upper bound on the CDF of in (11) as where. Also, from the fact we have (12) (16)

6 1662 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 7, APRIL 1, 2013 where. By plugging (15) (16) into (14), plugging (13) (14) into (12), the CDF of can be upper bounded as the equation at the top of the page. REFERENCES [1] S. Sanayei A. Nosratinia, Antenna selection in MIMO systems, IEEE Commum. Mag., vol. 42, no. 10, pp , Oct [2] A. F. Molisch M. Z. Win, MIMO systems with antenna selection, IEEE Microw. Mag., vol. 5, no. 1, pp , Mar [3]I.Berenguer,X.Wang,V.Krishnamurthy, AdaptiveMIMO antenna selection via discrete stochastic optimization, IEEE Trans. Signal Process., vol. 53, no. 10, pp , Nov [4] Z. Chen, J. Yuan, B. Vucetic, Analysis of transmit antenna selection/maximal-ratio combining in Rayleigh fading channels, IEEE Trans. Veh. Technol., vol. 54, no. 4, pp , Jul [5] H. Zhang H. Dai, Fast MIMO transmit antenna selection algorithms: a geometric approach, IEEE Commun. Lett., vol.10,no.11, pp , Nov [6] D. A. Gore A. Paulraj, MIMO antenna subset selection with space-time coding, IEEE Trans. Signal Process., vol. 50, no. 10, pp , Oct [7] Z. Chen, J. Yuan, B. Vucetic, Z. Zhou, Performance of Alamouti scheme with transmit antenna selection, Electron. Lett., vol. 39, no. 23, pp , Nov [8] D. J. Love, On the probability of error of antenna-subset selection with space-time block codes, IEEE Trans. Commun., vol. 53, no. 11, pp , Nov [9] S. Peters R. W. Heath, Nonregenerative MIMO relaying with optimal transmit antenna selection, IEEE Signal Process. Lett., vol. 15, pp , [10] H. A. Suraweera, P. J. Smith, A. Nallanathan, J. S. Thompson, Amplify--forward relaying with optimal suboptimal transmit antenna selection, IEEE Trans. Wireless Commum., vol. 10, no. 6, pp , Jun [11] M.Ju,H.K.Song,I.M.Kim, Jointrelay--antennaselection in multi-antenna relay networks, IEEE Trans. Commum., vol. 58, no. 12, pp , Dec [12] G. Zhang, W. Zhan, J. Qin, Transmit antenna selection in the Alamouti-coded MIMO relay systems, Wireless Pers. Commun., vol. 64, no. 4, pp , Feb [13] S. Alamouti, A simple transmit diversity technique for wireless communications, IEEE J. Sel. Areas Commum., vol. 16, no. 8, pp , Oct [14] X. Jin, J.-S. No, D.-J. Shin, Relay selection for decode--forward cooperative network with multiple antennas, IEEE Trans. Wireless Commun., vol. 10, pp , Dec [15] X. Jin, D.-S. Jin, J.-S. No, D.-J. Shin, Diversity analysis of MIMO decode--forward relay network by using near-ml decoder, IEICE Trans. Commun., vol. E94-B, no. 10, pp , Oct [16] M. Z. A. Khan B. S. Rajan, Single-symbol maximum-likelihood decodable linear STBCs, IEEE Trans. Inf. Theory, vol.52,no.5,pp , May 2006.