A Novel Spatial Using MIMO Spatial

Rajab M. Legnain, Roshdy H.M. Hafez, Ian D. Marsland Abdelgader M. Legnain Department of Systems and Computer Engineering Department of Electric and Electronics Engineering Carleton University, Ottawa, Canada University of Benghazi, Benghazi, Libya

Abstract-In this paper we propose a new Multiple-Input mance improvement over the SM, since it exploits the transmit Multiple-Output (MIMO) transmission scheme that combines diversity available in STBC. The simulation results showed the generalised spatial modulation (GSM) with MIMO spatial that STBC-SM offers 3-5 dB better bit error rate performance multiplexing technique. Unlike the GSM which uses N A active than SM and V-BLAST. antennas to transmit the same symbol, the proposed scheme uses the N A antennas to transmit different symbols simultaneously, In this paper we propose a new MIMO transmission which leads to increase the of the system. scheme based on the GSM combined with the spatial mul­ An optimal detector is used at the receiver to jointly estimate tiplexing. Unlike the GSM which transmits the same symbol the transmitted symbols as well as the index of active antennas over the active antennas, the proposed scheme uses N A an­ combination. However, the optimal detector suffers from a high tennas out of NT to transmit NA different symbols simulta­ computational complexity. To solve this problem we propose a < suboptimal detector which is based on a zero forcing detector. neously, where NA NT. The proposed scheme exploits the The performance of the proposed scheme is evaluated in an index of active antennas combinations instead of antenna index uncorrelated flat fading channel and compared with the optimal to convey information bits. As a results more information bits spatial modulation and vertical Bell Labs layered space-time. can be sent by the scheme, i.e., increased spectral efficiency.

Keywords-Spatial Modulation, Spatial Multiplexing, Antennas The proposed scheme forms a sequence of independent Combination, MIMO systems, Maximum Likelihood detection. random bits into blocks. Each block contains 10g2 (NcMN A) bits, where M is the modulation order and Nc is the number I. INTRODUCTION of combinations. The first 10g2(Nc) bits are used to select the N A transmit antennas combination from the available Spatial Modulation was first proposed by Mesleh et a1. in combinations, and the next 10g2(MNA) bits are modulated [1], where a third dimension is introduced beside the two using a conventional modulation scheme such as M-PSK or dimensional signal plane of the digital modulation. In the M-QAM and transmitted over the selected active antennas. SM, only one antenna out of NT antennas is active during For example, consider a system with NT = 5, NA = 2, and transmission, where the index of antenna, {i, i = 1,2, ... ,NT}, M = 2 (BPSK). Thus the system can convey five bits in each conveys IOg2(NT) bits. At the receiver, iterative-maximum time slots. Suppose that a block of five bits, [0 1 1 0 1], is ratio combining (i-MRC) is used to estimate both the trans­ to be transmitted. In this case, the symbols -1 and 1 will be mitted symbol and the index of the active antenna. Jeganathan transmitted on antennas 1 and 5, respectively. In Table I, we et a1. in [2] proposed an optimal detector for the SM. This illustrate a special example of the mapping of the proposed detector shows a significant improvement over the i-MRC scheme for NT = 5, NA = 2 and M = 2. Note that, when detector with reasonable complexity and outperforms vertical NA 1 the scheme becomes conventional SM. Bell Labs layered space-time (V-BLAST) [3]. Sphere decoder = (SD) was used for the SM detection in [4] in order to reduce This paper is organized as follows. In Section II, we the complexity of the SM optimal detector. It was shown in describ the mapper and the detectors (optimal and suboptimal) [4] the SM with SD can achieve a bit error rate performance of the proposed scheme. In Section III and Section IV, we close to the optimal SM. present the design of the active antennas combination and the computational complexity of the scheme, respectively. In In [5] and [6] Jeganathan et aI. presented a new modulation Section V and Section VI we presesnt simulation results and scheme based on the SM, called generalized space shiftkeying conclusion, respectively. (GSSK) and space shift keying (SSK), respectively. In SSK, the information bits are conveyed by only using the antenna Notations: Throughout the paper, the following no­ index, and in GSSK, the information bits are conveyed by only tations are used. Bold lowercase and bold uppercase letters using the combinations of active antenna indexes. denote vectors and matrices, respectively. We use [.]T, Tr[·] , . . Generalised SM was proposed in [7], [8] which extended []*, []H and [-jt to denote transpose, trace, conjugate, Hermi­ the concept of SM. In this scheme, a combination of active tian and pseudo-inverse of a matrix or a vector, respectively. Furthermore, we use to denote Frobenius norm of a antennas are selected to transmit the same symbol at each time 11.11 F instant. matrix or a vector, and E[·]to denote the expectation. We use n! , (�) and Lx J 2P to denote factorial, binomial coefficient Ba§ar et a1. in [9] employed space-time block coding and the largest integer less than or equal to x that is an integer (STBC) for SM. This scheme provides a significant perfor- power of 2, respectively. 978-1-4673-2821-0/13/$31.00 ©2013 IEEE Transmitter Receiver energy per time slot. In other words, the average transmit energy per symbol per time slot is J:j:.

...... ' A " The transmitted signal vector x = [Xl, X2, ... , XNTV can b 1 � l,Sj 6 o 1 � be written as ... 100011 o 1 * � ,0 N' 0 0

where Xi (i = 1,,,, , N T) represents the transmitted symbol on the ith antenna. All the elements of x are zeros, except the Fig. 1. The block diagram of the new scheme. elements that will be transmitted on the active antennas. Thus, N Table 1. PROPOSED SCHEME MAPPING: NT = 5, NA = 2 , M = 2. the proposed scheme can transmit 10g2(NcM A) bits in each time slots.

Block Input Active antennas Transmit symbol vector, x At the receiver end, the received samples can be expressed

00000 1, 2 [-1 -1 o 0 01 as

00001 1,2 [-1 1 o 0 0 I y Hx+n, (1) 00010 1, 2 [ 1 -1 o 0 0 I 00011 1,2 [ 1 1 0 0 0] where y = [Yl, Y2, '", NY RV is the NR x 1 received 00100 1,3 [-1 0-1 0 01 T samples vector, and n = [nl, "', nNR] is the NR x 1 00101 1, 3 [-1 o 1 o 0 I additive noise vector, where each element is assumed to be 00110 1,3 [ 1 0-1 o 0 I an independent and identically distributed (iid) zero mean 00111 1, 3 [ 1 o 1 o 0] complex Gaussian (ZMCG) random variable with variance aJv. 01000 1,4 [-1 0-1 0 o 1 H is the N R x N T channel matrix between transmit antennas 01001 1,4 [-1 001 01 and receive antennas, and is given by 01010 1,4 [ 1 0 0-1 01 01011 1,4 [ 1 0010] hl,l hl,2 hl,NT 2 22 2 01100 1,5 [-1 o 0 0 -1 I h l h , h N, T H (2) 01101 1,5 [-1 o 0 0 1 I ' 01110 1,5 [ 1 o 0 0 -1 I r ;� � 1 h 'l hN N' T 01111 1,5 [ 1 o 0 0 1] 10000 2,3 [ 0 -1 -1 0 01 where hji, is a complex fading coefficient between the ith 10001 2,3 [ 0 -1 1 o 0 I transmit antenna and the lh receive antenna, and is modeled

10010 2,3 [ 0 1 -1 o 0 I as an iid ZMCG random variable with unit variance. Equation 10011 2,3 [0 1 1 0 0] (1) can be rewritten as 10100 2,4 [0 -1 0-1 01 y = Gm s+n, (3) 10101 2,4 [0 -1 o 1 01 10110 2,4 [0 1 0-1 01 where Gm is the N R x N A channel matrix between transmit 10111 2,4 [0 1 o 1 0] active antennas and receive antennas, and m = 1" " Nc 11000 2,5 [0 -1 o 0 -1 I represents the index of the combination. 11001 2,5 [0 -1 o 0 1 I 11010 2,5 [ 0 1 0 0 -1 I A. Optimal Detector 11011 2,5 [0 1 o 0 1] The receiver uses maximum likelihood (ML) detector to es­ 11100 3,4 [0 o -1 -1 01 timate the combination index, and transmit symbol vector, 11101 3,4 [ 0 0-1 1 01 m, which is expressed as [10] 11110 3,4 [ 0 0 1 -1 01 s,

11111 3,4 [ 0 o 1 1 0] [m, s]= arg maxPr(y I Gm,s) m,s

II. SY STEM MODEL We consider a MIMO communications system with NT transmit antennas and N R receive antennas as shown in Fig. 1. where gmi, is the ith row of the matrix Gm, iY is the received b is a sequence of independent random bits to be transmitted sample on the ith receive antenna, and over a MIMO channel. The transmitter groups the incoming bits, b, into blocks of 10g2(NcMNA) bits. The first 10g2(Nc) bits are used to select the index of combination of active antennas, and the remaining NAlog2(M) bits are mapped into a complex signal constellation vector ... T is the conditional probability density function of y given s = [Sl S2 NS A] Gm to be transmitted over the N A active antennas, where Sk and s . Equation (4) jointly estimates both the combination ... (k = 1, ,NA) is selected from an M-ary complex signal index and the transmitted symbols by searching over all the constellation, such as M-QAM. The covariance matrix of sis combination of vector sand the channel matrix Gm . However, given by Rss = E[ssH]and must satisfiesthe power constraint, the complexity of this detector increases exponentially with the i.e., Tr [Rss ] = Es where Es denotes the average transmit modulation orders, M, and the antenna combination, Nc. Algorithm 1 Suboptimal detector IV. RECEIVER COMPLEXITY

= In this section, we analysis the computational complexity of (m,s) Detection(y,Gm) { the proposed scheme detector and compare it with the optimal SM detector. We use the term of floating-point operation (flop) 1: Zm = Grny, ZF Detector 2NRNA -NA +P to evaluate the complexity. During the analysis, we consider flops one flop is counted for either a complex addition/subtraction or complex multiplication. For simplicity, we ignore the real Quantization process operations such as addition and multiplication. The optimal SM detector in [2] is given by 3: [m] = arg maxPr (y 1 Gm, zm) ML detection 2NRNA - 1 flops 2 } [m, .§]= arg min 1Ihmll� 181 -2Re{yHhm8}) . (10) ms, ( The complexity of the optimal SM detector is equal to 2 NTM(3NR + 1) flops, where the term I hml ll� 181 needs NR + 1 flops and the term (yHhms) requires 2NR, which B. Suboptimal Detector computed NTM times. In this section we propose a suboptimal detector to reduce The detector complexity of the proposed scheme us­ the complexity of the optimal detector. The suboptimal detector ing optimal detector is com�uted as follows. From Equa­ is based on the zero forcing (ZF) and the ML detectors, where tion (4), the term I iY -gmis, l requires 2NA + 1 flops, which the ZF detector is first applied on each possible channels is computed NcMN AN R times, which results is total of matrix between the transmit antennas combination and all the NcMNANR(2NA + 1) receive antennas. Unlike the ML detector which searches over all possible symbol vectors and N c channel matrices, the The suboptimal detector has a complexity of (4N RN A - proposed detector uses ML function to search only over the NA +NR+P)Nc flops,where P is complexity of the pseudo­ vectors that obtained from ZF detector. The algorithm of the inverse, Grn = (G{;;Gm)G;;, and given by 3N�NR + N1 + proposed detector is described in Algorithm 1. � N1 + � N A flops. The complexity of the quantization process is ignored, since its complexity is very low compared to complex operation. For a spectral efficiencyof 12 bpslHz,the optimal SM with

III. COMBINATIONS OF ACTIVE ANTENNAS DESIGN 8 x 4 and 512-QAM has a complexity of 53,248 flops,while the

proposed scheme with 5 x 4, 8-QAM and NA = 2 (Nc = 8) The proposed scheme utilizes the index of antennas combi­ using optimal and suboptimal detector has complexity of nation to convey information bits. In this section, we introduce 114,688 and 1,520 flops, respectively. The main advantage an algorithm to design a table of active antennas combination. of the proposed detector is that it does not depend on the Consider a MIMO system with NT and N R transmit and modulation order, M . receive antennas, respectively, and only N A antennas are active :S during transmission, where NA N R . Therefore, the total V. SIMULATION RESULTS number of possible combinations, C, is In this section we provide simulation results for the pro­ T C = (6) posed scheme using Monte Carlo simulation, and compare (�:) - NA!(�� NA)!· these results with simulation results of the optimal SM [2] and The proposed scheme uses only Nc combinations out of the V-BLAST schemes. The V-BLAST schemes uses the minimum total possible combinations, C, where Nc can be calculated as mean square error ordered successive interference cancellation detector in [3]. We assume an uncorre1ated flat fading channel, (7) and the channel is perfectly known to the receiver. The noise on each receive antenna is assumed to be zero mean complex where p is an integer number. For example, assume MIMO Gaussian random variable with variance a'iv. The M-QAM system with eight transmit antennas, N 8, and only three T = modulation scheme with Gray code is used. antennas are active during transmission, N A = 3 . Thus, the number of combinations that are used in the proposed scheme In Fig. 2 we plot the BER performance of the 9 bpslHz is L 56 J . Therefore, the number of Nc = l m J 2P = 2P = 32 spectral efficiency for the 5 x 4 4-QAM new scheme with bits conveyed by the combination index is lOg2(32) = 5 bits. NA = 3, the 8 x 4 64-QAM optimal SM and the 3 x 4 8-QAM In contrast, the SM with eight transmit antennas, NT = 8, V-BLAST. The new scheme with optimal detector outperforms the antenna index can conveys only 3 bits. In other words, the the optimal SM and V-BLAST schemes, and provides SNR number of bits per symbol that can be transmitted by using gain of about 5dB and 8dB over the optimal SM and V-BLAST the SM and the new scheme are calculated, respectively, as at BER of 10-4, respectively. The performance of the new scheme is degraded when the suboptimal detector is used. The suboptimal detector has worse performance at high SNR, since it has lower diversity order than optimal SM which achieves full diversity. 10" c---�--�-��-�--�-----,

tilIE tilIE

10 15 20 25 30 SNR

Fig. 2. BER performance for a spectral efficiency of 9 bps/Hz. Fig. 3. BER performance for a spectral efficiency of 12 bps/Hz.

In Fig. 3, we extend the simulation to a spectral efficiency [2] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, "Spatial modulation: Optimal detection and performance analysis," IEEE Communications of 12 bpslHz. The new scheme has 5 x 4 8-QAM and Letters, vol. 12, no. 8, pp. 545-547, Aug. 2008. NA = 3, the optimal SM has 8 x 4 512-QAM transmission, [3] R. Bohnke, D. Wubben, V. Kuhn, and K. Kammeyer, "Reduced com­ and the V-BLAST has 4 x 4 8-QAM transmission. From the plexity MMSE detection for BLAST architectures," in IEEE Global figure, the new scheme with optimal and suboptimal detectors Telecommunications Conference, GLOBECOM'03., vol. 4, San Fran­ outperforms the optimal SM and V-BLAST. cisco, CA, USA, Dec. 2003, pp. 2258-2262. [4] A. Younis, R. Mesleh, H. Haas, and P. Grant, "Reduced complexity The performance improvement of the proposed scheme sphere decoder for spatial modulation detection receivers," in IEEE over optimal SM comes from the fact that the modulation order Global Telecommunications Conference, GLOBECOM, Miami, Florida, used in the proposed scheme is lower than that used in optimal USA, Dec. 2010. SM. [5] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, "Generalized space shift keying modulation for MIMO channels," in IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, VI. CONCLUSION PIMRC, Cannes, France, Sep. 2008. [6] J. Jeganathan, A. Ghrayeb, L. Szczecinski, and A. Ceron, "Space shift In this paper, we presented a new MIMO transrmSSlOn keying modulation for MIMO channels," IEEE Transactions on scheme based on GSM for high spectral efficiency. This Commmunicatios, vol. 8, no. 7, pp. 3692-3703, July 2009. scheme uses the index of the active antennas combination to [7] J. Fu, C. Hou, W. Xiang, L. Yan, and Y. Hou, "Generalised spatial convey information bits. Furthermore, it uses several antennas modulation with multiple active transmit antennas," in IEEE Global to transmit different symbols at the same time during one Telecommunications Conference, GLOBECOM, Miami, Flodrida, USA, Dec. 2010, pp. 839-844. symbol interval. The combination of active antennas is a subset [8] A. Younis, N. Serafimovski, R. Mes1eh, and H. Haas, "Generalised of a larger set of active antenna combinations. At the receiver, spatial modulation," in Conference Record of the Forty Fourth Asilomar an optimal detector is used to estimate the transmitted symbols Conference on Signals, Systems and Computers, Pacific Grove, CA, and the index of active antennas combination. This detector USA, Nov. 2010, pp. 1498-1502. suffers from a high computational complexity. To solve this [9] E. Basar, U. Aygolu, E. Panayirci, and H. Vincent Poor, "Space­ problem, however, we propose a suboptimal detector based on time block coding for spatial modulation," in IEEE 21st International the ZF detector. Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC, Istanbul, Turkey, Sep. 2010, pp. 803-808. The simulation results showed that the proposed scheme [10] J. Proakis and M. Salehi, Digital Communications. McGraw-Hill, using optimal detector outperforms the SM (using optimal 2008. detector) and V-LAST schemes significantly,but it suffer from high complexity. While the suboptimal detector outperforms the optimal SM at high spectral efficiency with very low complexity and less number of transmit antennas. So, the performance improvement of the new scheme over optimal SM and V-BLAST increases as the modulation order increases, which makes it a good candidate for high data rate transmission for LTE-Advanced.

REFERENCES

[I] R. Mesleh, H. Haas, C. Ahn, and S. Yun, "Spatial modulation-a new low complexity spectral efficiency enhancing technique," in First Interna­ tional Conference on Communications and Networking, ChinaCom'06., Bejing, China, Oct. 2006.