A Novel Spatial Modulation Using MIMO Spatial Multiplexing 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 spectral efficiency 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 ..