Abstract-Novel transmit antenna selection techniques are conceived for Spatial Modulation (SM) systems and their symbol error rate (SER) performance is investigated. Specifically, low-complexity Euclidean Distance optimized Antenna Selection (EDAS) and Capacity Optimized Antenna Selection (COAS) are studied. It is observed that the COAS scheme gives a better SER performance than the EDAS scheme. We show that the proposed antenna selection based SM systems are capable of attaining a significant gain in signal-to-noise ratio (SNR) compared to conventional SM systems, and also outperform the conventional MIMO systems employing antenna selection at both low and medium SNRs.Index Terms-Spatial modulation, antenna selection, diversity, limited feedback, capacity.
I. PRELIMINARIESW HEN considering a Spatial Modulation (SM) system [1]- [4] having N r receive and N t transmit antennas, which relies on a single RF chain at the transmitter, we have the system model of y = √ ρh i s + n, where y ∈ C Nr is the received signal vector, ρ is the average Signal-to-Noise Ratio (SNR) at each receive antenna, s is a random symbol selected from a unit-energy M -QAM or -PSK signal set represented by S, h i is the channel vector corresponding to the i th transmit antenna, and n ∈ C Nr is the noise vector. The entries of both n and of the channel matrix H obey the circularly symmetric complex-valued Gaussian distribution CN (0, 1). In SM, the input bitstream is divided into blocks of log 2 (N t M ) bits and in each such block, log 2 M bits select a symbol s from an M -QAM or M -PSK signal set, while log 2 N t bits select an antenna i out of N t transmit antennas for the transmission of the selected symbol s. Therefore, an SM symbol is comprised of the transmit antenna index and of the transmitted symbol from a conventional signal set. Let L = {i} Nt i=1 represent the set of transmit antenna indices. Assuming perfect Channel State Information at the Receiver (CSIR), the Maximum Likelihood (ML) detector conceived for this SM scheme is given by (î,ŝ) ML = arg min i∈L, s∈S y − √ ρh i s 2 2 . Let A represent the event of an antenna index error and S represent the event of a transmitted symbol error under ML detection. Then, the probability of a SM symbol error is given by P e (SM ) = Pr(A) + Pr(S, A c ), where A c represents the complement of A. Bounds on Pr(A) and Pr(S, A c ) can be easily derived, and are given byandIt is clear from (2) and (4) 1 that the diversity order of both Pr(A) and Pr(S, A c ) is only N r and hence the diversity order of P e (SM ) is N r . Fig. 1 plots P e (SM ), Pr(A) and Pr(S, A c ) explicitly, considering an SM system having N t = 4 and N r = 2 for various throughputs. Two important observations may be inferred from these plots:1) The diversity order (slope of the SER curve), associated with Pr(A) and Pr(S, A c ) are the same as formulated in (2) and (4).
2) As the number of bits/symbol increases (size of the QAM constellation), Pe(SM) is dominated by the probability Pr(S, A c ).Observe that Pr(S, A c ) given in ...