On the Effect of Gaussian Imperfect Channel Estimations on the Performance of Space Modulation Techniques

Space modulation techniques, such as spatial modulation (SM) and space shift keying (SSK), are efficient low complexity implementation of multiple input multiple output (MIMO) systems. In such techniques, a single transmit-antenna is activated during each time instant and the activated antenna index is used to convey information. Due to the novel method of conveying information, a major criticism arises on the practicality of such techniques in the presence of real-time imperfections such as channel estimation errors. Therefore, the aim of this paper is to shed light on this issue. The performance of such systems are analyzed in the presence of Gaussian imperfect channel estimations. More specifically, the performance of SSK system consisting of Nt transmit and Nr receive antennas with maximum-likelihood (ML) detection and imperfect channel state information (CSI) at the receiver is studied. The exact average bit error probability (ABEP) over Rayleigh fading channels is obtained in closed-form for Nt = 2 and arbitrary Nr; while union upper bound is used to compute the ABEP when Nt >; 2 and arbitrary Nr. Furthermore, simple and general asymptotic expression for the ABEP is derived and analyzed. Besides, the effect of imperfect CSI on the performance of SM, Alamouti and SSK schemes considering different number of channel estimation pilots are studied and compared via numerical Monte Carlo simulations. It is shown that, on the contrary to the raised criticism, space modulation techniques are more robust to channel estimation errors than Alamouti since the probability of error is determined by the differences between channels associated with the different transmit antennas rather than the actual channel realization.