Transmit Precoding for Receive Spatial Modulation Using Imperfect Channel Knowledge

Abstract

In this paper, motivated by the relatively new concept of Spatial Modulation (SM), we are addressing the problem of Receive-Spatial Modulation (R-SM) under two cases of imperfect channel knowledge at the transmitter side. In the first case, we adopt a statistical model for the channel uncertainties, whereas in the second one a worst-case approach is followed and the channel uncertainties are expressed as a bounded set. Based on Zero-Forcing (ZF) precoding and using standard tools from optimization theory, we derive closed form solutions that turn out to be robust. Simulation results show that the proposed schemes have a performance close to the perfect channel knowledge scenario in low and mid-low SNRs. Furthermore, these designs can be applied to wide range of channels with different correlation states combined with a transmit power gain.