Transmit precoding for receive spatial modulation using imperfect channel knowledge

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.