Detection of Spatial Modulation Signals in Doubly Selective Fading Channels with CSI Uncertainty

To detect spatially-modulated signals, a receiver needs the channel state information (CSI) about each transmit-receive antenna pair. Although the CSI (or channel response information) is never perfect and varies in time, most studies on spatial modulation (SM) systems assume perfectly known CSI and time-invariant channel. The spatial correlations among multiple spatial subchannels, which have to be considered when CSI is imperfect, are also often neglected. In this paper, we release the above assumptions and take the CSI uncertainty and the spatial and temporal selectivities into account. We derive the channel estimation error-aware maximum likelihood (CEEA-ML) detectors as well as several low-complexity suboptimal alternatives for PSK and QAM signals. As the CSI uncertainty depends on the channel estimator used, we consider two practical estimators in our derivations. Numerical results obtained by simulations show that the CEEA-ML detectors offer clear performance gain against conventional mismatched SM detector and, more importantly, the proposed suboptimal detectors incur negligible performance loss.