Reduced-Complexity ML Detection and Capacity-Optimized Training for Spatial Modulation Systems

Spatial Modulation (SM) is a recently developed low-complexity Multiple-Input Multiple-Output scheme that jointly uses antenna indices and a conventional signal set to convey information. It has been shown that the Maximum-Likelihood (ML) detector of an SM system involves joint detection of the transmit antenna index and of the transmitted symbol, hence, the ML search complexity grows linearly with the number of transmit antennas and the size of the signal set. To circumvent the problem, we show that the ML search complexity of an SM system may be rendered independent of the constellation size, provided that the signal set employed is a square- or a rectangular-QAM. Furthermore, we derive bounds for the capacity of the SM system and derive the optimal power allocation between the data and the training sequences by maximizing the worst-case capacity bound of the SM system operating with imperfect channel state information. We show, with the aid of our simulation results, that the proposed detector is ML-optimal, despite its lowest complexity amongst the existing detectors. Furthermore, we show that employing the proposed optimal power allocation provides a substantial gain in terms of the SM system´s capacity as well as signal-to-noise ratio compared to its equal-power-allocation counterpart. Finally, we compare the performance of the SM system to that of the conventional Multiple-Input Multiple-Output (MIMO) system and show that the SM system is capable of outperforming the conventional MIMO system by a significant margin, when both the systems are employing optimal power splitting.