Differentially-Encoded Rectangular Spatial Modulation Approaches the Performance of Its Coherent Counterpart

A simplified rectangular differential spatial modulation (S-RDSM) scheme is conceived for massive multiple-input multiple-output (MIMO) systems dispensing with the channel state information (CSI). In the proposed S-RDSM scheme, the information bits are first mapped to a conventional SM symbol and then rectangular differential encoding is invoked between a pair of SM symbols. Then a non-coherent detector relying on a forgetting factor is developed, which requires no CSI at the receiver. Explicitly, a low-complexity hard limited maximum likelihood (HL-ML) detector is conceived for our generalized S-RDSM scheme, which is characterized by our theoretical analysis. Furthermore, we derive the optimal forgetting factor in closed form, which is capable of significantly reducing the complexity of the associated optimization. Finally, the upper bounds of the average bit error probability (ABEP) are derived using the moment generating function (MGF), and are validated by our simulation results. Both the theoretical and simulation results have shown that the proposed S-RDSM system outperforms the existing non-coherent schemes, despite operating at 10% of the benchmarker's complexity, whilst approaching the performance of its coherent SM counterpart at a comparable complexity.