A Low-Complexity Optimal Sphere Decoder for Differential Spatial Modulation

Motivated by the concept of spatial modulation (SM), a differential scheme has been recently proposed. This scheme, termed as differential (D-)SM, dispenses with channel estimation while maintains a similar bit error rate (BER) performance to SM. The conventional optimal DSM detector based on a maximum likelihood (ML) criterion, however, gives rise to prohibitive computational complexity when either the space-domain or signal-domain constellation size is large. In this paper, we propose a low-complexity yet optimal detection algorithm for DSM by utilizing sphere decoding (SD). The complexity analysis concerning Euclidian distance equation for DSM-SD is derived. Simulation results show that the proposed DSM-SD algorithm maintains an identical BER performance and achieves a significant reduction of computational complexity compared with the DSM-ML algorithm. The DSM- SD algorithm is especially efficient when the number of receive antennas is large. Moreover, compared with SD applied to SM, its application to DSM is verified to be more useful and attractive.