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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 …