Multiple-Symbol Differential Detection for Spatial Modulation

Approximately 3 dB Signal-to-Noise Ratio (SNR) loss is always paid with conventional Differential Spatial Modulation (DSM) as compared to coherent Spatial Modulation (SM). In this paper, a Multiple-Symbol Differential Detection (MSDD) technique is proposed for DSM systems to mitigate the loss due to differential detection. The new scheme can greatly narrow the 3 dB performance gap by extending the observation interval for differential decoding. The technique uses maximum-likelihood sequence detection instead of traditional symbol-by-symbol detection, and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric is derived for an observation interval of arbitrary length. It is shown that for a moderate number of symbols, MSDD provides approximately 1.5 dB performance improvement over the conventional differential detection. In addition, a closed-form pairwise error probability and approximate bit error probability (BEP) are derived for multiple-symbol differential spatial modulation. Results show that the theoretical BEP matches well the simulated one. The BEP is shown to converge asymptotically with the number of symbols in the observation interval to that of the differential scheme with coherent detection