Multiple-Symbol Differential Detection for Spatial Modulation

Abstract

Approximately 3 dB Signal-to-Noise Ratio (SNR) loss is always paid with conventional Differential SpatialModulation (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 cangreatly narrow the 3 dB performance gap by extending the observation interval for differential decoding. The techniqueuses maximum-likelihood sequence detection instead of traditional symbol-by-symbol detection, and is carried out on theslow, 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 improvementover the conventional differential detection. In addition, a closed-form pairwise error probability and approximate biterror probability (BEP) are derived for multiple-symbol differential spatial modulation. Results show that the theoreticalBEP matches well the simulated one. The BEP is shown to converge asymptotically with the number of symbols in theobservation interval to that of the differential scheme with coherent detection.