A Differential Space–Time Modulation Scheme for Correlated Rayleigh Fading Channels: Performance Analysis and Design

Differential space-time modulation (DSTM) is an encoding technique for multiantenna systems that allows the receiver to detect the transmitted signals without the knowledge of the fading channels. It can be viewed as an extension of the differential phase-shift keying scheme in single antenna systems. In this paper, we investigate the performance of multiantenna systems employing DSTM under spatially correlated Rayleigh fading channels. We present three expressions for calculating the pairwise error probability (PEP) of the DSTM scheme. The first expression allows us to numerically calculate the exact PEP. The remaining two are closed-form expressions of the exact PEP at asymptotically high signal-to-noise ratios and the PEP upper bound. It is found that when the distance matrix is proportional to the identity matrix, the error probability is determined by the channel correlation matrix and the initial transmitted code matrix. Based on the new PEP upper bound, we derive a criterion for optimizing the initial code matrix for this special case. Simulation results show that the performance of the differential space-time coded systems can be significantly improved by designing the initial transmitted code matrix according to the proposed design criterion