Optimal and Suboptimal Differentially Coherent Reception of MDPSK in Time-Spread WSSUS Channel

A model of the wide-sense stationary uncorrelated scattering (WSSUS) channel with time-spread and additive white Gaussian noise is considered. The general expression for the symbol-by-symbol reception algorithm of M-ary differential phase shift keying (MDPSK), which realizes implicit diversity, is obtained. Depending on the type of impulse response receiver filter (demodulator kernel), the partial cases that follow from this expression are considered: optimal demodulator, conventional differentially coherent demodulator, demodulator with iterative kernel and its special cases. Relations for assessing the bit error probability of the considered demodulators in the case when signals are transmitted with binary and quadrature differential phase shift keying without taking into account intersymbol interference are derived. The performance bounds for the optimized binary and quadrature systems are determined. The results of the calculation of the bit error probability are presented.