Non-coherent multi-user detection of DPSK signals after differential demodulation

Differential phase-shift keying (DPSK) is commonly associated with a loss in performance when compared to coherent demodulation of PSK signals. Because DPSK avoids the problem of phase tracking, the performance loss may be deemed acceptable. When two or more users transmit simultaneously, such as in a frequency-hopping (FH) system with non-orthogonal hopping patterns, single-user differential demodulation cannot guarantee selecting the most probable hard decision for each symbol. In this paper, we consider the performance when collisions occur. For our technique, we first derive the resulting signal constellation from performing differential demodulation. Conditioned on that, and assuming knowledge of phase difference between the users, the optimal multi-user detection (MUD) algorithm is derived and analyzed to bound the performance of non-coherent demodulation. Based on the analysis, a sub-optimal 2-user MUD algorithm that requires no phase information is proposed and shown to attain significant performance improvement over single-user detection (SUD).