A Practical Differential Receiver for Amplify-and-Forward Relaying

A practical sequence detector of differential phase-shift keying (DPSK) is developed in closed-form for amplify-and-forward (AF) cooperative networks. This detector is applicable for general M-DPSK (M ≥ 2) with arbitrary sequence length N₈ ≥ 1, which includes a single-by-symbol detector as a special case N₈ = 1. In contrast to the maximum likelihood detector (MLD) and the best-known diversity combiner (DC), the proposed detector does not require the knowledge of the channel statistics (which are unknown a priori in practice) and yet, still achieving significant performance improvement. Specifically, for N₈ = 1, the proposed detector outperforms DC by 1.7 dB and achieves near ML performance. For N₈ ≥ 2, the proposed detector outperforms MLD and the performance gain compared with MLD increases as N₈ increases; this performance gain is approximately 1 dB for N₈ = 4.