Blind Per-State Detection of DPSK Over Correlated Fading Channels

We consider a differentially encoded phase-shift keying (DPSK) signal that is transmitted over a channel affected by correlated Rayleigh fading. For this problem, we derive the exact maximum
a posteriori
(MAP) symbol-detection algorithm. By analyzing its properties, we demonstrate that it can be implemented by a forward-backward estimator of the channel, followed by symbol-by-symbol completion to produce the
a posteriori
probabilities of the information symbols. The resulting algorithm can be employed as a soft-input-soft-output (SISO) block in turbo-iterative receivers and exhibits excellent performance, despite its limited computational complexity. The performance of the proposed algorithm is evaluated for time-domain modulations over time-varying channels and for frequency-domain modulations over frequency-selective channels.