Parallel Implementation of Decision-Aided Maximum-Likelihood Phase Estimation in Coherent $M$ -ary Phase-Shift Keying Systems

To make decision-aided (DA) maximum-likelihood (ML) phase estimation suitable for real-time processing, a parallel implementation is proposed. The variance of the phase error using the parallel DA ML is analytically examined. The bit-error-rate performance is also analytically investigated in different M-ary phase-shift keying (PSK) systems. The results show that parallel DA ML can outperform block Mth-power in binary PSK format, while suffering performance penalty originating from parallelism and pipelining in high-order PSK formats.