Design and performance analysis of non-data-aided carrier phase estimators for amplitude and phase shift keying signals

This study studies the feedforward (FF) non-data-aided (NDA) carrier phase estimation of the amplitude and phase shift keying (APSK) signals. The true Cramer-Rao bounds (CRBs) for NDA phase estimation of APSK signals are derived and evaluated numerically using Gauss-Hermite quadrature. The jitter variance of the FF Viterbi-Viterbi (V&V) algorithm is analysed assuming the absence of data pattern noise. It is proved that, when the design parameter μ=-2, the jitter variance is able to converge asymptotically to the modified CRB (MCRB) at high signal-to-noise ratios (SNRs). For practical application, the parameter μ is also optimised for 16/32/64-APSK signals at different SNRs. The analytical results of the jitter variance are verified by Monte-Carlo evaluations. It is shown that, for 32/64-APSK signals, the plain V-algorithm cannot approach the CRBs due to the data pattern noise. A modified V-algorithm based on the constellation partition and a linear combination of the sub-estimators is proposed to eliminate the divergence. Simulation results show that the jitter variance of the proposed estimator is very close to the CRB at the SNRs of interest and converges to the MCRB at high SNRs.