Adaptive windowed cross Wigner–Ville distribution as an optimum phase estimator for PSK signals

Abstract

Cross time-frequency distribution (XTFD), unlike the quadratic time-frequency distribution (QTFD), can represent phase information for phase shift keying (PSK) signals such as binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK). However, it suffers from interference due to duplicated terms that cause inaccuracy in the phase estimate. Thus, a time-dependent lag window is proposed in this article where the window width is adaptively adjusted according to the localized lag autocorrelation function (LLAC). This adaptive windowed cross Wigner-Ville distribution (AWXWVD) is proven capable to remove most of the duplicated terms. The instantaneous information bearing phase (IIB-phase) is then estimated from the peak of the cross time-frequency representation (XTFR). Simulation results show that the AWXWVD is an optimum phase estimator as it meets the Cramer-Rao lower bound (CRLB) at SNR>=5 dB and SNR>=6 dB for BPSK and QPSK signals respectively. The AWXWVD also outperforms the conventional IQ demodulator as a phase estimator with difference in the IIB-phase variance of about 5 dB.