Optimal Blind Carrier Recovery for MPSK Burst Transmissions

Abstract—This paper introduces and analyzes the asymptotic (large sample) performance of a family of blind feedforward non-linear least-squares (NLS) estimators for joint estimation of carrier phase, frequency offset, and Doppler rate for burst-mode phase-shift keying transmissions. An optimal or “matched ” nonlinear es-timator that exhibits the smallest asymptotic variance within the family of envisaged blind NLS estimators is developed. The asymp-totic variance of these estimators is established in closed-form ex-pression and shown to approach the Cramèr–Rao lower bound of an unmodulated carrier at medium and high signal-to-noise ra-tios (SNR). Monomial nonlinear estimators that do not depend on the SNR are also introduced and shown to perform similarly to the SNR-dependent matched nonlinear estimator. Computer sim-ulations are presented to corroborate the theoretical performance analysis. Index Terms—Burst transmission, carrier phase, Doppler rate, frequency offset,-ary phase-shift keying (MPSK), synchroniza-tion. I