Joint ML/MAP Estimation of the Frequency and Phase of a Single Sinusoid With Wiener Carrier Phase Noise

We address here the issue of jointly estimating angle parameters a single sinusoid with Wiener carrier phase noise and observed in additive, white, Gaussian (AWGN). develop theoretical foundation for time-domain, phase-based, joint maximum likelihood (ML) estimation unknown frequency initial phase, simultaneous posteriori probability (MAP) time-varying noise. The derivation is based on amplitude phase-form noisy received signal model together use best, linearized, additive observation due to AWGN. Our newly derived estimators are closed-form expressions, consisting both magnitude all samples. More importantly, they have low-complexity, sample-by-sample iterative processing structure, which can be implemented iteratively real-time. As basis comparison, Cramer-Rao lower bound (CRLB) ML Bayesian CRLB (BCRLB) MAP estimator presence noise, results simply depend signal-to-noise ratio (SNR), length variance. It theoretically shown that estimates obtained unbiased, mean-square error (MSE) attain CRLB/BCRLB at high SNR. MSE performance as function SNR, variance verified using Monte Carlo simulation, shows remarkable improvement accuracy large