Implementation of exact maximum likelihood phase estimators for a single real sinusoid in white Gaussian noise

In this Letter, estimation of the phase of a real sinusoid with known frequency in white Gaussian noise is addressed. Based on the Newton-Raphson iterative procedure, two simple realizations of exact maximum likelihood phase estimators for known and unknown amplitude are devised. Computer simulations are included to contrast the performance of the proposed algorithms with the approximate maximum likelihood estimate as well as Cramér-Rao lower bound for different phase values and signal-to-noise ratios. Copyright © 2005 The Institute of Electronics, Information and Communication Engineers.