Sample-Autocorrelation-Function-Based Frequency Estimation of a Single Sinusoid in AWGN

The problem of estimating the frequency of a single sinusoid observed in additive, white, Gaussian noise is addressed. An explicit, sample-autocorrelation-function-based, approximate maximum likelihood (ML) frequency estimator which does not require numerical search is derived. The structure of this estimator reveals that both the magnitude and the angle of the autocorrelation function should be utilized in estimation processing. Simulation results show that the estimator derived attains the Cramer-Rao lower bound at high signal-to-noise ratio, and has better performance than the planar filtered estimator developed in [22, 23] and the time-domain, approximate ML, received-signal-based estimator in [20, 21]. A new phase unwrapping algorithm is presented to faciliate an efficient, recursive implementation of the estimator. To have a better understanding on the sample-autocorrelation-function-based estimator, a geometric interpretation on the autocorrelation function is introduced. This interpretation allows us to propose a further simplified frequency estimator that resorts to the autocorrelation function angle increments to avoid phase unwrapping. By using the autocorrelation function expression, an alternative form to the frequency estimator of [20, 21] is derived.