Performance analysis of a correlator based maximum likelihood frequency estimator

In this paper we discuss the performance of a correlator based frequency estimator (CE). The estimator is statistically analysed for single-tone frequency estimation for an additive white Gaussian noise (AWGN) channel. The CE is a maximum likelihood estimator (ML) S. M. Kay (1993) which theoretically achieves the Cramer-Rao lower bound (CRB) S. M. Kay (1993) if properly implemented. Frequency estimates on the received single-tone signal are made by correlating the received signal with a locally generated signal by varying the frequency, and maximizing the energy at the output of the correlator. The statistical distribution of the frequency estimates, made by the CE is studied; we consider four different cases as discussed in the paper for the distribution, whilst providing simulation results to verify the analysis.