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) [7] which theoretically achieves the Cratner-Rao lower bound (CRB) [7] 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.