Generalized Kay estimator for the frequency of a single complex sinusoid

This article introduces a generalized version of Kay´s (1989) estimator for the frequency of a single complex sinusoid in complex additive white Gaussian noise (AWGN). Kay developed a maximum likelihood (ML) estimator based on differential phase measurements with a delay of one symbol interval. In this paper the corresponding ML estimator with an arbitrary delay in the differential phase measurements is derived. The proposed estimator reduces the variance at low SNR compared with Kay´s original estimator. The penalty for the reduced variance is a reduced estimation range. With sufficient delay the window function in the generalized Kay estimator is nearly uniform and the implementation complexity is reduced. Performance comparisons with an estimator based on differential phase measurements with a uniform window function is given. The proposed estimator is also compared with the Fitz (1991) estimator