Analysis and reduction of estimation bias for an iterative frequency estimator of complex sinusoid

Frequency estimation of a complex sinusoidal signal is a fundamental problem in signal processing. In this regard, Aboutanios and Mulgrew (A&M) proposed an iterative frequency estimator which can approach the theoretical bound in two iterations, thus, made it one of the best iterative estimators. In this paper, we theoretically analyze the two versions of the A&M estimator and show that the estimation biases of the two versions are not equivalent. The results of the theoretical analysis indicate that the bias of the first iteration can be accurately predicted by a polynomial equation. We then propose to use the roots of the polynomial equation to improve the estimation and reduce the bias. Experiments show that the proposed new estimator can significantly reduce the bias.