An Improved Eigendecomposition-Based Algorithm for Frequencies Estimation of Two Sinusoids

An eigendecomposition-based algorithm for frequencies estimation of two sinusoids has been proposed recently in [1]. It was shown that for a given received vector length M, each frequency ω can be estimated from a set of estimates of e^jmω, the number of which is [(M - 1)/2]. In this letter, an improved eigendecomposition-based algorithm is presented. We show that the frequency can be alternatively estimated from a set of estimates of e^jω. Compared with the previous algorithm, the number of estimates for each frequency is M -2, which is larger than [(M - 1)/2] when M > 3. Hence, the proposed improved algorithm is expected to achieve a better performance because more estimates of each frequency are available to average out the numerical error. Furthermore, in the proposed algorithm, the frequency is estimated from the estimate of e^jω directly, instead of e^jmω indirectly. Therefore, no additional procedures are needed. Numerical examples are provided to illustrate the improvement of the proposed method.