An Eigendecomposition-Based Algorithm for Frequencies Estimation of Two Sinusoids

This letter presents a new algorithm for frequencies estimation of two sinusoids observed in additive white Gaussian noise. By uniformly sampling the received signal, a received vector and its auto-correlation matrix are obtained. It is interesting to observe that the elements in the eigenvectors corresponding to the two largest eigenvalues of this auto-correlation matrix contain the information of frequencies. We then decode the information contained in the eigenvectors to obtain the frequencies by taking advantages of a set of special matrices formed from the elements in the eigenvectors. The proposed method can also be used to find the frequency of a single sinusoid observed in noise. Numerical results of the proposed method are obtained by simulations, and are used to compare with some existing methods.