Joint Frequency and DOA Estimation with Automatic Pairing Using the Rayleigh–Ritz Theorem

This paper presents a novel scheme for joint frequency and direction of arrival (DOA) estimation, that pairs frequencies and DOAs automatically without additional computations. First, when the property of the Kronecker product is used in the received array signal of the multiple-delay output model, the frequency-angle steering vector can be reconstructed as the product of the frequency steering vector and the angle steering vector. The frequency of the incoming signal is then obtained by searching for the minimal eigenvalue among the smallest eigenvalues that depend on the frequency parameters but are irrelevant to the DOAs. Subsequently, the DOA related to the selected frequency is acquired through some operations on the minimal eigenvector according to the Rayleigh–Ritz theorem, which realizes the natural pairing of frequencies and DOAs. Furthermore, the proposed method can not only distinguish multiple sources, but also effectively deal with other arrays. The effectiveness and superiority of the proposed algorithm are further analyzed by simulations.