Unitary-JAFE algorithm for joint angle-frequency estimation based on Frame-Newton method

摘要

The joint angle-frequency estimation (JAFE) based on the multidimensional ESPRIT is recently developed high-resolution parameter estimation technique for determining the directions of arrival (DOAs) and center frequencies of a number of narrow-band sources in a band of interest impinging on the far field of a planar array. In this paper, we present a simple and efficient joint angle-frequency estimation method via the unitary transformation, named as Unitary-JAFE algorithm. In the final stage of Unitary-JAFE, the matrix required to eigendecomposition is a complex unsymmetric matrix. For the eigendecomposition of a complex unsymmetric matrix, we will develop an effective algorithm based on Frame method and Newton iteration method, referred as Frame-Newton algorithm. The proposed method offers a number of advantages over other recently proposed ESPRIT-based techniques by taking advantage of the temporal smoothing, spatial smoothing, and forward-backward averaging techniques. Firstly, except for the final eigenvalue decomposition of dimension equal to the number of sources, it is efficiently formulated in terms of real-valued computation throughout. Secondly, in the final stage of the proposed algorithm, the real and imaginary parts of the i th eigenvalue of a matrix are one-to-one related to the frequency and direction of arrival (DOA) of the i th source. That is, the pairing of the estimated frequency and DOA is automatically determined. Thirdly, the proposed method avoids the joint diagonaliza-tion processing, which reduces the computation complexity. Finally, simulation results are presented verifying the efficacy of the proposed algorithm.