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

  • Authors:

  • Fulai Liu;Jinkuan Wang;Ruiyan Du

  • Affiliations:

  • Engineering Optimization and Smart Antenna Institute, Northeastern University at Qinhuangdao, China;Engineering Optimization and Smart Antenna Institute, Northeastern University at Qinhuangdao, China;Engineering Optimization and Smart Antenna Institute, Northeastern University at Qinhuangdao, China

  • Venue:
  • Signal Processing
  • Year:
  • 2010

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Abstract

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 diagonalization processing, which reduces the computation complexity. Finally, simulation results are presented verifying the efficacy of the proposed algorithm.