A new and efficient TSVD algorithm for estimating DOA (direction of arrival)

The introduction of the full paper reviews some references and then proposes our TSVD algorithm, which combines adroitly the SVD (singular value decomposition) algorithm with the Toeplitz algorithm. Sections 1 through 4 explain our TSVD algorithm. Section 2 briefs the SVD algorithm. Section 3 briefs the Toeplitz algorithm. The core of section 4 consists of: (1) we decompose the eigenvector of the coherent signal covariance matrix and obtain its maximum eigenvector value, with which we reconstruct a new matrix that possesses the properties of the Toeplitz algorithm; the new matrix is given in eq. (12); (2) we decompose the singular value of the new matrix; the minimum eigenvector value, corresponding to the small singular values, constitutes noise subspace, while the maximum eigenvector value, corresponding to the large singular values, constitutes signal subspace; (3) we utilize eq. (8) in section 2 to search for the spectral peak, thus estimating the DOA of the incident signal. Section 5 simulates our TSVD algorithm with two numerical examples; the simulation results, presented in Figs. 1 through 4, and their analysis show preliminarily that, compared with the conventional SVD and Toeplitz algorithms, our new algorithm produces more precise and stable estimations: when SNR (signal to noise ratio) is -10 dB, the SVD algorithm does not work, the estimation error of the Toeplitz algorithm is up to 2⁰, but the estimation error of our new TSVD algorithm is close to 0.