Research On High-Efficient Spatial Spectrum Estimation Algorithm

The spatial spectrum estimation techniques are usually used to estimate the arrival direction of signals in the processing bandwidth, including improving the angular resolution and accuracy, reducing the computational complexity and speeding up the algorithms. The angular resolution of conventional algorithms are restricted by Rayleigh limit, and the later appeared super-resolution algorithms which have the properties of high angular resolution and accuracy break the restriction. The most typical super-resolution algorithms are MUSIC and ESPRIT algorithm, which greatly promote the development of spatial spectrum estimation algorhthms. However, the calculation of these algorithms are too large for real-time processing, and the angular estimation accuracy is not very well in the case of limited snapshots, the high-efficient spatial spectrum estimation algorithm is proposed to solve these problems above .In this paper the research on high-efficient spatial spectrum estimation algorithm is opened up from the follow aspects: improving the estimation accuracy, reducing the computation of algorithm and improving the operating speed.First, this paper introduces the principle of the MUSIC algorithm briefly and comes to a conclusion that the calculation of the algorithm is too large for real-time processing, so a parallel processing method is proposed to solve this problem. The operation is converted to the field of real numbers by using real-valued preprocessing, by using Householder transformation , the covariance matrix is simplified to a tridiagonal matrix , the eigenvalue and eigenvector of the tridiagonal matrix , which are used in spectrum peak search, can be obtained by QR decomposition , and each stage of the algorithm is fit for multi-processor parallel processing.Second, the parallel algorithm is extended to the ESPRIT algorithm. The covariance matrix is transformed to a tridiagonal matrix by applying Lanczos transformation, then the tridiagonal matrix is decomposed by QR method with original displacement to simplified the Eigenvalue decomposition problem, at last, it's suitable for multi-processor parallel processing at the stage of the estimation of covariance matrix and eigenvalue decomposition.At last, the performance of MUSIC algorithm degrades in the case of limited snapshot, a reduced-dimension MUSIC algorithm based on Toeplitz matrix is learnt in this paper, and some improvement is applied to this method. The covariance matrix is estimated by applying reduced-dimension technique to the new data which is obtained by projecting the array data to the signal subspace, The reduced-dimension MUSIC algorithm is then applied to the projected data to estimate the DOA of target. However, the above reduced-dimension methods reduce the degrees of freedom of the antenna. A single snapshot MUSIC algorithm based on Toeplitz matrix is proposed to solve this problem, the covariance matrix is constructed according to the Toeplitz characteristic, and this method doesn't lose the degrees of freedom.The theoretical analysis and experimental results demonstrate that the research on parallel MUSIC and parallel ESPRIT algorithm is effctive, these methods can reduce the calculation greatly and improve the speed of processing with little impact on the performance of the algorithms. The single snapshot algorithms this paper proposed improve the estimation accuracy greatly, especially in low SNR situations, and these algorithms can estimate coherent signals correctly.