Research On Two-dimensional Spatial Spectrum Estimation Algorithms

Spatial spectrum estimation is of great importance to the research of array signal processing. It can obtain the direction of arrival(DOA) of the signal through measuring the energy distribution of the signal. Therefore, it can be used for spatial orientation of the target. Due to the fact that one-dimensional parameters have some limits in application, two-dimensional(2D) parameters are usually required to detect the direction of the target in three-dimensional space. Nevertheless, some common 2D spatial spectrum estimation algorithms have high computational complexity because of multi-dimensional spectrum peak searching, so that they are hardly used. Therefore, this paper did research on 2D spatial spectrum estimation algorithm and proposed a series of new algorithms, which are of great theoretical significance and application value.The main work in this paper is summarized as follows:1) A 2D spatial spectrum estimation algorithm based on successive multiple signal classification(S-MUSIC) is proposed. S-MUSIC algorithm gets the initial estimation with rotation invariance of subspace, and then simplifies 2D global searching in 2D-MUSIC by conducting one dimensional searching twice, in which the parameters can be automatically paired. Being free of 2D peak searching, it has a lower computational complexity and the angle estimation performance is very close to that of 2D-MUSIC algorithm.2) A 2D spatial spectrum estimation algorithm based on reduced-dimension Capon(RD-Capon) method is presented. RD-Capon algorithm can achieve 2D spectrum estimation by replacing the 2D global searching in 2D-Capon with one dimensional searching, in which the parameters can be automatically paired. Moreover, it has a lower computational complexity and the angle estimation performance is very close to 2D-Capon algorithm.3) A 2D spatial spectrum estimation algorithm based on successive propagator method(S-PM) is proposed. S-PM algorithm gets the initial estimation with rotation invariance of propagator matrix, and then simplifies 2D global searching in 2D-PM by conducting one dimensional searching twice, in which the parameters can be automatically paired. It has a lower computational complexity and the angle estimation performance is very close to 2D-PM algorithm.4) In order to achieve the 2D spatial spectrum estimation of coherent sources, two algorithms are put forward, which consist of the estimating signal parameters via rotational invariance techniques(ESPRIT) algorithm via spatial-smoothing(S-S) and the ESPRIT algorithm via reconstructing Toeplitz-like matrix. The ESPRIT algorithm via S-S would solve problems about low covariance matrix rank due to coherent signals. The covariance matrix will be pre-processed before 2D spatial spectrum estimation, so that the rank of covariance matrix can be restored to the number of the source. After that, the ESPRIT algorithm will be used to achieve the 2D spatial spectrum estimation. The ESPRIT algorithm via reconstructing Toeplitz-like matrix reconstructs a Toeplitz-like matrix to make a relationship between the rank and DOA by a special antenna array model. Notably, this method also eliminates the effect of signal correlation, and achieves decorrelation. Based on this, we obtain the estimation of 2D spatial spectrum with ESPRIT algorithm. Further, the two algorithms can realize the automatic matching of azimuth angle and elevation angle.