Research On Subspace Weighting Algorithm Based On Random Matrix Theory

As a key research direction of array signal processing,DOA estimation is widely used in the fields of radar,underwater acoustic survey and satellite communication systems.The traditional DOA estimation algorithm is derived under the premise that the number of snapshots is much larger than the number of elements.In the case of low signal-to-noise ratio where the number of snapshots is equal to or even smaller than the number of elements,the performance of the traditional DOA estimation algorithm is not good.Random matrix theory studies the asymptotic law of matrix eigenvalues and eigenvectors when the dimension of random matrix increases at the same rate.In this thesis,under the new asymptotic system where the number of snapshots and the number of array elements are arbitrary ratios,the random matrix theory is used to study the subspace weighting algorithm to optimize the DOA estimation performance.This thesis mainly studies the following three aspects:1.Study the change law of the eigenvalues and eigenvectors of the covariance matrix of the data samples received by the array when the number of snapshots and the number of array elements change at the same rate.When the signal energy is less than a certain threshold,the limit value of the eigenvalue of the covariance matrix of the low-rank signal sample is the same as that of pure noise,and the inner product of the corresponding eigenvector and the signal tends to zero.When the signal energy is greater than the threshold,the limit value of the eigenvalue of the signal sample covariance matrix is related to the ratio of the number of samples and the number of array elements,and the inner product of the corresponding eigenvector and the signal tends to a certain non-zero constant.2.Research the subspace weighting algorithm based on the singular value of random matrix.Using the results of the eigenvalues of the sample covariance matrix in the random matrix theory,the energy of each subspace is estimated,and then the subspace weighting matrix is constructed with the estimated energy.The simulation results show that this method is applicable when the signal sources are correlated or uncorrelated.In the case of small snapshots and low SNR,the estimation error and outliers probability of this method are lower than those of the classic MUSIC method and the weighting subspace method.3.Research on subspace weighting algorithm based on random matrix eigenvectors.The first-order perturbation is used to approximate the statistical characteristics of the eigenvectors of the sample covariance matrix,and then the asymptotic result of the projection norm of the sample covariance matrix signal subspace to the real signal in the random matrix theory is used to obtain the weighting matrix based on the eigenvector of the random matrix.The simulation results show that in the scenarios with correlated signal sources and low SNR,when the number of snapshots is less than10,the estimation error and outliers probability of this method are lower than other algorithms,and when the number of snapshots is higher than 10,the subspace weighting algorithm based on the singular value of the random matrix has the best performance.