Research Of DOA Estimation Algorithm Based On Coprime Sparse Array

Coprime sampling is an emerging sparse sampling method in recent years.Firstly,the signal is downsampled into two low-rate data stream(two downsampling factors are required to be a coprime pair of integer),and then the original signal can be recovered by the sampling relationship of the samples of two sub-channels.Coprime sampling has been widely used because it can break through the limit of Nyquist sampling theorem to estimate and analyze the signal.This idea can also be applied to DOA estimation,which is embodied in two uniform linear arrays with coprime intervals.At present,there are mainly two kinds of DOA estimation algorithms,including compression sensing algorithm and subspace decomposition algorithm.The compression sensing algorithm contains two steps.The first step is to establish a system model of compressed sensing and construct an overcomplete redundant dictionary with abundant candidate directions to ensure that the real direction of arrival is sparsely distributed in the dictionary.The second step is to find the optimal solution from the dictionary with the optimization arithmetic,thereby obtaining the DOA estimation.Obviously,the solving process of objective function involves complex recursive or iterative procedures so that the computational complexity is high.The latter algorithm is represented by the mainstream MUSIC algorithm,whose essence is to take use of the orthogonal property between signal subspace and noise subspace and do the eigenvalue decomposition of the covariance matrix of observed samples,and then construct spatial spectral function to search direction of arrival.However,there are many deficiencies in the theory,which are mainly reflected in the following two points:1)The MUSIC algorithm is proposed based on uniform linear array and is not applied to sparse array.2)It is not applicable to the samples of sparse array.So the spatial smoothing technology is needed,but it requires a large number of matrix operations with high complexity.This paper mainly analyzes these two kinds of algorithms based on coprime sparse array,and focuses on the latter.Based on the analysis of the deficiencies of existing algorithms,this thesis proposes corresponding solutions and theoretical supplement as:1)In order to make full use of the cross-correlation information between the coprime samples of two sub-channels and also consider the self-correlation information.The transforming relationship from the sparse observation covariance matrix to the covariance matrix of virtual ULA is proposed;2)The difference-set table traversal searching algorithm is proposed to greatly cut down the computational complexity and assure the timeliness of DOA estimation;3)The correctness of the difference-set table algorithm is proved from two angles;4)In order to obtain greater degree of freedom,a series of optimizations are made based on the traditional coprime array and a new coprime array is proposed.