Research On Sparse Array DOA Estimation Method Based On Matrix Rank Minimization

Direction of Arrival(DOA)estimation plays an important role in target detection,radar positioning,seismic exploration,satellite communication and other fields,which has been widely studied by scholars in recent decades.Sparse array can increase the aperture of the array while reducing the coupling among array elements,so that the DOA estimation algorithm based on sparse array is capable to identify more signal sources than the number of physical array elements.With the development and improvement of matrix rank minimization theory,the application of related algorithms in the field of DOA estimation has become more and more popular.Due to the DOA estimation algorithm based on matrix rank minimization can utilize the sparsity of the incoming signal in the spatial domain and the low rank characteristics of the received data matrix,such algorithms are able to realize the reconstruction of the entire data matrix with a small amount of observation data,and has gradually become a research focus in this field.However,there still are many problems concerned with this type of DOA estimation algorithm,such as the computational complexity of the algorithm,insufficient accuracy of coherent source DOA estimation,poor robustness,etc.For this reason,this paper carry out research of sparse array DOA estimation algorithm based on the matrix rank minimization theory,and the main contributions contain the following:1.The covariance matrix of the received signal of array can be reconstructed by the Toeplitz matrix with certain constraints,based on this feature(1)A method of DOA estimation for coprime array based on the atomic norm minimization is proposed.This method transforms the matrix rank minimization problem into the atomic norm minimization problem.By solving the dual problem of the latter one,the computational complexity of the traditional atomic norm minimization algorithm is effectively simplified,and the under-sampled signal can be accurately recovery.In order to further improve the performance of the above-mentioned algorithm on estimating coherent signal,a spatial filtering model is designed to filter the pre-estimated signal,which realizes the decoherence of the angle of the incoming wave signal.As a result,such filtering operation effectively enhances the DOA estimation performance of the algorithm for coherent sources.(2)A method of DOA estimation for coprime array based on alternating projection is proposed.This method transforms the non-convex matrix rank minimization optimization problem into alternating projections among multiple convex constraint sets,then the result of this algorithm will converge to a optimal covariance matrix after finite iterations.Compared with other DOA estimation algorithms for sparse array,the mentioned algorithm display better performance in the presence of element position errors.2.A DOA estimation method for sparse array based on the nuclear norm minimization is proposed.To solve the problem of the accuracy decrease for traditional DOA estimation method estimating the pitch and azimuth angles when take the coupling effect among the array elements into consideration,this method propose to use the vectorized co-variance matrix to construct the data column received by the virtual plane array elements.Based on the constructed data column,a low-rank matrix can be reliably recoveried via nuclear norm minimization,part of which can be used to construct a new data matrix with the combination of the data before restoration.New matrix can effectively reconstruct the received data of the virtual uniform planar array,and contribute greatly to realizing high-precision DOA estimation for sparse array.