Matrix Completion Based DOA Estimation With Partially Corrupted Data

Recovering unknown useful data from a small number of randomly samples is very important for array signal processing,such as direction of arriva l(DO A)estimation when the received data is corrupted.If the corrupted data is randomly distributed in the matrix,the matrix completion(MC)method can effective ly recover the corrupted data,so as to accurately estimate the direction of arriva l.However,if the distribution of corrupted data is concentrated,the unknown data cannot be recovered accurately and effectively,thereby affecting the estimation of DO A.For example,when the corrupted data is distributed over the entire row(column)of the matrix,the row(column)lacks sufficient relevant information and the matrix comp letion method fails.To this end,this paper studies the problem of DO A estimation when some antennas of the array are corrupted,and proposes FSS-MC algorithm and FSS-OptSpace algorithm for uniform linear array.The FSS-MC algorit hm uses the shift-invariant structural characteristics of the uniform linear array to solve the problem of DO A estimation when partial antennas are corrupted.The algorit hm divides the array into several sub-arrays by performing spatial smoothing operations on the array,so that the corrupted elements originally distributed in the entire row(column)are disrupted.The data matrix(reconstructio n matrix)obtained by the spatial smoothing scheme proves to be low rank and meets the incoherent condition,so the matrix completion algorithm can be used to recover the corrupted data in the reconstruction matrix.The matrix completion algorithm is essentia lly to minimize the kernel norm of the reconstructed matrix under the condition that the variable matrix matches the observation matrix(effective data).The FSS-MC algorithm consumes a lot of comput ing resources when minimizing the kernel norm,and the cvx toolkit is very slow when calculating large matrices.Therefore,the FSS-MC algorithm is not suitable for solving large-scale matrix recovery problems.However,the data matrices collected in practical applications such as recommendation systems,face recognit ion,and radar surveys,are relatively large.In view of the limitations of the FSS-MC algorithm,this paper further proposes the FSS-OptSpace algorithm.The FSS-O pt Space algorithm uses the structural characteristics of a uniform linear array to reorganize the data matrix through a spatial smoothing scheme so that each row / column has relevant information to recover corrupted data;and the problem of minimizing the kernel norm is transformed into the manifold optimization problem of minimizing left and right singular matrix.The optimal value is solved by the gradient descent method.Finally,the classical DO A estimation method is used to calculate the spatial spectral function.This paper makes a full simulation experiment analysis of the above t wo algorithms.The experimental results show that FSS-MC algorithm and FSS-OptSpace algorithm have good DO A estimation performance when some antennas of the array are corrupted,and FSS-OptSpace algorithm is suitable for DOA estimation of larger arrays.