The Recovery For Missed Data Caused By Elements Dificiency Utilizing Matrix Completion Theory

In the field of array signal processing,with the continuous expansion of array scale,more and more damage to the array element occurs.Once some array elements are damaged,it will affect the signal processing perofrmance of the entire system.How to solve the problem of array element defects in array signal processing has become an important research topic.Matrix completion is a kind of inverse problem under sparse constraints,which is closely related to compressed sensing.Matrix completion uses the low rank constraint of matrix to solve the underdetermined equation.The existing research has been applied to the recovery of missing data when antenna array elements are damaged,but it is limited to the condition of one-dimensional uniform linear array.It is very important and meaningful to explore the recovery method of the missing data in two-dimensional antenna array,so as to improve the performance of array signal processing including DOA.The main contents of this thesis are as follows:(1)In the case of regular square matrix,the receiving signal model is established,and the low rank property of matrix composed of each snapshot of the receiving signal matrix is analyzed.Then,combining theory and experiment,we choose IALM algorithm to recover the missing data.Through simulation experiments,the feasibility of the algorithm to recover missing data is illustrated.At the same time,the signal-to-noise ratio environment and the number of missing elements are pointed out.(2)For the case of any general array,the low rank property of the received data matrix is described,but the RIP property is not satisfied.Then,subspace constraints are introduced by virtual array interpolation and weighted matrix completion.The process of solving convex optimization problem by proximal gradient descent method is deduced in detail,and the specific steps of recovering missing data are given.Simulation results show that virtual array interpolation is reliable,and the performance of weighted matrix completion is worse than virtual array interpolation.