Array Diagnosis and DOA Estimation for Coprime Array under Sensor Failures.

A coprime array of N sensors can achieve O(N2) degrees of freedom (DOFs) by possessing a uniform linear array segment of size O(N2) in the difference coarray. However, the structure of difference coarray is sensitive to sensor failures. Once the sensor fails, the impact of failure sensors on the coarray structure may decrease the DOFs and cause direction finding failure. Therefore, the direction of arrival (DOA) estimation of coprime arrays with sensor failures is a significant but challenging topic for investigation. Driven by the need for remedial measures, an efficient detection strategy is developed to diagnose the coprime array. Furthermore, based on the difference coarray, we divide the sensor failures into two scenarios. For redundant sensor failure scenarios, the structure of difference coarray remains unchanged, and the coarray MUSIC (CO-MUSIC) algorithm is applied for DOA estimation. For non-redundant sensor failure scenarios, the consecutive lags of the difference coarray will contain holes, which hinder the application of CO-MUSIC. We employ Singular Value Thresholding (SVT) algorithm to fill the holes with covariance matrix reconstruction. Specifically, the covariance matrix is reconstructed into a matrix with zero elements, and the SVT algorithm is employed to perform matrix completion, thereby filling the holes. Finally, we employ root-MUSIC for DOA estimation. Simulation results verify the effectiveness of the proposed methods.