# Joint Block Low Rank and Sparse Matrix Recovery in Array Self-Calibration Off-Grid DoA Estimation

## TL;DR

This paper proposes a convex optimization approach for joint low-rank and sparse matrix recovery to improve off-grid DoA estimation in sensor arrays with calibration errors, demonstrating superior performance through simulations.

## Contribution

It introduces a novel convex optimization model that jointly exploits low-rank and block-sparsity structures for off-grid DoA estimation with array calibration errors.

## Key findings

- Outperforms existing methods in simulations
- Achieves near CRB performance
- Effectively handles calibration errors and off-grid effects

## Abstract

This letter addresses the estimation of directions-of-arrival (DoA) by a sensor array using a sparse model in the presence of array calibration errors and off-grid directions. The received signal utilizes previously used models for unknown errors in calibration and structured linear representation of the off-grid effect. A convex optimization problem is formulated with an objective function to promote two-layer joint block-sparsity with its second-order cone programming (SOCP) representation. The performance of the proposed method is demonstrated by numerical simulations and compared with the Cramer-Rao Bound (CRB), and several previously proposed methods.