Robust Reweighted ℓ2,1-Norm Based Approach for DOA Estimation in MIMO Radar Under Array Sensor Failures

Abstract

To alleviate the direction of arrival (DOA) estimation performance degradation under array sensor failures in multiple input multiple output (MIMO) radar, joint DOA estimation and missing data recovery is dealt with by a reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> -norm framework. Firstly, we employ a technique based on singular value decomposition (SVD) to reduce the dimension of the array data matrix and the sensitivity to observation noise. Then, a novel reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> -norm minimization framework is introduced to improve the robustness against model mismatch caused by sensor failures, which incorporates the recovery of the complete array data matrix into the sparse reconstruction and constructs the weight matrix for reweighting the mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> -norm minimization. Thereafter, the alternative direction method of multipliers (ADMM) under the augmented Lagrange multiplier (ALM) framework is applied to solve this multivariable optimization problem with multiple constraints, in which the sparse solution is iteratively obtained along with the recovery of the complete array data matrix. Finally, the estimation of DOAs can be achieved by finding the non-zero rows in the reconstructed sparse matrix. Simulations demonstrate that the proposed method has better estimation performance than the existing methods for handling array sensor failures and exhibits robustness in the face of a wide range of faulty sensor number.