MUSIC With Capped Frobenius Norm: Efficient Robust Direction-of-Arrival Estimator

Direction-of-arrival (DOA) estimation is a frequent need in the field of array signal processing. While many conventional algorithms achieve excellent performance in Gaussian noise, they are vulnerable to impulsive noise. Although several approaches have been proposed for robust DOA estimation against gross errors, their disadvantages might limit the applicability in practice. For instance, the maximum likelihood (ML) estimation-based algorithms involve high computational complexity, and & ell;(p)-multiple signal classification with p is an element of (1, 2) requires tweaking p for handling different noises. In this work, we devise a capped Frobenius norm (CFN) for complex-valued data inspired by the truncated least squares loss function. Since the cap threshold is the boundary to differentiate the normal and outlier-contaminated entries, we propose a normalized median absolute deviation-based strategy for its automatic determination. In doing so, the accurate estimation is achieved in both Gaussian and impulsive noise. As the CFN is nonconvex and nonsmooth, we exploit the half-quadratic theory to simplify the resultant problem into a tractable optimization, which is then handled by alternating convex optimization with computationally efficient closed-form solution. Furthermore, its convergence behaviors are analyzed, i.e., the objective function value is convergent, and there exists a subsequence in the variable sequence converging to a critical point. Simulation results exhibit its superior performance over several state-of-the-art algorithms in terms of estimation accuracy and resolution capability. MATLAB code is available at https://github.com/Li-X-P/Code-Robust-DOA-Estimator.