$\ell _{p}$ -MUSIC: Robust Direction-of-Arrival Estimator for Impulsive Noise Environments

A family of algorithms, named ℓ_p-MUSIC, for direction-of-arrival (DOA) estimation in impulsive noise is proposed. The ℓ_p-MUSIC estimator adopts the ℓ_p-norm (1 ≤ p 2) of the residual fitting error matrix as the objective function for subspace decomposition, rather than the Frobenius norm that is used in the conventional MUSIC method. Although the matrix ℓ_p-norm minimization based subspace decomposition will lead to a nonconvex optimization problem, two iterative algorithms are designed for achieving efficient solutions. The first algorithm is the iteratively reweighted singular value decomposition (IR-SVD), where the SVD of a reweighted data matrix is performed in each iteration. The second algorithm solves the nonconvex matrix ℓ_p-norm minimization by alternating convex optimization. Two complex-valued Newton´s methods with optimal step size in each iteration are devised to solve the resulting convex problem. The convergence of the iterative procedure is also proved. Numerical results verify that the ℓ_p-MUSIC methodology outperforms the standard MUSIC scheme and several existing outlier-resistant DOA estimation approaches in terms of resolution capability and estimation accuracy.