Smoothed optimization for sparse off-grid directions-of-arrival estimation

Abstract

This paper is concerned with the development of a computationally efficient optimization algorithm for off-grid direction finding using a sparse observation model. The optimization problem can be formulated as one smooth plus two nonsmooth functions. We propose two accelerated smoothing proximal gradient algorithms. The Nesterov smoothing methodology is utilized to reformulate nonsmooth functions into smooth ones, and the accelerated proximal gradient algorithm is adopted to solve the smoothed optimization problem. The computational efficiency and efficacy of the proposed algorithms are demonstrated numerically.