COFFEE: Covariance Fitting and Focusing for Wideband Direction-of-Arrival Estimation

This paper focuses on the problem of direction-of-arrival (DOA) estimation for multiple wideband source signals using a uniform linear array under the frequency bin model. We propose a covariance fitting and focusing-based estimation method, abbreviated as COFFEE. In particular, we develop a covariance fitting criterion for wideband DOA estimation and formulate a corresponding bilevel optimization problem by introducing focusing operations on covariance matrices. The bilevel optimization problem comprises an upper-level problem for covariance fitting and a lower-level one for the focusing matrices. We show that the upper-level problem can be cast as a rank-constrained semidefinite programming (SDP) and the lower-level problem has closed-form solutions. To solve the rank-constrained SDP, we develop an alternating direction method of multipliers algorithm, in which both subproblems are solved in closed form. We further propose an alternating iterative algorithm to solve the overall bilevel optimization problem. Extensive numerical results demonstrate that COFFEE outperforms state-of-the-art algorithms in terms of accuracy and resolution.