Direction-of-Arrival Estimation for Constant Modulus Signals via Convex Optimization

Several man-made signals in communications and array processing, e.g., phase-modulated and frequency-modulated signals, exhibit the constant modulus (CM) property. This paper is concerned about the problem of direction-of-arrival (DOA) estimation for CM source signals using linear arrays. Existing methods either rely on nonconvex optimization suffering from convergence or optimality issues or cannot fully use the CM property of signals or the array manifold due to great challenges brought by the highly nonconvex CM constraints. In this paper, we propose a convex optimization approach for CM DOA estimation based on atomic norm minimization. Our main contributions are summarized below. 1) To use the CM property, we define a CM atomic norm and formulate the CM DOA estimation problem as an ANM problem. 2) We propose a semidefinite programming, by introducing a series of positive-semidefinite structured matrices, to characterize the CM atomic norm and enable computations of the CM ANM problem. 3) Simulations are carried out that validate the advantageous performance of the proposed approach.