Direction-of-Arrival Estimation From a Mixture of Linear and Magnitude-Only Measurements

We address the issue of direction-of-arrival (DOA) estimation by utilizing both linear and magnitude-only (phaseless) measurements. We formulate the DOA estimation problem as an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{2,1}$</tex-math></inline-formula> norm minimization problem by exploiting joint sparsity among the multi-snapshot measurements. We propose an algorithm based on the alternating direction method of multipliers (ADMM) in which both subproblems admit closed-form solutions. The proposed approach does not require any reference signals. Simulation results demonstrate that combining outputs of conventional antennas with magnitude-only antennas significantly improves the accuracy of DOA estimation, and the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{2,1}$</tex-math></inline-formula>-ADMM algorithm outperforms the existing methods.