Gridless One-Bit Direction-of-Arrival Estimation Via Atomic Norm Denoising

Abstract

In this letter, a gridless one-bit direction-of-arrival (DOA) estimation approach with one-snapshot is proposed to be robust against the off-grid errors and sign inconsistency because of the one-bit measurements corrupted by additive noise. Different with the existing off-grid DOA estimators, an atomic norm minimization is considered to mitigate the grid mismatch with atoms instead of pre-divided discretized dictionary. Then, the sign inconsistency of one-bit measurements is solved by introducing a linear loss function. The resulting optimization problem is convex and can be equivalent to a semidefinite programming (SDP) problem, which, however, is computational demanding. Therefore, alternating direction multiplier method (ADMM) is employed to speed up the implementation. To avoid the spectrum searching, an effective dual polynomial method is developed with closed-form solution for DOA estimation. Meanwhile, the proposed method does not require <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a~prior$ </tex-math></inline-formula> information of the number of targets. Simulation results demonstrate the superiority and effectiveness of the proposed method.