One-Bit DoA Estimation for Deterministic Signals Based on $ \ell _{2,1}$-Norm Minimization

Abstract

One-bit direction-of-arrival (DoA) estimation has drawn considerable attention in recent years with the increasing demand for low power consumption and high sampling rate. In this work, the 1-bit DoA estimation for deterministic signals is addressed from the viewpoint of sparse matrix recovery. First, using maximum likelihood (ML) and compressive sensing techniques, 1-bit DoA estimation is formulated as an ML-based row sparse matrix optimization in terms of least-absolute-shrinkage-and-selection-operator form with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2,1}$</tex-math></inline-formula> regularization. After that, by complex-valued conjugate gradient and steepest descent operations, an iterative closed-form solution in the form of a row-sparse matrix is expected to be obtained. At last, the estimates of source numbers and DoAs are simultaneously completed by making sense of the structure of the row-sparse matrix. Numerical results showcase that the proposed algorithm outperforms the state-of-the-art approaches in terms of estimation accuracy.