Direction of Arrival Estimation for Coherently Distributed Sources With One-Bit Measurements

Abstract

High-precision (HP) analog-to-digital (A/D) converters incur high hardware cost and power consumption, while conventional point-source-based direction of arrival (DOA) estimation methods may suffer from model mismatch when the source energy is spatially distributed over a finite angular region. To address these challenges, this article investigates one-bit (OB) angular parameter estimation for coherently distributed (CD) sources and proposes a unified maximum likelihood (ML) estimation framework for jointly estimating the nominal angles and angular spreads from OB measurements. First, the OB likelihood function for CD sources is formulated, which directly captures the statistical structure of OB quantized observations but leads to a highly nonlinear optimization problem with respect to the angular parameters. To solve this problem efficiently, a coarse-to-fine solver is developed. Specifically, a sparse ML (SML) initialization stage is first performed over a discretized angular domain to obtain coarse estimates, followed by Gauss–Newton refinement in the continuous parameter domain. This two-stage design effectively alleviates grid mismatch and improves estimation accuracy. In addition, the OB Cramér–Rao bound (CRB) is derived as a theoretical performance benchmark for the considered estimation problem. Extensive experimental results validate the effectiveness of the proposed method and demonstrate its potential for power-efficient sensing applications such as automotive radar and large-scale antenna arrays.