On the Performance of One-Bit DoA Estimation via Sparse Linear Arrays

TL;DR

This paper explores the limits and proposes a new algorithm for direction of arrival estimation using one-bit measurements from sparse linear arrays, demonstrating improved performance over existing methods through theoretical analysis and simulations.

Contribution

It establishes identifiability conditions, derives a performance benchmark via a pessimistic CRB, and introduces a novel DoA estimation algorithm for one-bit SLA data.

Findings

The proposed algorithm outperforms existing methods in simulations.

A new performance benchmark for one-bit DoA estimation is established.

Identifiability conditions are linked to unquantized measurement cases.

Abstract

Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable attention in array processing thanks to their capability to provide enhanced degrees of freedom in resolving uncorrelated source signals. Additionally, deployment of one-bit Analog-to-Digital Converters (ADCs) has emerged as an important topic in array processing, as it offers both a low-cost and a low-complexity implementation. In this paper, we study the problem of DoA estimation from one-bit measurements received by an SLA. Specifically, we first investigate the identifiability conditions for the DoA estimation problem from one-bit SLA data and establish an equivalency with the case when DoAs are estimated from infinite-bit unquantized measurements. Towards determining the performance limits of DoA estimation from one-bit quantized data, we derive a pessimistic approximation of the corresponding Cram\'{e}r-Rao Bound (CRB). This pessimistic CRB is then used as a benchmark for assessing the performance of one-bit DoA estimators. We also propose a new algorithm for estimating DoAs from one-bit quantized data. We investigate the analytical performance of the proposed method through deriving a closed-form expression for the covariance matrix of the asymptotic distribution of the DoA estimation errors and show that it outperforms the existing algorithms in the literature. Numerical simulations are provided to validate the analytical derivations and corroborate the resulting performance improvement.