Detection and Estimation of Multiple DoA Targets with Single Snapshot Measurements

TL;DR

This paper presents a novel approach using sparse signal recovery and lasso optimization to detect the number of far-field targets and estimate their directions of arrival from a single snapshot, with finite sample and asymptotic tests for detection.

Contribution

It introduces new test statistics for source detection and a method to estimate the optimal regularization parameter for accurate DoA estimation from single snapshot data.

Findings

Effective detection of multiple sources at moderate to high SNR.

Accurate DoA estimation using the proposed lasso-based method.

New statistical tests improve detection probability control.

Abstract

In this paper, we explore the problems of detecting the number of narrow-band, far-field targets and estimating their corresponding directions of arrivals (DoAs) from single snapshot measurements. We use the principles of sparse signal recovery (SSR) for detection and estimation of multiple targets. In the SSR framework, the DoA estimation problem is grid based and can be posed as the lasso optimization problem. The corresponding DoA detection problem reduces to estimating the optimal regularization parameter ($\tau$) of the lasso problem for achieving the required probability of correct detection ($P_c$). We propose finite sample and asymptotic test statistics for detecting the number of sources with the required $P_c$ at moderate to high signal to noise ratios. Once the number of sources are detected, or equivalently the optimal $\hat{\tau}$ is estimated, the corresponding DoAs can be estimated by solving the lasso with regularization parameter set to $\hat{\tau}$.