Detection and Estimation of Multiple DoA Targets with Single Snapshot Measurements

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 $\widehat{\tau }$ is estimated, the corresponding DoAs can be estimated by solving the lasso with regularization parameter set to $\widehat{\tau }$.