Detection, estimation and grid matching of multiple targets with single snapshot measurements

We explore the problems of detecting the number of targets and estimating their corresponding directions of arrivals (DoAs) from single snapshot measurements using the grid based DoA signal models. The single snapshot DoA estimation can be performed using sparse signal recovery (SSR) or the block sparse recovery (BSR) frameworks for the on-grid and off-grid DoA models respectively. In these frameworks, the DoA estimation problem is posed as the solution to the lasso and group lasso optimization problems respectively. The problem of finding the number of targets reduces to estimating the optimum regularization parameter (τ) of the lasso or the group-lasso for achieving the required probability of correct detection (Pc). In this work, we propose finite-sample test statistics for detecting the number of sources with the required Pc at moderate to high SNRs. Once the number of sources are detected, or equivalently the optimal τˆ is estimated, the corresponding estimation and grid matching of the DoAs can be performed by solving lasso or group-lasso problem using the regularization parameter τˆ.