Title: Detection Estimation and Grid matching of Multiple Targets with Single Snapshot Measurements,
Abstract: In this work, we explore the problems of detecting the number of narrow-band,
far-field targets and estimating their corresponding directions from single
snapshot measurements. The principles of sparse signal recovery (SSR) are used
for the single snapshot 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. However, the SSR framework for DoA estimation gives
rise to the grid mismatch problem, when the unknown targets (sources) are not
matched with the estimation grid chosen for the construction of the array
steering matrix at the receiver. The block sparse recovery framework is known
to mitigate the grid mismatch problem by jointly estimating the targets and
their corresponding offsets from the estimation grid using the group lasso
estimator. The corresponding detection problem reduces to estimating the
optimal regularization parameter ($\tau$) of the lasso (in case of perfect
grid-matching) or group-lasso estimation problem for achieving the required
probability of correct detection ($P_c$). We propose asymptotic and finite
sample 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 estimation and grid matching of the DoAs can be performed by
solving the lasso or group-lasso problem at $\hat{\tau}$