Nonasymptotic Analysis of Direct-Augmentation ESPRIT for Localization of More Sources Than Sensors Using Sparse Arrays

Direction augmentation (DA), followed by a subspace method such as MUSIC or ESPRIT, is a successful approach that enables localization of more uncorrelated sources than sensors with a proper sparse linear array. In this paper, we carry out a nonasymptotic performance analysis of DA-ESPRIT in the practical scenario with finitely many snapshots. We show that more uncorrelated sources than sensors are guaranteed, with overwhelming probability, to be localized using DA-ESPRIT if the number of snapshots is greater than an explicit, problem-dependent threshold. Our result does not require a fixed source separation condition, which makes it unique among existing results. Numerical results corroborating our analysis are provided.