On the asymptotic resolvability of two point sources in known subspace interference using a GLRT-based framework

Abstract

The asymptotic statistical resolution limit (SRL), denoted by δ, characterizing the minimal separation to resolve two closely spaced far-field narrowband sources for a large number of observations, among a total number of M≥2, impinging on a linear array is derived. The two sources of interest (SOI) are corrupted by (1) the interference resulting from the M−2 remaining sources and by (2) a broadband noise. Toward this end, a hypothesis test formulation is conducted. Depending on the a priori knowledge on the SOI, on the interfering sources and on the noise variance, the (constrained) maximum likelihood estimators (MLEs) of the SRL subject to δ∈R and/or in the context of the matched subspace detector theory are derived. Finally, we show that the SRL which is the minimum separation that allows a correct resolvability for given probabilities of false alarm and of detection can always be linked to a particular form of the Cramér–Rao bound (CRB), called the interference CRB (I-CRB), which takes into account the M−2 interfering sources. As a by product, we give the theoretical expression of the minimum signal-to-interference-plus-noise ratio (SINR) required to resolve two closely spaced sources for several typical scenarios.