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.
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Contributor : Alexandre Renaux <>
Submitted on : Tuesday, January 8, 2013 - 3:16:16 PM
Last modification on : Wednesday, November 13, 2019 - 10:18:04 PM

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Mohammed Nabil El Korso, Remy Boyer, Alexandre Renaux, Sylvie Marcos. On the asymptotic resolvability of two point sources in known subspace interference using a GLRT-based framework. Signal Processing, Elsevier, 2012, 92 (10), pp.2471-2483. ⟨10.1016/j.sigpro.2012.03.011⟩. ⟨hal-00771379⟩

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