Angular resolution limit for deterministic correlated sources

TL;DR

This paper derives an explicit analytical expression for the angular resolution limit in direction-of-arrival estimation, considering correlated sources, and confirms its validity through numerical analysis.

Contribution

It provides the first explicit formula for the ARL for correlated sources and derives closed-form Cramér-Rao bounds, enhancing understanding of resolution limits.

Findings

Explicit ARL expression for correlated sources

Closed-form Cramér-Rao bounds derived

Impact of source correlation on resolution limit analyzed

Abstract

This paper is devoted to the analysis of the angular resolution limit (ARL), an important performance measure in the directions-of-arrival estimation theory. The main fruit of our endeavor takes the form of an explicit, analytical expression of this resolution limit, w.r.t. the angular parameters of interest between two closely spaced point sources in the far-field region. As by-products, closed-form expressions of the Cram\'er-Rao bound have been derived. Finally, with the aid of numerical tools, we confirm the validity of our derivation and provide a detailed discussion on several enlightening properties of the ARL revealed by our expression, with an emphasis on the impact of the signal correlation.