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On the Angular Resolution Limit Uncertainty

The Angular Resolution Limit (ARL), denoted by 6, is a key statistical quantity to measure our ability to resolve two closely-spaced narrowband far-field complex sources. In the literature, the ARL, denoted by δ0, is systematically assumed to be perfectly known for mathematical convenience. In this work, our knowledge on the ARL is supposed to be only partial, meaning that δ ~N (δ0, σδ2). The degree of uncertainty is quantified by the ratio ξ = δ20/σ2δ. Based on the Chernoff Upper Bound (CUB) on the minimal error probability, we show that the CUB is highly dependent on the degree of uncertainty, ξ. As by-product, the optimal s-value for which the CUB is the tightest upper bound is analytically studied.