Cramér-Rao bound and statistical resolution limit investigation for near-field source localization

In this paper, we investigate the performance analysis for near-field source localization in terms of the mean square error and resolvability. We first derive and analyze non-matrix, closed-form expressions of the deterministic Cramér-Rao bound for two closely spaced, time-varying near-field sources in the context of linear arrays. Numerical simulations confirm the validity of the obtained expressions. Using these expressions and based on Smith's criterion, we discuss the behavior of the statistical resolution limit with respect to some features of interest, namely, the correlation factor, the central frequency, the minimum resolution limit boundary and the array geometry. Finally, to avoid the complexity of the optimal geometry design procedure, we propose a fast, nearly optimal, array design scheme to enhance the capacity of resolvability under given constraints (e.g., number of sensors and array aperture).