Cramér-Rao Bounds and Resolution Benefits of Sparse Arrays in Measurement-Dependent SNR Regimes

This paper derives new non-asymptotic characterization of the Cramér-Rao Bound (CRB) of any sparse array as a function of the angular separation between two far-field narrowband sources in certain regimes characterized by a low Signal-to-Noise Ratio (SNR). The primary contribution is the derivation of matching upper and lower bounds on the CRB in a certain measurement-dependent SNR (MD-SNR) regime, where one can zoom into progressively lower SNR as the number of sensors increases. This tight characterization helps to establish that sparse arrays such as nested and coprime arrays provably exhibit lower CRB compared to Uniform Linear Arrays (ULAs) in the specified SNR regime.