Statistical resolution limit of two closely-spaced signal sources based on the RAO test

Abstract

Statistical Resolution Limit (SRL) is defined as the minimal separation to resolve two closely spaced signals. It is a significant metric to quantify performance in parameter estimation problems. For SRL analysis, since the method on the basis of the Generalized Likelihood Ratio test (GLRT) has problem of large amount of calculation, we put forward a RAO test approach. The RAO test only needs to estimate the maximum likelihood estimation (MLE) of the unknown parameters under the hypothesis H 0 , which effectively simplifies the derivation process. In this paper, the detection statistics of the proposed RAO test and the GLRT for the analysis of the SRL in the case of known and unknown noise variance are derived respectively. Simulations are carried out to compare the detection performance of the two methods. The simulation results verify the validity of the proposed method.