Statistical resolution limit based on Cramer-Rao bound

An extension study of Smith´s result is proposed. An exact Cramer-Rao bound expression of frequency difference is deduced. The Cramer-Rao bound expression is analyzed asymptotically for the closely spaced targets case. A general close form of statistical resolution limit (SRL) is provided based on the asymptotic results. The SRL proposed is a function of power ratio, phase difference, and SNR. It is found that the power ratio and phase difference affect the relationship between SRL and SNR severely in further examination of the effect of the power ratio and phase difference. Maximum likelihood Estimation (MLE) simulation results shows that the variance of the MLE is close to the CRB in the resolvable area, but departs the CRB at the predicted resolution limit point. Simulation results proved that the statistical resolution limit proposed is correct and accurate.