Analysis of SNR threshold for differential Doppler frequency measurement in digital receivers

There is a signal-to-noise ratio (SNR) below which the frequency of a coherent radar pulse train can be estimated no more accurately than the incoherent combination of the frequency estimates from the individual pulses. This SNR threshold applies to all frequency estimators, and defines a fundamental limit for passive location of radar emitters using differential Doppler. In this paper, an approximation to the estimation variance of any maximum likelihood (ML) type estimator is derived. The approximation is shown to be a very good predictor of the mean square error performance of ML estimators and the SNR at which the threshold occurs. A rigorous Barankin bound on any unbiased estimator of frequency is derived and compared to the above approximate estimation variance