The Barankin bound and threshold behavior in frequency estimation

This article presents the Barankin (1949) bound as a fundamental statistical tool. For the understanding of the threshold effect associated with the estimation of the frequency of a sinusoid in additive white Gaussian noise. It is shown that the threshold effect takes hold whenever the Barankin bound departs significantly from the Cramer-Rao bound. In terms of the signal-to-noise ratio (SNR) and the data length T, the quantity SNR×T/ln T is shown to be a good indicator for deciding whether the SNR is above threshold or not