Performance lower bound evaluation of frequency acquisition filters

A discrete-time nonlinear filtering problem is considered: the estimation of the frequency of a carrier in the presence of broad-band noise. A new filtering lower bound, based on rate distortion theory and the Bucy representation theorem, is used to evaluate the acquisition performance of two candidate filter designs. One filter design is a conventional spectral tracker based on the Fast Fourier Transform (FFT), while the other is an application of the Extended Kalman Filter (EKF). Performance is evaluated for a variety of signal-to-noise ratios (SNR) and acquisition bandwidths. Monte Carlo simulation results indicate that 1) the new lower bound is considerably tighter than the Cramér-Rao bound at low SNR; 2) the EKF is nearly optimal for narrow acquisition bandwidths, almost achieving the performance lower bounds; 3) for larger acquisition bandwidths, the performance of the EKF deteriorates significantly relative to the lower bounds.