Adaptive recovery of a Doppler shifted mobile communications signal using the RLS algorithm

This paper studies the ability of the exponentially weighted RLS algorithm to track a Doppler shifted BPSK communications signal. This is modeled as a chirped AR1 process in Gaussian white noise. Expressions for the optimum Wiener filter, noise misadjustment, and lag misadjustment are shown. It is shown that as in the chirped sinusoid case the error can be written in terms of the forgetting rate β=1-λ of the RLS algorithm; the noise misadjustment is of the order β and lag misadjustment of order 1/β². However, as the bandwidth of the signal increases the relative lag misadjustment is shown to decrease