The Radio Signal Phase Estimate Efficiency under the Fast Fades

Our study is concerned with the narrow-band radio signals phase estimation when these signals are deformed by fades and observed against white noise. Unlike the approach presented in the popular studies, we presume these fades to be fast, i.e. the fades correlation time is much less than the signal duration. We also consider the amplitude and the phase of the fading signal component as having Rayleigh and uniform probability distributions, correspondingly, that fits the case of the Rice fades. We find the analytical expressions for the probability density, as well as for the bias (systematic error) and the variance (error mean square) of the phase estimation in the presence of fades. We also analyze the influence of the fades depth on the efficiency of the radio signal phase measurement.