Statistical Estimation of Mean Signal Strength in a Rayleigh-Fading Environment

A commonly used model for signal fading in many types of communication channels is that the amplitude of the received signal at a given time is a Rayleigh-distributed random variable. In this paper we show how classical statistical techniques may be applied to the problem of estimating the Rayleigh distribution parameter (i.e., the mean), given samples from the distribution. In particular, we first consider the problem of estimating the population mean, given a sequence of independent samples. We derive an unbiased maximum-likelihood estimator. We show that this estimator is unique, and since it is based on a sufficient statistic, it is therefore "best" in the Blackwell-Rao sense of minimizing expected loss. Using this estimator, we then develop confidence intervals whose length can be used as a guide in selecting the required sample size. We then consider the same estimation problem when the signal samples are obtained from the output of a logarithmic receiver. We derive an interval estimator which does not require taking the antilogs of the log samples, and which is not appreciably worse than the "best" estimator.