  In this paper, we propose a statistical theory on measurement and estimation
of Rayleigh fading channels in wireless communications and provide complete
solutions to the fundamental problems: What is the optimum estimator for the
statistical parameters associated with the Rayleigh fading channel, and how
many measurements are sufficient to estimate these parameters with the
prescribed margin of error and confidence level? Our proposed statistical
theory suggests that two testing signals of different strength be used. The
maximum likelihood (ML) estimator is obtained for estimation of the statistical
parameters of the Rayleigh fading channel that is both sufficient and complete
statistic. Moreover, the ML estimator is the minimum variance (MV) estimator
that in fact achieves the Cramer-Rao lower bound.
