A statistical theory for the measurement and estimation of Rayleigh fading channel

TL;DR

This paper develops a statistical framework for measuring and estimating Rayleigh fading channels in wireless communications, identifying optimal estimators and measurement requirements for accurate parameter estimation.

Contribution

It introduces a complete statistical theory for Rayleigh channel estimation, including the derivation of the maximum likelihood estimator and measurement strategies.

Findings

Maximum likelihood estimator is sufficient and complete.

ML estimator achieves the Cramer-Rao lower bound.

Two testing signals of different strength improve estimation accuracy.

Abstract

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.