Measurement Complexity of Rayleigh Fading Channels

Rayleigh fading is a widely used channel model in wireless communications. The mean channel power is of practical importance in channel access, power control, handoff, modeling, and coverage analysis of wireless systems. A fundamental problem naturally arises: How many measurements are sufficient to estimate these parameters with the prescribed margin of error and confidence level? We first study the noise-free case in which only the second moment of the Rayleigh random variable is subject to measurement and estimation. It is demonstrated that the measurement sample size is roughly inversely proportional to the square of the margin of relative error and is linear with respect to the logarithm of the inverse of the gap between the confidence level and one. A closed-form formula is also obtained for the interval estimate of the second moment that is shown to be asymptotically tight. These sample complexity results are extended to the noisy case for interval estimation of the path loss and noise power. Our study shows that a typical margin of relative error can be achieved with near certainty and modest sample size.