Average Capacity Analysis of Continuous-Time Frequency-Selective Rayleigh Fading Channels with Correlated Scattering Using Majorization

TL;DR

This paper analyzes how correlated scattering affects the average capacity of frequency-selective Rayleigh fading channels, revealing conditions under which uncorrelated models are optimistic or pessimistic, using majorization theory.

Contribution

It introduces a majorization-based approach to compare average capacities under correlated and uncorrelated scattering, providing new insights into capacity bounds depending on channel knowledge and SNR.

Findings

Uncorrelated scattering maximizes average capacity with uninformed transmitter.

At low SNR, uncorrelated scattering provides a lower bound on capacity.

Theoretical results are illustrated with an Ornstein-Uhlenbeck process example.

Abstract

Correlated scattering occurs naturally in frequency-selective fading channels and its impact on the performance needs to be understood. In particular, we answer the question whether the uncorrelated scattering model leads to an optimistic or pessimistic estimation of the actual average capacity. In the paper, we use majorization for functions to show that the average rate with perfectly informed receiver is largest for uncorrelated scattering if the transmitter is uninformed. If the transmitter knows the channel statistics, it can exploit this knowledge. We show that for small SNR, the behavior is opposite, uncorrelated scattering leads to a lower bound on the average capacity. Finally, we provide an example of the theoretical results for an attenuated Ornstein-Uhlenbeck process including illustrations.