Gaussian Fading is the Worst Fading

TL;DR

This paper demonstrates that among stationary and ergodic fading processes with a given spectral distribution, Gaussian fading results in the lowest capacity pre-log at high SNR, highlighting its worst-case nature.

Contribution

It establishes that Gaussian fading is the worst-case scenario for capacity pre-log among all processes with the same spectral distribution and no mass point at zero.

Findings

Gaussian fading yields the smallest capacity pre-log.

The result applies to all stationary, ergodic fading processes with the same spectral distribution.

Gaussian fading is identified as the worst-case fading process for capacity growth.

Abstract

The capacity of peak-power limited, single-antenna, non-coherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log.