Gaussian Fading Is the Worst Fading

TL;DR

This paper demonstrates that Gaussian fading channels are the worst in terms of capacity pre-log among stationary ergodic processes with the same spectral distribution, highlighting the unique impact of Gaussian fading on channel capacity at high SNR.

Contribution

It establishes that Gaussian fading minimizes the capacity pre-log among all stationary ergodic fading processes with the same spectral distribution, extending to MISO channels.

Findings

Gaussian fading yields the smallest capacity pre-log among processes with the same spectral distribution.

Fading processes with a mass point at zero can have an even smaller pre-log than Gaussian.

Results extend to multiple-input single-output (MISO) fading channels with memory.

Abstract

The capacity of peak-power limited, single-antenna, noncoherent, 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 & ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary & ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of our results to multiple-input single-output fading channels with memory is also presented.