Gaussian Fading Is the Worst Fading

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.

💡 Research Summary

The paper investigates the high‑SNR behavior of peak‑power‑limited, single‑antenna, noncoherent flat‑fading channels with memory. The focus is on the capacity pre‑log, defined as the limiting ratio of channel capacity to log SNR as SNR → ∞. For Gaussian fading, the pre‑log is known to equal the Lebesgue measure of the set of frequencies where the derivative of the spectral distribution function F(λ) vanishes. The authors ask whether this value is the smallest possible among all stationary and ergodic fading processes that share the same spectral distribution.

The main result (Theorem 1) states that, provided the fading law has no atom at zero (i.e., Pr