  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.
