Gaussian Fading is the Worst Fading

The capacity of pear-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 given spectral distribution function whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log