Bandwidth occupancy of non-coherent wideband fading channels

Peaky and non-peaky signaling schemes have long been considered species apart in non-coherent wideband fading channels, as the first approaches asymptotically the linear-in-power capacity of a wideband AWGN channel with the same SNR, whereas the second reaches a nearly power-limited peak rate at some finite critical bandwidth and then falls to zero as bandwidth grows to infinity. In this paper it is shown that this distinction is in fact an artifact of the limited attention paid in the past to the product between the bandwidth and the fraction of time it is in use. This fundamental quantity, that is termed bandwidth occupancy, measures average bandwidth usage over time. The two types of signaling in the literature are harmonized to show that, for any type of signals, there is a fundamental limit - a critical bandwidth occupancy. All signaling schemes with the same bandwidth occupancy approach the capacity of wideband AWGN channels with the same asymptotic behavior as the bandwidth occupancy grows to its critical value. For a bandwidth occupancy above the critical, rate decreases to zero as the bandwidth occupancy goes to infinity.