  In non-coherent wideband fading channels where energy rather than spectrum is
the limiting resource, peaky and non-peaky signaling schemes have long been
considered species apart, as the first approaches asymptotically the capacity
of a wideband AWGN channel with the same average SNR, whereas the second
reaches a 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, called bandwidth occupancy, measures average bandwidth usage over
time. For all signaling schemes with the same bandwidth occupancy, achievable
rates approach to the wideband AWGN capacity within the same gap as the
bandwidth occupancy approaches its critical value, and decrease to zero as the
occupancy goes to infinity. This unified analysis produces quantitative
closed-form expressions for the ideal bandwidth occupancy, recovers the
existing capacity results for (non-)peaky signaling schemes, and unveils a
trade-off between the accuracy of approximating capacity with a generalized
Taylor polynomial and the accuracy with which the optimal bandwidth occupancy
can be bounded.
