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Unified Capacity Limit of Non-coherent Wideband Fading Channels

Author:
Felipe Gómez-Cuba  Jinfeng Du  Muriel Médard  Elza Erkip  


Journal:
IEEE Trans. Wireless Communications


Abstract(summary):

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, that is termed bandwidth occupancy, measures average bandwidth usage over time. As it turns out, a peaky signal that transmits in an infinite bandwidth but only for an infinitesimal fraction of the time may only have a small bandwidth occupancy, and so does a non-peaky scheme that limits itself to the critical bandwidth even though more spectrum is available, so as to not degrade rate. The two types of signaling in the literature are harmonized to show that, for all signaling schemes with the same bandwidth occupancy, rates converge to the wideband AWGN capacity with the same asymptotic behavior as the bandwidth occupancy approaches its critical value, and decrease to zero as the occupancy goes to infinity. This unified analysis not only recovers previous results on capacity bounds for (non-)peaky signaling schemes, but also reveals the fundamental tradeoff between precision and accuracy when characterizing the maximal achievable rate.


Page:
43-57


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