Unified Capacity Limit of Non-Coherent Wideband Fading Channels
2015 (English)In: IEEE Transactions on Information Theory, ISSN 0018-9448Article in journal (Refereed) Submitted
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. 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 any type of signals, there is a fundamental limit---a critical bandwidth occupancy. All signaling schemes with the same bandwidth occupancy approach the linear-in-power capacity of wideband AWGN channels with the same asymptotic behavior as the bandwidth occupancy approaches its critical value. For a bandwidth occupancy above the critical value, rate decreases 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 accuracy and convergence when characterizing the maximal achievable rate.
Place, publisher, year, edition, pages
Wideband regime, peaky signals, non-peaky signals, bandwidth occupancy
IdentifiersURN: urn:nbn:se:kth:diva-159102OAI: oai:DiVA.org:kth-159102DiVA: diva2:782546
FunderSwedish Research Council
Submitted to IEEE Transactions on Information Theory, Jan. 2015.
The first two authors contributed equally to this work.2015-01-212015-01-212015-04-07Bibliographically approved