Noncoherent Capacity of Underspread Fading Channels

Abstract

We derive bounds on the noncoherent capacity of wide-sense stationary uncorrelated scattering (WSSUS) channels that are selective both in time and frequency, and are underspread, i.e., the product of the channel's delay spread and Doppler spread is small. For input signals that are peak constrained in time and frequency, we obtain upper and lower bounds on capacity that are explicit in the channel's scattering function, are accurate for a large range of bandwidth and allow to coarsely identify the capacity-optimal bandwidth as a function of the peak power and the channel's scattering function. We also obtain a closed-form expression for the first-order Taylor series expansion of capacity in the limit of large bandwidth, and show that our bounds are tight in the wideband regime. For input signals that are peak constrained in time only (and, hence, allowed to be peaky in frequency), we provide upper and lower bounds on the infinite-bandwidth capacity and find cases when the bounds coincide and the infinite-bandwidth capacity is characterized exactly. Our lower bound is closely related to a result by Viterbi (1967).The analysis in this paper is based on a discrete-time discrete-frequency approximation of WSSUS time-and frequency-selective channels. This discretization explicitly takes into account the underspread property, which is satisfied by virtually all wireless communication channels.

Capacity of OFDM Systems Over Fading Underwater Acoustic Channels

“…• Information of the attenuation (7) and the ambient noise PSD (29) of the UW channels are available at both the transmitter and the receiver.…”

“…Exact calculation of the mutual information is infeasible due to the non-Gaussian distribution of [28]. Note that [29] (37) where , , and since the input has an i.i.d. distribution and every block of the channel coefficients has the same distribution.…”

“…Our model assumes the ICI variance (47) is negligible compared to that of the ambient noise (29). In the simulation, we limit the ICI variance to be at least 3 dB lower than .…”

Low SNR — When only decoding will do

“…With such "spread spectrum" like signals, Telatar and Tse [3] shows that the mutual information is inversely proportional to the number of resolvable paths. The critical importance of channel knowledge has been discussed in [3], [6], [8]- [10], where the loss of mutual information due to imperfectness of channel estimation is upper and lower bounded in [8], and a flashing signalling with unbounded amplitude is proposed in [9] for the case with imperfect channel knowledge. If the signal peakedness is constraint both in time and frequency, the noncoherent capacity bounds have been characterized in [10].…”

Impact of Feedback and Side-Information on the Asymptotic Capacity of Single-Input Multiple-Output Fading Channels With Memory

“…There are again many families of such noncoherent models, reaching from block-fading models (fading remains perfectly unchanged during a certain time, before it takes on a new, possibly dependent value [2]- [4]), to underspread fading channels (the fading process is wide-sense stationary and uncorrelated in the delay, and the product of the delay and Doppler spread is small [5] (and references therein)), and to stationary fading models [6]- [8].…”