On Capacity of the Writing onto Fast Fading Dirt Channel

TL;DR

This paper analyzes the capacity of the Writing onto Fast Fading Dirt channel, revealing how fading impacts the effectiveness of transmitter knowledge and providing approximate capacity characterizations for various fading distributions.

Contribution

It introduces approximate capacity characterizations for the WFFD channel under different fading distributions, highlighting the impact of fading on channel capacity and transmitter knowledge utility.

Findings

Capacity approximates AWGN capacity scaled by fading probability.

Fading can significantly reduce the benefit of transmitter channel state knowledge.

Certain fading distributions allow treating fading as additional noise without much capacity loss.

Abstract

The "Writing onto Fast Fading Dirt" (WFFD) channel is investigated to study the effects of partial channel knowledge on the capacity of the "writing on dirty paper" channel. The WFFD channel is the Gel'fand-Pinsker channel in which the output is obtained as the sum of the input, white Gaussian noise and a fading-times-state term. The fading-times-state term is equal to the element-wise product of the channel state sequence, known only at the transmitter, and a fast fading process, known only at the receiver. We consider the case of Gaussian distributed channel states and derive an approximate characterization of capacity for different classes of fading distributions, both continuous and discrete. In particular, we prove that if the fading distribution concentrates in a sufficiently small interval, then capacity is approximately equal to the AWGN capacity times the probability of this interval. We also show that there exists a class of fading distributions for which having the transmitter treat the fading-times-state term as additional noise closely approaches capacity. Although a closed-form expression of the capacity of the general WFFD channel remains unknown, our results show that the presence of fading can severely reduce the usefulness of channel state knowledge at the transmitter.