On Capacity of the Writing onto Fast Fading Dirt Channel

The Writing onto Fast Fading Dirt (WFFD) channel is investigated to study the effect of partial channel knowledge on the performance of interference pre-cancellation. The WFFD channel is the Gel'fand-Pinsker channel in which the channel output is the sum of the channel input, white Gaussian noise, and a fading-times-state term. The fading-times-state term is obtained as the 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 such 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.