  In this paper, we examine the effects of imperfect channel estimation at the
receiver and no channel knowledge at the transmitter on the capacity of the
fading Costa's channel with channel state information non-causally known at the
transmitter. We derive the optimal Dirty-paper coding (DPC) scheme and its
corresponding achievable rates with the assumption of Gaussian inputs. Our
results, for uncorrelated Rayleigh fading, provide intuitive insights on the
impact of the channel estimate and the channel characteristics (e.g. SNR,
fading process, channel training) on the achievable rates. These are useful in
practical scenarios of multiuser wireless communications (e.g. Broadcast
Channels) and information embedding applications (e.g. robust watermarking). We
also studied optimal training design adapted to each application. We provide
numerical results for a single-user fading Costa's channel with
maximum-likehood (ML) channel estimation. These illustrate an interesting
practical trade-off between the amount of training and its impact to the
interference cancellation performance using DPC scheme.
