The impact of phase fading on the dirty paper coding channel

The impact of phase fading and side information on the classic Costa's dirty paper coding channel is studied. A variation of this model is considered in which the channel state is affected by a phase fading sequence which is known at the receiver but not at the transmitter. Although the capacity of this channel has been established, it is expressed as the solution of the maximization which cannot be easily determined. To circumvent such difficulty, we derive alternative inner and outer bounds to capacity and determine a regime in which the two expressions are to within a finite distance. We consider two distributions of the phase fading process: circular binomial and circular uniform. For circular binomial fading we show that binning with Gaussian signaling approaches capacity, as in the channel without phase fading. When fading is circular uniform, instead, binning with Gaussian signaling is no longer effective and novel interference avoidance strategies are developed for this case.