The Impact of Phase Fading on the Dirty Paper Channel
The impact of phase fading on the classical Costa dirty paper coding channel is studied. We consider a variation of this channel model in which the amplitude of the interference sequence is known at the transmitter while its phase is known at the receiver. Although the capacity of this channel has already been established, it is expressed using an auxiliary random variable and as the solution of a maximization problem. To circumvent the difficulty evaluating capacity, we derive alternative inner and outer bounds and show that the two expressions are to within a finite distance. This provide an approximate characterization of the capacity which depends only on the channel parameters. We consider, in particular, two distributions of the phase fading: circular binomial and circular uniform. The first distribution models the scenario in which the transmitter has a minimal uncertainty over the phase of the interference while the second distribution models complete uncertainty. For circular binomial fading, we show that binning with Gaussian signaling still approaches capacity, as in the channel without phase fading. In the case of circular uniform fading, instead, binning with Gaussian signaling is no longer effective and novel interference avoidance strategies are developed to approach capacity.