The Impact of Phase Fading on the Dirty Paper Channel

The impact of phase fading on the classical Costa’sdirty paper coding channel is studied. We consider a variationof this channel model in which the amplitude of the interferencesequence is known at the transmitter while its phase is known atthe receiver. Although the capacity of this channel has alreadybeen established, it is expressed using an auxiliary randomvariable and as the solution of a maximization problem. Tocircumvent the difficulty evaluating capacity, we derive alterna-tive inner and outer bounds and show that the two expressionsare to within a finite distance. This provide an approximatecharacterization of the capacity which depends only on thechannel parameters. We consider, in particular, two distributionsof the phase fading: circular binomial and circular uniform. Thefirst distribution models the scenario in which the transmitter hasa minimal uncertainty over the phase of the interference whilethe second distribution models complete uncertainty. For circularbinomial fading, we show that binning with Gaussian signalingstill approaches capacity, as in the channel without phase fading.In the case of circular uniform fading, instead, binning withGaussian signaling is no longer effective and novel interferenceavoidance strategies are developed to approach capacity.