  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.
