The impact of phase fading on the dirty paper coding channel

Abstract

The impact of phase fading on the classical Costa's 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.

On the capacity of the dirty paper channel with fast fading and discrete channel states

“…VI. The conditions in (7) indeed reflect the interpretation in Fig. 4: this term is the smallest distance between two contiguous regions in X + cAS when X is restricted to be an integer number in ⌈ √ P ⌉ .…”

“…Here in is shown that the rate loss from full state pre-cancellation is vanishing, since state and input still combine in a predictable manner. In [7], we derived the approximate capacity for the WDP channel in which the state is multiplied by uniform binomial fading by further develop bounding techniques originally developed in [8]. The results in [7] are further extended in [9] to include more general fading distribution, although restricted to the case of discrete support.…”

“…In [7], we derived the approximate capacity for the WDP channel in which the state is multiplied by uniform binomial fading by further develop bounding techniques originally developed in [8]. The results in [7] are further extended in [9] to include more general fading distribution, although restricted to the case of discrete support. Contributions: We investigate the capacity of the "Writing of Fast Fading Dirt" (WFFD) channel, a variation of the WDP channel in which the state sequence is multiplied by a fast fading process.…”

On Capacity of the Writing Onto Fast Fading Dirt Channel

“…In [7], the first inner and outer bounds to capacity are obtained while [8] studies the outage probability for this model. In [9], we show the approximate capacity of this model for some classes of the phase fading. Achievable rates under Gaussian signaling are derived in [10] for the case of Gaussian distributed fast fading.…”

On the Capacity of the Carbon Copy onto Dirty Paper Channel

“…In [14] algorithms are also proposed to determine the optimal linear pre-coding strategies which are shown to outperform Costa's linear assignment in the multiple antenna setting. In [15], we derive the capacity to within a constant gap for the channel in which the fading only takes two possible values: this result is extended in [16] to include more general fading distribution and to consider the case in which the fading sequence is not known either at the transmitter or at the receiver.…”