On Capacity of the Dirty Paper Channel with Fading Dirt in the Strong Fading Regime

TL;DR

This paper characterizes the capacity of the dirty paper channel with fading interference in the strong fading regime, revealing that capacity pre-log is inversely proportional to the number of fading states.

Contribution

It provides an approximate capacity characterization for the dirty paper channel with unknown transmitter fading, specifically in the strong fading regime.

Findings

Capacity pre-log factor equals the inverse of the number of fading states.

Approximate capacity characterization is achieved under strong fading conditions.

Fading variability significantly impacts the channel capacity in this model.

Abstract

The classical writing on dirty paper capacity result establishes that full interference pre-cancellation can be attained in Gelfand-Pinsker problem with additive state and additive white Gaussian noise. This result holds under the idealized assumption that perfect channel knowledge is available at both transmitter and receiver. While channel knowledge at the receiver can be obtained through pilot tones, transmitter channel knowledge is harder to acquire. For this reason, we are interested in characterizing the capacity under the more realistic assumption that only partial channel knowledge is available at the transmitter. We study, more specifically, the dirty paper channel in which the interference sequence in multiplied by fading value unknown to the transmitter but known at the receiver. For this model, we establish an approximate characterization of capacity for the case in which fading values vary greatly in between channel realizations. In this regime, which we term the strong fading regime, the capacity pre-log factor is equal to the inverse of the number of possible fading realizations.