Bounds and lattice-based transmission strategies for the phase-faded dirty-paper channel

We consider a fading version of the dirty-paper problem, as proposed by Grover and Sahai. In this formulation, the various signals involved are complex-valued, and the interference (known only to the transmitter) is multiplied by a random complex-valued coefficient, whose phase is known only to the receiver. We focus on a compound channel formulation, and seek to maximize the worst-case performance. We present an achievable strategy modeled on the lattice-based approach of Erez, Shamai and Zamir and propose heuristic methods to optimize its parameters. We also derive an upper bound on the maximum achievable transmission rates. Our bounds are shown to be tight in some settings, yielding a complete characterization of capacity. We also provide simulation results, indicating the practical effectiveness of our approaches.