Dirty Paper Coding for Fading Channels with Partial Transmitter Side Information

TL;DR

This paper investigates Dirty Paper Coding over fading channels with partial transmitter knowledge, proposing algorithms for optimal inflation factor determination and analyzing high-SNR behavior, demonstrating the robustness of DPC in MIMO broadcast scenarios.

Contribution

It introduces iterative algorithms for optimal inflation factor calculation in FDPC with partial CSIT and proves high-SNR scaling laws showing DPC's effectiveness without full CSIT.

Findings

Algorithms effectively determine inflation factors.

FDPC achieves max scaling of min(t,r) log SNR.

DPC-based strategies outperform beamforming in multi-user scenarios.

Abstract

The problem of Dirty Paper Coding (DPC) over the Fading Dirty Paper Channel (FDPC) Y = H(X + S)+Z, a more general version of Costa's channel, is studied for the case in which there is partial and perfect knowledge of the fading process H at the transmitter (CSIT) and the receiver (CSIR), respectively. A key step in this problem is to determine the optimal inflation factor (under Costa's choice of auxiliary random variable) when there is only partial CSIT. Towards this end, two iterative numerical algorithms are proposed. Both of these algorithms are seen to yield a good choice for the inflation factor. Finally, the high-SNR (signal-to-noise ratio) behavior of the achievable rate over the FDPC is dealt with. It is proved that FDPC (with t transmit and r receive antennas) achieves the largest possible scaling factor of min(t,r) log SNR even with no CSIT. Furthermore, in the high SNR regime, the optimality of Costa's choice of auxiliary random variable is established even when there is partial (or no) CSIT in the special case of FDPC with t <= r. Using the high-SNR scaling-law result of the FDPC (mentioned before), it is shown that a DPC-based multi-user transmission strategy, unlike other beamforming-based multi-user strategies, can achieve a single-user sum-rate scaling factor over the multiple-input multiple-output Gaussian Broadcast Channel with partial (or no) CSIT.