Dirty Paper Coding for fading channels with partial transmitter side information

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 les 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.