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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 studiedfor the case in which there is partial and perfect knowledge of the fadingprocess H at the transmitter (CSIT) and the receiver (CSIR), respectively. Akey step in this problem is to determine the optimal inflation factor (underCosta's choice of auxiliary random variable) when there is only partial CSIT.Towards this end, two iterative numerical algorithms are proposed. Both ofthese algorithms are seen to yield a good choice for the inflation factor.Finally, the high-SNR (signal-to-noise ratio) behavior of the achievable rateover the FDPC is dealt with. It is proved that FDPC (with t transmit and rreceive antennas) achieves the largest possible scaling factor of min(t,r) logSNR even with no CSIT. Furthermore, in the high SNR regime, the optimality ofCosta's choice of auxiliary random variable is established even when there ispartial (or no) CSIT in the special case of FDPC with t <= r. Using thehigh-SNR scaling-law result of the FDPC (mentioned before), it is shown that aDPC-based multi-user transmission strategy, unlike other beamforming-basedmulti-user strategies, can achieve a single-user sum-rate scaling factor overthe multiple-input multiple-output Gaussian Broadcast Channel with partial (orno) CSIT.

Dirty Paper Coding for Fading Channels with Partial Transmitter Side Information