On compound channels with side information at the transmitter

Costa has proved that for noncausally known Gaussian interference at a power constrained transmitter communicating over an additive white Gaussian noise channel there is no capacity loss when compared to a scenario where interference is not present. For the case of a transmitter communicating over a quasistatic (i.e., nonergodic) fading channel, his method does not apply. In this correspondence, we derive upper and lower bounds on the capacity of compound channels with side information at the transmitter, first for finite alphabet channels and then, based on this result, for channels on standard alphabets (this includes real alphabets). For the special case of a degenerate compound channel with only one possible realization, our bounds are equivalent to the well-known capacity with side-information formula of Gel´fand and Pinsker. For the quasistatic fading channel, when fading is Ricean, we suggest a scheme based on our lower bound for which the performance is found to be relatively good even for moderate K-factor. As K→∞, the uncertainty on the channel vanishes and our scheme obtains the performance of dirty paper coding, namely that the interference is perfectly mitigated. As K→0, the proposed scheme treats the interferer as additional noise. These results may be of importance for the emerging field of cognitive radios where one user may be aware of another user´s intended message to a common receiver, but is unaware of the channel path gains.