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On the dirty paper channel with fading dirt

We consider a generalization of Costa's “writing on dirty paper” channel. In this generalization, the interference is multiplied by a fading coefficient, which changes in an i.i.d. manner between time instances, according to a general distribution. The value of this fading coefficient is unknown at the transmitter, representing a realistic scenario of imperfect channel state information at the transmitter. For this model, we characterize the achievable rates under Gaussian signaling, and present some illustrative examples in an effort to enhance the insight into this setting.