Noisy DPC and Application to a Cognitive Channel

In this paper, we first consider a channel that is contaminated by two independent Gaussian noises S ∼ N (0, Q) and Z0 ∼ N (0, N0). The capacity of this channel is computed when independent noisy versions of S are known to the transmitter and/or receiver. It is shown that the channel capacity is greater then the capacity when S is completely unknown, but is less then the capacity when S is perfectly known at the transmitter or receiver. For example, if there is one noisy version of S known at the transmitter only, the capacity is 1 2 log(1+ P Q(N1/(Q+N1))+N0 ), where P is the input power constraint and N1 is the power of the noise corrupting S. We then consider a Gaussian cognitive interference channel (IC) and propose a causal noisy dirty paper coding (DPC) strategy. We compute the achievable region using this noisy DPC strategy and quantify the regions when it achieves the upper bound on the rate.