Capacity Bounds and High-SNR Capacity of the Additive Exponential Noise Channel With Additive Exponential Interference

Communication in the presence of a priori known interference at the encoder has gained great interest because of its many practical applications. In this paper, additive exponential noise channel with additive exponential interference (AENC-AEI) known non-causally at the transmitter is introduced as a new variant of such communication scenarios‎. First, it is shown that the additive Gaussian channel with a priori known interference at the encoder when the transmitter suffers from a fast-varying phase noise can be modeled by the AENC-AEI. Then, capacity bounds for this channel under a non-negativity constraint as well as a mean value constraint on input are derived‎. ‎Finally, it is shown both analytically and numerically that the upper and lower bounds coincide at high signal to noise ratios (SNRs), and therefore‎, ‎the capacity of the AENC-AEI at high SNRs is obtained. Interestingly, this high SNR-capacity has a simple closed-form expression and is independent of the interference mean, analogous to its Gaussian counterpart.