Capacity of Bernoulli-Gaussian interference channels in Rayleigh fading with full CSI

In this paper, we investigate the channel capacity of a Bernoulli-Gaussian (BG) interference channel in Rayleigh fading when the channel state information (CSI) is known at both the transmitter and receiver via tight lower and upper bounds. Specifically, we first derive an upper bound on the channel capacity assuming a Gaussian-distributed output. Under this assumption, an optimal power adaptation scheme is established and the upper-bound is obtained in closed-form. By assuming a Gaussian-distributed input, we then adopt the derived power adaptation scheme to establish a lower bound on channel capacity. A simple approximation of the instantaneous output entropy using a piecewise-linear curve fitting (PWLCF)-based scheme is then developed, which provides a closed-form estimation of the lower bound with a predetermined error level. Finally, a comparison between the derived upper and lower bounds are made. Both analytical and numerical results show that these two bounds are tight in a wide range of input power levels and they can be used effectively to estimate the channel capacity.