On the capacity of Bernoulli-Gaussian impulsive noise channels in Rayleigh fading

In this paper, we investigate the channel capacity of an additive Bernoulli-Gaussian (BG) impulsive noise channel in Rayleigh fading via lower and upper bounds. To this end, we first show that the differential entropy of the BG impulse noise can be established in closed-form using Gaussian hypergeometric function 2F1 (1, 1; .; .). This closed-form expression allows us to derive a lower bound on the capacity limit obtained by a Gaussian input using the Gauss-Hermite quadrature formula. We also derive in closed-form two upper bounds on the channel capacity. The first upper bound is obtained under the assumption of full knowledge of noise state, while the second upper bound is developed using a Gaussian distributed output. At high power regions, the lower bound achieved by Gaussian inputs and the upper bound generated by Gaussian inputs are indistinguishable. These two bounds can therefore be used as an accurate estimation for the channel capacity. When the channel input power is small compared to the power of the impulsive noise component, the lower bound obtained by using a Gaussian input and the upper bound under the perfect knowledge of impulse noise state are almost identical, which are useful to predict the capacity. The establishment of the lower bound and the two upper bounds in closed-form helps us to confirm the near-optimality of the Gaussian input in a wide range of input power levels over BG impulsive noise channels in Rayleigh fading.