Estimating information rates of Bernoulli-Gaussian impulsive noise channels in Rayleigh fading

This paper presents simple methods to tightly estimate the information rate achieved by a Gaussian input and the constrained capacity of a finite-alphabet input of a Bernoulli-Gaussian (BG) impulsive noise channel in Rayleigh fading. Specifically, under the assumption of a Gaussian input, we propose a novel approach to calculate the achievable rate by examining the instantaneous output entropy in two regions of channel gains. In the high-gain region, the rate is evaluated via an upper bound obtained under the Gaussian output assumption. In the other region, we apply the piecewise-linear curve fitting (PWLCF) method to estimate the rate. It is then demonstrated that the information rate achieved by Gaussian inputs can be effectively calculated with a pre-determined accuracy. For a finite-alphabet input, we detail a PWLCF-based method to estimate the constrained capacity. In particular, we first propose a numerical technique to calculate the instantaneous output entropy using 2-dimensional Gauss-Hermite quadrature formulas. The average output entropy is then obtained using PWLCF. Combined with the closed-form expression the entropy of the BG impulse noise, an accurate estimation of the constrained capacity is finally established.