Optimal Signaling Scheme and Capacity Limit of PLC Under Bernoulli-Gaussian Impulsive Noise

This paper studies the optimal signaling scheme and capacity of the Bernoulli-Gaussian impulsive noise channel to shed new light on the impact of impulsive noise on spectral efficiency of power-line communications systems. First, by focusing on the practically typical case with impulse power that is much higher than signal power, we develop a tight approximation to the differential entropy of Bernoulli-Gaussian noise. Closed-form tight lower and upper bounds on the capacity are then derived. By comparing these bounds, it is demonstrated that the capacity decreases with an increasing impulse occurrence rate and the Gaussian signaling scheme is nearly optimal. We then focus on the case with an impulse power lower than signal power to develop tight lower and upper bounds. We subsequently show that the Gaussian signaling can approach the capacity in this region as well. In addition, channel erasure is shown to be very effective for the impulsive noise channel when impulse power is higher than signal power, but it introduces rate loss when impulse power is sufficiently lower than signal power. Illustrative simulation results confirm the analytical derivations and show their applications to estimate the maximum achievable rate of a power-line communication link with practical parameters.