Capacity bound analysis for visible light communications with a Gaussian mixture noise

This paper investigates the channel capacity bounds and asymptotic performance gap for high and low signal-to-noise ratio (SNR) in a point-to-point visible light communication system with a Gaussian mixture (GM) noise. The considered GM noise with arbitrary means is utilized to model any non-Gaussian engineering-relevant channel accurately. By imposing peak and average optical intensity constraints, a lower bound is derived using the entropy-power inequality and the variational method. The upper bounds for high-SNR and low-SNR scenarios are obtained based on the concept of an "optimal input distribution that diverges to infinity," the dual expression of capacity, and perfect knowledge of the noise state. Furthermore, our asymptotic analysis reveals a slight discrepancy between all SNRs' lower and upper bounds. Meanwhile, in the limit where the SNR tends to zero, the exact slope of the capacity is given. To delve deeper into the analysis, we explore the exact capacity bounds and asymptotic gap by eliminating the peak optical intensity constraint. Finally, we validate all derived capacity bounds through numerical results using practical parameters.