On the Low-SNR Asymptotic Capacity of Two Types of Optical Wireless Channels under Average-Intensity Constraints
Longguang Li
TL;DR
This work resolves the exact low-SNR capacity of two fundamental optical wireless channels under average-intensity constraints: the Gaussian optical intensity channel and the Poisson optical intensity channel. By employing a duality-based upper bound with carefully chosen auxiliary distributions and MAP-based achievability arguments, the authors prove that $\mathsf{C}_{\text{G}}(\mathcal{E}) \sim \frac{1}{\sqrt{2}} \mathcal{E} \sqrt{\log \frac{1}{\mathcal{E}}}$ and $\mathsf{C}_{\text{P}}(\mathcal{E}) \sim \mathcal{E} \log\log \frac{1}{\mathcal{E}}$ as $\mathcal{E} \to 0^+$. The results close existing capacity gaps and provide exact constants for the low-SNR regime, with methods that may extend to multi-antenna OWC systems. The work advances fundamental understanding of intensity-modulated/direct-detection channels and informs system design under stringent average-power constraints.
Abstract
In this paper, we study two types of optical wireless channels under average-intensity constraints. One is called the Gaussian optical intensity channel, where the channel output models the converted electrical current corrupted by additive white Gaussian noise. The other one is the Poisson optical intensity channel, where the channel output models the number of received photons corrupted by a dark current. When the average input intensity $\mathcal{E}$ is small, the capacity of the Gaussian optical intensity channel is shown to scale as $\mathcal{E}\sqrt{\frac{\log\frac{1}{\mathcal{E}}}{2}}$, and the capacity of the Poisson optical intensity channel as $\mathcal{E}\log\log\frac{1}{\mathcal{E}}$. This closes the existing capacity gaps in these two channels.