On the Low-SNR Asymptotic Capacity of Two Types of Optical Wireless Channels under Average-Intensity Constraints

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.