Optimal Power Allocation for Poisson Channels with Time-Varying Background Light

In this paper, we study Poisson fading channels with time-varying background light. Different from most of the existing work on fading Poisson channel that focus on the case with time-varying channel gain, our model is motivated by indoor optical wireless communication systems, in which the noise level is affected by the strength of the background light. We study both the single-input single-output and the multiple-input and multiple-output channels. For each channel, we consider scenarios with and without delay constraints. For the case without a delay constraint, we characterize the optimal power allocation scheme that maximizes the ergodic capacity. For the case with a strict delay constraint, we characterize the optimal power allocation scheme that minimizes the outage probability. We also provide several numerical examples to demonstrate the analytic results.