Achievable Rates and Signal Detection for Photon-Level Photomultiplier Receiver Based on Statistical Non-Linear Model

We characterize practical optical signal receiver in a wide range of signal intensity for optical wireless communication, from discrete pulse regime to continuous waveform regime. We first propose a statistical non-linear model based on the photomultiplier tube (PMT) multi-stage amplification and Poisson channel, and then derive the optimal and tractable suboptimal duty cycle with peak-power and average-power constraints for on-off key (OOK) modulation in the linear regime. Subsequently, a threshold-based classifier is proposed to distinguish the PMT working regimes based on the non-linear model. Moreover, the performance of mean power detection and photon counting detection under maximum likelihood (ML) criterion for the sampling interval shorter than dead time is evaluated from both theoretical and numerical perspectives. The proposed model can be adopted to select the optimal duty cycle and analyze the detection performance of PMT output signal in real applications.