A Statistical Non-Linear Model and Analysis for Photon-Level Photomultiplier Receiver

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 photomultiplier tube (PMT) multi-stage amplification and Poisson channel, and then derive the optimal and tractable suboptimal duty cycle with peak-power constraint and average-power constraint for on-off key (OOK) modulation in the linear regime. Subsequently, a threshold-based classifier is proposed to distinguish three PMT working regimes based on the non-linear model. The performance of photon counting detection with optimal threshold for different sampling rates 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.