Statistical Non-linear Model, Achievable Rates and Signal Detection for Photon-level Photomultiplier Receiver

We characterize the practical 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 linear regime. Subsequently, a threshold-based classifier is proposed to distinguish the PMT working regimes based on the non-linear model. Moreover, we derive the approximate performance of mean power detection with infinite sampling rate and finite over-sampling rate in the linear regime based on small dead time and central-limit theorem. We also fomulate a signal model in the non-linar regime. Furthermore, the performance of mean power detection and photon counting detection with maximum likelihood (ML) detection for different sampling rates is evaluated from both theoretical and numerical perspectives. We can conclude that the sample interval equivalent to dead time is a good choice, and lower sampling rate would significantly degrade the performance.
Comment: 39 pages, 14 figures