  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.
