Characterization of a Practical Photon Counting Receiver in Optical Scattering Communication

We characterize the practical photon-counting receiver in optical scattering communication with finite sampling rate and electrical noise. In the receiver side, the detected signal can be characterized as a series of pulses generated by photon-multiplier tube (PMT) detector and held by the pulse-holding circuit. Those pulses are then sampled by the analog-to-digital convertor (ADC) with finite sampling rate and counted by a rising-edge pulse detector. However, finite small pulse width incurs dead time effect that may lead to sub-Poisson distribution on the recorded pulses. We analyze the first-order and second-order moments on the number of recorded pulses with finite sampling rate and existing shot noise at the receiver side. In order to simplify the further analysis on the error probability, we adopt binomial distribution approximation on the number of recorded pulses in each slot. A tractable holding time and decision threshold selection rule is provided aiming to maximize the minimal Kullback-Leibler (KL) distance between the two distributions. The performances of the proposed sub-Poisson distribution and the binomial approximation are verified by the experimental results. The equivalent arrival rate and holding time predicted by the sub-Poisson model are validated by the simulation results. Besides, the numerical results show that the proposed holding time and decision threshold selection rule performs close to the optimal one.