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 (PMT) detector and held by the pulse-holding circuits, which are then sampled by the analog-to-digit convertor (ADC) with finite sampling rate and counted by a rising-edge pulse detector. However, the finite small pulse width incurs the dead time effect that may lead to sub-Poisson distribution on the recorded pulses. We analyze first-order and second-order moments on the number of recorded pulses with finite sampling rate at the receiver side under two cases where the sampling period is shorter than or equal to the pulse width as well as longer than the pulse width. Moreover, we adopt the maximum likelihood (ML) detection. In order to simplify the analysis, 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 performance of proposed sub-Poisson distribution and the binomial approximation are verified by the experimental results. The equivalent arrival rate and holding time predicted by the of sub-Poisson model and the associated proposed binomial distribution on finite sampling rate and the electrical noise are validated by the simulation results. The proposed the holding time and decision threshold selection rule performs close to the optimal one.
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