We characterize the practical photon-counting receiver in optical scatteringcommunication with finite sampling rate and electrical noise. In the receiverside, the detected signal can be characterized as a series of pulses generatedby photon-multiplier (PMT) detector and held by the pulse-holding circuits,which are then sampled by the analog-to-digit convertor (ADC) with finitesampling rate and counted by a rising-edge pulse detector. However, the finitesmall pulse width incurs the dead time effect that may lead to sub-Poissondistribution on the recorded pulses. We analyze first-order and second-ordermoments on the number of recorded pulses with finite sampling rate at thereceiver side under two cases where the sampling period is shorter than orequal to the pulse width as well as longer than the pulse width. Moreover, weadopt the maximum likelihood (ML) detection. In order to simplify the analysis,we adopt binomial distribution approximation on the number of recorded pulsesin each slot. A tractable holding time and decision threshold selection rule isprovided aiming to maximize the minimal Kullback-Leibler (KL) distance betweenthe two distributions. The performance of proposed sub-Poisson distribution andthe binomial approximation are verified by the experimental results. Theequivalent arrival rate and holding time predicted by the of sub-Poisson modeland the associated proposed binomial distribution on finite sampling rate andthe electrical noise are validated by the simulation results. The proposed theholding time and decision threshold selection rule performs close to theoptimal one.
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