Characterization on Practical Photon Counting Receiver in Optical Scattering Communication

We characterize the practical photon-counting receiver in optical scattering communication with a finite-sampling rate and electrical noise. 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 a 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 to maximize the minimal Kullback-Leibler (KL) distance between the two distributions. The performances of proposed sub-Poisson distribution and the binomial approximation are verified by the experimental results. The equivalent photon arrival rate and pulse holding time predicted by the sub-Poisson model and the associated proposed binomial distribution are well validated by the simulation results, where the finite-sampling rate and electrical noise are considered. The proposed holding time and decision threshold selection rule performs close to the optimal ML receiver.