On the sum-rate capacity of poisson multiple access channel with non-perfect photon-counting receiver

We investigate two-user sum-rate capacity for Poisson channel considering practical photon-counting receiver, including finite sampling rate and dead time. The sum-rate capacity reduction due to photon-counting loss is characterized and compared with that of continuous Poisson channel. We show that the sum-rate capacity with non-perfect receiver approaches the capacity of continuous time Poisson channel as the sampling time and dead time both approach zero. For optimal transmission strategy, we demonstrate three possible transmission strategies, including only one active user and two active users. In addition, we study the special case of identical peak power constraint for each user. We adopt majorization method to demonstrate that the optimal duty cycle for the two users must be the same and unique. Furthermore, we analyze the sum-rate capacity for multiple input single output (MISO) multiple-access channel (MAC). We propose a sufficient condition on dead time where the sum-rate capacity of the Poisson MISO-MAC is equivalent to that of single input single output, and the equivalence would not hold for sufficient large peak power or dead time. The theoretical capacity results are validated by numerical results.