# On the Sum-Rate Capacity of Poisson Multiple Access Channel with Non-Perfect Photon-Counting Receiver

## TL;DR

This paper analyzes the sum-rate capacity of Poisson multiple access channels with non-perfect photon-counting receivers, revealing unique transmission strategies and capacity reductions compared to Gaussian channels, and extends the analysis to MISO configurations.

## Contribution

It introduces new capacity characterizations for Poisson MAC with non-ideal photon-counting, including optimal duty cycle conditions and capacity equivalence with SISO under specific conditions.

## Key findings

- Three transmission strategies identified for two-user Poisson MAC.
- Capacity reduction due to photon-counting loss quantified.
- Sum-rate capacity of Poisson MISO MAC shown to be equivalent to SISO under certain conditions.

## Abstract

We first investigate two-user nonasymmetric sum-rate Poisson capacity with non-perfect photoncounting receiver under certain condition and demonstrate three possible transmission strategy, including only one active user and both active users, in sharp contrast to Gaussian multiple access channel (MAC) channel. The two-user capacity reduction due to photon-counting loss is characterized compared with that of continuous Poisson channel. We then study the symmetrical case based on two different methods, demonstrating that the optimal duty cycle for two users must be the same and unique, and the last method maybe can extend to multiple users. Furthermore, we analyze the sum-Rate capacity of Poisson multiple input single output (MISO) MAC. By converting a non-convex optimization problem with a large number of variables into a non-convex optimization problem with two variables, we show that the sum-rate capacity of the Poisson MISO MAC is equivalent to that of SISO under certain condition.