Interference-Limited Multiuser Photon-counting Channel with Incomplete Information: A Bayesian Game Approach for Optimum Transmission

In this paper, we consider a multiuser photoncounting Poisson channel and focus on a game-theoretic approach that permits each user with conflicting objectives to decide transmission strategies. We consider a block fading multiuser channel and characterize the received signal as a continuous-time photon-counting receiver. In particular, to account for the incomplete information due to the randomness in the channel, we model the problem as a Bayesian game and analyze the interaction of users with conflicting objectives. With peak and average power constraints imposed and assuming that each user is only aware of the probability distribution of the interfering channel gains, different transmit strategies corresponding to channel randomness are illustrated. It is demonstrated that the transmission strategy of any user is a function of the number of users present in the network. Moreover, it is shown that with appropriate selection of the transmit strategy, all users can improve their quality of service by minimizing the level of interference.