Optimal interference range for minimum Bayes risk in binomial and Poisson wireless networks

Interference is the main performance-limiting factor in most wireless networks. Protocol interference model is extensively used in the design of wireless networks. However, the setting of interference range, a crucial part of the protocol interference model, is rather heuristic and remains an open problem. In this paper, we use the stochastic geometry and the direct approach to obtain the associated feasibility distributions. After that, we use the binary hypothesis testing to achieve the Bayes risk under binomial point process (BPP) and Poisson point process (PPP), respectively. According to the first derivative of the Bayes risk, we provide the equation to achieve the optimal interference range for minimum Bayes risk. We extend the method proposed by Wildman et al. to a more general situation. Furthermore, we show that for infinite PPP, those two methods converge to the same results. Several numerical results for wireless networks under BPP, finite PPP, and infinite PPP are given. Simulation results show that in the finite wireless network, the BPP method performs better than the PPP method.