Optimal SNR-based coverage in Poisson cellular networks with power density constraints

This paper studies the coverage maximization for wireless networks in which base station (BS) locations are drawn from a homogenous spatial Poisson point process, and user locations are arbitrary. A user is covered for communication if its received signal-to-noise-ratio (SNR) is above a given threshold value, and the objective is to maximize the coverage probability under per unit area power density constraints. The resulting optimization problem is solved analytically by making use of the underlying concavity in the objective function when transmissions are impaired only by a power-law bounded path loss. Our results show that the optimal transmit power per BS is independent of the power density constraint, and the solution to the optimization problem represents the Pareto optimal boundary between the power density constraint and the coverage probability. Then, these results are extended to a system in which transmissions are impaired by both path loss and fading. The resulting optimization problem with fading turns out to be a non-convex optimization problem. In this case, we provide tight upper bounds on the optimal coverage probability. The paper also discusses the importance of using bounded path loss models for coverage maximization problems in wireless networks, and shows that an unbounded model will lead to trivial solutions.