The penalty for random deployment in hexagonal lattice networks with perturbed interferers

Base station (BS) locations are usually modelled using one of two extremes: at one end is a deterministic, hexagonal, location model; while at the other is a random deployment following a Poisson point process (PPP). However, real-world networks follow neither extreme; as such, in this paper, we focus on a modified perturbed hexagonal lattice model that, in terms of regularity, lies in between the PPP and the perfect hexagonal lattice models. In our modified perturbed hexagonal lattice, the location of all interfering BSs, except for the serving BS under consideration, are perturbed. We provide a simple and tight upper bound on the average total interference in an interference-limited reuse-1 network. The bound is presented in the form of a polynomial in the distance from the serving BS and another polynomial in the normalized perturbation. The presented formulation is useful in obtaining simple analytical expressions for various network parameters such as SIR and/or coverage probability. As an added benefit, the formulations here quantify the loss in the coverage probability in moving from the perfect lattice model to a random BS deployment. We use simulations to illustrate the accuracy of the theory developed.