In the fractional frequency reuse (FFR) system, the bandwidth is partitioned into orthogonal subbands such that users in the cell-center region use the subbands of a frequency reuse factor (FR factor) equal to 1, whereas users in the cell-edge region exploit the subbands of an FR factor larger than 1. The distance threshold, which is used to distinguish the cell-edge region from the cell-center region, is an important factor in FFR system performance. In this paper, we study the optimal distance threshold to maximize system throughput in the downlink cellular networks, including aerial base stations. Subject to the constraint that a given target outage probability is satisfied, the optimal distance threshold is analyzed as a function of the cell size. It is proven that when the sizes of all cells in the network are scaled at the same rate, the optimal distance threshold normalized by the cell size is nondecreasing in the cell size. The analytical results in this paper provide a system design guideline for initial planning of FFR cellular networks of different sizes, including macro, pico, and femto systems. In particular, for size-scalable aerial networks comprising base stations in the sky, such as balloons or unmanned aerial vehicles, our analysis offers insight into the design of the distance threshold with regard to the cell size.
