  Interference management techniques are critical to the performance of
heterogeneous cellular networks, which will have dense and overlapping coverage
areas, and experience high levels of interference. Fractional frequency reuse
(FFR) is an attractive interference management technique due to its low
complexity and overhead, and significant coverage improvement for
low-percentile (cell-edge) users. Instead of relying on system simulations
based on deterministic access point locations, this paper instead proposes an
analytical model for evaluating Strict FFR and Soft Frequency Reuse (SFR)
deployments based on the spatial Poisson point process. Our results both
capture the non-uniformity of heterogeneous deployments and produce tractable
expressions which can be used for system design with Strict FFR and SFR. We
observe that the use of Strict FFR bands reserved for the users of each tier
with the lowest average SINR provides the highest gains in terms of coverage
and rate, while the use of SFR allows for more efficient use of shared spectrum
between the tiers, while still mitigating much of the interference.
Additionally, in the context of multi-tier networks with closed access in some
tiers, the proposed framework shows the impact of cross-tier interference on
closed access FFR, and informs the selection of key FFR parameters in open
access.
