  Multi-tier architecture improves the spatial reuse of radio spectrum in
cellular networks, but it introduces complicated heterogeneity in the spatial
distribution of transmitters, which brings new challenges in interference
analysis. In this work, we present a stochastic geometric model to evaluate the
uplink interference in a two-tier network considering multi-type users and base
stations. Each type of tier-1 users and tier-2 base stations are modeled as
independent homogeneous Poisson point processes, and tier-2 users are modeled
as locally non-homogeneous clustered Poisson point processes centered at tier-2
base stations. By applying a superposition-aggregation-superposition approach,
we quantify the interference at both tiers. Our model is also able to capture
the impact of two types of exclusion regions, where either tier-2 base stations
or tier-2 users are restricted in order to avoid cross-tier interference. As an
important application of this analytical model, an intensity planning scenario
is investigated, in which we aim to maximize the total income of the network
operator with respect to the intensities of tier-2 cells, under constraints on
the outage probabilities of tier-1 and tier-2 users. The result of our
interference analysis suggests that this maximization can be converted to a
standard convex optimization problem. Finally, numerical studies further
demonstrate the correctness of our analysis.
