  In heterogeneous cellular networks (HCNs), it is desirable to offload mobile
users to small cells, which are typically significantly less congested than the
macrocells. To achieve sufficient load balancing, the offloaded users often
have much lower SINR than they would on the macrocell. This SINR degradation
can be partially alleviated through interference avoidance, for example time or
frequency resource partitioning, whereby the macrocell turns off in some
fraction of such resources. Naturally, the optimal offloading strategy is
tightly coupled with resource partitioning; the optimal amount of which in turn
depends on how many users have been offloaded. In this paper, we propose a
general and tractable framework for modeling and analyzing joint resource
partitioning and offloading in a two-tier cellular network. With it, we are
able to derive the downlink rate distribution over the entire network, and an
optimal strategy for joint resource partitioning and offloading. We show that
load balancing, by itself, is insufficient, and resource partitioning is
required in conjunction with offloading to improve the rate of cell edge users
in co-channel heterogeneous networks.
