  Two-tier networks, comprising a conventional cellular network overlaid with
shorter range hotspots (e.g. femtocells, distributed antennas, or wired
relays), offer an economically viable way to improve cellular system capacity.
The capacity-limiting factor in such networks is interference. The cross-tier
interference between macrocells and femtocells can suffocate the capacity due
to the near-far problem, so in practice hotspots should use a different
frequency channel than the potentially nearby high-power macrocell users.
Centralized or coordinated frequency planning, which is difficult and
inefficient even in conventional cellular networks, is all but impossible in a
two-tier network. This paper proposes and analyzes an optimum decentralized
spectrum allocation policy for two-tier networks that employ frequency division
multiple access (including OFDMA). The proposed allocation is optimal in terms
of Area Spectral Efficiency (ASE), and is subjected to a sensible Quality of
Service (QoS) requirement, which guarantees that both macrocell and femtocell
users attain at least a prescribed data rate. Results show the dependence of
this allocation on the QoS requirement, hotspot density and the co-channel
interference from the macrocell and surrounding femtocells. Design
interpretations of this result are provided.
