  In this paper, we propose a resource allocation algorithm for the downlink of
sectorized two-dimensional (2-D) OFDMA cellular networks assuming statistical
Channel State Information (CSI) and fractional frequency reuse. The proposed
algorithm can be implemented in a distributed fashion without the need to any
central controlling units. Its performance is analyzed assuming fast fading
Rayleigh channels and Gaussian distributed multicell interference. We show that
the transmit power of this simple algorithm tends, as the number of users grows
to infinity, to the same limit as the minimal power required to satisfy all
users' rate requirements i.e., the proposed resource allocation algorithm is
asymptotically optimal. As a byproduct of this asymptotic analysis, we
characterize a relevant value of the reuse factor that only depends on an
average state of the network.
