A scalable framework is developed to allocate radio resources across a large
number of densely deployed small cells with given traffic statistics on a slow
timescale. Joint user association and spectrum allocation is first formulated
as a convex optimization problem by dividing the spectrum among all possible
transmission patterns of active access points (APs). To improve scalability
with the number of APs, the problem is reformulated using local patterns of
interfering APs. To maintain global consistency among local patterns,
inter-cluster interaction is characterized as hyper-edges in a hyper-graph with
nodes corresponding to neighborhoods of APs. A scalable solution is obtained by
iteratively solving a convex optimization problem for bandwidth allocation with
reduced complexity and constructing a global spectrum allocation using
hyper-graph coloring. Numerical results demonstrate the proposed solution for a
network with 100 APs and several hundred user equipments. For a given quality
of service (QoS), the proposed scheme can increase the network capacity several
fold compared to assigning each user to the strongest AP with full-spectrum
reuse.

通过对运行速度缓慢的密集部署的小型基站进行交互用户关联和频谱分配来开发可扩展的框架，以满足给定的流量统计需求。通过将频谱划分给所有可能的主动访问点 (AP) 的传输模式来首先将联合用户关联和频谱分配表述为凸优化问题。