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A scalable framework is developed to allocate radio resources across a largenumber of densely deployed small cells with given traffic statistics on a slowtimescale. Joint user association and spectrum allocation is first formulatedas a convex optimization problem by dividing the spectrum among all possibletransmission patterns of active access points (APs). To improve scalabilitywith the number of APs, the problem is reformulated using local patterns ofinterfering APs. To maintain global consistency among local patterns,inter-cluster interaction is characterized as hyper-edges in a hyper-graph withnodes corresponding to neighborhoods of APs. A scalable solution is obtained byiteratively solving a convex optimization problem for bandwidth allocation withreduced complexity and constructing a global spectrum allocation usinghyper-graph coloring. Numerical results demonstrate the proposed solution for anetwork with 100 APs and several hundred user equipments. For a given qualityof service (QoS), the proposed scheme can increase the network capacity severalfold compared to assigning each user to the strongest AP with full-spectrumreuse.

Scalable Spectrum Allocation and User Association in Networks with Many Small Cells