text: 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.
  @cite_5: This paper studies the joint user association and resource allocation in heterogeneous networks (HetNets) from a novel perspective, motivated by and generalizing the idea of fractional frequency reuse. By treating the multi-cell multi-user resource allocation as resource partitioning among multiple reuse patterns, we propose a unified framework to analyze and compare a wide range of user association and resource allocation strategies for HetNets, and provide an optimal benchmark for network performance. The enabling mechanisms are a novel formulation to consider all possible interference patterns or any pre-defined subset of patterns, and efficient sparsity-pursuit algorithms to find the solution. A notable feature of this formulation is that the patterns remain fixed during the resource optimization process. This creates a favorable opportunity for convex formulations while still considering interference coupling. More important, in view of the fact that multi-cell resource allocation is very computational demanding, our framework provides a systematic way to trade off performance for the reduction of computational complexity by restricting the candidate patterns to a small number of feature patterns. Relying on the sparsity-pursuit capability of the proposed algorithms, we develop a practical guideline to identify the feature patterns. Numerical results show that the identified feature patterns can significantly improve the existing strategies, and jointly optimizing the user association and resource allocation indeed brings considerable gain.
summary: @cite_5 , a slow-timescale model similar to the model considered in this paper was proposed. User association and spectrum allocation are jointly optimized to maximize the sum rate under proportional fairness constraints. There are two major differences between @cite_5 and our approach here. First, we allow rather realistic stochastic traffic, whereas @cite_5 is limited to backlogged traffic and rate maximization. Second, the proposed algorithm in @cite_5 avoids exponential complexity by limiting to a small number of global patterns a priori . Here, the proposed scalable solution includes all possible patterns as candidates.