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In heterogeneous networks (HetNets), the load between macrocell base stations (MBSs) and small-cell base stations (SBSs) is imbalanced due to their different transmission powers and locations. This load imbalance significantly impacts system performance and affects the experience of mobile users (MUs) with different priorities. In this paper, we aim to distributively optimize the user association in HetNets with various user priorities to solve the load balancing problem. Since the user association is a binary matching problem, which is NP-hard, we propose a distributed belief propagation (BP) algorithm to approach the optimal solution. We first develop a factor graph model, using the network topology, to represent this user association problem. With this factor graph, we propose a novel distributed BP algorithm by adopting the proportional fairness as the objective. Next, we theoretically prove the existence of the fixed point in our BP algorithm. To be more practical, we develop an approximation method to significantly reduce the computational and communication complexity of the BP algorithm. Furthermore, we analyze some properties of the factor graph relevant to the performance of the BP algorithm using the stochastic geometry. Simulation results show that 1) the proposed BP algorithm well approaches the optimal system performance and achieves a much better performance compared with other association schemes and that 2) the analytical results on the average degree distribution and sparsity of the factor graph match with those obtained from the Monte Carlo simulations. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the intercell interference coordination (ICIC) problem in heterogeneous cellular networks with randomly deployed small-cell base stations (BSs). Current research on ICIC mainly focuses on optimizing the spectrum and power allocations at BSs, whereas the user–BS association is treated as a separate issue. Nevertheless, the user–BS association problem is an important issue in ICIC and should be jointly optimized with resource allocations to achieve global optimality. In this paper, with the objective of maximizing the system sum rate in a distributed manner, we propose a novel belief propagation (BP) algorithm to jointly optimize user association, subchannel assignment, and power allocation. We first develop a factor graph model to decompose the network-wide objective and constraints into multiple local utilities. Then, we transform the maximization of local utilities into the estimations of marginal distributions and propose a distributed BP algorithm to solve the estimations. Simulations show that our distributed BP algorithm dramatically improves the performance compared with the benchmark scheme. [ABSTRACT FROM AUTHOR]