User association and backhaul bandwidth allocation for 5G heterogeneous networks in the millimeter-wave band

User association and wireless backhaul allocation in a two-tier heterogeneous network (HetNet) operating in the millimeter wave (mmWave) band is investigated. The macro cell tier base station (BS) is assumed to be equipped with large-scale antenna arrays, while the small cell BSs only have single-antenna capability and they rely on the wireless link to the macro BS for backhaul. To balance the throughput and the fairness, the sum of logarithmic user rate is chosen as the network utility for the optimization problem. A distributed algorithm based on hierarchical primal and dual decomposition is proposed. Firstly, the primal decomposition transforms the original problem into two sub-problems, the wireless backhaul bandwidth allocation subproblem and the user association subproblem. Secondly, biasing on the received signal-to-interference-plus-noise ratio (SINR) is introduced to the small cell tier to achieve traffic offloading. Finally, the optimal solution X∗ for the user association subproblem can be obtained from the Lagrange dual function through the dual decomposition when the Karush-Kuhn-Tucker condition or the Slater's condition holds. While achieving the same optimal performance, the proposed distributed algorithm converges much faster than the exhaustive search method. Simulation results reveal that the system throughput is improved as we increase the large-scale antenna array size and the number of users. The impact of changing the number of small cell BSs is insignificant. In addition, the system throughput achieved by the distributed algorithm outperforms that of the conventional maximum SINR based user association strategy.