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This paper studies the problem of energy efficiency (EE) maximization via user association, power, and backhaul (BH) flow control in the downlink of millimeter wave BH heterogeneous networks. This problem is mathematically formulated as a mixed-integer non-linear program, which is non-convex. To get a tractable solution, the initial problem is separated into two sub-problems and optimized sequentially. The first is a joint user association and power control sub-problem for the access network (AN) (AN sub-problem). The second is a joint flow and power control sub-problem for the BH network (BH sub-problem). While the BH sub-problem is a convex optimization problem and hence can be efficiently solved, the AN sub-problem assumes the form of a generalized assignment problem, which is known to be NP-hard. To that end, we utilize Lagrangian decomposition to propose two polynomial time solution techniques that obtain a high-quality solution for the AN sub-problem. The first, referred to as Technique A, uses dynamic programming, the subgradient method, and a heuristic. The second, named Technique B, uses the multiplier adjustment method, the sorting algorithm, and a heuristic. Simulation results are used to demonstrate the effectiveness of the proposed energy efficient user association, power, and BH flow control algorithms as compared with benchmark user association schemes that incorporate the BH sub-problem algorithm, in terms of the total AN power, BH power, and overall network (AN plus BH) EE. The computational complexity and practical implementation of the proposed algorithms are discussed.

Energy Efficient User Association, Power, and Flow Control in Millimeter Wave Backhaul Heterogeneous Networks