Abstract
Heterogeneous networks (HetNets) and millimeter wave (mmWave) communications have been recognized as two of the most promising techniques for future cellular networks. HetNets possess the ability to significantly increase network capacity and coverage, while the mmWave bands have an abundant spectrum to support gigabit-per-second data transmission for backhauling. Due to the extreme pathloss and the unreliable transmission of mmWave signals over longer distances, multi-hop mmWave transmissions have been identified as a backhaul (BH) solution in HetNets. On the other hand, energy efficiency (EE) has been identified as a prime design factor for cellular networks because of their rising energy costs. In this paper, two optimization frameworks for maximizing the EE of HetNets with multi-hop mmWave BH links are explored. The first framework, referred to as joint EE, power, and flow control (JEEPF), considers enforcing a strict throughput requirement on all user equipment (UEs) and maximizing the network EE via the joint optimization of power and BH flows. The second framework, referred to as joint EE, power, flow, and throughput (JEEPFT), allows an acceptable range of throughput requirements for each UE and maximizes the network EE via the joint optimization of power, BH flows, and UEs' achievable throughputs. It is observed that this little change (i.e., strict vs. an acceptable range of throughput requirements) causes a drastic difference in the formulations of both problems. The JEEPF simplifies to power minimization problem (which is convex), while the JEEPFT is a ratio of throughput to power (which is fractional and non-convex). Two solution techniques that obtain the optimal solution are proposed for the JEEPFT optimization framework. Simulation results are used to demonstrate the superiority of the JEEPFT framework over the JEEPF and other simple benchmark schemes. The computational complexity of the JEEPFT solution techniques is discussed.