In this paper, a massive MIMO enabled backhaul model for two-tier heterogeneous networks with in-band full-duplex transmission and imperfect CSI is provided. Because of a massive number of antennas at the macro base station and densification of small cells, circuit power consumption increases in the system. It is requisite to study energy efficiency of such backhaul networks. This paper aims at maximizing EE for optimal user association, spectrum allocation, and power allocation while accounting for QoS and backhaul constraints. A joint optimization problem is formulated as a non-convex mixed integer non-linear problem which provides an un-affordable computational complexity. To crack the problem efficiently, it is progressively divided into sub-problems until each one is convex and is solved separately to obtain the optimal solution. Furthermore, complexity of the proposed algorithm is evaluated and Jain’s fairness index is measured. Simulation results of the proposed distributive algorithm are shown and compared with that of the existing algorithm (Max SINR) to manifest the strength of the proposed algorithm. The impact of self-interference cancellation factor and channel estimation error on EE is clearly reflected by the numerical results. In addition, it is observed that using the proposed algorithm results in better EE than increasing the number of antennas.

在本文中，针对带内全双工传输和CSI不完善的两层异构网络，提供了一种支持大型MIMO的回程模型。由于宏基站上的天线数量众多，并且小型小区的密度很高，因此系统中的电路功耗增加。研究这种回程网络的能源效率是必要的。本文旨在在考虑QoS和回程约束的同时，最大化EE以实现最佳用户关联，频谱分配和功率分配。将联合优化问题表述为非凸混合整数非线性问题，该问题提供了难以承受的计算复杂性。为了有效地解决该问题，将其逐步划分为多个子问题，直到每个问题都是凸的为止，并分别进行求解以获得最优解。此外，评估了所提算法的复杂度，并测量了Jain公平指数。展示了所提出的分布式算法的仿真结果，并将其与现有算法（Max SINR）的仿真结果进行比较，以证明所提出算法的强度。数值结果清楚地反映了自干扰消除因子和信道估计误差对EE的影响。另外，观察到，与增加天线数量相比，使用所提出的算法可产生更好的EE。数值结果清楚地反映了自干扰消除因子和信道估计误差对EE的影响。另外，观察到，与增加天线数量相比，使用所提出的算法可产生更好的EE。数值结果清楚地反映了自干扰消除因子和信道估计误差对EE的影响。另外，观察到，与增加天线数量相比，使用所提出的算法可产生更好的EE。