1536-1276 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TWC.2017.2702158, IEEE Transactions on Wireless Communications 1 Centralized and Distributed Energy Efficiency Designs in Wireless Backhaul HetNets Tri Minh Nguyen, Student Member, IEEE, Animesh Yadav, Member, IEEE, Wessam Ajib, Senior Member, IEEE, and Chadi Assi, Senior Member, IEEE Abstract—This paper studies the joint design of downlink transmit beamforming and power allocation in two-tier wireless backhaul small cell heterogeneous networks. We consider the reverse time division duplexing combined with equal spectrum splitting between two tiers for interference mitigation. We for- mulate a constrained optimization problem with the objective of maximizing the proposed access energy efficiency, defined by the ratio of the sum achievable rate at the users to the overall consumed power, where the power consumption model includes the adaptive decoding power. The formulated problem is non- convex and generally NP-hard. To solve it, we first apply the high complexity branch-and-bound algorithm to find the global optimal solution. Then, we develop a lower complexity algorithm which iteratively solves the convex approximated problem until convergence. Compared to conventional methods, this algorithm converges faster to a solution that is very close to the global optimal solution achieved by the branch-and-bound approach. Finally, we exploit the framework of alternating direction method of multipliers (ADMM) on the convex approximated problem to develop a distributed algorithm. Numerical results are obtained to show the improvement of our proposed model with much better power conservation compared to different design of fixed circuit power assignment. Index Terms—Beamforming, centralized, distributed, energy efficiency, optimization, power allocation, heterogeneous net- works, wireless backhaul. I. I NTRODUCTION The evolution and widespread acceptance of 5G networks has strongly relied on its promise of providing thousand-fold enhancement of network capacity [2]. Among others, network densification is considered as a key candidate technology for achieving the desired capacity [3]. Not surprisingly, achieving maximum throughput with minimal energy consumption has recently become an extremely attractive area of research [4]. According to [5], almost 80% of the total network energy is consumed at base station (BS) sites; thus, saving energy on such dense networks simply translates to greener and more economical communications. Motivated by the need for energy efficiency operation and deployment, which also helps in lowering operational cost for mobile network operators and contributes less CO 2 emission to the environment, maintaining Tri Minh Nguyen is with École de Technologie Supérieure (ÉTS), Montreal, QC, Canada. Animesh Yadav is with Memorial University. Wessam Ajib is with the Department of Computer Science, Univesité du Québec à Montréal. Chadi Assi is with CIISE, Concordia Univer- sity, Montreal, Canada (email: {minh-tri.nguyen.1@ens.etsmtl.ca}, {ani- meshy@mun.ca} {wessam.ajib}@uqam.ca, {assi@ciise.concordia.ca}). This work was supported in parts by the Fonds de Recherche du Québec - Nature et Technologies (FRQNT), 2015-2016. A part of this work has been presented in IEEE GLOBECOM 2016 [1]. the optimal resource management is equally vital to attain the best system energy efficiency (EE) [6]. Currently, deploying more BSs generally exposes the chal- lenging cost problem of installing more fiber backhaul links. To overcome this burden, wireless backhaul (WB) [7] emerged to present a simple and viable solution to solve the expensive backhaul architecture installation obstacle in dense networks. Unlike the conventional wired backhaul architecture in small cell networks where information is transported via fiber links, WB enables these small cell access points (SAPs) to transmit and receive backhaul data over-the-air. According to [8], it is sufficiently mature to activate the WB operation in the sub–6 GHz spectrum band with the available hardware. By replacing (or coexisting with) the fiber connection, the operators can confide WB to solve the problem of installation and difficulties for the backhaul deployment in urban and some rural areas. However, WB communication (WBC) must guarantee both high speed and reliable backhaul transmissions to maintain a certain level of quality of service (QoS). In light of these observations, it is imperative to consider an EE design for WB. A. Related work WB concept was first proposed in the standard IEEE 802.16 mesh networks [9]. By enabling WB transmission, the authors in [9] developed an algorithm based on linear optimization that maximizes the total network throughput to design an optimal routing and scheduling strategy for the medium access control layer. In the 5G context, WB technology was widely revisited in various network scenarios and, interestingly, ex- tended to different spectrum bands [8]. Specifically, in the 60–80 GHz band, known as mm-wave, the authors of [10] presented a novel idea for small cells equipped with mm- wave transmitters to effectively align their transmit beam under wind induced impairments. In the sub–6 GHz band, some works proposed to reuse the available hardware and implementation to accommodate WBC concurrently with the wireless access communications (WAC). By employing the reverse time division duplex (RTDD) model, the authors in [11], [12] considered the joint bandwidth allocation and user association that maximizes the achievable downlink (DL) sum log rate of small cells when the macrocell base station (MBS) is equipped with large antenna. In [13], the authors studied the admission control of SAPs in order to permit WB to serve as many SAPs as possible while guaranteeing QoS rates. The authors of [14] were the first ones to consider the optimization of scheduling and power control that maximizes the mm-wave