1

On Designing Energy-Efficient HeterogeneousCloud Radio Access Networks

Qiang Liu, Tao Han, Nirwan Ansari, Gang Wu

Abstract—Heterogeneous cloud radio access network (H-CRAN) promises higher energy efficiency (EE) than the con-ventional cellular networks by centralizing the baseband signalprocessing into the baseband unit (BBU) pool hosted by cloudcomputing platforms. Because of the difference between H-CRANand conventional cellular networks, existing energy-efficient net-working mechanisms designed for conventional cellular networkscannot fully leverage H-CRAN in terms of reducing the networkenergy consumption. In this paper, we bridge this gap byproposing a radio resource management scheme to optimizethe network energy efficiency (NEE) of H-CRAN. We developa network energy consumption model that characterizes theenergy consumption of radio access points (RAPs), fronthaul,and the BBU pool in H-CRAN. Based on the network energyconsumption model, we formulate the NEE optimization problemwith the consideration of the capacity constrained fronthaul.The NEE optimization problem is a mixed integer non-linearprogramming problem (MINLP). We propose the H-CRANenergy-efficient radio resource management (HERM) algorithmto solve the NEE optimization problem efficiently. Variousproperties of the proposed solution are derived and extensivesimulations are conducted. The simulation results show that theHERM algorithm significantly improves the NEE of H-CRAN. Ascompared with a baseline algorithm in which the radio resourcemanagement is not optimized, HERM boosts the NEE by 59%under the dynamic network traffic. As compared to an energy-efficient radio resource allocation (ERA) algorithm which doesnot optimize the energy consumption of the BBU pool, the NEE ofH-CRAN achieved by the HERM algorithm is up to 51% betterthan that by the ERA algorithm with network traffic dynamics.

Index Terms—Energy efficiency, Resource management, H-CRAN, Heterogeneous fronthaul.

I. INTRODUCTION

THE fifth generation mobile communication system (5G)is expected to support massive connections with higher

data rate, lower latency, ultra-higher reliability and higherenergy efficiency [1]. Heterogeneous networks (HetNet) andcloud radio access networks (C-RAN) are promising tech-nologies to reduce energy consumption and improve energyefficiency of cellular networks toward 5G [2], [3].

In HetNet, small cell base stations (ScBSs) are deployed toprovide high-speed data transmissions in a small area whilemacro BSs are designed to provide seamless coverage to a

Q. Liu and T. Han are with the Department of Electrical and ComputerEngineering at the University of North Carolina at Charlotte, Charlotte, NC.E-mail: {qliu12, tao.han}@uncc.edu

N. Ansari is with Helen and John C. Hartmann Department of Electricaland Computer Engineering at New Jersey Institute of Technology, Newark,NJ. E-mail: nirwan.ansari@njit.edu

G. Wu is with National key laboratory on Communication at the Univer-sity of Electronic Science and Technology of China, Chengdu, China. E-mail:wugang99@uestc.edu.cn

This work is partially supported by the US National Science Foundationunder Grant No. 1731675, No. 1320468, and the Faculty Research Grantprovided by the University of North Carolina at Charlotte.

eRRH RRHWired

fronthaul

Wireless

fronthaul

The BBU pool

RF

RFPHY

RFPHY

RFPHY

RF

RF

RF

Fig. 1. The H-CRAN architecture.

large area. The dense deployment of ScBSs supports massivemobile connections and significantly increases the networkthroughput. However, such a network deployment may leadto extensive coverage overlaps among base stations (BSs)and severe inter-BS interference in HetNet. As a result, theadvantages of HetNet will be neutralized by the interferenceand the complicated BS coordination required in ultra-densemobile networks [4].

C-RAN decouples the RF and baseband signal processingto the remote radio head (RRH) and baseband unit (BBU),respectively. BBUs are centralized as a BBU pool whichis implemented on cloud computing platforms. Owing tothe centralized baseband signal processing, the channel stateinformation (CSI) can be efficiently shared among BBUs.By leveraging the CSI information, C-RAN allows large-scale cooperative communications and thus mitigates the se-vere inter-BS interference. Moreover, since the BBU pool isimplemented on cloud computing platforms, the computingresource for baseband signal processing can be dynamicallyprovisioned based on the traffic demand [5]. However, theseparation of the BBU and RRH imposes stringent capacitydemand on fronthaul that carries the baseband signal betweenthe BBU and RRH. Therefore, the limited fronthaul capacitymay greatly impact the performance of C-RAN.

Heterogeneous cloud radio access network (H-CRAN),which leverages the centralized signal processing mechanismof C-RAN and the heterogeneous BS deployment scheme ofHetNet, is a promising network architecture for next genera-tion mobile communications [4], [6], [7]. As compared withC-RAN, H-CRAN introduces the enhanced RRHs (eRRHs)which support baseband signal processing functions. In H-CRAN, the eRRH is deployed to provide wide-area seamlesscoverage while the RRH is deployed to provision high-speeddata transmission to a small area as shown in Figure 1. Sincethe eRRH is able to process baseband signal, the fronthaulcapacity requirements are alleviated in H-CRAN [4], [8], [9].

H-CRAN combines the merits of both HetNet and C-RANand thus has the potential of significantly enhance the energy

2

efficiency of mobile networks. However, designing energy-efficient H-CRAN is a challenging and yet undeveloped re-search topic. In H-CRAN, the baseband signal processingfunctions are partially implemented in the BBU pool. As aresult, the energy consumption model of H-CRAN is funda-mentally different from conventional cellular networks [10].Owing to these differences, the existing energy-efficient net-working solutions cannot be directly applied to H-CRAN.Moreover, the separation of the RF and baseband signalprocessing introduces a stringent requirement on the capacityof the fronthaul that connects the RRH/eRRH and BBUpool. Although optical fiber links are capable to provide highcapacity, their availability is very limited due to the prohibitivedeployment cost in large-scale H-CRAN [11]. Therefore, cost-effective wireless fronthaul will be indispensable in deployingH-CRAN [4], [12]. The wireless fronthaul may not provideas high capacity as optical fiber links and thus become thebottleneck of H-CRAN. Meanwhile, optical fiber fronthaul canalso be the bottleneck when the network traffic loads are notwell balanced. Hence, the capacity of fronthaul is a uniquenetworking constraint which should be carefully considered indesigning energy-efficient networking solutions in H-CRAN.

In this paper, we study the network energy efficiency(NEE) of the downlink data transmission in H-CRAN withconstrained fronthaul capacity. In order to analyze the NEEof H-CRAN, we build a comprehensive energy consumptionmodel that characterizes the energy consumption of RRHs,eRRHs, fronthaul, and the BBU pool in H-CRAN. Basedon the energy consumption model, the resource block (RB)assignments and corresponding power allocations determinesthe network energy consumption. Therefore, we formulatethe NEE optimization problem to investigate the optimal RBassignment and power allocation strategy that minimizes thenetwork energy consumption in H-CRAN. On formulating theproblem, we consider multiple practical constraints such asusers’ minimum data rates, the maximum transmission powerof RRHs and eRRHs, and the maximum fronthaul capacity.The NEE optimization problem turns out to be a mixed integernon-linear programming (MINLP) problem which is generallyNP-hard [13].

We propose the H-CRAN energy-efficient radio resourcemanagement (HERM) algorithm to solve the NEE problemefficiently. The HERM algorithm first transforms the ob-jective function of the NEE optimization problem from adivisional-form to a subtractive-form by using the Dinkelbachalgorithm [14]. Then, the l0-norm approximation methodis adopted to approximate the non-convex l0-norm as l1-norm [15]. Next, the HERM algorithm optimizes the RBassignments and corresponding power allocation based onthe Lagrangian-dual method [16], [17]. The optimality andconvergence of the HERM algorithm is analyzed and proved.We also discuss the practicality of the HERM algorithm interms of implementing the algorithm in a practical H-CRAN.The performance of the HERM algorithm is evaluated withextensive simulations, which show that the HERM algorithmsignificantly improves the NEE of H-CRAN. As comparedwith a baseline algorithm in which the radio resource manage-ment is not optimized, the HERM algorithm boosts the NEE

by 59%. As compared to an energy-efficient radio resourceallocation (ERA) algorithm which does not optimize theenergy consumption of the BBU pool, the NEE of H-CRANachieved by the HERM algorithm is up to 51% better thanthat by the ERA algorithm. Moreover, the simulation resultsalso reveal several insights on optimizing energy efficiency ofcloud-based radio access networks.

The main contributions of this paper can be summarized asfollows.• We develop a comprehensive network energy consump-

tion model that characterizes the energy consumption ofRRHs, eRRHs, fronthaul, and the BBU pool in H-CRAN.The network energy consumption model is essential forstudying the energy efficiency of H-CRAN.

• We mathematically formulate and analyze the NEE max-imization problem in H-CRAN with the consideration ofmultiple practical constraints such as users’ minimumdata rates, the maximum transmission power of RRHsand eRRHs, and the maximum fronthaul capacity. Theproblem formulation and analysis lay a foundation forinvestigating the performance and tradeoff in optimizingthe energy efficiency of H-CRAN.

• We design the HERM algorithm to solve the NEEmaximization problem efficiently. The optimality andconvergence of the HERM algorithm is analyzed andproved. The implementation of the HERM algorithm inpractical H-CRAN is discussed.

• We validate the HERM algorithm via extensive networksimulations. The simulation results are well analyzed andreveal several insights on optimizing energy efficiency ofcloud-based radio access networks.

The remainder of this paper is organized as follows. InSection II, we briefly review the related works. In Section III,we describe the system model of H-CRAN and formulatethe NEE optimization problem. In Section IV, we designthe HERM algorithm to solve the problem. In Section V,the practical implementation of the HERM algorithm in H-CRAN is discussed. In Section VI, we evaluate the algorithmvia extensive simulations, and analyze the results. Finally, weconclude our works in Section VII.

II. RELATED WORK

Energy-efficient mobile networks have been extensivelystudied over recent years [18], [19]. In this section, webriefly overview on energy-efficient networking solutions inconventional mobile networks, e.g., LTE, and the cloud basedradio access network.

A. Energy Efficiency in Conventional Mobile Networks

In a mobile network, the radio access network, which ismainly composed of BSs, is the major energy consumer [20].Therefore, most of energy-efficient networking solutions forconventional mobile networks focus on reducing the energyconsumption of BSs. These solutions can be classified intothree categories [18], [21], [22]. The first one includes radiosource management algorithms that optimize the energy effi-ciency of mobile networks [23]–[25]. The second category

3

designs the BS sleep mode algorithms, which dynamicallyswitch BSs to the low-power mode according to their trafficloads [26]–[28]. The third category aims to power mobile BSswith renewable energy [29]–[32]. Although these solutionsprovide some insights in designing energy-efficient mobilenetworks, they are not directly applicable to cloud-basedradio access networks because of the architectural differencesbetween convectional mobile networks and C-RAN.

B. Energy Efficiency in Cloud-based Radio Access Networks

As cloud-based radio access networks emerge as a promis-ing networking architecture for next generation mobile net-works, energy-efficient C-RAN becomes an important researchtopic. Many have addressed energy efficiency problems inC-RAN from different aspects. Liu et al. [33] poposed anetwork energy consumption model and designed a joint userassociation and resource allocation algorithm to optimize theenergy efficiency in H-CRAN. Peng et al. [34] investigatedthe enhanced soft fractional frequency reuse (S-FFR) schemefor energy-efficient H-CRAN. This scheme considers the RRHand fronthaul energy consumption. Tang et al. [35] studied thecross-layer resource allocation problem in C-RAN to minimizethe network energy consumption. Pompili et al. [36] proposedan elastic resource utilization framework for C-RAN. Thisframework improves C-RAN energy efficiency by dynamicallygrouping virtual base stations into clusters according to trafficcondition.

The limited fronthaul capacity has been considered inoptimizing the energy efficiency of C-RAN. In order tominimize the transmission power of C-RAN, Vu et al. [37]proposed the jointly coordinated beamforming and admissioncontrol scheme in downlink C-RAN with fronthaul capacityconstraints. Dhifallah et al. [38] studied energy efficient beam-forming and backhaul power control schemes in C-RAN withheterogeneous backhaul. Oliva et al. [39] proposed a novelarchitecture named Xhaul which integrates the fronthaul andbackhaul and provides an adaptive, shareable and cost-efficienttransport network solution.

These existing works usually focus on the energy efficiencyof certain networking devices, e.g., RRH and fronthaul. Ourpaper studies the network energy efficiency in H-CRANbased on a comprehensive network energy consumption modelthat characterizes the energy consumption of all networkingdevices in the downlink H-CRAN. Moreover, in our paper,multiple practical networking constraints have been consideredin designing the energy efficient networking solutions.

III. SYSTEM MODEL AND PROBLEM FORMULATION

In this section, we first describe the system model includingthe network architecture, wireless communication model, fron-thaul model, and network energy consumption model. Then,we mathematically formulate the network energy efficiency(NEE) maximization problem and analyze its properties.

A. System Model

1) Network Architecture: We consider a H-CRAN thatconsists of multiple RRHs and eRRHs. The RRHs onlyhave the RF signal processing functions while the eRRHs

are able to process both RF and baseband signals. Thebaseband signal processing functions of RRHs are carriedby the BBU pool implemented on a cloud computingplatform. The RRHs and eRRHs are connected to the BBUpool via heterogeneous fronthaul, e.g., optical fiber cablesand wireless communication links, which facilitates thejoint resource management. Denote Ms, Me, and K asthe sets of RRHs, eRRHs, and UEs, respectively. Then,M = Ms ∪ Me is the set of radio access points (RAPs)including both RRHs and eRRHs in the H-CRAN. The numberof RAPs and UEs are M = |M| and K = |K|, respectively.

NOTATION

αk,m,n The RB assignment indicatorA The RB assignment matrixP The power allocation matrixK The set of UEsM The set of RAPsN The set of RBsCm The effective fronthaul capacity of the mth RAPηNEE The network energy efficiency (NEE)gk,m,n The channel gain for mth RAP to kth UE on nth RBPT The network energy consumptionPB The energy consumption of the BBU poolPFm The energy consumption of the mth fronthaulPRm The energy consumption of the mth RRHP static The static energy consumption of the entire networkpk,m,n The allocated power for mth RAP to kth UE on nth

RBRT The sum-rate of the networkRk,m,n The maximum achievable data rate of mth RAP to

kth UE on nth RB

2) Wireless Communication Model: We adopt the orthogo-nal frequency division multiple access (OFDMA) in H-CRANdownlink transmission. We consider the large-scale channelfading such as distance-dependent path loss and shadowing,and assume the CSI can be obtained by the BBU pool foroptimizing the radio resource allocation [3]. Denote Bs and Beas the frequency bandwidth allocated to the RRH and eRRH,respectively. For the sake of simplicity of the presentation, weassume Bs = Be and use Be to represent the total bandwidthin either RRH or eRRH. The spectrum reuse factors for bothRRHs and eRRHs are 1. That is, the total bandwidth in anindividual RAP, e.g., RRH and eRRH, is Be. The bandwidth ina RAP is divided into multiple resource blocks (RBs), and eachRB is exclusively assigned to one UE in a resource allocationinterval. Denote N as the set of RBs in a RAP. Then, thenumber of RBs in a RAP is N = |N |.

Denote pk,m,n and gk,m,n as the transmission power andchannel gain from the mth RAP to the kth UE on the nth RB,respectively. Then, the maximum achievable data rate [40] ofthe kth UE using the nth RB in the mth RRH be calculatedas

Rk,m,n =BeN

log2

(1 +

pk,m,ngk,m,nσBe/N

), (1)

4

where σ is the power spectrum density of the aggregated in-terference, including the co-channel interference among RAPsand the additive white Gaussian noise.

Denote αk,m,n as the RB assignment indicator. If thenth RB of the mth RAP is assigned to the kth UE,αk,m,n = 1; otherwise, αk,m,n = 0. Then, we construct twoK × M × N variable matrices, A = [αk,m,n]K×M×N andP = [pk,m,n]K×M×N , to represent the RB assignment andpower allocation, respectively. Note that user association isindicated in the expression of αk,m,n, i.e.,

∑n∈N αk,m,n > 0

indicates that the kth UE is associated with the mth RAP.Therefore, the sum-rate of the network RT can be expressedas

RT (A,P) =∑k∈K

∑m∈M

∑n∈N

αk,m,nRk,m,n. (2)

3) Fronthaul Model: The digitized in-phase and quadraturesamples of the baseband signals are transmitted from RRHsand eRRHs to the BBU pool over the common public radiointerface (CPRI) interface in the mobile networks [9], [41].The transmission of the digitized in-phase and quadrature sam-ples via fronthaul requires more than 10 times of the originalwireless data bandwidth [42]. As a result, fronthaul may bethe bottleneck of cloud-based radio access networks. The func-tional split can potentially alleviate the transmission bottleneckby shifting some baseband signal processing functions fromthe BBU pool to RRHs [42]–[44]. Therefore, eRRHs maydemand less fronthaul capacity than RRHs because eRRHshave the baseband signal processing functions. Meanwhile,since heterogeneous fronthaul is considered in the H-CRAN,the capacity of fronthaul varies depending on the transmissiontechnologies, e.g., optical fiber and wireless communications.Therefore, we model the fronthaul capacity constraint as∑

k∈K

∑n∈N

αk,m,nRk,m,n ≤ Cm,∀m ∈M, (3)

where Cm is defined as the effective fronthaul capacity of themth RAP. Denote λ as the ratio of the bandwidth required fromtransmitting the digitized in-phase and quadrature samplesover the original wireless data bandwidth. Let Cmaxm be thefronthaul capacity of the mth RAP. Then, Cm = Cmaxm /λ.The value of Cm depends on the fronthaul transmissiontechnologies. For example, optical fiber fronthaul has a largereffective capacity than wireless fronthaul.

4) Network Energy Consumption Model: Because of thearchitectural difference between the conventional mobile net-works and H-CRAN, the energy consumption model designedfor the conventional mobile networks is not appropriate for H-CRAN. Hence, we build the a comprehensive network energyconsumption model that characterizes the energy consumptionof RRHs, eRRHs, the BBU pool, and fronthaul in H-CRAN.The network energy consumption model is expressed as

PT =∑m∈M

(PRm + PFm) + PB , (4)

where PRm , PFm , and PB denote the energy consumption ofthe mth RAP, the fronthaul of the mth RAP, and the BBUpool, respectively.

The power consumption of a RAP is composed of the static

and dynamic power consumption. The static power consump-tion is required to run the RAP while the dynamic powerconsumption is usually proportional to the traffic load [45].Therefore, the energy consumption of the mth RAP can bewritten as

PRm = PR,Sm + ∆m

∑k∈K

∑n∈N

αk,m,npk,m,n, (5)

where PR,Sm denotes the static energy consumption of the mthRAP and ∆m is the energy factor of the mth RAP characteriz-ing the relationship between the dynamic power consumptionand the traffic load. The value of ∆m is determined by the typeof the RAP. With the baseband signal processing function, aneRRH consumes more dynamic power than a RRH. Therefore,an eRRH has a larger energy factor than a RRH.

On modelling the energy consumption of fronthaul, we con-sider the time-division multiplexing (TDM) fronthaul whichcan be switched to the sleep mode for energy savings [46],[47]. The power consumption of fronthaul is dominated by itsstatic power consumption [10]. Therefore, we do not model thedynamic power consumption which depends on the traffic loadcarried by fronthaul. Then, the fronthaul power consumptionof the mth RAP can be expressed as

PFm =

{PF,Am , Im 6= 0,PF,Sm , Im = 0,

(6)

where PF,Am and PF,Sm denote the fronthaul power consump-tion of the mth RAP in the active and sleep mode, respectively.Im =

∑k∈K

∑n∈N αk,m,npk,m,n reflects whether the fron-

thaul link in the mth RAP carries traffic loads. If Im 6= 0 , itindicates the fronthaul link carries traffic loads, and thus thefronthaul link is in the active mode; otherwise, the fronthaullink is in the sleep mode. For the sake of simplicity in theanalysis, we rewrite Eq. (6) as

PFm = PF,Sm + (PF,Am − PF,Sm )‖Im‖0. (7)

The power consumption of the BBU pool is closely relatedto the computing workloads for the baseband signal process-ing [10]. Since the BBU pool is implemented on cloud com-puting platforms, we assume that, given a RAP in H-CRAN,there is a corresponding virtual machine (VM) initialized toprocess baseband signals for the RAP [36], [48]. Hence, theenergy consumption of the BBU pool is PB =

∑m∈M PBm , in

which PBm is the power consumption of the VM that processesbaseband signals for the mth RAP. The power consumptionof a VM in the BBU pool depends on the traffic load in itscorresponding RAP. Therefore, the power consumption of theVM that serves the mth RAP is modeled as

PBm = PB,Sm + ρm∑k∈K

∑n∈N

αk,m,n, (8)

where PB,Sm is the static power of the mth RAP’s cor-responding VM. ρm is an energy factor characterizes therelationship between the VM power consumption and the radioresource utilization [10]. The value of ρm is determined by thecomputing architecture and hardware equipment of the BBUpool [10].

∑k∈K

∑n∈N αk,m,n represents the occupied radio

resources.

5

Based on the above analysis, the network energy consump-tion model of H-CRAN expressed in Eq. (4) can be rewrittenas

PT (A,P) =∑

m∈M(PR,Sm + PF,Sm + PB,Sm )

+∑

m∈Mρm

∑k∈K

∑n∈N

αk,m,n

+∑

m∈M(∆mIm + (PF,Am − PF,Sm )‖Im‖0).

(9)In the following analysis, we define P static =∑m∈M(PR,Sm + PF,Sm + PB,Sm ) for the sake of simplicity.

B. Optimization Problem Formulation

Our objective is to obtain the optimal RB assignmentA and power allocation P that maximize the NEE of H-CRAN without violating the practical constraints such as theminimum data rate requirement, the fronthaul capacity, andthe maximum transmission power. The NEE of H-CRAN isdefined as

ηNEE (A,P) =RT (A,P)

PT (A,P), (10)

Then, the NEE optimization problem can be mathematicallyformulated as

max{A,P}

ηNEE (A,P)

s.t.C1 :

∑m∈M

∑n∈N

αk,m,nRk,m,n ≥ rmink ,∀k ∈ K

C2 :∑k∈K

∑n∈N

αk,m,npk,m,n ≤ Pmaxm ,∀m ∈M

C3 :∑k∈K

∑n∈N

αk,m,nRk,m,n ≤ Cm,∀m ∈M

C4 :∑k∈K

αk,m,n ≤ 1,∀m ∈M, n ∈ N

C5 : αk,m,n = {0, 1},∀k ∈ K,m ∈M, n ∈ N ,

(11)

where rmink and Pmaxm are the minimum data rate requirementof the kth UE and the maximum transmission power of themth RAP, respectively. In the optimization problem, C1 are theminimum data rate constraints of UEs; C2 are the maximumtransmission power constraints of RAPs; C3 are the fronthaulcapacity constraint. C4 and C5 regulate the RB assignment inH-CRAN. C4 restricts that a RB can be assigned to at mostone UE. C5 imposes the binary RB assignment in H-CRAN.

In the NEE optimization problem, the fractional-form ob-jective function is non-convex. The l0-norm in the networkenergy consumption model imposes addition difficulties onsolving the problem. With the binary RB assignment, the NEEoptimization problem is a mixed integer non-linear program-ming (MINLP) problem which is NP-hard and difficult to besolved [13], [23], [34]. In the following section, we will solvethe problem and analyze the performance of the solution.

IV. THE HERM ALGORITHM

In this section, we present the H-CRAN energy-efficientradio resource management (HERM) algorithm to solve theNEE problem efficiently. The flow chart of the HERM algo-rithm is shown in Fig. 2. The HERM algorithm first transformsthe objective function of the NEE optimization problem to asubtractive-form using the Dinkelbach algorithm [14]. Then,

Problem Transformation

(Dinkelbach Algorithm)

The NEE Optimization Problem

Converge

Optimal

Solution

Approximation

Yes

No

RB and Power Allocation

(Lagrangian-Dual Method)

Converge NoYes

q

0l norm

* *,A P

Fig. 2. The flow chart of the HERM algorithm.

the l0-norm approximation method is adopted to approximatethe non-convex l0-norm as l1-norm [15]. Next, the HERMalgorithm optimizes the RB assignments and correspondingpower allocation based on the Lagrangian-dual method [16],[17].

A. Problem Transformation

The objective function of the NEE optimization problem isin the fractional-form, which makes the problem highly non-convex. In order to solve this problem efficiently, we use theDinkelbach algorithm to transform the objective function fromthe fractional-form into the subtractive-form [14]. We denote(A∗,P∗) as the optimal solution to the following problem:

max{A,P}

RT (A,P)− q∗ · PT (A,P)

s.t. C1 ∼ C5.(12)

Lemma 1. When RT (A∗,P∗) − q∗PT (A∗,P∗) = 0,(A∗,P∗) is the optimal solution to the NEE optimizationproblem.

Proof: This lemma is proved in Appendix A.According to Lemma 1, if the optimal q∗ is obtained, the

NEE optimization problem can be transformed to the problemin Eq. (12). That is, the solution to the problem in Eq. (12)solves the NEE optimization problem. Therefore, we applythe Dinkelbach algorithm to obtain the optimal q∗ iteratively.At the beginning, the q is initialized. In each iteration, theproblem in Eq. (12) with fixed q will be solved. By solvingthe problem in Eq. (12), q will be updated and converged tothe optimal NEE q∗.

B. l0-norm Approximation

After the above problem transformation, the NEE optimiza-tion problem is still non-convex because of the l0-norm in thenetwork energy consumption model PT (A,P). The l0-normof a vector calculates the number of non-zero entries in thevector, and can be approximated as

‖X‖0 =

|X|∑i=1

βi |Xi|, (13)

where Xi is the mth component of vector X and βi is theweight of Xi [15]. Since Im ≥ 0, based on this l0-norm

6

approximation method, we remove the l0-norm in the energyconsumption model by letting

‖Im‖0 ≈ βmIm. (14)

Here, βm is the weight of the fronthaul link of the mth RAP.

As a result of the approximation, the network energyconsumption can be expressed as

PT (A,P) = P static +∑

m∈Mρm

∑k∈K

∑n∈N

αk,m,n

+∑

m∈M(∆m + βm(PF,Am − PF,Sm ))Im.

(15)

Hence, the NEE maximization problem is approximatelytransformed to

P0 : max{A,P}

RT (A,P)− q∗ · PT (A,P)

s.t. C1 ∼ C5. (16)

βm in Eq. (15) is calculated as

βm = h(Im, τ) =ξ

Im + τ, (17)

where Im is from the previous iteration. τ and ξ are constantregularization factors which regulate the stability and controlprecision of the l0-norm approximation. The value of βm isiteratively updated based on Eq. (17) until it converges in theHERM algorithm.

Note that Im represents the traffic load in the mth fronthaul.In the above iterative updates of βm, the fronthaul with lightertraffic loads (smaller Im) will be assigned larger weights.This weight assignment will further reduce the traffic loadin the fronthaul in the next iteration, and eventually force thefronthaul into the sleep mode.

C. Optimal RB and Power Allocation

In this part, we design the RB and power allocation al-gorithm to solve Problem P0 by using the Lagrangian-dualmethod [16]. We first replace the binary variable, ak,m,n,in Problem P0 with a continuous variable αk,m,n ∈ [0, 1].Therefore, Problem P0 is relaxed to

P1 : max{A,P}

RT (A,P)− q∗ · PT (A,P)

s.t. C1 ∼ C4,

αk,m,n ∈ [0, 1],∀k ∈ K,m ∈M, n ∈ N .(18)

Then, we prove that the solution to the relaxed problemobtained through the RB and power allocation algorithm solvesProblem P0.

When the number of RBs is large, Problem P1 satisfies thetime-sharing conditions. As a result, the duality gap betweenthe primal and dual problems approaches zero [49]. Hence,the RB and power allocation algorithm is designed based onthe Lagrangian-dual method [16].

The Lagrangian of Problem P1 can be expressed as

L (A,P,µ,γ,υ) =∑k∈K

∑m∈M

∑n∈N

αk,m,nRk,m,n

−q[P static +

∑k∈K

∑m∈M

∑n∈N

αk,m,n(∆Empk,m,n + ρm

)]+∑k∈K

µk

( ∑m∈M

∑n∈N

αk,m,nRk,m,n − rmink

)−∑

m∈Mγm

(∑k∈K

∑n∈N

αk,m,npk,m,n − Pmaxm

)−∑

m∈Mυm

(∑k∈K

∑n∈N

αk,m,nRk,m,n − Cm),

(19)where µ = {µk|k ∈ K}, γ = {γm|m ∈ M}, andυ = {υm|m ∈ M} are the Lagrange multipliers correspond-ing to the minimum data rates of UEs rmin

k , the maximumtransmission power of RAPs Pmax

m , and the fronthaul capacityCm, respectively. We define ∆E

m = ∆m + βm(PF,Am − PF,Sm )to simplify the mathematical presentation.

The Lagrange dual function is

g(µ,γ,υ) = max{A,P}

L(A,P,µ,γ,υ) (20)

and the Lagrange dual problem can be expressed as

min{µ,γ,υ}

g (µ,γ,υ)

s.t. µ ≥ 0,γ ≥ 0,υ ≥ 0.(21)

Based on the Lagrangian-dual method, we decompose thedual problem into N independent sub-problems with the samestructure expressed as

g(µ,γ,υ) =∑n∈N

gn (µ,γ,υ)− q∗P static −∑k∈K

µkrmink

+∑

m∈MγmP

maxm +

∑m∈M

υmCm,

(22)where

gn(µ,γ,υ) =max{A,P}

∑k∈K

∑m∈M

αk,m,n((1 + µk − υm)Rk,m,n

−(γm + q∗∆Em)pk,m,n − q∗ρm).

(23)Let

f(A,P) =∑k∈K

∑m∈M

αk,m,n((1 + µk − υm)Rk,m,n

−(γm + q∗∆Em)pk,m,n − q∗ρm).

(24)Then, we can derive

∂f(A,P)

∂P= αk,m,n((1 +µk − υm)

∂Rk,m,n∂pk,m,n

− γm + q∗∆Em).

(25)When αk,m,n = 1, the optimal power allocation can becalculated by setting ∂f(A,P)/∂P = 0 according to theKarush-Kuhn-Tucker (KKT) condition [16]. So the optimalpower allocation is

p∗k,m,n =

[ωk,m,n −

σBeNgk,m,n

, 0

]+, (26)

where [x]+ is defined as max{x, 0}. The optimal power

allocation p∗k,m,n is in the form of the multi-level water filling.

7

The water filling level is expressed as

ωk,m,n =BeN ln 2

· 1 + µk − υmγm + q∗∆E

m

. (27)

The water filling level ωk,m,n depends on the Lagrangemultipliers and weighted factors, q∗ and βm. For example,υm controls the power allocation in the mth RAP so that thetraffic load in fronthaul does not exceed its capacity. That is,υm may constrain the maximum transmission power of themth RAP.

After deriving p∗k,m,n, Eq. (24) can be expressed as

f(A,P∗) =∑k∈K

∑m∈M

αk,m,nHk,m,n, (28)

where

Hk,m,n = (1 + µk − υm)R∗k,m,n−(γm + q∗∆E

m

)p∗k,m,n − q∗ρm.

(29)

Given m and n, we define K = {k|Hk,m,n > 0, k ∈ K}.Based on Eqs. (26) and (24), the optimal RB assignment canbe determined as

α∗k,m,n =

{1, k = arg max

k∈KHk,m,n

0, otherwise.(30)

After we obtain the optimal power allocation and RBassignment, we use the sub-gradient method [16] to solve theLagrange dual problem shown in Eq. (21). The sub-gradientof dual function in the ith iteration is

∇µk(i) =∑

m∈M

∑n∈N

αk,m,nRk,m,n − rmink ,∀k ∈ K,

∇γm(i) = Pmaxm −

∑k∈K

∑n∈N

αk,m,npk,m,n,∀m ∈M,

∇υm(i) = Cm −∑k∈K

∑n∈N

αk,m,nRk,m,n,∀m ∈M.

(31)

The dual variables in the ith iteration are updated as

µk(i) = [µk(i− 1)− δµ(i)×∇µk(i)]+,∀k ∈ K,

γm(i) = [γm(i− 1)− δγ(i)×∇γm(i)]+,∀m ∈M,

υm(i) = [υ(i− 1)− δυ(i)×∇υ(i)]+,∀m ∈M.

(32)

where δµ(i), δγ(i), and δυ(i) are the positive step sizes. If thestep sizes satisfy the infinite travel condition, it is guaranteedthat dual variables will converge to the optimal solution [16].

The pseudo code of the RB and power allocation algorithmis shown in Alg. 1. At the beginning of the algorithm, weinitialize Lagrange multipliers and the iteration step sizes.Then, we calculate the power allocation and RB assignmentbased on Eqs. (26) and (30). Next, Lagrange multipliers areupdated according to Eqs. (31) and (32). When Lagrangemultipliers converge, the optimal power allocation and RBassignment are derived.

Lemma 2. {A∗, P∗} maximizes ηNEE(A,P) of Problem P0.

Proof: The proof is presented in Appendix B.The proof of the Lemma 2 means that, using the RB and

power allocation algorithm, we can obtain the optimal solutionto Problem P0 by solving the relaxed problem in which

Algorithm 1: The RB and Power Allocation Algorithm

1 Initialize Lagrange multipliers µ, γ, and υ;2 Initialize the iteration step sizes δµ, δγ , and δυ;3 while (Lagrange multipliers do not converge) do4 Calculate A,P using Eqs. (26) and (30);5 Update µ,γ,υ according to Eqs. (31) and (32);

6 Return: {A∗,P∗};

the binary RB assignment is replaced by the fractional RBassignment.

D. The Pseudo Code of the HERM Algorithm

The HERM algorithm integrates the problem transforma-tion, l0-norm approximation, and the RB and power allocationalgorithm to solve the NEE optimization problem. The pseudocode of the HERM algorithm is shown in Alg. 2. q∗ andβm are introduced in the problem transformation and l0-normapproximation, respectively. According to the Dinkelbach al-gorithm [14] and the l0-norm approximation method [15], thevalues of q∗ and βm should be derived via iterative processes.Therefore, there are two loops in the HERM algorithm. Theinner loop aims to calculate the value of βm while the outerloop is to obtain the value of q∗. Given the values of q∗ andβm, the RB assignment and power allocation are optimizedby using Alg. 1.

Lemma 3. The HERM algorithm converges to the optimalsolution.

Proof: The proof is presented in Appendix C.

E. Computational Complexity Analysis

The computational complexity of the HERM algorithm iscalculated as Nq · Nβ · Nµ,γ,υ · O(KMN). Nq and Nβ arethe numbers of iterations required for obtaining q∗ and β,respectively. Based on the Dinkelbach algorithm [14] andthe l0-norm approximation method [15], Nq and Nβ shouldbe fairly small numbers. Nµ,γ,υ is the number of iterationsrequired for converging Lagrange multipliers µ, γ, υ in Alg. 1.The value of Nµ,γ,υ depends on multiple factors such asthe step size and the distance between initial and optimalvalues. We analyze the convergence performance in terms ofthe value of Nµ,γ,υ in Appendix D. O(KMN) is the numberof operations required in calculating the RB assignment andpower allocation. The convergence of the HERM algorithmwill be evaluated through extensive simulations presented inSection VI.

V. THE PRACTICALITY OF THE HERM ALGORITHM

In this section, we discuss the implementation of the HERMalgorithm, and the timescales of the radio resource manage-ment and the fronthaul sleep mode.

A. Implementation and Communication Protocol

Fig. 3 illustrates the implementation of the HERM algo-rithm in H-CRAN. The HERM algorithm is implemented onthe cloud computing platform and collects CSI from BBUs.

8

Algorithm 2: The HERM Algorithm

1 Initialize the convergence conditions ε1 and ε2;2 Initialize q∗ and β;3 Set iteration indexes i = 1 ;4 while (q∗ does not converge) do5 Set j = 1;6 while (β does not converge) do7 Solve Problem P0 to obtain A(j),P(j) using

Alg. 1;

if∣∣∣β(j)m − β(j−1)

m

∣∣∣/β(j−1)m ≤ ε2,∀m ∈M then

8 Return: β∗ = β(j) and{A(i),P(i)

}={A(j),P(j)

};

else9 Update β based on Eq. (17) ;

10 Set j = j + 1;

if (RT(A(i),P(i)

)− q∗PT

(A(i),P(i)

)≤ ε2) then

11 Return: {A∗,P∗} ={A(i),P(i)

},

q∗ = RT(A(i),P(i)

)/PT(A(i),P(i)

), and

I∗m =∑k∈K

∑n∈N

a∗k,m,np∗k,m,n, ∀m ∈M;

else12 Update qi = RT

(A(i),P(i)

)/PT(A(i),P(i)

);

13 Set i = i+ 1;

14 Return: {A∗,P∗} and I∗m,∀m ∈M;

Meanwhile, the HERM algorithm also learns UEs’ data raterequirements and fronthaul capacity. With this information,the HERM algorithm optimizes the RB assignment and powerallocation. Based on the RB assignment, H-CRAN determinesthe UE-RAP association and turns the fronthaul without anytraffic load into the sleep mode.

With the HERM algorithm, the communication procedurescan be briefly described in the following steps:

1) UEs attach to the network via a RAP and send their CSIand data rate requirements to the BBU pool.

2) The HERM algorithm learns the fronthaul capacity,collects the UE information including CSI and data raterequirements from the BBU pool, and optimizes the RBassignment and power allocation.

3) Based on the RB assignment, H-CRAN informs UEsabout the updated UE-RAP association.

4) UEs switch their carrier frequencies based on the up-dated UE-RAP association. In H-CRAN, a UE may re-ceive signals on two different carrier frequencies becausethe RRH and eRRH occupy different frequency bands.If the updated UE-RAP association requires a UE tohandover from a RRH (eRRH) to an eRRH (RRH),the UE should switch its carrier frequency accordingly.After updating their carrier frequencies, UEs are readyto receive downlink data.

5) The HERM algorithm, based on the RB assignment,informs the fronthaul controller to turn the fronthaulwithout any traffic load into the sleep mode.

Fronthaul

Sleep

Mode

Control

RRH/eRRH Cloud Computing Platform

BBU

BBU

BBU

BBU

BBU

RB Assignment

Power Allocation

Fronthaul Mode

HERM Algorithm

Fig. 3. The practical implementation of the HERM algorithm

6) The BBU pool processes the downlink data transmissionaccording to the RB assignment and power allocation.

B. Timescale Discussion

In the HERM algorithm, we dynamically optimize the radioresource management and the fronthaul sleep mode. Onemajor concern may be the different operation timescales ofthe radio resource management and the fronthaul sleep mode.In current mobile networks, e.g., LTE, the transmission timeinterval (TTI) is 1 ms [50]. Therefore, the RB assignmentand power allocation can be managed on a timescale of 1 ms.However, managing radio resource on such a small timescalemay lead to excessive computing and communication over-heads. Moreover, the channel coherence time may be muchlarger than one TTI. Therefore, the TTI building technique,which enables the combination and scheduling of multipleconsecutive subframes, is supported in the LTE system [50].As a result, the practical operation timescale of radio resourcemanagement can be several milliseconds.

Regarding the fronthaul, the passive optical network (PON)emerges as a key fronthaul solution for future cloud-basedradio access network [51]. In PON, the optical line termi-nal (OLT) is responsible for receiving the upstream dataand broadcasting downstream data to optical network units(ONUs). The ONU can be switched into the sleep for energysavings when it does not carry any traffic load [52]. The sleepmode in ONU operates at a timescale of several millisec-onds [52]. Therefore, it is possible to operate the dynamicradio resource management and the fronthaul (ONU) sleepmode using the same timescale.

VI. SIMULATION RESULTS AND ANALYSIS

In this section, we set up simulations to evaluate theperformance of the HERM algorithm. In the simulations, weconsider one eRRH and multiple RRHs. The system bandwidthBT is 20 MHz. RRHs and UEs are randomly distributed in thenetwork. Denote d as the distance between a RAP (eRRH orRRH) and a UE in kilometers. The path loss between an eRRHand a UE is modeled as 128.1 + 37.6 log10(d). The path lossbetween a RRH and a UE is modeled as 140.7+36.7 log10(d).The standard deviation of the shadow fading of eRRHs andRRHs are 8 dB and 10dB, respectively [53]. Since eRRHssupport baseband signal processing, we assume that the fron-thaul capacity demand of eRRHs is 10 times less than that ofRRHs according to the typical baseband signal sampling ratioof LTE networks [4].

In the simulations, the maximum transmission power Pmaxm

of eRRHs and RRHs are 43 dBm and 29 dBm, respec-tively [53]. The static power consumption PR,Sm of eRRHs

9

TABLE IDEFAULT VALUE OF SIMULATION PARAMETERS

Variable Default value Variable Default valueK 20 M 10N 20 σ -154 dBmPF,Am 37 Watt PF,Sm 22.2 WattPB,Sm 12 Watt rmin

k 5 Mbps

and RRHs are 84 Watts and 3.5 Watts, respectively [45].The static power consumption of the eRRH is larger than thatof the RRH because the eRRH supports the baseband signalprocessing functions. The parameters ρm and ∆m are 5.676and 4.75, respectively [10]. Table I summarizes the defaultvalues of important parameters in the simulations.

In the simulations, we compare the proposed HERM algo-rithm with the following algorithms:• Baseline Algorithm [23]: In the baseline algorithm, UEs

are associated with the nearest RAP. The RBs are evenlyassigned to all UEs with the same transmission power.The fronthaul link is switched to the sleep mode if itdoes not carry any traffic load.

• Energy-efficient Radio resource Allocation (ERA) Al-gorithm [34]: The ERA algorithm does not optimizethe energy consumption of the BBU pool. Hence theenergy consumption of the BBU pool for the mth RAPis PB,Sm + ρmN as shown in Eq. 8.

A. Impact of the number of UEs

Figs. 4 and 5 show the NEE under different algorithmsversus the number of UEs. It can be seen from Fig. 4 that thenetwork achieves a higher energy efficiency when there area larger number of UEs. When the number of UEs is small,the traffic load in the network is light, and the static powerconsumption dominates the overall power consumption of thenetwork. Therefore, the network has a low energy efficiency.When the number of users increase, the network is saturatedwith the traffic loads. Thus, the network efficiency reachesits maximum value. However, as shown in the figure, theHERM algorithm improves the NEE by 51% as comparedto the ERA algorithm when the traffic load is light in thenetwork. The energy savings of the HERM algorithm comefrom the optimization of the BBU pool. That is, the HERMalgorithm is able to dynamically switch the VMs in the BBUpool into the sleep mode when the traffic load is light inthe network. As compared to the baseline algorithm, theHERM algorithm achieves about 59% improvement in theNEE when the network traffic load is heavy. The energyefficiency improvement is mainly a result of the optimizationof the RRH transmission and fronthaul operation.

Fig. 5 shows a breakdown of the energy consumption in H-CRAN with different number of UEs. Since the BBU poolcarries the baseband signal processing, a large number ofUEs lead to heavy computing workloads in the BBU pool.Therefore, the energy consumption of the cloud platform,where the BBU pool is implemented, increases significantlywith the increment of the number of UEs. This indicates thatthe energy consumption of the BBU pool is closely related

to the traffic load in the network. Since the functionality ofthe RRH is simplified to carry only the RF signal processing,the energy consumption of the RRH is much less than that ofthe cloud platform and fronthaul. As the energy consumptionof the BBU pool dominates the energy consumption of H-CRAN, optimizing the cloud resource management is essentialin achieving energy efficient H-CRAN.

B. Impact of the fronthaul capacity

Fig. 6 shows the NEE of different algorithms versus thefronthaul capacity. In the simulation, we assume that thereare high-capacity fronthaul, e.g., optical fiber links, and low-capacity fronthaul, e.g., wireless links. In order to quantifythe impact of the fronthaul capacity on the NEE, we set thecapacity of the high-capacity fronthaul to be 4 times largerthan that of low-capacity fronthaul. In Fig. 6, x-axis is thecapacity of high-capacity fronthaul and y-axis is the networkenergy efficiency. The figure shows that the NEE improves asthe fronthaul capacity increases. When the fronthaul capacityis sufficiently large, e.g., 0.5 Gbps in the simulation, theNEE reaches its maximum value. This is because a smallfronthaul capacity constrains the radio resource managementfrom achieving the optimal NEE. As the fronthaul capacityincreases, the constraint is slacking, thus leading to a betterNEE. The fronthaul capacity increase will eventually eliminatethe fronthaul capacity from the constraints in optimizing theNEE. Therefore, after reaching a certain value, the fronthaulcapacity does not impact the NEE.

Fig. 6 also shows the performance comparison between theHERM and ERA algorithms. Since the HERM algorithm op-timizes the energy consumption in the BBU pool, it improvesthe NEE by 52% as compared with the ERA algorithm. Boththe HERM and ERA algorithms achieve better NEE whenthere are more UEs in the network. However, the performancegap between the HERM and ERA algorithms shrinks. This isbecause an increasing number of UEs may gradually saturatethe network, which leaves a smaller room for improving theNEE.

C. Impact of the maximum transmission power

Fig. 7 evaluates the NEE versus the maximum transmissionpower, Pmaxm , of RRHs with different algorithms. In thissimulation, the maximum transmission power of the eRRHis 20 Watts. As shown in the figure, the NEE with theHERM and ERA algorithms improves with the increase ofthe maximum transmission power in the RRH. However, whenPmaxm reaches a certain value, e.g., 9 Watts in the simulation,the NEE does not improve any more. When Pmaxm is small, thedata rates of UEs are constrained by Pmaxm . Therefore, increas-ing Pmaxm enhances the throughput of the network and thusimproves the NEE. When Pmaxm is large, additional energyconsumption caused by allocating more transmission powerto UEs is not compensated by the throughput improvement interms of the NEE. Therefore, the HERM and ERA algorithmsdo not allocate additional power to UEs. Hence, the NEE keepsconstant after Pmaxm reaches a certain value. As compared withthe ERA algorithm, the NEE of the HERM algorithm improves15% and 7% under the small and large Pmaxm , respectively.

10

1 5 9 13 17 21 25 29 330

0.05

0.10

0.15

0.20

0.25

The number of UEs

Netw

ork

En

erg

y E

ffic

ien

cy (

Mb

its/

s/Jo

ule

)

51%51%

59%

ERAERAHERMHERM

BaselineBaseline

ERAHERM

Baseline

6%

Fig. 4. The NEE versus the number of UEs.

1 9 250

200

400

600

800

1000

1200

The number of UEs

En

erg

y c

on

sum

pti

on

(W

att

)

RAPsThe BBU pool

FronthaulRAPsThe BBU pool

Fronthaul

358.2

215.6

1039

355.9

207

908.1

302.8

187.8

355.5

Fig. 5. Network energy consumption breakdown.

0.01 0.09 0.17 0.25 0.33 0.41 0.49

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.06

HERM, K=10 UEs

HERM, K=5 UEs

ERA, K=5 UEs

ERA, K=10 UEs

HERM, K=10 UEs

HERM, K=5 UEs

ERA, K=5 UEs

ERA, K=10 UEs

The fronthaul capacity (Gbps)

Netw

ork

En

erg

y E

ffic

ien

cy (

Mb

its/

s/Jo

ule

)

52%

28%

Fig. 6. The NEE versus Cm.

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.1 1 2 3 4 5 6 7 8 9 10 11

P mmax (Watt)P mmax (Watt)

ERAERAHERMHERM

BaselineBaselineERAHERM

Baseline

15%15%81%

Netw

ork

En

erg

y E

ffic

ien

cy (

Mb

its/

s/Jo

ule

)

7%7%

Fig. 7. The NEE versus Pmaxm .

1 10 20 30 40 50 60 70 80 900.05

0.10

0.15

0.20

0.25

0.30

The energy factor of the RAPs m

Netw

ork

En

erg

y E

ffic

ien

cy

(M

bit

s/s/

Jou

le)

ERAERAHERMHERM

BaselineBaselineERAHERM

Baseline

6%

21%

68%

87%

Fig. 8. The NEE versus ∆m.

0 3 6 9 12 15 18 21 24 27 30

The energy factor of the BBU pool

ERAERAHERMHERM

BaselineBaselineERAHERM

Baseline

m

Netw

ork

En

erg

y E

ffic

ien

cy (

Mb

its/

s/Jo

ule

)

0

0.1

0.2

0.3

0.4

0.5

55%

37%

Fig. 9. The NEE versus ρm.

The performance gap between the HERM and ERA algorithmsshrinks with the increase of Pmaxm . This because a larger Pmaxm

leads to a higher throughput which generates more workloadsof baseband signal processing in the BBU pool. The heavy-loaded BBU pool leaves a small room to the HERM algorithmfor further improving the energy efficiency.

Both the HERM and ERA algorithms show significantlybetter performance than the baseline algorithm. Besides, theNEE with the baseline algorithm decreases after Pmaxm reachesa certain value. This is because the baseline algorithm allocatesas much power as available without any optimization on theenergy efficiency.

D. Impact of energy factors

In the network energy consumption model, there are twoenergy factors, ∆m and ρm. ∆m characterizes the relationshipbetween the dynamic power consumption and the traffic loadin the mth RRH; ρm defines the relationship between the VMenergy consumption and the radio resource allocation. In thissimulation, we evaluate how these energy factors impact theNEE. To quantify the impact, we assume that ∆m = ∆n andρm = ρn, ∀m,n ∈M.

Fig. 8 shows the NEE under different algorithms versus theenergy factor ∆m. It can be observed that the NEE decreaseswith the increase of ∆m. This because a larger ∆m results inmore energy consumption in transmitting the same amount ofdata traffic in a RAP. When ∆m is small, e.g., ∆m = 1, theNEE with the HERM algorithm is 21% better than that withthe ERA algorithm. When ∆m increases to 80, the HERMalgorithm is only 6% better than the ERA algorithm in termsof the NEE. That is, the advantage of the HERM algorithmis gradually neutralized by an increasing ∆m. The reason isthat a large ∆m makes RAPs the dominant energy consumer

The energy factor of the BBU pool m

0.1

0.8

0.2

0.3

0.4

0.5

0.6

0.7

Net

wo

rk E

ner

gy

Eff

icie

ncy

(M

bit

s/s/

Joul

e)

K=10 UEsK=10 UEsK=20 UEsK=20 UEs

K=5 UEsK=5 UEsK=10 UEsK=20 UEs

K=5 UEs

0 3 6 9 12 15 18 21 24 27 30

Fig. 10. The NEE versus ρm with different numbers of UEs.

in the network. As a result, the optimization in the BBU poolprovided by the HERM algorithm does not enable a significantperformance improvement. Fig. 8 also shows that both theHERM and ERA algorithms can achieve much higher energyefficiency than the baseline algorithm.

Fig. 9 shows the impact of ρm on the NEE with differentalgorithms. As shown in the figure, a larger ρm leads to alower energy efficiency because more energy is consumedfor processing the same amount of baseband signals in theBBU pool. The advantage of the HERM algorithm in termsof optimizing the NEE becomes more significant with a largerρm. For example, when ρm = 9 and ρm = 27, the NEEachieved by the HERM algorithm are 37% and 55% betterthan that with the ERA algorithm, respectively. This indicatesthat optimizing the BBU pool is more important in a lessenergy-efficient cloud platform.

Fig. 10 shows the NEE achieved by the HERM algorithmversus ρm under different numbers of UEs. As shown in thefigure, when ρm is large, e.g., ρm = 24, the NEE with differentnumbers of UEs tends to be the same. When ρm is small, thestatic power consumption accounts for the largest parts of the

11

overall energy consumption in the network. As a result, whenthe number of UEs increases, the network may serve moretraffic loads at the cost of slightly higher traffic-dependentenergy consumption (dynamic energy consumption). Whenρm is large, the profit (higher data rate) achieved by servingmore UEs is neutralize by the energy consumption increment.Therefore, the network tends to have the same NEE underdifferent number of UEs when ρm is large.

VII. CONCLUSION

In this paper, we have studied the impact of the radioresource management on the energy efficiency of H-CRAN.We have developed a network energy consumption modelthat catheterizes the energy consumption of base stations(BSs), fronthaul, and the BBU pool in H-CRAN. Based onthe network energy computing model, we have formulatedthe network energy efficiency optimization problem and de-signed H-CRAN energy-efficient radio resource management(HERM) algorithm to solve the problem. We have provedthe convergence and optimality of the HERM algorithm andvalidated its performance through extensive simulations. Thesimulation results have revealed insights on optimizing theenergy efficiency of H-CRAN under different network condi-tions.

APPENDIX APROOF OF LEMMA 1

Denote (A,P) as any feasible solution to the problemin Eq. (12). Since (A∗,P∗) is the optimal solution to theproblem,

RT (A∗,P∗)− q∗PT (A∗,P∗) ≥ RT (A,P)− q∗PT (A,P).(33)

Because RT (A∗,P∗) − q∗PT (A∗,P∗) = 0, RT (A,P) −q∗PT (A,P) ≤ 0. PT (A,P) is the H-CRAN power consump-tion which is larger than zero. Therefore,

RT (A,P)

PT (A,P)≤ q∗. (34)

Hence,RT (A,P)

PT (A,P)≤ RT (A∗,P∗)

PT (A∗,P∗). (35)

Thus, (A∗,P∗) maximizes RT (A,P)PT (A,P)

while satisfying allthe constraints in the NEE optimization problem. That is,(A∗,P∗) is the optimal solution to the NEE optimizationproblem. Then, the lemma is proved.

APPENDIX BPROOF OF LEMMA 2

In order to prove Lemma 2, we first prove {A∗,P∗} is theoptimal solution to Problem P1 and then prove that {A∗,P∗}is also the optimal solution to Problem P0.

A. The optimal solution to Problem P1:

To prove {A∗,P∗} is the optimal solution to Problem P1,we first show that {A∗,P∗} derived based on the HERMalgorithm maximizes f(A,P), and then prove the convergenceof Lagrange dual function g(µ,γ,ν).

Proposition 1. {A∗,P∗} maximizes f(A,P).

Proof: Denote {A,P} as any feasible RB assignmentand power allocation. Let {A∗,P∗} be the RB assignmentand power allocation obtained derived based on Eqs. (30) and(26), respectively. Since f(A,P) is convex with respect toP, P∗ is derived based on the Karush-Kuhn-Tucker (KKT)condition [16]. Therefore, f(A,P∗) ≥ f(A,P).

Let α∗k,m,n be the RB assignment derived using the HERMalgorithm. Then, f(A∗,P∗) =

∑k∈K

∑m∈M

α∗k,m,nHk,m,n, and

f(A∗,P∗)−f(A,P∗)

=∑k∈K

∑m∈M

(α∗k,m,nHk,m,n − αk,m,nHk,m,n

)(36)

Since∑k∈K

∑m∈M α∗k,m,n = 1,

∑k∈K

∑m∈M αk,m,n = 1

and

α∗k,m,n =

{1, k = arg max

k∈KHk,m,n

0, otherwise,(37)

f(A∗,P∗)− f(A,P∗) ≥ 0. (38)

Therefore, the power allocation and RB assignment derivedusing the HERM algorithm maximizes f(A,P).

After deriving {A∗,P∗}, we obtain g(µ,γ,υ) based onEqs. (22), (23), and (24) in each iteration.

Proposition 2. g(µ,γ,υ) converges if the step sizes in up-dating the Lagrangian multipliers are properly selected.

Proof: The convergence of the Lagrangian multipliersare well proved in Proposition 8.2.4 in [17]. For the sake ofbrevity, we omit the detailed proof.

Based on the above analysis, we can conclude that the powerallocation and RB assignment derived by the HERM algorithmoptimize Problem P0.

B. The optimal solution to Problem P0

According to Eq. (30)), α∗k,m,n equals either 0 or 1. There-fore, the RB assignment derived by the HERM algorithmis the binary RB assignment that satisfies the constraints ofProblem P0. Therefore, the RB assignment derived by theHERM algorithm is the optimal solution to Problem P0. Sincethe problem relaxation does not impact the power allocation.Therefore, the optimal RB assignment and power allocation,{A∗,P∗}, derived by the HERM algorithm optimizes P0.

APPENDIX CPROOF OF LEMMA 3

We prove the convergence of the HERM algorithm byshowing the convergence of β and q∗, respectively.

A. The convergence of β

The HERM algorithm relies on the iterative weight updatesin Eq. (17) to deactivate fronthaul for energy savings. It ischallenging to prove the convergence of β under arbitraryreweighting function. However, we show that if the reweight-ing function is chosen as

h(Im, τ) =1

(Im + τ) ln(1 + τ−1), (39)

12

where ξ = 1ln(1+τ−1) . The l0-norm approximation in the

HERM algorithm can be seen as a special case of themajorization-minimization (MM) algorithms [54] [55] and isguaranteed to converge.

B. The convergence of q∗

Define F (q) = max{A,P}

{RT (A,P)− qPT (A,P)

}.

Proposition 3. F (q) is a strictly monotonic decreasing func-tion with respect to q.

Proof: Denote{A1,P1

}and

{A2,P2

}as the solutions

to F (q1) and F (q2), respectively. Then,

F (q1) = max{A,P}

{RT (A,P)− q1PT (A,P)

}= RT

(A1,P1

)− q1PT

(A1,P1

)> RT

(A2,P2

)− q1PT

(A2,P2

) (40)

Assume q2 > q1. Since PT(A2,P2

)≥ 0

RT(A2,P2

)− q1PT

(A2,P2

)≥ RT

(A2,P2

)− q2PT

(A2,P2

)= F (q2)

(41)

Therefore, F (q1) > F (q2). Hence, F (q) is a strictly mono-tonic decreasing function with respect to q.

Proposition 4. F (q) is a non-negative function when p is de-termined by any feasible RB assignment and power allocation.

Proof: Denote{A1,P1

}as any feasible RB assignment

and power allocation. According to the Dinkelbach algo-rithm [14],

q1 =RT(A1,P1

)PT (A1,P1)

. (42)

Therefore,

F (q1) = max{A,P}

{RT (A,P)− q1PT (A,P)

}≥ RT

(A1,P1

)− q1PT

(A1,P1

)= 0.

(43)

Hence, F (q) is larger than zero when p is determined by anyfeasible RB assignment and power allocation.

Given Propositions 3 and 4, the convergence of q∗ can beproved by showing that q∗ increases in each iteration. When q∗

keeps increasing, F (q∗) will gradually decrease to zero. OnceF (q∗) = 0, q∗ converges. Next, we show that q∗ increases ineach iteration. In the HERM algorithm, the value of q∗ in the(i+ 1)th iteration is updated according to

q(i+1) = RT(A(i),P(i)

)/PT(A(i),P(i)

)(44)

Here, {A(i),P(i)} is the optimal solution to F (q(i)). There-fore,

F (q(i)) = RT(A(i),P(i)

)− q(i)PT

(A(i),P(i)

). (45)

Since F (q(i)) > 0 until q∗ converges,

RT(A(i),P(i)

)− q(i)PT

(A(i),P(i)

)> 0 (46)

Hence,

q(i) < RT(A(i),P(i)

)/PT(A(i),P(i)

)= q(i+1). (47)

As q(i+1) increases, F (q(i+1)) will eventually reach zero.Then, q(i+1) converges to q∗.

Therefore, with the proofs of the convergence β and q∗, wecan conclude that the proposed HERM algorithm converges.Since F (q∗) reaches its maximum value when q∗ converges,the HERM algorithm converges to the optimal solution.

APPENDIX DTHE VALUE OF Nµ,γ,υ

Denote φ(i) = [µ(i),γ(i),υ(i)] and δ = [δµ, δγ , δυ]as the Lagrangian multipliers in the ith iteration and thecorresponding step sizes, respectively. Define φ(0) and φ∗

as the initial and optimal Lagrangian multipliers, respectively.The sub-gradient of the dual function expressed in Eq. (31) isdefined as ∇ (φ). Let

Cj = supi>0{‖f‖| f ∈ ∇φj(i) ∪∇φj(i− 1)} . (48)

Then, C =∑j∈φ

Cj . The value of Nµ,γ,υ can be derived based

on the following proposition.

Proposition 5. For any positive scalar ε, we have

min0≤i≤Nµ,γ,υ

g(φ(i)) ≤ g∗ +δC2 + ε

2, (49)

where Nµ,γ,υ is given by

Nµ,γ,υ =

⌊‖φ(0),φ∗‖2

δε

⌋. (50)

Proof: The proposition can be proved by showing thatg(φ(i)) keeps decreasing in each iteration until reaching itsminimum value if the step size δ is properly selected. Nµ,γ,υis derived when g(φ(i)) is optimized. The detail proof can befound in Proposition 8.2.3 in [17].

REFERENCES

[1] I. F. Akyildiz, S. Nie, S.-C. Lin, and M. Chandrasekaran, “5G roadmap:10 key enabling technologies,” Computer Networks, vol. 106, pp. 17–48,2016.

[2] A. Damnjanovic, J. Montojo, Y. Wei, T. Ji, T. Luo, M. Vajapeyam,T. Yoo, O. Song, and D. Malladi, “A survey on 3GPP heterogeneousnetworks,” IEEE Wireless Communications, vol. 18, no. 3, pp. 10–21,June 2011.

[3] C. Mobile, “C-RAN: the road towards green RAN,” White Paper, ver,vol. 2, 2011.

[4] M. Peng, C. Wang, V. Lau, and H. V. Poor, “Fronthaul-constrainedcloud radio access networks: Insights and challenges,” IEEE WirelessCommunications, vol. 22, no. 2, pp. 152–160, 2015.

[5] A. Checko, H. L. Christiansen, Y. Yan, L. Scolari, G. Kardaras, M. S.Berger, and L. Dittmann, “Cloud RAN for mobile networks—a tech-nology overview,” IEEE Communications surveys & tutorials, vol. 17,no. 1, pp. 405–426, 2015.

[6] S. Buzzi, C. L. I, T. E. Klein, H. V. Poor, C. Yang, and A. Zappone, “Asurvey of energy-efficient techniques for 5G networks and challengesahead,” IEEE Journal on Selected Areas in Communications, vol. 34,no. 4, pp. 697–709, April 2016.

[7] G. Wu, C. Yang, S. Li, and G. Y. Li, “Recent advances in energy-efficient networks and their application in 5G systems,” IEEE WirelessCommunications, vol. 22, no. 2, pp. 145–151, April 2015.

[8] K. Miyamoto, S. Kuwano, J. Terada, and A. Otaka, “Performanceevaluation of mobile fronthaul optical bandwidth reduction and wirelesstransmission in split-phy processing architecture,” in Optical FiberCommunications Conference and Exhibition, March 2016, pp. 1–3.

13

[9] ——, “Split-phy processing architecture to realize base station coordi-nation and transmission bandwidth reduction in mobile fronthaul,” in2015 Optical Fiber Communications Conference and Exhibition (OFC),March 2015, pp. 1–3.

[10] D. Sabella, A. De Domenico, E. Katranaras, M. A. Imran, M. Di Giro-lamo, U. Salim, M. Lalam, K. Samdanis, and A. Maeder, “Energyefficiency benefits of ran-as-a-service concept for a cloud-based 5Gmobile network infrastructure,” IEEE Access, vol. 2, pp. 1586–1597,2014.

[11] J. Bartelt, G. Fettweis, D. Wubben, M. Boldi, and B. Melis, “Hetero-geneous backhaul for cloud-based mobile networks,” in IEEE VehicularTechnology Conference (VTC Fall). IEEE, 2013, pp. 1–5.

[12] X. Ge, H. Cheng, M. Guizani, and T. Han, “5G wireless backhaulnetworks: challenges and research advances,” IEEE Network, vol. 28,no. 6, pp. 6–11, 2014.

[13] K. G. Murty and S. N. Kabadi, “Some NP-complete problems inquadratic and nonlinear programming,” Mathematical Programming,vol. 39, no. 2, pp. 117–129, 1987.

[14] W. Dinkelbach, “On nonlinear fractional programming,” ManagementScience, vol. 13, no. 7, pp. 492–498, 1967.

[15] E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity byreweighted `1 minimization,” Journal of Fourier analysis and applica-tions, vol. 14, no. 5-6, pp. 877–905, 2008.

[16] S. Boyd and L. Vandenberghe, Convex optimization. Cambridgeuniversity press, 2004.

[17] D. P. Bertsekas, A. Nedi, A. E. Ozdaglar et al., Convex analysis andoptimization. Athena Scientific, 2003.

[18] D. Feng, C. Jiang, G. Lim, L. J. Cimini, G. Feng, and G. Y. Li, “A surveyof energy-efficient wireless communications,” IEEE CommunicationsSurveys & Tutorials, vol. 15, no. 1, pp. 167–178, 2013.

[19] N. Ansari, T. Han, and M. Taheri, “Gate: greening at the edges,” IEEEWireless Communications, vol. 23, no. 2, pp. 62–69, 2016.

[20] A. Fehske, G. Fettweis, J. Malmodin, and G. Biczok, “The globalfootprint of mobile communications: The ecological and economicperspective,” IEEE Communications Magazine, vol. 49, no. 8, pp. 55–62,2011.

[21] T. Han and N. Ansari, “On optimizing green energy utilization forcellular networks with hybrid energy supplies,” IEEE Transactions onWireless Communications, vol. 12, no. 8, pp. 3872–3882, 2013.

[22] R. Xie, F. R. Yu, H. Ji, and Y. Li, “Energy-efficient resource allocationfor heterogeneous cognitive radio networks with femtocells,” IEEETransactions on Wireless Communications, vol. 11, no. 11, pp. 3910–3920, 2012.

[23] Q. Chen, G. Yu, R. Yin, and G. Y. Li, “Energy-efficient user associationand resource allocation for multistream carrier aggregation,” IEEETransactions on Vehicular Technology, vol. 65, no. 8, pp. 6366–6376,Aug 2016.

[24] H. Pervaiz, L. Musavian, Q. Ni, and Z. Ding, “Energy and spectrumefficient transmission techniques under QoS constraints toward greenheterogeneous networks,” IEEE Access, vol. 3, pp. 1655–1671, 2015.

[25] X. Zhang, R. Yu, Y. Zhang, Y. Gao, M. Im, L. Cuthbert, and W. Wang,“Energy-efficient multimedia transmissions through base station coop-eration over heterogeneous cellular networks exploiting user behavior,”IEEE Wireless Communications, vol. 21, no. 4, pp. 54–61, 2014.

[26] J. Wu, Y. Bao, G. Miao, S. Zhou, and Z. Niu, “Base-station sleepingcontrol and power matching for energy–delay tradeoffs with burstytraffic,” IEEE Transactions on Vehicular Technology, vol. 65, no. 5, pp.3657–3675, 2016.

[27] S. Zhang, J. Gong, S. Zhou, and Z. Niu, “How many small cells canbe turned off via vertical offloading under a separation architecture?”IEEE Transactions on Wireless Communications, vol. 14, no. 10, pp.5440–5453, 2015.

[28] T. Han and N. Ansari, “On greening cellular networks via multicellcooperation,” IEEE Wireless Communications Magazine, vol. 20, no. 1,pp. 82–89, Feb. 2013.

[29] ——, “A traffic load balancing framework for software-defined radioaccess networks powered by hybrid energy sources,” IEEE/ACM Trans-actions on Networking, vol. 24, no. 2, pp. 1038–1051, April 2016.

[30] V. Chamola, B. Sikdar, and B. Krishnamachari, “Delay aware resourcemanagement for grid energy savings in green cellular base stations withhybrid power supplies,” IEEE Transactions on Communications, 2016.

[31] T. Han and N. Ansari, “Powering mobile networks with green energy,”IEEE Wireless Communications, vol. 21, no. 1, pp. 90–96, Feb. 2014.

[32] J. Yang and S. Ulukus, “Optimal packet scheduling in a multiple accesschannel with energy harvesting transmitters,” Journal of Communica-tions and Networks, vol. 14, no. 2, pp. 140–150, April 2012.

[33] Q. Liu, G. Wu, Y. Guo, Y. Zhang, and S. Hu, “Energy efficient resourceallocation for control data separated heterogeneous-CRAN,” in IEEEGlobal Communications Conference (GLOBECOM), Dec 2016, pp. 1–6.

[34] M. Peng, K. Zhang, J. Jiang, J. Wang, and W. Wang, “Energy-efficientresource assignment and power allocation in heterogeneous cloud radioaccess networks,” IEEE Transactions on Vehicular Technology, vol. 64,no. 11, pp. 5275–5287, 2015.

[35] J. Tang, W. P. Tay, and T. Q. Quek, “Cross-layer resource allocation withelastic service scaling in cloud radio access network,” IEEE Transactionson Wireless Communications, vol. 14, no. 9, pp. 5068–5081, 2015.

[36] D. Pompili, A. Hajisami, and T. X. Tran, “Elastic resource utilizationframework for high capacity and energy efficiency in cloud ran,” IEEECommunications Magazine, vol. 54, no. 1, pp. 26–32, 2016.

[37] V. N. Ha and L. B. Le, “Joint coordinated beamforming and admissioncontrol for fronthaul constrained cloud-rans,” in 2014 IEEE GlobalCommunications Conference. IEEE, 2014, pp. 4054–4059.

[38] O. Dhifallah, H. Dahrouj, T. Y. Al-Naffouri, and M.-S. Alouini, “Jointhybrid backhaul and access links design in cloud-radio access networks,”in IEEE Vehicular Technology Conference. IEEE, 2015, pp. 1–5.

[39] A. De la Oliva, X. C. Perez, A. Azcorra, A. Di Giglio, F. Cavaliere,D. Tiegelbekkers, J. Lessmann, T. Haustein, A. Mourad, and P. Iovanna,“Xhaul: toward an integrated fronthaul/backhaul architecture in 5Gnetworks,” IEEE Wireless Communications, vol. 22, no. 5, pp. 32–40,2015.

[40] T. S. Rappaport et al., Wireless communications: principles and practice.prentice hall PTR New Jersey, 1996, vol. 2.

[41] N. C. A. L. Ericsson AB, Huawei Technologies Co. Ltd, N. Solutions,and N. G. . C. KG, “CPRI specification 6.1,” Jul. 2014. [Online].Available: http://www.cpri.info/

[42] J. i. Kani, J. Terada, K. I. Suzuki, and A. Otaka, “Solutions forfuture mobile fronthaul and access-network convergence,” Journal ofLightwave Technology, vol. 35, no. 3, pp. 527–534, 2017.

[43] N. J. Gomes, P. Assimakopoulos, M. K. Al-Hares, U. Habib, andS. Noor, “The new flexible mobile fronthaul: Digital or analog, or both?”in Proc. ICTON 2016, Jul. 2016, pp. 1–4.

[44] Reply LS on Formation of IEEE 1914 Next Generation FronthaulInterface Working Group. 3GPP RAN3, May 2016.

[45] G. Auer, O. Blume, V. Giannini, I. Godor, M. Imran, Y. Jading, E. Ka-tranaras, M. Olsson, D. Sabella, P. Skillermark et al., “D2. 3: Energyefficiency analysis of the reference systems, areas of improvements andtarget breakdown,” EARTH, pp. 1–69, 2010.

[46] A. R. Dhaini, P.-H. Ho, G. Shen, and B. Shihada, “Energy effi-ciency in tdma-based next-generation passive optical access networks,”IEEE/ACM Transactions on Networking, vol. 22, no. 3, pp. 850–863,2014.

[47] S. S. Lee and A. Chen, “Design and analysis of a novel energy efficientethernet passive optical network,” in IEEE 2010 Ninth InternationalConference on Networks (ICN). IEEE, 2010, pp. 6–9.

[48] K. Guo, M. Sheng, J. Tang, T. Q. Quek, and Z. Qiu, “Exploiting hybridclustering and computation provisioning for green c-ran,” IEEE Journalon Selected Areas in Communications, vol. 34, no. 12, pp. 4063–4076,2016.

[49] W. Yu and R. Lui, “Dual methods for nonconvex spectrum optimiza-tion of multicarrier systems,” IEEE Transactions on Communications,vol. 54, no. 7, pp. 1310–1322, 2006.

[50] “LTE; evolved universal terrestrial radio access (E-UTRA); mediumaccess control (MAC) protocol specification (3GPP TS 36.321 version12.5.0 release 12).” [Online]. Available: http://www.etsi.org/deliver/etsi ts/136300 136399/136321/12.05.00 60/ts 136321v120500p.pdf

[51] L. Valcarenghi, K. Kondepu, A. Sgambelluri, F. Cugini, P. Castoldi,R. A. Morenilla, D. Larrabeiti, and B. Vermeulen, “SDN-controlledenergy-efficient mobile fronthaul: An experimental evaluation in fed-erated testbeds,” in European Conference on Networks and Communi-cations (EuCNC). IEEE, June 2016, pp. 298–301.

[52] L. Shi, B. Mukherjee, and S.-S. Lee, “Energy-efficient PON with sleep-mode ONU: progress, challenges, and solutions,” IEEE Network, vol. 26,no. 2, 2012.

[53] X. Chu, D. Lopez-Perez, Y. Yang, and F. Gunnarsson, HeterogeneousCellular Networks: Theory, Simulation and Deployment. CambridgeUniversity Press, 2013.

[54] B. K. Sriperumbudur, D. A. Torres, and G. R. Lanckriet, “Amajorization-minimization approach to the sparse generalized eigenvalueproblem,” Machine learning, vol. 85, no. 1-2, pp. 3–39, 2011.

[55] B. Dai and W. Yu, “Energy efficiency of downlink transmission strategiesfor cloud radio access networks,” IEEE Journal on Selected Areas inCommunications, vol. 34, no. 4, pp. 1037–1050, 2016.