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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 11, NOVEMBER 2015 5275

Energy-Efficient Resource Assignment and PowerAllocation in Heterogeneous Cloud Radio

Access NetworksMugen Peng, Senior Member, IEEE, Kecheng Zhang, Jiamo Jiang, Jiaheng Wang, Member, IEEE, and

Wenbo Wang, Member, IEEE

Abstract—Taking full advantage of both heterogeneous net-works and cloud access radio access networks, heterogeneouscloud radio access networks (H-CRANs) are presented to en-hance both spectral and energy efficiencies, where remote radioheads (RRHs) are mainly used to provide high data rates forusers with high quality of service (QoS) requirements, whereasthe high-power node (HPN) is deployed to guarantee seamlesscoverage and serve users with low-QoS requirements. To miti-gate the intertier interference and improve energy efficiency (EE)performances in H-CRANs, characterizing user association withRRH/HPN is considered in this paper, and the traditional softfractional frequency reuse (S-FFR) is enhanced. Based on theRRH/HPN association constraint and the enhanced S-FFR, anenergy-efficient optimization problem with the resource assign-ment and power allocation for the orthogonal-frequency-division-multiple-access-based H-CRANs is formulated as a nonconvexobjective function. To deal with the nonconvexity, an equivalentconvex feasibility problem is reformulated, and closed-form ex-pressions for the energy-efficient resource allocation solution tojointly allocate the resource block and transmit power are derivedby the Lagrange dual decomposition method. Simulation resultsconfirm that the H-CRAN architecture and the correspondingresource allocation solution can enhance the EE significantly.

Index Terms—Fifth-generation (5G), fractional frequency reuse(FFR), green communication, heterogeneous cloud radio accessnetwork (H-CRAN), resource allocation.

Manuscript received March 11, 2014; revised July 12, 2014, September 10,2014, and November 25, 2014; accepted December 5, 2014. Date of publicationDecember 12, 2014; date of current version November 10, 2015. The work ofM. Peng, K. Zhang, and W. Wang was supported in part by the NationalNatural Science Foundation of China under Grant 61222103, by the NationalBasic Research Program of China (973 Program) under Grant 2013CB336600and Grant 2012CB316005, by the State Major Science and Technology Spe-cial Projects under Grant 2013ZX03001001, by the Beijing Natural ScienceFoundation under Grant 4131003, and by the Specialized Research Fund forthe Doctoral Program of Higher Education under Grant 20120005140002. Thework of J. Wang was supported by the National Natural Science Foundationof China under Grant 61201174, by the Natural Science Foundation of JiangsuProvince under Grant BK2012325, and by the Fundamental Research Fundsfor the Central Universities. The review of this paper was coordinated byDr. F. Gunnarsson.

M. Peng, K. Zhang, and W. Wang are with the Key Laboratory of UniversalWireless Communications for Ministry of Education, Beijing University ofPosts and Telecommunications, Beijing 215233, China (e-mail: [email protected]; [email protected]; [email protected]).

J. Jiang is with the Institute of Communication Standards Research, ChinaAcademy of Telecommunication Research of MIIT, Beijing 100191, China(e-mail: [email protected]).

J. Wang is with the National Mobile Communications Research Laboratory,Southeast University, Nanjing 210096, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2014.2379922

I. INTRODUCTION

C LOUD radio access networks (C-RANs) are being recog-nized to curtail capital and operating expenditures, as well

as to provide a high transmission bit rate with fantastic energyefficiency (EE) performances [1], [2]. Remote radio heads(RRHs) operate as soft relay by compressing and forwardingthe received signals from the mobile user equipment (UE) tothe centralized baseband unit (BBU) pool through wire/wirelessfronthaul links. To highlight the advantages of C-RAN, thejoint decompression and decoding schemes are executed inthe BBU pool [3]. However, the nonideal fronthaul with lim-ited capacity and long time delay degrades performances ofC-RANs. Furthermore, it is critical to decouple the control anduser planes in C-RANs, and RRHs are efficient to provide highcapacity without considering functions of control planes. Howto alleviate the negative influence of the constrained fronthaulon EE performances and how to broadcast control signalings toUEs without RRHs are still not straightforward in C-RANs [4].

Meanwhile, high-power nodes (HPNs; e.g., macro or microbase stations) existing in heterogeneous networks (HetNets) arestill critical to guarantee the backward compatibility with thetraditional cellular networks and support the seamless coveragesince low-power nodes (LPNs) are mainly deployed to providehigh bit rates in special zones [5]. Under the help of HPNs,the unnecessary handover can be avoided, and the synchronousconstraints among LPNs can be alleviated. Accurately, althoughthe HetNet is a good alternative to improve both coverage andcapacity simultaneously, there are two remarkable challenges toblock its commercial applications: 1) Coordinated multipointtransmission and reception needs a huge number of signal-ings in backhaul links to mitigate the intertier interferencesbetween HPNs and LPNs, whereas backhaul capacity is oftenconstrained; 2) the ultradense LPNs improve capacity with thecost of consuming too much energy, which results in low EEperformances.

To overcome these aforementioned challenges in bothC-RANs and HetNets, a new architecture and technologyknown as the heterogeneous cloud radio access network (H-CRAN) is presented as a promising paradigm for future het-erogeneous converged networks [6]. The H-CRAN architectureshown in Fig. 1 takes full advantage of both C-RANs andHetNets, where RRHs with low energy consumption cooperatewith each other in the BBU pool to achieve high cooperativegains. The BBU pool is interfaced to HPNs for coordinating the

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5276 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 11, NOVEMBER 2015

Fig. 1. System architecture of the proposed H-CRANs.

intertier interferences between RRHs and HPNs. Only the frontradio frequency and simple symbol processing functionalitiesare configured in RRHs, whereas the other important basebandphysical processing and procedures of the upper layers areexecuted in the BBU pool. By contrast, the entire communi-cation functionalities from the physical to network layers areimplemented in HPNs. The data and control interfaces betweenthe BBU pool and HPNs are S1 and X2, respectively, which areinherited from definitions of the Third-Generation PartnershipProject (3GPP) standards. Compared with the traditionalC-RAN architecture in [1], H-CRANs alleviate the fronthaulconstraints between RRHs and the BBU pool by incorpo-rating HPNs. The control and broadcast functionalities areshifted from RRHs to HPNs, which alleviates capacity andtime delay constraints on the fronthaul and supports the bursttraffic efficiently. The adaptive signaling/control mechanismbetween connection-oriented and connectionless is supportedin H-CRANs, which can achieve significant overhead savingsin the radio connection/release by moving away from a pureconnection-oriented mechanism.

In H-CRANs, the RRH/HPN association strategy is criticalfor improving EE performances, and main differences from thetraditional cell association techniques are twofold. First, thetransmit power of RRHs and HPNs is significantly different.Second, the inter-RRH interferences can be jointly coordinatedthrough the centralized cooperative processing in the BBUpool, whereas the intertier interferences between HPNs andRRHs are severe and difficult to mitigate. Consequently, it isnot always efficient for UEs to be associated with neighborRRHs/HPNs via the strongest receiving power mechanism [7].As shown in Fig. 1, though obtaining the same receiving powerfrom RRH1 and HPN, both UE1 and UE2 prefer to associatewith RRH1 because lower transmit power is needed and moreradio resources are allocated from RRH1 than those from theHPN. Meanwhile, the association with RRHs can decreaseenergy consumption by saving massive use of air conditioning.

Based on the aforementioned RRH/HPN association char-acteristics, the joint optimization solution for resource block(RB) assignment and power allocation to maximize EE per-

formances in the orthogonal frequency-division multiple access(OFDMA)-based H-CRANs is researched in this paper.

A. Related Work

OFDMA is a promising multiaccess technique for exploitingchannel variations in both frequency and time domains to pro-vide high data rates in the fourth-generation (4G) and beyondcellular networks. To be backward compatible with 4G systems,the OFDMA is adopted in H-CRANs by assigning differentRBs to different UEs. Recently, the radio resource allocation(RA) to maximize the spectral efficiency (SE) or meet diversequality of service (QoS) requirements in OFDMA systems hasattracted considerable attention [8]–[11]. The relay selectionproblem in a network with multiple UEs and multiple amplify-and-forward relays is investigated in [8], where an optimalrelay selection scheme whose complexity is quadratic in thenumber of UEs and relays is presented. Li et al. in [9] proposedan asymptotical resource allocation algorithm via leveragingthe cognitive radio (CR) technique in open-access OFDMAfemtocell networks. The resource optimization for spectrumsharing with interference control in CR systems is researchedin [10], where the achievable transmission rate of the secondaryuser over Rayleigh channels subject to a peak power constraintat the secondary transmitter and an average interference powerconstraint at the primary receiver is maximized. In [11], theoptimal power allocation for minimizing the outage probabilityin point-to-point fading channels with the energy-harvestingconstraints is investigated.

The EE performance metric has become a new design goaldue to the sharp increase of the carbon emission and operatingcost of wireless communication systems [12]. The EE-orientedradio resource allocation has been studied in various networks[13]–[16]. In [13], the distributed power allocation for multicellOFDMA networks taking both EE and intercell interferencemitigation into account is investigated, where a biobjectiveproblem is formulated based on the multiobjective optimizationtheory. To maximize the average EE performance of multipleUEs each with a transceiver of constant circuit power, thepower allocation, RB allocation, and relay selection are jointlyoptimized in [14]. The active number of subcarriers and thenumber of bits allocated to each RB at the source nodes areoptimized to maximize EE performances in [15], where theoptimal solution turns out to be a bidirectional waterfilling bitallocation to minimize the overall transmit power. To maximizeEE performances under constraints of total transmit powerand interference in CR systems, an optimal power allocationalgorithm using equivalent conversion is proposed in [16].

Intuitively, the intercell or intertier interference mitigationis key to improving both SE and EE performances. Someadvanced algorithms in HetNets, such as cell association andfractional frequency reuse (FFR), have been proposed in [17]and [18], respectively. In [19], a network utility maximizationformulation with a proportional fairness objective is presented,where prices are updated in the dual domain via coordinatedescent. In [20], energy-efficient cellular networks through theemployment of the base station with sleep-mode strategies,

PENG et al.: RESOURCE ASSIGNMENT AND POWER ALLOCATION IN H-CRANs 5277

as well as small cells, are researched, and the correspondingtradeoff issue is discussed as well.

To the best of our knowledge, there is lack of solutions formaximizing the EE performance in H-CRANs. Particularly, theRRH/HPN association strategy should be enhanced fromthe traditional strongest received power strategy. Furthermore,the radio resource allocation to achieve an optimal EE per-formance in H-CRANs is still not straightforward. To dealwith these problems, the joint optimization solution with theRB assignment and power allocation subject to the RRH/HPNassociation and interference mitigation should be investigated.

B. Main Contributions

The goal of this paper is to investigate the joint optimiza-tion problem with the RB assignment and power allocationsubject to the RRH/HPN association and intertier interferencemitigation to maximize EE performances in the OFDMA-basedH-CRAN system. The EE performance optimization is highlychallenging because the energy-efficient resource allocationin H-CRANs is a nonconvex objective problem. Differentfrom the published radio resource optimization in HetNets andC-RANs, the characteristics of H-CRANs should be high-lighted and modeled. To simplify the coordinated schedulingbetween RRHs and the HPN, an enhanced soft fractionalfrequency reuse (S-FFR) scheme is presented to improve per-formances of cell-center-zone UEs served by RRHs with indi-vidual spectrum frequency resources. The contributions of thispaper can be summarized as follows.

• To overcome challenges in HetNets and C-RANs,H-CRANs are presented as cost-efficient potential solu-tions to improve spectral and energy efficiencies, in whichRRHs are mainly used to provide high data rates for UEswith high-QoS requirements in the hot spots, whereasHPNs are deployed to guarantee seamless coverage forUEs with low-QoS requirements.

• To mitigate the intertier interference between RHHs andHPNs, an enhanced S-FFR scheme is proposed, wherethe total frequency band is divided into two parts. Onlypartial spectral resources are shared by RRHs and HPNs,whereas the other is solely occupied by RRHs. The exclu-sive RBs are allocated to UEs with high-rate-constrainedQoS requirements, whereas the shared RBs are allocatedto UEs with low-rate-constrained QoS requirements.

• An energy-efficient optimization problem with the RBassignment and power allocation under constraints of theintertier interference mitigation and RRH/HPN associ-ation is formulated as a nonconvex objective function.To deal with this nonconvexity, an equivalent convexfeasibility problem is reformulated, based on which, an it-erative algorithm consisting of both outer- and inner-loopoptimizations is proposed to achieve the global optimalsolution.

• We numerically evaluate EE performance gains ofH-CRANs and the corresponding resource allocation op-timization solution. Simulation results demonstrate thatEE performance gain of the H-CRAN architecture over

Fig. 2. Principle of the proposed enhanced S-FFR scheme. (a) TraditionalS-FFR. (b) Enhanced S-FFR.

the traditional C-RAN/HetNet is significant. The pro-posed iterative solution is converged, and its EE perfor-mance gain over the baseline algorithms is impressive.

The remainder of this paper is organized as follows. InSection II, we describe the system model of H-CRANs, theproposed enhanced S-FFR, and the problem formulation. Theoptimization framework is introduced in Section III. Section IVprovides simulations to verify the effectiveness of the proposedH-CRAN architecture and the corresponding solutions. Finally,we conclude this paper in Section V.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The traditional S-FFR is considered as an efficient intercelland intertier interference coordination technique, in which theservice area is partitioned into spatial subregions, and eachsubregion is assigned to different frequency subbands. Asshown in Fig. 2(a), the cell-edge-zone UEs do not interferewith cell-center-zone UEs, and the intercell interference canbe suppressed with an efficient channel allocation method [21].The HPN is mainly used to deliver the control signalings andguarantee the seamless coverage for UEs accessing the HPN(denoted by HUEs) with low-QoS requirements. By contrast,the QoS requirement for UEs accessing RRH (denoted byRUEs) is often with a higher priority. Consequently, as shownin Fig. 2(b), an enhanced S-FFR scheme is proposed to mitigatethe intertier interference between HPNs and RRHs, in whichonly partial radio resources are allocated to both RUEs andHUEs with low-QoS requirements, and the remaining radioresources are allocated to RUEs with high-QoS requirements.In the proposed enhanced S-FFR, RUEs with low-QoS require-ments share the same radio resources with HUEs, which isabsolutely different from that in the traditional S-FFR. If thetraditional S-FFR is utilized in H-CRANs, only the cell-center-zone RUEs share the same radio resources with HUEs, whichdecreases the SE performance significantly. Furthermore, it ischallenging to judge whether UEs are located in the cell-edgeor cell-center zone for the traditional S-FFR.

These aforementioned problems are avoided in the proposedenhanced S-FFR, where only the QoS requirement should bedistinguished for RUEs. On the one hand, to avoid the intertierinterference, the out-band frequency is preferred for use accord-ing to standards of HetNets in 3GPP [22], which suggests thatRBs for HPNs should be orthogonal with those for RRHs. On


the other hand, to save the occupied frequency bands, the in-band strategy is defined as well in 3GPP [22], which indicatesthat both RUEs and HUEs share the same RBs although theintertier interference is severe. To be completely compatiblewith both in-band and out-band strategies in 3GPP, only two RBsets Ω1 and Ω2 are divided in this proposed enhanced S-FFRscheme. Obviously, if locations of RUEs could be known andthe traffic volume in different zones is clearly anticipated, moreRB sets in Ω1 could be divided to achieve higher performancegains. The division of two RB sets in the proposed enhancedS-FFR is a good tradeoff between performance gains andimplementing complexity/flexibility.

The QoS requirement is treated as the minimum transmissionrate in this paper, which is also called the rate-constrained QoSrequirement. In this paper, the high- and low-rate-constrainedQoS requirements are denoted as ηR and ηER, respectively. Forsimplicity, it is assumed that there are N and M RUEs per RRHoccupying the RB sets Ω1 and Ω2, respectively. In the OFDMA-based downlink H-CRANs, there are total K RBs (denoted asΩT ) with bandwidth B0. These K RBs in ΩT are categorizedinto two types: Ω1 is only allocated to RUEs with high-rate-constrained QoS requirements, and Ω2 is allocated to RUEs andHUEs with low-rate-constrained QoS requirements. Since allsignal processing for different RRHs is executed on the BBUpool centrally, the inter-RRH interferences can be coordinated,and the same radio resources can be shared among RRHs.Hence, the channel-to-interference-plus-noise ratio (CINR) forthe nth RUE occupying the kth RB can be divided into twoparts, i.e.,

σn,k =

⎧⎨⎩

dRnhR

n,k

B0N0, k ∈ Ω1

dRnhR

n,k

(PMdMn hM

n,k+B0N0)

, k ∈ Ω2

(1)

where dRn and dMn denote the path loss from the served RRHand the reference HPN to RUE n, respectively. hR

n,k and hMn,k

represent the channel gain from the RRH and HPN to RUEn on the kth RB, respectively. PM = PM

max/M is the allowedtransmit power allocated on each RB in HPN, andPM

max denotesthe maximum allowable transmit power of HPN. N0 denotesthe estimated power spectrum density of both the sum of noiseand weak inter-RRH interference (in dBm/Hz).

The sum data rate for each RRH can be expressed as

C(a,p) =N+M∑n=1

K∑k=1

an,kB0log2(1 + σn,kpn,k) (2)

where n ∈ {1, . . . , N} denotes the RUE allocated to the RBset Ω1, and n ∈ {N + 1, . . . , N +M} denotes the RUE al-located to the RB set Ω2. The (N +M)×K matrices a =[an,k](N+M)×K andp = [pn,k](N+M)×K represent the feasibleRB and power allocation policies, respectively. an,k is definedas the RB allocation indicator, which can only be 1 or 0,indicating whether the kth RB is allocated to RUE n. pn,kdenotes the transmit power allocated to RUE n on the kth RB.

According to [12], the total power consumption P (a,p) forH-CRANs mainly depends on the transmit power and circuit

power. When the power consumption for the fronthaul is con-sidered, the total power consumption per RRH is written as

P (a,p) = ϕeff

N+M∑n=1

K∑k=1

an,kpn,k + PRc + Pbh (3)

where ϕeff , PRc , and Pbh denote the efficiency of the power am-

plifier, circuit power, and power consumption of the fronthaullink, respectively.

Similarly, the sum data rate for the HPN can be calculated as

CM (aM,pM) =T∑

t=1

M∑m=1

at,mB0log2(1 + σt,mpt,m) (4)

where t ∈ {1, . . . , T } denotes the HUE allocated to the RBset Ω2. The T ×M matrices aM = [at,m]T×M and pM =[pt,m

m]T×M represent the feasible RB and power allocationpolicies for the HPN, respectively. at,m is defined as the RBallocation indicator, which can only be 1 or 0, indicatingwhether the mth RB is allocated to the HUE t. pmt,m denotesthe transmit power allocated to the HUE t on the mth RB. σt,m

represents the CINR of the tth HUE on the mth RB. The totalpower consumption of the HPN can be given by

PM (aM,pM) = ϕMeff

T∑t=1

M∑m=1

at,mpt,mM + PM

c + PMbh

(5)where pMt,m denotes the transmission baseband power for theHPN when the mth RB is allocated to the tth HUE, whichforms the transmit power vector pM for all HUEs. ϕM

eff , PMc ,

and PMbhdenote the efficiency of power amplifier, the circuit

power, and the power consumption of the backhaul link be-tween the HPN and BBU pool, respectively. Considering thatthe HPN is mainly utilized to extend the coverage and providebasic services for HUEs, the same downlink transmit power fordifferent HUEs over different RBs is assumed as pMt,m = PM ,where PM has been defined in (1).

The overall EE performance for the H-CRAN with L RRHsand 1 HPN can be written as

γ =L ∗ C(a,p) + CM (aM,pM)

L ∗ P (a,p) + PM (aM,pM). (6)

For the dense RRH deployed H-CRAN, L is much largerthan 1. The intertier interference from RRHs to HUEs remainsconstant when the density of RRHs is sufficiently high, andhence, the downlink SE and EE performances for the HPN canbe assumed to be stable. Therefore, C(a,p) is much larger thanCM (aM,pM), and PM (aM,pM) can be ignored if L∗P (a,p)is sufficiently large. When L is sufficiently large, the overall EEperformance in (6) for the H-CRAN can be approximated as

γ ≈ L ∗ C(a,p)

L ∗ P (a,p)=

C(a,p)

P (a,p). (7)

According to (7), the overall EE performance mainly de-pends on the EE optimization of each RRH. To make surethat HUEs meet the low-rate-constrained QoS requirement, theinterference from RRHs should be constrained and not larger


than the predefined threshold δ0. Consequently, to optimizedownlink EE performances, the core problem is converted tooptimize EE performance of each RRH with constraints on theintertier interference to the HPN from RRHs when the densityof RRHs is sufficiently high.

Problem 1 (EE Optimization): With the constraints on the re-quired QoS, intertier interference and maximum transmit powerallowance, the EE maximization problem in the downlink H-CRAN can be formulated as

max{a,p}

C(a,p)

P (a,p)=

N+M∑n=1

K∑k=1

an,kB0log2(1 + σn,kpn,k)

ϕeff

N+M∑n=1

K∑k=1

an,kpn,k + PRc + Pbh

(8)

s.t.N+M∑n=1

an,k = 1, an,k ∈ {0, 1} ∀ k (9)

K∑k=1

Cn,k ≥ ηR, 1 ≤ n ≤ N (10)

K∑k=1

Cn,k ≥ ηER, N + 1 ≤ n ≤ N +M (11)

N+M∑n=N

an,kpn,kdR2Mk hR2M

k ≤ δ0, k ∈ ΩII (12)

N+M∑n=1

K∑k=1

an,kpn,k ≤ PRmax, pn,k ≥ 0 ∀ k, ∀n

(13)

where Cn,k = an,kB0log2(1 + σn,kpn,k), and constraint (9)denotes the RB allocation limitation that each RB cannot beallocated to more than one RUE at the same time. The con-straints of (10) and (11) corresponding to the high- and low-rate-constrained QoS requirements specify the minimum datarate of ηR and ηER, respectively. Equation (12) puts a limitationon pn,k to suppress the intertier interference from RRHs toHUEs that reuse the RB k ∈ ΩII. dR2M

k and hR2Mk represent the

corresponding path loss and channel gain on the kth RB fromthe reference RRH to the interfering HUE, respectively. In (13),PRmax denotes the maximum transmit power of the RRH.Based on the enhanced S-FFR scheme, the interference to

HUE is constrained, and the SINR threshold ηHUE , which isthe minimum SINR requirement for decoding the signal ofHUE successfully, is defined to represent the constraint of (12).When allocating the mth RB to the tth HUE, the SINR (ηt,m)larger than ηHUE can be given by

ηt,m = PMdMmhMt,m/(L ∗ δ0 +B0N0) ≥ ηHUE . (14)

Obviously, the optimal RB allocation policy a∗ and powerallocation policy p∗ with constraints of diverse QoS require-ments and variable ηHUE to maximize the EE performance inProblem 1 is a nonconvex optimization problem due to forms

of the objective function and the RB allocation constraint in(9), whose computing complexity exponentially increases withthe number of binary variables [23]. Intuitively, Problem 1 isa mixed-integer programming problem, and the fractional ob-jective makes it complicated and difficult to be solved directlywith the classical convex optimization methods.

III. ENERGY-EFFICIENT RESOURCE

ALLOCATION OPTIMIZATION

Here, we propose an effective method to solve Problem 1 in(8), where we first exploit the nonlinear fractional programmingfor converting the objective function in Problem 1, upon whichwe then develop an efficient iterative algorithm to solve thisEE performance maximization problem.

A. Optimization Problem Reformulation

Since the objective function in Problem 1 is classified as anonlinear fractional programming [24], the EE performance ofthe reference RRH can be defined as a nonnegative variable γin (7) with the optimal value γ∗ = C(a∗,p∗)/P (a∗,p∗).

Theorem 1 (Problem Equivalence): γ∗ is achieved if andonly if

max{a,p}

C(a,p)− γ∗P (a,p) = C(a∗,p∗)− γ∗P (a∗,p∗) = 0

(15)

where {a,p} is any feasible solution of Problem 1 to satisfyconstraints (9)–(13). �

Proof: See Appendix A. �Based on the optimal condition stated in Theorem 1,

Problem 1 is equivalent to Problem 2 as follows if we can findthe optimal value γ∗. Although γ∗ cannot be directly obtained,an iterative algorithm (see Algorithm 1 below) is proposedto update γ while ensuring that the corresponding solution{a,p} remains feasible in each iteration. The convergence canbe proved, and the optimal RA for solving Problem 2 can bederived.

Algorithm 1 Energy-Efficient Resource Assignment andPower Allocation

1: Set the maximum number of iterations Imax, convergencecondition εγ and the initial value γ(1) = 0.

2: Set the iteration index i = 1 and begin the iteration (OuterLoop).

3: for 1 ≤ i ≤ Imax

4: Solve the resource allocation problem with γ(i) (InnerLoop);

5: Obtain a(i),p(i), C(a(i),p(i)), P (a(i),p(i));6: if C(a(i),p(i))− γ(i)P (a(i),p(i)) < εγ then7: Set {a∗,p∗} = {a(i),p(i)} and γ∗ = γ(i);8: break;9: else10: Set γ(i+1)=C(a(i),p(i))/P (a(i),p(i)) and i= i+1;11: end if12: end for


Problem 2 (Transformed EE Optimization):

max{a,p}

C(a,p)− γ∗P (a,p)

s.t. (9)−(13). (16)

Note that Problem 2 is a tractable feasibility problem. �Hence, the objective function of the fractional form in (8) is

transformed into the subtractive form. To design the efficientalgorithm for solving Problem 2, we can define an equivalentfunction F (γ) = max{a,p} C(a,p) − γP (a,p) with the fol-lowing lemma.

Lemma 1: For all feasible a, p, and γ, F (γ) is a strictlymonotonic decreasing function in γ, and F (γ) ≥ 0. �

Proof: See Appendix B. �Due to the constraint of (9), the feasible domain of a is a

discrete and finite set consisting of all possible RB allocations,and thus, F (γ) is generally a continuous but nondifferentiablefunction with respect to γ.

B. Proposed Iterative Algorithm

Based on Lemma 1, an iterative algorithm is proposed tosolve the transformed Problem 2 by updating γ in each iterationas Algorithm 1.

The proposed iterative Algorithm 1 ensures that γ increasesin each iteration. It can be observed that two nested loops exe-cuted in Algorithm 1 can achieve the optimal solution to max-imize EE performances. The outer loop updates γ(i+1) in eachiteration with the C(a(i),p(i)) and P (a(i),p(i)) obtained in thelast iteration. In the inner loop, the optimal RB allocation policya(i) and power allocation policy p(i) with a given value of γ(i)

are derived by solving the following inner-loop Problem 3.Problem 3 (Resource Allocation Optimization in the Inner

Loop):

max{a,p}

C(a,p)− γ(i)P (a,p)

s.t. (9)−(13) (17)

where γ(i) is updated by the last iteration in the outer loop. �In fact, with the help of the proposed Algorithm 1, the

solution to Problem 3 converges, and the optimal solution ispresented. The global convergence has the following theorem.

Theorem 2 (Global Convergence): Algorithm 1 always con-verges to the global optimal solution of Problem 3. �

Proof: See Appendix C. �The optimization problem in (17) is nonconvex and hard to

be solved directly. Generally speaking, if (17) can be solvedby the dual method, there exists a nonzero duality gap [25].The duality gap is defined as the difference between the optimalvalue of (17) (denoted by EE∗) and the optimal value of thedual problem for (17) (denoted by D∗). Fortunately, it can bedemonstrated that the duality gap between (17) and the dualproblem is nearly zero when the number of RBs is sufficientlylarge [26], which is illustrated as the following theorem.

Theorem 3 (Duality Gap): When the number of RBs issufficiently large, the duality gap between (17) and its dualproblem is nearly zero, i.e., D∗ − EE∗ ≈ 0 holds. �

Proof: See Appendix D. �

C. Lagrange Dual Decomposition Method

Hence, according to Theorem 3, Problem 3 in the ith outerloop can be solved by the dual decomposition method. Withrearranging constraints (10)–(13), the Lagrangian function ofthe primal objective function is given by

L(a,p,β,λ, ν)

=

N+M∑n=1

K∑k=1


− γ(i)

(ϕeff

N+M∑n=1

K∑k=1


)

+

N∑n=1

βn

[K∑

k=1

an,kB0log2(1 + σn,kpn,k)− ηR

]

+

N+M∑n=N+1

βn

[K∑

k=1

an,kB0log2(1 + σn,kpn,k)− ηER

]

+

K∑k=1

λk

(δ0 −

N+M∑n=1

an,kpn,kdR2Mk hR2M

k

)

+ ν

(PRmax −

N+M∑n=1

K∑k=1

an,kpn,k

)(18)

where β = (β1, β2, . . . , βN+M ) � 0 is the Lagrange multi-plier vector associated with the required minimum data rateconstraints (10) and (11). λ = (λ1, λ2, . . . , λK) � 0 is theLagrange multiplier vector corresponding to the intertier inter-ference constraint (12), and λk = 0 for k ∈ ΩI. ν ≥ 0 is theLagrange multiplier for the total transmit power constraint (13).The operator � 0 indicates that the elements of the vector areall nonnegative.

The Lagrangian dual function can be expressed as

g(β,λ, ν)

= max{a,p}

L(a,p,β,λ, ν)

= max{a,p}

{K∑

k=1

N+M∑n=1

[(βn + 1)an,kB0log2(1 + σn,kpn,k)

− γ(i)ϕeffan,kpn,k

−λkan,kpn,kdR2Mk hR2M

k −νan,kpn,k]

− γ(i)(PRc + Pbh

)−

N∑n=1

βnηR

−N+M∑n=N+1

βnηER +

K∑k=1

λkδ0 + νPRmax

}(19)

and the dual optimization problem is reformulated as

min{β,λ,ν}

g(β,λ, ν)

s.t. β � 0,λ � 0, ν ≥ 0. (20)


It is obvious that the dual optimization problem is alwaysconvex. In particular, the Lagrangian function L(a,p,β,λ, ν)is linear with βn, λk , and ν for any fixed an,k and pn,k, whereasthe dual function g(β,λ, ν) is the maximum of these linearfunctions. We use the dual decomposition method to solve thisdual problem, which is first decomposed into K independentproblems as

g(β,λ, ν) =

K∑k=1

gk(β,λ, ν)− γ(i)(PRc + Pbh

)

−N∑

n=1

βnηR −N+M∑n=N+1

βnηER +K∑

k=1

λkδ0 + νPRmax (21)

where

gk(β,λ, ν)

= max{a,p}

{N+M∑n=1

[(1 + βn)an,kB0log2(1 + σn,kpn,k)

− γ(i)ϕeffan,kpn,k

− λkan,kpn,kdR2Mk hR2M

k − νan,kpn,k]}

.

(22)

Supposed that the kth RB is allocated to the nth UE, i.e.,an,k = 1, it is obvious that (22) is concave in terms of pn,k.With the Karush–Kuhn–Tucker condition, the optimal powerallocation is derived by

p∗n,k =

[ω∗n,k −

1σn,k

]+(23)

where [x]+ = max{x, 0}, and the optimal waterfilling levelω∗n,k is derived as

ω∗n,k =

B0(1 + βn)

ln 2(γ(i)ϕeff + λkdR2M

k hR2Mk + ν

) . (24)

Then, substituting the optimal power allocation obtained by(23) into the decomposed optimization problem (22), we canhave

gk(β,λ, ν) = max1≤n≤N+M

{(1 + βn)B0

[log2

(ω∗n,kσn,k

)]+−(γ(i)ϕeff+λkd

R2Mk hR2M

k +ν)

×[ω∗n,k −

1σn,k

]+}. (25)

With (24) and (25), the optimal RB allocation indicator forthe given dual variables can be expressed as

a∗n,k =

{1, n = arg max

1≤n≤N+MHn,k

0, otherwise(26)

where

Hn,k =[(1 + βn)log2

(ω∗n,kσn,k

)]+− (1 + βn)

ln 2

[1 − 1

ω∗n,kσn,k

]+

. (27)

Then, the subgradient-based method [27] can be utilized tosolve the given dual problem, and the subgradient of the dualfunction can be written as

∇β(l+1)n =

K∑k=1

C(l)n,k − ηR, 1 ≤ n ≤ N (28)

∇β(l+1)n =

K∑k=1

C(l)n,k − ηER, N + 1 ≤ n ≤ N +M (29)

∇λ(l+1)k =

⎧⎨⎩

0, ∀ k ∈ ΩI

δ0 −N∑

n=1a(l)n,kp

(l)n,kd

R2Mk hR2M

k , ∀ k ∈ ΩII

(30)

∇ν(l+1) =PRmax −

N∑n=1

K∑k=1

a(l)n,kp

(l)n,k (31)

where a(l)n,k and p

(l)n,k represent the RB allocation and power

allocation, which are derived by the dual variables of the lthiteration, respectively, and C

(l)n,k = a

(l)n,kB0log2(1 + σn,kp

(l)n,k).

∇β(l+1)n , ∇λ

(l+1)k , and ∇ν(l+1) denote the subgradient uti-

lized in the (l + 1)th inner-loop iteration. Hence, the updateequations for the dual variables in the (l + 1)th iteration aregiven by

β(l+1)n =

[β(l)n − ξ

(l+1)β ×∇β(l+1)

n

]+∀n (32)

λ(l+1)k =

[λ(l)k − ξ

(l+1)λ ×∇λ

(l+1)k

]+∀ k (33)

ν(l+1) =[ν(l) − ξ(l+1)

ν ×∇ν(l+1)]+

(34)

where ξ(l+1)β , ξ(l+1)

λ , and ξ(l+1)ν are the positive step sizes.

IV. RESULTS AND DISCUSSIONS

Here, the EE performance of the proposed H-CRAN andcorresponding optimization solutions are evaluated with sim-ulations. There are N = 10 RUEs located in each RRH withthe high-rate-constrained QoS and allocated by the orthogonalRB set Ω1. M is varied to denote the number of RUEs with low-rate-constrained QoS requirements. In the case of M = 0, thereare no RUEs to share the same radio resources with HUEs, andthus, there are no intertier interferences. Otherwise, there areM(> 0) RUEs with the low-rate-constrained QoS interferedwith by the HPN. We assume that dPn = 50 m, dMn = 450 min the case of 1 ≤ n ≤ N , and dPn = 75 m, dMn = 375 m in thecase of N + 1 ≤ n ≤ N +M . The distance between the refer-ence RRH and HUEs who reuse the kth RB is dR2M

k = 125 m.


The number of total RBs is K = 25, and the system bandwidthis 5 MHz. The total transmit power of HPN is 43 dBm andequally allocated on all RBs. It is assumed that the path-lossmodel is expressed as 31.5 + 40.0 ∗ log10(d) for the RRH-to-RUE link and 31.5 + 35.0 ∗ log10(d) for the HPN-to-RUE andRRH-to-HUE links, where d denotes the distance between thetransmitter and the receiver in meters. The number of simula-tion snapshots is set at 1000. In all snapshots, the fast-fadingcoefficients are all generated as independent and identicallydistributed Rayleigh random variables with unit variances. Thelow- and high-rate-constrained QoS requirements are assumedto be ηER = 64 kbit/s and ηR = 128 kbit/s, respectively.

We assume the static circuit power consumption to be PRc =

0.1 W and the power efficiency to be ϕeff = 2 for the poweramplifiers of RRHs. For HPNs, they are assumed to be PM

c =10.0 W and ϕM

eff = 4, respectively [28]. The power consump-tion for both RRHs and HPNs to receive the channel stateindication and coordination signaling are taken into account,i.e., the power consumption of the fronthaul link Pbh, and thebackhaul link between the HPN and the BBU pool Pbh areassumed to be 0.2 W.

A. H-CRAN Performance Comparisons

To evaluate EE performance gains of H-CRANs, the tradi-tional C-RAN, two-tier HetNet, and one-tier HPN scenariosare presented as baselines. Only one HPN and one RRH areconsidered in the H-CRAN scenario. Similarly, only two HPNsare considered in the one-tier HPN scenario, and one HPNand one pico base station (PBS) are considered in the two-tierHetNet scenario. For the one-tier C-RAN scenario, two RRHsare considered, in which one RRH is used to replace the HPNin H-CRANs.

– One-tier HPN: All UEs access the HPN, and the RB setΩ1 and Ω2 are allocated to the cell-center-zone and cell-edge-zone UEs, respectively. The optimal power and RBallocations are based on the classical waterfilling and themaximum signal-to-interference-plus-noise ratio (SINR)scheduling algorithms, respectively. The number of cell-center-zone UEs is 10, and the number of cell-edge-zoneUEs with the low-rate-constrained QoS requirement isvaried from 1 to 10.

– Two-tier overlaid HetNet: The orthogonal RB set Ω1 andΩ2 are allocated to the PBS and HPN, respectively. Thestatic circuit power consumption for the PBS is PP

c =6.8 W, and the power efficiency is ϕP

eff = 4 for the poweramplifiers in PBS. Note that RBs allocated to the PBSand HPN are orthogonal with no intertier interferences.The number of RUEs served by the PBS keeps constantand is set at 10, and the number of HUEs served byHPN is varied. Note that UEs served by the HPN in thisscenario are denoted by HUEs with low-rate-constrainedQoS requirements to be consistent with other baselines.

– Two-tier underlaid HetNet: All RBs in the set Ω1 and Ω2

are fully shared by UEs within the covering areas of thePBS and HPN. The optimal power and RB allocations areadopted to enhance EE performances [9]. The locations

Fig. 3. Performance comparisons among one-tier HPN, two-tier HetNet, one-tier C-RAN, and two-tier H-CRAN.

and number of UEs served by the HPN and PBS are sameas those in the two-tier overlaid HetNet scenario.

– One-tier C-RAN: All RBs in the set Ω1 and Ω2 are fullyshared by RUEs. There are ten cell-center-zone RUEsand M cell-edge-zone RUEs in each RRH. Each RRHcovers the same area coverage of the PBS in the two-tierHetNet scenario. The optimal power and RB allocationsare based on the classical waterfilling and maximum SINRalgorithms, respectively.

– Two-tier H-CRAN: The orthogonal RBs in set Ω1 areonly allocated to RUEs, whereas RBs in Ω2 are sharedby cell-edge-zone RUEs and HUEs, where the proposedoptimal solution subject to the interference mitigationand RRH/HPN association is used. The number of cell-center-zone RUEs keeps constant and is set at 10, and thenumber of cell-edge-zone RUEs is varied to evaluate EEperformances.

As shown in Fig. 3, EE performances are compared amongthe one-tier HPN, two-tier underlaid HetNet, two-tier overlaidHetNet, one-tier C-RAN, and two-tier H-CRAN. The EE per-formance decreases with the number of accessing UEs in theone-tier HPN scenario because more power is consumed tomake cell-edge-zone UEs meet the low-rate-constrained QoSrequirements. The EE performance becomes better in the two-tier HetNet than that in the one-tier HPN because lower transmitpower is needed and higher transmission bit rate is achieved.Due to spectrum reuse and the fact that the interference isalleviated by the optimal solution in [9], the EE performancein the two-tier underlaid HetNet scenario is better than thatin the two-tier overlaid HetNet scenario. Furthermore, the EEperformance in the two-tier H-CRAN scenario is the bestdue to the gains from both the H-CRAN architecture and thecorresponding optimal radio resource allocation solution. Notethat the EE performance of one-tier C-RAN is a little worse than


Fig. 4. Convergence evolution under different optimization solutions.

that of H-CRAN because it suffers from the coverage limitationwhen RRH covers the area that the HPN serves in the two-tierH-CRAN. Meanwhile, the EE performance of one-tier C-RANis better than that of both one-tier HPN and two-tier HetNetdue to the advantages of centralized cooperative processing andenergy consumption savings.

B. Convergence of the Proposed Iterative Algorithm

To evaluate EE performances of the proposed optimal re-source allocation solution (denoted by “optimal EE solution”),two algorithms are presented as baselines. The first baselinealgorithm is based on the fixed power allocation (denoted by“fixed power”), i.e., the same and fixed transmit power is set fordifferent RBs, and the optimal power allocation derived in (23)is not utilized. The second baseline algorithm is based on thesequential RB allocation (denoted by “sequential RB”), wherethe RB is allocated to RUEs sequentially. The presented twobaseline algorithms use the same constraints of (9)–(13) as theoptimal EE solution does. There are 12 RRHs (i.e., L = 12)uniformly spaced around the reference HPN.

The EE performances of these three algorithms with differentallowed interference threshold under varied iteration numbersare shown in Fig. 4. The number of RUEs with low-rate-constrained QoS requirement is assumed as M = 3. It can begenerally observed that the plotted EE performances are con-verged within three iteration numbers for different optimizationalgorithms. On the other hand, these two baseline algorithmsare converged more quickly than the proposal does becausethe proposal has higher computing complexity. Furthermore,the maximum allowed intertier interference, which is definedas δ0 in (12), should be constrained to make the HUE workefficiently. To evaluate δ0 impacting on the EE performance,ηHUE described in (14) denoting the maximum allowed in-tertier interference is simulated. The large ηHUE indicates thatthe constraint of δ0 should be controlled to a low level, whichsuggests decreasing the transmit power and even forbidding theRB to be allocated to RUEs. Consequently, the EE performancewhen ηHUE is 0 dB is better than that when it is 20 dB. The

Fig. 5. EE performance comparisons under different SINR thresholds ofHUEs ηHUE .

Fig. 6. EE performance comparisons under different maximum allowedtransmit power of RRHs.

EE performance decreases with the increasing SINR thresholdηHUE for these three algorithms.

C. EE Performances of the Proposed Solutions

Here, key factors impacting the EE performances of the pro-posed radio resource allocation solution are evaluated. Since EEperformances are closely related to constraints (12)–(13), thevariables ηHUE and PR

max are two key factors to be evaluatedin Figs. 5 and 6, respectively. The ratio of Ω1 to ΩT impactingon EE performances is evaluated in Fig. 7 to show performancegains of the enhanced S-FFR.

In Fig. 5, EE performances under the varied SINR thresholdsof HUEs ηHUE are compared among different algorithms whenthe maximum allowed transmit power of RRH is 20 or 30 dBm.When ηHUE is not sufficiently large, the EE performance


Fig. 7. EE performance comparisons for different ratios of Ω1 to ΩT .

almost keeps stable with the increasing ηHUE because the in-tertier interference is not severe due to adoption of the enhancedS-FFR. However, the EE performance declines for these twobaseline algorithms when the SINR threshold ηHUE is over10 dB. While the proposed optimal EE solution can sustainmore intertier interferences, and the EE performance deterio-rates after ηHUE is over 14 dB, indicating that the proposedsolution can mitigate more intertier interferences and providehigher bit rates for HUEs than the other two baselines do.Summarily, the proposed optimal EE solution can achieve thebest EE performance, whereas the “fixed power” algorithm hasthe worst EE performance, and the “sequential RB” algorithmis in-between. Furthermore, the EE performances for thesethree algorithms are strictly related to the maximum allowedtransmit power of the RRH, and the EE performance withPRmax = 30 dBm is better than that with PR

max = 20 dBm.To further evaluate the impact of the maximum allowed

transmit power of RRHs PRmax on EE performances, Fig. 6 com-

pares the EE performance of different algorithms in terms ofPRmax. In this simulation case, ηHUE is set at 0 dB, the number

of RUEs with low-rate-constrained QoS requirements is set at4, and the iteration number is set at 5. The maximum allowedtransmit power of the HPN is set at 43 dBm, and the maxi-mum allowed transmit power of RRH varies within [14 dBm,36 dBm] with the step size of 2 dBm. When PR

max is not large,EE performances increase almost linearly with the rising PR

max

for all three algorithms. When PRmax ≥ 22 dBm, both the SE

performance and the total power consumption increases almostlinearly with the rising PR

max. Therefore, the EE performancealmost keeps stable. As shown in Fig. 6, EE performancesof the “sequential RB” algorithm are often better than thoseof the “fixed power” algorithm due to the waterfilling powerallocation gains indicated in (23). Furthermore, the proposedsolution can achieve the best EE performance due to gains ofRB assignment and power allocation.

In addition to ηHUE and PRmax, the ratio between Ω1 and Ω2

has a significant impact on the EE performance of H-CRANs.

The EE performances of the H-CRAN under the enhancedS-FFR with different ratios of Ω1 to ΩT are evaluated in Fig. 7,where the number of RUEs with low- and high-rate-constrainedQoS requirements is set at M = 5 and M = 10, respectively.Meanwhile, the number of total RBs is K = 25, and the systembandwidth is 5 MHz. Each UE is allocated by at least one RBto guarantee the minimal QoS requirement. Fig. 7 suggeststhat the EE performance increases almost linearly with theratio of Ω1 to ΩT . With more available exclusive RBs forRRHs, there are fewer intertier interferences because the sharedRBs specified for RUEs and HUEs decrease. The increasingratio of Ω1 to ΩT results in the drastically increasing of theexpectation of SINRs for RUEs. Furthermore, since the intertierinterference is mitigated by configuring few shared RBs, thetransmission power of RUEs increases due to the proposed wa-terfilling algorithm in (23), which further improves the overallEE performances of H-CRANs. Moreover, the EE performanceincreases with the rising maximum allowed transmit power ofRRH PR

max, which verifies the simulation results in Fig. 6 again.These results indicate that more radio resources should beconfigured for Ω1 if only the EE performance optimization ispursued. However, the fairness of UEs should be consideredjointly, and some necessary RBs should be fixed for both HUEsand cell-edge-zone RUEs to guarantee the seamless coverageand successful delivery of the control signalings to all UEs inthe real H-CRANs, which is a challenging open issue for futureresearch.

V. CONCLUSION

In this paper, the EE performance optimization for H-CRANshas been analyzed. In particular, the RB assignment and powerallocation subject to the intertier interference mitigation andthe RRH/HPN association have been jointly optimized. To dealwith the optimization of resource allocations, a nonconvex frac-tional programming optimization problem has been formulated,and the corresponding Lagrange dual decomposition methodhas been proposed. Simulation results have demonstrated thatperformance gains of H-CRANs over the traditional HetNetand C-RAN are significant. Furthermore, the proposed optimalenergy-efficient resource allocation solution outperforms theother two baseline algorithms. To maximize EE performancesfurther, the advanced S-FFR schemes with more RB sets shouldbe researched, and the corresponding optimal ratio of differentRB sets should be designed in the future.

APPENDIX APROOF OF THEOREM 1

By following a similar approach presented in [29], we proveTheorem 1 with two septated steps.

First, the sufficient condition of Theorem 1 should beproved. We define the maximal EE performance of Problem 1as γ∗ = C(a∗,p∗)/P (a∗,p∗), where a∗ and p∗ are the optimalRB and power allocation policies, respectively. It is obvious thatγ∗ holds, i.e.,

γ∗ =C(a∗,p∗)

P (a∗,p∗)≥ C(a,p)

P (a,p)(35)


where a and p are the feasible RB and power allocation policiesfor solving Problem 1. Then, according to (35), we can derivethe following formulas:

{C(a,p)− γ∗P (a,p) ≤ 0

C(a∗,p∗)− γ∗P (a∗,p∗) = 0.(36)

Consequently, we can conclude that max{a,p}C(a,p)−γ∗P (a,p) = 0, and it is achievable by the optimal resourceallocation policies a∗ andp∗. The sufficient condition is proved.

Second, the necessary condition should be proved. Supposedthat a∗ and p∗ are the optimal RB and power allocation policiesof the transformed objective function, respectively, we can haveC(a∗, p∗)− γ∗P (a∗, p∗) = 0. For any feasible RB and powerallocation policies a and p, they can be expressed as

C(a,p) − γ∗P (a,p) ≤ C(a∗, p∗)− γ∗P (a∗, p∗) = 0. (37)

The above inequality can be derived as

C(a,p)

P (a,p)≤ γ∗ and

C(a∗, p∗)

P (a∗, p∗)= γ∗. (38)

Therefore, the optimal resource allocation policies a∗ andp∗ for the transformed objective function are also the optimalresource allocation policies for the original objective function.The necessary condition of Theorem 1 is proved.

APPENDIX BPROOF OF LEMMA 1

We can define an equivalent function as

F (γ) = max{a,p}

C(a,p) − γP (a,p) (39)

and we assume that γ1 and γ2 are the optimal value for thesetwo optimal RB allocation solution {a1,p1} and {a2,p2},where γ1 > γ2. Then

F (γ2) =C(a2,p2)− γ2P (a2,p2)

>C(a1,p1)− γ2P (a1,p1)

>C(a1,p1)− γ1P (a1,p1) = F (γ1). (40)

Hence, F (γ) is a strictly monotonic decreasing function interms of γ.

Meanwhile, let a′ and p′ be any feasible RB and power allo-cation policies, respectively. If we set γ ′ = C(a′,p′)/P (a′,p′),then

F (γ ′) = max{a,p}

C(a,p)− γ ′P (a,p)

≥C(a′,p′)− γ ′P (a′,p′) = 0. (41)

Hence, F (γ) ≥ 0.

APPENDIX CPROOF OF THEOREM 2

Supposed that γ(i) and γ(i+1) represent the EE performanceof the reference RRH in the ith and (i+ 1)th iteration ofthe outer loop, respectively, where γ(i) > 0, and γ(i+1) > 0,neither of them is the optimal value γ∗. Meanwhile, γ(i+1) isgiven by γ(i+1) = C(a(i),p(i))/P (a(i),p(i)), where a(i) andp(i) are the optimal RB and power solutions of Problem 3 inthe ith iteration of the outer loop, respectively. Note that γ∗

is defined as the achieved maximum EE performance for allfeasible RA solutions {a,p}, and thus, γ(i+1) cannot be largerthan γ∗, e.g., γ(i+1) ≤ γ∗. It has been proved that F (γ) > 0in Lemma 1 when γ is not the optimal valur to achieve themaximum EE performance. Thus, F (γ(i)) can be written as

F(γ(i)

)=C

(a(i),p(i)

)− γ(i)P

(a(i),p(i)

)=P

(a(i),p(i)

)(γ(i+1) − γ(i)

)> 0. (42)

Equation (42) indicates that γ(i+1) > γ(i) due toP (a(i),p(i)) > 0, which suggests that γ increases in eachiteration of the outer loop in Algorithm 1. According toLemma 1, the value of F (γ) decreases with the increasingnumber of iterations due to the incremental value of γ.

On the other hand, it has been proved that the optimalconditionF (γ∗) = 0 holds in Theorem 1. Algorithm 1 ensuresthat γ monotonically increases. When the updated γ increasesto the achievable maximum value γ∗, Problem 2 can be solvedwith γ∗ and F (γ∗) = 0. Then, the global optimal solutions a∗

and p∗ are derived. We update γ in the iterative algorithm tofind the optimal value γ∗. It can be demonstrated that F (γ)converges to zero when the number of iterations is sufficientlylarge and the optimal condition as stated in Theorem 1 issatisfied. Therefore, the global convergence of Algorithm 1 isproved.

APPENDIX DPROOF OF THEOREM 3

We can rewrite (17) as

C(a,p) − γ(i)P (a,p)

=N+M∑n=1

K∑k=1


− γ(i)

(ϕeff

N+M∑n=1

K∑k=1


)

=

K∑k=1

(N+M∑n=1


−N+M∑n=1

γ(i)ϕeffan,kpn,k −γ(i)

K

(PRc + Pbh

)).

(43)


It is obvious that for the given RB allocation scheme, ifletting

fk(pn,k) =N+M∑n=1


−N+M∑n=1

γ(i)ϕeffan,kpn,k −γ(i)

K

(PRc + Pbh

)(44)

then (43) can be written as C(a,p) − γ(i)P (a,p) =∑Kk=1 fk(pn,k), where pn,k ∈ CN , and fk(·) : CN → R

is not necessarily convex. Similarly, constraints (9)–(13) canbe expressed as the function of pn,k with

∑Kk=1 hk(pn,k) ≤ 0,

where hk(·) : CN → RL, and L represents the number of

constraints. Thus, (17) can be expressed as

EE∗ = max

K∑k=1

fk(pn,k) (45)

s.t.K∑

k=1

hk(pn,k) ≤ 0 (46)

where 0 ∈ RL. To prove the duality gap between (17) and theoptimal value of its dual problem D∗ is zero, a perturbationfunction v(H) is defined and can be written as

v(H) = maxK∑

k=1

fk(pn,k) (47)

s.t.K∑

k=1

hk(pn,k) ≤ H (48)

where H ∈ RL is the perturbation vector.Following [25], if v(H) is a concave function of H , the

duality gap between D∗ and EE∗ is zero. Therefore, to provethe concavity of v(H), a time-sharing condition should bedemonstrated as follows.

Definition 1 (Time-Sharing Condition): Let p1∗n,k and p2∗

n,k bethe optimal solutions of (47) to v(H1) and v(H2), respectively.Equation (45) satisfies the time-sharing condition if for anyv(H1) and v(H2), there always exists a solution p3

n,k to meetK∑

k=1

hk

(p3n,k

)≤αH1 + (1 − α)H2 (49)

K∑k=1

fk(p3n,k

)≥αfk

(p1∗n,k

)+ (1 − α)fk

(p2∗n,k

)(50)

where 0 ≤ α ≤ 1.Now, we should prove that v(H) is a concave function of

H . For some α, it is easy to find H3 satisfying H3 = αH1 +(1 − α)H2. Let p1∗

n,k, p2∗n,k and p3∗

n,k be the optimal solutionswith these constraints of v(H1), v(H2), and v(H3), respec-tively. According to the definition of the time-sharing condition,there exists p3

n,k satisfying∑K

k=1 hk(p3n,k) ≤ αH1 + (1 −

α)H2 and∑K

k=1 fk(p3n,k) ≥ αfk(p

1n,k) + (1 − α)fk(p

2∗n,k).

Since p3∗n,k is the optimal solution to v(H3), it is ob-

vious that∑K

k=1 fk(p3∗n,k) ≥

∑Kk=1 fk(p

3n,k) ≥ αfk(p

1∗n,k) +

(1 − α)fk(p2∗n,k) holds. Then, the concavity of v(H) is proved.

Since v (H) is concave, (45) could be proved to satisfy thetime-sharing condition. The time-sharing condition is alwayssatisfied for the multicarrier system when the number of carriersgoes to infinity [26], such as the OFDMA-based H-CRANsystem in this paper. We can let p1

n,k and p2n,k be two feasible

power allocation solutions. There are α percentages of thetotal carriers to be allocated the power with p1

n,k, whereas theremaining (1 − α) percentages of the total carriers are allocatedthe power with p2

n,k. Then,∑K

k=1 fk(pn,k) is a linear com-bination, which is expressed as αfk(p1

n,k) + (1 − α)fk(p2n,k).

Therefore, the constraints are linear combinations, and it isproved that (45) satisfies the time-sharing condition. Conse-quently, v(H) is a concave function of H , and the duality gapbetween D∗ and EE∗ should be zero. This theorem is proved.

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Mugen Peng (M’05–SM’11) received the B.E. de-gree in electronics engineering from Nanjing Uni-versity of Posts and Telecommunications, Nanjing,China, in 2000 and the Ph.D. degree in communica-tion and information system from Beijing Universityof Posts and Telecommunications (BUPT), Beijing,China, in 2005.

After completing the Ph.D. degree, he joinedBUPT, where he has been a Full Professor with theSchool of Information and Communication Engi-neering since October 2012. In 2014, he became an

Academic Visiting Fellow with Princeton University, Princeton, NJ, USA. Heis leading a research group focusing on wireless transmission and networkingtechnologies with the Key Laboratory of Universal Wireless Communications(Ministry of Education), BUPT. He has authored/coauthored over 40 refereedIEEE journal papers and over 200 conference proceeding papers. His mainresearch areas include wireless communication theory, radio signal procesing,and convex optimizations, with particular interest in cooperative commu-nication, radio network coding, self-organization networking, heterogeneousnetworking, and cloud communication.

Dr. Peng is currently on the Editorial/Associate Editorial Board of the IEEECommunications Magazine, IEEE Access, the International Journal of An-tennas and Propagation (IJAP), China Communication, and the InternationalJournal of Communications System (IJCS). He has been the Guest LeadingEditor for the Special Issues of IEEE Wireless Communications, IJAP, and theInternational Journal of Distributed Sensor Networks. He received the 2014IEEE ComSoc AP Outstanding Young Researcher Award and the Best PaperAward at GameNets 2014, CIT 2014, ICCTA 2011, IC-BNMT 2010, and IETCCWMC 2009. He received the First Grade Award of Technological InventionAward from the Ministry of Education of China for the hierarchical cooperativecommunication theory and technologies and the Second Grade Award of Sci-entific and Technical Progress from the China Institute of Communications forthe coexistence of multiradio access networks and 3G spectrum management.

Kecheng Zhang received the B.S. degree intelecommunication engineering from Beijing Uni-versity of Posts and Communications (BUPT),Beijing, China, in 2012, where he is currently work-ing toward the Ph.D. degree with the Key Labora-tory of Universal Wireless Communications for theMinistry of Education.

His research interests include radio resource allo-cation optimization and cooperative communicationsin heterogeneous cloud radio access networks.

Jiamo Jiang received the Ph.D. degree in commu-nication and information systems from Beijing Uni-versity of Posts and Telecommunications, Beijing,China, in 2014.

He is currently with the Institute of Commu-nication Standards Research, China Academy ofTelecommunication Research of MIIT, Beijing. Hisresearch focuses on self-organizing networks andenergy-efficient resource allocation in heterogeneousnetworks.

Jiaheng Wang (S’08–M’10) received the B.E. andM.S. degrees from Southeast University, Nanjing,China, in 2001 and 2006, respectively, and thePh.D. degree in electrical engineering from TheHong Kong University of Science and Technology,Kowloon, Hong Kong, in 2010.

He is currently an Associate Professor with theNational Mobile Communications Research Labora-tory, Southeast University. From 2010 to 2011, hewas with the Signal Processing Laboratory, ACCESSLinnaeus Center, KTH Royal Institute of Technol-

ogy, Stockholm, Sweden. He also held a visiting position with the Departmentof Computer and Information Science, University of Macau, Macau. Hisresearch interests mainly include optimization in signal processing, wirelesscommunications, and networks.

Dr. Wang serves as an Associate Editor for the IEEE SIGNAL PROCESSING

LETTERS. He received the Humboldt Fellowship for Experienced Researchersand the Best Paper Award at WCSP 2014.

Wenbo Wang (M’95) received the B.S., M.S., andPh.D. degrees from Beijing University of Postsand Telecommunications (BUPT), Beijing, China, in1986, 1989, and 1992, respectively.

He is currently the Dean of TelecommunicationEngineering with BUPT. He is also the AssistantDirector of the Academic Committee with the KeyLaboratory of Universal Wireless Communication(Ministry of Education), BUPT. He has publishedmore than 200 journal and international conferencepapers and six books and holds 12 patents. His re-

search interests include radio transmission technology, wireless network theory,broadband wireless access, and software radio technology.

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