Spectrum-Energy Efficiency Optimization forDownlink LTE-A for Heterogeneous Networks

Chan-Ching Hsu and J. Morris Chang, Senior Member, IEEE

Abstract—Heterogeneous networks have been pointed out to be one of the key network architectures that help increase system

capacity and reduce power consumption for efficient communications. Although conceivably, high operational efficiency brings a high

profit for mobile service providers, it is noteworthy that the potential for maximizing the profit has not been explored for the

heterogeneous environment. This paper investigates profitability for network operators with the spectrum-energy efficiency metric on

the downlink of LTE Advanced communication systems. We pursue optimal policies by employing the techniques of cell size zooming,

user migration, and sleep mode in the deployment of different base station types. The problem is formulated as a quasiconvex

optimization problem and it is transformed into an equivalent form of the MILP problem; the former is solved with a bisection algorithm

and the latter is approached by an off-the-shelf software package. Since the formulated optimization problem is NP hard, a sub-optimal

approach with a lower computational complexity is also proposed. Numerical analysis through case studies are presented to evaluate

the efficiency improvements, and demonstrate the performance of the near-optimal solution.

Index Terms—Network optimization, energy-efficient, spectrum efficiency, heterogeneous network

Ç

1 INTRODUCTION

TOTAL mobile traffics of thewholemobileworld are grow-ing fast; the increasing demand over the last mile access

networks has motivated the network operators to extendand upgrade infrastructure in order to provide guaranteedcoverage and data services. Fourth generation technologiessuch as LTE cellular systems have been developed and areexpected to be important technologies to improve end-userthroughput and network capacity. With such technologicalcapability to improve information services, mobile operatorshave been experiencing annual increases in data traffic vol-umes and so in revenues. Meanwhile, [1] points out that theoperational expenditure accounts for more than 18 percentof the energy bill, and that 60 percent of the power consump-tion in the network equipment is from base stations (BSs).The increasing data amount raises the profit at the expenseof energy consumption increased.

From the mobile operator perspective, it is of interest tooperate wireless networks in an economically efficient fash-ion. It was analyzed in [2] that deploying different types ofBSs is able to help on expenditure reduction and increaserevenues. Thus, a hybrid of cellular deployments providesgreat leeway to the network operators to attain financialimprovements [3]. Nevertheless, one of the concerns withHetNets is the growing number of small cell sites. The totalenergy consumption of all femtocells will amount morethan 3:784� 109 kWh/annum according to [4]. Thisraises important questions about the energy efficiency

implications of HetNet deployment. Hence, energy efficientoperation in a heterogeneous setting becomes a pressingissue in order to reduce the energy expenditure.

On the other hand, when evaluating the energy savingmechanisms, the impact on spectrum efficiency should alsobe taken into account. The authors in [5] analyzed the trade-off between the two metrics. The derived analytical expres-sion shows that the increase in energy efficiency willinevitably bring down the spectrum efficiency. Schemesaimed at joint optimization of energy efficiency and spectralefficiency should be well studied. However, these two net-work efficiency improvement problems are focused andstudied disjointedly in the literature. Therefore, in thispaper, a spectrum-energy efficiency optimization model isdeveloped for the heterogeneous network environments.We define maximizing network spectrum-energy efficiencyas optimizing the spectrum allocation while minimizing thetotal energy consumption.

There is a long-term economic objective of spectrum-energy efficiency optimization. The spectrum-energy effi-ciency can be considered as a metric to quantify the revenue-per-cost capacity, serving as an indicator of operators profit-ability. It is a generalized objective function that maximizesthe ratio of spectrum efficiency over energy consumed forthe service operation. The goal is to attain a network designwhich is cost-effective, improving the data rate per resourcesmanaged (resource blocks and energy). As an efficient net-work is capable of growing in data volume conveyed suc-cessfully, within given cost in terms of energy consumption,the revenue then increases, coming from expanded dataservices offered. With the optimal service rate per resource,themost profitable network design can be realized.

In this research, the spectrum-energy efficiency in cellularcommunication systems is defined as the bits/s-per-RB-per-Joule capacity, which depends on the served data rate, allo-cated transmit power, resource blocks (RBs) and static BS

� The authors are with the Department of Electrical and Computer Engineer-ing, Iowa State University, Ames, IA 50011.E-mail: {cchsu, morris}@iastate.edu.

Manuscript received 10 Mar. 2015; revised 30 May 2016; accepted 20 June2016. Date of publication 7 July 2016; date of current version 31 Mar. 2017.For information on obtaining reprints of this article, please send e-mail to:reprints@ieee.org, and reference the Digital Object Identifier below.Digital Object Identifier no. 10.1109/TMC.2016.2584046

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1536-1233� 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

energy consumption.We propose tomigrate user equipment(UE) (i.e., mobile devices), switch OFF and zoom in/out BSs.To obtain the optimal operation, a quasiconvex program-ming problem is developed, and is transformed into aMixedInteger Linear Programming problem (MILP), where consid-ered are association, spatial, resource, operation and serviceconstraints. The decision space contains BS-UE-Modulationassociation assignments and BS operationmode.

The contributions are summarized as follows: (i) Wepresent an analytical framework for optimal BS operation,user association and modulation scheme selection in Het-Nets. Our objective is to maximize spectrum-energy effi-ciency, i.e., maximizing profitability of network serviceproviders. We stress on techniques to enhance the utiliza-tion of resource blocks and thus to better amortize thelicense costs of frequency bands for HetNets. (ii) Two heu-ristic approaches are proposed to find near-optimal solu-tions. The bisection method produces a solution differentfrom the optimal within a predefined tolerable value; thedevised heuristic algorithm reaches a sub-optimal solutionwith computational tractability. We run extensive simula-tions based on non-uniform BS topologies and traffic distri-bution scenarios to verify performance of the optimizationframework, and heuristics.

The remainder of this paper is organized as follows. Wereview related work in the next section; in Section 3, a systemmodel is presentedwhich portrays the studied heterogeneousnetwork environment. The spectrum-energy efficiency opti-mization scheme is then proposed in Section 4. The heuristicapproaches in Section 5 are proposed to enhance the compu-tation efficiency, followed by the numerical experiments inSection 6. Finally, Section 7 concludes this paper.

2 RELATED WORK

Several approaches have been pursued to reduce energy con-sumption. Dynamic BS operation has been investigated,allowing a significant amount of energy to be saved, moti-vated by the traffic load fluctuation [6], [7], [8], [9]. Large sav-ings, depending on temporal-spatial traffic dynamics, areshown to be possible. Niu et al. [10] proposes centralized anddistributed algorithms to verify the reduction of power con-sumption of a cellular network with cell zooming, and toavoid coverage holewhen BSs are turned off. Somework onlycount transmit power, and the load-independent componentsof the energy consumption, i.e., power for active/sleepmode,is not considered. Kelif et al. [11] finds the minimal transmis-sion power that ensures coverage and capacity, but is not suf-ficient to reduce the energy consumption. Bhaumik et al. [12]switches between two radii that minimize consumptiondepending on the hourly traffic, which is a simple case. Badicet al. [13] compares cell sizes and concludes that smaller cellsare more favorable for high energy efficiency. In our design,cell size does not alternate between fixed radii, and no prede-fined traffic threshold or fixed traffic volume is based on sothat responding to dynamicsmore effectively.

A well-deployed HetNet will not only bring better per-formance on coverage and capacity but also higher energy-efficiency [14], [15], [16]. However, network planning isprimarily an off-line activity and is not necessarily fine inhandling dynamic scenarios. Cloud radio access network

(C-RAN), on the other hand, is proposed, utilizing central-ized processing, separated from the radio access units anddynamical network switching, to address the efficiencyissues [17]. Yet a C-RAN with large-scale centralization mayincur enormous fronthaul expenditure. In contrast, ourapproach is proposed as an enhancement to the existingLTE RAN. Our prior work [18] studies the spectrum-energyefficiency in only the homogeneous setting; in this work,beside the heterogeneous environment, the differences canbe presented as follows: (i) considering the effects of modu-lation scheme, association and spatial constraints to formu-late a more sophisticated model, (ii) modifying the modelfor a different spectrum partitioning model enablingenhanced Inter-Cell Interference Coordination [19], and (iii)further proposing algorithms for dynamic BS operation anduser association as well as presenting analysis.

3 NETWORK MODELS

In our work, the broadband wireless communication systemis considered which consists of different kinds of BSs andmanages multiple users. Spectrum-energy efficiency is usedto assess network capacity and defined as served trafficover allocated resource block per energy consumed. Thegoals are to (i) maximize spectrum-energy efficiency, (ii)obtain the optimal BS operation mode, and (iii) assign serv-ing BSs to users with designated modulation techniquesthat satisfy rate requirements of associated users. A list ofthe key mathematical notations is shown in Table 1.

Cell zooming and sleep mode operations as shown inFig. 1 are of benefit to enhancing spectrum-energy effi-ciency. Fig. 1a shows a wireless access network formed withfive macro (green circles) plus six femto cells (pink circles),where the central macro cell is surrounded by four macrosand works with 4 femto cells.1 BSs are located at the

TABLE 1List of Key Mathematical Notations

BA set of macro cells, amBO set of femto cells, ofBS set of BSs, fbsg ¼ fa1; . . . ; aM; o1; . . . ; oFgQK set of modulation techniques, qkUL set of users, fulg ¼ fx1; ; xN; w1; . . . ; wEgC BS-UE connectivity matrix, csl ¼ f0; 1g; 8s 2 BS; l 2 UL

I traffic demand matrix, il; 8l 2 UL

P transmit power matrix, pslk; 8s 2 BS; l 2 UL; k 2 QK

D resource block number matrix, rlk; 8l 2 UL; k 2 QK

V set of transmit power parameters, vsl ; 8s 2 BS; l 2 UL

dsl distance between BS s and user lL total number of users, jUXj þ jUWjRb network blocking ratioS total number of BSs, jBAj þ jBOjHm set of femto cells in the macro cell, hm

g ¼ f; 8m 2 BA

Pactive basic active energy consumption vector, psactive; 8sPsleep sleep mode energy consumption vector, pssleep; 8s 2 BS

Pmax maximum total transmit power vector, psmax; 8s 2 BS

R maximum number of RB vector, Rm; 8m 2 BA

Y BS-UE-Modulation association matrix, ðyslkÞS�L�KZ BS operation mode vector, ðzsÞ1�S

1. In our research, we consider femto-cells to represent small cellswhich are installed outdoor and managed by mobile operators. Theresult can be extended into HetNets consisting of other types of smallersites such as micro BSs.

1450 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 16, NO. 5, MAY 2017

respective center of the cells, designated with numbers;users are distributed among BSs, denoted by red points. InFig. 1b macro BS-2 and other femto cells work in sleepmode, together reducing energy consumption. An exampleis provided from Fig. 1c to illustrate cell zooming and usermigration. Macro BS-0 and femto BS-5, BS-6 zoom out toassociate with the users migrating from macro BS-2 or BS-3;consequently, macro BS-2 and BS-3 are allowed to reducethe coverage with decreased power. With the networkblocking ratio, macro BS-4 chooses to sleep, disconnectingwith the tolerable number of users. Moreover, connectionthrough different modulation technique selections results indifferent levels of spectrum-energy efficiency.

In this work, when switched to sleep mode, BSs are nottotally shut down and still have the ability to broadcast stan-dard messages. BSs in sleep mode periodically broadcastbeacon messages, and any user able to receive the messagescan synchronize with BSs. When users are synchronized,necessary information is obtained and estimated. Based onthe captured information, users are associated with BSs. Inother words, the coverage shown in the figure is the BS asso-ciation range instead of the broadcast range. Hence, blockedusers are always allowed to request for service.

3.1 Overview

We present the optimization model for the BS spectrum-energy efficiency problem as follows. Let UL ¼ fu1; . . . ; uLgbe the set of UEs, and each UE device has a set of modulationschemes,QK, for data transmission. Let BA ¼ fa1; . . . ; aMg bethe set of macro base stations and BO ¼ fo1; . . . ; oFg the set offemto base stations, respectively; BA is combined with BO,introducing a new set comprising both types of base stations,BS ¼ fa1; . . . ; aM; o1; . . . ; oFgwith cardinality jBSj ¼ S.

Problem Statement. Given (i) transmission power, pslk,between L users and a finite number of S stations with Kmodulation techniques, (ii) user rate requirements, il,required number of resource blocks, rlk, (iii) blocking ratio,Rb, and (iv)maximumpower, Ps

max, available resource blocks,Rm, basic active and sleep mode power usage of BSs, Ps

active

and Pssleep, the problem is to maximize the system spectrum-

energy efficiency, by associating users and BSs through desig-nated modulation techniques. The decision space consistingof association matrix (Y) and operationmode vector (Z) is definedas follows

� Y ¼ fyslkg: Equals 1 if user l is assigned to base sta-tion s through modulation k; 8s 2 BS; l 2 UL; k 2 QK,and 0 otherwise.

� Z ¼ fzsg: Equals 1 if base station s is in the activestate ; 8s 2 BS, and 0 otherwise.

With information on power and carrier requirements,when yslk is asserted, the traffic demand is satisfied for ul viamodulation technique k, and os has to be the value of onecorrespondingly. The BS cell size is the equivalent of thearea within which BSs are able to serve users by tuning uptransmission power (pslkÞ. Cell zooming is present by com-parison of the service areas of two statues at consecutiveoperation times. In other words, as the service area varieswith the adjusted transmit power level, the BS is undertak-ing cell zooming.

3.2 Association and Spatial Constraints

Eq. (1) realizes the traffic request from an associated user issatisfied through a direct link with a BS. Each user can beserved by up to one BS through one modulation technique.For an individual BS s, if the result of

Pl2UL;k2QK

yslk is equal

to 0, it means s operates in sleep mode. Furthermore, theidea of user migration is put into action if an user is associ-ated with a BS which is different from the one it formerlyconnected

Xs2BS;k2QK

yslk � 1; 8l 2 UL: (1)

Continuity Constraint. To prevent intermittent data trans-mission on the users, we distinguish existing users fromnew coming ones. The existing users are inclined to com-plete the ongoing sessions with continuous associationsessions; the new coming users arrive at the network andseek for being associated with no data transmission yet.In this context, the set of users is partitioned into two, UL ¼fUX;UWg with cardinality L ¼ N þ E. The first partpresents the set of new arrival users with UX ¼ fx1; . . . ; xNg;the second part represents the set of existing users withUW ¼ fw1; . . . ; wEg. To allow active users to be not service-discontinued, the following constraint is imposed. Note thatwhen UL ¼ UX, the association continuity is not taken intoaccount X

s2BS;k2QK

ysek ¼ 1; 8e 2 UW: (2)

Topology Constraint. The scheme of frequency reuse helpBSs prevent interfering with the neighboring; as the cell sizeis adjustable, nevertheless, BSs could overexpand the trans-mission range, seriously interfering others sharing the samespectrum. Considering such impact, limiting individualtransmit power is effective; therefore, whether user l isattainable for BS s can be determined in terms of the trans-mit power with modulation K, which requires the highestsensitivity and SNR among QK

Fig. 1. BS operations, cell zooming in/out, sleep mode, and user migration to enhance network performance.

HSU AND CHANG: SPECTRUM-ENERGY EFFICIENCY OPTIMIZATION FOR DOWNLINK LTE-A FOR HETEROGENEOUS NETWORKS 1451

CðpslK; psÞ ! csl ¼1; if pslK < ps; 8s 2 BS; l 2 UL;0; otherwise;

�

where ps is a maximal individual transmit power, which canbe estimated considering BSs were deployed at fixed loca-tions. csl ¼ 1 means cell s can reach l in terms of transmitpower. Then it is expressed as follows that BSs should onlyconsider users within the reachable range as a feasible setX

k2QK

yslk � csl ; 8s 2 BS; l 2 UL: (3)

3.3 Power and Carrier Constraints

Two parameters are tied to modulation selection, transmitpower and resource block. Given the traffic rate required atthe user, the power and resource block number are obtainedthat are necessary for modulation schemes at the BS.Each modulation and coding scheme (MCS) is able to sup-port a data rate; the transmission time is captured by theresource block number. Through modulations, a trafficrequirement can be met by different numbers of resourceblocks in given time duration, i.e., more resource blocks areallocated to achieve same data rate for lower MCS. We con-sider a quasi-static network scenario, where il; 8i 2 UL,remains unchanged within every operation period, whilechanging across periods. Individual rate requirements, il,are randomly chosen from the set of supported rates by thephysical layer (Table 2). rlk indicates the number of resourceblock for user l through modulation technique k.

Resource Block Constraint. The total number of resourceblocks a BS serves should not be greater than the availablenumber (Rm; 8m 2 BA) on the channel bandwidth in a speci-fied symbol time. This constraint is ensured by the follow-ing equation:

Xhmg 2Hm;l2UL;k2QK

½ðymlk þ yhmglk Þ � rlk� � Rm; 8m: (4)

As the available spectrum span is finite, the number ofresource blocks to transmit data over the span is limited. Weassume that non-overlapping spectrum bands are used, andhence there is no co-channel interference. In other words,orthogonal radio resources are allocated to macrocell andsmall cell users; the cross-tier and co-tier interference arecompletely eliminated.We further assume that small cells useorthogonal channels. Therefore, the different subsets ofmobile users assigned to each small cell do not interfere witheach other.

When operating within a macro cell’s coverage, a femtocell allocates a portion of m’s available frequency for trans-missions. Hm ¼ fhm

1 ; . . . ; hmGmg; 8m 2 BA denotes the set of

femtos f sharing spectrum with the macro m. To calculate

the number of resource blocks for individual data transmis-sions with modulation technique k, the equation for theresource block number, rlk, given the rate requirement, il, isconsidered as [20]

Rðil; kÞ ! rlk; 8l 2 UL; k 2 QK:

Transmission Power Constraints. Receiver sensitivity isregarded as the minimum power at the receiver side for theguaranteed signal strength, from which the necessary trans-mission power level, pslk, can be calculated as according to [21]

P ðil; vsl ; kÞ ! pslk; 8s 2 BS; l 2 UL; k 2 QK;

where vsl represents the propagation gains and attenuationby miscellaneous losses between s and l. It is shown the lin-ear model can offer approximation for the transmissionpower with respect to the carried traffic load, and has beenadopted in [12]. In this work, the model is applied to cap-ture the dependency of traffic volume and resource blocks.BSs are considered to scale their power consumption to traf-fic load; a higher user population implies higher transmitpower from the base station generally. The constraints ontotal transmission power constraints are as follows:X

l2UL;k2QK

ðymlk � pmlkÞ � Pmmax; 8m 2 BA; (5)

Xl2UL;k2QK

ðyflk � pflkÞ � Pfmax; 8f 2 BO: (6)

Receiver sensitivity is listed in Table 2 [22]. As BS antennasare assumed to transmit ideally, feeder losses, connectorlosses and jumper losses are not considered. We considerfast fading margin and building penetration loss, whosevalues are assumed in simulation [23]. The COST-231 Hataand COST-Walfisch-Ikegami models are considered forpath loss. We assumed the BS antenna height is 30(m) andthe users’ antenna height is 1(m).

We consider a scenario where for each cell, the input datafor optimization are reported periodically, which is commonin many real network deployments [24]. Besides, the time-scales of changing parameters for all practical purposes are inthe order of a fewminutes (typically, 5-15 mins). Thus, recon-figuration ought to happen whenever: 1) input informationchanges significantly in some cells, or 2) when a maximumduration elapses since the last reconfiguration. In addition, ifthe estimated improvement upon new reconfiguration issmall, then the previous configuration can be retained.

3.4 Operation and Service Constraints

If it is an BS operating in active mode, bs is equal to one for s.Eqs. (7) and (8) together ensure that a BS switches into activemode as long as delivering services; otherwise the BS switchto sleep mode without serving users

zs �X

l2UL;k2QK

yslk; 8s 2 BS; (7)

yslk � zs; 8s 2 BS; l 2 UL; k 2 QK: (8)

The total number of connected users must be higher thanthe required number of active users as follows:X

s2BS;l2UL;k2QK

yslk � d; (9)

TABLE 2Parameters per Modulation Scheme

Modulation Sensitivity(dBm)

Data bitper symbol

Data rate(Mbps)

QPSK1/2 �96 1.0 2.216QAM1/2 �90 2.0 4.416QAM3/4 �87 3.0 6.664QAM3/4 �80 4.5 9.9

1452 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 16, NO. 5, MAY 2017

where d ¼ Sð1�RbÞ and Rb denotes the blocking ratio, theratio of users not associated among total users demandingservices. No single user is considered to be blocked if the rateis set to zero. Note that there could be no feasible solutionsdue to insufficient resources to serve users. In this case, opera-tors can consider two alternatives: (i) increase the blockingratio, (ii) treat existing users as new coming in the model.Having a high blocking ratio can lead to the situation wheremany new coming users have difficulty in getting mobileservices; seeing existing users as new arrival can result in thesituation where the service continuity is not guaranteed. Onuser side, theymay experience a data rate drop overall, whichcommonly occurs when the network is congested. However,when available recourses are sufficient for data transmission,none of the alternatives is needed to be taken.

In LTE, BSs in sleep mode periodically wake up andbroadcast beacon messages. The instantaneous channel-quality in time domain at the terminals is estimated and fedback to the BS for power level adjustment (pslk); the informa-tion about the number of RBs for user requirements can becollected during the resource allocation procedure (rlk).When users are able to synchronize with BSs, the informa-tion concerning transmit power can be used as input to ourmodel without knowing the user locations. Once users havebeen associated, they will periodically send information tomaintain communication. We assume no rapid channel-quality variations in frequency domain.

4 SPECTRUM-ENERGY EFFICIENCY PROBLEM

We define the spectrum efficiency as a summation of theindividual served traffic divided by the allocated resourceblock number of associated users since the resources are dis-tributed separately. The next expression presents the spec-trum efficiency achieved

SðY; I;DÞ ¼X

s2BS;l2UL;k2QK

ilrlk� yslk

� �:

A BS operates in either sleep mode, taking a low energylevel, or in active mode, consuming a basic running energyplus the energy for transmission. The energy a sleeping BSconsume isPs

sleep; the energy consumed by an active BS comesfrom the basic activemode energyPs

active plus the energy usedto serve its users,

Pl2UL;k2QK

ðpslk � yslkÞ; 8s 2 BA. The overall

energy consumption is expressed as

EðY;Z;P;Pactive;PsleepÞ ¼Xm2BA

ðPmactive � zmÞ

þXf2BO½Pf

sleep � ð1� zfÞ� þX

s2BS;l2UL;k2QK

ðpslk � yslkÞ

þXf2BOðPf

active � zfÞ þXm2BA

½Pmsleep � ð1� zmÞ�:

To fulfill the requirement, BSs chooses MCS, deliveringdata at a necessary level of transmit power over a sufficientnumber of resource blocks. The model is designed for find-ing the optimal operation policy for BSs by deciding yslkand zs. When yslk in the solution is equal to 1, user l is asso-ciated with BS s through modulation technique k, whichcorresponds to rlk resource blocks and pslk to satisfy therequirement il.

The formulation for the BS operation and user associa-tion assignment problem can be expressed as follows:

maxSðY; I;DÞ

EðY;Z;P;Pactive;PsleepÞs:t: Constraints ð1Þ-ð9Þ;

yslk; zs 2 f0; 1g; 8s 2 BS; l 2 UL; k 2 QK:

(10)

The problem (10) has the objective function to maximizethe spectrum-energy efficiency. Note that due to the energyrequired for sleep mode, the energy consumption functionEð�Þ has a lower bound even though no associations isformed by BSs. The case, therefore, will not arise that totalenergy consumption is very small (e.g., goes to zero). How-ever, the problem involves a fractional objective functionwhich we reformulate into a MILP problem to obtain theoptimal solution.

4.1 Problem Transformation

In (10), although the constraints are linear, the objectivefunction is a ratio of two linear terms, hence making themodel nonlinear. To eliminate the nonlinearity, the objectivefunction must be transformed to be pure linear; also whenthere exists a solution to the transformed model, a solutioncan also be found to the original model. The objective func-tion can be transformed to a linear function as follows. Sincein the original problem, the denominator is always positiveover the feasible sets of Y and Z, variables ms

lk, ns and t areintroduced, which hold ms

lk ¼ t � yslk and ns ¼ t � zs, and

t ¼ 1Eð�Þ. The transformed problem is presented below

maxX

s2BS;l2UL;k2QK

ilrlk� ms

lk

� �

s:t:Xm2BA

½ðPmactive � Pm

sleepÞ � nm� þ t �M � Pmsleep

þXf2BO½ðPf

active � PfsleepÞ � nf � þ t � F � Pf

sleep

þX

s2BS;l2UL;k2QK

ðpslk � mslkÞ ¼ 1;

Xs2BS;k2QK

mslk � t; 8l 2 UL

Xs2BS;k2QK

msek ¼ t; 8e 2 UW

Xk2QK

mslk � t � csl ; 8s 2 BS; l 2 UL;

Xl2UL;k2QK

ðpmlk � mmlkÞ � t � Pm

max; 8m 2 BA

Xl2UL;k2QK

ðpflk � mflkÞ � t � Pf

max;8f 2 BO

Xhmg 2Hm;l2UL;k2QK

½rlk � ðmmlk þ m

hmglk �Þ � t �Rm;8m

Xl2UL;k2QK

mslk � ns; 8s 2 BS

mslk � ns;8s 2 BS; l 2 UL; k 2 QKX

s2BS;l2UL;k2QK

mslk � t � d;

mslk; ns; t � 0; 8s 2 BS; l 2 UL; k 2 QK:

(11)

HSU AND CHANG: SPECTRUM-ENERGY EFFICIENCY OPTIMIZATION FOR DOWNLINK LTE-A FOR HETEROGENEOUS NETWORKS 1453

Provided t > 0 at the optimal solution, this LP problemis equivalent to the fractional objective problem except thebinary condition of decision variables. The values of thevariables yslk and zs in the optimal solution to the fractionalobjective problem are obtained from dividing optimal ms

lk

and ns by t. As decision variables in the fractional objectivemodel are binary, it is necessary to impose on the trans-formed model the constraints which reflect the binaryproperty. We know if yslk is zero, then ms

lk must be zero;otherwise, ms

lk ¼ t if yslk ¼ 1. In the following constraints,binary variables are introduced, as

lk and bs, as well as aconstant value Q holding a value greater than ms

lk, ns and t.

mslk � t �Q � as

lk � �Q;8s; l; kns � t �Q � bs � �Q;8s; l; kmslk � t þQ � as

lk � Q;8s; l; kns � t þQ � bs � Q;8s; l; k

mslk � Q � as

lk; 8s; l; kns � Q � bs; 8s; l; k

aslk;bs 2 f0; 1g; 8s; l; k

Problem (10) is equivalent to (11) given the fact that

yslk ¼mslkt; zs ¼ ns

t, 8s 2 BS; l 2 UL; k 2 QK and t ¼ 1

Eð�Þ. The

MILP problem considers transmission power, as Eð�Þ is oneof the transformed constraints. Since the the value of t hasthe impact on both ms

lk and ns, not only rlk but also pslk influ-ences the objective value.

5 APPROACHES TO SOLVE THE PROBLEM

Software packages, CPLEX for instance, are able to solveMILP problems; however, amajor disadvantage ofMILP is itscomputational complexity. Because MILP is NP-hard in gen-eral, computational requirements can grow significantly asthe number of binary variables increases. Motivated to gener-ate less computationally intensive methods, we develop twotechniques solving the formulated problem by finding subop-timal solutions, which are discussed in the following.

Remark 1. The formulated problem is NP-hard by reduc-tion from the set-packing problem.

Proof. In set packing problems, given a universal set V anda set F which consists of some subsets of V , a packing is asubset G F of sets such that all sets in G are pairwisedisjoint. To obtain the reduction from the set-packingproblem, we consider a simplified version of the formu-lated problem where a HetNet consists of a single macro,a single small cell, and N UEs. We first set the overallenergy consumption as a constant so that the objectivefunction is linear. Suppose there is only one modulationscheme, and resource blocks and transmit power arealways sufficient. Both BSs are active, and all users areassociated with either of them. For UEs, the transmitpower is identical from BSs. In this case, the overallenergy consumption is constant, and we maximize spec-trum efficiency as optimizing spectrum-energy efficiency.

Let UL ¼ V , and F can be constructed based on thetopological relation constraint. For Fs F , Fs consists ofall sets formed by possible coverage of BS s. The user com-position, based on possible coverage, varies from set to set

in Fs. Given all possible UE and BS combinations, theproblem becomes finding the pack of BS subsets whereUEs are not overlapping such that spectrum efficiency ismaximized. The set-packing problem has a solution if andonly if the constructed problem has a solution.2 tu

5.1 Quasiconvex Optimization Problem

A quasiconvex problem takes the form

min fðxÞs:t: fkðxÞ � 0; k ¼ 1; . . . ;m;

Ax ¼ b;

where f : Rn ! R is quasiconvex, f1; . . . ; fm are convex, andak 2 Rn and bk 2 R for k ¼ 1; . . . ; p; are affine. The objectivefunction in (10) is quasiconvex according to Definition 1.

Definition 1. A function f : Rn ! R is quasiconvex if itsdomain domðfÞ and all its sublevel sets Sa are convex

Sa ¼ fx 2 domðfÞjfðxÞ � ag; 8a 2 R:

Proof. Let the function

SðY; I;DÞEðY;Z;P; Pm

active; PfsleepÞ

¼ fðxÞ ¼ aTxþ b

cTxþ d:

As domðfÞ ¼ fxjcTxþ d > 0g and its a-sublevel set is

Sa ¼ fxjcTxþ d > 0; ðaTxþ bÞ=ðcTxþ dÞ � ag¼ fxjcTxþ d > 0; ðaTxþ bÞ � aðcTxþ dÞg;

which is convex. Therefore, fðxÞ is quasiconvex. tuThe inequality constraints are convex because they are

linear and the equality constraint is affine since the solutionset of a linear equation is an affine set. Hence (Objective-Function) is a quasiconvex optimization problem, whoseglobal optimum can be computed via a sequence of convexfeasibility problems. Let f denote the optimal value of thequasiconvex object function. Given g 2 R, if the convex fea-sibility problem of (12) is feasible, then we have f � g

find x

s:t: fðxÞ � g;

fkðxÞ � 0; k ¼ 1; . . . ;m;

Ax ¼ b:

(12)

Conversely, if the above problem is infeasible, then we canconclude f < g: Thus we can check whether the optimalvalue f is less or more than a given value g: Algorithm 1shows the procedure of the bisection method for solving the

2. Hardness can also be shown by reduction from the budgeted wel-fare maximization problem. An instance can be created as follows, fol-lowing the same assumption and example, but the resource blocks arelimited to each BS and same number of RBs are required for UEs. Inthis case, maximizing spectrum-energy efficiency is equivalent to maxi-mizing total traffic, and the constraint is the RB constraint, in otherwords, the budget. Corresponding to each item, we create a UE. Thereare two BSs (bidders), each of which has same traffic demand fromsame user. Note if the BSs are constrained with same resource blocknumber, it can be reduced from a partition problem.

1454 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 16, NO. 5, MAY 2017

problem. It starts with a range ½l; h� that is known to containf. Then we solve the feasibility problem at its mid-pointa ¼ ðlþ hÞ=2. Depending on whether it is feasible, the algo-rithm continues on the identified half of the interval. Thealgorithm is guaranteed to converge in dlog 2ððh� lÞ="Þeiterations. The bisection algorithm is less expensive in termsof computation complexity.

Algorithm 1.Max xfðxÞGiven l � f � h and the tolerance " > 0;while ðh� lÞ > " doa ¼ ðhþ lÞ=2;Solve the feasibility problem (12);if feasible then l ¼ a;else h ¼ a;

end

Algorithm 2. Spectrum-Energy Efficiency Maximization

Input: S; L;K;M;F;N;E;Rb;BS;UL;QK;BA;BO;UX;UW;C; I;D;P;Hm;R;Pactive;Psleep and Pmax:

Output:Y and Z.1: Compute gslk 2 V; 8s; l; k;2: for l ¼ N þ 1 to L do3: Find s and k combination that gives best gslk;4: yslk 1 and zs 1;5: for s ¼ 1 toM do6: Macro-Femto();7: Sleeping();8: while there exists an s that can cover more users do9: Zooming();10: for l having no service and s active do11: if exists s; l; k combination to improve C then12: yslk 1 and zs 1;13: while constraint (9) is not satisfied do14: Find s;8zs ¼ 0 covering the most non-served users;15: for csl ¼ 1 do16: if yslk 1 satisfies constraints (4)-(6) then17: yslk 1 and zs 1;18: for l having association do19: if there exists a k that can improve C then20: yslk 1 and zs 1;21: return Y and Z.

5.2 Heuristic Algorithm

In the wireless communication environment the number ofusers changes and the requirements fluctuate frequently;hence, heuristic algorithms are favored to solve the pro-posed optimization model in real time. The approach isshown in Algorithm 2, which accepts same input. While thedetermination of operation and association depends oninformation that changes in each frame, thereby tacklingthe maximization problem within the per-frame optimizeddecision, the algorithm can perform maximization at coarsetime scales if per-frame efficiency maximization is infeasibledue to practical constraints. Since the ongoing connectionsare guaranteed to be maintained, the situation is preventedwhere BSs are switched on and off between solutions. BSsreport dynamic parameters to facilitate the solution: (i) UX,UW, I (D, P are then estimated with each MCS through the

screening procedure), and (ii) C through the ranging pro-cess. Other input of Algorithm 2 is static and determinedwith the network deployment by operators. Although capa-ble of reducing computation time, when the heuristicapproach is applied to an extremely large-size network, thesolution might not be able to obtained in the time of a frame.In this regard, tuning the algorithm by further reducing itscomplexity can be a fix.

A preliminary solution is initialized by, for each existinguser, selecting the cell and modulation technique which incombination allow the best single link spectrum-energy effi-ciency. The solution is first updated in the manner ofmigrating active users from macro cells to femto ones, look-ing for the opportunity of sleeping macro BSs. Then, theheuristics seeks for favorable possibilities under whichusers can be reassociated with the active cells other thancurrent ones. If all users are swept into its neighboring BSs,the cell can be switched to sleep mode. Subsequently, theremay exist users who are not served. Without activating BSsin a sleep state, assigning these users to awake BSs couldbenefit improving system spectrum-energy efficiency. Onthe other hand, the constraint on the served user numbermight not be presently fulfilled, which is responded to asinactive BSs encompassing the most non-served users willbe turned on, accommodating the users with no association.Lastly, a better solution can be achieved through changingmodulation technique to live links for improving systemspectrum-energy efficiency. Overall, the computation com-plexity of the algorithm is OðSL3KÞ.

5.3 Algorithm Description

The spectrum-energy efficiency of a single link (gslk ¼ilrlkpslk) is

computed for each combination of BS, user and modulationtechnique. An initial solution is suggested with existingusers to choose best gslk; 8s 2 BS; k 2 QK. Macro-Femto()looks into active macro BSs in order for examining the possi-bility of user migration to femto cells facilitating sleepingmacro cells. During Macro-Femto(), associated users withthe macro cell are considered for being migrated to femtocells. Two conditions are necessary for getting into a sleepstate: all the users are able to be migrated and energy con-sumption can be reduced. Running many femto cells mayconsume energy more than that what can be reduced fromsleep macro BSs, which is not beneficial to spectrum-energyefficiency improvement. Therefore, starting from the macrocell that could have the highest migrated user number,Sleeping() chooses femto cells that require less amount ofenergy to sleep. During the procedure, if the total transmist

power of a femto BS is higher than Pfmax; 8f 2 BO, modula-

tion technique will be adjusted to reduce the imposedenergy, fromuserswho need the highest transmitting power.

Moreover, it is with the intention of economizing onenergy consumption by engaging fewer BSs in active mode.Starting from the one showingmost active users in coverage,active BSs connect users who were served by others as manyas they can, providing constraints (4)-(6) are not violated,which essentially is what Zooming() for. In the case of theinsufficient resource block number or total power to deploy,appropriate modulation adjustment is considered. Specifi-cally, depending on which resource is not sufficient, forusers taking high transmit power or large resource blocks,

HSU AND CHANG: SPECTRUM-ENERGY EFFICIENCY OPTIMIZATION FOR DOWNLINK LTE-A FOR HETEROGENEOUS NETWORKS 1455

modulation is tuned till no more adjustments can or isneeded to be made. For no-service users, two active BSs arechosen to bring two highest gslk. From the user giving best gslk,if efficiency can be improved, users pick first choices in thefirst iteration; if the total served user number cannot beaccepted, second choices come to play for the rest with noassociation. Until the blocking ratio constraint is met, BSs areturned on and provide the users services via bestmodulationmethod. Then the solution is updated if spectrum-energyefficiency can be enhanced bymodulation adjustment.

6 NUMERICAL RESULTS

This section presents case studies where the wireless widearea network (WWAN) is assumed such as LTE Advancedusing OFDMA interface for the downlink. The case studiesare conducted to evaluate the effectiveness of the formu-lated mathematical model and proposed heuristic algorithmin terms of produced solutions, and the computational effi-ciencies in multi-cell-multi-users scenarios. We first evalu-ate performance improvements of the proposed solution,and then compare our scheme with others to show the effec-tiveness. The computation cost and solution obtained by theheuristic algorithm are studied as well. The main systemparameters taken into account in the simulations are tabu-lated in Table 3 unless stated otherwise.

As WWAN spans a relatively large area, we separateareas of coverage into three geographic areas, urban (cen-tral), rural (peripheral) and suburban (in-between) regions.The building penetration loss correction values vary inthese areas, which are 12, 18, and 15 dB, respectively [23];the area percentages are 65, 15, and 20 percent, respectively.

Three types of user distribution are considered across theentire area. Fig. 2a shows the illustrative Type 1 networklayout, in which 80 percent of the users are in the urbanarea, 12.5 percent suburban and 7.5 percent rural, respec-tively; Type 2 distribution is plotted in Fig. 2b, where theperipheral region has a larger population. The other type ofuser distribution is uniform, for which user numbers arebasically the same in the three areas. In our study, the fre-quency reuse three scheme is adopted on macro BSs and theresource block constraint is expressed as Eq. (4); for eachmacrocellular BS, it shares the reused radio resource withits small cells. The constraint can be modified in order towork with any given spectrum allocation policy where fre-quency bands are allocated individually. For instance, insplit spectrum macrocell-femtocell, certain portion of theavailable spectrum resources are dedicated to each tier toavoid interference problems among the tiers.

6.1 Solving the Model

Fig. 3 shows the results obtained from four schemes for caseswith user numbers from 800 to 2,600 and Type 1 distribution.There are 15 macro and 10 femto BSs, and the blocking ratiois 6 percent. The four schemes includes homogeneous mac-rocellular network, heterogeneous network consisting ofboth macrocell and femto cell sites, proposed frameworkthat optimizes spectrum-energy efficiency of HetNets, andheuristic approach that solves the formulated problem(Algorithm 2), respectively. In Fig. 3a first two schemes serveall users, and therefore fulfils more data requirements,whereas the proposed solution is allowed to block users;hence in the cases with numbers from 800 to 1,400, it servesless. For other cases, since servingmore users improves spec-trum-energy efficiency, all users are served. In Fig. 3b, withoptimal modulation selection, the proposed scheme obtainsthe highest spectrum efficiency for all cases, which is onaverage improved by 92 percent from HetNet scenarios,while HetNets outperform homogeneous macrocellularnetworks slightly. Note that the improvement in spectrumefficiency correlates with small cell user number. We runadditional simulations and the results show as more smallcells are introduced, the improvement in spectrum efficiencyincreases. Since the possibility of being associated with smallcells increases, we can expect the increase in the percentageof users associated through betterMCS.

TABLE 3System Parameters

Parameter Value

Channel bandwidth 10 MHz, frequency reuse 3Sleep mode power Pm

sleep ¼ 8; P fsleep ¼ 0:028 (W)

Active mode power Pmactive ¼ 500; P f

active ¼ 5 (W)Maximum transmission power Pm

max ¼ 40; P fmax ¼ 0:14 (W)

Required data rate Random (0-9.9 Mbps per user)User arrival rate � ¼ 30 per macrocellResource block number 600 per DL subframe

Fig. 2. Illustration of node distribution setup.

1456 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 16, NO. 5, MAY 2017

Fig. 3c shows the total energy consumed by differentschemes in different cases. For the homogeneous networkscheme, without turning off BSs, all BSs stay active even inunsaturated networks (i.e., L < 1;200), resulting in heavyoverall energy consumption, whereas the HetNet schemeconsumes more energy than because femtos account for theadditional energy use for transmission and being active. Forour scheme, when 800 users are in the network, almost halfof the BSs are switch off, saving more than 45 percent energyin comparison with that of the HetNet scheme. But the dif-ference becomes to around 7 percent when the user numbergrows to 1,000 and 1,200; all macro cells stay active to servemore than 1,400 users. As the number of users increases, theenergy consumption difference decreases between the Het-Net scheme and the proposed scheme due to the decreasednumber of BSs that can operate in sleep mode. For example,while 1,200 users are considered, six more macro BSs remainactive compared with the case of 800 users. In the solution,the BSs differ in service range based on the distribution ofusers and their traffic service requirements through adjust-ing the modulation scheme and transmit power, carryingout cell zooming in/out. The BSs with no users to serve canbe turned off, applying BS sleep mode; the users may con-nect with another BSs, realizing migration.

Fig. 3c depicts the performance improvement on spec-trum-energy efficiency. It is shown that the spectrum-energy

efficiency is increased slightly in the HetNet scheme fromthe homogeneous scheme, whereas the efficiency capacityimproves substantially in the proposed scheme with anaverage improvement of 114 percent. When the user num-ber is 800, because a significant number of BSs are in sleepmode, the efficiency is enhanced by almost 250 percent.Spectrum-energy efficiency takes into account energy effi-ciency and spectrum efficiency together. By maximizingthis efficiency capacity, both metrics can be improved.Note that optimizing either metric does not necessarilyachieve optimal spectrum-energy efficiency due to thetrade-off.

6.2 Comparative Schemes

We next compare the suggested scheme against six differentconfigurations. They are (i) no optimization is realized uponthe HetNet, (ii) the change of MCS selection is not considered(ms

lk0 ¼ 0; 8s 2 BS; l 2 UL; k0 2 QK n fkg, where k is the origi-

nal MCS selection for users), (iii) optimization does not

migrate users (ms0lk ¼ 0; 8s0 2 BS n fsg; l 2 UL; k 2 QK, where s

is the original BS user l is associated with), (iv) BSs do notzoom out to cover neighboring users; hence, coverage willnot be extended (effecting Eq. (3)), (v) the BSs with no usersto serve originally are not considered to associate with any inoptimal solutions (n0s ¼ 0; 8s0 2 BS, where s0 is BS has no userswithin its original coverage), and (vi) the proposed

Fig. 3. Performance comparisons among four schemes.

HSU AND CHANG: SPECTRUM-ENERGY EFFICIENCY OPTIMIZATION FOR DOWNLINK LTE-A FOR HETEROGENEOUS NETWORKS 1457

maximization scheme is applied. Except the first configura-tion, the spectrum-energy capacity is optimized for all others.

Fig. 4 shows our results. Without optimizing MCS, thespectrum-energy capacity drops by on average 33 percent,whichmeans themost sensitive dependence is onMCS selec-tion, compared with the other three key configurations. Thereason is optimizing theMCS selection picks better MCS val-ues than the default MCS in the sense of balancing overallenergy consumption and resources (e.g., higher power butless RBs). We did the experiment to verify that the capacitydifference becomes greater with more UEs, due to moreMCS selection improvement opportunities. Furthermore, inFig. 4, since migration operation is excluded, the existingmobile users cannot be re-associated with other BSs, result-ing in more BSs that are needed to be activated; therefore5.5 percent decrease from the proposed configuration. Simi-larly, the differential between default cell zooming and theproposed solution averages out 5 percent, for which themain reason is without the ability to expand coverage areas,the chances are reduced that the serving users are taken overby other BSs and the BS is allowed to be in sleep mode.Lastly, the performance of the default cell on/off configura-tion depends on the distribution of UEs. When no UEs are inthe coverage of femtos, they are switched off; when moreUEs appear in the area of femtos, they cannot sleep.

Table 4 presents improvements in spectrum-energy effi-ciency for various numbers of nodes with different userdistribution considerations. It is manifested that the optimi-zation model is capable of being scaled, as the spectrum-energy efficiency can be improved by more than 91 percentfor a variety of network settings regardless of the numberof nodes and user distribution. For operators, it is economi-cally essential to be concerned about how efficientlyresource blocks are utilized and energy is consumed. Theformulated model looks for assignments (BSs, users andmodulation/coding schemes) which together contribute thebest spectrum-energy efficiency.

6.3 Solution with Other Spectrum PartitioningModel

To show that our formulation can adopt other spectrumsharing model between macro and femto cells, we alsoevaluate our algorithms considering small cells resources

are allocated using frequency reuse of 1. In this section weincorporate our model with Almost Blank Sub-frames (ABSperiods), which are a recently proposed and discussed tech-nique by the 3GPP project [25]. ABS periods are certain peri-ods designated for each macro to remain silent, over whichthe femto can use for down-link transmissions, improvingperformance to users close to the femto. We modify the pro-posed formulation to jointly optimize ABS parameters foreach cell. The goal of our evaluation is to compare our pro-posed solution with other alternative schemes.

We follow the operational LTE network setup in [26] toevaluate our algorithms in the context where ABS is used.An area of around 8.9 km2 is selected which has 28 macroBSs and 10 femto BSs. The user locations are uniformlychosen, and we chose a user density of around 190 users/sq-km (urban). In addition, we create user hotspots around4 femtos which have doubled user density, and one otherfemto has 50 percent more traffic. We also perform evalua-tion by varying the user density around the macro cells to95 users/sq-km (sub-urban) and 50 users/sq-km (rural)without altering the hot-spot user densities around theselected femtos.

6.3.1 Optimal ABS Parameters

For fair comparison, alongwith ABS patterns, we consider aswell the concept of cell selection bias (CSB), allowing users tobias its association towards small cells by amargin; thereforeextending cell range [19]. We compare our algorithm to theschemes with the following two (ABS, CSB) combinations:(1/8, 0 dBm) and (2/8, 5 dBm). We also compare with thescheme where based on the user association from fixed ABSand CSB pattern, the modulation scheme selection is opti-mized to improve efficiency. Furthermore, a 2-step local opti-mal based scheme is implemented. This scheme works asfollows. First, each femto maximizes the total improvementof efficiency with serving all users within the coverage rangethrough bestmodulation schemes fromusers. This step read-ily provides the solution on users that associate with femtos.In the next step, each macro m obtains the fraction (for

Fig. 4. The proposed scheme versus baseline schemes.

TABLE 4Spectrum-Energy Efficiency Improvement in Scenarios

Number of Nodes UserDistribution

Spectrum-EnergyEfficiency ImprovedMacroBS FemtoBS User

Type 1 95.39%15 25 4,000 Type 2 99.43%

Uniform 95.48%

Type 1 93.30%18 30 5,000 Type 2 96.54%

Uniform 94.03%

Type 1 94.07%18 35 6,000 Type 2 96.81%

Uniform 94.99%

Type 1 91.51%20 40 7,000 Type 2 97.54%

Uniform 95.06%

Type 1 92.84%20 45 8,000 Type 2 97.62%

Uniform 95.71%

1458 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 16, NO. 5, MAY 2017

example, xm) of RBs occupied by femtos within its coveragerange and then macro offers dRmxme as ABS-sub-frames.Each femto can only use minimum number of ABS-sub-frames offered by its macros. Then, with the decision on fem-tos, the decision is made by optimization on the remainingusers that associate with macros. We consider serving allUEswith a blocking ratio of 0.

Fig. 5 compares our algorithm to different network widefixed ABS settings. The fixed (ABS, CSB) setting of (2/8, 5dBm) performs the worst due to more activated stations.With CSB, the problem of under-utilization of femto cellsmay be eased, since more users are expected to be offloadedfrom macros. While the resource block constraint accountsfor QoS requirements of the UEs, however, we need to care-fully deal with the situation where small cells are under-uti-lized. It is likely that the increase in utilization at the smallcell is limited with the CSB technique due to low user asso-ciation, resulting in stations remain in operation. Thisunderlines the importance of the problem being addressed.

On the other hand, with optimal modulation schemeselection, efficiency can be improved from fixed configura-tion as shown from the optimal fixed schemes in the figure.However, the optimal fixed schemes fail to account for theoverall active BS number as they only optimize modulationselection, whereas the local optimal scheme and the pro-posed algorithm do not necessarily activate all BSs. Ourscheme outperforms the local optimal one since it furtherreduces the number of active femtos in the network;although it is small for the considered network deployment,the margin can increase substantially in the case of densedeployment of small cells, which is a typical developmentin practice. On the other hand, the local optimal scheme iseasy to implement and could be promising with additionalminor changes for a lower-complexity solution.

6.3.2 Base Station Sleep Mode Strategies

In this section, we compare with other schemes that mini-mize the power consumption at each BS. Similar to [4], [27],we implement polices of random and strategic sleeping toswitch off BS. In random sleeping, we model the sleepingstrategy as a Bernoulli trial such that each station remains inoperation with probability q, independently of all the others.Instead of randomly switching BSs off, we can switch off

BSs when their activity levels are low. Specifically, wemodel the strategic sleeping as a function sð�Þ. If the activitylevel of the coverage area associated with the BS has activitylevel x, then it continues to operate with probability sðxÞ,independently. We consider two models of random sleep-ing: binarywhere BSs sleep with probability 0:5, and uniformwhere the probability is drawn from a uniform ½0; 1� randomvariable. We also consider two models of activity levels forthe strategic sleeping: dynamic where if the activity level inthe coverage area associated with the BS is a, then the BSstays awake with probability a, and static where if the activ-ity level associated with a BS is greater than a predefined

threshold (14 in our study [28]), then the BS stays awake with

probability 1 or it stays awake with probability 0:5 other-wise. We define the activity level as, on each BS, the totalnumber of RBs to serve associated UEs divided by the avail-able RBs for data transmission.

BSs are randomly picked to be activated based on thestay-awake probabilities, and the procedure continues tillsatisfying the blocking ratio constraint. Then, based on theactive/sleep mode decision, user association and modula-tion scheme selection are optimized. Fig. 6 shows the spec-trum-energy efficiency for different schemes, including thesleeping strategies, local optimal scheme and proposedalgorithm. The blocking ratio is set to 7.5 percent and theABS value is fixed at 3

8. From the figure, it is shown that atleast one of the strategic sleeping strategies is better thanrandom sleeping ones. Although the margin is small, differ-ent schemes do not necessarily have a same set of active BSsor same number of active BSs.

We also see that both of proposed algorithm and localoptimal scheme have bigger margins of improvement overrandom and strategic sleeping policies. This is because thefour sleeping strategies do not taken into account the optionof cooperation among BSs to further minimize energy con-sumption. Therefore, awake BSs may serve the same areas,which are opportunities for further energy savings. Never-theless, different from our algorithm, since the local optimalscheme solves the problem in two levels (first femto andthen macro), a global optimal solution is difficult to obtain.The figure shows the proposed algorithm performs betterfor different user densities, suggesting the algorithm isadaptive to fluctuations in traffic activity levels.

Fig. 5. Comparison of ABS pattern. Fig. 6. Comparison of sleeping strategy.

HSU AND CHANG: SPECTRUM-ENERGY EFFICIENCY OPTIMIZATION FOR DOWNLINK LTE-A FOR HETEROGENEOUS NETWORKS 1459

6.4 Heuristic Algorithm Results

The formulated model is solvable with CPLEX 12.5, whichis a software package dedicated to finding the optimal solu-tion to a MILP problem. The optimal results obtained byCPLEX are taken as the benchmarks to evaluate the pro-posed heuristic counterparts; the comparisons are measuredon a machine equipped with eight cores. The performanceof the devised heuristic approach is shown in Fig. 3. It isindicated that the proposed heuristic algorithm can providesolutions which are very close to the optimum. The pro-posed algorithm demonstrates computation efficiency asshown in Fig. 7. The solving times of the bisection methodare also compared for " ¼ 0.1 and 0.01, which are the tolera-ble difference value between the feasible solution with opti-mality. The computation time of the proposed algorithmincreases relatively slightly with the problem size, whereasthe computation time shows an exponential growth. In thecase of 2,800 users, finding the optimal solution spendsmore than 630 times as the computation time with the heu-ristics, and bisection methods takes more than 170 timeswhen " is 10 percent.

More scenarios are considered to assess the overall effec-tiveness of the designed algorithm. In Table 5 the problemsize grows as numbers of BSs and users increase. The BSnumber is the summation of macro and femto BS numbers;the computation times of finding the optimal and near-opti-mal solutions are listed, where solution difference is the

difference between the spectrum-energy efficiency values inpercentage. The difference made is subtle by the heuristicalgorithm. In contrast, the proposed heuristic approachsaves 99 percent of computation times. In addition, weexam the HetNets with a constant number of 18 macroand 30 femto BSs with � ¼ 36 and 24. The user numberresiding in the networks varies from 2,600 to 4,100 withdifferent user distributions. From Table. 6, the devisedheuristics is able to produce spectrum-energy efficiencywhose mean difference from optimality is less than 2 per-cent. This illustrates that the heuristic algorithm can findeffective solutions for the considered network topologiesand BS system types. We find that the solutions from ourproposed algorithm are fairly close to the optimum for allthe considered cases. As the problem size goes up withlarger numbers of BSs and users, the computation timerises significantly for obtaining optimal solutions; theheuristic method solves problems more efficiently. Thecomputational efficiency demonstrates scalability of theheuristics in large-scale networks.

7 CONCLUSION

Frommobile service providers’ perspectives, saving energy isable to reduce operating expense, and improving spectrumefficiency can increase revenue. To achieve an increase inprofitability, it is desired that wireless access networks followa spectral and energy efficient design. In this paper, we con-duct a study on the issue of spectrum-energy efficiency maxi-mization in LTE-A HetNets, aiming at gaining energy savingand spectrum efficiency improvements. The problem is for-mulated into the optimization framework that considers theuser association, BS operation determination and resources(RBs and energy) allocation. For computational comparison,the bisection approach is adapted to solve the quasiconvexproblem, and CPLEX is performed to approach the trans-formed MILP problem. The heuristic algorithm is developedto suggest a computationally tractable solution to the optimi-zation problem. It is shown in the simulation results that spec-trum-energy efficiency is able to be improved significantlyfrom the homogeneous and heterogenous networks in thepresented scenarios; also, the optimization problem can besolved efficiently by the proposed algorithm. The establishedframework lays economic foundation for advanced green

Fig. 7. The solving time comparison.

TABLE 5Average Solution Difference and Computation Time

Number ofNodes Solution

Difference

Solving Time (Second)

BS User CPLEX Heuristics

40 3,000 0.0013% 194.98 0.82

40 3,500 0.0015% 251.34 1.02

48 4,000 0.0015% 437.38 1.26

48 4,500 0.0016% 585.58 1.41

53 5,000 0.0018% 713.48 1.73

53 5,500 0.0021% 841.26 1.92

60 6,000 0.0020% 1230.91 2.35

60 6,500 0.0020% 1429.50 2.57

65 7,000 0.0022% 1679.79 3.03

65 7,500 0.0023% 1930.13 3.35

TABLE 6Gap for Different Topology Types and BS Parameters

1460 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 16, NO. 5, MAY 2017

wireless networks, providing a guideline for operators inefforts of efficiency and profitability improvements.

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Chan-Ching Hsu received the MS degree incomputer engineering from Iowa State University.He is working toward the PhD degree in theDepartment of Electrical and Computer Engineer-ing, Iowa State University. His research interestsinclude multicell processing, green radio, optimi-zation, cognitive and heterogeneous cellular sys-tems, and (beyond) 4G systems.

J. Morris Chang received the PhD degree incomputer engineering from North Carolina StateUniversity. He is an associate professor at IowaState University. He received the UniversityExcellence in Teaching Award at the Illinois Insti-tute of Technology in 1999. His research interestsinclude wireless networks and computer sys-tems. Currently, he is an editor of the Journal ofMicroprocessors and Microsystems, and of theIEEE IT Professional. He is a senior member ofthe IEEE.

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HSU AND CHANG: SPECTRUM-ENERGY EFFICIENCY OPTIMIZATION FOR DOWNLINK LTE-A FOR HETEROGENEOUS NETWORKS 1461