38 IEEE COMMUNICATIONS LETTERS, VOL. 18, NO. 1, JANUARY 2014

Traffic-Aware Energy Optimization in Green LTE Cellular SystemsNavrati Saxena, Bharat J. R. Sahu, and Young Shin Han

AbstractCommercial deployment of 4G LTE networks andrapid penetration of smart phones have exponentially increasedthe wireless data traffic, thus increasing the energy consumptionand greenhouse (CO2) gas emission. The concept of green 4GLTE networks lies in the development of energy efficient LTEsystems for reducing the greenhouse emissions as well as opera-tors energy bill. In this letter we first identify the complexity ofthe optimal traffic awareness in LTE networks and subsequentlydesign a cooperative communication framework for traffic-awareenergy optimization. The LTE eNBs explore an informationtheoretic approach to capture the dynamics and uncertainty ofnetwork traffic. Subsequently, using an online, stochastic gametheoretic algorithm, the eNBs communicate amongst themselvesto optimize the traffic awareness. Optimal traffic awareness helpsin reducing the network energy consumption. Simulation resultsdemonstrate that our framework results in almost 22% (40 KW-Hr) daily energy savings across a LTE network of 400 cells.

Index TermsGreen wireless, NP hard, game theory, entropy.

I. INTRODUCTION

THE ever increasing demand of wireless data traffic andthe requirement for ubiquitous access has triggered a dra-matic expansion of cellular infrastructures and rapid increasein energy demands, thus resulting in increasing greenhouse(CO2) gas emissions. Green cellular networks are graduallyemerging to improve the networks energy efficiency and en-vironmental sustainability. Moreover, green cellular networksare also the key to reduce the operating expenditure (opex) ofmobile operators, as the cellular radio access is responsiblefor majority ( 70%) of their energy bill. Efficient design androll out of green cellular networks faces numerous challengesin control, communications and energy optimizations. Recentsurvey [8] of research activities in green cellular networkspoints out that major mobile operators have already initi-ated several experimental projects, like OPERANet (FranceTel.), Green Radio (Vodafone/British Tel.), ERATH (Tel.-Italia/DoCoMo), Green Touch (Telefonica/China Mob.), [8]etc. Similarly, green energy models [7], resource manage-ment [4], BS switching-on/off [13], cell zooming [11], andtraffic awareness [12] are some of the major research initiativesto mention.

In this letter we first identify the complexity of the optimaltraffic awareness in 4G LTE cellular networks. Next, byexploring the information theory, we introduce a new strategy

Manuscript received August 9, 2013. The associate editor coordinating thereview of this letter and approving it for publication was G. Lazarou.

N. Saxena is with the Electrical and Computer Engineering Department,Sungkyunkwan University, Korea (e-mail: navrati@skku.edu).

B. J. R. Sahu is with LNMIIT, India.Y. S. Han is with Sungkyul University, Korea.The work is supported by the Faculty Research Fund, Sungkyunkwan

University, 2012, S-2012-1393-000.Digital Object Identifier 10.1109/LCOMM.2013.111213.131809

X2 InterfaceSwitched on Green eNBs

Switched off Green eNB

Fig. 1. Green LTE eNBs.

for capturing the traffic uncertainty in LTE systems. Subse-quently, we propose a new online, stochastic game theoreticalgorithm to optimize the traffic awareness. Optimal trafficawareness leads to the optimal switching-off/on of LTE eNBs,thereby resulting in minimum energy consumption. Simulationresults on a typical LTE network points out that the proposedapproach can improve the daily average energy efficiency ofthe eNB by 30% while achieving 22% (40 KWatt-Houror 144 MJ) of daily energy savings with negligible overhead.

The remainder of this letter is organized as follows: Sec-tion II discusses the complexity of optimal traffic awareness inLTE systems and introduces a new information theoretic ap-proach for traffic profiling. Section III delineates our proposedgame-theoretic algorithm for near-optimal traffic estimationand analyzes its bounds. Section IV explores traffic awareeNB switching-on/off for minimum energy consumption. Sim-ulation results in Section V demonstrates the efficiency of ourapproach. Finally, we discuss the conclusions in Section VI.

II. OPTIMAL TRAFFIC AWARENESS IN LTE NETWORKSFigure 1 shows an example LTE network with the eNBs

inter-connected by X2 interface. As most cellular networksexperience some periodic busy (or peak) and non-busy (off-peak) hours of traffic, an optimal traffic awareness is the keyfor sustainable, energy efficient (green) network operations. Inthis Section we first discuss the complexity of optimal trafficawareness in green LTE networks and propose a frameworkfor its modeling and processing.

A. Complexity of Optimal Traffic Awareness ProblemFor achieving network traffic awareness, LTE eNBs need

to make intelligent and proactive estimation (or prediction)of traffic it is going to experience in near future. Thus, theoptimal traffic awareness problem is defined as follows: Fora group of proactive traffic estimations (or predictions) by eNBs spread across R regions, the objective is to maximizethe number of successful traffic estimations or predictions

1089-7798/13$31.00 c 2013 IEEE

SAXENA et al.: TRAFFIC-AWARE ENERGY OPTIMIZATION IN GREEN LTE CELLULAR SYSTEMS 39

(i.e. when predicted traffic profile matches with the actualtraffic). The problem turns out to be NP-hard. We prove itby reducing the problem into Set-Packing problem a popularNP-hard [6] problem. The input to the Set Packing problemis a set S = {S1, S2, . . . , S} of subsets of the universalset U = {1, 2, . . . , }. Given the condition that each elementfrom the universal set U can be covered by at most one subsetfrom S, the objective of Set Packing Problem is to maximizethe number of mutually disjoint subsets from S. The maxi-mum successful traffic prediction process in a LTE networkinvolving a total traffic profiles and traffic predictions,is equivalent to the Set Packing problem with subsets anda universal set U of elements. The prediction process, forevery eNB i, is a collection of its possible traffic profiles,{i}. Every such prediction is mapped to a particular subsetSi. Each single traffic profile, i, is mapped to an elementof a subset Si. The strategy that maximizes the number ofsuccessful predictions is basically the one that maximizes thenumber of disjoint subsets from S, which completes our proof.

B. Traffic Awareness - An Information Theoretic FrameworkThe dynamics of user application traffic and wireless chan-

nel conditions inherently creates an uncertainty of wirelesstraffic in cellular networks. From information theoretic per-spective, Shannons entropy [5] is a fair measure to quantifythis uncertainty. Naturally, we can argue that it is impossi-ble for any cellular network to make a correct estimationof wireless traffic by exchanging any less information, onthe average, than this uncertainty. Our proposed frameworkfirst samples the continuous network traffic, experienced atindividual eNBs, into discrete traffic profiles of identicalrange. In order to prevent any loss of traffic information,we maintain the sampling rate sufficiently higher than thesampling theorem [5]. We can now represent the discretetraffic information by a sequence of symbols 1, 2, . . . ,n, where every symbol actually represents a sampled trafficprofile. As busy and non-busy hour network traffic exhibitssome stochastic patterns, we argue that the LTE networkscan learn the traffic profiles over time in an on-line fashion.Characterizing the traffic pattern as a probabilistic sequence,we can define it as a stochastic process T = {Ti}, with jointentropy H(T1, T2, . . . , Tk) expressed as:

H(T1, T2, . . . , Tk) =k

i=1

H(Ti|T1, T2, . . . , Ti1)

H(T ) = Pr() log2[Pr()], (if Pr() = 0)= 0, (if Pr() = 0), (1)

where Pr() represents the probability associated with thetraffic profile . The cellular networks need to minimize thisentropy for optimal traffic awareness. Note that, consideringevery individual eNB independently fails to consider thecorrelation between the traffic patterns across multiple eNBs.Intuitively, independent traffic awareness for each individualeNB actually increases the overall joint traffic uncertainty.We can prove it from the fact that conditioning reduces

entropy [5]; i.e. for any stochastic process T = Ti,H(T ) = H(T1, T2, . . . , Tn)

=

ni=1

H(Ti|Ti1, . . . , T1) n

i=1

H(Ti) (2)

In the next section we discuss our near-optimal, stochasticgame-theoretic algorithm to optimize the traffic entropy H(T ).

III. GAME THEORETIC NEAR-OPTIMAL TRAFFICAWARENESS

As every eNB wants to optimally predict its own traffic, theobjective of the entire LTE networks is to achieve a suitablebalance among the set of all eNBs. This motivates us to solvethe problem by using stochastic game theory, with eNBs asthe players and the traffic predictions as their strategies.

A. Nash Traffic Entropy Estimation AlgorithmWe assume that the LTE eNBs are fully rational in the

sense that they can fully use their current traffic profiles toconstruct future traffic estimations. Each eNB i keeps a countCjaj representing the number of times an eNB j has madea traffic prediction (strategy) aj Aj in the past. When thegame is encountered, eNB i believes the relative frequencies ofeach of js traffic prediction as indicative of js current trafficestimate. So for each eNB j, the eNB i believes that eNB jpredicts traffic (plays action) aj Aj with the probability:

Pr(aj)i =Cjaj

bjAj Cjbj

(3)

All the eNBs exchange their traffic estimation informationusing the X2 interface and updates its possible information.The decision making component of the eNBs learns andacquires a strategy that minimizes the overall uncertainty oftraffic profiles. Our proposed algorithm, named Nash Traffic-Entropy-Learning (NTEL), combines new experience with theold to produce statistically improved future traffic estimations.The reward r takes into account the success rate of trafficprediction. In the initial state, we assume the traffic probabilityto be zero, i.e. Pr() = 0, which corresponds to the entropyvalue zero, i.e. Hi0 = 0. At each time t, every eNB makesits traffic estimation. After that, it observes its own reward,estimations made by other eNBs and their rewards. It thenestimates its own Nash Equilibrium strategies (estimations)1, 2, . . . , n at that stage and updates its own entropy as:

Hjt+1 = (1 t)Hjt + trit + n

j

jtHjt

, (4)

where (t, t) [0, 1]. Eventually, the framework gets cog-nizant to proactively estimate traffic with high accuracy.

B. Convergence ProofThe convergence proof of NTEL is based on two assump-

tions: (1) Every states and decisions are visited infinitely often(2) The learning rate t [0, 1]. Our proof relies on theresult shown in [9], which states that if there exists a pseudo-contraction operator t, utility function U , (0, 1) and a

40 IEEE COMMUNICATIONS LETTERS, VOL. 18, NO. 1, JANUARY 2014

sequence t 0, which converges to zero with probability1, such that |tU tU| |U U| + t, where U isthe utility in Nash Equilibrium, then the following conditionholds: Pr[(Ut+1 = (1t)Ut+t[tUt]) U] = 1. Now,replacing the utility function U by entropy Ht, we get:

Pr [(Ht+1 = (1 t)Ht + t[tHt]) H] = 1,where tHk = rk + 1 . . . nHk, k [1, n] (5)

We can now conclude that our NTEL algorithm almost surelyconverges to Nash-Equilibrium, i.e. Pr[Ht+1 H] 1.

C. Worst-Case Analysis

We use the basic assumption that every eNB attempts tobenefit from the underlying strategy. The resulting perfor-mance degradation provides the basis for worst-case anal-ysis or coordination ratio, i.e. the ratio of worst possibleNash-Equilibrium and the near-optimal. The worst-case co-ordination ratio of eNBs taking decisions is given by(

log2 log2 log2

). The proof follows from the fact that the problem

is identical to throwing of balls in bins and attempting tofind expected maximum number of balls in a bin [14]. Next,we prove that the coordination ratio of eNBs with decisionsis upper-bounded by the following equation:

T = 3 +4 log2 . (6)

Any eNB i maintains beliefs about the decision of other eNBsand estimate the Expected Entropy (E[H ]) at time (t + 1)as: E[Ht+1] =

aiAH

it+1

j =i Pr(a

i)j . We term it asthe Nash equilibria cost Ncost. The coordination ratio is theworst case ratio: W = max{Ncost/Hopt}, where Hopt isthe optimal entropy. As computing the optimal is an NP-hardproblem, for the purpose of upper bound of W , it suffices touse simple approximations: Hopt max{Hit+1, E[Ht+1]/n}.Now, using Azuma-Hoeffmans inequality [9], we will showthat the entropy of a given traffic estimation j exceeds(T1)Hopt with probability at most 12 . Then, the probabilitythat the maximum entropy on all estimations does not exceed(T 1)Hopt is at least 1 . It follows that the expected maxi-mum entropy is bounded by (1 1 )(T1)Hopt+ 1 (Hopt) THopt. It remains to show the probability that the entropy ofa given traffic estimation j exceeds (T 1)Hopt is indeedsmall, at most 12 . Let Xi be a random variable denoting thecontribution of eNB i towards the entropy of decision j. Inparticular, Pr[Xi = H1] = P and Pr[Xi = 0] = 1P . Now,considering the martingale Mt = X1+ . . .+Xt+E[Xt+1]+. . .+E[Xn]. Note that |Mt+1Mt| = |Xt+1E[Xt+1]| Ht+1. We can then apply the Azuma-Hoeffmans inequal-ity [9]: P [Sn E[Sn] x] exp

( 12x2/

i H

it+1

2)

. Forx = (T 3)Hopt, E[Sn] =

E[Xi] 2Hopt, and we

get the entropy of j exceeding (T 1)Hopt with probabilityat most exp

( 12x2/

i H

it+1

2)

. It is easy to establish thattH

it+1

2 max{H21 ,

i(Hit+1/)

2} H2opt. Thus,the probability that entropy of j exceeds (T 1)Hopt is atmost exp

( 12 (T 3)2/). For T = 3 + 4 log2 , thisprobability becomes 1/2 and the proof is complete.

IV. TRAFFIC-AWARE ENB SWITCH ON/OFFOptimal predictive traffic-awareness helps in designing an

optimal strategy for eNB switch on/off. The strategy needs toconsider the QoS (delay and loss) constraints, cell coverageand network stability. When an eNB is switched off theneighboring eNBs need to take care of mobile users and thetraffic associated with the switched off eNB. We increase thepower of neighboring eNBs and explore CoMP to provide thecoverage and prevent any possible outage. For a single eNBserving users, the total energy consumption is:

Etot = Econst ton +

i=1

(Ei ti) + Eidle tidle, (7)

Ei = Emax min{

1

RBi,max

[Rmin,

(Lx,iL

)]},

where Econst and ton are constant power consumption andpower-on duration of eNBs, Ei and ti are the transmissionpower and transmission duration for UE i; Eidle and tidleare the idle-mode power consumption and idle-mode duration,Emax is the maximum transmission power, RB is the numberof subcarriers assigned to the UE, Rmin is the minimumpower reduction rate to prevent UEs with good channels totransmit at very low power level, Lx,i is the percentile pathloss(with shadowing) for the UE i, L is the overall pathloss and [0, 1] is the balancing factor for UEs with bad and goodchannels. Self Organizing Networks (SON) server triggers andexecutes the eNB switch on/off algorithm in following manner:

1) Using NTEL algorithm, mentioned in section III-A, eacheNB estimates its own traffic as well as its neighboringeNBs traffic through the X2 interface.

2) The algorithm now sorts and selects the eNBs in theincreasing order of the estimated traffic load.

3) The selected eNB is switched off, if the transfer of theselected eNBs traffic to the neighboring eNBs does notresult in the violation of 3GPP QoS (delay and loss)standards [2], and the neighboring eNBs can manageto increase their transmission power E and exploreCoMP to provide radio coverage to the parts coveredby the selected eNB.

4) The algorithm continues with the next eNB, until themaximum number of eNBs are switched off or all eNBsare checked.

Eventually, the algorithm provides near-optimal traffic-awareenergy conservation, while preserving the QoS constraints.

V. SIMULATION RESULTSFor performance evaluation of NTEL, we have simulated

a typical urban scenario, consisting of 400 cells, with a cellradius of 800 meters and 600 active mobile users per cell. Wehave used the RF parameters according to 3GPP evaluationcriteria [1], which mentions an eNB transmission and idlepower of 43 dBm and 0.19 dBm respectively, penetrationloss of 20 dB, = 0.8, and UEs maximum power of 24dBm. For the different traffic models, traffic parameters andtraffic-mix, we have used the popular 3GPP NGMN evaluationcriteria [10]. We have considered the specific QoS (delayand loss) constraints mentioned in 3GPP standards [2]. We

SAXENA et al.: TRAFFIC-AWARE ENERGY OPTIMIZATION IN GREEN LTE CELLULAR SYSTEMS 41

0 20 40 601.4

1.5

1.6

1.7

1.8

1.9

2

x 105

DaysTotal Energy Consumed (in WattHour)

(A)

Existing LTE SystemsProposed LTE Systems

0 5 10 15 20 251

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

Hour of the Day

Energy Efficiency (in bits/Joule)

(B)

Existing LTE SystemsProposed LTE Systems

10 11 12 13 14 15 16 17 18 19 200

2

4

6

8

10

12

14

16

18

20

RF Power (in Watts)

Percentage of Energy Savings

(C)

Fig. 2. (a) Energy consumption dynamics for two months; (b) daily energy efficiency dynamics in bits/Joule; (c) sensitivity with RF power dynamics.

TABLE IOVERHEAD ANALYSIS

Computational Traffic Energy Energy Overhead /Overhead Overhead Overhead Savings Savings8.2 106 3.3 1010 bits 211 KJ 144 MJ 0.15%

perform the simulation experiments for 60 days and reportthe average values with 98% confidence interval. Figure 2(A)demonstrates daily total power consumption dynamics acrossthe entire network (all 400 eNBs). It points out that theinherent near-optimal traffic awareness enables our strategy toachieve a 22% (40 KWatt-Hr or 144 MJ) lower total powerconsumption in comparison to existing LTE cellular systems.In order to capture the effects of both traffic and energy dy-namics, we have used the energy efficiency metric, measuredas traffic transmitted by unit energy. Figure 2(B) depicts thatour proposed scheme offers 30% improvement in energyefficiency over existing LTE systems. Figure 2(C) shows thesensitivity of energy savings offered by our proposed strategywith changes in eNBs transmission (RF) power. It clearlypoints out that for different RF power in the range of 20 Wattsto 10 Watts (i.e. 43 - 40 dBm), NTEL consistently provides 19%-20% of daily energy savings. Finally, we analyzethe daily average numerical and traffic overhead (over X2interface) in Table I. It demonstrates that NTEL daily incurs 8.2 106 numerical operations and 3.3 1010 bits ofextra traffic across entire 400 eNBs. Following the benchmarksin [3], we point out in Table I, that total daily energy overheadin NTEL is merely 211 KJ, which is negligible ( 0.15%)comparing to 144 MJ energy savings offered.

VI. CONCLUSIONIn this letter we have proposed a new cooperative frame-

work for traffic aware energy consumption in green LTEnetworks. We introduce a new information theoretic strategy

for capturing the traffic uncertainty. Subsequently, we proposea new stochastic game theoretic algorithm to optimize thetraffic traffic awareness. Optimal traffic awareness helps inreducing the energy consumption by selectively switching-on/off the green LTE eNBs. Simulation results on a denseLTE network with 400cells demonstrate that the strategy canimprove the daily average energy efficiency by 30% with 22% (40 KWatt-Hour) daily energy savings and negligibleoverhead.

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