Research Article Playing Radio Resource Management Games ...downloads.hindawi.com/journals/misy/2016/3798523.pdf · consumption has been considered in various scenarios, including

Research ArticlePlaying Radio Resource Management Games inDense Wireless 5G Networks

PaweB Sroka and Adrian Kliks

The Chair of Wireless Communications Poznan University of Technology Poznan Poland

Correspondence should be addressed to Paweł Sroka pawelsrokaputpoznanpl

Received 1 August 2016 Revised 3 October 2016 Accepted 1 November 2016

Academic Editor Ioannis Moscholios

Copyright copy 2016 P Sroka and A KliksThis is an open access article distributed under theCreative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper considers the problem of an efficient and flexible tool for interference mitigation in ultradense heterogeneous cellular5G networks Several game-theory based approaches are studied focusing on noncooperative games where each base stationin the end tries to maximize its payoff An analysis of backhaul requirements of investigated approaches is carried out with aproposal of a mechanism for backhaul requirements reduction Moreover improvements in terms of energy use optimization areproposed to further increase the system gains The presented simulation results of a detailed ultradense 5G wireless system showthat the discussed game-theoretic approaches are very promising solutions for interferencemitigation outperforming the algorithmproposed for LTE-Advanced in terms of the achieved spectral efficiency Finally it is proved that the introduction of energy-efficientand backhaul-optimized operation does not significantly degrade the performance achieved with the considered approaches

1 Introduction

As increase in signal coverage throughput guarantees ofefficient service delivery and finally highly effective spectrumutilization were said to be the main goals of the secondthird and fourth generations of cellular systems [1 2] it isthe integration of various networks with energy efficiencythat is foreseen as the key factor for further developmentof wireless networks Higher internetwork integration resultsin higher steeringcontrol data exchange which influencestraffic growth in backhaul and core networks At the sametime the topic of energy efficiency in futurewireless networksbecame a significant research area in recent years It is ofhigh interest for mobile network operators (MNOs) sinceby the application of sophisticated solutions overall energyconsumption can be improved leading to a further reductionof operational expenditures [2ndash5]

11 Related Work In general the minimization of energyconsumption has been considered in various scenariosincluding cellular networks (eg where optimization amongall access network [6 7] backhauling and core networks[8 9] can be considered) other noncellular wireless networks(ie noncellular networks [10ndash12]) and wired networks

(including optical networks [13ndash15]) Various solutions havebeen proposed targeting different aspects of communica-tions and networking such as advanced radio resource andinterferencemanagement enabling throughput enhancementor transmit power reduction (eg [16ndash18]) turning selectednetwork nodes into sleep mode (eg base stations opticalmodules [19ndash21]) depending on the traffic requirements orenergy-efficient routing (eg [22 23]) One can observe thatthe holistic view of all network elements is necessary in orderto assess real gains that can be achieved by the applicationof selected energy-aware solutions Indeed it is probable thatall benefits observed in one place as a result of the applicationof a selected algorithm can be lost by the increase of energyconsumption in another place In other words it is importantto analyze as wide spectrum of aspects as possible during thedevelopment of any new energy-efficient solution

12 Scope and Novelty In this work we concentrate on theapplication of advanced radio resource and interferencemanagement algorithms for dense urban wireless networks(access network) which maximize the total cell throughputand optimize the energy usage by the base stations Thedetailed and accurate simulation scenario proposed in theEU METIS2020 project for such an environment has been

Hindawi Publishing CorporationMobile Information SystemsVolume 2016 Article ID 3798523 17 pageshttpdxdoiorg10115520163798523

2 Mobile Information Systems

120m12

0m

12m12

m

21m6 floors of 35m each

210 UEs

Figure 1 Considered scenario Manhattan-like dense urban network

selected as the enabler for making simulations close to reality[24] The algorithms for interference coordination proposedfor 4G networks (known as enhanced intercell interferencecoordination (eICIC) [25ndash27]) have been compared with oursolutions based on the application of game-theoretic toolsLet us note that the game theory has already been consideredmany times as a valuable tool in the context of cellularnetworks In our work we tried to analyze the effectiveness ofthe proposed game-theoretic tools from the point of view oftheir practical implementationThus we not only discuss theconvergence time (which results in a delay in the system) butalso analyze how the traffic observed in the backhaul and corenetworks will be affected by the application of our algorithmsThe novel aspects covered by this paper are the following

(a) Provision of new solutions for radio resource andinterference management in dense urban 5G net-works that maximize cell throughput with the min-imization of overall energy consumption taking intoaccount the traffic increase in the backhaul network

(b) Summary and definitions of various game-theoretictools that can be used for achieving this goal andtheir comparison with the eICIC technique (pleasenote that scenarios with and without network nodecoordination have been considered)

(c) Analysis of the influence of applying the proposedtool on backhaul traffic and the potential increase ofthe energy consumed in that part of the network

Let us stress that the main aim of this paper is to comparedifferent slow-time-scale interference management mecha-nisms that can be considered as candidates for future 5Gnetworks assuming an identical simulation setup Howeverwe do not intend to use identical game and auctionmodels forevery case as different definitions can be assumed dependingon the game type and optimization criteria

The paper is organized as follows First the systemmodelconsidered for experimentation is discussed in Section 2Once it is presented the proposal for energy-efficient gamingin such a scenario is provided Then Section 3 presentsdetailed game definitions together with suggested ways ofachieving the equilibrium expected for each game Theanalysis of backhaul traffic being often a heavy burden of newsophisticated algorithms such as the coordinated multipoint(CoMP) is provided in Section 4 while the achieved com-puter simulation results are shown anddescribed in Section 5Finally the paper is concluded

2 System Model of a Dense Network

In order to analyze the efficiency of the proposed algo-rithms in reducing energy consumption in the context ofnext-generation networks a dense urban scenario has beenselected for consideration where multiple outdoor userterminals communicate with macro or micro base stationsdeployed on buildings and managed by MNO

21 Detailed Model Characterization In this work the use-case developed in the METIS 2020 project [24] has beenconsidered where a Manhattan-like dense urban wirelessnetwork ismodeled It is assumed thatmobile users utilize theorthogonal frequency division multiple access (OFDMA)technology with the frequency reuse factor equal to 1 tocommunicate with one of the sectoral antennas deployedby MNO on surrounding buildings as shown in Figure 1One can observe that 119873 = 21 antennas are installed in theconsidered area with three main 120∘ sectoral macro anten-nas mounted on the central-building and 9 pairs of 120∘sectoral micro antennas deployed close to the neighboringbuildings As the macro base stations are mounted onrooftops (5-meter highmasts have been used) themicro base

Mobile Information Systems 3

stationsrsquo antennas are located at the heights of 10m and 3mseparated from the building wall Each building contains sixfloors (35m high each) and has a square base of the size of120m times 120m The streetsrsquo width including both sidewalksand lanes is set to 12m The number of full-buffer staticand uniformly distributed user equipment (UE) pieces in theconsidered area was set to 119869 = 520 It means that the averagenumber of users served by one base station is equal to = 52021 = 248

The bandwidth available for each of the base stations(BSs) is divided into time-frequency blocks with the BSstransmitting in each of the blocks using one of the selectedpower per subcarrier levels These levels are selected out ofthe set 119875 = 119901low 119901high as shown in Figure 2

Let us now describe the scenario using mathematicalformalism The set of all users is represented hereafter as 119869with 119869119894 denoting the set of users served by BS 119894 At each timeinterval each BS divides the available resources among upto 10 UE pieces according to the proportional fairness (PF)rule Let |ℎ(119904)119894119895 |2 denote the channel gain between the 119894th BSand 119895th UE on subcarrier 119904 (ℎ(119904)119894119895 isin C) and let 1205902119895 be thenoise variance at receiver 119895 (we assume that each mobile userpossesses the knowledge on channel attenuation based on theobserved pilot signals from all base stations this informationcan be then delivered to the serving base station)The signal-to-interference plus noise ratio (SINR) for UE 119895 served by BS119894 on subcarrier 119904 is given as follows

120574(119904)119894119895 =10038161003816100381610038161003816ℎ(119904)119894119895

100381610038161003816100381610038162 119901(119904)119894

1205902119895 + sum119897isin119872cup119870119894100381610038161003816100381610038161003816ℎ(119904)119897119895

1003816100381610038161003816100381610038162 119901(119904)119897

(1)

where 119901(119904)119894 denotes the transmit power of BS 119894 on subcarrier 119904and 119872 cup 119870 represents the set of base stations (players)

In our work we assume that all BSs are interested inachieving at least the minimum throughput 119879min and mini-mizing the operating costs expressed by the total consumedenergy The throughput achieved by the 119895th UE served by BS119894 can be then calculated as

119879119894119895 = sum119905

sum119904

119877119904119894119895 (119905) sdot 120577119904119894119895 (119905) (2)

Here 120577119904119894119895(119905) represents the allocation of subcarrier 119904 at time 119905 toUE 119895 by BS 119894 with 120577119904119894119895(119905) isin 0 1 and the rate of UE 119895 servedby BS 119894 on subcarrier 119904 119877119904119894119895 is calculated depending on thetransmitted transport block size determined as specified inthe 3GPP Long Term Evolution (LTE) specification [28]

22 Backhaul Connection All BSs can exchange controland signaling information using a dedicated interface Forfurther backhaul traffic analysis (see Section 4) it is arbitrarilyassumed that each micro base station is fiber-connecteddirectly to the macro base station as illustrated in Figure 3 Itis for example the fiber-to-the-antenna together with radio-over-fiber technology that can act as the technical enablerfor the realization of such a backhaul network Please notehowever that other realizations of backhaul connections

are possible (wired but nonfiber wireless etc) but such adetailed analysis is out of the scope of this paper Let usnote that backhaul load optimization is not directly includedin any of the compared interference management solutionswith backhauling considered only as a contribution to overallenergy consumption

23 Energy-Efficient Gaming in Dense Networks Spectrumand energy efficiency are the key figures of merit in thecontext of next-generation networks especially in the caseof dense user (UE) deployment Referring to the formerrequirement in the considered scenario all base stationsshare the same frequency spectrum that is a full frequencyreuse case is implemented together with advanced interfer-ence management solutions among base stations and servedusers In the context of contemporary cellular networks suchtechniques as intercell interference coordination (ICIC) inLTE or eICIC with almost-blank subframes (ABS) in LongTerm Evolution-Advanced (LTE-A) have been proposed [25ndash27] We would like to concentrate on a solution that willachieve at least the same efficiency level as the nowadayssolutions Thus among various proposals for such radioresource management (RRM) we select game-theoretic toolswhere each wireless network entity is treated as a player in aspecified game These tools have already been proved to beeffective in RRM in various scenarios for example [29ndash34]

In this work we have decided to utilize game-theoretictools in a practical scenario but focusing on achieving bothspectrum and energy efficiency In particular the followingassumptions have beenmade first the game is played amongbase stations (mobile users do not participate actively inthat game) in a noncooperative way second the same setof game strategies is defined for each player third the gameand playersrsquo payoffs are defined in a way that promotesenergy efficiency while achieving throughputrate better thanor at least comparable to eICIC solutions Following theapproach known from LTE-A RRM algorithms we assumethat energy efficiency can be achieved by the adaptive assign-ment of power levels and radio resource blocks among usersdepending on their position and effective signal-to-noiseratio Taking into account the assumptions 16 transmissionstrategies have been identified They define the transmitpower levels on certain frequency subbands that might beselected by BSs as illustrated in Figure 4

First the selection of the given strategy will be madefor the period of time of one frame which consists of 10subframes (also known as transmission time interval (TTI))of 1ms each thus the potential change of the power allocationscheme in the time-frequency planewill bemade every 10msIn our proposal the considered frequency band of 119873RB =100 resource blocks (RBs) (equivalent to 20MHz) is furtherdivided into three subbands of 33 33 and 34RBs respectivelyIn other words the bandwidth of these subbands equals 33 sdot200 kHz = 66MHz and 34 sdot 200 kHz = 68MHz Each player(macro ormicro base station) can transmit with either base orreduced transmit power denoted as 119875TX119887 and 119875TX119903 Sixteenpower allocation schemes among 10 TTIs have been selectedas represented in Figure 4 It has been arbitrarily assumedthat the value of the reduced transmit power is 10 dBm lower


Time

Base station 1

Base station 2

Base station 3

Frequency

Figure 2 Resource allocation among three base stations

than the base transmit power in the entire 10MHz widthfrequency band Furthermore it has been decided that thetotal transmit power for a macro base station is set to 46 dBm(or equivalently 26 dBm per one RB) and for a micro basestation 33 dBm (or equivalently 13 dBm per one RB)

One can observe that in such an approach the energyefficiency will be achieved by the advanced assignment ofselected strategies among playing base stations However asit will be discussed later the application of such an approachresults in a high need of distributing detailed and accurate


3

2

2

Figure 3 Exemplary backhaul connection

100

RBs=

20

MH

z

Freq

uenc

y33

RBs

33

RBs

34

RBs

Time

Strategies

10 TTIs = 1 frame = 10 subframes = 10ms

0 1 2 3 4 5 6 7

8 9 10 11 12 13 14 15

Base PTXReduced PTX

Figure 4 Class of strategies considered in game definitions


context-information between network nodes (players) Forexample the exchange of the exact values of signal-to-noiseratios between the base station and each user could benecessary In our work we will also discuss this practicalaspect of our solution that is a backhaul traffic analysis willbe provided as the inclusion of this part of the network iscrucial for a fair overall analysis of energy efficiency

In order to assess the energy efficiency of the proposedsolutions we express this variable arbitrarily in terms of theaverage number of bits per Hz per Joule per cell The secondmetric used for the assessment of the algorithm quality is thetotal power consumed in a given period of time

3 Energy Efficiency Game Definition

31 Game Definition The problem of intercell interferencemitigation can be described using the following normal-formgame definition

G = (119872 cup 119870 119860 119880119894119894isin119872cup119870) (3)

Let us assume that at each time instant 119905 BS 119894 selects its actionfrom a finite set 119860 following the probability distribution

120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (4)

where 120587(120572(119899)119894 )119894 (119905) denotes the probability that BS 119894 plays action120572(119899) As a result of playing one of the strategies the 119894th basestation will receive a payoff denoted hereafter as 119880119894(120572(119896)119894 )Such a payoff can be defined as for example total throughputobserved by the base station reduced by the costs thatthis base station has to pay for playing this strategy (egenergy consumption) Thus in general the aim of each BSis to maximize its payoff with or without cooperation withother BSs achieving the so-called game equilibrium In whatfollows wewill extend and adapt this simplemodel accordingto the requirements referred to the selected equilibrium

32 Selected Equilibria

321 Nash Equilibrium One of the most popular conceptsis the one known as the Nash equilibrium When the basestation plays the Nash equilibrium strategy denoted as 120572lowast119894[35 36] the following relation will hold

119880119894 (120572lowast119894 120572minus119894) ge 119880119894 (120572119894 120572minus119894) forall119894 isin 119878 (5)

where 120572119894 represents the possible strategy of the 119894th BSwhereas 120572minus119894 defines the set of strategies chosen by the otherBSs that is 120572minus119894 = 120572119895 119895 = 119894 and 119878 is the BSs set of cardinality119899The idea behind theNash equilibrium is to find the point ofan achievable rate region (which is related to the selection ofone of the available strategies) from which any player cannotincrease its utility (increase the total payoff)without reducingother playersrsquo payoffs

Payoff Definition The achievement of the Nash equilibriumwill be considered as an example of a noncooperative game

where base stations optimize their own periods and donot consider the overall system performance Moreover weassume that no additional information needs to be sentbetween the players In such a case the utility or better thepayoff of the BS 119894 will be defined as the rate observed by thisplayer

119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894) (6)

Boltzmann-GibbsDistributionAn immediate question ariseshow to guarantee the achievement of the Nash equilibriumOne of the well-known learning approaches effective interms of the speed of convergence is to use the logit learningalso known as Boltzmann-Gibbs learning The equilibriumachieved following the Boltzmann-Gibbs rule is a specialcase of the 120598-Nash equilibrium that can be learned in a fullydistributed manner [37] The Boltzmann-Gibbs distributioncan be described using

120573119894120598 (119880119894119905 (120572119894120572minus119894)) = 119890(1120598119894)119880119894119905(120572119894 120572minus119894)sum120572lowast119894isin119860119894

119890(1120598119894)119880119894119905(120572lowast119894 120572minus119894) (7)

where for player 119894 120573119894120598(119880119894119905(120572119894120572minus119894)) is the probability ofchoosing action 120572119894 at time 119905 119860 119894 is the set of available actionsand for 120598119894 = 120598 forall119894 the value 1120598 is interpreted as thetemperature parameter that impacts the convergence speed

Strategy Identification In our work we are comparing variousequilibria In order to ensure the clarity and readability ineach section we provide a unique identifier used further onin the text with reference to a certain scenario Hereafterthe Nash equilibrium and the scenario described in thissubsection will be referred to as NE

322 Correlated Equilibrium Let us now focus on the ideaof the correlated equilibrium where in a nutshell the jointprobability of performing selected actions by players is takeninto account [38] Contrary to the Nash equilibrium theachievement of the correlated equilibrium assumes in ourcase active information exchange among players In generalat each time instant each BS plays one of the 119873 strategies120572(119899) 1 le 119899 le 119873 Therefore assuming that set 119860 is discreteand finite at least one equilibrium exists that represents thesystem state when a player cannot improve its payoff (utility)when other players do not change their behavior Such a stateis known as the correlated equilibrium (CE) which is definedas follows

sum120572minus119894isin119860

120587 (120572lowast119894 120572minus119894) (119880119894 (120572lowast119894 120572minus119894) minus 119880119894 (1205721015840119894 120572minus119894)) ge 0

forall1205721015840119894 120572lowast119894 isin 119860 forall119894 isin 119872 cup 119870 (8)

In (8) 120587(120572lowast119894 120572minus119894) is the probability of playing strategy 120572lowast119894 inthe case when other BSs select their own strategies 120572119895 119895 =119894 Probability distribution 120587 is a joint point mass function ofthe different combinations of BSs strategies As in [29] theinequality in the correlated equilibriumdefinitionmeans thatwhen the recommendation for BS 119894 is to choose action 120572lowast119894


then choosing any other action instead of 120572lowast119894 cannot result ina higher expected payoff for this BS

Payoff Definition Let us formulate the set of actions selectedby all BSs as 120572 = 120572119894 cup 120572minus119894 where 120572minus119894 is a set of actionsselected by all BSs other than 119894 We can introduce therate-dependent Vickrey-Clarke-Groves (VCG) [30] auctionmechanism where each BS aims to maximize utility 119880119894 forall119894defined as

119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894) minus 120577119894 (120572119894120572minus119894) (9)

where 120577119894 denotes the cost (rate loss) introduced by BS 119894 to allother BSs which is evaluated as follows

120577119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894) minussum119897 =119894

119877119897 (120572119897120572) (10)

The use of the VCG auction mechanism based on rateleads to the maximization of the overall performance of thesystem by exploiting cooperation between nodes Howeverin modern wireless systems UE pieces are more interestedin fulfilling their quality of service (QoS) requirements thanin maximizing their rate Therefore as an alternative onecan consider a satisfaction-based VCG auction mechanismwith satisfaction V119894 defined as in (19) and (21) that can beformulated as


where 120595119894 denotes the satisfaction-based cost evaluated asfollows

120595119894 (120572119894120572minus119894) = sum119897 =119894

119891119897 (120572119897120572minus119894) minussum119897 =119894

119891119897 (120572119897120572) (12)

Regret-Matching Learning To achieve CE a centralizedapproach can be applied which is however very complex[30] According to [39] the procedure of regret-matchinglearning can be used to iteratively achieve CE In [29ndash31] amodified regret-matching learning algorithm is proposed tolearn in a distributive fashion how to achieve the correlatedequilibrium by solving the VCG auction which aims atminimizing the regret of selecting a certain action RegretREG(119879) of BS 119894 at time119879 for playing action120572(119899) instead of otheractions is given as follows

REG(119879)119894 (120572(119899)119894 120572(minus119899)119894 ) ≜ max 119863(119879)119894 (120572(119899)119894 120572(minus119899)119894 ) 0 (13)

where

119863(119879)119894 (120572(119899)119894 120572(minus119899)119894 )

= max119895 =119899

1119879sum119905le119879

(119880119905119894 (120572(119895)119894 120572minus119894) minus 119880119905119894 (120572(119899)119894 120572minus119894)) (14)

where 119880119905119894 (120572(sdot)119894 120572minus119894) is the utility at time 119905 119863119879119894 (120572(119899)119894 120572(minus119899)119894 ) isthe average payoff that BS 119894 would have obtained if it hadplayed another action compared with 120572(119899)119894 every time in thepastThus the positive value of119863119879119894 (120572(119899)119894 120572(minus119899)119894 )means that BS

119894 would have obtained a higher average payoff when playinga different action than 119899 Finally given the regrets for all 119873actions the probability of BS 119894 selecting strategy 119899 can beformulated as follows

120587(120572(119899)119894 )119894 (119879) = 1 minus 1120583(119879minus1)REG

(119879minus1)119894 (120572(119899)119894 120572(minus119899)119894 ) (15)

where

120583(119879minus1) = sum119899 REG(119879minus1)119894 (120572(119899)119894 120572(minus119899)119894 )119873 minus 1 (16)

Strategy Identification The correlated equilibrium achievedthrough the application of the regret-matching algorithmsdescribed above will hereafter be denoted as CEpure

323 Correlated Equilibrium with Reduced Complexity Oneof the main burdens related to the practical application ofthe correlated equilibrium concept described in the previ-ous subsection is the need for a fast exchange of detailedinformation about channel states for each mobile user or atleast payoffs observed by each base station (BS) (player) Theexchange of accurate data will result in a high traffic increaseobserved in the backhaul network as will be discussed indetail in Section 4 Thus let us now introduce the conceptof achieving equilibrium with the regret-matching algorithmwhere the complexity is reduced In this approach the utilityfunctions as well as the whole regret-matching algorithm andVCG auctions are kept unchanged except for the fact that ineach iteration only the payoff of the strategy selected by eachBS is circulated in the network among other players insteadof the whole table of payoffs

Strategy Identification In order to distinguish this solutionfrom the application of the pure correlated equilibrium wedenote this scenario as CEreduced

324 GeneralizedNash Equilibrium Satisfaction EquilibriumThe achievement of the satisfaction equilibrium [40] rep-resenting a specific case of the so-called generalized Nashequilibrium is an example of the goal of a noncooperativegame with assumed information exchange The process oflearning the satisfaction equilibrium (SE) can be describedusing the elements of the following game

G = (119872 cup 119870 119860 119891119894119894isin119872cup119870) (17)

where 119872cup119870 represents a set of players (BSs)119860denotes a setof available actions and 119891119894 is the satisfaction correspondenceof player 119894 which indicates whether player is satisfied Thecorrespondence is defined as 119891119894(120572minus119894) = 120572119894 isin 119860 119880119894(120572119894120572minus119894) geΓ119894 with 119880119894(120572119894120572minus119894) representing a playerrsquos observed utilitywhen playing action 120572119894 and Γ119894 denoting the minimum utilitylevel required by player 119894 A state of the game when all playerssatisfy their individual constraints simultaneously is referredto as the satisfaction equilibrium (SE) which is defined asfollows [40]


Action profile 120572+ is an equilibrium for the game

G = (119872 cup 119870 119860 119891119894119894isin119872cup119870)if forall119894 isin 119872 cup 119870 120572+119894 isin 119891119896 (120572+minus119894)

(18)

Satisfaction Correspondence and Payoff Definition The exis-tence of SE depends mainly on the set of constraints imposedon the utility function with the feasibility of the constraintsas a necessary condition

For the considered scenario where BSs act as gameplayers the satisfaction correspondence can be defined inrelation to the satisfaction level of all users served by the BSas shown below

119891119894 (120572119894120572minus119894) = 110038161003816100381610038161198691198941003816100381610038161003816sum119895isin119869119894

119904119894119895 (120572119894120572minus119894) (19)

where 119904119894119895(120572119894120572minus119894) is the satisfaction of UE 119895 when BS selectsaction 120572119894 Individual UE satisfaction can be defined using thebinary representation

119904119894119895 (120572119894120572minus119894) =1 if 119879119895 ge 119879min0 otherwise (20)

Alternatively one can consider a relaxed version of individualUE satisfaction using the sigmoid function

119904119894119895 (120572119894120572minus119894)

=

1 if 119879119895 ge 119879min1

1 + exp (120573 sdot (119879119895 minus (1 minus 120573) sdot 119879min)) otherwise

(21)

Please note that compared to the case of the correlatedequilibrium the payoff of each player is strictly defined by thesatisfaction correspondence and does not refer explicitly tothe rate as it is the case with the correlated equilibrium

Learning Satisfaction Equilibrium We assume that the gameplayers undertake actions in consecutive time intervals withonly one action selected per interval At each interval a playeralso observes whether it is satisfied or not The selection ofactions in each time interval is done based on the probabilitydistribution

120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (22)

which is known as the probability distribution of exploration[40] Under such assumptions SE can be found using thebehavioral rule which states that the next action taken byplayer 119894 is as follows

120572119894 (119905) =120572119894 (119905 minus 1) if 119891119894 (119905 minus 1) = 1120572119894 (119905) sim 120587119894 (119905) otherwise (23)

The choice of probability distribution 120587119894(119905) may impact theconvergence time and should also allow for the exploration of

all actions (thus all actions should have nonzero probability)A simple choice may be to use uniform probability distribu-tion 120587(120572(119896)119894 )119894 (119905) = 1|119860| On the other hand more sophisticatedprobability distribution update methods may be used thatincrease the convergence speed for example based on thenumber of times an action has been selected previously [40]

The main problem with the learning solution presentedabove is that it neglects the utilities observed by playersin the process of updating the probability distribution Analternative approach has been proposed in [41] where thedecentralized optimization is performed using the modifiedbehavioral rule that accounts for observed utilities Thisapproach known as the satisfaction equilibrium search algo-rithm (SESA) utilizes the knowledge of individual utilitiesto increase the probability of selecting actions that providea higher payoff

Strategy Identification Solutions based on the use of thesatisfaction equilibrium will be denoted hereafter as SEbinaryand SEsigmoid where the former describes a case where thesatisfaction is represented by a binary function as in (20) andthe latter identifies a case where the sigmoid function definedin (21) is used

33 Energy Efficiency Factor in Game Definitions So far wehave discussed strategies that guarantee rate maximizationthrough appropriate resource and interference managementLet us note that the achievement of the satisfaction equilib-rium can be interpreted as a game where energy efficiencyis taken into accountmdashonce a player is satisfied it will notbe considered in the ongoing process of resource allocationfor other players It means that the wastage of redundantlyassigned resources will be minimized thus leading to betterenergy utilization in the system However the solutionspresented in the previous section that utilize the correlatedequilibrium have to be modified in order to lead to anoverall energy efficiency improvement in the system Thuswe propose including the cost of energy consumption in thegame definition and in particular we propose modifying thepayoff functions

Payoff Definition In order to achieve better energy utilizationby the base stations while keeping the average cell rateunchanged we propose defining the payoff of the 119894th BS asfollows

119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894)1 + 119901(119879)119894

minus 119894 (120572119894120572minus119894) (24)

where 119901(119879)119894 stands for the total transmit power of the 119894th BSand 119894 denotes the cost (rate loss) introduced by BS 119894 to allother BSs which is evaluated as follows

119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894)1 + 119875(119879)

119897

minussum119897 =119894

119877119897 (120572119897120572)1 + 119875(119879)

119897

(25)


Table 1 Comparison of strategies

Strategy name ID Payoff definition Information exchanged1 Nash equilibrium NE Cell rate achieved by base station see (6) None

2 Correlated equilibrium CEpureIt is as for NE but the cost of rate reductionobserved by other players is considered see (9) Channel information or payoff table

3 CE reduced CEreducedAs for number 2 but reduced backhaul trafficonly the chosen payoff is updated Payoff value for selected strategy

4 Satisfaction equilibriumbinary SEbinary

Wastage of redundantly assigned resources isminimized satisfaction correspondence iscalculated as (20)

None

5 Satisfaction equilibriumsigmoid SEsigmoid

It is as for 4 but satisfaction correspondence iscalculated as (21) Satisfaction table

6 Energy efficiency (sdot)119864Selected strategies have been modified toinclude energy efficiency in the payoffdefinition as in (24) in Section 33

As in 2ndash5

7 Quantization (sdot)11987616-level quantization of the informationexchanged among players is appliedSection 34

As in 2ndash5 but with reduced binaryrepresentation to 4 bits

8 Energy efficiency andquantization (sdot)119864119876

Mixed strategies utilize energy efficiencyincreasing payoff definition and quantizationSection 35

As in 7

Similarly to account for the energy utilization factorwhen considering the satisfaction equilibrium (19) is mod-ified as follows

119891119894 (120572119894120572minus119894) =(1 10038161003816100381610038161198691198941003816100381610038161003816) sum119895isin119869119894 119904119894119895 (120572119894120572minus119894)

1 + 119875(119879)119897

(26)

with the satisfaction of UE 119895 119904119894119895(120572119894120572minus119894) calculated using (21)Strategy Identification The above concept has been appliedto the following strategies CEpure CEreduced and SEsigmoid Inorder to uniquely distinguish the new solutions we use thesubscript (sdot)119864 that is the following identifiers will be usedCEpure119864 CEreduced119864 and SEsigmoid119864

34 Backhaul Traffic Reduction As has been discussed inSection 323 the application of each of the solutionsdescribed in this section requires the exchange of a relativelyhigh amount of traffic Although its influence on the energyconsumed by the backhaul network will be discussed later itis obvious that any reduction of the amount of control infor-mation is beneficial Thus following the solutions discussedin Section 33 we propose a further simplification of thealgorithm by the application of the quantization procedureto the payoff values distributed among players So far wehave assumed that each base station circulates either thefull information about the channel between itself and allserved users or the table of payoffs In the strategy denotedas CEreduced119864 only the values related to the selected strategyhave to be delivered to other players However both the chan-nel information and payoff value are double values whichhave to be binary represented using for example 32 bitsIn order to reduce such information overhead we proposequantizing the information about the payoff value to four bitsthat is the index of one of only sixteen representative values

of the payoff can be circulated One can observe that by theapplication of such an approach the backhaul traffic will bereduced at least 8 times (if the 32-bit representation is used)

Strategies Identification As previously the idea of informationquantization has been applied to the strategies CEpureCEreduced and SEsigmoid which are now denoted as CEpure119876CEreduced119876 and SEsigmoid119876

35 Mixed Solution Finally we have jointly applied theconcepts described in Sections 33 and 34 The strategies aredenoted as CEpure119864119876 CEreduced119864119876 and SEsigmoid119864119876

36 Strategy Comparison In order to briefly compare thesolutions described above we gathered the concise informa-tion in Table 1

4 Backhaul Traffic Analysis

One of the key problems in the practical realization of thisapproach is the amount of data that has to be circulatedamong active playersmdashBSs (eg in the correlated equilibriumscenario) This parameter is strictly related to the observeddelays in data delivery to the BS thus it is important to assessthe information burden added to the backhaul networkMoreover it is easy to predict that even highly sophisticatedsolutions in terms of the guaranteed rate or throughputwill not be practically deployed if they either will causenonacceptable delays in the network or will require highinfrastructure investments In both cases the application ofsuch an algorithm will result in a direct or indirect costincrease that may not be acceptable for the MNO As we dealwith a highly realistic scenario of dense wireless networksin this paper the key goal of this chapter is to discuss


the technical feasibility of the considered game-theoreticsolutions

Following the assumption presented in Section 22 letus remember that each player has a fiber connection withanother in a star topology (ie one or two hops are requiredto deliver data between any two nodes) (fiber connection isour technology of choice since solutions like fiber-to-the-antenna FTTA andor radio-over-fiber RoF based tech-niques are often of the highest interest from theMNOpoint ofview eg [42ndash44] an interested reader is encouraged to alsofollow the related work on the connection between wirelessand optical parts of the communications network [45ndash47])Although we select optical fibers as a way of ensuring basestation connectivity other solutions such as Gigabit Ethernetor wireless backhauling can also be considered In the use-case discussed in this paper we intentionally chose a fiber-based network as a quite mature technology that enablesthe achievement of high data rates in the network Oncethe reference technology is selected we need to estimate thetraffic load due to the application of the proposed solutionsIn our calculations we will focus on the algorithm utilized inthe correlated equilibriumcase since it is characterized by thehighest needs for data exchange However let us again notethat backhaul optimization is not part of any of the consideredgames and is used only for the purpose of comparing theenergy consumption

In the simplest case every base station needs to exchangewith other nodes the information about the channel char-acteristics to the served users ℎ(119904)119894119895 and the probability dis-tribution for each of the possible playing strategies In thefollowing we fix the binary representation of each valueexchanged between nodes to 32 bits Such a matrix withchannel information contains 119873RB sdot entries where 119873RBstands for the total number of RBs and for the averagenumber of users served by one base station (ie = 119869119873where 119873 is the total number of base stations) Assuminguniform user deployment in the considered area (ie approx = 52021 asymp 25) the required number of bits to betransferred is equal to 1198791 = 32 sdot sdot 119873RB sdot 119873 sdot 119873 = 32bits sdot25users sdot 100RBs sdot 21first hop sdot 17 sdot 21second hop = 44064 sdot 106bits per 10 TTIs which corresponds to approx 44GbpsAdditionally in order to circulate the selected strategy (oneof 16 in our case) each base station needs to send 4 bitsresulting in total traffic 1198792 = 4 sdot 119873 sdot 119873 = 1296 bits per10 TTIs Such a great number of bits that would have to beexchanged will definitely disqualify such an algorithm fromfurther considerations due to its nonpracticality Hopefullysuch a great burden can be strongly reduced since insteadof channel information payoff matrices can be exchanged Inparticular in order to distribute the matrix of payoffs (of thesize calculated as the number of strategies times the numberof base stations) we need to send 1198793 = 32bits sdot 16strategies sdot18first hop sdot 18second hop = 10512 bits per 10 TTIs Thus thetotal traffic increase observed in the backhaul network equalsapprox 119879119905 = 11Mbps

In order to assess the cost of energy consumption increasedue to the higher traffic in the backhaul network we haveevaluated the typical values of power consumed by the

contemporary equipment used by operators of fiber net-works A detailed analysis of this problem is presented in [14]Due to the short distances between the nodes in the network(less than 2 km) there is no need for any in-line amplifiersThus one has to account for the power consumed by thebooster the power amplifier and eventually the optical crossconnects with the regenerator deployed on the intermediatenode (macro base station) Following [14] two models ofenergy consumption can be analyzedmdashone that relies onthe measurements of contemporary devices available on themarket and another that is based on an analytical modelIn the former case the change in traffic of 11Mbps has infact no measurable effect on the power consumed by theoptical devices It is due to the fact that the values of powerconsumption refer to particular classes of optical devices orsimply do not depend on the traffic load (eg optical lineamplifier OLA used for a short span of 2 km consumesa constant power of 65W while a transpondermuxponderfor 25G traffic and for 10G traffic needs 25W and 50Wresp) A change of the overall traffic by 11Mbps will notresult in a change of for example transponder class Inother words following the first approach backhaul powerconsumptionwill be kept unchangedThus let us nowdiscussthe problem of power consumption with the applicationof analytic models presented in formula (4) in [14] Onecan observe that the exact power consumption depends onvarious parameters such as power efficiency values (denotedas 119875119862) cooling and facilities overhead 120578119888 traffic protection120578pr hop count 119867 demand capacity 119863119862 and the numberof traffic demands 119873119889 An exemplary formula for powerconsumed by for example OLA is

119875OLA = 120578119888120578pr119863119862119873119863 119875OLA119862OLA

119867 120572119871119871OLA

(27)

where 119871OLA is the optical amplification span length and 120572119871is the average (lightpath) link length One can observe thatfor a given backhaul network topology all of the componentsremain the same except for the number of traffic demandsand average demand capacity Analogous conclusions can bedrawn for a power model of any other backhaul networkelement Thus one needs to find the value of the followingrelation 119875(1)OLA119875(2)OLA = 119863(1)119862 119873(1)119863 119863(2)119862 119873(2)119863 where the super-scripts (1) and (2) represent the states of the system withand without the backhaul traffic generated by the algorithmsdiscussed in this paper However based on the discussion andresults (Figures 8ndash10) from [14] it can be concluded that theincrease of the total consumed power due to a traffic increaseof 11Mbps is rather negligible

The above discussion is valid for the most demandingsolution that is the one that utilizes the concept of thecorrelated equilibrium with full information exchange Sinceall other algorithms require less steering data to be exchangedin the backhaul network it can be concluded that from thepoint of viewof energy consumption by the backhaul networkthe application of any algorithm discussed in this paper hasonly a negligible effect Clearly such an analysis has to berepeated for certain technologies and solutions applied byMNO


Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15

Micro BS range expansion (dB)

0

02

04

06

08

1

12

14

16

No ICICLTE-A eICICDynamic eICICeICIC FMANE

CEpureCEreducedSEsigmoidSEbinary

Figure 5 Average cell spectral efficiency for the considered baseline solutions

5 Simulation Results and Analysis

To investigate the properties and validity of the consideredgame-based solutions system-level Monte-Carlo simulationsof the system described in Section 2 have been carried outAs a simulation parameter the micro BS cell range expansionfactor has been used with five values considered 5 75 10125 15 [dB] As a reference four configurations have beenused

(i) a plain system with no interference mitigation(denoted as no ICIC)

(ii) a system utilizing LTE-A fixed eICIC with four ABSspecified for macro BSs (hereafter denoted as LTE-AeICIC)

(iii) a system using a dynamic LTE-A eICIC mechanismproposed in [48] (denoted as dynamic eICIC)

(iv) a system using an adaptivemechanism of FastMutingAdaptation with PF criterion employed proposed in[49] (denoted as eICIC FMA)

Among the game-based solutions three of them namelyCEpure CEreduced and a proposed version of SEsigmoid havealso been considered in the energy-efficient backhaul-optimized and mixed forms

51 Baseline Solutions In Figure 5 the average cell spectralefficiency (number of bits per second per unit bandwidth)for baseline solutions is presented One can notice that thehighest spectral efficiency is achieved in approaches thatassume rich information exchange with CEpure outperform-ing other solutions The gain observed for CEpure versus theplain system or the system using LTE-A eICIC is over 20with the CEreduced performing only slightly worse (up to a5 decrease compared to CEpure) Therefore when analyzingthe spectral efficiency one can state that the game-basedapproach using the correlated equilibrium is a very promising

solution for interference mitigation One can also notice thatthere is no improvement or even decrease in the spectralefficiency when eICIC methods are used compared to thecase with no interference mitigation This indicates that themain victims of interference in the considered case are themacro UE pieces that are affected by micro BSs transmissionIn such a situation eICIC cannot improve the throughputof macro UE pieces as it specifies almost-blank subframes(ABSFs) formacro BSs only On the other hand the proposedapproaches using CE or SE optimize the use of resources inboth macro and small BSs thus improving the performanceof macro UE pieces experiencing high interference

The performance of all methods improves with theincrease of the range expansion (RE) parameter whichcorresponds to a higher number of UE pieces connected tosmall BSs In the case of high RE the UE pieces that wouldotherwise be assigned to a macro BS and experience highinterference are connected to small BSs and benefit fromthe use of eICIC or other interference mitigation solutionsMoreover small BSs usually provide services for a smallernumber of UE pieces than macro BSs Thus offloading usersto small BSs results in a higher number of UE pieces beingscheduled for transmission

The solutions based on the SE concept perform morepoorly than CE because of the nature of the correspondencefunction ForUE pieces that achieve the required throughputany further increase in data rate does not increase theirsatisfactionTherefore the system spectral efficiency is tradedfor improvement in general user satisfaction represented byachieving certain required throughput

52 Energy-Efficient Solutions The properties of the consid-ered game-based solutions can also be used to improve theenergy efficiency of the system Therefore energy-efficientversions of selected algorithms have also been considered inthe investigation Figures 6 and 7 present the comparisonof baseline and energy-efficient versions in terms of the


0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15


No ICICLTE-A eICICDynamic eICICeICIC FMACEpure

CEreducedSEsigmoidCEpureECEreducedESEsigmoidE

Figure 6 Average cell energy efficiency for the considered baseline and energy-efficient solutions

Aver

age t

otal

cons

umed

pow

er (W

)

0

20

40

60

80

100

120

140

160

5 75 10 125 15




Figure 7 Average consumed power for the considered baseline and energy-efficient solutions

achieved average cell energy efficiency and total powerconsumed by the system respectively One can notice that ahuge gain in energy efficiency can be achieved when usingenergy-optimized versions of CEpure and SEsigmoid for highRE values where most of the traffic is offloaded to micro BSsMoreover it can be observed in Figure 7 that 3-4 times lowertransmit power is used in the case of the energy-optimizedsolutions when compared to the plain system or the systemusing eICIC

In most cases the highest energy efficiency is achievedwhen using the SEsigmoid approach The reason for suchbehavior is the nature of the SE correspondence functionFor UE pieces that achieve the required throughput levels afurther increase in their utility can be achieved by decreasingthe transmit power Therefore energy efficiency increases at

the cost of a slight reduction of spectral efficiency which isindicated in Figure 8

A very interesting observation can be made about thebehavior of the energy-optimized CEreduced solution Onecan notice that due to the reduced exchange of informationbetween the BSs the optimization mechanisms of energyusage cannot determine the gains from the use of otherstrategies thus theymostly operate on the basis of throughputanalysis This results in almost identical performance of theenergy-optimized approach as of the baseline CEreduced

The introduction of energy efficiency optimization doesnot degrade the gains of the considered approaches in termsof spectral efficiency As shown in Figure 8 the spectralefficiency achieved with the energy-optimized solutions isalmost the same as that for the baseline algorithms The only


0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15




Figure 8 Average cell spectral efficiency for the considered baseline and energy-efficient solutions

0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15


No ICICCEpureCEreducedSEsigmoid

CEpureQCEreducedQSEsigmoidQ

Figure 9 Average cell spectral efficiency for the considered baseline and backhaul-optimized solutions

exception is the CEpure119864 in the case of the RE factor equal to15 dB where the very high energy efficiency is achieved at thecost of reduced spectral efficiency which is still higher thanfor the plain system

53 Backhaul-Optimized Solutions The algorithms based onCE or SE can yield high gains in terms of spectral andenergy efficiency However control information needs to beexchanged between BSs In order to reduce the burden on thebackhaul network an approach based on payoff quantizationhas been proposed where four bits are used to represent eachpayoff value exchanged in the backhaul Figure 9 presentsthe comparison of spectral efficiency achieved with baselineand backhaul-optimized solutions One can notice that theintroduction of quantization results in a minor performance

degradation for several cases however the gains in terms ofspectral efficiency are still significant when compared to theplain system

An interesting observation is that there is hardly any lossin spectral efficiency when using CEreduced119876 or SEsigmoid119876compared to CEpure119876 This indicates that quantization has abigger impact when using solutions based on full exchangeof information When using the SE approach the charac-teristics of the correspondence function reduces the cost ofquantization Similarly for CEreduced119876 the limited exchangeof information and thus slower convergence mitigates theimpact of quantization errors

Similarly the mixed approach has been evaluated whereboth energy-efficient and backhaul-optimized approachesare applied simultaneously Figures 10 and 11 present the


5 75 10 125 15


0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)


CEpureEQCEreducedEQSEsigmoidEQ

Figure 10 Average cell spectral efficiency for the considered baseline and mixed solutions

0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15


No ICIC CEpureEQCEreducedEQSEsigmoidEQ

CEpureECEreducedESEsigmoidE

Figure 11 Average cell energy efficiency for the considered baseline and mixed solutions

achieved average cell spectral efficiency and average cellenergy efficiency respectively One can notice that the useof the mixed approach does not significantly degrade theperformance of the considered algorithms with reference tothe baseline solutions The conclusions are the same as thosefor the energy- and backhaul-optimized solutions Thusboth improvements are promising and perfectly applicableapproaches that provide the means of practical implementa-tion of the considered game-theoretic schemes

54 Summary The proposed game-based solutions havebeen evaluated in terms of spectral efficiency energy effi-ciency and total consumed power The simulation resultsclearly indicate that the most promising solutions are theCEpure and SEsigmoid algorithms with both providing signif-icant increase in terms of spectral and energy efficiency In

practical systems SE might be a more suitable solution asusually UE pieces use services that require some minimal oraggregate data rate that can be represented using the satisfac-tion correspondence function By using different satisfactiondefinitions for different services one can easily distinguishthe different payoffs of many UE pieces based on the servicesthey use

One can notice the significant improvement of CE and SEcompared to the eICIC methods as these are not suitable forscenarios with small- to macro-layer interference By treatingthe micro andmacro BSs equally in the case of CE and SE wecan improve the performance of UE pieces connected to themacro BS that are victims of strong interference Moreoverthe use of the dynamic eICIC approach does not bring anyimprovement as the considered scenario is a low mobilityone


The proposed energy-efficient modification furtherincreases the energy savings of both the CE and SE solutionsHigh energy efficiency has been observed especially in thecase of the SE approach In the case of CE a high reductionof energy consumption is achieved only in the case of a highRE parameter where most of the UE pieces are connected tosmall BSs

From the practical point of view the most suitable solu-tion would be the CEreduced one as it requires the exchange ofthe smallest amount of information in the backhaul networkHowever one can notice that it benefits less from the energy-optimized approach than other solutions Furthermore thepractical application of the considered approaches with fullinformation exchange is possible and cost-effective thanksto the robustness of the considered algorithms against theinaccuracy of payoff values caused by quantization Only aminor reduction in the achieved spectral efficiency has beenobserved for CEpure119876 and SEsigmoid119876 when compared to theirbaseline solutions

Finally one can state that the use of different powerlevels in selected subbands by the BSs provides an increasein the spectral efficiency of the system This increase isindependent of the type of users that are affected by thehighest interference For the case when both macro UEpieces or small cell UE pieces are the interference victims animprovement in system performance can be observed whenusing the considered game-theoretic solutions based on CEand SE This is in contrast to the eICIC solutions based onthe use of ABSF as these aim at the reduction of interferencefrom the macro to small cell layer in the downlink

6 Conclusion

The goal of this work was to propose an efficient and flexibletool for radio resource management in the context of itspractical implementation in future wireless networks Basedon the presented results of simulations carried out for ahighly accurate model of a dense urban network it canbe concluded that the application of the proposed game-theoretic algorithms guarantees the achievement of high cellthroughput while at the same time minimizing the energyconsumed by the base station All algorithms discussed inthis paper concentrate on the optimization of the overallenergy consumption and such strategies are preferred thatminimize the consumed energy while ensuring high datarates observed by all users All of the algorithms havebeen compared with the solution known from the LTE-A standards eICIC and have proved their effectivenessMoreover based on the detailed discussion of the trafficincrease in the backhaul network it can be concluded that thecost of practical implementation of the proposed solutions forRRMwill be rather negligible when considering the backhaulrequirements

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work by Paweł Sroka has been partly performed in theframework of the FP7 project ICT-317669 METIS which waspartly funded by the EuropeanUnion His work has been alsosupported by the PolishMinistry of Science and Higher Edu-cation funds for the status activity Project DSPB08810161The work by Adrian Kliks has been supported by the EUH2020 Project COHERENT under Contract 671639

References

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[2] Z Hasan H Boostanimehr and V K Bhargava ldquoGreen cellularnetworks a survey some research issues and challengesrdquo IEEECommunications Surveys and Tutorials vol 13 no 4 pp 524ndash540 2011

[3] M A Marsan and M Meo ldquoEnergy efficient wireless internetaccess with cooperative cellular networksrdquo Computer Networksvol 55 no 2 pp 386ndash398 2011

[4] L M Correia D Zeller O Blume et al ldquoChallenges andenabling technologies for energy aware mobile radio networksrdquoIEEECommunicationsMagazine vol 48 no 11 pp 66ndash72 2010

[5] E Hossain V K Bhargava and G P Fettweis Eds GreenRadio Communication Networks Cambridge University PressCambridge Uk 2012

[6] K S Ko B C Jung andD K Sung ldquoOn the energy efficiency ofwireless random access networks with multi-packet receptionrdquoin Proceedings of the 2013 IEEE 24th Annual International Sym-posium on Personal Indoor and Mobile Radio Communications(PIMRC rsquo13) pp 1666ndash1670 London UK September 2013

[7] Q-D Vu L-N Tran M Juntti and E-K Hong ldquoEnergy-efficient bandwidth and power allocation for multi-homingnetworksrdquo IEEE Transactions on Signal Processing vol 63 no7 pp 1684ndash1699 2015

[8] X Ge H ChengMGuizani and THan ldquo5Gwireless backhaulnetworks challenges and research advancesrdquo IEEE Networkvol 28 no 6 pp 6ndash11 2014

[9] S Tombaz K W Sung and J Zander ldquoOn metrics and modelsfor energy-efficient design of wireless access networksrdquo IEEEWireless Communications Letters vol 3 no 6 pp 649ndash6522014

[10] J Baliga R W A Ayre K Hinton and R S Tucker ldquoEnergyconsumption in wired and wireless access networksrdquo IEEECommunications Magazine vol 49 no 6 pp 70ndash77 2011

[11] Y Zhang ldquoPerformance modeling of energy managementmechanism in IEEE 80216e mobile WiMAXrdquo in Proceedings ofthe IEEE Wireless Communications and Networking Conference(WCNC rsquo07) pp 3205ndash3209 IEEE Hong Kong March 2007

[12] T Adame A Bel B Bellalta J Barcelo and M Oliver ldquoIEEE80211AH theWiFi approach for M2M communicationsrdquo IEEEWireless Communications vol 21 no 6 pp 144ndash152 2014

[13] N Benzaoui Y Pointurier T Bonald J-C Antona Q Weiand M Lott ldquoPerformance analysis in a next generation opticalmobile backhaul networkrdquo in Proceedings of the 16th Interna-tional Conference on Transparent Optical Networks (ICTON rsquo14)pp 1ndash4 July 2014


[14] W Van Heddeghem F Idzikowski W Vereecken D ColleM Pickavet and P Demeester ldquoPower consumption modelingin optical multilayer networksrdquo Photonic Network Communica-tions vol 24 no 2 pp 86ndash102 2012

[15] U Bauknecht and F Feller ldquoDynamic resource operation andpower model for IP-over-WSON networksrdquo in Advances inCommunication Networking 19th EUNICEIFIP WG 66 Inter-national Workshop Chemnitz Germany August 28ndash30 2013Proceedings vol 8115 of Lecture Notes in Computer Science pp1ndash12 Springer Berlin Germany 2013

[16] H Li ldquoMulti-agent Q-learning of channel selection in multi-user cognitive radio systems a two by two caserdquo in Proceedingsof the IEEE International Conference on Systems Man andCybernetics (SMC rsquo09) pp 1893ndash1898 IEEE San Antonio TexUSA October 2009

[17] C Han and S Armour ldquoEnergy efficient radio resource man-agement strategies for green radiordquo IET Communications vol5 no 18 pp 2629ndash2639 2011

[18] A Kliks N Dimitriou A Zalonis andOHolland ldquoWiFi trafficoffloading for energy savingrdquo in Proceedings of the 2013 20thInternational Conference on Telecommunications (ICT rsquo13) pp1ndash5 Casablanca Morocco May 2013

[19] J Christoffersson ldquoEnergy efficiency by cell reconfigurationMIMO to non-MIMO and 3-cell sites to omnirdquo in Proceedingsof the IEEE 73rd Vehicular Technology Conference (VTC rsquo11) pp1ndash5 IEEE Yokohama Japan May 2011

[20] P Kolios V Friderikosy and K Papadaki ldquoSwitching off lowutilization base stations via store carry and forward relayingrdquoin Proceedings of the IEEE 21st International Symposium onPersonal Indoor and Mobile Radio Communications Workshops(PIMRC rsquo10) pp 312ndash316 September 2010

[21] N Sapountzis S Sarantidis T Spyropoulos N Nikaein andU Salim ldquoReducing the energy consumption of small cellnetworks subject to QoE constraintsrdquo in Proceedings of the 2014IEEEGlobal Communications Conference (GLOBECOM rsquo14) pp2485ndash2491 Austin Tex USA December 2014

[22] Q Li M Xu Y Yang L Gao Y Cui and J Wu ldquoSafeand practical energy-efficient detour routing in IP networksrdquoIEEEACM Transactions on Networking vol 22 no 6 pp 1925ndash1937 2014

[23] J Zuo C Dong H V Nguyen S X Ng L-L Yang and LHanzo ldquoCross-layer aided energy-efficient opportunistic rout-ing in ad hoc networksrdquo IEEE Transactions on Communicationsvol 62 no 2 pp 522ndash535 2014

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[27] R4-10493Way Forward on Candidate TDMPatterns for Evalu-ation of eICIC Intra-Frequency Requirements 3GPP StandardJacksonville Fla USA 2010

[28] 3GPP TS 36300 ldquo3rd Generation Partnership Project Tech-nical Specification Group Radio Access Network EvolvedUniversal Terrestrial Radio Access (E-UTRA) and EvolvedUni-versal Terrestrial Radio Access Network (E-UTRAN) Overaldescription v 1130rdquo 2012

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[31] P Sroka and A Kliks ldquoDistributed interference mitigationin two-tier wireless networks using correlated equilibriumand regret-matching learningrdquo in Proceedings of the EuropeanConference on Networks and Communications (EuCNC rsquo14)June 2014

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[33] J-H Yun andK G Shin ldquoAdaptive interferencemanagement ofOFDMA femtocells for co-channel deploymentrdquo IEEE Journalon Selected Areas in Communications vol 29 no 6 pp 1225ndash1241 2011

[34] M Haddad S E Elayoubi E Altman and Z Altman ldquoAhybrid approach for radio resource management in heteroge-neous cognitive networksrdquo IEEE Journal on Selected Areas inCommunications vol 29 no 4 pp 831ndash842 2011

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[36] E G Larsson E A Jorswieck J Lindblom and RMochaourabldquoGame theory and the flat-fading gaussian interference channelanalyzing resource conflicts in wireless networksrdquo IEEE SignalProcessing Magazine vol 26 no 5 pp 18ndash27 2009

[37] S Lasaulce and H Tembine Game Theory and Learning forWireless Networks Fundamentals and Applications AcademicPress Cambridge Mass USA 2011

[38] R J Aumann ldquoSubjectivity and correlation in randomizedstrategiesrdquo Journal of Mathematical Economics vol 1 no 1 pp67ndash96 1974

[39] SHart andAMas-Colell ldquoA simple adaptive procedure leadingto correlated equilibriumrdquoEconometrica vol 68 no 5 pp 1127ndash1150 2000

[40] S M Perlaza H Tembine S Lasaulce and M DebbahldquoQuality-of-service provisioning in decentralized networks asatisfaction equilibrium approachrdquo IEEE Journal on SelectedTopics in Signal Processing vol 6 no 2 pp 104ndash116 2012

[41] S M Perlaza H Tembine S Lasaulce and M DebbahldquoSatisfaction equilibrium a general framework for QoS pro-visioning in self-configuring networksrdquo in Proceedings of theIEEE Global Communications Conference Configuring Networks(GLOBECOM rsquo10) Miami Fla USA December 2010

[42] K M Maamoun and H T Mouftah ldquoA survey and a novelscheme for RoF-PON as FTTx wireless servicesrdquo in Proceedingsof the 6th International Symposium on High Capacity OpticalNetworks and Enabling Technologies (HONET rsquo09) pp 246ndash253IEEE Alexandria Egypt December 2009

[43] J Beas G Castanon I Aldaya A Aragon-Zavala and G Cam-puzano ldquoMillimeter-wave frequency radio over fiber systems asurveyrdquo IEEE Communications Surveys amp Tutorials vol 15 no4 pp 1593ndash1619 2013

[44] V A Thomas M El-Hajjar and L Hanzo ldquoPerformanceimprovement and cost reduction techniques for radio over fiber


communicationsrdquo IEEE Communications Surveys amp Tutorialsvol 17 no 2 pp 627ndash670 2015

[45] N Ghazisaidi M Maier and C M Assi ldquoFiber-wireless (FiWi)access networks a surveyrdquo IEEE Communications Magazinevol 47 no 2 pp 160ndash167 2009

[46] Y Liu L Guo B Gong et al ldquoGreen survivability in Fiber-Wireless (FiWi) broadband access networkrdquoOptical Fiber Tech-nology vol 18 no 2 pp 68ndash80 2012

[47] B Kantarci N Naas and H T Mouftah ldquoEnergy-efficient DBAand QoS in FiWi networks constrained to metro-access con-vergencerdquo in Proceedings of the 14th International Conference onTransparent Optical Networks (ICTON rsquo12) pp 1ndash4 CoventryUK July 2012

[48] S Vasudevan R N Pupala and K Sivanesan ldquoDynamiceICICmdasha proactive strategy for improving spectral efficienciesof heterogeneous LTE cellular networks by leveraging usermobility and traffic dynamicsrdquo IEEE Transactions on WirelessCommunications vol 12 no 10 pp 4956ndash4969 2013

[49] B Soret and K I Pedersen ldquoCentralized and distributedsolutions for fastmuting adaptation in LTE-AdvancedHetNetsrdquoIEEE Transactions on Vehicular Technology vol 64 no 1 pp147ndash158 2015

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

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Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

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Advances in

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Biomedical Imaging


ArtificialNeural Systems

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Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



120m12

0m

12m12

m

21m6 floors of 35m each

210 UEs

Figure 1 Considered scenario Manhattan-like dense urban network

selected as the enabler for making simulations close to reality[24] The algorithms for interference coordination proposedfor 4G networks (known as enhanced intercell interferencecoordination (eICIC) [25ndash27]) have been compared with oursolutions based on the application of game-theoretic toolsLet us note that the game theory has already been consideredmany times as a valuable tool in the context of cellularnetworks In our work we tried to analyze the effectiveness ofthe proposed game-theoretic tools from the point of view oftheir practical implementationThus we not only discuss theconvergence time (which results in a delay in the system) butalso analyze how the traffic observed in the backhaul and corenetworks will be affected by the application of our algorithmsThe novel aspects covered by this paper are the following

(a) Provision of new solutions for radio resource andinterference management in dense urban 5G net-works that maximize cell throughput with the min-imization of overall energy consumption taking intoaccount the traffic increase in the backhaul network

(b) Summary and definitions of various game-theoretictools that can be used for achieving this goal andtheir comparison with the eICIC technique (pleasenote that scenarios with and without network nodecoordination have been considered)

(c) Analysis of the influence of applying the proposedtool on backhaul traffic and the potential increase ofthe energy consumed in that part of the network

Let us stress that the main aim of this paper is to comparedifferent slow-time-scale interference management mecha-nisms that can be considered as candidates for future 5Gnetworks assuming an identical simulation setup Howeverwe do not intend to use identical game and auctionmodels forevery case as different definitions can be assumed dependingon the game type and optimization criteria

The paper is organized as follows First the systemmodelconsidered for experimentation is discussed in Section 2Once it is presented the proposal for energy-efficient gamingin such a scenario is provided Then Section 3 presentsdetailed game definitions together with suggested ways ofachieving the equilibrium expected for each game Theanalysis of backhaul traffic being often a heavy burden of newsophisticated algorithms such as the coordinated multipoint(CoMP) is provided in Section 4 while the achieved com-puter simulation results are shown anddescribed in Section 5Finally the paper is concluded

2 System Model of a Dense Network

In order to analyze the efficiency of the proposed algo-rithms in reducing energy consumption in the context ofnext-generation networks a dense urban scenario has beenselected for consideration where multiple outdoor userterminals communicate with macro or micro base stationsdeployed on buildings and managed by MNO

21 Detailed Model Characterization In this work the use-case developed in the METIS 2020 project [24] has beenconsidered where a Manhattan-like dense urban wirelessnetwork ismodeled It is assumed thatmobile users utilize theorthogonal frequency division multiple access (OFDMA)technology with the frequency reuse factor equal to 1 tocommunicate with one of the sectoral antennas deployedby MNO on surrounding buildings as shown in Figure 1One can observe that 119873 = 21 antennas are installed in theconsidered area with three main 120∘ sectoral macro anten-nas mounted on the central-building and 9 pairs of 120∘sectoral micro antennas deployed close to the neighboringbuildings As the macro base stations are mounted onrooftops (5-meter highmasts have been used) themicro base





120574(119904)119894119895 =10038161003816100381610038161003816ℎ(119904)119894119895

100381610038161003816100381610038162 119901(119904)119894

1205902119895 + sum119897isin119872cup119870119894100381610038161003816100381610038161003816ℎ(119904)119897119895

1003816100381610038161003816100381610038162 119901(119904)119897

(1)



119879119894119895 = sum119905

sum119904

119877119904119894119895 (119905) sdot 120577119904119894119895 (119905) (2)








Time

Base station 1

Base station 2

Base station 3

Frequency





3

2

2


100

RBs=

20

MH

z

Freq

uenc

y33

RBs

33

RBs

34

RBs

Time

Strategies


0 1 2 3 4 5 6 7

8 9 10 11 12 13 14 15

Base PTXReduced PTX







G = (119872 cup 119870 119860 119880119894119894isin119872cup119870) (3)


120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (4)








119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894) (6)



119890(1120598119894)119880119894119905(120572lowast119894 120572minus119894) (7)













120577119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894) minussum119897 =119894

119877119897 (120572119897120572) (10)




120595119894 (120572119894120572minus119894) = sum119897 =119894

119891119897 (120572119897120572minus119894) minussum119897 =119894

119891119897 (120572119897120572) (12)



where

119863(119879)119894 (120572(119899)119894 120572(minus119899)119894 )

= max119895 =119899

1119879sum119905le119879




120587(120572(119899)119894 )119894 (119879) = 1 minus 1120583(119879minus1)REG

(119879minus1)119894 (120572(119899)119894 120572(minus119899)119894 ) (15)

where






G = (119872 cup 119870 119860 119891119894119894isin119872cup119870) (17)





(18)



119891119894 (120572119894120572minus119894) = 110038161003816100381610038161198691198941003816100381610038161003816sum119895isin119869119894

119904119894119895 (120572119894120572minus119894) (19)




119904119894119895 (120572119894120572minus119894)

=

1 if 119879119895 ge 119879min1


(21)



120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (22)









119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894)1 + 119901(119879)119894

minus 119894 (120572119894120572minus119894) (24)


119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894)1 + 119875(119879)

119897

minussum119897 =119894

119877119897 (120572119897120572)1 + 119875(119879)

119897

(25)








None




As in 2ndash5





As in 7



1 + 119875(119879)119897

(26)















119875OLA = 120578119888120578pr119863119862119873119863 119875OLA119862OLA

119867 120572119871119871OLA

(27)




Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15


0

02

04

06

08

1

12

14

16

















0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15





Aver

age t

otal

cons

umed

pow

er (W

)

0

20

40

60

80

100

120

140

160

5 75 10 125 15











0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15





0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15











5 75 10 125 15


0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)




0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







120574(119904)119894119895 =10038161003816100381610038161003816ℎ(119904)119894119895

100381610038161003816100381610038162 119901(119904)119894

1205902119895 + sum119897isin119872cup119870119894100381610038161003816100381610038161003816ℎ(119904)119897119895

1003816100381610038161003816100381610038162 119901(119904)119897

(1)



119879119894119895 = sum119905

sum119904

119877119904119894119895 (119905) sdot 120577119904119894119895 (119905) (2)








Time

Base station 1

Base station 2

Base station 3

Frequency





3

2

2


100

RBs=

20

MH

z

Freq

uenc

y33

RBs

33

RBs

34

RBs

Time

Strategies


0 1 2 3 4 5 6 7

8 9 10 11 12 13 14 15

Base PTXReduced PTX







G = (119872 cup 119870 119860 119880119894119894isin119872cup119870) (3)


120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (4)








119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894) (6)



119890(1120598119894)119880119894119905(120572lowast119894 120572minus119894) (7)













120577119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894) minussum119897 =119894

119877119897 (120572119897120572) (10)




120595119894 (120572119894120572minus119894) = sum119897 =119894

119891119897 (120572119897120572minus119894) minussum119897 =119894

119891119897 (120572119897120572) (12)



where

119863(119879)119894 (120572(119899)119894 120572(minus119899)119894 )

= max119895 =119899

1119879sum119905le119879




120587(120572(119899)119894 )119894 (119879) = 1 minus 1120583(119879minus1)REG

(119879minus1)119894 (120572(119899)119894 120572(minus119899)119894 ) (15)

where






G = (119872 cup 119870 119860 119891119894119894isin119872cup119870) (17)





(18)



119891119894 (120572119894120572minus119894) = 110038161003816100381610038161198691198941003816100381610038161003816sum119895isin119869119894

119904119894119895 (120572119894120572minus119894) (19)




119904119894119895 (120572119894120572minus119894)

=

1 if 119879119895 ge 119879min1


(21)



120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (22)









119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894)1 + 119901(119879)119894

minus 119894 (120572119894120572minus119894) (24)


119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894)1 + 119875(119879)

119897

minussum119897 =119894

119877119897 (120572119897120572)1 + 119875(119879)

119897

(25)








None




As in 2ndash5





As in 7



1 + 119875(119879)119897

(26)















119875OLA = 120578119888120578pr119863119862119873119863 119875OLA119862OLA

119867 120572119871119871OLA

(27)




Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15


0

02

04

06

08

1

12

14

16

















0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15





Aver

age t

otal

cons

umed

pow

er (W

)

0

20

40

60

80

100

120

140

160

5 75 10 125 15











0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15





0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15











5 75 10 125 15


0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)




0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Time

Base station 1

Base station 2

Base station 3

Frequency





3

2

2


100

RBs=

20

MH

z

Freq

uenc

y33

RBs

33

RBs

34

RBs

Time

Strategies


0 1 2 3 4 5 6 7

8 9 10 11 12 13 14 15

Base PTXReduced PTX







G = (119872 cup 119870 119860 119880119894119894isin119872cup119870) (3)


120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (4)








119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894) (6)



119890(1120598119894)119880119894119905(120572lowast119894 120572minus119894) (7)













120577119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894) minussum119897 =119894

119877119897 (120572119897120572) (10)




120595119894 (120572119894120572minus119894) = sum119897 =119894

119891119897 (120572119897120572minus119894) minussum119897 =119894

119891119897 (120572119897120572) (12)



where

119863(119879)119894 (120572(119899)119894 120572(minus119899)119894 )

= max119895 =119899

1119879sum119905le119879




120587(120572(119899)119894 )119894 (119879) = 1 minus 1120583(119879minus1)REG

(119879minus1)119894 (120572(119899)119894 120572(minus119899)119894 ) (15)

where






G = (119872 cup 119870 119860 119891119894119894isin119872cup119870) (17)





(18)



119891119894 (120572119894120572minus119894) = 110038161003816100381610038161198691198941003816100381610038161003816sum119895isin119869119894

119904119894119895 (120572119894120572minus119894) (19)




119904119894119895 (120572119894120572minus119894)

=

1 if 119879119895 ge 119879min1


(21)



120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (22)









119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894)1 + 119901(119879)119894

minus 119894 (120572119894120572minus119894) (24)


119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894)1 + 119875(119879)

119897

minussum119897 =119894

119877119897 (120572119897120572)1 + 119875(119879)

119897

(25)








None




As in 2ndash5





As in 7



1 + 119875(119879)119897

(26)















119875OLA = 120578119888120578pr119863119862119873119863 119875OLA119862OLA

119867 120572119871119871OLA

(27)




Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15


0

02

04

06

08

1

12

14

16

















0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15





Aver

age t

otal

cons

umed

pow

er (W

)

0

20

40

60

80

100

120

140

160

5 75 10 125 15











0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15





0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15











5 75 10 125 15


0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)




0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




3

2

2


100

RBs=

20

MH

z

Freq

uenc

y33

RBs

33

RBs

34

RBs

Time

Strategies


0 1 2 3 4 5 6 7

8 9 10 11 12 13 14 15

Base PTXReduced PTX







G = (119872 cup 119870 119860 119880119894119894isin119872cup119870) (3)


120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (4)








119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894) (6)



119890(1120598119894)119880119894119905(120572lowast119894 120572minus119894) (7)













120577119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894) minussum119897 =119894

119877119897 (120572119897120572) (10)




120595119894 (120572119894120572minus119894) = sum119897 =119894

119891119897 (120572119897120572minus119894) minussum119897 =119894

119891119897 (120572119897120572) (12)



where

119863(119879)119894 (120572(119899)119894 120572(minus119899)119894 )

= max119895 =119899

1119879sum119905le119879




120587(120572(119899)119894 )119894 (119879) = 1 minus 1120583(119879minus1)REG

(119879minus1)119894 (120572(119899)119894 120572(minus119899)119894 ) (15)

where






G = (119872 cup 119870 119860 119891119894119894isin119872cup119870) (17)





(18)



119891119894 (120572119894120572minus119894) = 110038161003816100381610038161198691198941003816100381610038161003816sum119895isin119869119894

119904119894119895 (120572119894120572minus119894) (19)




119904119894119895 (120572119894120572minus119894)

=

1 if 119879119895 ge 119879min1


(21)



120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (22)









119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894)1 + 119901(119879)119894

minus 119894 (120572119894120572minus119894) (24)


119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894)1 + 119875(119879)

119897

minussum119897 =119894

119877119897 (120572119897120572)1 + 119875(119879)

119897

(25)








None




As in 2ndash5





As in 7



1 + 119875(119879)119897

(26)















119875OLA = 120578119888120578pr119863119862119873119863 119875OLA119862OLA

119867 120572119871119871OLA

(27)




Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15


0

02

04

06

08

1

12

14

16

















0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15





Aver

age t

otal

cons

umed

pow

er (W

)

0

20

40

60

80

100

120

140

160

5 75 10 125 15











0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15





0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)

5 75 10 125 15











5 75 10 125 15


0

02

04

06

08

1

12

14

16

Aver

age c

ell s

pect

ral e

ffici

ency

(bps

Hz)




0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








G = (119872 cup 119870 119860 119880119894119894isin119872cup119870) (3)


120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (4)








119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894) (6)



119890(1120598119894)119880119894119905(120572lowast119894 120572minus119894) (7)













120577119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894) minussum119897 =119894

119877119897 (120572119897120572) (10)




120595119894 (120572119894120572minus119894) = sum119897 =119894

119891119897 (120572119897120572minus119894) minussum119897 =119894

119891119897 (120572119897120572) (12)



where

119863(119879)119894 (120572(119899)119894 120572(minus119899)119894 )

= max119895 =119899

1119879sum119905le119879




120587(120572(119899)119894 )119894 (119879) = 1 minus 1120583(119879minus1)REG

(119879minus1)119894 (120572(119899)119894 120572(minus119899)119894 ) (15)

where






G = (119872 cup 119870 119860 119891119894119894isin119872cup119870) (17)





(18)



119891119894 (120572119894120572minus119894) = 110038161003816100381610038161198691198941003816100381610038161003816sum119895isin119869119894

119904119894119895 (120572119894120572minus119894) (19)




119904119894119895 (120572119894120572minus119894)

=

1 if 119879119895 ge 119879min1


(21)



120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (22)









119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894)1 + 119901(119879)119894

minus 119894 (120572119894120572minus119894) (24)


119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894)1 + 119875(119879)

119897

minussum119897 =119894

119877119897 (120572119897120572)1 + 119875(119879)

119897

(25)








None




As in 2ndash5





As in 7



1 + 119875(119879)119897

(26)















119875OLA = 120578119888120578pr119863119862119873119863 119875OLA119862OLA

119867 120572119871119871OLA

(27)




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6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








120577119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894) minussum119897 =119894

119877119897 (120572119897120572) (10)




120595119894 (120572119894120572minus119894) = sum119897 =119894

119891119897 (120572119897120572minus119894) minussum119897 =119894

119891119897 (120572119897120572) (12)



where

119863(119879)119894 (120572(119899)119894 120572(minus119899)119894 )

= max119895 =119899

1119879sum119905le119879




120587(120572(119899)119894 )119894 (119879) = 1 minus 1120583(119879minus1)REG

(119879minus1)119894 (120572(119899)119894 120572(minus119899)119894 ) (15)

where






G = (119872 cup 119870 119860 119891119894119894isin119872cup119870) (17)





(18)



119891119894 (120572119894120572minus119894) = 110038161003816100381610038161198691198941003816100381610038161003816sum119895isin119869119894

119904119894119895 (120572119894120572minus119894) (19)




119904119894119895 (120572119894120572minus119894)

=

1 if 119879119895 ge 119879min1


(21)



120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (22)









119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894)1 + 119901(119879)119894

minus 119894 (120572119894120572minus119894) (24)


119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894)1 + 119875(119879)

119897

minussum119897 =119894

119877119897 (120572119897120572)1 + 119875(119879)

119897

(25)








None




As in 2ndash5





As in 7



1 + 119875(119879)119897

(26)















119875OLA = 120578119888120578pr119863119862119873119863 119875OLA119862OLA

119867 120572119871119871OLA

(27)




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5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






(18)



119891119894 (120572119894120572minus119894) = 110038161003816100381610038161198691198941003816100381610038161003816sum119895isin119869119894

119904119894119895 (120572119894120572minus119894) (19)




119904119894119895 (120572119894120572minus119894)

=

1 if 119879119895 ge 119879min1


(21)



120587119894 (119905) = (120587(120572(1)119894 )119894 (119905) 120587(120572(2)119894 )119894 (119905) 120587(120572(119873)119894 )119894 (119905)) (22)









119880119894 (120572119894120572minus119894) ≜ 119877119894 (120572119894120572minus119894)1 + 119901(119879)119894

minus 119894 (120572119894120572minus119894) (24)


119894 (120572119894120572minus119894) = sum119897 =119894

119877119897 (120572119897120572minus119894)1 + 119875(119879)

119897

minussum119897 =119894

119877119897 (120572119897120572)1 + 119875(119879)

119897

(25)








None




As in 2ndash5





As in 7



1 + 119875(119879)119897

(26)















119875OLA = 120578119888120578pr119863119862119873119863 119875OLA119862OLA

119867 120572119871119871OLA

(27)




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5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










None




As in 2ndash5





As in 7



1 + 119875(119879)119897

(26)















119875OLA = 120578119888120578pr119863119862119873119863 119875OLA119862OLA

119867 120572119871119871OLA

(27)




Aver

age c

ell s

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ency

(bps

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5 75 10 125 15


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er (W

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nerg

y effi

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zJ)

5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









119875OLA = 120578119888120578pr119863119862119873119863 119875OLA119862OLA

119867 120572119871119871OLA

(27)




Aver

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5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Aver

age c

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(bps

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5 75 10 125 15


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5 75 10 125 15





Aver

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otal

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)

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Aver

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y effi

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cy (b

itH

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5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

1

2

3

4

5

6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15





Aver

age t

otal

cons

umed

pow

er (W

)

0

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6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

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age c

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5 75 10 125 15





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6

Aver

age c

ell e

nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




5 75 10 125 15


0

02

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age c

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(bps

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5

6

Aver

age c

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nerg

y effi

cien

cy (b

itH

zJ)

5 75 10 125 15













6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







6 Conclusion


Competing Interests


Acknowledgments


References




























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in

















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in

















Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Documents

Research Article Playing Radio Resource Management Games ...downloads.hindawi.com/journals/misy/2016/3798523.pdf · consumption has been considered in various scenarios, including