A Spatial Optimization based Adaptive CoverageModel for Green Self-Organizing Networks

Gokhan Secinti and Berk CanberkDepartment of Computer Engineering

Istanbul Technical University, Maslak, 34396 Istanbul, TURKEYEmail: {secinti, canberk}@itu.edu.tr

Abstract—The deployment of Self-Organizing Networks(SONs) based architectures has emerged as one of the keypoints in the 3GPP LTE-Advanced Standard, which aims toembed auto-management skills into the next generation mobilenetworks. However, the high traffic demands and the increasednumber of nomadic users have led dense eNodeB coverage, thuschallenging the SON management in terms of energy efficiency.Considering these crucial SON challenges, we propose a noveladaptive network coverage model for energy-efficient SONs usinga special spatial optimization method. This novel method is basedon the Voronoi diagram optimization to provide the minimumnumber of active eNodeBs for high energy saving. The pro-posed model mathematically analyzes all the operating eNodeBsdeployed in a specific SON area in terms of the utilization,by identifying them by a two-parameter function. These arethe spatial coordinates and the utilization of the eNodeB. ThiseNodeB-specific mathematical model leads to find the redundanteNodeBs with less utilization, deactivate them and rearrangethe coverage area with the remaining active eNodeBs using theVoronoi specific optimization. This optimization is solved by anovel heuristic with the aid of a parameter called assignmentfactor, in order to maximize the utilization for the remainingactive eNodeBs in the green SON architecture. This spatialoptimization based algorithm aims to adaptively deploy energy-effective cell coverage. The thorough evaluation results provethe generic energy-efficiency of the proposed adaptive coveragealgorithm while maintaining the ENodeB utilization above thesatisfying QoS levels.

I. INTRODUCTION

The significant increase of data traffic via wireless deviceshave led the 3GPP (The 3rd Generation Partnership Project)towards solutions such as the Long Term Evolution-Advanced(LTE-Advanced) in order to fulfill the IMT Advanced (Inter-national Mobile Telecommunications-Advanced) requirements.These wireless traffic demands have brought a huge amountof energy consumption with them [1]. Beside the energyconsumption, in order to satisfy these traffic demands andincreased number of mobile users, a large number of eNodeBsin LTE-Advanced Systems have to be densely deployed [2].LTE-Advanced Standard handles these condense and crowdeddeployment needs by embedding auto-management skills intothe next generation mobile networks. To this end, the de-ployment of green Self-Organizing Networks (SONs) hasemerged as one of the crucial key points in the 3GPP LTE-Advanced Standard for both operators and users to satisfy therapidly growing energy-killer capacity needs as well as to saveoperational expenditures [3], [4].

One of the crucial Green-SON features to maintain this

”self” characteristic is the self-optimization which is the pro-cess of the autonomous monitoring, auto-tuning of networkcoverage, and the maximization of the network’s utilizationto maintain the robustness, agility and scalability of thecommunication. Here, the network coverage should be intelli-gently determined to provide less energy-consumption. Morespecifically, some deployed eNodeBs are just active for somespecific time period due to the geographical patterns they arein. In these cases, they can be forced to be deactivated if theirnetwork load and utilization are below a threshold. Therefore,an adaptive activation and deactivation of Home eNodeBs areto be managed considering the spatial vicinity of each eNodeBsfor energy saving.

In the current literature, there are several works dealingwith green SON architecture which is standardized with 3GPPLTE group Self-Organizing Network [5]. Self-optimizationfeature is analyzed in details in [6]. [7] provides intenseoverview about current techniques, test-beds and possiblechallenges while designing energy efficient wireless networks.[8] formulates the energy efficient transmission, implementedin 3GPP LTE/LTE-Advanced systems, for individual user bya nonlinear integer resource optimization. In [9], the authorsdevelop an optimal sleep/wakeup schemes in heterogeneousnetworks, composed of macro and femto base stations, whereasin [10] three cellular network deployment strategies wereinvestigated in terms of energy efficiency for variable trafficconditions. [11] spatially analyzes the handover procedureof a SON implemented in cellular networks. In [12], theneighbor cell list management is spatially studied for het-erogeneous SON deployments. At [13], the coverage andcapacity optimization is presented as use cases to demonstratesuccessful coordination of multiple independent SON func-tions. [14] draws analytical derivation about SON deploymentperformance by defining new parameters. [15], [16] propose aradiation adaptation scheme for QoS and adaptive sectorisationin cellular networks using spatial information of the mobileusers to depict user geographical distributions statistically.

In most of the recent studies, as some has been afore-mentioned, the LTE-Advanced based SON designs have notbeing spatially optimized in terms of energy efficiency, but interms of capacity and other network specific QoS parameters.However, we strongly believe that a robust and agile greenSON architecture relies on the spatial vicinities and adaptivecoverage schemes in which the eNodeBs are intelligentlydistributed. Since some eNodeBs are less used, a consider-able amount of energy saving can be obtained by adaptively

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deactivating them and rearranging the coverage. Therefore,the activation-deactivation phases of eNodeBs should be auto-optimized to mitigate redundant energy consumption for lessused eNodeBs. Considering these ideas, we propose a novelspatial optimization based adaptive coverage model by makingthe following contributions:

• The spatial vicinities of all the operating eNodeBsdeployed in a specific SON area are mathematicallymodeled by proposing a two-parameter spatial func-tion. These parameters are the geographical coordi-nates and the network utilization of eNodeBs.

• The proposed Voronoi diagram specific optimizationprocedure uses this EnodeBs mathematical model tolocate eNodeBs with less utilization, deactivate themand rearrange the coverage area adaptively with theremaining active eNodeBs.

• The proposed optimization is solved by a novelheuristic called Enhanced Branch and Bound (EBB)using a parameter called ”assignment factor”, in orderto maximize the utilization for the remaining activeeNodeBs in the green SON architecture.

• The energy efficiency is maximized while maintainingthe utilization of the overall green SON.

The paper is organized as follows. In Section II,the networkarchitecture and the different modules of the proposed adaptivecoverage model are detailed. Section III gives the performanceevaluation of the proposed model in terms of energy efficiencyand utilization. We finalize the paper by summarizing theachievements in Section IV.

II. NETWORK ARCHITECTURE AND PROPOSEDFRAMEWORK

In this paper, we assume that all the eNodeBs and theimmobile User Equipments (UE) are normally distributed in agiven urban area. The proposed framework is embedded intoeach eNodeB in order to monitor and analyze the behaviors ofUEs connected to them. The framework takes two critical dataas inputs in order to rearrange the coverage in an adaptiveand energy efficient manner. Specifically, these critical dataare the geometric coordinates which represent the localizationinformation of eNodeBs and the network utilization which isparametrized as the number of UEs.

ProposedFramework

eNodeB

Utilizations

LocalizationsMapping

VoronoiDiagram

eNodeBAnalysis

Green andAdaptiveCoverage

Determination

Fig. 1. Proposed Framework

As seen in Figure 1, the framework uses the predefinedlocation and utilization information of eNodeBs to createVoronoi diagram of the system. We assume that all of theeNodeBs are active and in the operating mode in the initialtopology. An algorithm which is an enhanced version of theBranch and Bound algorithm [17] has been used in orderto solve the Voronoi based optimization problem. We haveadded some policies to improve memory efficiency as an en-hancement to BB algorithm. After the initial Voronoi diagramhas been determined, the properties of the eNodeBs havebeen analyzed and the necessary variables such as utilizationsand adjacencies of eNodeBs have been determined for theproposed Enhanced Branch and Bound algorithm (EBB). Thenthe framework determines the optimal topologies in termsof energy consumption by using Voronoi diagrams and EBBalgorithm. In the next subsections, we will detail each moduleof the proposed framework which are Mapping-Voronoi Di-agram, eNodeB Analysis and Green and Adaptive CoverageDetermination.

A. Mapping-Voronoi Diagram

We represent the topology of the eNodeB network as aVoronoi diagram. Voronoi diagram is a dual graph of Delau-nay triangulation. We used Bowyer-Watson [18] algorithm todetermine the initial topology. We present eNodeBs as sites inthe Voronoi diagram and the distances between the eNodeBscan be seen as the edges of Delanuay Triangulation. Euclideandistance has been used to represent the distances betweeneNodeBs. The abstraction of the Voronoi Diagram provides theadjacencies between the eNodeBs in the optimization process.We assume that when we cease the operation of an eNodeB, itsexpected utilization will scatter over the adjacent ones. Thusthe decision of the switching off an eNodeB depends on theexpected utilization of that eNodeB as much as the expectedutilization of its neighbors. When an eNodeB is switched off,if the expected utilization of any of its neighbor eNodeBs donot exceed maximum possible number of consumers then weresolve the switching off that eNodeB is a feasible step in ourframework.

B. eNodeB Analysis and Modelling

An eNodeB is identified as a two-parameter spatial func-tion:

eNodeBi = {(xi, yi), ci} (1)

where (xi, yi) is static coordinates of the eNodeBi and ci isthe number of consumers who are expected to use eNodeBi

simultaneously. We have defined the expected utilization valuesof the eNodeBs by the sets C. C defines the set of theaverage number of consumers in the adaptive topology. Everyelement belonging to the set C represents the average numberof expected consumers for an operating eNodeB. The totalnumber of consumers in a region ‖C‖ can be defined as‖C‖ =

∑|C|i=0 ci.

The proposed framework must satisfy the needs of everyconsumer. Thus the framework must keep sufficient numberof eNodeBs operational in order to provide the needs of theexpected UEs. We represent the maximum number of UEsthat can be served simultaneously by one eNodeB with δ.This value defines our key threshold value in the spatial

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�

�

�

�

u4 u2u1

u3

(a) Initial topology

�

�

�

�

u4

d2d1

d3

u2

u1

u3

(b) Distances between eNodeBs andUtilizations

�

�

�

u1

u3

u2

(c) Final topology

Fig. 2. An example of the ceasing operation of an eNodeB

optimization. We aim to optimize the energy consumptionby switching off redundant eNodeBs, i.e. eNodeBs with lessutilization.

When an eNodeB is switched off, its workload will bedistributed among its adjacent eNodeBs. So we try to switchoff maximum number of redundant eNodeBs as long as theirneighbor eNodeBs have expected number of consumers whichis smaller than the threshold (δ). In this distribution process,edges in the Delaunay Triangulation have been used, weightsof these edges represent the Euclidean distance betweeneNodeBs. In this framework, we assume that the workloadassigned to an adjacent eNodeB and the distance betweeneNodeBs are inversely proportional. If the utilization valuesof all the adjacent eNodeBs are still equal or lower than thethe threshold (δ) then the ceasing the operation of the eNodeBis feasible. An example of such distribution is given in theFigure 2.

In the given example in the Figure 2(a), we try to switchoff the eNodeB4 which is in the center of the given region.As can be seen, eNodeB4 has three neighbors which meansthat its utilization has to be divided into three partitions. In thefirst step, distribution of the workload is calculated to satisfythe Equations 2 as,

c4 =∑k

1 pi w.r.t. p1 · d1,4 = p2 · d2,4 = p3 · d3,4 (2)

where pi is number of consumers which transferred fromeNodeB4 to eNodeBi , k is the number of eNodeBs which areadjacent to eNodeB4 and di,4 is Euclidean distance betweenthe eNodeBi and eNodeB4 as seen in Figure 2(b).

After that, we need to check the updated utilizations of theadjacent eNodeBs as in Equation 3.

cnew1 = c1 + p1cnew2 = c2 + p2cnew3 = c3 + p3

}∀i cnewi ≤ δ (3)

If the defined conditions as in the Equation 3 are satisfied,then the underlined eNodeB, in this case eNodeB4, could beturned off as in Figure 2(c) in order to reduce energy con-sumption. Consequently, the load of the deactivated eNodeBis distributed among its neighbors and the new coverage isadaptively rearranged with the remaining active eNodeBs.

However, there does not have to be a unique topologywith the least energy consumption. Several different topologies

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(a) (b)

Fig. 3. (a) Example for the different possible topologies with the same energyconsumption, (b) Example of the Local Maximum eNodeBs

which have the least energy consumption may exist and couldbe calculated using the framework. Thus we have defined aparameter that measures the assignments of the UEs in orderto decide which topology coverage we should choose fromthe set of candidate topologies which have the same energyconsumption. The rearrangement of the UEs is required whenan utilized eNodeB is switched off. The UEs have to bereassigned from the non-operating eNodeB to the adjacentoperational eNodeB. The Assignment Factor has been definedas the product of the distance and the number of the UEswhich have been reassigned. When an eNodeBj is switchedoff, Assignment Factor is calculated as in Equation 4.

Assignment Factorj =∑

dj,i · pi (4)

where dj,i is the Euclidean distance and pi is the number ofconsumers which are assigned from eNodeBj to eNodeBi.

An initial topology has been given in the Figure 3(a)as an example. In this topology, we assume that the sumof the UEs can be satisfied with just one eNodeB. So theframework estimates four different solutions which have thesame energy consumption. On the each branch operation in theEBB algorithm, the assignment which is realized by closinga redundant eNodeB has been kept with the solution as avariable. Thus we calculate the sum of the assignment factorsin the solutions cumulatively and this assignment values havebeen used to choose the best one (in terms of UE satisfaction)between the solutions which have equal energy consumption.

C. Green and Adaptive Coverage Determination

The coverage determination is modeled as an optimizationproblem in which we solve with EEB. Note that, we aredealing with an optimization problem, we choose to imple-ment a suitable algorithm to reduce the search space. Theframework finds the most suitable solution for the definedvalue function in the search space. We define this functionto calculate the reduction in the overall energy consumptionand then implement this function as a value function in EBBalgorithm. If a solution is declared as unfeasible, it meansthat its subsolutions which are derived from the main oneare also unfeasible. Hence the possible search space could bereduced dramatically by detecting the unfeasible solutions. So,another important function of the EBB algorithm, feasibilityfunction, has been defined. This function checks the utilizationsof the each operating eNodeB after closing an eNodeB anddetermines the applicability of the new solution. The pseudocode of the main function and the search function have beengiven in Algorithm 1. The algorithm starts with an initial

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topology and try to determine all other feasible topologies withless energy consumption. Firstly, main function adds initialtopology to the list where all feasible solutions are kept. Thenit tries to find new feasible topologies derived from the initialone, by running search function. After that, search functionruns recursively on the given topology. The Search functioncloses the active eNodeBs in the solution one at a time andchecks the feasibility of the new solution. The Close and thefeasibility functions have been implemented as in theAlgorithm 2. The Close function begins with determining theneighbors of the given eNodeB in order to close the eNodeB.Afterward the UEs on the closing eNodeB is distributed amongits neighbors. After the update of the utilization values ofoperating eNodeBs in the current solution, we have to checkthe feasibility of the solution. A solution can be identified asfeasible if the utilizations of all its operational eNodeBs arebelow the maximum possible utilization (δ).

Algorithm 1 Enhanced Branch and Bound Algorithm (EBB)1: List Solutions � List of all possible solutions2: function BBALGORITHM(initialTopology)3: Add initialTopology to Solutions4: search (initialTopology)5: end function6: function SEARCH(solution)7: for all eNodeB in solution do8: Create newSolution from solution9: Close eNodeB in newSolution

10: if isFeasible(newSolution) then11: Add newSolution to Solutions12: search (newSolution)13: end if14: end for15: end function

Algorithm 2 Sub-Functions of EBB Algorithm1: function CLOSE(eNodeB)2: List neighbors < eNodeB >3: Fill neighbors with adjacent eNodeBs to eNodeB4: Distribute costumers of eNodeB among its neighbors5: Calculate assignment factor due to the closing6: end function7: function ISFEASIBLE(solution)8: for all eNodeB in solution do9: if (# of Consumers in eNodeB) > δ then

10: return FALSE11: end if12: end for13: return TRUE14: end function

III. PERFORMANCE EVALUATION

In this section, first, we should state the possible differencesof the test domains. Our primary goal is determining possibleenergy efficient topologies from predefined eNodeB modeldefined in Subsection II-B. These topologies may vary in termsof different attributes such as the coordinates of eNodeBs, thenumber of eNodeBs and the overall utilization in the region.The overall utilization is defined as

u(t) =‖C‖

δ · n(5)

where ‖C‖ is total number of UEs in the region, δ is themaximum possible number of UEs which could be servedby an eNodeB simultaneously and n is the total number ofeNodeBs in the test region. During the evaluation, we assumethat the δ is equal to 15 in order to fulfill the putative QoSof UEs. The overall utilization, the coordinates and number ofeNodeBs vary for different test processes. Proposed frameworkstates the all possible topologies with lower energy consump-tion for any given domain. But when framework completes itsexecution, there can be different topologies with same energyefficiency. In this case, the framework returns the one whichhas the lowest assignment factor.

A java applet has been developed to evaluate the perfor-mance of the proposed framework. This applet also providesan interface to create network topologies and to show thecalculated energy efficient topologies. The performance ofthe proposed framework has been evaluated under the fourdifferent aspects. First, a predefined case has been examinedand the possible variants of test domains have been pointedout. Then, the behavior of the energy efficiency has beeninterpreted versus the number of eNodeBs . Third, the changein the energy efficiency w.r.t. the overall utilization has beenexamined and modeled with using the regression analysis.Finally, the energy saving ratio has been calculated in the lastsubsection of the performance evaluation.

A. Energy Saving in a Predefined Topology

The results of the proposed framework have been given fora domain in which the attributes of topology are predefined.This domain contains 12 eNodeBs with overall utilizationwhich is equal to 50% . The theoretical best case for thisdomain is to close 6 eNodeBs, because it is 50% utilized.However it is not always a possible topology. The reason isas follows: During the proposed spatial optimization, eNodeBswhich have reached its maximum number of expected UEs willprevent its adjacent eNodeBs from ceasing their operation. Ifwe switch off the adjacent eNodeBs, the scattered UEs fromthese eNodeBs will force the fully loaded eNodeBs to exceedthe δ. So any derived solution will be a unfeasible one. Thissituation highly depends on the spatial attributes (coordinates)of the eNodeBs rather than the number of the eNodeBs in thedomains. An example is given in the Figure 3(b) to give anfurther explanation for this situation. In this example, thereare 7 eNodeBs in the region with the defined utilizations. Weassume the δ is equal to 15, in this case it can be said thattwo eNodeBs which are located in the center of the regionare fully utilized. On the other hand, the other 5 eNodeBshave a very few utilizations with respect to the ones in thecenter and the UEs of these 5 eNodeBs can be satisfied byjust one eNodeB. However it is not possible to cease anyof the eNodeBs’ operation because on each try at least oneeNodeB will exceed its maximum possible utilization. So theframework will be unable to provide any energy efficiency. Butif these eNodeBs with exact same utilizations were positioneddifferently in the region, the framework could switched off thesome of the eNodeBs in order to reduce energy consumption.

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In this test domain, our framework determines 6 possibleoptimal topologies which even contain the theoretical bestcase. The normalized energy efficiency and the normalizedassignment factors of these solutions have been given in theFigure 4(a). Each of these solutions provides different energyefficiency with respect to the assignment factor. As the numberof non-operational eNodeBs increases, UEs are required toassign to a distant operational eNodeBs in order to get service.The required assignment factor increases rapidly in orderto reduce energy consumption near the theoretical best case(which is equal to 0.5) as seen in the Figure 4(a). Theoreticalbest case may provide the best energy efficiency but with theworst costumer satisfaction.

As a result of this evaluation we aim to emphasize thechange of required assignment factor with respect to the energysaving. In the following evaluation sections we primarily showthe energy consumption without assignment factor in order toprovide neat analysis.

B. Energy Efficiency vs Number Of eNodeBs

The energy efficient topologies have been examined in thissection for different topologies which has various number ofeNodeBs. Test domains in this evaluation have the exact samepredefined overall utilization value which is equal to % 60. Butsize of these domains varies from 10 eNodeBs to 30 eNodeBs.

There are four lines in the Figure 4(b) which representthe energy consumption in theoretical best case, the possiblebest case with the least consumption, medians of the solutioninterval between [possible best case line - maximum energyconsumption line] and the maximum energy consumption(where all eNodeBs are operational). The dots in between thepossible best case line and the the maximum energy consump-tion line represent the different possible efficient topologieswhich have lower assignment factors than the dots on thepossible best case line. The relations between assignmentfactor and energy consumption are similar as the one in Figure4(a) for each set of eNodeBs. The points which are closer thethe possible best case line have the greater required assignmentfactors and points on the the maximum energy consumptionline have their required assignment factors equal to zero.

As seen in the Figure 4(b); it is not always possible toreach theoretical best case. It can be conclude that energyefficiency depends on the spatial attributes of the topology(coordinates of the eNodeBs) not the size of the topology(number of eNodeBs).

C. Energy Efficiency vs the Overall Utilization

In this evaluation, the performance analysis has been madeover the domains which has the same set of eNodeBs but withdifferent overall utilization ratio. These test sets contain thesame number of eNodeBs with the exact same coordinates.Overall utilization affects the detection of the energy efficienttopologies. In the Figure 4(c), the results of 9 different sce-narios have been shown which their utilizations differ between10% and 100%. As seen in the Figure 4(c), the probability ofthe detection of the topologies which are near to theoreticalbest case line is increasing while the overall utilization of thesystem is getting lower.

Specifically, three lines have been chosen from the Figure4(c). These are Best Possible Case line (G(u)), Median ofSolution Interval line (M(u)) and Max. Energy Consumptionline (W (u)). (G(u)) defines the best possible energy efficienttopologies with the maximum assignment factor, (M(u)) isdefined by the medians of the possible topology set which triesto optimize both energy and the movement required from UEsand (W (u)) defines the worst energy consumption but withthe zero assignment factor. Relationship between the points onthese lines have been estimated by using regression analysisand the functions for each line have been calculated as inEquation 6.

G(u) = AG · u3 +BG · u2 + CG · u1 +DG

M(u) = AM · u3 +BM · u2 + CM · u1 +DM

W (u) = 1(6)

where A,B,C,D are the coefficients of the cubic regressionanalysis with the error value equals to 2.137 · 10−31. Thesefunctions give the normalized energy consumption ([0, 1]) fora given overall utilization ([0, 1]). These functions have beenused in the sub-section III-D in order to estimate the overallenergy saving.

D. Overall Energy Saving

The usage of an eNodeB for a given time duration T (day)has been modeled by using Gaussian Distribution which is

defined as g (t) = a · e−(t−b

c )2

, where (a, b, c) are the param-eters of the Gaussian Distribution. This function estimates thenumber of the expected UEs of an eNodeB for the time t.In order to acquire the normalized utilization value we shoulddivide the output of the function g(t) by (δ).

If the energy efficient policy ignores the assignment factorand chooses the best possible case in terms of energy efficiencythen the average energy consumption for a day can be derivedfrom the Equations 6. The Overall Energy Consumption isdefined in the Equation 7 as with the function G(u) whereinput of the function u is the normalized utilization of theregion.

OEC = nP

∫ T

0

G(g(t)/δ)dt (7)

where n number of eNodeBs, P is the energy consumption ofan eNodeB during a time T in and OEC is the Overall EnergyConsumption in the duration T . If we expand the functionsG(), g() and evaluate the integral, then OEC can be writtenas follows.

OEC = nP

⎡⎢⎢⎣

a3

δ3AG

a2

δ2BG

aδCG

DG

⎤⎥⎥⎦∫ T

0

[e−( t−b

c)6

e(t−b

c)4

e−( t−b

c)2

1]dt

(8)

If the proposed framework has not been used, it means thatall the eNodeBs are always operational, leading the overallenergy consumption which can be defined as in Equation 9.

MEC = nP

∫ T

0

W (g(t)/δ)dt = T · nP (9)

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5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

Number Of Operating eNodeBs

Nor

mal

ized

Val

ues

Normalized Energy ConsumptionNormalized Assignment Factor

(a)

10 12 14 16 18 3022 24 26 28 30200.5

0.6

0.7

0.8

0.9

1

Number Of eNodeBs

Nor

mal

ized

Ene

rgy

Con

sum

ptio

n

Possible Best CaseMedians of The Solution IntervalTheorical Best CaseMaximum Energy Consumption

(b)

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Overal Utilization

Nor

mal

ized

Ene

rgy

Con

sum

ptio

n

Theorical Best CaseBest Possible CaseMedians of The Solution IntervalMaximum Energy Consumption

(c)

Fig. 4. (a)The Results of the Framework for Predefined Topology, (b) Possible Energy Efficient Topologies for Different Number of eNodeBs, (c) PossibleEnergy Efficient Topologies for Different Overall Utilization

where MEC is the maximum energy consumption.

The following Equation 10 is derived from the Equations 7and 9 in order to calculate the ratio of energy efficiency whichis provided by the proposed framework.

S = 1−nP

∫ T

0G(g(t)/δ)dt

T · nP= 1−

∫ T

0G(g(t)/δ)dt

T(10)

where S is the ratio of the energy saving in the coverage area.

Using the previous evaluations and the equations above, itis concluded that the average energy saving of the frameworkis calculated as 58 percent in this scheme of evaluation.

IV. CONCLUSION

In this paper, a novel energy-efficient SON coverage modelis proposed. The proposed architecture mathematically modelsthe spatial vicinities of all the operating eNodeBs deployedin a specific SON area by proposing a two-parameter spatialfunction. The proposed Voronoi diagram based optimizationprocedure uses this eNodeBs mathematical model to locateless used eNodeBs with redundant network utilization, todeactivate them and to rearrange the coverage area adaptivelywith the remaining active eNodeBs. The proposed optimizationis solved by a novel heuristic with the aid of the proposedassignment factor parameter, which maximizes the utilizationfor the remaining active eNodeBs in the green SON archi-tecture. Evaluation demonstrates that the energy saving of theproposed model due to the deactivation of redundant eNodeBsis almost 58% while maximizing the network utilization.Future work consists of adapting a similar green procedureinto the self-healing and self-configuration features of 3GPPSON architecture.

ACKNOWLEDGMENT

This paper was supported by Turkish Telecom (TT) Re-search Group, TT Collaborative Research Awards, 2014.

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The 11th Annual IEEE CCNC - Smart Spaces and Wireless Networks

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