Finding Green Spots and Turning the Spectrum Dial:Novel Techniques for Green Mobile Wireless Networks

Giordano Fusco∗, Milind Buddhikot†, Himanshu Gupta∗, and Sivarama Venkatesan†

∗Stony Brook University †Alcatel-Lucent Bell Labs{fusco,hgupta}@cs.sunysb.edu {milind.buddhikot,venkat.venkatesan}@alcatel-lucent.com

ABSTRACT

The information and communication technology (ICT) in-dustry accounts for at least 2% of the world energy con-sumption [1], [2], and a considerable part of this energyis consumed by cell phone towers. Currently, resources arestatically allocated to offer the best service during peak hours.Energy could be saved if the power is allocated adaptively,depending on the current users’ demand. We provide analgorithm that minimizes power consumption by selectivelyturning on or off cell towers and deciding which power toassign to the active ones and what frequencies to use, so as tomaintain full coverage and respect users’ capacity demands.This algorithm can be executed at regular time intervals totune up the network adaptively. We ran simulations with realdata, and all experiments show that the total power allocatedis proportional to the number of active users.

I. INTRODUCTION

We propose techniques to optimize energy consumption inthe context of cellular networks. In particular, we exploit twoopportunities for energy usage optimization:

(1) Finding Green Spots in the Network: We minimizeenergy consumption of cell towers by (i) selectivelypowering off certain cell towers, and (ii) assigning onlyminimal power to the active ones, without compromisingon the desired coverage and user-capacity requirements.We propose an algorithm to determine the above selec-tion and assignment to optimize energy consumption.

(2) Turning the Spectrum Dial: We note that signal “propa-gates farther” (i.e., has a lower attenuation rate) at lowerfrequencies, and thus, higher coverage can be providedusing fewer base stations. Here, the resulting higher-interference is managed by powering-off the remainingcell towers and/or using reduced power for the activetowers. Thus, our algorithm (i) selects the set of activecell towers, and (ii) assigns frequencies and powers tothem, so as to satisfy the given coverage and capacityrequirements minimizing the total energy consumption.

By running our algorithm at periodic time intervals, thenetwork can be adaptively tuned up for the current trafficdemand. We ran simulation using real data and we obtainedthat the total power allocated is proportional to the number ofactive users.

II. RELATED WORK

Some recent works have addressed the problem of selectionof cell towers in other to reduce energy consumption, butfor very simple and specific distributions of cell towers. Forinstance, [3], [4], [5], [6] consider star-shaped topologies,and estimate the energy saved by turning off boundary celltowers while enlarging the coverage radius of the central ones.Also, [7] considers a scenario with two operators, each ofwhich covers completely the area. They estimate how muchenergy can be saved by turning off one of them at night andthey consider different switch-off patterns. None of the aboveworks addresses the problem in a general network topology,or proposes an algorithm to select a set of active nodes.

In our work, we minimize only the downlink power, whichis the power used by cell towers to transmit to the users, asopposed to the uplink power used by the users to transmitto the towers. To the best of our knowledge, [8] is the onlywork that has addressed the problem of joint power anduser assignment for the downlink case. However their methodworks only for single frequency, while we are also lookingfor an assignment of frequencies to the users. In addition,they assume that all cell towers are always on, while in ourmodel there is a fixed amount of power needed just to turnon a cell tower. In addition, [9], [10], [11] have addressed theproblem of joint assignment of power and users to the towers,for the uplink transmission. However, uplink and downlinktransmissions have some fundamental differences [8].

We extend a method from [12]. Moscibroda, Wattenhofer,and Zollinger study the problem of assigning power andscheduling a set of links so that they do not interfere eachother. The goal of the their paper is to provide a schedule ofbounded length, while in our case, the goal is to minimize thepower. The other major difference is that the sender-receiverpairs are fixed in [12], while in our case we also determinean assignment of users to cell towers.

III. THE PROBLEM

The goal is to minimize the total energy in a given timeinterval by allocating cell towers’ resources depending onthe current cellular traffic conditions. The energy consumedby a cell tower can be computed using the formula in [13].Since energy is linear in the power allocated to a cell tower,minimizing the power is equivalent to minimize the energy. So,we formulate our problem as a power minimization problem.

2011 IEEE International Symposium on Dynamic Spectrum Access Networks (DySPAN) - Posters

978-1-4577-0178-8/11/$26.00 ©2011 IEEE 613

A. The model

We start by defining the characteristics of cell towers, thenwe will give a formal definition of active users, and finally wewill describe how a cell tower can satisfy an active user.

Definition 1 (Cell tower). Each cell tower t has a givenlocation. The total power of a cell tower is the sum of twofactors, Tt and Pt. The factor Tt is the power needed justto turn t on (for example it accounts for the cooling system,the power amplifier, etc.). When t is on, Pt is the sum of thepower used for communicating with the users.

Definition 2 (Active user). An active user u is one receiving1

(either voice or data). User’s locations are given (we willmention later how to handle users’ mobility). Each user uhas a demand threshold βu for successful communication (thephysical interpretation of βu is explained below). Each activeuser must be assigned to a cell tower, which satisfies hisdemand.

How towers satisfy users. We adopt the signal to inferenceplus noise ratio (SINR) model. A tower t should provide anamount of power Pt,u to a user u such that

SINRu =gt,uPt,uIu +N

≥ βu (1)

where gt,u is the gain of the power from t to u, Iu is the totalinterference perceived by u, and N is the ambient noise. Weassume that the noise N is given in input. The transmissionfrom t to u happens on a certain frequency f which is setwhen u is assigned to t. Each user perceives interferencewhen other towers transmit using the same frequency. LetPi

(f)be the total power used by tower i on frequency f .

Then, the interference perceived by the user u is given byIu =

∑i 6=t gi,uPi

(f)where gi,u is the gain of the power from

tower i to user u. By rearranging the terms, we obtain thata tower t satisfies a user u when the power allocated to thatuser is

Pt,u ≥βugt,u

∑i6=t

gi,uPi(f)

+N

(2)

Each cell tower uses a fraction of its total power to commu-nicate to each user assigned to it. So, the total communicationpower of a cell tower t is given by Pt =

∑u Pt,u.

Physical interpretation. In real applications, when a useru wants to establish a communication, he has a capacitydemand Cu, which represents the bit rate at which he desiresto transmit. We are going to explain how this capacity demandtranslates into a demand threshold. Under appropriate Gaus-sian assumptions, a cell tower t can satisfy the user’s capacitydemand Cu if Shannon’s law Cu ≤ Bu log2(1 + SINRu) is

1In our model, we consider only the downlink transmissions. We believethat the highest energy saving comes from optimizing the power used inthe downlink, becuause downlink transmissions use much higher energy thanuplink ones. Also optimizing the uplink energy is very difficult because it isan inherently distributed problem, since the uplink transmission is done bythe users.

respected. Here, Bu is the bandwidth assigned to user u, andSINRu is the signal to inference plus noise ratio, as explainedabove. We assume that the value of Bu is given, and it dependson the protocol (some protocols allow several values of Bu,but we are leaving that as a future extension). Then, a celltower satisfies the user’s capacity demand, if the power Pt,uis chosen such that

SINRu =gt,uPt,uIu +N

≥ 2Cu/Bu − 1 = βu (3)

B. Problem formulation

We consider the energy saving problem at two differentlevels:• Snapshot: find a power assignment to save energy in a

particular time interval;• Long-term: find power assignments dynamically for a

contiguous set of time intervals.We start by describing the problem for a single time interval:

Problem 1 (Snapshot). We are given:• the location of a set of cell towers T , and for each towert ∈ T , the power Tt needed to turn it on;

• the locations of the active users U and, for each useru ∈ U , an estimation of his demand threshold βu.

The problem is to choose• which towers to turn on, and which total communication

power to allow to each of them,• which tower to assign each user,• which power to allocate to each user,• and which frequency to use in each transmission,

in order to minimize the total power consumption (i.e. sumof cell towers’ activation power and communication power)while satisfying all users’ demands (according to (2)).

Problem 1 is a sub-problem of the following one.

Problem 2 (Long-term). Given periodic estimations of theuser’s capacity demands, determine an optimal solution of theSnapshot Problem for a contiguous set of time intervals.

However, in the rest of the paper, we focus our attention onthe Snapshot problem, because the Long-term Problem can besolved by finding solutions of the Snapshot Problem at regulartime intervals.

C. Estimating the future active users

Our problem requires to know the future users’ locationsand their demand thresholds. This information can be givenfrom an external source, like for example a statistical studyof users’ trends. Otherwise, it could be estimated from therecent traffic load at the base stations. For the purpose of ourproblems, a user’s location can also be looked upon as an“aggregation” of users at that point, with the correspondingtotal demand threshold. This view can help handle mobileusers. In fact, if the users locations are dense enough, thenmobile users can actually move from one location to the otherwhile maintaining their coverage.

614

IV. THE ALGORITHM

We organize the presentation of our algorithm in threeincremental steps. We start by explaining the core method(see Section IV-A), which allows to find an assignment ofusers to towers, to decide which frequency to use and whichpower to allocate to each transmission. This method uses allthe cell towers that are currently on. Then, in Section IV-B,we are going to show how to use Section IV-A’s methodas a subroutine of an algorithm to determine which towerscan be turned off. This algorithm based on the assumptionthat all frequencies belong to the same spectrum band2 andhave similar length of propagation. Finally, we discuss how toextend our algorithm (see Section IV-C) to consider differentset of frequencies with different lengths of propagation.A. Assigning frequencies and power

At the core of our algorithm, there is a method calledUsers Assignment, which finds an assignment of users totowers, and decides which frequency and which power toassign to each transmission. This method receives as inputthe locations of the users and the locations of the towers thatare currently turned on.

The Users Assignment method is composed by two parts.First, we assign users to cell towers, using all availablefrequencies and a “reasonable” amount of power in eachtransmission (Assign All Frequencies subroutine). Then, weminimize the power while keeping the chosen assignment ofusers to towers and frequencies (Optimize Powers subroutine).

The Assign All Frequencies subroutine is an extension ofan algorithm by Moscibroda, Wattenhofer and Zollinger [12].The problem addressed in [12] is a scheduling problem withsome similarities and some differences respect to our problem.We start by describing their scheduling problem, and how itis related to ours, and then we will present our extensions.[12]’s Scheduling Problem. We are given a set of links, withthe corresponding locations of senders and receivers. A linkis successfully scheduled if the SINR at the receiver is biggerthan a given parameter β. The transmission power of eachsender can be set arbitrarily. The goal is to find the shortestschedule (i.e. a sequence of time slots) in which all links aresuccessfully scheduled in one of the time slots.

In a similar way as [12]’s Scheduling Problem, we arelooking for a power to assign to each transmission, suchthat the SINR is respected. Also, [12]’s time slots can beconverted directly into frequencies in our solution, by usingone frequency for each time slot. However, there are somefundamental differences between [12]’s Scheduling Problemand our Snapshot Problem:• Multiple candidate assignments: In [12], each link is

composed by exactly one choice of sender and receiver,while in our problem each user (receiver) can be associ-ated to any one of the cell towers (senders). This impliesthat we need to select one out of a candidate set of links.

2A spectrum band is a contiguous segment of the frequency spectrum. Forthe purpose of our algorithm, a spectrum band represents a set of frequencieswith similar properties.

• Power minimization: Our goal is to minimize the totalpower, while [12]’s goal is to minimize the length of theschedule (which corresponds to minimize the number offrequencies in our case).

It is important to notice that [12]’s algorithm assigns thepower of all links before scheduling them. This is done bysetting the power scaling factor defined as follow, and whichalso plays an important role in our algorithm.

Definition 3 (Power scaling factor). The power scaling factorτ(l) of a link l is an amplification parameter given to its power,which is set to Pl = 4N(3nβ)τ(l)dαl , where N is the noise,n is the number of links, α and β are the SINR parameters,and dl is the distance between sender and receiver.

Since the method in [12] is not robust against shadowing,our method inherits the same problem. In order to be adoptedin practice, we suggest to slightly increase all users’ demandthresholds β. This will help in case some users require moretransmission power to overcome shadowing effects.Our extensions. We now explain our extensions in details,starting from the one to handle multiple candidate assignmentsfor each user.Multiple candidate assignments. In the Snapshot Problem,each user can be assigned to any cell tower. However, assign-ing users to closer towers requires less power than assigningthem to farther towers. For this reason, we restrict the possibleassignments of users to towers as follow. Let d(min)u be thedistance of user u to his closest tower. We allow each user uto be assigned only to towers that are within distance 2d

(min)u .

Note that the factor 2 can be easily extended to any constantk in our algorithm and analysis. In order to let all links of thesame user fit in the same length class, we enlarge the lengthclasses as follow. We consider two overlapping sets of lengthclasses. In one set, length classes are defined as

C ′0 = [0, 2], C ′1 = [2, 8], . . . , C ′i = [22i−1, 22i+1], . . . (4)

and in the other one as

C ′′0 = [1, 4], C ′′1 = [4, 16], . . . , C ′′i = [22i, 22i+2], . . . (5)

Each user is inserted in the length class that can contain all hiscandidate assignments from d

(min)u to 2d

(min)u (ties are broken

arbitrarily).Our algorithm, proceeds in a similar way as [12]’s Schedul-

ing Algorithm, but with the following modifications. Each setof length classes is considered separately. Length classes aremerged into superclasses in a similar way as [12]’s SchedulingAlgorithm. For each superclass S, it considers users u ∈ S indecreasing order of d(min)u . Among the possible assignmentsof u, it chooses the one that can be successfully scheduled theearliest, still making sure that already scheduled links remainsuccessfully scheduled after adding it.Power minimization. Our problem requires to minimize thepower, but [12]’s Scheduling algorithm minimizes the lengthof the schedule, which corresponds to minimize the numberof frequencies. We observe that the power used by [12]’s

615

Scheduling Algorithm depends on the power scaling factorτ assigned to each user, and we suggest to modify [12]’smethod as follow. Let T be the bound on τ . When lengthclasses are merged into superclasses, if the number of classesto be merged is larger than T , then classes are merged intoseveral superlasses, each containing at most T classes. Then,the algorithm proceeds like before. This new parameter T isused in a binary search to find his smallest value, such thatthe length of the schedule is within the number of allowedfrequencies. The extremes of the binary search are 1 and τmax,where τmax = blog ∆c/dlog(3nβ)e is the maximum valuethat τ can assume, and ∆ = 2 maxu d

(min)u .

Power optimization. The power assigned by the method abovemight be higher than what is actually needed. For this reasonafter power and frequencies are assigned as above, we shouldrun a few iteration the following iterative method. At eachiteration, for each user, the Optimize Power method computesthe actual interference from the other users, and it sets theminimum power needed to transmit successfully. This processterminates when not much progress can be made, or afterrunning for a maximum number of iterations.Alternative Heuristic. In our algorithm, we used the value of τas a parameter for the binary search. This is helpful to inheritsome theoretical results from [12] and prove a performanceguarantee on our algorithm (see [14]). However, we also sug-gest a heuristic that gives similar results in practice, but runsslightly faster because it avoids computing an exponentiationat each iteration (see Section V). This heuristic consists insetting the power of each user u to Pu = (I+N)βud

αtu in the

Assign All Frequencies algorithm, and doing a binary searchon I instead of T during the power minimization step.Performance guarantee. The theoretical analysis of the per-formance guarantee of our method is omitted due to lack ofspace. We refer the reader to the full version of the paper [14].

B. Deciding which towers to turn off

In this section, we describe how to use the Users Assign-ment algorithm as a subroutine of an algorithm that determineswhich cell towers can be turn off. We use a greedy algorithm,which starts with all towers on and progressively determinesif there is any advantage in turning off some of them.Towers Selection Algorithm. We start with all towers turnedon, and we run the Users Assignment algorithm to determinethe total power of the current solution. The total power isthe sum of the powers needed to keep the towers on andthe total communication power. Then, we try to turn offeach cell towers in turn and, for each new configuration, werecompute the users assignments. We choose the configurationwith smallest total power and we iterate again. The processterminates when there is no advantage in turning off anyadditional cell tower.

Note that, at each step of the algorithm, we do not need torecompute the full user assignment from scratch. In fact, weonly need to reprocess the superclasses containing the usersassigned to the tower that was just turned off.

C. Algorithm for spectrum selection

We conclude this section by describing an extension tothe algorithms presented in the previous sections that allowsto select different spectrum bands. A spectrum band is acontiguous segment of the frequency spectrum. In the previoussections, we assumed that all frequencies have the samepropagation length. This is true only for frequencies belongingto the same spectrum band and which are close each other. Theextension presented in this section allows to use frequencieswith different lengths of propagation.

We are going to describe the method for two sets offrequencies, coming from two spectrum bands. However, thismethod can be easily extended to a larger number of sets offrequencies.Spectrum Selection Algorithm. The idea is to duplicate the celltowers. We call H one of the copies, and L the other one.The Assign Min Frequencies With Power Bound algorithmis modified as follow. We build two separate frequency’sassignments at the same time, one for H and one for L. Usersare considered one by one like before. Each user has somecandidate assignments with towers in H and some candidateassignments with towers in L. When a candidate assignmentto a tower in H is considered, the user is tested against thefrequency’s assignment for H , and similarly for L. Each useris assigned to the earliest frequency either in the set of H orin the set of L. When the SINR is computed, the appropriatepath loss exponent should be used depending on which set offrequency is being examined.

V. SIMULATIONS

In this section, we present an experimental evaluation ofthe algorithms proposed in Section IV. In all simulations, weuse real locations of cell towers of a large service provider.In Section V-A, we compare the two methods proposed inSection IV on some small-scale scenarios. In Section V-B weconsider some larger-scale scenarios which are more realistic.In particular, we apply our algorithm to an urban area and amore rural one.

A. Comparison between methods

We compare the two methods proposed Section IV. We callτ -method the one that does binary search on T , and I-heuristicthe one that does binary search on I .

In all experiments of this section, we use subsets of celltowers in the network of a large service provider in a denseurban area. We vary the number of cell towers form 25 to 100.We assume that cell towers consume 0W when they are offand require 200W to be turned on.

In the considered regions, we draw a grid. Each grid cellrepresents an “aggregation” of users in that area, and it ispassed as a single active user to the program. We vary thenumber of grid cells from 49 to 256. For each grid cell u,we assume a cumulative capacity demand to bandwidth ofCu/Bu = 1.2, which implies βu = 2Cu/Bu − 1 ' 1.3. Weassume that there are only 30 frequencies available. The pathloss parameter is α = 2.5. The noise is set to N = 10−5.

616

49 100 156 210 256

0

1000

2000

3000

4000

5000

6000

7000

8000

τ methodheuristic I

number of users

tota

l pow

er

25 50 75 100

0

2000

4000

6000

8000

10000

12000

14000

τ methodheuristic I

number of cell towers

tota

l pow

er

(a) (b)

Fig. 1. (a) Total power in function of the number of users with 50 celltowers. (b) Total power in function of the number of cell towers with 256users.

In Figure 1(a), the number of cell towers is kept constantto 50, and the number of users is varied form 49 to 256.As expected, when the number of user increases, the totalpower consumption increases. Figure 1(b) shows the oppositescenario. The number of users is fixed to 256, and the numberof cell towers is varied form 25 to 100. It is interesting toobserve that, as the number of cell towers increases, the totalpower slightly decreases. This can be explained as follow.When the number of cell tower increases, the number ofcandidate assignments for each user increases. Hence, it ismore likely to find an assignment that requires less power.

In both plots in this sections (Figure 1), we can see thatboth methods behaved in a comparable way. However the I-heuristic runs slightly faster, because the τ -method requiresto compute an exponentiation for each user at each iteration.For this reason, we are going to use only the I-heuristic in theexperiments of the next section.

B. Realistic scenarios

In this section, we show the results of the I-heuristic in twolarge scale scenarios:• UA: a subset of cell towers in a dense urban area.• RA: a subset of cell towers in a more rural area.For the UA simulations, we selected an area of 7000 ×

6064 m2 containing 150 cell towers, and for the RA oneswe selected an area of 38110× 46660 m2 containing 300 celltowers. Even if the RA setup has more cell towers than the UAone, its area is much bigger, and hence its density is lower.Like the previous section, we assume that cell towers consume0W when they are off and require 200W to be turned on.

We simulate 3 scenarios:• high load: we draw a grid with 50× 50 = 2500 cells• medium load: we draw a grid with 40× 40 = 1600 cells• low load: we draw a grid with 30× 30 = 900 cells

We could imagine that the high load represents a peak time,while the low load represents an off-peak scenario, like in themiddle of the night. Each grid cell represents an “aggregation”of users, and it is passed as a single active user to the pro-gram. For each grid cell u, we assume a cumulative capacitydemand to bandwidth of Cu/Bu = 1.2, which implies thatβu = 2Cu/Bu − 1 ' 1.3. We assume that each cell tower hastwo spectrum bands, with 100 frequencies each, for a total of

High-load (2500 users)Med-load (1600 users)

Low-load (900 users)

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

UARA

number of users

tota

l pow

er

Fig. 2. Total power in function of the number of users for the UA and RAscenarions.

200 frequencies. The path loss parameter is α = 2.5 for thelower-band frequencies and α = 3.5 for the higher-band ones.The noise is set to N = 10−5.

The results of the I-heuristic are in Figure 2. In both theUA and the RA scenarios, the total power for the low load isless than half the total power for the high load. Since in oursimulations we did not consider the effect of shadowing, theseresults should be taken as an upper bound on the amount ofenergy that can be saved in a real application. However, evenif the precise amount of power saved depends on the particularchoice of parameters and environment conditions, the commontrend in all our simulations is that our algorithm allocates anamount of power proportional to the load conditions.

REFERENCES

[1] McKinsey & Company, “The impact of ict on global emissions,” onbehalf of the Global eSustainability Initiative (GeSI), Tech. Rep., 2007.

[2] Global Action Plan, “An inefficient truth,”http://www.globalactionplan.org.uk/, Report, 2007.

[3] S. Bhaumik, G. Narlikar, S. Chattopadhyay, and S. Kanugovi, “Breatheto stay cool: Adjusting cell sizes to reduce energy consumption,” inGreenComm, 2010.

[4] M. Ajmone Marsan, L. Chiaraviglio, D. Ciullo, and M. Meo, “Optimalenergy savings in cellular access networks,” in GreenComm, 2009.

[5] L. Chiaraviglio, D. Ciullo, M. Meo, and M. Ajmone Marsan, “Energy-efficient management of UMTS access networks,” in ITC, 2009.

[6] ——, “Energy-aware UMTS access networks,” in W-Green, 2008.[7] M. Ajmone Marsan and M. Meo, “Energy efficient management of two

cellular access networks,” in GreenMetrics, 2009.[8] F. Rashid-Farrokhi, K. J. R. Liu, and L. Tassiulas, “Downlink power

control and base station assignment,” IEEE Communications Letters,vol. 1, no. 4, pp. 102–104, 1997.

[9] S. V. Hanly, “An algorithm for combined cell-site selection and powercontrol to maximize cellular spread spectrum capacity,” IEEE Journalon Selected Areas in Communications, vol. 13, no. 7, pp. 1332–1340,1995.

[10] R. D. Yates, “A framework for uplink power control in cellular radiosystems,” IEEE Journal on Selected Areas in Communications, vol. 13,no. 7, pp. 1341–1347, 1995.

[11] R. D. Yates and C.-Y. Huang, “Integrated power control and base stationassignment,” IEEE Transactions on Vehicular Technology, vol. 44, no. 3,pp. 638–644, 1995.

[12] T. Moscibroda, R. Wattenhofer, and A. Zollinger, “Topology controlmeets sinr: The scheduling complexity of arbitrary topologies,” inMobiHoc, 2006, pp. 310–321.

[13] O. Arnold, F. Richter, G. Fettweis, and O. Blume, “Power consumptionmodeling of different base station types in heterogeneous cellularnetworks,” in Future Network and MobileSummit, 2010.

[14] G. Fusco, M. Buddhikot, H. Gupta, and S. Venkatesan, “Finding greenspots and turning the spectrum dial: Novel techniques for green mobilewireless networks,” Bell Labs Internal Technical Memorandum, 2011.

617