dynamic deployment of small cells - universidad de granada

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. [XXX], NO. [XXX], [XXX] 1

Dynamic Deployment of Small Cellsin TV White Spaces

Pablo Ameigeiras, David M. Gutierrez-Estevez, Jorge Navarro-Ortiz

Abstract—The operation of small cells in TV white spaces(TVWSs) represents a coexistence challenge due to their un-planned deployment, their heterogeneous transmission technolo-gies, and the scarcity of TVWS channels in crowded cities.Whenever a new small cell is switched on, a spectrum reassign-ment of already deployed small cells can be used to avoid highinterference and enable coexistence. However, as users may turnon and off their small cells at times, these reassignments may leadto frequent reconfigurations of already deployed small cells. Forthis reason, a solution named Small Cell Dynamic Deployment(SCDD) is designed to reassign TVWS channels only to the smallcells in the neighborhood of the new one. A channel allocationis proposed for SCDD formulated as an exact potential game.Its exact potential function is the sum of the average capacity ofthe small cells considered in the game. Results show that SCDDrequires a few channel reconfigurations of already deployed smallcells because the channel assignment outside the neighborhoodof the new cell remains unchanged. However, SCDD providesa performance similar to the case in which the allocation maymodify the channels of all small cells already deployed.

Index Terms—TV White Space, small cell, channel allocation,potential games, game couplings.

I. INTRODUCTION

ACCORDING to the latest global mobile data trafficreports [1][2], mobile data traffic is experiencing an

unprecedented growth, and it is expected to keep growingat a high rate in the coming years. This explosive growthhas accentuated the spectrum shortage for commercial mobileradio services [3].

One way that can contribute to deal with the spectrumscarcity problem is the usage of TV white spaces (TVWSs).This allows unlicensed operation in a TV channel that is notbeing used by any licensed service at a particular location

Manuscript received March 2, 2014; revised [DATE]; accepted September21, 2014. Date of publication [DATE]; date of current version [DATE]. Thiswork was supported by the Spanish Ministry of Science and Innovation(project TIN2013-46223-P) and the ”Granada Excellence Network of Innova-tion Laboratories” (GENIL) project (project PYR-2014-18).

Copyright (c) 2013 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

Pablo Ameigeiras and Jorge Navarro-Ortiz were visiting researchers withthe Broadband Wireless Networking Laboratory, School of Electrical andComputer Engineering, Georgia Institute of Technology, USA. Their researchstays were funded by the GENIL scheme for Stays Abroad for PHDs (GENIL-SAP). They are with the Department of Signal Theory, Telematics andCommunications of the University of Granada, Granada, 18071 Spain (e-mail:[email protected]; [email protected]).

David M. Gutierrez-Estevez was a PhD student with the Broadband Wire-less Networking Laboratory, School of Electrical and Computer Engineering,Georgia Institute of Technology, USA (e-mail: [email protected]).He is now Principal Engineer with Huawei Technologies in Santa Clara, CA,USA.

and at a particular time. In September 2010, the FederalCommunications Commission (FCC) released revised rulesregarding access to the TVWSs in the USA [4] including theregulation of a TV band database that provides information onthe available channels at a given location.

Another partial solution to deal with the traffic growthand the spectrum scarcity is traffic offloading through smallcells and Wi-Fi access points (APs) [5]. Small cells are low-power operator-managed wireless access points that operate inlicensed spectrum [6].

In this paper, we concentrate on the operation of smallcells in the TVWSs as a mechanism to offload traffic frommobile networks. One of the main challenges for networksoperating in TVWSs is their coexistence [7]. Very differentnetwork technologies such as IEEE 802.11af [8], ECMA 392[9], IEEE 802.22 [10] and 3G or 4G mobile technologiescould potentially benefit from operating in the TV band spec-trum. However, these technologies present very heterogeneouscharacteristics including network architecture, device category,transmission power, operational bandwidth, modulation andcoding schemes, and especially medium access techniques(e.g. TDMA, CSMA/CA, and OFDMA). Hence, the simul-taneous operation of these systems in the same channelsis challenging. In this respect, the IEEE 802 LAN/MANstandards committee approved the P802.19.1 standardizationproject to develop a standard for coexistence among dissimilaror independently operated wireless devices and networks [11].IEEE 802.19.1 system proposes an architecture for eitherdiscovery service or management service. With the first ser-vice, the system detects neighbor networks which may causeharmful interference. With the second, the system decidesoperational parameters for the coexisting networks [12].

Several researchers have investigated coexistence inTVWSs. In [13], Filin et.al. evaluated the performance of thediscovery service of the IEEE 802.19.1 coexistence system atthe early stages of the standard development. Similarly, in [14]Wang et.al. designed a registration signaling procedure for theIEEE 802.19.1 system, and evaluated its impact on the channelselection decisions taken by TVWS networks for coexistence.Their results already point out the potential benefits of theIEEE 802.19.1 system’s discovery service. In [15], Jankuloskaet.al. proposed a joint power and channel allocation algorithmfor Wi-Fi-like systems operating in TVWSs. Their solutionis based on a Nash Bargaining, and it aims at maximizingthe number of supported users. In [16], Ye et.al. expressedthe coexistence in TVWSs as a total interference minimiza-tion problem. They used Simulated Annealing (SA) to dealwith the optimization problem and provided an algorithm to

2 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. [XXX], NO. [XXX], [XXX]

automatically choose the parameters required for SA.We refer the reader to [17]-[19] and references therein for a

comprehensive overview of spectrum allocation algorithms ingeneral cognitive radio networks. In [20], Peng et.al. proposedto reduce the spectrum allocation problem to a variant ofthe graph coloring problem. However, solutions based ongraph coloring are optimized for a fixed topology, and needto be refreshed up on topology changes. In [21], Cao et.al.proposed a distributed approach to spectrum allocation fornetworks with frequent topology changes, such as mobile ad-hoc networks. The same authors further delved into distributedspectrum management architectures in [22],[23]. Although thesolutions in [21]-[23] are interesting, they assume a simplisticinterference model in which interference is merely modeledwith a binary geometry metric.

In this paper we aim at designing a coexistence solutionfor a network of unplanned small cells in TVWSs by meansof channel allocation. As users may turn on and off theirsmall cells at times [24], channel reassignments may leadto frequent reconfigurations of already deployed small cells.These reconfigurations would ultimately degrade the qualityexperienced by the end users. For this reason, we proposea Small Cell Dynamic Deployment (SCDD) solution, whichreassigns TVWS channels to only the small cells in the neigh-borhood of a recently switched on small cell. The channels ofthe small cells outside the neighborhood are unaffected. Thegoal is to reduce the number of already deployed small cellsthat require a channel reassignment each time a new small cellis deployed.

In combination with the limited neighborhood conceptfor dynamic deployment, SCDD includes a novel channelallocation algorithm that incorporates an interference modelmuch more accurate than the one in [21]-[23]. We formulatethe coexistence problem as a maximization of the averagenetwork capacity. To solve it, we propose a non-cooperativegame in which the players are the small cells. The utilityfunction associated to each small cell includes its averagecapacity and the corresponding degradation caused to the restof the small cells due to interference. We will demonstrate thatthis game is an exact potential game, and its exact potentialfunction is equal to the average network capacity. Therefore,in this game the small cells are jointly trying to maximizethe average network capacity. To be able to incorporate theaverage cell capacity in the utility function of our game, webase our solution on the IEEE 802.19.1 architecture. Ourproposed SCDD solution could be incorporated in a practicalimplementation platform as the one presented in [25].

The main contributions of this paper are the following:• The proposal of a novel exact potential game to enable

coexistence through channel allocation for small cells inTVWSs. The exact potential function of the game is theaverage network capacity.

• The proposal of applying channel allocation in a smallneighborhood around a new small cell instead of consid-ering all small cells already deployed. In addition, thedemonstration that the exact potential property of theproposed game is preserved when the channel allocationof the small cells outside the neighborhood is fixed.

Fig. 1. IEEE 802.19.1 system architecture.

• We show that if the limited neighborhood includes asufficient number of small cells, the proposed channelallocation game provides a performance similar to thecase in which the game is applied to all the small cells.

• The proposal of an adaptive algorithm that dynamicallyestimates the required number of small cells and reassignsTVWS channels to them. This algorithm achieves avery low number of TVWS channel reallocations in thealready deployed small cells whereas the performancedegradation is almost negligible compared to spectrumreassignment applied to the whole network.

Although our solution has been specifically designed forTVWSs, if similar coexistence information is available forother systems (e.g. with dedicated spectrum), our solutionwould also be applicable in such systems.

The rest of the paper is organized as follows. The systemmodel is presented in section II. The general problem formu-lation and the exact potential game for channel allocation areexplained in section III. The proposed channel allocation usinga limited neighborhood is presented in section IV. The SCDDsolution and its dynamic estimation of the neighborhood size isdescribed in section V. The performance results are presentedin section VI. Finally, the main conclusions are drawn insection VII.

II. SYSTEM MODEL

LET us consider a network of small cells that operatein TV white spaces. These small cells provide wireless

access to users located within their coverage area. Hereafter,we will refer to these small cells simply as nodes. Let usdenote the overall set of nodes in the network as L = 1, ..., l.These nodes are controlled by a Coexistence Manager CM 1

[12], which provides operational parameters to its networknodes to enable coexistence (see Fig. 1). For the sake ofreadability, we have included a table with all the variablesused in this paper in Appendix B.

The network nodes are assumed to operate as portable modeII devices, so that they can signal their geolocation. However,the user’s terminals may operate as portable mode I devices,

1In order to improve scalability, several CMs can be used to control alarge deployment of small cells. We assume that the involved CMs wouldcooperate as if they were only one CM by using the centralized decisionmaking [26]. It shall also be noticed that the required signaling for registrationand reconfiguration commands is low [26].

AMEIGEIRAS et al.: DYNAMIC DEPLOYMENT OF SMALL CELLS IN TV WHITE SPACES 3

which may not have geolocation capability. The CoexistenceManager has information about the location of each nodei ∈ L, but it has no information about the locations of theuser’s terminals. We assume that user’s terminals are uniformlydistributed within the nodes coverage area. We also assumethat both the nodes and the terminal devices transmit at a fixedpower on each channel. Note that the maximum transmissionpower is 40mW in adjacent TV channels and 100mW in non-adjacent ones.

The Coexistence Manager CM has information about theset of TVWS channels K = 1, ..., k available for operationbased on signaling from a TVWS database. We representthe set of channels used by node i ∈ L with a vectorsi = c1, ..., cj , ..., cnT where ∀j cj ∈ K. We also assumethat each node has a number of available radios that limitsthe maximum number of channels used by the node, i.e.∀i, |si| ≤ ri, where ri is the number of node i’s availableradios. We define function δ(si, c) for node i and channel cas:

δ(si, c) =

0, if c ∈ si

1, if c /∈ si(1)

Additionally, let Si be the set of all possible channel com-binations available to node i, and S the channel combinationspace, that is the Cartesian product of each node’s set ofpossible channel combinations, i.e. S = S1× ...×Si× ...×Sl.

Let us assume that each node i ∈ L has a coverage regionRi, and a user served by node i on channel c and located ata position (x, y) ∈ Ri has a signal to interference ratio γc

i :

γci (x, y,s1, ..., si, ...sl) =

gi(x, y) · Pic

Ic(x, y) +∑∀j∈L,j =i gj(x, y) · Pjc · δ(sj , c)

(2)

where Ic denotes the primary to secondary interference onchannel c plus thermal noise, Pic the transmission power ofnode i on channel c, and gi(x, y) the path gain from node ito position (x, y).

To simplify our model, we disregard the effect of fastfading in the signal to interference ratio. Nevertheless, γc

i

is not constant in our system because the path gain fromeach node gi vary with the user location due to the effectsof deterministic path loss and shadow fading. Likewise, theprimary to secondary interference also vary with the userlocation. Futhermore, γc

i also depends on the set of channelss1, ..., si, ...sl used by the nodes in L.

The maximum data rate of a user served by node ion a channel c can be calculated by the Shannon capac-ity as V c

i = Wu log2(1 + γci (x, y, s1, ..., si, ...sl)), where

Wu is the fraction of the channel bandwidth assigned bythe node to the user. As γc

i is not constant, V ci is not

constant too. Then, we compute its average E[V ci ] =∫∞

0Wu log2(1 + γc

i ) pγci(γc

i /s1, ..., si, ...sl)dγci over posi-

tions (x, y) ∈ Ri and assuming a fixed channel allocations1, ..., si, ...sl. pγc

i(γc

i /s1, ..., si, ...sl) denotes the conditionalprobability density function of the signal to interference ratioof a user served by node i on channel c, located in po-sitions (x, y) ∈ Ri, and conditioned to channel allocation

s1, ..., si, ...sl. We define the average capacity of node i overregion Ri on channel c as the sum of the average maximumdata rates of all users served by this node on this channel[27]. Considering a TDMA, FDMA, or TDMA-FDMA systemin which all users are allocated the same bandwidth, E[V c

i ]becomes the same for all users served by node i. In that case,the average capacity of node i over region Ri on channel ccan be expressed as:

f(i, c/s1, ..., si, ...sl) =∑∀u∈i

E[V ci ] =

∑∀u∈i

∫ ∞0

Wu log2(1 + γci ) pγc

i(γc

i /s1, ..., si, ...sl)dγci =∫ ∞

0

W log2(1 + γci ) pγc

i(γc

i /s1, ..., si, ...sl)dγci

(3)

where u ∈ i denotes that the user is served by node i, and Wis the bandwidth of channel c.

We assume that CM has information about the transmissionpower and the location of a each node ∈ L. Hence, itcan evaluate the signal level received from each node ata given position (e.g. based on Radio Environment Maps).We assume that CM can use such information to estimatethe average capacity f(i, c/s1, ..., si, ...sl) by integrating theShannon capacity W log2(1 + γc

i (x, y, s1, ..., si, ...sl)) overthe coverage region Ri.

III. PROBLEM FORMULATION: ENABLING COEXISTENCEBY CHANNEL ALLOCATION

IN this section we make a proposal to provide coexistencebetween the nodes ∈ L through the execution of a novel

channel allocation algorithm. We mathematically formulatethe coexistence problem as a channel allocation problem inwhich the objective is the maximization of the average networkcapacity. We compute the average network capacity as the sumof the average node capacity of all nodes ∈ L:

ΩL =∑∀j∈L

∑∀c∈K

f(j, c/s1, ..., si, ...sl) · δ(sj , c) (4)

Then, the coexistence problem is formulated as follows:

maxsi,∀i∈L

ΩL

subject to |si| ≤ ri, ∀i ∈ L(5)

This optimization problem is equivalent to a 0-1 integerprogram in which the variables are equal to δ(si, c). Therefore,it belongs to the class of NP-hard problems [28]. All the exactalgorithms for its solution have an exponential complexity. Forthat reason, next we propose a game theoretical approach todeal with this coexistence problem. We consider the followingnon-cooperative game ΓL = ⟨L, Si ∀i ∈ L, Ui ∀i ∈ L⟩,where each node i is a player with a strategy space Si and autility function Ui. Let us define the utility function as:


Ui =∑∀c∈K

δ(si, c) ·[f(i, c/s1, ..., si, ...sl)

−∑

∀j∈L,j =i

(f(j, c/s1, ...,∅, ...sl)

− f(j, c/s1, ..., si, ...sl))· δ(sj , c)

]=∑∀c∈K

δ(si, c) ·[∑∀j∈L

f(j, c/s1, ..., si, ...sl) · δ(sj , c)

−∑

∀j∈L,j =i

f(j, c/s1, ...,∅, ...sl) · δ(sj , c)]

(6)

The objective of utility function Ui is to evaluate thepotential average network capacity benefit if node i transmitson channel c. For this, we include in Ui the average capacityachieved by node i if transmits on channel c. Additionally,we subtract in Ui the degradation of the average capacity ofthe rest of nodes transmitting on channel c if node i uses thischannel. This measure is computed over all channels on whichnode i transmits. Then, we can have the following theorem:

Theorem 1: The non-cooperative game ΓL =⟨L, Si ∀i ∈ L, Ui ∀i ∈ L⟩ is an exact potential game, andits exact potential function is:

PL(s1, ..., si, ...sl) = ΩL (7)

That is, the exact potential function PL : S → R satisfies∀i ∈ L and si, si

′ ∈ Si:

Ui(si, s−i)− Ui(si′, s−i) = PL(si, s−i)− PL(si

′, s−i) (8)

where s−i is the set of strategies selected by players ∈ Lexcept player i.

Proof: The proof of Theorem 1 is given in Appendix A.

Since our proposed game has an exact potential and thenumber of players and their strategies is finite, the game hasthe finite improvement path (FIP) property. This means that,regardless of the order of the play and the initial conditionof the game, the myopic learning process based on one-sidedbetter reply dynamic converges to a Nash equilibrium [29].Moreover, in a potential game players try to jointly maximizethe potential function PL [29]. Hence, in game ΓL playerstry to maximize the average network capacity, which was theobjective of the coexistence problem formulation.

IV. CHANNEL ALLOCATION ON A LIMITEDNEIGHBORHOOD

THE consumer deployment of small cells in TV WhiteSpaces is expected to lead to a frequently changing

interference scenario due to users turning on and off their smallcells. To accommodate a new small cell, the strategy of apply-ing channel allocation to all small cells previously deployedin the network would possibly trigger the reconfiguration of alarge number of small cells. With such a strategy, the channelsassigned to the new small cell would affect the channels of itsneighbors, which, in turn, could affect the channels of theirneighbors, propagating hence the changes. For that reason, inthis section we propose a new optimization problem in which

Fig. 2. Channel allocation on a limited neighborhood.

only the new small cell and a set of neighbor small cells aresubject to change their channels (see Fig. 2). The channels ofthe small cells outside the neighborhood remain unaffected.

Let us n denote the new node to be switched on. Let usassume that CM partitions the set of nodes ∈ L in threedisjoint subgroups. First, set N1 includes the node n andits neighbor nodes. These nodes are subject to change theirchannels. Second, set N2 represents the nodes outside theneighborhood of node n, thus N1 ∩ N2 = ∅. These nodesdo not change their channel, but their level of interferencemay influence the channel assignment of nodes ∈ N1. Wedefine set N as N = N1 ∪ N2. Third, the remaining nodes∈ L \N , are ignored in the problem formulation since thoseare considered to have a negligible interference impact on thechannel assignment of nodes ∈ N1.

In this scenario we compute the average network capacityof the nodes ∈ N as:

ΩN =∑∀j∈N

∑∀c∈K

f(j, c/s1, ..., si, ...sn) · δ(sj , c) (9)

With these assumptions, the coexistence problem is nowformulated as follows:

maxsi,∀i∈N1

ΩN

subject to |si| ≤ ri,∀i ∈ N1(10)

Let us consider the game ΓN =⟨N, Si ∀i ∈ N, Ui ∀i ∈ N⟩. ΓN is equal to the game ΓL

presented in section III but just comprising the nodes ∈ N .Therefore, its potential function is PN (s1, ..., si, ...sn) = ΩN .In addition, the utility function Ui for this game onlyconsiders the nodes ∈ N . To solve (10), we have to restrictthe game ΓN to be played only by the nodes ∈ N1. For this,we apply to ΓN the concept of game-couplings presented in[30].

Definition 1: ΓN is a (N1, ..., NJ )-coupling of P-games if:• N1, ..., NJ are groups partitioning N , i.e. N j ∩ N j ′ =

∅,∀j, j′ \ 1 ≤ j ≤ j′ ≤ J , and N1 ∪ ... ∪NJ = N . Thegroups are fixed: no player can choose its group.

• For any j and any fixed vector s−j ∈ S−j of playersin N−j , the sub-game ΓN |N−j←s−j (played by N j) hasproperty P . N−j is the set of nodes /∈ N j , and S−j =×i∈N−jSi is the strategy space of the nodes ∈ N−j .


ΓN |N−j←s−j denotes the sub-game of ΓN (played byN j) that arises when the strategies of the nodes outsidegroup j are fixed according to s−j .

We consider ΓN as a (N1, N2)-coupling of games in whichN1 and N2 are the nodes inside and outside the neighborhoodrespectively. We denote as S1 = ×i∈N1 si and S2 = ×i∈N2 sithe strategy space of the nodes N1 and N2 respectively.ΓN |N2←s2 denotes the sub-game played only by the nodes∈ N1, in which the strategies of the nodes ∈ N2 are fixedaccording to their selected strategies s2 ∈ S2.

To solve (10), we aim at verifying that the sub-gameΓN |N2←s2 is an exact potential game.

Theorem 2: The sub-game ΓN |N2←s2 is an exact potentialgame.

Proof: As PN is the potential function of ΓN then, bydefinition, it satisfies:

Ui(si, s−i)− Ui(si′, s−i) = PN (si, s−i)− PN (si

′, s−i),

∀i ∈ N(11)

If we consider any node i ∈ N1, then s−i = s1−i∪s2, wheres1−i is the set of strategies selected by players ∈ N1 exceptplayer i. Then, from (11) it follows that:

Ui(si, s−i)−Ui(si′, s−i) =

Ui(si, s1−i, s

2)− Ui(si′, s1−i, s

2) =

PN (si, s1−i, s

2)− PN (si′, s1−i, s

2) =

PN |N2←s2(si, s1−i)− PN |N2←s2(si

′, s1−i),

∀i ∈ N1

(12)

where PN |N2←s2 is the potential function for the gameΓN |N2←s2 . Since ΓN |N2←s2 is an exact potential game, theexact potential property of the channel allocation game ispreserved when the channel allocation of the nodes outsidethe neighborhood is fixed.

V. SMALL CELL DYNAMIC DEPLOYMENT SOLUTION

IN this section we propose an adaptive solution that providesthe set of small cells composing the limited neighborhood

and their assigned channels. This solution is named Small CellDynamic Deployment (SCDD). The Coexistence Manager isassumed to apply SCDD whenever a new node is switchedon. The goal of SCDD is to reduce the number of small celreconfigurations while achieving an interesting performance.For this goal, SCDD evaluates the performance of the gameΓN |N2←s2 proposed in section IV for various sets of neighbornodes. SCDD selects the smallest neighborhood that yields aperformance similar to applying channel allocation in a largeset of neighbor nodes. The performance is measured in termsof average network capacity and network throughput at 5%outage. The latter performance indicator is defined next.

Let us Vi denote the maximum data rate of a user located ata position (x, y) ∈ Ri and served by node i on all its channels.We calculate it as:Vi(x, y, s1, ..., si, ...sn) =∑∀c∈K

V ci (x, y, s1, ..., si, ...sn) · δ(si, c) =∑

∀c∈K

Wu log2(1 + γci (x, y, s1, ..., si, ...sn)) · δ(si, c)

(13)

As in the case of γci , Vi varies with user locations (x, y) ∈ Ri

and the set of channels s1, ..., si, ...sn used by the nodesin N . Considering a fixed channel allocation, the randomvariable Vi has a conditional probability density functionpVi(vi/s1, ..., si, ...sn).

We further define a random variable V that denotes themaximum data rate of a user located at position (x, y) ∈ R,where R =

∪∀iRi. V = Vi if the user is located in region Ri

and served by node i. Let pV (v/s1, ..., si, ...sn) denote theconditional probability density function of V conditioned tochannel allocation s1, ..., si, ...sn. It can be derived as follows:

pV (v/s1, ..., si, ...sn) =∑∀i∈N

pVi(v/u ∈ i, s1, ..., si, ...sn) · p(u ∈ i) (14)

where u ∈ i denotes that the user is located at a position(x, y) ∈ Ri and served by node i, and p(u ∈ i) is theprobability of that event. Then, we denote Ψ as the networkthroughput at 5% outage, and define it as the value that fulfills:∫ Ψ

0

pV (v/s1, ..., si, ...sn)dv = 0.05 (15)

We also assume that CM can estimate the network throughputat 5% outage based on its information of the received signallevel from each node.

Next, we describe the SCDD algorithm. Whenever a newnode n is to be deployed, the algorithm starts by selecting theset of all its interfering nodes N . For this, the algorithm in-cludes in set N each node i which satisfies that the interferencelevel to node n on some channel exceeds a given threshold, i.e.Pi ·gni > interference threshold. gni denotes the path gainfrom node i to node n, and Pi is the maximum transmissionpower of node i on any channel, i.e. Pi = max∀c∈KPic.

Next, the set of neighbor nodes N1 is to be derived. Toderive N1, the SCDD algorithm sorts the nodes ∈ N bydescending level of path gain gni. The resulting set N fulfills∀i, j ∈ N , i < j ⇒ gni ≥ gnj . Then, the algorithm createsset N1 composed of the first num of neigh nodes of set Nand the new node n.

The algorithm iteratively considers different sets N1 withdifferent number of neighbors. It starts with maxN1 neigh-bors, and it later reduces them down to minN1 in steps of∆num of neigh. In each iteration, the algorithm derives theset N2 = N \ N1, plays the sub-game ΓN |N2←s2 , andextracts the statistics. Additionally, the algorithm identifiesthe maximum average network capacity Ω∗ and the maximumnetwork throughput at 5% outage Ψ∗ across all iterations.

After all iterations, the algorithm selects the optimumnumber of neighbors as the minimum number for which theaverage network capacity and the network throughput at 5%outage exceed a certain threshold thr relative to Ω∗ and Ψ∗.

VI. PERFORMANCE RESULTS

In this section we present the results of the performanceevaluation of the potential games presented in sections III andIV, and the SCDD solution presented in section V.


SCDD Algorithm1. Select N

N ← i \ Pi · gni > interference threshold2. Sort nodes in N by descending gni

N ← N

for ∀i, j ∈ N dogni ≥ gnj ⇒ i < j

end for3. Iteratively determine N1 and play sub-game ΓN |N2←s2

Ω∗ = 0, Ψ∗ = 0for num of neigh = maxN1 : ∆num of neigh : minN1 do

N1 ←i \ i ∈ N, i ≤ num of neigh

N1 ← N1 ∪ nN2 ← N \N1

Play sub-game ΓN |N2←s2 and extract statistics Ω and ΨΩ(num of neigh) = ΩΨ(num of neigh) = Ψif Ω > Ω∗ then Ω∗ = Ω end ifif Ψ > Ψ∗ then Ψ∗ = Ψ end if

end for4. Select N1

optnum of neighopt ←minnum of neigh \

Ω(num of neigh) > thr · Ω∗ ANDΨ(num of neigh) > thr ·Ψ∗

N1opt ←

n ∪

i \ i ∈ N, i ≤ num of neighopt

A. Simulation setup

For the performance evaluation, we have implemented anetwork simulator in MatLab [31] that computes the path loss,the signal level and the average node capacity. The consideredscenario and the simulation setup are described next.

The deployment area is a square of size 200m x 200m. Aset of 20 nodes are randomly distributed over the area. Thepath loss is computed according to the model for suburbanareas presented in [32]. The model includes a Gaussianrandom variable that accounts for the shadowing effects atthe indoor receiver. We set its standard deviation equal to6.4dB as described in [32] for suburban residence. Availablechannels are assumed to be adjacent TVWS channels, so thetransmission power of all nodes is set to 40mW. The primaryto secondary interference plus the thermal noise is assumedto be -100dBm for all considered channels. We consider amaximum number of available TVWS channels equal to 10,which is in consonance with the values provided by Hessarand Roy in [33]. They report an average number of availableTVWS channels equal to 7.3 for portable/personal devices inareas with a minimum population density of 1000 persons persquare mile. They also report an average number of availableTVWS channels ranging from almost zero to 9.8 in selectedcities of the United States. Each node i is assumed to serve acircular crown region Ri. This region is centered at the nodelocation and has inner and outer radiuses of 2m and 20mrespectively. The area of the deployment scenario is dividedinto pixels of size 1m x 1m. The simulator calculates the signalto interference ratio and the Shannon capacity in the pixels ofregion Ri ∀i. From this, the simulator computes the averagenode capacity for all nodes, and the network throughput at5% outage. Nodes are assumed to have a number of availableradios that limits the maximum number of channels they

can transmit on. In our simulations we consider 1, 2 and 4radios per node, which is similar to the frequency segmentsdefined in IEEE 802.11af [8] and could be applicable to LTE-A small cells using several component carriers. Nodes are notallowed to select a strategy with less than 1 radio. 50 snapshotshave been simulated for each analyzed case and the resultshave been averaged from all snapshots. Snapshots are networkinstances with different node locations in the deployment area.

We consider a static and a dynamic deployment scenario.In the static scenario, at the beginning of each snapshot allnodes are deployed together and a random channel assignmentis carried out. Then, the game is executed. The initial channelassignment for the game is the random channel assignment.In the dynamic scenario, the deployment starts without anynetwork node. Later, nodes are deployed one by one untilcompleting all nodes. Each time a new node is deployed,the set of neighbor nodes N1 is derived and the game isexecuted. The initial channel assignment for the game isthe one provided by the game when the previous node wasdeployed.

B. Analysis of the performance results

1) Channel allocation applied to all network nodes: In thissubsection we present the results obtained in the evaluation ofthe potential game presented in section III. A static deploymentscenario is considered. We evaluated the cases of numberof available channels = [2,3,4,5,6,7,8,9,10] and number ofavailable radios = [1,2,4]. Fig. 3 and 4 depict the averagenetwork capacity and the network throughput at 5% outagerespectively.

For comparison purposes, we implemented Peng’s solutionfor spectrum assignment [20], which is based on a graphcoloring approach. We utilized the centralized Max-Sum-Reward rule since it has a similar objective to our solution, i.e.to maximize the total throughput in the system. We assumetwo nodes interfere with each other if they are located within adistance of 40m, that is, twice the radius of the node coverageregion. Peng’s channel reward is constant over all nodes inour considered scenario. We refer to this solution as ’Graph’.The performance of the random channel assignment (referredas ’Random’) is also included for comparison.

The results show that the game yields an increased averagenetwork capacity with a higher number of available channelsor a higher number of available radios. Similarly, the gameproduces an increased network throughput at 5% outage witha higher number of available channels. However, it presentsa reduced network throughput at 5% outage with a highernumber of available radios. This is because a larger number ofavailable radios implies a higher frequency reuse, and thereforean increased interference level especially at the edge of theregion served by each node. Although the bandwidth of thenode also increases with the number of radios, the first effectis predominant when the number of available channels isrelatively low.

Another observation is that a player (node) may select anumber of channels lower than its number of available radios(see Fig. 5). This is controlled by the utility function Ui


2 3 4 5 6 7 8 9 100.5

1

1.5

2

2.5

3

Number of Available Channels

Ave

rage

Net

wor

k T

hrou

ghpu

t (G

bps)

1 Radios−Game1 Radios−Graph1 Radios−Random2 Radios−Game2 Radios−Graph2 Radios−Random4 Radios−Game4 Radios−Graph4 Radios−Random

Fig. 3. Performance of channel allocation applied to all nodes of the network:average network capacity.

2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35

40

45


Net

wor

k T

hrou

ghpu

t at 5

% O

utag

e (M

bps)

1 Radios−Game1 Radios−Graph1 Radios−Random2 Radios−Game2 Radios−Graph2 Radios−Random4 Radios−Game4 Radios−Graph4 Radios−Random

Fig. 4. Performance of channel allocation applied to all nodes of the network:network throughput at 5% outage.

defined in (6). If a node transmits on a large number ofchannels it causes a degradation of the average capacity of therest of the nodes of the network due to increased interference.If this degradation is larger than the average capacity obtainedby this node, then it reduces the number of selected channelsto improve its utility. The effect is more pronounced for alarger number of available radios or lower number of availablechannels.

As it can be observed, the performance (both the averagenetwork capacity and the network throughput at 5% outage)of our solution outperforms both the graph coloring andrandom approaches. Moreover, for certain snapshots, the graphcoloring approach switches off some nodes, which degradesthe performance, and in particular the network throughput at5% outage.

2 3 4 5 6 7 8 9 100.5

1

1.5

2

2.5

3

3.5

4


Ave

rage

Num

ber

of T

rans

mitt

ing

Rad

ios

1 Radios2 Radios4 Radios

Fig. 5. Performance of channel allocation applied to all nodes of the network:average number of transmitting radios.

TABLE IPERFORMANCE OF CHANNEL ALLOCATION IN STATIC AND DYNAMIC

DEPLOYMENTS: NETWORK THROUGHPUT (MBPS) AT 5% OUTAGE.

Available Deployment Available Channelsradios scenario 2 4 6 8

static - 0.9 8.1 13.24 radiosdynamic - 1.4 6.8 10.2

static 0.5 6.3 17.9 322 radiosdynamic 0.5 5.6 16.2 27.7

static 0.9 12.5 26 35.41 radiodynamic 0.9 12.5 26 35.7

2) Channel allocation in a limited neighborhood: In thissubsection we present the results obtained in the evaluation ofthe potential game presented in section IV. For this evaluationa dynamic deployment scenario is considered. We evaluatedthe cases of number of available channels = [2,4,6,8,10],number of available radios = [1,2,4], and number of neighbors= [0,2,4,6,8,10].

The obtained results present the following trends: 1) For allevaluated cases of available channels and radios, the networkthroughput at 5% outage is considerably reduced for a verylow number of neighbors (see Fig. 7 for the case of 4 availableradios). However, increasing the number of neighbors beyonda certain value does not yield any benefit in terms of networkthroughput at 5% outage. On the other hand, for all evaluatedcases of available channels and radios, the effect of the numberof neighbors on the average network throughput is minor(see Fig. 6 for the case of 4 available radios). 2) For allevaluated cases of available channels and radios, the usageof a sufficient number of neighbors provides a performancesimilar to the case when the neighborhood includes all nodesalready deployed (see the triangles on the right of Fig. 6 and7). 3) Although not depicted here, the effect of the reduction ofthe network throughput at 5% outage in a small neighborhoodis less pronounced with fewer available radios.

Additionally, the performance differences between the static


0 1 2 3 4 5 6 7 81.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

Number of Neighbors

Ave

rage

Net

wor

k T

hrou

ghpu

t (G

bps)

limited neighborhoodall nodes

10 Channels

8 Channels

6 Channels

4 Channels

Fig. 6. Performance of channel allocation applied in a limited neighborhood:average network capacity. Number of available radios ri equals 4.

0 1 2 3 4 5 6 7 80

5

10

15

20

25

Number of Neighbors

Net

wor

k T

hrou

ghpu

t at 5

% O

utag

e (M

bps)

limited neighborhoodall nodes

4 Channels

10 Channels

8 Channels

6 Channels

Fig. 7. Performance of channel allocation applied in a limited neighborhood:network throughput at 5% outage. Number of available radios ri equals 4.

and dynamic deployment scenarios are also worth mentioning.See the comparison of the network throughput at 5% outagefor both cases in Table I. In these results the dynamic deploy-ment case considers a neighborhood composed of all nodesalready deployed. The static scenario provides an improvednetwork throughput at 5% outage over the dynamic one fora large number of available channels with two and especiallyfour radios. In the dynamic scenario nodes are deployed one byone, and the non-cooperative game is executed each time a newnode is deployed. As in each iteration the game uses an initialchannel assignment equal to the one obtained in the previousiteration, the quality of the obtained Nash Equilibrium isaffected.

3) Channel allocation in an adaptive neighborhood: In thissubsection we present the results obtained in the evaluation ofthe SCDD solution. For this evaluation a dynamic deployment

2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35

40

45


Net

wor

k T

hrou

ghpu

t at 5

% O

utag

e (M

bps)

1 Radios−adaptive2 Radios−adaptive4 Radios−adaptive1 Radios−all nodes2 Radios−all nodes4 Radios−all nodes

Fig. 8. Performance of channel allocation applied in an adaptive neighbor-hood: network throughput (Mbps) at 5% outage. Number of available radiosri equals 4.

scenario is considered. Each time a new node is deployed, theSCDD solution is applied to obtain the limited neighborhoodand the assigned channels. For comparison purposes, we alsoevaluate the strategy in which channel allocation is applied toall nodes already deployed. We evaluated the cases of numberof available channels = [2,4,6,8,10], and number of availableradios = [1,2,4]. For the evaluation of SCDD, we set minN1 =0, maxN1 = 10, ∆num of neigh = 2, and thr = 90%.

For all evaluated number of channels and radios, SCDD andchannel allocation applied to all nodes provide very similaraverage network capacity. The improvement considering allnodes over SCDD is at most 1.2%. The comparison in terms ofnetwork throughput at 5% outage is depicted in Fig. 8. For thisperformance indicator, the improvement considering all nodesover SCDD is at most 4.1%. However, for some evaluatedcases SCDD yields an improved network throughput at 5%outage over the case with all nodes. This is because SCDDuses the network throughput at 5% outage as an indicator toselect the optimum neighborhood (see section V).

Additionally, SCDD yields a low number of reconfigu-rations of already deployed nodes (see Table II). For allevaluated cases, on average less than one extra node requireschannel reconfiguration when a new node is deployed. Theaverage is computed over all 50 snapshots. In worst case,the maximum number of channel reallocations of extra nodesis lower than 3.6 for all considered number of channels andradios. The maximum is also averaged over all 50 snapshots.

From these results we conclude that SCDD achieves a sim-ilar performance compared to the case of channel allocationwith all nodes while producing a very limited number ofchannel reconfigurations.

VII. CONCLUSIONS

IN this paper we present a solution that enables coexistencefor the dynamic deployment of unplanned small cells in


TABLE IIAVERAGE NUMBER OF RECONFIGURATIONS OF ALREADY DEPLOYED

NODES PER NEW NODE USING AN ADAPTIVE NEIGHBORHOOD.

Available Available Channelsradios 2 4 6 8 10

mean (×10−1) - 7.4 9.1 8.3 9.74 radiosmax - 2.5 3.0 3.0 3.6

mean (×10−1) 4.6 6.2 5.2 4.3 3.82 radiosmax 1.7 2.5 2.4 2.2 2.3

mean (×10−1) 3.2 3.2 2.2 0.9 1.31 radiomax 1.7 1.9 1.7 1.6 1.6

TVWSs. Each time a new small cell is deployed, the proposedSCDD solution assigns channels only to the new small cell andthe small cells in its neighborhood. The channels of the smallcells outside its neighborhood remain unaffected.

For channel allocation we develop an exact potential gamein which the potential function is the average network capac-ity. We demonstrate that the exact potential property of theproposed game is preserved when the channel allocation isapplied only to the small cells in the neighborhood of the newone. The evaluation of this potential game has provided aninteresting performance in terms of average network capacityand network throughput at 5% outage for all tested cases ofavailable channels and radios.

Additionally, the proposed SCDD solution adaptively selectsthe set of small cells that compose the limited neighborhood.The results showed that the proposed solution requires a fewchannel reconfigurations in already deployed nodes. However,its performance was similar to a spectrum reassignment ap-plied to all network nodes.

APPENDIX APROOF OF THEOREM 1

Let us proof that the function PL(s1, ..., si, ...sl) defined in(7) satisfies ∀i ∈ L and si, si

′ ∈ Si:

Ui(si, s−i)− Ui(si′, s−i) = PL(si, s−i)− PL(si

′, s−i) (16)

and it is therefore an exact potential function.We first develop the left side of equality (16):

Ui(si = c1, ..., cn, s−i)− Ui(si′ = c′1, ..., c′m, s−i) =∑

∀c∈K

δ(si, c) ·l∑

j=1

f(j, c/s1, ..., si, ...sl) · δ(sj , c)

−∑∀c∈K

δ(si, c) ·l∑

j=1,j =i

f(j, c/s1, ...,∅, ...sl) · δ(sj , c)

−∑∀c∈K

δ(si′, c) ·

l∑j=1

f(j, c/s1, ..., si′, ...sl) · δ(sj , c)

+∑∀c∈K

δ(si′, c) ·

l∑j=1,j =i

f(j, c/s1, ...,∅, ...sl) · δ(sj , c) =

=∑

∀c∈si\(si∩si′)

( l∑j=1

f(j, c/s1, ..., si, ...sl) · δ(sj , c))

+∑

∀c∈si∩si′

( l∑j=1

f(j, c/s1, ..., si, ...sl) · δ(sj , c))

−∑

∀c∈si\(si∩si′)

( l∑j=1,j =i

f(j, c/s1, ...,∅, ...sl) · δ(sj , c))

−∑

∀c∈si∩si′

( l∑j=1,j =i

f(j, c/s1, ...,∅, ...sl) · δ(sj , c))

−∑

∀c∈si′\(si∩si′)

( l∑j=1

f(j, c/s1, ..., si′, ...sl) · δ(sj , c)

)

−∑

∀c∈si∩si′

( l∑j=1

·f(j, c/s1, ..., si′, ...sl) · δ(sj , c))

+∑


( l∑j=1,j =i

f(j, c/s1, ...,∅, ...sl) · δ(sj , c))

+∑

∀c∈si∩si′

( l∑j=1,j =i

f(j, c/s1, ...,∅, ...sl) · δ(sj , c))=

l∑j=1

( ∑∀c∈si\(si∩si′)

f(j, c/s1, ..., si, ...sl) · δ(sj , c))

−l∑

j=1,j =i


f(j, c/s1, ...,∅, ...sl) · δ(sj , c))

−l∑

j=1

( ∑∀c∈si′\(si∩si′)

f(j, c/s1, ..., si′, ...sl) · δ(sj , c)

)

+

l∑j=1,j =i

( ∑∀c∈si′\(si∩si′)

f(j, c/s1, ...,∅, ...sl) · δ(sj , c))

Now, we develop the right side of equality (16):

PL(si = c1, ..., cn, s−i)− PL(si′ = c′1, ..., c′m, s−i) =

l∑j=1

∑∀c∈K

f(j, c/s1, ..., si, ...sl) · δ(sj , c)

−l∑

j=1

∑∀c∈K

f(j, c/s1, ..., si′, ...sl) · δ(sj , c) =

l∑j=1


f(j, c/s1, ..., si, ...sl) · δ(sj , c)

+∑


f(j, c/s1, ..., si, ...sl) · δ(sj , c)

+∑

∀c∈si∩si′∀c∈K\(si∪si′)

f(j, c/s1, ..., si, ...sl) · δ(sj , c))

−l∑

j=1


f(j, c/s1, ..., si′, ...sl) · δ(sj , c)

+∑


f(j, c/s1, ..., si′, ...sl) · δ(sj , c)

+∑

∀c∈si∩si′∀c∈K\(si∩si′)

f(j, c/s1, ..., si′, ...sl) · δ(sj , c)

)


We can observe that the function f(j, c/s1, ..., si, ...sl) ·δ(sj , c) = f(j, c/s1, ...,∅, ...sl) · δ(sj , c), ∀c ∈ si

′ \ (si ∩ si′).

Similarly, the function f(j, c/s1, ..., si′, ...sl) · δ(sj , c) =

f(j, c/s1, ...,∅, ...sl) · δ(sj , c), ∀c ∈ si \ (si ∩ si′). Addition-

ally, f(j, c/s1, ..., si, ...sl) · δ(sj , c) = f(j, c/s1, ..., si′, ...sl) ·

δ(sj , c), ∀c ∈ si ∩ si′ and ∀c ∈ K \ (si ∩ si

′). Therefore, wecan rewrite the right side of (16) as:

l∑j=1


f(j, c/s1, ..., si, ...sl) · δ(sj , c))

+

l∑j=1

( ∑∀c∈si′\(si∩si′)

f(j, c/s1, ...,∅, ...sl) · δ(sj , c))

−l∑

j=1


f(j, c/s1, ...,∅, ...sl) · δ(sj , c))

−l∑

j=1

( ∑∀c∈si′\(si∩si′)

f(j, c/s1, ..., si′, ...sl) · δ(sj , c)

)

But f(i, c/s1, ...,∅, ...sl) · δ(si, c) is equal to zero ∀c ∈si′ \ (si∩ si

′). Similarly f(i, c/s1, ...,∅, ...sl) ·δ(si′, c) is alsoequal to zero ∀c ∈ si \ (si ∩ si

′). Then, we have:l∑

j=1


f(j, c/s1, ..., si, ...sl) · δ(sj , c))

+

l∑j=1,j =i

( ∑∀c∈si′\(si∩si′)

f(j, c/s1, ...,∅, ...sl) · δ(sj , c))

−l∑

j=1,j =i


f(j, c/s1, ...,∅, ...sl) · δ(sj , c))

−l∑

j=1

( ∑∀c∈si′\(si∩si′)

f(j, c/s1, ..., si′, ...sl) · δ(sj , c)

)

which is therefore equal to the left side of (16).

APPENDIX BSOME NOTATIONS USED IN THIS PAPER

For the sake of readability, Table III includes the variablesused in this paper.

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cj channel jf(i, c/s1, ..., si, ...sl) average capacity of node i on channel cgi(x, y) path gain from node igni path gain from node i to node nIc(x, y) primary to secondary interference on channel c

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[33] F. Hessar and S. Roy, “Capacity considerations for secondary networksin TV White Space,” CoRR, vol. abs/1304.1785, 2013.

Pablo Ameigeiras received his M.Sc.E.E. degree in1999 by the University of Malaga, Spain. He carriedhis Master Thesis at the Chair of CommunicationNetworks, Aachen University (Germany). In 2000,he joint the Cellular System group at the AalborgUniversity (Denmark) where he carried out his Ph.D.thesis. After finishing his Ph.D., Pablo worked inOptimi/Ericsson. In 2006, he joined the Departmentof Signal Theory, Telematics, and Communicationsat the University of Granada (Spain). Since then, hehas been leading several projects in the field of LTE

and LTE-Advanced systems. Currently, his research interests include 4G and5G wireless systems.

David M. Gutierrez-Estevez obtained his Ph.D.degree in August 2014 at the Broadband WirelessNetworking Laboratory of Georgia Tech in Atlanta,USA. He worked under the supervision of Prof. Ian.F. Akyildiz on the topic of Interference Analysisand Mitigation for Heterogeneous Cellular Networkswith a fellowship from Fundacin Caja Madrid. Inaddition, he obtained his M.S. in Electrical andComputer Engineering also from Georgia Tech in2011 with a fellowship from Fundacin la Caixa,and his Engineering Degree in Telecommunications

from University of Granada, Spain, in 2009. He is now Principal Engineerwith Huawei Technologies in Santa Clara, CA, USA. Previously, he was aresearch assistant at Fraunhofer Heinrich Hertz Institute in Berlin, Germany.He also held internship positions at Qualcomm in San Diego, CA, USA, andat Fraunhofer Institute for Integrated Circuits in Erlangen, Germany.

Jorge Navarro-Ortiz received his M.Sc. E.E. degreeby the University of Malaga (Spain) in 2001. Afterworking at Nokia Networks, Optimi/Ericsson andSiemens, he joined the Department of Signal Theory,Telematics and Communications of the University ofGranada as Assistant Professor in 2006, where hefinished his Ph.D. thesis in 2010 with the EuropeanDoctorate mention after performing a research stayat the Dipartimento di Ingegneria dell’Informazioneof the University of Pisa. Since June until September2012 he was a visiting researcher with the BWN lab

of the School of Electrical and Computer Engineering of the Georgia Instituteof Technology. His research interests include cognitive radio, heterogeneousnetworks, LTE and LTE-Advanced systems among others.

dynamic deployment of small cells - universidad de granada

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