Throughput-EfﬁcientDynamicCoalitionFormationin ......cooperative spectrum sensing CRs is the topic of [13]. Using a merge-and-split based coalition formation game model, the authors

Hindawi Publishing CorporationEURASIP Journal on Wireless Communications and NetworkingVolume 2010, Article ID 653913, 13 pagesdoi:10.1155/2010/653913

Research Article

Throughput-Efficient Dynamic Coalition Formation inDistributed Cognitive Radio Networks

Zaheer Khan,1 Janne Lehtomaki,1 Marian Codreanu,1 Matti Latva-aho,1 and Luiz A. DaSilva2

1 Centre for Wireless Communications (CWC), University of Oulu, 90 570 Oulu, Finland2 CTVR the Telecommunications Research Centre, Trinity College Dublin, Dublin 2, Ireland

Correspondence should be addressed to Zaheer Khan, [email protected]

Received 12 February 2010; Revised 25 July 2010; Accepted 30 October 2010

Academic Editor: Sangarapillai Lambotharan

Copyright © 2010 Zaheer Khan et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We formulate the problem of distributed throughput-efficient sensing in cognitive radio (CR) networks as a dynamic coalitionformation game based on a Markovian model. The proposed coalition formation enables the CRs to increase their achievablethroughput, under the detection probability constraint, while also taking into account the overhead in sensing reports combining.The dynamic model of coalition formation is used to express and model the behavior of the coalition forming CRs over time.In the proposed game, CRs form coalitions either to increase their individual gains (selfish coalition formation) or to maximizethe overall gains of the group (altruistic coalition formation). We show that the proposed coalition formation solutions yieldsignificant gains in terms of reduced average false alarm probability and increased average throughput per CR as compared to thenon-cooperative solutions. Given a target detection probability for a coalition, we adopt a weighted target detection probability forindividual CRs in a coalition. We find that the weighted target detection probability for individual CRs results in increased averagethroughput per CR as compared to when each CR is assigned the same target detection probability in a coalition.

1. Introduction

Access to radio spectrum has traditionally been regulatedby government agencies. This approach to radio spectrummanagement has been mostly successful in interferenceavoidance, but at the expense of efficiency in overall spec-trum utilization. Cognitive radio networks are envisionedto utilize the radio spectrum more efficiently throughopportunistic access to licensed frequency spectrum. ACR utilizes spectrum opportunistically by monitoring thelicensed frequency spectrum to reliably detect the licensed(primary) user signals and operating whenever the primaryuser is absent. The detection of primary user signals iscalled spectrum sensing. As with any detection problem,the two types of errors associated with spectrum sensingare false alarms and missed detections. The lower themissed detection probability, the better the primary user isprotected. However, to increase the achievable throughputof the CRs, the false alarm probability must also be low.Thus, there exists an inherent tradeoff between protection ofprimary users and achievable throughput for the cognitiveradio network [1, 2].

Cooperation in sensing can reduce the false alarmprobability of the cooperating CRs [3, 4]. In cooperativespectrum sensing, each CR performs spectrum sensing andsends its sensing report to a data collector known as thefusion center. To reduce signaling cost, the report may bebinary (hard decision), consisting of zeros (primary user notpresent) and ones (primary user present). Hard decisionsmay be combined at the fusion center using, for example,“OR”, “AND”, and “MAJORITY” rules [1, 2]. However, indistributed CR networks, individual CRs need to interactwith each other without a centralized fusion center.

This paper formulates the problem of distributedthroughput-efficient sensing in cognitive radio networks asa dynamic coalition formation game based on a Markovianmodel. Our model is dynamic in the sense that distributedCRs reach self-organizing stable coalition structures (whereno two coalitions have an incentive to merge) througha time-evolving sequence of steps. We model coalitionstructures as a sequence of random variables describing thestate of the CR network, and the transition mechanismbetween coalition structures is modeled as a Markov chain[5–7]. The dynamics of the coalition formation enable us to

2 EURASIP Journal on Wireless Communications and Networking

analyze (1) How are the coalitions formed? and (2) How doCRs arrive at equilibrium? We choose a coalition formationframework as it provides tools for the radios to decide whichcoalitions to form to achieve their goals more efficientlyvia cooperation [8–10]. In coalition formation, a coalitionis a set of distinct, autonomous agents or players whichmay cooperate in order to increase their individual gains,which we call as selfish cooperation. Or they may cooperateto maximize the overall gains of the group, which we callaltruistic cooperation [11, 12]. A key question this papertries to address is how to coordinate distributed cognitiveradios to perform cooperative sensing to minimize their falsealarm probabilities and therefore increase their achievablethroughput, under a probability of detection constraint. Ourmodel also takes into account the overhead in combiningsensing reports.

Two different game theoretic analyses of distributedcooperative spectrum sensing are presented in [13, 14]. In[14], an evolutionary game theoretic framework is used toanalyze the interactions among distributed selfish CRs incooperative sensing. It is assumed in [14] that the selfishCRs overhear the detection results from the other CRs andcan free ride by refusing to take part in spectrum sensing.Hence [14] models the spectrum sensing problem as anoncooperative game. Distributed coalition formation forcooperative spectrum sensing CRs is the topic of [13]. Usinga merge-and-split based coalition formation game model,the authors in [13] analyze the average missed detectionprobability per CR. However, unlike [13], we propose a valuefunction that encourages collaborating CRs to minimizetheir false alarm probabilities for a given target primary userdetection probability ( ˜Pd). This is an important requirementfor coexistence with primary users; otherwise, CRs willnot be allowed to operate in the primary user band [15].Moreover, in contrast with [13], the coalition formationmodel proposed in this paper also takes into account theoverhead in combining sensing reports within a coalition.In [5], a dynamic coalition formation game based on aMarkovian model is used to analyze the selfish interactionsamong distributed nodes for spectrum sharing in an inter-ference channel. Unlike [5], we analyze the interactionsamong CRs for the problem of distributed throughput-efficient sensing in CR networks. Moreover, selfish coalitionformation proposed in [5] for distributed networks maylead to a suboptimal equilibrium where nodes, through theirinteractions, reach an undesirable coalition structure froma network point of view. Hence, we extend the dynamicmodel of coalition formation proposed in [5] to determinewhether and how the coalitional behavior of CRs will changeif coalition formation is “not entirely selfish”.

In this paper, using a coalition game-theoretic frameworkwe devise distributed cooperative strategies for CRs that areeither selfish or altruistic. We propose a coalition formationmodel for these CRs to utilize primary user spectrumefficiently, under the constraint of a target probability ofdetection. We take into account the cost of distributedcooperative sensing in terms of overhead in combiningsensing reports within a coalition. We analyze the impactof this cost on the distributed cooperative strategies of CRs.

Given a target detection probability for a coalition, we alsoadopt a weighted target detection probability for individualCRs in a coalition and analyze its impact on the averagethroughput per CR. We model the stable network structurethat emerged as a result of the dynamic coalition formationas the absorbing state of a Markov chain. Using absorbingMarkov chain theory, we analyze the mean μ and the varianceϑ2 of the time for the game to reach the stable coalitionstructures. We propose a technique to reduce the time takenby the CRs to form a stable coalition. Using simulationswe assess the performance of the proposed altruistic andselfish coalition formation solutions in terms of gains inincreased average throughput per CR. We compare theseresults to the throughput achieved by a noncooperativestrategy and by the grand coalition (when all the CRscooperate). We also determine average maximum coalitionsizes for both altruistic and selfish coalition formationsolutions. Finally, we evaluate the impact of the distancebetween the primary user transmitter and the distributed CRnetwork on cooperative strategies of the distributed CRs.

The rest of the paper is organized as follows. Section 2presents the system setup, while Section 3 introduces theproposed coalition formation game for distributed spec-trum sensing. Section 4 introduces the dynamic coalitionformation model for the proposed game. Section 5 presentssimulation results and an analysis of the proposed dynamiccoalition formation model, and Section 6 concludes thepaper.

2. System Setup

The system setup used in this paper includes a primaryuser transmitter and a distributed CR network of n activeCRs (transmitter/receiver pairs). The CRs are uniformly andindependently distributed in a circle with radius Rs andcentered at the coordinates (β, 0). The PU (primary usertransmitter) is at coordinates (0, 0) as shown in Figure 1.This corresponds to, for example, using only downlinkfrequencies for CR access. The primary user and CRs areboth assumed to use a time-slotted system with perfecttime synchronization, and one transmission by primary usercorresponds to one time slot, as in [16, 17]. In this approach,the primary user is either present for the whole time slot, orabsent for the whole time slot. The CRs use the beginningof each slot for sensing. We assume that n cognitive radiosemploy energy detection to make primary user detectionobservations in the frequency band they are monitoring. Theprobability of primary user present is denoted by PH1 . Inorder to detect the primary user, each CR can either sensethe spectrum on its own (noncooperative strategy) or itcan perform cooperative sensing by forming coalitions withother CRs (cooperative strategy).

Let us represent the received signal-to-noise ratio (SNR)from the primary user to the ith CR by

γi = Piσ2

, (1)

where σ2 represents noise power and Pi = κPPU/dαi is the

signal power received by CR i. PPU is the primary user’s signal

EURASIP Journal on Wireless Communications and Networking 3

power, di is the distance between the primary user and the ithCR, α is the path-loss exponent and κ is a scalar. In our systemsetup we assume a complex-valued PSK primary user signaland circular symmetric complex Gaussian (CSCG) noise. Forthe CSCG noise case the probability of false alarm of CR i fora chosen detection threshold λi is given by [4, 18]

Pf ,i(λi) = Q((

λiσ2− 1

)

√

N)

, (2)

where Q(·) is the tail probability for the standard normaldistribution and N represents the time-bandwidth product,given as N = τsW , where τs is the sensing duration and W isthe measurement bandwidth. For a chosen threshold λi, theprobability of detection of CR i is approximated by [4, 18]

Pd,i(

λi, γi) = Q

(

(

λiσ2− γi − 1

)

√

N

2γi + 1

)

. (3)

To protect the primary user against harmful interferencefrom the CRs, the detection probability is fixed at a desiredtarget value, ˜Pd. In practice, ˜Pd is required to be close to 1 [2].The probability of false alarm of each CR i for the targeted ˜Pdcan be rewritten as

Pf ,i

(

˜Pd, γi)

= Q(√

2γi + 1Q−1(

˜Pd)

+√

Nγi)

. (4)

It may be seen from (4) that a high detection probabilityrequirement may lead to a high false alarm probabilityfor an individual CR if its γi is low, thus reducing theachievable throughput of that CR. In this case, the individualCRs may interact to form coalitions to help decrease thefalse alarm probability. Within a coalition, sensing decisionsby individual CRs are transmitted over the narrowbandcommon control channel to a CR selected as a coalitionhead. Although the optimal decision fusion rule is the Chair-Varshney rule [19], for simplicity of implementation weassume that an OR fusion rule is used by the coalition headto combine the individual CR sensing decisions within acoalition. The OR rule is a simple decision rule explainedas follows: if one out of |S| CRs in a coalition detects theprimary user, the final decision for the coalition declares aprimary user is present, where |S| represents the number ofCRs in a coalition S. CRs in any coalition S decide to transmitor not, based on the final combined sensing decision of thecoalition head. Therefore, the probabilities of detection andfalse alarm of a coalition head are also the probabilities ofdetection and false alarm of each CR i that is the member ofS.

Assuming that all decisions are conditionally indepen-dent (this means that the sensing measurements performedby CRs are independent, but that for each CR the samehypotheses {H0,H1}, H0 = PU not present and H1 =PU present, apply) then using the OR rule, the detectionprobability of the coalition S is given as

Pd,S = 1−|S|∏

i=1

(

1− Pd,i)

. (5)

For a given ˜Pd, the individual CR’s target probability ofdetection in a coalition using OR fusion rule is written as(assuming same target probability of detection for every CR,as in [4, 14])

˜Pd,i = 1−(

1− ˜Pd)1/|S|

. (6)

The probability of false alarm of each CR i for the ˜Pd,i can bewritten as

Pf ,i

(

˜Pd,i, γi)

= Q(√

2γi + 1Q−1(

˜Pd,i

)

+√

Nγi)

. (7)

However, it may happen that some of the CRs have betterreceived SNR from the PU than the others. To gain fromthis SNR diversity, we adopt a weighted target probability ofdetection for any CR i ∈ S. The weighted target probabilityof detection modifies ˜Pd,i in (6) and takes a sensing CR’sreceived SNR γi into consideration. We propose to useweighted target probability of detection for CR i given by

˜Pwd,i = 1−(

1− ˜Pd)γi/

∑

j∈S γj. (8)

While we make no claims as to the optimality of theselected weighting method, these probabilities preserve therelationship in (5) and assign a higher expectation ondetection accuracy to the CRs that experience higher SNR.We justify the use of ˜Pwd,i as follows. For a given SNR γi andN , false alarm probability of CR i is a function of the targetdetection probability for that CR (see (7) and Figure 2). Itcan be seen from Figure 2 that the impact of target detectionprobability on the false alarm probability of individual CRsvaries for the different values of γi. If a CR has high γi, forinstance γi = 0.05, then the target detection probability haslittle impact on its false alarm probability. However, if a CRhas low γi, for instance γi = 0.005, then the target detectionprobability has strong impact on its false alarm probability.

In this approach, the CR with high γi is assigned relativelyhigh target detection probability. However, due to high γi,the assignment of high target detection probability has littleimpact on the false alarm probability of that CR. The CR withlow γi is assigned relatively low target detection probabilitywhich results in low false alarm probability for that CR (seeFigure 2), as compared to when each CR is assigned the sametarget detection probability in a coalition.

The probability of false alarm of each CR i for the ˜Pwd,i iswritten as

Pf ,i

(

˜Pwd,i, γi)

= Q(√

2γi + 1Q−1(

˜Pwd,i

)

+√

Nγi)

. (9)

Using the OR rule, the false alarm probability Pf ,S of thecoalition S is given as

Pf ,S = 1−|S|∏

i=1

(

1− Pf ,i

)

. (10)

It may be seen from (7) and (9) that, for a given ˜Pd andN , theCRs with low values of γi have incentives to form coalitionsas it helps to decrease Pf ,i (due to the increase in Q−1( ˜Pd,i) or

Q−1( ˜Pwd,i) term which in turn decreases Pf ,i). However, for agiven Pf ,i the coalitional false alarm probability given by (10)is an increasing function of coalition size |S|.


(II) System setup

PU CR3 CR1

CR2

Rsβ

Figure 1: Topology of a cognitive radio network.

3. Coalition Game-Theoretic Framework forDistributed Cooperative Sensing

Coalition game theory provides useful tools to decide whichgroup of players will cooperate with each other to efficientlyachieve their goals [8, 20]. Therefore, to analyze cooperativeinteractions among CRs performing distributed spectrumsensing, we model the problem as a coalition game.

3.1. Preliminaries. Let N = {1, 2, . . . ,n} denote the set ofplayers (CRs) playing the coalition game. A coalition, S,is a subset of N, S ⊆ N. An individual non-cooperatingplayer is called a singleton coalition and the set N is calledthe grand coalition, where all players cooperate. The utilityof a coalition in a coalition game is called the coalitionvalue, and is denoted by v. Coalitions are assumed to benon-overlapping, that is, CRs are members of at most onecoalition.

The most common form of a coalition game is thecharacteristic function form. In the characteristic functionform (CFF) of coalition games, utilities achieved by theplayers in a coalition are unaffected by those outside it.

Definition 1. A nontransferable utility (NTU) game is acoalition game in CFF, in which the value v(S) of a coalitionS cannot be arbitrarily divided among the coalition’s players.In such games, each player will have its own value within acoalition S. The value function ϕi(S) represents the value ofplayer i that belongs to a coalition S.

3.2. Throughput of a CR. For a noncooperative CR networkwith periodic spectrum sensing, each slot consists of sensingduration τs and data transmission duration Tf − τs. Tofocus on the coalition formation model for the sensing-throughput tradeoff problem in distributed CR networks;we assume that the entire primary user band is divided intoK subbands and, when the primary user is absent each CRoperates exclusively in one of the K subbands. (We do notanalyze scheduling policies in this work and assume a verysimple and predetermined orthogonal sub-band allocationpolicy for the CRs when the primary user band is free foraccess. Our ongoing work, outside the scope of this paper,addresses competition among CRs for subbands that are

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

offa

lse

alar

m

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99

Target detection probability

γi = 0.05γi = 0.04γi = 0.03

γi = 0.02γi = 0.01γi = 0.005

Figure 2: Probability of false alarm for different detection probabil-ities and for different values of SNR, N = 6000.

free.) This assumption is in line with the other models in theliterature [14, 21]. For the noncooperative case, the averagethroughput of the CR i is approximated by [1, 14]

Ri = PH0

(

1− τsT f

)

(

1− Pf ,i

)

ri, (11)

where PH0 is the probability of primary user absent, Tf

represents the total frame length and ri represents thetransmission rate of the CR i to its receiver when the primaryuser is absent.

In distributed CR networks when CRs decide to performcooperative sensing by forming coalitions with one anotherthey may incur overhead costs in terms of time delay dueto the process of coalition formation and due to combiningsensing reports within a formed coalition. Note that thetime delay due to the process of coalition formation dependson how frequently the coalition process is initiated whichin turn depends on changes in the network configuration(for, e.g., CR mobility, etc.). However, the time delay indata transmissions of a coalition due to the overhead incombining sensing reports is periodic (since this overheadis incurred in every time slot). In this work, we analyzethe impact of overhead costs in terms of time spent duringcombining sensing reports on the throughput of distributedCRs. We ignore the overhead in terms of time delay due tothe process of coalition formation. One of the extensionswe envision for our current work is the consideration ofthe effects due to overhead in terms of spending time andresources due to the process of coalition formation and alsothe effects due to overhead in terms of energy consumed bya coalition head to collect and combine sensing reports.

When the CRs decide to form a coalition then theentire coalition cannot transmit data until sensing reportsare collected and the final combined sensing decision is


Sensing stage

τs

Data transmission stage

Data transmissionτc report

combining stage

τc is a variable

Figure 3: Time slot structure with sensing, sensing report combin-ing and data transmission stages.

transmitted to all the coalition members (see Figure 3). Onesimple method of sensing reports collection by the coalitionhead can be stated as follows. The coalition head grants acontention free channel to individual cognitive radios bypolling them (using their identity numbers) for transmittingtheir local decisions. The coalition head may employ around-robin scheduler [22, 23], and on being polled, a CRtransmits its local decision to the coalition head. In thissensing reports collection method there is cost in terms oftime delay in data transmissions of a coalition due to theoverhead in combining sensing reports. This cost generallyincreases with the number of coalition forming CRs as moredecisions need to be reported to the coalition head. Theaverage throughput of the CR i considering the cost in termsof overhead in sensing reports combining within a coalitionis approximated as

Ri = PH0

(

1− τsT f− τcT f

(|S| − 1)

)

(

1− Pf ,S

)

ri, (12)

where τc is the time spent on reporting a sensing decision tothe coalition head.

For a target detection probability, ˜Pd, the CRs mayform coalitions to reduce their false alarm probability andtherefore increase their average throughput given by (12).The coalition forming CRs may also increase their averagethroughput by reducing their sensing time τs via jointcoalitional sensing. However, we note that for the distributedspectrum sensing problem when the coalition forming CRsare allowed to vary sensing time τs, it generates significantuncertainties in the coalition values. For instance, if twoor more CRs reduce their sensing time τs (or in otherwords increase their data transmission time) via formingthe coalition S then it may happen that the CRs in S starttransmitting data while some CRs outside S may still besensing. This may lead to a change in the coalition value(in terms of false alarm probabilities) of the CRs outside thecoalition S. To avoid this uncertainty in the coalition valuedue to CR transmissions, we fix the sensing duration τs foreach individual CR.

3.3. Coalition Value with Nontransferable Utility. For a targetdetection probability, ˜Pd, and the fixed sensing durationτs, the coalition value v(S) must characterize the incentivesto form coalitions in terms of the decreased false alarmprobability Pf ,S of the coalition. Moreover, the coalitionvalue must also take into account the cost in terms of delayin data transmissions of a coalition due to the overhead in

combining sensing reports. A suitable coalition value thatsatisfies the above requirements is given by

v(S) = (ϕ1(S),ϕ2(S), . . . ,ϕ|S|(S))

=(

R1, R2, . . . , R|S|)

,(13)

where ϕi(S) denotes the average throughput for CR i given by(12), for i = 1, 2, . . . , |S|. In the proposed coalition formationgame, each CR has it is own value within a coalition and itsnontransferable due to the following reasons.

Indivisible False Alarm Probability. The probability of falsealarm Pf ,i of each CR i, where i ∈ S, is also given by theprobability of false alarm of the coalition S, that is, Pf ,S (asexplained in Section 2) and it cannot be divided among theradios.

Indivisible Cost. Each CR incurs the same cost in terms ofoverhead in combining sensing reports, that is, (τc/T f )(|S|−1), and this cost cannot be divided among the CRs.

Indivisible Bandwidth. Finally, each CR operates exclusivelyin one of the K subbands. Therefore, they cannot arbitrarilydivide the spectrum among themselves.

Therefore, each CR will have its own value within thecoalition S and hence, the proposed game is an NTU game.

When two or more CRs form a coalition S, then anyCR within S is selected as a coalition head to combinethe individual CR sensing decisions within the coalition.The decisions to form coalitions by the CRs are based onconsensus, that is, a coalition is formed only if it is acceptableto everyone involved. We also assume that CRs are myopic,that is, CRs care only about their current payoffs.

3.4. Selfish Coalition Formation

Definition 2. Internal stability means that no CR has anincentive to leave its coalition to become a singleton(individual noncooperative CR), that is, ϕi(S1) ≥ v({i}), forall i ∈ S1.

We assume that CRs are individually rational, that is,CRs seek to maximize their payoffs, conditional on feasibility.Therefore, for selfish coalition formation, the merge of twocoalitions only occurs when all CRs in the new coalition Sare at least as well off through the merge as they were beforeit. Mathematically speaking, coalitions S1 and S2 will mergeto form S only: if for all i, j, where i ∈ S1 and j ∈ S2,(ϕi(S) − ϕi(S1)) ≥ 0 and also (ϕj(S) − ϕj(S2)) ≥ 0. Dueto this coalition formation condition, whenever CRs agreeto form S the new coalition is internally stable, that is, noCR has an incentive to become a singleton (an individualnoncooperative CR).

3.5. Altruistic Coalition Formation. The model of selfishcoalition formation discussed above is in line with muchof the coalition formation literature, which assumes that


users form coalitions to maximize their individual payoffs.However, it is equally interesting to investigate the questionof whether and how the achievable throughput of CRswill change if CRs are assumed to be “not entirely selfish”.Intuitively, we want to model the case when two or moreCRs propose to form a new coalition S by taking intoaccount one another’s welfare. Before studying altruisticcoalition formation, we first define the concept of altruisticcontribution of a coalition as follows [11].

Definition 3. Let S1 and S2 be two disjoint coalitions. Thealtruistic contribution of S1 to S, where S = S1∪S2, is aS1 (S) =∑

i∈S2(ϕi(S) − ϕi(S2)); the altruistic contribution of S2 to S

is aS2 (S) = ∑

i∈S1(ϕi(S) − ϕi(S1)); and the sum of altruistic

contributions of S1 and S2 is a(S) = aS1 (S) + aS2 (S).

In simple words, the altruistic contribution of coalition S1

to S represents the change in the value of the CRs in S2, whenthe CRs in S1 are added to the coalition S. It can be easilyseen that if any proposed coalition S has a(S) > 0, then themerger of S1 and S2 to form S would do more good thanharm to the overall value of the coalition S. Formally, weassume that to maximize the achievable throughput of theproposed coalition S, an altruistic coalition decides to formthe coalition S whenever

a(S) > 0. (14)

4. A Markovian Model ofCoalition Formation Game

To model all n CR coalitions, we define coalition structuresas follows.

Definition 4. A coalition structure is a partition of N intoexhaustive and disjoint subsets, where each subset is acoalition. The set of all possible coalition structures isdenoted as C.

In this section, we introduce a dynamic model of coali-tion formation for distributed cooperative spectrum sensingin CR networks where multiple distributed CRs coexistand opportunistically access the spectrum. In the proposeddynamic coalition formation game the CRs follow a timeevolving sequence of steps to reach self-organizing stablespectrum sensing coalition structures. Coalition structuresin the dynamic coalition formation game are modeled asa sequence of random variables describing the state of thesystem, with the mechanism of transitions between coalitionstructures represented by a Markov chain. To incorporateslow changes in the network configuration (for, e.g., due toCR mobility), the initial round of coalition formation gamerestarts some time T after reaching equilibrium. This timeT may be assigned according to variations in the networkconfiguration. We assume that during one round of coalitionformation the received primary user’s SNR, that is, γi, and thetransmission rate ri of each CR i does not change. At the verybeginning of each round of the coalition formation game,

the distributed CR network is composed of all singletoncoalitions, that is, noncooperative CRs.

4.1. A Coalition Formation Game Model. The coalitionformation game involves five steps. The five steps of theproposed model are summarized as follows:

Node Discovery. Discover the CRs within the network.

Initialization. Each individual CR computes its received SNRγi from the PU.

Coalition Formation Proposal. (a) At each time slot, eachcoalition, with probability p, proposes a new coalitionstructure. In this process, one of the CRs in the coalitionacts on its behalf. (In the case of singleton coalitions, eachsingleton coalition, i.e., each CR, individually proposes a newcoalition structure with some probability p; when two ormore CRs form a coalition S, then any CR within S is selectedas a coalition head to propose a new coalition structurewith some probability p on behalf of that coalition.) (b)The evolution from one coalition structure to the next canonly occur through the merging of two existing coalitions.For instance, any coalition head of any existing coalition S1

may propose to merge with another coalition S2, formingS1 ∪ S2 = S.

Coalition Formation Decision. (a) When the CRs areassumed to be selfish then they form a coalition if for alli, j, where i ∈ S1 and j ∈ S2, (ϕi(S) − ϕi(S1)) ≥ 0 and also(ϕj(S) − ϕj(S2)) ≥ 0. (b) When the CRs are assumed to bealtruistic then they form a coalition if a(S) > 0. (see Sections3.4 and 3.5 for the details).

Steps (3) and (4) of the coalition formation are repeateduntil all the coalitions have made their coalition formationdecisions, resulting in a final stable coalition structure CF .

Coalitional Spectrum Sensing. Each CR within a coalitioncomputes its local sensing decision and transmits it to thecoalition head over the common control channel. The coali-tion head combines the local sensing decisions (including itsown sensing decision) using an OR decision fusion rule.

The proposed distributed coalition formation can be per-formed by coalition formation message exchanges betweenCRs over a common control channel. In practice, if all CRsuse the same control channel to report sensing decisions totheir respective coalition heads then the reporting time mayincrease. To decrease the reporting time coalitions may usedifferent control channels. However, since the number ofavailable channels in general is limited and the number ofcoalitions may be large, control channels must be spatiallyreused. For simplicity, we have assumed different reportingchannels for each coalition.

4.2. Dynamics of Coalition Formation: Game Model. Thedynamic coalition process can be modeled using a Markovchain, with each state representing a different coalition


structure. A finite set C = {C1, C2, . . . , C|C|} of all possiblecoalition structures for n CRs forms the state space of thecoalition formation game. Our work in [5] provides furtherdetail on this modeling, including examples of the Markovchain structure for n = 3, and n = 4 transmitter/receiverpairs.

4.2.1. Selfish Coalition Formation. Any coalition may pro-pose a coalition structure change to another coalition inthe current state Ck, and if all the CRs in the proposedcoalition are at least as well as before the merge, the gamemoves to Cl. When each ofm prevailing coalitions with someprobability p proposes a new coalition structure then thetransition probabilities for the n CR selfish coalition gamewith coalition structures as state space C are given as

PCkCl =2p(

1− p)(|Ck|−1)

|Ck| − 11[(vi(S)−vi(S1))≥0,(vj (S)−vj (S2))≥0],

∀i, j, where i ∈ S1, j ∈ S2,

PCkCk = 1−∑

Cl∈Φl

PCkCl ,

(15)

where 1[X] is an indicator function equal to 1 if condi-tion X is satisfied, and zero otherwise, v(S1) and v(S2)are the values of the two coalitions participating in thecoalition formation to form the proposed coalition S,v(S) is the value of the proposed coalition S, and Φl

represents the set of all new possible coalition structurestates to which coalitions can transit from Ck. The setΦl is given as Φl = {{S1 ∪ S2, S3, . . . , S|Ck|}, {S1, S2 ∪S3, . . . , S|Ck|}, . . . , {S1, S2, . . . , S(|Ck|−1) ∪ S|Ck|}}. Given |Ck| >1 coalitions in the present state Ck, it is possible to transitionfrom Ck to one of the |Φl| possible states, where |Φl| can becalculated as

|Φl| =⎛

⎝

|Ck|2

⎞

⎠. (16)

For instance, if the number of coalitions |C1| = 3, then itis possible to move from the state C1 to one of |Φl| = 3different states (besides itself), provided that the coalitionformation condition is satisfied. As explained previously, twocoalitions can merge only if all CRs within the proposedcoalition S are at least as well off as before the merge.The indicator function 1[(vi(S)−vi(S1))≥0, (vj (S)−vj (S2))≥0] in (15)represents the possible agreement or disagreement amongthe CRs participating in the coalition game to form theproposed coalition S. As the transition probability at anypresent state Ck does not depend upon the prior states of thecoalition structures, the Markov property holds.

4.2.2. Altruistic Coalition Formation. For the altruistic-cooperation case, the indicator function (coalitionformation decision) in (15) is changed from1[(vi(S)−vi(S1))≥0, (vj (S)−vj (S2))≥0] to 1[a(S)>0]. It simply meansthat each CR now decides to merge if the merger of two

coalitions would do more good than harm to the overallvalue of the merged coalition S.

Using simulation results in Section 5.3 we will comparethe performance of the coalition formation based on altru-istic decision with the selfish decision in terms of averagethroughput per CR, for different network sizes.

Using standard theory of absorbing Markov chains onecan calculate how long will it take for the process to reachstable coalition structures, that is, one can calculate the meantime μ and its variance ϑ2 for the dynamic coalition gamestarting from the initial state of all singleton coalitions toreach stable coalition structures (where no two coalitionshave an incentive to merge) [5].

In Section 5.3, we analyze the mean μ and the variance ϑ2

of the time for the proposed coalition formation to reach thestable coalitions.

5. Dynamic Game Analysis andSimulation Results

To perform the coalition formation, CRs need to exchangetheir received primary user’s signal-to-noise ratio (SNR).The amount of information exchange necessary to reachstable coalition structures can be measured by the totalnumber of coalition formation proposals sent by the n CRsduring the coalition formation process. For instance if Mnumber of coalition formation proposals are sent duringthe entire coalition formation process and each proposalrequires the exchange of D messages for coalition heads totake a coalition formation decision then to reach equilibriumM × D messages need to be exchanged among the CRs.When we are not taking into account the loss of coalitionformation proposals due to collisions among distributeduncoordinated CRs then in the worst case, that is, wherealmost all proposals are rejected, the number of proposals

is only( n

2

)

+∑n−2

i=1 i, where( n

2

)

+∑n−2

i=1 i = n2 − 2n + 1.Thus for the worst case, coalition formation proposals can besaid to be order of O(n2). In the best case, that is, where allproposals are accepted and the coalition formation leads tothe formation of the grand coalition, the number of coalitionformation proposals necessary is only n. Thus for the bestcase, coalition formation proposals can be said to be order ofO(n). In practical scenarios the complexity is between thesetwo extremes.

This reduction in the information exchange is due to thereason that when coalitions are formed then instead of all theCRs only the coalition heads exchange proposals on behalf oftheir respective coalition members.

5.1. Stable Coalition Structures. As CRs form self-organizingspectrum sensing coalition structures, we analyze underwhat conditions the coalition formation process will reacha stable coalition structure (where no two coalitions have anincentive to merge anymore).

Selfish Coalition Formation. For the proposed selfish coali-tion formation, a coalition structure state C∗ is an


equilibrium state if it satisfies the following condition

∀S j , Sk,k /= j ∈ C∗,

for some i ∈ S j

(

ϕi(

S j ∪ Sk)

− ϕi(

S j

))

< 0,

(17)

or for some i ∈ Sk(ϕi(Sk ∪ S j)− ϕi(Sk)) < 0.The above stated condition ensures that no two coalitions

in the prevailing coalition structure C∗ have an incentive tomerge anymore.

The following simple fact proves that the selfish coalitionformation process converges to an equilibrium state: In theproposed selfish coalition formation, if a certain coalitionstructure is not an equilibrium state, there must exist at leasttwo coalitions that can decide to merge to improve theirvalue functions. As long as such two coalitions exist, thecoalition structure changes to another coalition structure,until an equilibrium state is reached.

Altruistic Coalition Formation. For the proposed altruisticcoalition formation, a coalition structure C∗ is an equilib-rium state if it satisfies the following condition

∀S j , Sk,k /= j ∈ C∗, if a(S) ≤ 0. (18)

Following the same reasoning as we did for the selfishcoalition formation process, it is easy to see that the altruisticcoalition formation process converges to an equilibrium.

5.2. Coalition Sizes. The study of coalition formation in wire-less networks has previously focused on cohesive games [24],that is, games where the value of the grand coalition formedby the set of all users N is at least as large as the sum of thevalues of any partition of N. The authors in [24], also assumethat there is no cost to the coalition formation process. Insuch coalition games, coalition structure generation is trivialbecause the wireless nodes always benefit by forming thegrand coalition.

However, many coalition game models of wireless nodecooperation are not cohesive (see, e.g., [25]). In suchnetwork scenarios, the network welfare maximizing coalitionstructure varies.

For the proposed selfish coalition formation where CRsseek to maximize their payoffs, conditional on feasibility, itis interesting to note that the higher the γi (the signal powerreceived by CR i), the lower the Pf ,i given by (7). CRs withhigh values of γi may have either less or no incentive tocooperate with CRs with low values of γi (or with high Pf ,i).Hence, cooperation among all CRs is desirable only whenall CRs experience similar γi. Therefore, in the proposedcoalition formation, the grand coalition of all the CRs maynot always form.

For the proposed altruistic coalition formation whereCRs seek to merge if the merger of two coalitions would domore good than harm to the overall value of the mergedcoalition, it is interesting to note that the CRs with high γivalues may form coalitions with the CRs having low γi valuesas long as the overall value of the newly formed coalition S isincreased.

Using simulation results in Section 5.3 we will presentaverage maximum number of CRs per formed coalition forboth selfish and altruistic coalition formation.

5.3. Simulation Results. Using simulation our aim is tocompare the performance (for, e.g., in terms of averagethroughput per CR) of the coalition structure that emergesas the outcome of the proposed coalition formation solutionsto a noncooperative solution and to the grand coalition.

For simulation illustrations, the following distributed CRnetwork is set up: n CRs are uniformly and independentlydistributed in a circle with radius Rs = 1000 m and centeredat the coordinates (β, 0). The PU transmitter is at coordinates(0, 0) as shown in Figure 1. The sensing time τs = 1 ms,the time-bandwidth product is set as N = 6000, and theframe duration is set to be Tf = 100 ms. We set the pathloss exponent α = 3. The PU power Pi, scalar κ andnoise power σ2

i are set at a value such that γi (PU’s SNRat CR i) at the coordinates (β, 0) = (2000, 0) is −15 dB.The probability of primary user present is assumed to bePH1 = 0.2. To keep our simulation analysis simple, weassume that all the CRs have the same transmission rate,that is, ri = r = log(1 + SNRs) = 3.4594 bits/sec/Hzin (12), where SNRs is signal-to-noise ratio from a CR toits receiver. Simulations were performed by “dropping” theCRs randomly around the coordinates (β, 0). For the targetdetection probability ˜Pd = 0.9 and ˜Pd = 0.99, in Figures 4(a)and 4(b), we show the average (averaged over the simulationruns) throughput per CR for different network sizes, whenall CRs sense independently (noncooperative strategy), andwhen CRs can form coalitions (selfish and altruistic). Itcan be seen from Figures 4(a) and 4(b) that the proposedcoalition formation (both selfish and altruistic) yields animprovement in the average throughput as compared tothe noncooperative solution. However, the selfish coalitionformation solution leads to a loss in average throughputas compared to the altruistic coalition formation solution.In Figure 5, we compare the performance of altruistic andselfish coalition formation solutions with the noncooperativesolution in terms of average false alarm probability per CRfor different network sizes. It can be seen that the altruisticcoalition formation solution significantly reduces the averagefalse alarm per CR, as compared to both selfish coalitionformation and noncooperative solutions. It can also be seenfrom Figures 4 and 5 that the weighted target detectionprobability for individual CRs in a coalition results in betteraverage throughput and reduced average false alarm per CRas compared to when each CR is assigned the same targetdetection probability.

When the overhead cost, that is, the cost in terms ofcollecting and combining sensing reports at the coalitionhead is not taken into account then the altruistic coalitionformation solution yields the same results as if all theCRs perform cooperative sensing, that is, form the grandcoalition, see Figure 6. This is because, for no overheadcost, with increasing the number of cooperating CRs, atarget detection probability may be achieved by havinglow detection probability at the individual CRs. The low


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Figure 4: Average throughput per CR for different network sizes and for different scenarios. (a) Average throughput (bits/sec/Hz) per CR,˜Pd = 0.9, β = 2000 m and τc in (12) is set to 0.001ms (the time spent for reporting a sensing decision to the coalition head). Given atarget detection probability for a coalition, “same Pd,i” means that each CR is required to satisfy the same target probability of detection (see(7)), whereas “weighted Pd,i” means that each CR is required to satisfy an SNR-dependent target detection probability (see (9)). (b) Averagethroughput per CR, ˜Pd = 0.99, β = 2000 m and τc in (12) is set to 0.001 ms.

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Figure 5: Average false alarm per CR for different network sizes,˜Pd = 0.99, τc in (12) is set to 0.001 ms and β = 2000 m.

detection probability at the individual CRs is translatedto a low false alarm probability and therefore increasein throughput. However, in practice the reporting of thelocal CR sensing decisions to the report combining entity(coalition head, fusion center, etc.) incurs overhead in thesense that the entire reporting group cannot transmit until

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Altruistic with no overhead cost (weighted Pd,i)Grand coalition with no overhead cost (weighted Pd,i)Altruistic with overhead cost (weighted Pd,i)Grand coalition with overhead cost (weighted Pd,i)

Figure 6: Comparison of the proposed altruistic coalition forma-tion solution with the grand coalition for different scenarios.

all the sensing reports are collected and combined by thatentity. In the literature (also in IEEE 802.22), polling ofCRs by the report combining entity is suggested for thecollection of sensing reports [3, 23, 26]. This method hascommunication overhead that increases linearly with thenumber of cooperating CRs. When the overhead cost of


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Coalition formation for 20 CRs (altruistic same Pd,i)Coalition formation for 20 CRs (selfish same Pd,i)Coalition formation for 20 CRs (selfish weighted Pd,i)Coalition formation for 20 CRs (altruistic weighted Pd,i)

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Coalition formation for 20 CRs (altruistic same Pd,i)Coalition formation for 20 CRs (selfish same Pd,i)Coalition formation for 20 CRs (selfish weighted Pd,i)Coalition formation for 20 CRs (altruistic weighted Pd,i)

(b)

Figure 7: Average throughput per CR for different network sizes and for different scenarios. (a) Average maximum coalition size for selfishand altruistic coalition formation solutions, when the values of τc (the time spent for reporting a sensing decision to the coalition head) arevaried between 0.001 ms to 0.017 s, ˜Pd = 0.99 and β = 2000 m. (b) Average throughput per CR for selfish and altruistic coalition formationsolutions, when the values of τc (the time spent for reporting a sensing decision to the coalition head) are varied between 0.001 ms to 0.017s,˜Pd = 0.99 and β = 2000 m.

collecting and combining sensing reports is taken intoaccount (e.g., τc in (12) is set to 1 ms) then it can be seen inFigure 6 that the performance of the grand coalition degradessignificantly as the number of CR increases, as compared tothe altruistic coalition formation solution. In Figure 7(a), wecompare the performance of altruistic and selfish coalitionformation solutions in terms of average throughput per CRfor a network size of 20 CRs. In this figure, we show thatfor small τc, the altruistic coalition formation (same Pd,i)solution yields significant average throughput gains whencompared with the selfish coalition formation solution (samePd,i). However, when τc is large then the selfish coalitionformation solution (same Pd,i) either outperforms or at leastmatches altruistic solution (same Pd,i) with respect to averagethroughput per CR. This is because the average coalition sizefor the altruistic coalition formation solution (same Pd,i) islarge as compared to the selfish coalition formation solution(same Pd,i), see Figure 7(b), and for large values of τc, thesensing reporting overhead becomes significant. Due to thisreason, the large coalitions can be more costly as comparedto the small ones.

To illustrate the above situation, we can construct anexample, for n = 3 CRs, where the altruistic coalitionformation solution (same Pd,i) outperforms selfish solution(same Pd,i) when τc is small. However, for the same scenario,when τc is set to be large then selfish coalition solution (samePd,i) may outperform altruistic solution (same Pd,i).

Example 1. Let γ1 = 0.0263, γ2 = 0.0148 and γ3 = 0.0233be the received primary user’s SNRs at n = 3 CRs. Inthis three-CR game, when τc = 0.001 ms and assuming

r1 = r2 = r3 = 3.4594 bits/sec/Hz then calculatingcoalition values using (13) and rules explained in Sections3 and 4 we obtain v({1}) = 0.9968, v({2}) = 0.3076,v({3}) = 0.7718, v({1, 2}) = (0.9198, 0.9198), v({1, 3}) =(1.4433, 1.4433), v({2, 3}) = (0.8272, 0.8272), v({1, 2, 3}) =(1.3036, 1.3036, 1.3036). It may be seen that the altruisticcoalition solution (same Pd,i) for this scenario results inthe formation of grand coalition {{1, 2, 3}} of all CRs.However, the selfish coalition solution (same Pd,i) resultsin the formation of either {{1, 3}, {2}} or {{2, 3}, {1}}.Since, v({1, 2, 3}) is greater than v({1, 3}) + v({2}) andv({2, 3}) + v({1}), therefore, the altruistic solution (samePd,i) outperforms the selfish solution (same Pd,i) for thisscenario. However, when τc = 15 ms then we obtain v({1}) =0.9968, v({2}) = 0.3076, v({3}) = 0.7718, v({1, 2}) =(0.7805, 0.7805), v({1, 3}) = (1.2247, 1.2247), v({2, 3}) =(0.7019, 0.7019), and v({1, 2, 3}) = (0.9086, 0.9086, 0.9086).It may be seen that the selfish coalition solution (same Pd,i)for this scenario results in the formation of {{1, 3}, {2}}.However, the altruistic coalition solution (same Pd,i) resultsin the formation of either {{1, 2, 3}} or {{1, 3}, {2}}. Since,v({1, 3}) + v({2}) is greater than v({1, 2, 3}), therefore, theselfish solution (same Pd,i) either outperforms or at leastmatches altruistic solution (same Pd,i) for this scenario.

It can also be seen from Figure 7(a) that for very largevalues of τc, the altruistic solution (same Pd,i) matches theselfish solution (same Pd,i) in terms of average throughputper CR. This is because for very large values of τc there areeither very little or no gains in terms of average throughputper CR for coalition formation, and network structure is


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0 500 1000 1500 2000 2500 3000 3500 4000 4500

β (meters)

Coalition formation (selfish)Coalition formation (altruistic)

Independent disjointcoalitions

Individual non-cooperation CRs

(singleton coalitions)

Figure 8: Average maximum coalition size for selfish and altruisticcoalition formations, when parameter β (distance between theprimary base station and the center of the CR network, see Figure 1)is varied between 0 m to 4500 m, τc = 0.001 msec and n = 30 CRs.

mostly composed of individual noncooperative CRs (seeFigure 7(b)).

In Figure 8, we vary the parameter β (distance betweenthe primary user base station and the center of the dis-tributed CR network, see Figure 1), and show average max-imum coalition sizes for the selfish and altruistic coalitionformation solutions. It can be seen from Figure 8 that forlarge β, the network for such scenarios is composed ofcoalitions of large sizes. In this figure, we also show thatfor the given simulation scenario the altruistic coalitionformation solution results in the formation of the grandcoalition of all CRs whenever β ≥ 2000 m. As the valueof parameter β is decreased, the network for such scenariosis composed of independent disjoint coalitions of smallersizes. It can also be seen from Figure 8 that as the valueof the parameter β is reduced to 500 m then the coalitionformation solution results in a network structure mostlycomposed of individual noncooperative CRs, that is, allsingleton coalitions.

The two figures in Figures 9(a) and 9(b) illustrate themean and variance of the time for the altruistic coalitionformation to converge to an absorbing state with differentprobabilities p of coalition formation proposal. In Figures9(a) and 9(b), simulation results are generated by droppingn = 6 CRs in a circle with radius Rs = 1000 m and centeredat the coordinates (2000,0) (other simulation parameters, forinstance sensing time, slot duration, and so forth, are set tobe the same as explained in the beginning of Section 5.3).The stable coalition structure that emerges as the outcomeof the coalition formation may be different for the differentdrops of CRs in the distributed CR network. Therefore, weevaluate the mean and variance of the time to converge tothe stable coalition structure (absorbing state) for any single

random drop. For the target detection probability ˜Pd = 0.99and τc = 0.001 ms, when CRs propose altruistic coalitionswith some probability p then the process converges to thegrand coalition (absorbing state for a single random dropfor the given simulation scenario). The mean and varianceof the time to converge to the grand coalition are evaluatedfor different p as follows: We repeat the coalition formationfor the same drop of CRs with different probability p ofcoalition formation proposal. Figure 9(a) shows that forsmall p, μ is high because the mean time between coalitionformation messages is too long. If p is too high then the meantime between coalition formation messages is shorter but thenumber of coalition message collisions is higher, resultingin a longer time between coalition structure changes. Thissuggests that depending on the number of radios in the gamethere is an optimum value for p. We illustrate this optimumvalue for n = 6 CRs in Figure 9(a).

6. Conclusions

We apply a coalitional game-theoretic framework to thestudy of stable network partitions for the problem ofdistributed throughput-efficient sensing in cognitive radio(CR) networks. We devise distributed cooperative strategiesfor cognitive radios that are either selfish or altruistic. Wepropose a coalition formation model for these CRs to utilizeprimary user spectrum efficiently, under the constraint ofprobability of detection. The proposed coalition formationmodel also takes into account the overhead in sensing reportscombining. We demonstrate that when each CR is assignedthe same target detection probability in a coalition thenfor small to moderate values of sensing reporting time, thealtruistic solution yields significant gains in terms of averagethroughput per CR as compared to the selfish and non-cooperative solutions. However, for large values of sensingreporting time, the selfish solution either outperforms or atleast matches altruistic solution in terms of average through-put per CR. We then adopt a weighted target detectionprobability for individual CRs in a coalition. We find thatthe weighted target detection probability for individual CRsresults in higher average throughput as compared to wheneach CR is assigned the same individual target detectionprobability in a coalition. We also find that when CRs areassigned weighted target detection probabilities in a coalitionthen the altruistic coalition formation solution significantlyincreases the average throughput per CR, as compared tononcooperative solution, selfish coalition formation, andthe grand coalition of all CRs. Our work employs anabsorbing Markov chain model to model the equilibriumstate (where no two coalitions have an incentive to merge)of the proposed coalition formation. Using a Markovianmodel of the coalition game, we analyze the dynamics ofthe coalition formation game and the stability of differentnetwork partitions in a distributed cognitive radio network.We also analyze the mean μ and variance σ2 of the timefor the game to reach the stable coalition structures. Finally,we also show the impact of the distance between theprimary user transmitter and the distributed CR network oncooperative strategies of the distributed CRs.


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Figure 9: Mean time and its variance for the altruistic coalition formation of n = 6 CRs to form the grand coalition (absorbing state fora single random drop for the given simulation scenario) from the transient state of all singleton coalitions for different probabilities p ofcoalition formation proposal. The dwell time in each state is set to 0.001 ms.

Funding

This work was funded by the Finnish Funding Agency forTechnology and Innovation (TEKES) and by Academy ofFinland.

Acknowledgment

The material in this paper was presented in part at the5th International Conference on Cognitive Radio OrientedWireless Networks and Communications (CrownCom),Cannes, France, June, 2010.

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Photograph © Turisme de Barcelona / J. Trullàs

Preliminary call for papers

The 2011 European Signal Processing Conference (EUSIPCO 2011) is thenineteenth in a series of conferences promoted by the European Association forSignal Processing (EURASIP, www.eurasip.org). This year edition will take placein Barcelona, capital city of Catalonia (Spain), and will be jointly organized by theCentre Tecnològic de Telecomunicacions de Catalunya (CTTC) and theUniversitat Politècnica de Catalunya (UPC).EUSIPCO 2011 will focus on key aspects of signal processing theory and

li ti li t d b l A t f b i i ill b b d lit

Organizing Committee

Honorary ChairMiguel A. Lagunas (CTTC)

General ChairAna I. Pérez Neira (UPC)

General Vice ChairCarles Antón Haro (CTTC)

Technical Program ChairXavier Mestre (CTTC)

Technical Program Co Chairsapplications as listed below. Acceptance of submissions will be based on quality,relevance and originality. Accepted papers will be published in the EUSIPCOproceedings and presented during the conference. Paper submissions, proposalsfor tutorials and proposals for special sessions are invited in, but not limited to,the following areas of interest.

Areas of Interest

• Audio and electro acoustics.• Design, implementation, and applications of signal processing systems.

l d l d d

Technical Program Co ChairsJavier Hernando (UPC)Montserrat Pardàs (UPC)

Plenary TalksFerran Marqués (UPC)Yonina Eldar (Technion)

Special SessionsIgnacio Santamaría (Unversidadde Cantabria)Mats Bengtsson (KTH)

FinancesMontserrat Nájar (UPC)• Multimedia signal processing and coding.

• Image and multidimensional signal processing.• Signal detection and estimation.• Sensor array and multi channel signal processing.• Sensor fusion in networked systems.• Signal processing for communications.• Medical imaging and image analysis.• Non stationary, non linear and non Gaussian signal processing.

Submissions

Montserrat Nájar (UPC)

TutorialsDaniel P. Palomar(Hong Kong UST)Beatrice Pesquet Popescu (ENST)

PublicityStephan Pfletschinger (CTTC)Mònica Navarro (CTTC)

PublicationsAntonio Pascual (UPC)Carles Fernández (CTTC)

I d i l Li i & E hibiSubmissions

Procedures to submit a paper and proposals for special sessions and tutorials willbe detailed at www.eusipco2011.org. Submitted papers must be camera ready, nomore than 5 pages long, and conforming to the standard specified on theEUSIPCO 2011 web site. First authors who are registered students can participatein the best student paper competition.

Important Deadlines:

P l f i l i 15 D 2010

Industrial Liaison & ExhibitsAngeliki Alexiou(University of Piraeus)Albert Sitjà (CTTC)

International LiaisonJu Liu (Shandong University China)Jinhong Yuan (UNSW Australia)Tamas Sziranyi (SZTAKI Hungary)Rich Stern (CMU USA)Ricardo L. de Queiroz (UNB Brazil)

Webpage: www.eusipco2011.org

Proposals for special sessions 15 Dec 2010Proposals for tutorials 18 Feb 2011Electronic submission of full papers 21 Feb 2011Notification of acceptance 23 May 2011Submission of camera ready papers 6 Jun 2011

Documents

Throughput-EfﬁcientDynamicCoalitionFormationin ......cooperative spectrum sensing CRs is the topic of [13]. Using a merge-and-split based coalition formation game model, the authors