Mobile Netw ApplDOI 10.1007/s11036-014-0507-x

Cooperative Spectrum Prediction in Multi-PU Multi-SUCognitive Radio Networks

Xiaoshuang Xing · Tao Jing · Wei Cheng · Yan Huo ·Xiuzhen Cheng · Taieb Znati

© Springer Science+Business Media New York 2014

Abstract Spectrum sensing is considered as the corner-stone of cognitive radio networks (CRNs). However, sens-ing the wide-band spectrum results in delays and resourcewasting. Spectrum prediction, also known as channel sta-tus prediction, has been proposed as a promising approachto overcome these shortcomings. Prediction of the chan-nel occupancy, when feasible, provides adequate meansfor an SU to determine, with a high probability, when toevacuate a channel it currently occupies in anticipation ofthe PU’s return. Spectrum prediction has great potentialto reduce interference with PU activities and significantlyenhance spectral efficiency. In this paper, we propose anovel, coalitional game theory based approach to investi-gate cooperative spectrum prediction in multi-PU multi-SU

X. Xing · T. Jing (�) · Y. HuoSchool of Electronics and Information Engineering,Beijing Jiaotong University, Beijing, Chinae-mail: tjing@bjtu.edu.cn

X. Xinge-mail: 10120170@bjtu.edu.cn

Y. Huoe-mail: yhuo@bjtu.edu.cn

W. ChengDepartment of Computer Science, University of MassachusettsLowell, Massachusetts, USAe-mail: wcheng@cs.uml.edu

X. ChengDepartment of Computer Science, The George WashingtonUniversity, Washington DC, USAe-mail: cheng@gwu.edu

T. ZnatiDepartment of Computer Science, University of Pittsburgh,Pittsburgh, PA 15260, USAe-mail: znati@cs.pitt.edu

CRNs. In this approach, cooperative groups, also referredto as coalitions, are formed through a proposed coalitionformation algorithm. The novelty of this work, in compari-son to existing cooperative sensing approaches, stems fromits focus on the more challenging case of multi-PU CRNsand the use of an efficient coalition formation algorithm,centered on the concept of core, to ensure stability. The-oretical analysis is conducted on the upper bound of thecoalition size and the stability of the formed coalition struc-ture. A through simulation study is performed to assessthe effectiveness of the proposed approach. The simula-tion results indicate that cooperative spectrum predictionleads to more accurate prediction decisions, in comparisonwith local spectrum prediction individually performed bySUs. To the best of our knowledge, this work is the first touse coalitional game theory to study cooperative spectrumprediction in CRNs, involving multiple PUs.

Keywords Cognitive radio networks · Cooperativespectrum prediction · Coalitional game theory ·Coalition formation

1 Introduction

With the proliferation of various forms of mobile devices,the radio spectrum has fast become a scarce and expen-sive resource. Various spectrum utilization studies, however,have shown large portions of the overall spectrum remainseverely under-utilized, while demand for bandwidth con-tinues to increase [1, 2]. To achieve better management ofspectral resources, cognitive radio [3–9] has emerged as apromising technology to harness the potential of unusedspectrum in an opportunistic manner. Cognitive radionetworks (CRNs) typically involve two classes of users:

Mobile Netw Appl

primary users (PUs), who are incumbent licensees of thespectrum, and secondary users (SUs), who are allowed toopportunistically operate on licensed spectrum bands, aslong as their transmissions do not cause harmful interfer-ence with the activities of the PUs.

In order to enhance spectrum sharing, while keeping theimpact of interference on PUs at a minimal level, a num-ber of spectrum sensing methods have been proposed toallow SUs to locate spatially and/or temporally availablespectrum holes. A major challenge in spectrum sensing isthe ability of the underlying sensing technique to detectweak PU signals with minimal delay. Measurement studies,however, have shown that the non-negligible delay, intro-duced by the underlying hardware platform, can negativelyimpact the accuracy of spectrum sensing. Moreover, sens-ing the wide-band spectrum results in a waste of resources.To tackle these shortcomings, spectrum prediction [10], alsoknown as channel status prediction, has been proposed as analternative approach to manage spectrum holes.

There are two types of spectrum prediction techniques.Local spectrum prediction, in which each SU senses the cur-rent channel state and uses a hidden Markov model (HMM)to predict the future channel states, has been investigatedin [11, 12] for real-time spectrum sensing to avoid interfer-ence caused by the response delay, and in [13] to enable anSU to leave its currently occupied channel before the PUstarts transmission. Recent work [14–16] show that whenthe performance of an individual is worse than that within agroup, individuals are motivated to form cooperative groupsto maximize the benefit of the system and/or themselves,resulting in cooperative spectrum prediction. Designingefficient cooperation algorithms with high prediction accu-racy and low false alarm rate, however, entail numerouschallenges, including the ability of the algorithm to over-come the natural selfish behavior of wireless users and tominimize implementation overhead. In [17], a cooperativespectrum sensing approach, where SUs form cooperativegroups to improve their sensing accuracy, is studied. In thisapproach, the cooperative group formation process is con-structed as a coalitional game and each cooperative group,referred to as a coalition, is formed by balancing the trade-off between the gain in terms of detection probability andthe cost in terms of false alarm rate.

In this paper, we use a coalition-based approach for spec-trum prediction, but, contrary to previous work, the focus ison the challenging problem of cooperative spectrum predic-tion to improve prediction accuracy. Within this framework,four unique and significant contributions are achieved: first,the focus of this work goes beyond a single PU CRN andaddresses the more practical and challenging multi-PU sce-nario; second, we define a preference order for the SU andpropose a novel coalition formation algorithm; third, weprove the stability of the core of the coalition structure,

formed by our algorithm; last, we conduct simulation withdifferent number of PUs and SUs to validate the effective-ness of the proposed cooperative prediction algorithm in amulti-PU, multi-SU CRN environment. To the best of ourknowledge, this work is the first to use a coalitional gametheory based framework for accurate cooperative spectrumprediction in CRNs, with multiple PUs.

The rest of the paper is organized as follows. The sys-tem model and some preliminary knowledge are brieflydescribed in Section 2. We design the coalitional gamebased cooperative spectrum prediction scheme in Section 3.Simulation results are presented and analyzed in Section 4.And, we conclude the paper in Section 5.

2 Network model and preliminaries

2.1 System model and problem description

In this paper, we consider a database-assisted CRN, whichconsists of M PUs and N SUs. The set of PUs and SUs aredenoted by M = {1, 2, · · · , M} and N = {1, 2, · · · , N},respectively. M orthogonal channels are allocated to M pri-mary users, with ci, i ∈ M , representing the channel ownedby PU i. In this CRN, a database consisting of the locationsand licensed channels associated to all PUs is available tothe SUs. It is worth noting that this architecture is similarto the one suggested in the second memorandum opinionand order (FCC 10–174) [18]. Based on the IEEE 802.22standard specifications, which require that a cognitive radionetwork device vacate its spectrum band within 2 secondsafter the appearance of a PU [19], we assume that the CRNsystem is time-slotted and the length of a slot is expressedin seconds.

At the beginning of each time slot, the busy/idle statusof a channel is detected by the SUs via energy detectionbased spectrum sensing techniques [20, 21]. The spectrumsensing process of SU j ∈ N on channel ci, i ∈ M , isillustrated in Fig. 1. Based on this process, SU j obtains anobservation ot

ji on the true state qti of channel ci at each

time slot t . The observation otji is the local decision of SU j

regarding the primary channel status qti . SU j ’s decision on

ci is a detection, if otji = busy and qt

i = busy, and a false

Fig. 1 An illustration of the spectrum sensing process in time-slottedsystem

Mobile Netw Appl

alarm, if otji = busy and qt

i = idle. Based on the analyticalmodel presented in [21], the closed-form expression of thedetection probability, Pdji , and the false alarm probability,Pfji , are represented in Eqs. 1 and 2, respectively.

Pdji = e−δ2

m−2∑

n=0

1

n!(

δ

2

)n

+(

1 + γ ji

γ ji

)m−1

(1)

×[e− δ

2(1+γ ji ) − e−δ2

m−2∑

n=0

1

n!

(δγ ji

2(1 + γ ji)

)n]

Pfji = Γ(m, δ

2

)

Γ (μ)(2)

In the above expressions, δ is the energy threshold ofthe energy detector, m is the time bandwidth product, γ ji

is the average SNR of SU j on channel ci , and Γ (., .)

represents the incomplete gamma function, while Γ (.) rep-resents the gamma function. Furthermore, γ ji is defined as

γ ji = Pihij

σ 2 , where Pi represents the transmit power of PU

i, σ 2 represents the Gaussian noise variance and hij repre-sents the path loss between PU i and SU j ; hij is defined ashij = κ

dμij

, where κ is the path loss constant, μ is the path

loss exponent, and dij is the distance between PU i and SUj .

Let Pmji be the miss detection(otji = idle and

qti = busy

)probability of SU j on channel ci , then:

Pmji = 1 − Pdji (3)

In the spectrum sensing process illustrated by Fig. 1,the channel occupancy states (busy or idle), determined bythe PU activities (on or off), form a Markov process [22].These states are hidden since they are not directly observ-able. On the other hand, each SU j generates its observationsequence based on its spectrum sensing results, which formsthe set of observation states. This process is a normal ran-dom process that depends on both the PU activities and thespectrum sensing accuracy of SU j (i.e., Pdji and Pfji).Therefore, the spectrum sensing process can be modeled asa HMM. Define the hidden state space as X = {x0, x1},with x0 = 0 and x1 = 1 indicating that the primary chan-nel is idle and busy, respectively. Similarly, the observationstate space is defined as Y = {y0, y1}, with y0 = 0 andy1 = 1 indicating that the spectrum sensing result is idle andbusy, respectively. Then the HMM can be described by itsparameters λ = (π, A, B), where π is the initial state dis-tribution: π = [πi]1×2, with πi = Pr

(q0 = xi

), i = 0, 1;

A is the state transition probability matrix: A = [aij ]2×2,with aij = Pr

(qt+1 = xj |qt = xi

), i, j = 0, 1; and B

is the emission probability matrix: B = [bjk]2×2, withbjk = Pr

(ot = yk|qt = xj

), j, k = 0, 1. It is clear that in a

perfect case it holds that b11 = Pdji and b01 = Pfji .

After sensing channel ci for T slots, SU j forms an obser-

vation sequence Oji ={o1ji , · · · , oT

ji

}and trains a specific

HMM. As discussed in [23], HMM based local spectrumprediction can be performed by each SU to make a local pre-diction decision of the future channel status of ci . In orderto improve the prediction accuracy, we propose a coalitionalgame theory based cooperative prediction scheme. Prior todescribing the scheme, we briefly introduce in the followingtwo subsections preliminary issues and definitions related toHMM based local spectrum prediction and coalitional gametheory, respectively.

2.2 HMM Based local spectrum prediction

There are two stages in the HMM based local spectrum pre-diction algorithm [23], with the first one being the HMMtraining process and the second one being the predictiondecision making process.

In the HMM training process, each SU estimates theparameters of the HMM. For SU j ∈ N , it forms an

observation sequence Oji ={o1ji , · · · , oT

ji

}through T -slot

spectrum sensing on channel ci . Then, the training processcan be considered as an optimization problem which aimsto find the optimal parameters that maximize the probabilityof obtaining the observation sequence Oji :

λ∗ji = arg max Pr(Oji |λji) (4)

Performing the Baum-Welch algorithm [24] leads to thesolution of the optimization problem described in Eq. 4. We

use λ∗ji =(π∗

ji , A∗ji , B

∗ji

)to denote the optimal solution.

With the estimated parameters λ∗ji =(π∗

ji , A∗ji , B

∗ji

),

SU j makes a local prediction about the future state ofchannel ci in the prediction decision making process. Theprediction decision is made according to the following rule:

oT+1ji =

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

1,

if Pr(oT+1ji = 1|Oji, λ

∗ji

)≥ Pr

(oT+1ji = 0|Oji, λ

∗ji

)

0,

if Pr(oT+1ji = 1|Oji, λ

∗ji

)< Pr

(oT+1ji = 0|Oji, λ

∗ji

)

(5)

2.3 Preliminaries of coalitional game theory

According to [25], a coalitional game can be defined asfollows:

Definition 1 (Coalitional Game) A coalitional game G isa pair (N , (�j )j∈N ), where N is a finite player set withj being an individual player. Each player attempts to form acoalition (cooperative group) with others and cooperatively

Mobile Netw Appl

work on certain tasks in order to gain benefits for itselfand/or for the whole system. �j is the preference order ofplayer j on Dj(N ) with Dj(N ) being the set of coalitionsthat j belongs to. For any two coalitions R ∈ Dj(N ) andS ∈ Dj(N ), R �j S indicates that player j prefers to joincoalition R than coalition S.

Each player j ∈ N tries to form a coalition accordingto the preference order �j , and different coalition structurescan be constructed during the coalition formation process.

Definition 2 (Coalition Structure) A coalition structureω = {S1, S2, · · · , SK}, with K ≤ |N | being a positiveinteger, and Sk �= ∅, k ∈ {1, 2, · · · , K}, being a certaincoalition, is a partition of the player set N that satisfies:1) ∪K

k=1Sk = N and 2) Sk ∩ Sl = ∅ for any k, l ∈{1, 2, · · · , K} with k �= l.

Different coalition formation process may lead to differ-ent coalition structures. However, not all the possible coali-tion structures are stable. The concept of core is proposed toindicate the set of stable coalition structures.

Definition 3 (Core) The core of a coalitional game is theset of stable coalition structures which guarantees that nogroup of players have incentives to leave the coalitions theycurrently belong to or join other coalitions.

In practice, players can cooperatively work to achieve aset of given tasks, either to improve their own benefits orthe benefit of the system, only when they succeed in form-ing a stable coalition. Such an observation underscores theimportance of the core when applying the coalitional gametheory.

3 Coalitional game based cooperative spectrumprediction

In this section, we study the cooperative spectrum pre-diction via a coalitional game based approach, where thesecondary users are considered as the players who attemptto form coalitions and cooperatively predict the future chan-nel status. Coalition formation is an important process inour coalitional game based cooperative spectrum prediction;through this process, a coalition structure consisting of sev-eral coalitions can be constructed. Within each coalition,an SU is elected as the coalition leader, whose responsi-bility includes collecting the local prediction results fromother members of the coalition and making a final coopera-tive prediction decision through data fusion. Different datafusion rules, such as the OR rule, the AND rule, and the K-out-of-N rule, have been proposed. Teguig et al. compared

the performance of these data fusion rules in [26] via a sim-ulation study based on an ROC curve analysis, and theirresults indicate that the OR rule has better detection per-formance than the AND rule, and that the K-out-of-N ruletakes some tradeoff between the AND rule and the OR rule,with the AND rule and the OR rule being its special casesof K = N and K = 1, respectively. According to the analy-sis in [26], we make a cooperative prediction decision basedon the OR data fusion rule to provide better performance inthis study.

The considered multi-PU multi-SU scenario bringsa specific challenge to the design of the cooperativespectrum prediction scheme. Due to the hardware limita-tions, each SU can only sense one channel and form oneobservation sequence at a time [27]. According to Eqs. 4and 5, however, the observation sequence is necessary inorder to predict future states of a channel. Since it is impos-sible for an SU to make prediction for more than onechannel at the same time, each SU should choose onlyone channel to sense and predict with the assistance of thedatabase. Consequently, SUs should be first classified intoM categories, with each category Ci, i = {1, 2, · · · , M},being the set of SUs choosing channel ci for sensingand predicting. Based on this classification, a coalitionstructure ωi = {

Si1, S

i2, · · · , Si

K

}is formed for each

category Ci , where Sik is the kth coalition for category i,

and K is the total number of coalitions in category i.Note that different categories may have different number ofcoalitions. In the following subsections, we describethe proposed category classification method, define thepreference order of the secondary users, design the coali-tion formation algorithm, and analyze the property of theproposed algorithm.

3.1 Category classification: channel selectionfor spectrum sensing and prediction

In this subsection, a category classification proposition isgiven to solve the channel selection problem for each SU.According to this proposition, each SU chooses the chan-nel on which it gains the highest sensing and predictionaccuracy.

Proposition 1 SU j is always classified into category Ci ,when PU i is the nearest primary user from SU j .

Proof It can be seen from Eqs. 4 and 5 that both the estima-tion process and the prediction process are dependent on theobservation sequence. Consequently, when provided with amore accurate observation sequence Oji , SU j can betterestimate the parameters of the HMM. Furthermore, usingmore precise estimates of λ∗ji and Oji , SU j can make moreaccurate prediction of future states of channel ci . Thus, if

Mobile Netw Appl

SU j is capable of performing the highest sensing accuracyon channel ci , SU j chooses ci for spectrum sensing andprediction to improve its sensing and prediction accuracy.

The sensing accuracy of SU j on channel ci can be

defined as Paji = Pdji+(1−Pfji )

2 , with 0 ≤ Pdji ≤ 1 beingthe sensing accuracy when the true channel state is busy and0 ≤ 1 − Pfji ≤ 1 being the sensing accuracy when thetrue channel state is idle. According to Eq. 2, Pfji is onlydependent on the time bandwidth product m and the energythreshold δ of the energy detector. Consequently, SU j hasthe same false alarm probability on all primary channels.That is, for any i1 �= i2 ∈ M , it holds Pfji1 = Pfji2 . There-fore, Pdji has the decisive influence on the sensing accuracy.

Substitute γ ji = Pihij

σ 2 into Eq. 1, we have:

Pdji = e−δ2

m−2∑

n=0

1

n!(

δ

2

)n

+(

Piκ + σ 2dμij

Piκ

)m−1

·⎡

⎢⎣e

σ2dμij

δ

2(σ2dμij+Pi κ) − e−

δ2

m−1∑

n=0

1

n!

(δPiκ

2(σ 2dμij + Piκ)

)n⎤

⎥⎦ (6)

In Eq. 6, δ, κ, μ, σ 2, and m are all constants. Assumingthat the transmission power of all the primary users are thesame, then Pdji is a decreasing function of dij , the distancebetween SU j and PU i. Thus SU j has the highest sens-ing accuracy on channel ci when PU i is the nearest onefrom SU j , and it will choose ci for spectrum sensing andprediction to improve its sensing and prediction accuracy.

Therefore, we show that SU j is always classified intocategory i (Ci), when PU i is the nearest primary user fromSU j .

3.2 Preference order of secondary users

After the category classification process, the SUs are clas-sified into M categories. Based on this classification, coali-tions are formed within each category. As described inSection 2.3, the SUs of a category Ci, i = 1, 2, · · · , M ,seek to form coalitions in order to improve the networkperformance (unselfish players) or their own performance(selfish players). In this paper, we consider the case whereSUs are selfish players, whose intention is to improve theirown prediction accuracy through forming coalitions. Basedon this assumption, we derive the preference order of thesecondary users. Since coalitions are formed within eachcategory, we study the coalition formation problem within aspecific category Ci .

According to [17], the cooperative miss prediction (i.e.,the predicted state is idle while the true channel state isbusy) probability Ψm and cooperative prediction false alarm(i.e., the predicted state is busy while the true channel state

is idle) probability Ψf of coalition Sik , with coalition leader

a (SU a), are, respectively, defined by:

Ψm

(Si

k

)= Πj∈Si

k[ψmji(1 − Peja) + (1 − ψmji)Peja] (7)

Ψf

(Si

k

)= 1−Πj∈Si

k[(1−ψfji)(1−Peja)+ψfjiPeja] (8)

In the above expressions, ψmji and ψfji represent thelocal miss prediction probability and local prediction falsealarm probability of SU j ∈ Si

k , respectively; and Peja

represents the probability that an error occurs during thetransmission from SU j to the coalition leader a. AdoptingBPSK modulation in Rayleigh fading environments, Peja isgiven by [28]:

Peja = 1

2

(1 −

√γ ja

1 + γ ja

)(9)

where γ ja is the average SNR from SU j to the coalition

leader a given by γ ja = Pj hja

σ 2 , with Pj being the transmitpower of SU j , hja being the transmission gain between SUj and its coalition leader a, and σ 2 being the Gaussian noisevariance. In order to minimize the reporting error, coalitionleader should be appropriately selected so that the followingholds:

a = arg max

∑j∈{Si

k\a} γ ja

| {Sik \ a

} | (10)

where{Si

k \ a}

represents the set of SUs in coalition Sik

except SU a and | {Sik \ a

} | represents the coalition size.It is clear from Eqs. 7 and 8 that SU j can decrease

its miss prediction probability at the cost of increasingits prediction false alarm probability by joining coalitionSi

k . Thus, the improved prediction accuracy for SU j is(Ψd

(Si

k

)− ψdji

) − (Ψf

(Si

k

)− ψfji

), where Ψd

(Si

k

) =1 − Ψm

(Si

k

)and ψdji = 1 − ψmji represent the cooper-

ative prediction (i.e., the predict result is busy while thetrue channel state is busy) probability and local predictionprobability, respectively. Furthermore, similar to the missdetection and false alarm constraint recommended by IEEE802.22 for spectrum sensing, we define a miss predictionconstraint α and a prediction false alarm constraint β for thechannel status prediction. Based on the desired values of α

and β, a utility function φj

(Si

k

)can be associated with each

SU j ∈ N to assess the performance improvement for SU j

resulting from joining coalition Sik, i ∈ {1, 2, · · · , M}, k ∈

{1, 2, · · · , K}.

φj

(Si

k

)={

(Ψd

(Si

k

)−ψdji)−(Ψf

(Si

k

)−ψfji

), if Ψf

(Si

k

) ≤ β

0, otherwise

(11)

Mobile Netw Appl

Under the prediction false alarm constraint, we have:

φj

(Si

k

)=(Ψd

(Si

k

)− ψdji

)−(Ψf

(Si

k

)− ψfji

)

=(Ψd

(Si

k

)− Ψf

(Si

k

))− (ψdji − ψfji)

Let V(Si

k

) = Ψd

(Si

k

) − Ψf

(Si

k

)denote the value of

coalition Sik , we have:

φj

(Si

k

)= V

(Si

k

)− (ψdji − ψfji) (12)

Based on the above analysis, we define the preference orderfor SUs in the coalitional game (N , (�j )j∈N ) as:

Sik �j Si

l := φj

(Si

k

)≥ φj

(Si

l

)(13)

In the above expression, Sik and Si

l are two differentpotential coalitions within Category i (Ci), and j ∈ Si

k ∩Sil .

The preference order between two coalitions shows that SUj prefers to joint the coalition which results in the greaterimprovement of the prediction accuracy.

For a specific SU j , the value of ψdji and ψfji areboth fixed; consequently, φj

(Si

k

) ≥ φj

(Si

l

) ⇔ V(Si

k

)�

V(Si

l

). Stated differently, V

(Si

k

)� V

(Si

l

)means coali-

tion Sik is worthier than Si

l , so that for any SU j ∈ Sik ∩ Si

l

coalition Sik is preferred over Si

l . Similarly, we can define anordering � among coalitions. More specifically, for any twocoalitions R and S, we have:

R � S := V (R) ≥ V (S) (14)

3.3 Coalition formation algorithm

According to the analysis in the last subsection, the coali-tion value V (·) is an important factor to be considered whenforming coalitions. However, it’s not necessary for SUs tocompare the values of all potential coalitions. Since the pre-diction false alarm probability of a coalition increases withthe number of SUs in the coalition, coupled with the con-straint β imposed on the prediction false alarm, the size ofa coalition is upper bounded. Consequently, coalitions witha large number of SUs should not be considered, as they donot satisfy the prediction false alarm constraint.

To derive the upper bound of the coalition size, we firstconsider a perfect case where the reporting channel exhibitsno error, i.e., ∀j ∈ Si

k, Peja = 0. Then the prediction falsealarm probability of coalition Si

k is given by:

Ψf

(Si

k

)= 1 − Πj∈Si

k(1 − ψfji) (15)

Let ψf i = minj∈Sikψfji , the prediction false alarm con-

straint can be described as:

1 − (1 − ψf i)|Si

k | ≤ Ψf

(Si

k

)≤ β, (16)

where∣∣Si

k

∣∣ represents the size of the coalition Sik , i.e., the

number of SUs in coalition Sik . Solving Eq. 16, we obtain:

∣∣∣Sik

∣∣∣ ≤ log(1 − β)

log(1 − ψf i)(17)

Since in the perfect case a coalition can accommodatea larger number of SUs compared to the imperfect case,the upper bound of the coalition size resulting from Eq. 17is also the upper bound of the coalition size under imper-fect channel conditions. Denote this upper bound by Bu. Wehave:

Bu = log(1 − β)

log(1 − ψf i)(18)

Coalitions with no more than Bu SUs are referred to aspossible coalitions.

Based on Section 3.2 and the analysis carried out above,we propose a coalition formation algorithm whose pseu-docode is presented in Algorithm 1.

3.4 Stability of the formed coalition structure

In practice, coalitions must be stable, so that SUs have noincentive to leave their current coalitions and form newones. In this section, we investigate the stability of thecoalition structure formed by the proposed Coalition For-mation Algorithm. According to Definition 3, the core ofa coalitional game indicates the set of the stable coalitionstructures of the game. We use this definition to first provethe existence of the core of the proposed coalition formationalgorithm and then prove that the coalition structure formedby our algorithm belongs to the core.

As stated in [29], the common ranking property (pro-posed by Farrel and Sotchmer [30]) guarantees the non-emptiness of the core in the coalitional game.

Definition 4 A game G = (N , (�j )j∈N ) satisfies thecommon ranking property iff there exists an ordering � over2N \ {∅} such that for any j ∈ N and any R, S ∈ Dj(N )

we have R �j S ⇔ R � S.

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It can be seen from Eqs. 12, 13 and 14 that for anyj ∈ R ∩ S, R � S ⇔ R �j S. We can, therefore,state that for any j , such that R, S ∈ Dj(N ), we haveR �j S ⇔ R � S. This proves that the proposed coalitionalgame satisfies the common ranking property, and, therefore,the core of the proposed game is not empty. We next provethat the coalition structure formed by our algorithm belongsto the core of the game.

Theorem 1 The coalition structure formed by Algorithm 1belongs to the core of the coalitional game.

Proof According to Algorithm 1, for each category i,coalition Si

1 has the highest value among all the possible

coalitions. Therefore, for ∀j ∈ Si1, S

i1 ∈ Dj(N ), it holds

that V(Si

1

) ≥ V(Si

1

)⇒ Si

1 � Si1 ⇒ Si

1 �i Si1. That is, SU

j prefers Si1 to any other possible coalitions in Dj(N ); thus

it has no incentives to leave Si1 and form new coalitions.

Next, we consider coalition Si2. We first note that SUs in

Si1 will not form coalitions with any other SU who is not

a member of Si1, including those in Si

2. Taking members ofSi

1 out of consideration, coalition Si2 has the highest value

among all the possible coalitions. Thus for ∀j ∈ Si2, S

i2 ∈

Dj(N ) it holds that V(Si

2

) ≥ V(Si

1

)⇒ Si

2 � Si1 ⇒

Si2 �i Si

1. So that SU j ∈ Si2 has no incentives to leave Si

2,either.

Similar analysis can be carried out for other coalitions,which proves that the formed coalition structure is (i) stableand (ii) belongs to the core of the game.

4 Simulation

A simulation study is performed to assess the effectivenessof the proposed coalition formation algorithm. In this sim-ulation study, the parameters are set according to the valuesprovided in [17], which are listed in Table 1.

First, we form a cognitive radio network with 3 PUs(denoted by black squares) and 21 SUs (denoted by bluecircles). The PUs and SUs are all randomly deployed in a3km × 3km square area as shown Fig. 2.

According to Eqs. 1 and 2, the detection probability andfalse alarm probability in spectrum sensing are both depen-dent on the energy detection threshold δ. Consequently, theprediction probability and prediction false alarm probabilityin spectrum prediction are also dependent on δ. In Fig. 3,we examine the theoretical average detection probability perSU (ADP) and the theoretical average false alarm probabil-ity per SU (AFP) of spectrum sensing, and the theoreticalaverage prediction probability per SU (APP) and the the-oretical average prediction false alarm probability (APFP)

of spectrum prediction when δ varies. The results showthat the average false alarm probability of spectrum predic-tion is always higher than that of spectrum sensing, whilethe average prediction probability is always lower than theaverage detection probability. This indicates that the perfor-mance of spectrum prediction can not be better than thatof spectrum sensing. Moreover, it can be seen that a higherprediction probability always comes with a higher predic-tion false alarm probability. Thus when forming coalitionsto improve the prediction accuracy we should always con-sider the tradeoff between the prediction probability and theprediction false alarm probability; thus Eq. 11 is a properdescription. Also it can be seen that these probabilities aredifferent for different categories which implies the influenceof geo-location on the performance of spectrum sensing andprediction.

Performing our proposed coalition formation algorithmfor the CRN shown in Fig. 2, the formed coalition struc-ture is ω1 = {{8, 14}, {3, 19}, {6}, {9, 20}}, ω2 = {{1},{2, 10, 11, 15}, {7, 16, 18, 21}}, ω3 = {{4, 12}, {5}, {13,

17}}. We can see that the coalition sizes of ω2 are rela-tively bigger than those of ω1 and ω3. As shown in Fig. 2,SUs of category 2 are relatively farther from PU 2 so thatthe local spectrum sensing/prediction gains relatively lowerdetection/prediction probability, therefore coalitions withlarger sizes can provide the SUs more benefits. This resultis consistent with that shown in Fig. 3, which indicates thatthe average local detection and prediction probabilities ofcategory 2 are lower than those of category 1 and 3.

Next, we discuss the performance results of local andcooperative spectrum prediction, described in Table 2. Tosimplify notation, we denote local spectrum prediction andcooperative spectrum prediction by LSP and CSP, respec-tively. We also note that each SU tends to form a coalitionthat has the greatest potential to improve its prediction accu-racy. The results show that it is not always the case thatall SUs achieve performance gains based on spectrum pre-diction. For example, SUs 7, 11, and 13 do not increasetheir prediction accuracy through cooperation. This, how-ever, does not imply that the proposed cooperative spectrumprediction scheme is not effective. It is obvious that mostSUs improve their prediction accuracy through the proposedcooperative spectrum prediction scheme. Those SUs whoare far away from PUs, such as SU 2 and SU 18, have theopportunity to achieve significant performance from coop-erative spectrum prediction. It is also worth noting that SUs,who do not see a significant increase in their predictionaccuracy (e.g., SU 7, 11, and 13), retain the same accuracywith local prediction.

We also conduct simulations for different number of PUswhen the number of SUs is always set to be seven timesthat of the PUs. We change the number of PUs from 1 to10 and randomly construct three different networks for each

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Table 1 System parametersParameter Meaning Value

m Time bandwidth product 5

κ Path loss constant 1

μ Path loss exponent 3

σ 2 Gaussian noise variance −90dBm

PPU Transmission power of PU 100mW

PSU Transmission power of SU 10mW

Fig. 2 The simulated network

Fig. 3 Average detection probability and false alarm probability of spectrum sensing, and average prediction probability and prediction falsealarm probability of channel status prediction for different energy detection threshold δ

Table 2 Prediction accuracy of LSP and CSP

SU 1 2 3 4 5 6 7 8 9 10 11

LSP (%) 90.1 60.2 87.2 89.2 87.7 89.5 88 90.8 88.2 83.8 87.3

CSP (%) 90.1 87.2 89.4 89.5 87.7 89.5 87.3 91.3 88.3 87.2 87.2

SU 12 13 14 15 16 17 18 19 20 21

LSP (%) 87.8 87.1 91.6 85.2 86.3 80.1 56.5 88.1 87.8 85.2

CSP (%) 89.5 86.4 91.3 87.2 87.3 86.4 87.3 89.4 88.3 87.3

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Fig. 4 Prediction accuracy vs.the number of PUs

case. We investigate the performance from the perspectiveof average prediction accuracy, and the simulation resultsare given by Fig. 4.

We can see from Fig. 4 that the average predictionaccuracy of both local and cooperative spectrum predictionincreases with the number of PUs in the simulated scenario.The reason is due to the fact that we assume the numberof SUs is always 7 times that of the PUs; thus, when thenumber of PUs increases, the CRN becomes a dense net-work and the average distance between an SU and a PUdecreases. Consequently, the average detection probabilityof spectrum sensing is increased and the SU forms a moreaccurate HMM with more precise model parameters. This inturn increases the average prediction accuracy of spectrumprediction. It is also obvious that the average predictionaccuracy of our cooperative spectrum prediction schemeis always higher than the local one. Furthermore, the

proposed scheme achieves significant performanceimprovement when the number of PUs is small and the net-work is sparse. Moreover, it should be noticed that there is asharp decrease in the prediction accuracy of local spectrumprediction when there exist 9 PUs in the system. This is dueto the fact that in the three randomly constructed networksmany SUs are located far away from the PUs, therebyresulting in poor local prediction accuracy. However, theprediction accuracy of cooperative spectrum prediction isnot affected since the cooperative scheme exploit the ben-efits of those SUs that near to PUs. This implies that ourcooperative spectrum prediction scheme has the potentialto always achieve steady performance improvement.

Last, we investigate the influence of the number of SUson our cooperative spectrum prediction scheme. We fix thenumber of PUs to 3 and change the number of SUs from 10to 40. In Fig. 5, the performance of local and cooperative

Fig. 5 Prediction accuracy vs.the number of SUs

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spectrum prediction are denoted by solid red bar anddashed green bar, respectively. We observe that the proposedcooperative spectrum prediction scheme always improvesspectrum prediction accuracy. It can also be seen that theperformance improvement becomes less significant as thenumber of SUs increases. The reason is similar to the onediscussed in the previous experiment.

5 Conclusions and future work

In this paper, we propose a novel cooperative spectrum pre-diction scheme for multi-PU multi-SU CRNs. We model thecooperative group formation process as a coalitional gameand propose a coalition formation algorithm. The upperbound of the coalition size is derived and the stability of theformed coalition structure is analyzed theoretically. A seriesof simulation study is conducted to verify the effectivenessof our design. Our results indicate that the prediction accu-racy can be improved as SUs can make better predictiondecisions through cooperation. Our future work includesthe investigation of effective mechanisms to expand chan-nel status prediction to a larger number of future timeslots.

Acknowledgments The authors would like to thank the supportfrom the National Natural Science Foundation of China (Grant No.61371069, 61272505, and 61172074), and the National Science Foun-dation of the US (CNS-1162057 and CNS-1265311).

References

1. Huang W, Wang X (2012) Capacity scaling of general cognitivenetworks. IEEE/ACM Trans Netw 20(5):1501–1513

2. Wang X, Huang W, Wang S, Zhang J, Hu C (2011) Delay andcapacity tradeoff analysis for motioncast. IEEE/ACM Trans Netw19(5):1354–1367

3. Li W, Cheng X, Jing T, Cui Y, Xing K, Wang W (2013) Spectrumassignment and sharing for delay minimization in multihop multi-flow crns. IEEE J Sel Areas Commun (JSAC) 31(11):2483–2493

4. Haykin S (2005) Cognitive radio: brain-empowered wireless com-munications. IEEE JSAC 23(2):201–220

5. Xing X, Jing T, Huo Y, Li H, Cheng X (2013) Channel quality pre-diction based on bayesian inference in cognitive radio networks.IEEE INFOCOM

6. Akyildiz IF, Lee WY, Vuran MC, Mohanty S (2006) Next gener-ation/dynamic spectrum access/cognitive radio wireless networks:a survey. Comput Netw J Elsevier 50:2127–2159

7. Li H, Cheng X, Li K, Xing X, Jing T (2013) Utility-based coop-erative spectrum sensing scheduling in cognitive radio networks.IEEE INFOCOM Mini-Conf

8. Li W, Cheng X, Jing T, Xing X (2013) Cooperative multi-hoprelaying via network formation games in cognitive radio networks.IEEE INFOCOM

9. Song M, Xin C, Zhao Y, Cheng X (2012) Dynamic spectrumaccess: from cognitive radio to network radio. IEEE Wirel Com-mun 19(1):23–29

10. Xing X, Jing T, Cheng W, Huo Y, Cheng X (2013) Spectrumprediction in cognitive radio networks. IEEE Wirel Commun20(2):90–96

11. Chen Z, Guo N, Hu Z, Qiu R (2011) Experimental validation ofchannel state prediction considering delays in practical cognitiveradio. IEEE TVT 60(4):1314–1325

12. Chen Z, Hu Z, Qiu R (2009) Quickest spectrum detection usinghidden markov model for cognitive radio. IEEE MILCOM:1–7

13. Akbar I, Tranter W (2007) Dynamic spectrum allocation in cogni-tive radio using hidden markov models: poisson distributed case.IEEE SoutheastCon:196–201

14. Li Z, Yu F, Huang M (2009) A cooperative spectrum sensing con-sensus scheme in cognitive radios. IEEE INFOCOM:2546–2550

15. Yang Y, Liu Y, Zhang Q, Ni L (2010) Cooperative boundarydetection for spectrum sensing using dedicated wireless sensornetworks IEEE INFOCOM:1–9

16. Shehory O, Kraus S (1998) Methods for task allocation via agentcoalition formation. Artif Intell 101(1–2):165–200

17. Saad W, Han Z, Debbah M, Hjorungnes A, Basar T (2009) Coali-tional games for distributed collaborative spectrum sensing incognitive radio networks. IEEE INFOCOM:2114–2122

18. Fcc 10-174: Second memorandum opinion and order (2010)19. Kim H, Shin K (2010) Asymmetry-aware real-time dis-

tributed joint resource allocation in ieee 802.22 wrans. IEEEINFOCOM:1–9

20. Fehske A, Gaeddert J, Reed J (2005) A new approach to signalclassification using spectral correlation and neural networks. IEEEDySPAN:144–150

21. Digham F, Alouini M-S, Simon M (2003) On the energy detectionof unknown signals over fading channels. IEEE ICC 5:3575–3579

22. Ghosh C, Cordeiro C, Agrawal D, Rao M (2009) Markov chainexistence and hidden markov models in spectrum sensing. IEEEPERCOM:1–6

23. Tumuluru VK, Wang P, Niyato D (2012) Channel status predictionfor cognitive radio networks. Wirel Commun Mob Comput:862–874

24. Welch LR (2003) Hidden Markov models and the Baum-Welchalgorithm. IEEE Inf Theory Soc Newsl 53(4)

25. Bogomolnaia A, Jackson MO, Barbera WTS, Demange G, Green-berg J, Breton ML (2002) The stability of hedonic coalitionstructures. Games Econ Behav 38(2):201–230

26. Teguig D, Scheers B, Le Nir V (2012) Data fusion schemesfor cooperative spectrum sensing in cognitive radio networks.Commun Inf Syst Conf:1–7

27. Yi S, Zeng K, Xu J (2012) Secondary user monitoring in unslottedcognitive radio networks with unknown models. Wirel AlgoritmSyst Appl 7405:648–659

28. Proakis J (2001) Digital communications. McGraw-Hill, NewYork

29. Banerjee S, Konishi H, Sonmez T (1998) Core in a simplecoalition formation game. Soc Choice Welf 18:135–153

30. Farrell J, Scotchmer S (1988) Partnerships. Q J Econ 103(2):279–297