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Spectrum-efficient Resource Allocation Frameworkfor Cooperative Opportunistic Wireless Networks

Mohamed AbdelRaheem, Member, IEEE, Mohammad J. Abdel-Rahman, Member, IEEE,Mustafa El-Nainay, Member, IEEE, and Scott F. Midkiff, Senior Member, IEEE

Abstract—Dynamic spectrum access (DSA) is a promisingapproach to alleviate spectrum scarcity and improve spectrumutilization. Recently, several cooperative communication schemeshave been proposed to further enhance spectrum utilizationin DSA networks. Existing cooperation designs are either tai-lored for primary-secondary user (PU-SU) cooperation andnot applicable to SU cooperation, or focus on the potentialbenefits of SUs cooperation without investigating how SUs agreeon cooperating and the conditions that lead to improve theirperformance. In this paper, we introduce a spectrum-efficientresource allocation framework based on SUs cooperation, wherethe resources include the free spectrum access time, availablechannels, and relays. First, we formulate the interactions betweenthe cooperating SUs and a PU using a discrete-time Markovchain (DTMC). Using this DTMC and Nash bargaining, wedetermine the new spectrum access times for SUs based on everynodes utility. We also derive the conditions under which all SUsimprove their performance by cooperation. Second, considering amulti-channel multi-SU infrastructure network, we formulate twooptimization problems for jointly allocating channels to SUs andselecting the cooperating SU pairs. We corroborate our analyticalfindings with detailed simulations that evaluate SUs cooperationgains and the optimality of the proposed joint allocation schemes.

Index Terms—Dynamic spectrum access, cooperative commu-nications, Markov chain, Nash bargaining.

I. INTRODUCTION

THE massive growth in wireless devices and mobile traffichas motivated extensive research on improving spectrum

utilization. Among the promising solutions is dynamic spec-trum access (DSA). DSA tries to address the rising demandby allowing spectrum-agile devices with cognitive radio capa-bilities, a.k.a. secondary users (SUs), to access the availablespectrum in a dynamic fashion, without interfering with co-located incumbent users, a.k.a. primary users (PUs). In thisway, DSA can significantly improve the spectrum utilization.

Cooperation among different nodes is shown to have thepotential for enhancing the performance of DSA networks andit can be categorized into two categories:

M. AbdelRaheem was with the Bradley Department of Electrical andComputer Engineering, Virginia Polytechnic Institute and State University,Blacksburg, VA 24061 USA. He is now with the Electrical EngineeringDepartment, Assiut University, Assiut, Egypt (e-mail: mohmedht@vt.edu,m.abdelraheem@aun.edu.eg).

M. J. Abdel-Rahman, and S. F. Midkiff are with the Bradley Departmentof Electrical and Computer Engineering, Virginia Polytechnic Institute andState University, Blacksburg, VA 24061 USA (e-mail: { mo7ammad, mid-kiff}@vt.edu).

M. El-Nainay is with the Computer and Systems Engineering Department,Alexandria University, Alexandria, Egypt (e-mail: ymustafa@alexu.edu.eg).

Fig. 1: Examples of SU direct and cooperative transmissions.

• Cooperation between PUs and SUs – In this model,the PU provides part of its spectrum to SUs while SUshelp the PU to improve its transmission performance. Theauthors in [1]–[7] modeled the cooperation between PUsand SUs as market-driven spectrum trading to reallocatethe resources.

• Cooperation between SUs – In this model, SUs coop-erate with each other either (i) to enhance the sensingaccuracy (see, for example, [8]) or (ii) to enhance thetransmission characteristics, such as throughput (see, forexample, [9]–[13]).

In the PU-SU cooperation schemes proposed in [1]–[7], thePU is given a superior role over the SU. For example, the PUacts in [1]–[3] as a monopolist, in [4], [5] as a leader of theStackelberg game, and in [6], [7] as a seller. These modelscannot be used to study SUs cooperation, where no SU has asuperior role over the others. Existing work on SUs coopera-tion focuses only on studying the potential performance gainsbrought by cooperation, without studying how SUs agree oncooperating with each other or the conditions under whichcooperation is beneficial for all cooperating SUs. In this paper,we aim to answer these questions. Furthermore, consideringa multi-channel multi-SU infrastructure network, we proposejoint optimization schemes for allocating channels to SUs andfor selecting the cooperating SU pairs.

In our previous work [12], [13], we showed that utilizingcooperative transmission via intermediate relays reduces sig-nificantly the negative effect of PU interruption on the SUstransmission compared to the case when the SUs transmitdirectly to the destination.

Figure 1 illustrates this idea. Assume a secondary networkwith multiple slow and fast SUs transmitting data packet to asecondary access point (SAP) by utilizing the available whitespaces in the licensed spectrum. If the slow SU utilizes DT as

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in Figure 1(a), it has to abort its first two transmission attemptsdue to the interruption of the PU before it achieves a successfultransmission in the third attempt. On the other hand, the SUmay utilize cooperative transmission via an intermediate relayas shown in Figure 1(b). In the cooperative transmission, thetwo hops are done at higher data rates (shorter transmissiontimes) than the direct transmission and the relay is able tobuffer the transmitted packet till the PU is absent and so itwill utilize the available white spaces more efficiently thanthe DT.

Our Contribution – Based on the previous idea, weestablish a spectrum-efficient resource allocation frameworkfor cooperative SUs that allocates the free spectrum accesstime, channels and relays among SUs.The main contributionsof this paper are as follows:

1. Considering a single-channel system that consists of a PUand a pair of cooperating SUs:• We formulate a discrete-time Markov chain (DTMC)

model to capture the interactions between the PU andthe cooperating SUs, assuming an interweave spectrumsharing paradigm [14], in which the PU and the SUcannot access the same spectrum portion simultane-ously. The cooperating SU pair consists of a slow SUwhich has a low transmission rate and a fast SU whichhas a high transmission rate and relays the packetsof the slow SU. Our model considers three differentSUs’ channel access mechanisms.In contrast to existingMarkov models (e.g., [15], [16]), our DTMC modelexplicitly captures the ability of SUs to transmit co-operatively and models the relay’s own transmissionas well. We use our DTMC model to derive differenttransmission characteristics, such as the SUs spectrumefficiency and throughput.

• Using our DTMC model, and adopting a utility func-tion that considers both the throughput as well as theenergy consumption, we use the Nash bargaining todetermine the new free spectrum access time shares forthe cooperating nodes based on their utility functions.We derive the conditions under which both SU andits relay improve their performance in terms of thethroughput and the power efficiency by cooperation.

2. Considering a multi-channel multi-SU infrastructure net-work, we formulate two optimization problems for jointly(i) allocating channels to SUs and (ii) selecting the cooper-ating SU pairs based on the bargaining based free spectrumshares. The first optimization problem aims to maximize theoverall network throughput subject to individual SU ratedemands. The goal of the second optimization problem isto minimize the maximum (among SUs) difference betweenthe throughput and the rate demand.

These two points, sequentially, form a two-step fair andfriendly resource allocation framework that optimizes theglobal network objective without harming any cooperatingnodes. In this framework, every node gets a free spectrum timeshare that is proportional to its contribution in the cooperationprocess.Paper Organization – The rest of the paper is organized

Fig. 2: Cooperative multi-channel secondary network.

as follows. We present our system model in Section II. TheDTMC model of the PU-SUs is presented and the Nash-bargaining-based SU spectrum access times are determined inSection III. In Section IV, we investigate the optimal channelallocation and SU pairing problem. Detailed performanceevaluation is provided in Section V. Finally, in Section VI weconclude the paper and provide directions for future research.

II. SYSTEM MODEL

In this section, the system and network models are pre-sented. Moreover, the motivation of the proposed work in latersections is established.

A. Network Model

As shown in Figure 2, the system model consists of asecondary infrastructure network with one SAP, number ofsecondary users (SUs) and secondary relays (SRs)1. The sec-ondary network operates under the coverage of more than onePU (three in Figure 2) where the SUs can access the licensedchannels using an interweave spectrum sharing mechanism.The PU, SU and SR use synchronized slotted Media AccessControl (MAC) protocol to access the spectrum where the datatransmission time spans an integer numbers MPU , MSU andMSR of time slots for the PU, SU and SR, respectively. SUsare assumed to have the ability to perform accurate spectrumsensing at the beginning of each time slot. Once detecting aPU on a given channel, SUs immediately vacate this channel.

We assume the network nodes are arranged in three differenttransmission ranges from the SAP. It is assumed that all SUs’packets have the same length and the data rate of every SUdepends on its distance to the SAP. We define three data ratesnamed R1, R2, and R3 with transmission time spans 4m,2m, and m time slots, respectively where m is a parameterthat reflects the time resolution of the transmission. A nodecan transmit its packets directly to the destination, henceforthreferred to as direct transmission, or through another nodewhich acts as a relay, henceforth referred to as cooperativetransmission. In the cooperation mode, the SU uses Decode

1Generally, we will refer to secondary node with slow rate which asks forthe help by (SU) and for the fast rate node that, besides transmitting its owndata, can relay the slow nodes ones, by (SR) .

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(a) DT (b) L(1a)

(c) L(1b) (d) L2

Fig. 3: Example of secondary direct and cooperative transmissionsat different cooperation levels between the SU and the SR.

and Forward (DF) cooperative communication. In DF, theSU transmits its data to an intermediate relay using rateR(SU→SR) in transmission time T(SU→SR) in the first hop.The relay decodes the data then forwards it to the desti-nation (SAP) using rate R(SR→SAP ) in transmission timeT(SR→SAP ) in the second hop. By neglecting the decodingtime, the overall transmission time and data rate are givenby (1) and (2), respectively [17]:

TCC = T(SU→SR) + T(SR→SAP ), (1)1

RCC=

1

R(SU→SR)+

1

R(SR→SAP ). (2)

We define two cooperation levels between the SU and theSR according to the two hops rates and the net achieved rate.The cooperation level is determined by the number of timeslots (transmission time) required to transmit the SU packetMSU over the two-hops from the SU to the SR M(SU→SR)

and from the SR to the SAP M(SR→SAP )2. Considering that

the SU non-cooperative direct transmission (DT) consumes4m time slots; the two levels of cooperation between the SUand SR are defined as follows:

1) L(1) : MSU = 3m

a) L(1a) : M(SU→SR) = m,M(SR→SAP ) = 2mb) L(1b) : M(SU→SR) = 2m,M(SR→SAP ) = m

2) L(2) : MSU = 2m,M(SU→SR) = m,M(SR→SAP ) = m

Levels L(1a) and L(1b) have the same throughput perfor-mance, but they differ in the rate of each hop which isa concern in calculating the utility as will be shown inSection III-C. As a numerical example, if the SU DT rate tothe SAP is 6 Mbps that consumes 4m time slots, it can use anintermediate relay in cooperation level L(1a) such that, the firsthop rate is 24 Mbps (consumes m time slots) and the secondhop rate is 12 Mbps (consumes 2m time slots). That yieldsto a net cooperative transmission that consumes 3m time slotsand cooperative throughput of 8 Mbps. Figure 3 shows the DTand different cooperation levels of this example.

B. Secondary User Access Mechanisms

In this paper, we consider three spectrum access mechanismused by the SAP to control the secondary nodes’ (SUs andSRs) access to the free spectrum in the non-cooperative mode.These access mechanisms determine the secondary nodes

2Here we refer to the transmission in uplink direction but the sameprocedure applies for the downlink direction.

(a) EAP

(b) ETT

(c) ESTT

Fig. 4: Illustration of SU and SR free spectrum shares at differentaccess mechanisms.

disagreement utility if they are not cooperating. The threeaccess mechanisms are defined as follows.

• Equal Access Probability (EAP): In this mechanism, theSAP gives equal access for all nodes regardless of theirdata rates, cooperation level, or the primary user activity.

• Equal Transmission Time (ETT): In this method, the SAPcontrols the access probability such that, on average,different nodes have equal access to the free spectrum.In this case, the SAP does not account for the node datarate or the transmission efficiency.

• Equal Successful Transmission Time (ESTT): In thismechanism, every node gets an equal successful trans-mission time. In other words, the SAP compensates eachnode for its loss due to interruption by the PU.

Figure 4 shows SU and SR shares of the free spectrumfor the three different access mechanisms where tSU and tSRare the total transmission times (total shares) of the SU andSR, respectively, and τSU and τSR are the total successfultransmission time of the SU and SR, respectively. The dashedportions represent the wasted times due to PU interruptions.

As can be noticed from Figure 4, EAP is the most beneficialaccess mechanism for the SU and the worst for the SR asit does not give any access priority for any node over theother and allows every node to transmit the same number ofpackets regardless of its rate or transmission efficiency. Thatcauses the SU (which transmits with low data rate) to occupymost of the available free spectrum time share. On the otherhand, ETT is the best for the SR and the worst for the SU asit does not compensate a slow node for its lower rate nor itslost packets. ESTT can be considered a compromise accessmechanism between EAP and ETT as it compensates thenodes for their lost packets. Detailed analysis of the differentaccess mechanism performance is provided in Section III-B.

Based on the adopted secondary access mechanisms, eachnode gets a certain free spectrum access time share in the non-cooperative mode. If a pair of nodes agreed to cooperate, they

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will re-divide their shares according to the Nash bargainingsolution based on a utility function that combines throughput,energy consumption and the disagreement utility of each node.Based on these bargaining based free spectrum access shares,nodes are paired and channels are allocated in an optimumway to achieve global objective.

III. PU-SU-SR COOPERATION MODEL

In this section, we investigate the cooperation processbetween an SU and an SR. The cooperation is modeled asa resource exchange process where the SR sacrifices part ofits energy in forwarding the SU packets and in return, theSU vacates part of its dedicated free spectrum time shareto the SR. The goal is to find the amount of free spectrumtime the SU should give to the SR based on the utility bothachieve after cooperating and the disagreement utility if theydid not cooperate. We define the utility function to considerboth throughput and energy. After defining the SU and SRutilities in cooperative and non-cooperative modes (disagree-ment points), we use the Nash Bargaining Solution (NBS) tofind the new free spectrum shares after the cooperation. Thecooperation between any SU and SR must not affect othersecondary nodes’ spectrum shares as they only re-allocatetheir non-cooperative share using the bargaining process. Tocalculate the SU and SR utilities, we model the interactionbetween the PU, SU and SR using a DTMC and from thismodel we obtain the necessary transmission characteristicssuch as efficiency and throughput.

A. PU-SU-SR Transmissions Interaction DTMC Model

In this subsection, we present the PU, SU, SR interactionDTMC model in interweave spectrum sharing mechanismfor the three secondary user access mechanisms presentedin Section II. This model quantifies the effect of the PUactivity on the performance of the secondary users in the non-cooperative and cooperative modes. The PU activity affects thetransmission performance of the secondary nodes as it forcesthem to re-transmit their packets due to the interruption causedby the PU transmission. From the analysis of the DTMCmodels we extract different transmission characteristics liketransmission efficiency and throughput that will be used tocalculate the SU and SR utilities in Section III-C.

The transition diagrams shown in Figures 5(a)and 5(b) represent examples of the PU-SU-SR non-cooperative and cooperative DTMC models, respectively, forMPU = 2,MSU = 3 (in non-cooperative mode), MSU = 2(in cooperative mode), and MSR = 1. Each state 3 is labeledby three letters (PSR), where, P represents the PU status, Srepresents the SU status, and R represents the SR status. Theletter (A) is used to indicate that the node (PU, SU or SR) isactively transmitting its own packet. The letter (A∗) indicatesthat the SU or the SR is waiting for the PU to finish itstransmission to start its own. The letter (a) indicates that thissecondary node (SU or SR) is waiting for its turn to accessthe free spectrum and start its transmission. For example,

3In this paper, we use the words ‘state’ and ‘time slot’ interchangeably.

state (A2A∗a) means that the PU is actively transmitting its

packet in its second time slot while the SU is waiting for thePU to be idle to start its own transmission and the SR is idle.State (AnA∗a) has the same meaning of (AnA

∗a) but usedto indicate that the PU started its transmission after the SUfinished its first hop transmission to preserve the memorylessproperty of the Markov chain in the cooperative mode.

The probability values PPUIand PPUA

are the probabilityof the PU being idle or active, respectively and they describethe PU activity pattern. If values of PPUI

and PPUAare

exactly known and they are stable over the time we can usethem directly in the proposed model. However, these valuesare usually unknown for the SAP and change according tothe type of the transmitted data. The common characteristicknown by the SAP about the PU activity is its activitylevel ρ or, by other words, the channel utilization level. Toovercome this point, for a given value of ρ we calculate thecorresponding range of values of PPUI

and PPUAthat result

in this PU activity level. The SAP based its calculation forthe SU and SR performance, for a given PU activity level, onthe average performance over range of transition probabilitieswhich give the same PU activity level. A separate DTMCmodel named stand-alone DTMC is designed to model thePU transmission for a given level of PU activity. Fromthis DTMC model, the targeted transition probabilities arecalculated. The DTMC model, the transition probabilitiescalculations, and their effect on the performance are providedin the appendix.

The value of P(X→Y ) is the probability that secondary nodeY starts a transmission after secondary node X has finishedits transmission. The value of this probability is determinedaccording to the secondary access mechanism used (EAP, ETT,or ESTT).

The final values of the transition probabilities are calculatedbased on the PU activity and according to the adopted sec-ondary user free spectrum access mechanism. For example,in the non-cooperative DTMC model shown in Figure 5(a),after state (IA3a), which means the SU is active transmittingin the last time slot and the PU and SR are idle, the DTMCcan move to state (A1A

∗a) if the PU becomes active withprobability (1 − PPUI

) and the SU stays active (SR is idle)with probability (P(SU→SU)) that gives a total transitionprobability of ((1 − PPUI

) P(SU→SU)). In the same waythe DTMC can move from state (IA3a) to state (IA1a)with a transition probability equal to (PPUI

P(SU→SU)),or to state (A1aA

∗) with a transition probability equal to((1 − PPUI

) P(SU→SR)), or to state (IaA) with a transitionprobability equal to (PPUI

P(SU→SR)).The main difference between the non-cooperative and the

cooperative model is that, in the cooperative model, if the firsthop is finished successfully, the SR can buffer the SU’s packetif the PU becomes active until the PU becomes idle again, thentransmits the packet without the need to repeat the first hoptransmission.

For the PU, the PU activity level ρ equals the summationof all active state occupancy distributions for the different

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(a) (b)

Fig. 5: (a) PU-SU-SR non-cooperative DTMC (b) PU-SU-SR cooperative DTMC.

transmission scenarios and calculated as:

ρ =

MPU∑i=1

π(AiA∗a) + π(AiA∗a) + π(AiaA∗). (3)

The calculated value of ρ using equation (3) must be equalto the given value to ensure that the SU and SR interactionwith the PU is modeled correctly such that it does not affectthe PU activity.

The successful active occupancy distributions for the SUand SR can be calculated by multiplying the occupancydistribution of the last active state by the number of time-slots per transmission (by this way we count only the timeslots resulted in the successful transmission) as shown inequations (4) and (5) for the SU and the SR, respectively.

π(SUA) = MSU π(IA(MSU )a) (4)

π(SRA) = MSR π(IaA(MSR)). (5)

The transmission efficiency of the SU and the SR can becalculated by dividing the spectrum occupancy state distribu-tions resulting in a successful transmission over all active stateoccupancy distributions including those that were wasted dueto the PU interruption.

The SU and SR efficiencies are given by:

ηSU =π(SUA)∑MSU

i=1 π(IAia)

(6)

ηSR =π(SRA)∑MSR

i=1 π(IaAi)

. (7)

The SU and SR throughputs are given by:

TSU = RSU π(SUA) (8)TSR = RSR π(SRA), (9)

where RSU and RSR are the data rate of the SU and the SR,respectively.

B. Analysis of Different Access Mechanisms

In this subsection, we analyze the three non-cooperativeaccess mechanisms proposed in Section II using the DTMCmodels shown in Fig. 5 (a) and (b). The goal is to calculate

the SU and SR transmission efficiency and the throughput, foreach of the proposed secondary access mechanisms using theset of relations described by equations (6)-(9).

1) Non-cooperative mode:

EAP – To achieve equal spectrum access probabilitiesfor both the SU and the SR, the values of the transitionprobabilities are set as follows:

P(SU→SU) = P(SU→SR) = P(SR→SR)

= P(SR→SU) = 0.5. (10)

The value of PPUIand PPUA

are calculated from the stand-alone DTMC models shown in the appendix. The probabilitymatrix P then can be constructed and the occupancy distri-butions of different states are calculated by solving equations(43) and (44) as done for the PU stand-alone DTMC modelin the appendix. After finding the different state occupancydistributions, the transmission efficiency and throughput canbe calculated using equations (6)-(9).

ETT – In ETT, both the SU and the SR have equal freespectrum access time (tsu = tsr in Figure 4) which leads toequal summation of all the state occupancy distributions forthe SU and the SR,

MSR∑i=1

π(IaAi) =

MSU∑i=1

π(IAia) =1− ρ

2. (11)

From the DTMC model, the relation between two consec-utive SU or SR state occupancy distribution πn and πn−1 inthe non-cooperative mode can be written as:

πn = PPUIπ(n−1), (12)

which can be generalized as,

πn = P iPUIπ(n−i). (13)

By expressing the different state occupancy distributionsof the SU using the last state π(IA(MSU )a) according toequation (13) and by substituting its value in (11), then thevalue of π(IA(MSU )a) can be calculated from it. The rest ofSU state occupancy distributions can be calculated accordingto (13). The same procedure can be used for the SR.

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ESTT – In ESTT, the SU and SR have the same successfultransmission time (τSU = τSR in Figure 4), which maybe translated to the relation between the state occupancydistributions for the SU and SR using the following twoequations:

MSU π(IA(MSU )a) = MSR π(IaA(MSR)) (14)

MSR∑i=1

π(IaAi) +

MSU∑i=1

π(IAia) = 1− ρ. (15)

As in ETT, the different state occupancy distributions canbe expressed using the last state occupancy distribution and,by using equations (14) and (15), the different state occupancydistributions can be calculated.As in EAP, after finding the different state occupancy dis-tributions, the transmission efficiency and throughput can becalculated using (6)-(9).

The values of the access probabilityP(SU→SU), P(SU→SR), P(SR→SU), and P(SR→SR),can be calculated by substituting the PU, SU and SRoccupancy states distributions in (43) and solving it with thefollowing two equations:

P(SU→SU) + P(SU→SR) = 1 (16)

P(SR→SR) + P(SR→SU) = 1. (17)

2) Cooperative mode: If the SU and SR are cooperatingand they adopt the same non-cooperative access method, theSU calculations are different from the non-cooperative modefor ETT and ESTT.

For EAP, the transition probabilities have the same valuesas the non-cooperative case and the different state occupancydistribution, efficiency and throughput are calculated using thesame techniques used in the non-cooperative mode.

For ETT and ESTT, as the SU transmission is done over twohops, the calculations are different from the non-cooperativecase. For the SU, if the first hop transmission spans l time slotsand the second hop spans k time slots such that l+k = MSU ,the relation between the last state occupancy distribution ofthe first hop transmission π(IAla) and the last state occupancydistribution of the second hop transmission from the SR to theSAP π(IA(MSU )a) = π(IA(l+k)a) is given by as:

π(IAla) = π(IA(l+k)a). (18)

That is because for a single SU cooperative transmission, theDTMC goes through the last state of the fist hop only one timeas there is no-retransmission for the first hop if the DTMCreached this state. Also, in the same way, the DTMC goesthrough the last state of the second hop only one time atevery cooperative transmission. By using equation (13), wecan express any state occupancy distribution in the first hopusing π(IAla) as follows:

π(IA(l−i)a) =π(IAla)

P iPUI

. (19)

The same can be applied for the second hop by using

π(IA(l+k)a) as follows:

π(IA(l+k−i)a) =π(IA(l+k)a)

P iPUI

. (20)

Using the last two equations, the relation betweenπ(IA(l+k)a) and π(IA(l+i)a) can be found and so, as in thenon cooperative case, we can express the different SU stateoccupancy distributions using π(IA(l+k)a). Using the sameprocedure used in the non-cooperative mode for ETT andESTT, the different state occupancy distribution, transmissionefficiency and throughput can be calculated.

C. Utility Model

The utility function for the SU and SR is defined as thedifference between the achieved normalized throughput andthe normalized energy [2]. The utility for node s is defined asfollows:

Us = Ts − Cs Es, (21)

where Ts is the normalized throughput of node s and Es isits normalized energy. The factor Cs is the energy evaluationfactor. The normalized throughput and energy for node s canbe defined using the following two equations:

Ts = tsRsRmin

ηs (22)

Es = ts, (23)

where ts is the free spectrum time share the node s gets, Rs isthe data rate, Rmin is the lowest rate used in the model and thetransmission power is set to be equal to one. The value of Csindicates the preference of the node between the energy andthroughput. For example, when Cs < 1, it means that the nodeprefers to achieve higher throughput over to save its energy.Equation (23) is valid only in the non-cooperative case wherethe SR does not contribute in the SU’s transmission. For thecooperative case, we account for the energy consumed by theSR to relay the SU packets, including the power consumed inthe transmission and reception of the packet.

In the cooperative mode, the definition of the normalizedenergy will be different for the SU and SR. For the SR, thenormalized energy will be defined as:

E(SRcoo) = t(SRcoo) + t(SUcoo) εSR + γ(1− εSR) tSU , (24)

where γ is the ratio of the power consumed in the SU packetreception by the SR to the power used in the transmission,εSR is the ratio of the time of the second hop cooperativetransmission to the total time of the two hops cooperativetransmission. The value of εSR depends on the cooperationlevel used, for example, εSR = (2/3) in L1a, (1/3) in L1b,and (1/2) in L2. The values of t(SUcoo) and t(SRcoo) are theSU and SR free spectrum time shares in the cooperative mode.For the SU, the normalized energy in the cooperative mode isdefined as:

ESUcoo= (1− εSR) t(SUcoo). (25)

tsu and tsr are selected such that they satisfy, in boththe cooperative and non-cooperative modes, the following

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equation:1− ρ = tSU + tSR. (26)

D. Bargaining Model

To decide the shares of the cooperating SU and SR pair,we use the bargaining theory where both nodes bargain overtheir entire share. Nash bargaining solution (NBS) [18] isused to find the share of every node, where the originaltotal access time shares assigned to both the SU and SR issubjected to the bargaining process. The two player bargainingproblem consists of a pair (F, d), where F is called the feasibleset of allocations and it is closed and convex and d is thedisagreement point. The utility of each player in the non-cooperative mode is used as a disagreement point if the nodesrefused to cooperate. The NBS is unique and satisfies thefollowing axioms.

1) Individual Rationality, IR: This axiom implies that everynode get a bargaining utility higher than its disagreementone. To realize this axiom, the bargaining solution needsto satisfy the following equation,

f1(F, d) ≥ d1 and f2(F, d) ≥ d2 (27)

where (d1, d2) are the disagreement utilities.2) Pareto Optimality, PO: The bargaining solution is Pareto-

optimal. For a feasible set F , the allocation x = (x1, x2)is Pareto efficient if there exists no other point y =(y1, y2) such that Uy1 ≥ Ux1 and Uy2 ≥ Ux2 wherethe strict inequality is satisfied for at least one player andUzn represents the utility resulted from the allocation zfor player n.

3) Symmetry, SYM: The solution does not discriminate be-tween players if they are indistinguishable.

4) Scale Invariant, SINV: Transforming the bargaining prob-lem by any linear scale transformation ψ changes thesolution by the same transformation.

ψ(f(F, d)) = f(ψ(F ), ψ(d)). (28)

5) Independence of Irrelevant Alternatives, IIA: The axiomstates that for any closed and convex set Z,

G ⊂ F andf(F, d) ∈ G⇒ f(G, d) = f(F, d). (29)

The axiom implies that eliminating the not chosen feasi-ble alternatives should not affect the solution.

The unique NBS for two players is obtained by solving thefollowing equation:

f(F, d) = arg(x1,x2)∈F

max (x1 − d1)(x2 − d2)

subject to x1 ≥ d1 and x2 ≥ d2(30)

where d1 and d2 are the disagreement points for players oneand two, respectively.

Figure 6 shows the graphical representation of NBS as theintersection of the Pareto optimal boundary of the utility andthe hyperbola of equation (30) for different cooperation levelsbetween the SU and SR. After finding the NBS solution (the

SU utility (USU

)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

SR u

tility

(U

SR)

0

0.25

0.5

0.75

1

1.25

1.5

USU vs. USR usingtSU + tSR = (1 − ρ)

USU vs. USR usingf = (USU − dSU )(USR − dSR)

NBS solution point

L1a

L1b

L2

Fig. 6: NBS graphical representation at different cooperationlevels for ρ = 50%, CSU = CSR = 0.25, and γ = 0.7.

values of USU and USR), the cooperative free spectrum sharescan be re-calculated using (21).

IV. NODE PAIRING AND CHANNEL ALLOCATIONPROBLEM

In this section, we investigate the optimal way to pair thesecondary nodes (slow and fast ones) and allocate channels tothem in a secondary infrastructure network based on the NBSfree spectrum time shares.

A. Network Setup

We consider an infrastructure network with a set N def=

{1, 2, . . . , N} of SUs uniformly distributed within a circulararea that is divided into a number of regions characterizedby the direct transmission rate R ∈ RD

def= {R1, R2, . . . , Rl}

between each region’s SUs and the SAP. Every SU n cantransmit/receive packets from the SAP with a rate Rn ∈ R. Inaddition, each SU is able to transmit to other SU r usingdirect transmission rate Rnr ∈ {0, R1, R2, . . . , Rl} whereRnr = 0, means that these two SUs are out of the transmissionrange of each other. There is a set of transmission channelsC def

= {1, 2, . . . , C}, each one is characterized by its primaryuser activity ρc.

The initial share for node n, In, defines the amount offree spectrum access time share the node will get comparedto those of all nodes operating at the same channel in non-cooperative mode. The initials shares are determined by theSAP by controlling the access probability of every node.The value of the initial share depends on the non-cooperativeaccess mechanism used. For example, for N nodes operatingat the same channel, the initial shares for at different secondaryaccess mechanism are:• EAP: IEAP = [ Rmax

η1·R1, Rmax

η2·R2, . . . , Rmax

ηN ·RN]

• ETT: IETT = [1, 1, . . . , 1]

• ESTT: IESTT = [1

η1,

1

η2, . . . ,

1

ηN]

where Rmax is the maximum rate in the network.

8

For every pair of SUs, if they agreed to cooperate, they re-divide their initial shares among themselves according to theirutilities using NBS. The share division ratio between node nand relay r over channel c is defined as Scnr and decides theshares for every combination of SU pairs at different channelswhere Scnr = (1 − Scrn) and Scnn = 0.5 ∀n ∈ N ,∀c ∈ C,where Scnn represents the direct transmission share of SU n.The transmission rate Rcnr is the net achieved rate for SU nif it cooperates with SU r over channel c, and Rcnn representsthe direct transmission rate of SU n over channel c. The valuesof S and η are pre-calculated as mentioned in Section III.

B. Resource Allocation Problem Formulations

Let xcn, c ∈ C, n ∈ N , be a binary variable that representthe channels allocation such that:

xcn =

{1, if SU n will operate over channel c0, otherwise

and ynr, n, r ∈ N , be a binary variable that indicates thecooperation relation between secondary nodes such that:

ynr =

{1, if nodes n and r will cooperate0, otherwise.

Two notes are to be taken into consideration. First, if ynn =1, that means that SU n uses direct transmission. Second,the cooperation rule between two SUs is not reversible, thatmeans if node r helps node n, node n cannot help node r.The achieved throughput T of node n is defined as follows:

Tn =

C∑c=1

N∑r=1

{xcn ynr Bcnr Rnr ηcnr

1− ρc∑NSU

l=1 xcl Il

},

(31)where Bcnr is the bargaining based spectrum time share fornode n that cooperates with node r over channel c and equalsto,

Bcnr = (In + Ir) Scnr −

(∑Ni=1 yni − 1∑Ni=1 yni

)In, (32)

where the second term in (32) is subtracted to ensure that, inthe case of an SR that helps more than one SU, the share ofthe SR is not counted more than one time in the summationover all nodes in (31). That can be illustrated by the followingexample. Suppose that SR (R) helps two SUs (S1 andS2) withinitial shares are as follows IR = 20%, I(S1) = 40% andI(S2) = 40% and the bargaining based shares over channel (c)are S(cRS1) = S(cRS2) = 50% . If equation (32) includes onlythe first term, the nodes’ shares will be B(cRS1) = B(cRS2) =30% and B(cS1R) = B(cS2R) = 30% , the sum of all sharesin this case will be 120% which is incorrect as the share ofthe relay is counted twice. To avoid this calculation error, thesecond term is added to correct the share of the SR. Accordingto (31) the value of B(cRS1) = B(cRS2) = 20%, so the SR willget only 40% of the free spectrum share of the three nodesand S1 and S2, each will get 30%.

Node n’s demand dn is set to be proportional to its datarate capability and equals to (Rn/Rmin) where Rmin is the

minimum rate in RD. The SAP tries to satisfy β × 100% ofeach node’s demand where 0 ≤ β ≤ 1.

We define two optimization problems with different objec-tives that use bargaining based shares and aims to maximizethe total network throughput (BBS-1) or minimize the maxi-mum difference between any node demand and the achievedthroughput (BBS-2).

BBS-1 aims to maximize the total network throughput andsatisfies all nodes demands with a certain percentage β×100%.

Problem 1 (BBS-1):

maximize{xcn,ynr}

{N∑n=1

Tn

}(33)

subject to: ∑c∈C

xcn = 1,∀n ∈ N (34)

ynr = yrn,∀n, r ∈ N (35)∑r∈N

yzr = 1,∀z ∈ Ns (36)

xcr ≥ xcn ynr,∀c ∈ C,∀n, r ∈ N (37)∑r∈N

ynn ynr ≤ 1,∀n ∈ N (38)

Tn ≥ β dn,∀n ∈ N (39)xcn ∈ {0, 1} ,∀c ∈ C,∀n ∈ N (40)ynr ∈ {0, 1} ,∀n, r ∈ N . (41)

Constraint (34) ensures that every SU operates only over onechannel. Constraint (35) ensures that the cooperation matrixis symmetric. Constraint (36) ensures that every slow nodes ∈ NS (nodes with low direct transmission data rate thatasks for a relay help) receives help by at maximum onerelay. To ensure that every cooperating pair’s nodes belongto the same channel, constraint (37) is used. If the SR n ishelping at least one SU, the value of ynn must be set to 0by constraint (38). For example, if SR n is helping SU m,that means ynm = 1. However, equation (33) will try to setalso ynn to 1 to maximize the global throughput which willresult in an incorrect value as the time share of the SR will beadded twice. Constraint (38) will prevent both ynn and ynmfrom being equal to one at the same time. As the cooperation isalways beneficial for both nodes and for the global objective,only ynm will be set to 1. Constraint (39) ensures that everynode gets β × 100% of its demand for a given value of β.

The previous formulation gives the slow nodes the minimumdemand while allocating the rest of resources to the othernodes with high rate. The problem will fail to achieve asolution if any node does not receive β×100% of its demand.

The second problem (BBS-2) aims to minimize the maxi-mum difference between any node demand and the achievedthroughput such that it maximizes the excess capacity ifwhat the node gets is higher than its demand or minimizethe demand shortage if the demand is not satisfied. All theconstraints of problem BBS-1 apply here also except ofconstraint (39) which is relaxed such that the problem has

9

TABLE I: Numerical values of various parameters.Parameter ValueSU # of time slots per packet (MSU ) 32PU # of time slots per packet (MPU ) 16PPUA

range 0.2 to 0.8Energy evaluation factor CSU = CSR 0.1γ 0.7 (see [19])Modulation BPSK, QPSK, 16QAMData rate 6, 12, 24 MbpsDemand (d) 1, 2, 4 MbpsPath loss exponent 3.5Transmission power 0.5 mWChannel type Rayleigh flat fadingSuccessful reception BER threshold 10−3

Number of nodes N 10Number of channels C 3PU activity ρ 0.4, 0.6, 0.8

a solution in the case of demand shortage.

Problem 2 (BBS-2):

minimize{ xcn,ynr,c∈C,n,r,∈N

}maximumn∈N

{β dn − Tnβ dn

}(42)

subject to:(34)− (38), (40), and (41).

V. PERFORMANCE EVALUATION

In this section, we evaluate the performance of coopera-tive communications in secondary infrastructure networks ascompared to non-cooperative secondary networks. In theseexperiments, for the cooperation scheme, normalized metricsare obtained by dividing each metric by its non-cooperativecounterpart. The values of the PU transition probabilities arecalculated as in the appendix and the SU and SR performanceare averaged over range of PPUA

and its corresponding PPUI

values. The numerical values of the simulation parameters arelisted in Table I unless otherwise specified.

A. Secondary Cooperative Transmission Performance

In this experiment, we evaluate the effect of SU cooperationon the spectrum successful utilization using the DTMC model.We modify the DTMC model such that the relay is a passiverelay that only helps the SU without transmitting its ownpackets. Figure 7 shows the SU transmission efficiency as afunction of PU activity ρ at different cooperation levels and forthe direct transmission case. As shown in the figure, utilizingcooperation enhances the efficiency of the SU transmission.As a consequence, the normalized transmission of the SUis enhanced significantly, especially at high values of PUactivity as the cooperation is efficient in reducing the effect ofPU interruption and so, enhance the throughput performancecompared to the direct transmission as shown in Figure 8.

B. Performance of Bargaining-based Cooperation

In these experiments, we study the SU and SR performanceunder cooperation.

1) Effect of the PU activity: Figure 9 shows the SR NBSbased free spectrum share percentage from the total sharesdedicated for the SU and SR after cooperation. Also, the SRshares in the non-cooperative and cooperative modes with thesame non-cooperative access mechanisms (EAP) as a functionof the PU activity ρ are shown. When using bargaining basedcooperation, the SR gets a higher share than that of the non-cooperative mode or the cooperative mode with the same EAPaccess mechanism. Also, the NBS based SR free spectrumshare increases as the PU activity increases to compensate forits increased energy dissipation in relaying the SU packets dueto the increase in PU interruptions. Such compensation doesnot occur in the other two methods resulting in decreasingthe SR shares with the increasing of PU activity. Figures 10and 11 show the SR and SU normalized utility and throughput,respectively. As shown in the figures, both the SR and the SUachieve higher utility and throughput than the non-cooperativecase and the rational enhancement (compared to the non-cooperative case) increases as the PU activity increases wherethe cooperative transmission performance is much better thanthe non-cooperative case.

2) The effect of the non-cooperative access mechanism: Asmentioned in Section III-D, the disagreement point determinesthe bargaining power of each player and affects the bargainingresult. The effect of the non-cooperative access mechanismutility (disagreement point) is shown in Figure 12. When thenodes adopt ETT as a non-cooperative access mechanism, theSR has the highest NBS cooperative share compared to ESTTand EAP (and vice versa for EAP). When EAP is used in thenon-cooperative share, the SR has the lowest cooperative sharebut it has the highest increasing rate with PU activity.

3) The effect of the power evaluation factor CK: Figure 13shows the SR free spectrum share percentage (from the SUand SR original shares) as a function of energy evaluationfactor CK . As shown in the figure, as the value of CKincreases the amount of share the SR gets increases as itspower value increases. That results in decreasing the SU sharesand, subsequently, its throughput to the point where the SUcooperation throughput may be lower than the non cooperativeone. At this point, the SU still achieves a higher utility as ittransmits at lower throughput but with a higher efficiency thatleads to an enhancement in the total utility compared to thenon-cooperative case. Whether the SU achieves throughputenhancement or not depends on the value of the energyevaluation factor, the PU activity and the cooperation level.Figure 14 shows the PU activity threshold ρth for SU through-put to benefit form cooperation. The region to the left of everycurve indicates the values of CSU = CSR and ρ where the SUachieves a beneficial cooperation in terms of the throughput.Also, it is clear that, as the cooperation level between the SUand SR increases the threshold value of CSU = CSR increases.This mean that, the SU and SR throughput enhancement athigher cooperation levels is able to compensate any increasein the energy consumption occurs compared to at lower levels,even if the nodes have a higher evaluation for their energy.For example, in L1a, the SU achieves a higher throughput forCSU = CSR lower than approximately 0.225 for any value ofρ. From CSU = CSR ≈ 0.225 to 0.3 the cooperation is bene-

10

0 10 20 30 40 50 60 70 80PU Activity Level (ρ) (%)

0

0.2

0.4

0.6

0.8

1

Tra

nsm

issi

on e

ffic

ienc

y (η

)

Non-cooperativeL

1a and L

1b

L2

Fig. 7: SU efficiency (ηSU ) vs. PU activity(ρ)(%).

0 10 20 30 40 50 60 70 80PU Activity (ρ)(%)

0

1

2

3

4

5

SU N

orm

aliz

ed th

roug

hput

Non CooperativeCoop. L

1a or L

1b

Coop. L2

Fig. 8: SU normalized throughput vs. PUactivity (ρ)(%) .

0 10 20 30 40 50 60 70 80PU Activity Level (ρ)(%)

10

20

30

40

50

60

SR f

ree

spec

trum

sha

re (

%) EAP non-cooperative

EAP cooperativeNBS based cooperative

Fig. 9: SR free spectrum shares for differ-ent cases at L1b .

0 10 20 30 40 50 60 70 80PU Activity (ρ)(%)

1

1.5

2

2.5

3

3.5

4

Nor

mal

ized

Util

ity

SUSR

Fig. 10: SU and SR normalized utility inthe cooperative mode for cooperation levelL1b.

0 10 20 30 40 50 60 70 80PU Activity (ρ)(%)

1

1.5

2

2.5

3

3.5

Nor

mal

ized

Thr

ough

put

SUSR

Fig. 11: SU and SR normalized through-put in cooperative mode for cooperationlevel L1b.

0 10 20 30 40 50 60 70 80PU activity (ρ)(%)

40

45

50

55

60

65

70

75

SR f

ree

spec

trum

sha

re (

%)

EAPETTESTT

Fig. 12: SR NBS shares for differ-ent non-cooperative access mechanisms atL1b .

fits for the SU after certain values of ρ. For CSU = CSR ≥ 0.3the SU cannot get an enhancement in the throughput at anyvalue of ρ.

4) Energy efficiency evaluation: Figure 15 shows the en-ergy performance (normalized throughput to the normalizedenergy ratio) for NBS based cooperation for different coop-eration levels compared to the non-cooperative counterparts.As indicated in the figure, cooperation enhances the energyperformance more than in the non-cooperative case. Also, asthe level of cooperation increases, the energy performanceimproves as the nodes transmit more packets at lower power.In all cases, the energy efficiency reduces as the PU activityincreases with a more severe negative effect on the non-cooperative cases.

C. Node Pairing and Channel Allocation

In these experiments, we evaluate the node pairing andchannel allocation problem. We consider the EAP accessmechanism in all experiments. All problems are formulatedin CPLEX [20] with a confidence interval of 90%.

1) Effect of demand satisfaction percentage (β): Figure 16compares the performance of BBS-1 and BBS-2 in termsof the average throughput for all nodes and for slow nodes

(nodes need SRs help) only. At a low value of β, BBS-1 barely satisfies the demand of the slow nodes and givesthe rest of resources to the nodes with high data rate. Thatresults in low average throughput for the slow nodes buta high value of throughput averaged over all nodes. As βincreases, the resource allocation is changed to satisfy the slownodes’ demand (for example, assigning channels with lowerPU activity to slow SUs), that may result in lowering the fastnodes’ rate and the total network rate. As a result, the slownodes average rate increases and the average rate of all nodesdecreases. The same trend continues until a certain value of β(0.4 in this experiment), where after that, there is no solutionfor the problem. For BBS-2, the achieved throughput is mainlyconstant for different values of β as expected and the valueof β is constant for all nodes.

2) Effect of PU activity ρ: In this experiment, we study theeffect of the PU activity on the achieved throughput for BBS-2. To show the effect of node cooperation on the throughputfor different values of ρ, we compare the throughput whencooperation is enabled between SUs with that when SUs useonly direct transmission (direct transmission can be enforcedby setting the value of ynn = 1,∀n ∈ N in the optimiza-tion problem formulation). Figure 17 shows the normalizedthroughput as a function of ρ. As can be inferred from the

11

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 C

SU =C

SR

30

40

50

60

70

80

90

SR f

ree

spec

trum

sha

re (

%) L

1a

L1b

L2

Fig. 13: SR share vs. CK = CSU = CSR

and ρ = 50%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8C

SU =C

SR

0

10

20

30

40

50

60

PU A

ctiv

ity th

resh

old

(%) L

1a

L1b

L2

Fig. 14: The PU activity threshold for SUthroughput enhancement.

0 10 20 30 40 50 60 70 80PU Activity (ρ)(%)

-1

0

1

2

3

Tot

al th

roug

hput

/ Tot

al e

nerg

y

Non-Coop. L1a

Coop. L1a

Non-Coop. L1b

Coop. L1b

Non-Coop L2

Coop. L2

Fig. 15: Energy efficiency for non-cooperative EAP.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1β

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Thr

ough

put (

Mbp

s)

BBS-1, all nodesBBS-2, all nodesBBS-1, slow nodesBBS-2, slow nodes

Fig. 16: Average throughput vs. β for thetwo proposed optimization problems.

20 30 40 50 60 70 80Average PU activity (ρ)(%)

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

Nor

mal

ized

thro

ughp

ut

BBS-2, all nodes

Fig. 17: Average normalized throughputvs. average PU activity ρ.

10 20 30Number of secondary nodes

1.25

1.5

1.75

2

2.25

Nor

mal

ized

thro

ughp

ut

BBS-2, slow nodesBBS-2, all nodes

Fig. 18: Average normalized throughputVS. number of nodes for C = 2.

figure, the cooperation-enabled throughput is always higherthan that of the direct transmission and the enhancementincreases as the PU activity increases because the cooperationcan reduce the negative effect of PUs interruption comparedto direct transmission.

3) Effect of the number of secondary nodes: As shownin Figure 18, for the slow nodes, the average normalizedthroughput increases as the node density increases becausethe availability of potential relays increases. The averagenormalized throughput for the entire network increases withan even higher rate than that of the slow nodes. That canbe understood by referring to Figure 11 where as a result ofcooperation, the relay (fast node) gets a much higher increasein the throughput compared to the nodes that it helps.

VI. CONCLUSIONS AND FUTURE RESEARCH

In this paper, we introduced a spectrum-efficient bargaining-based resource allocation framework for cooperative secondaryusers in cognitive radio networks. This framework takes intoconsideration the effect of the PU activity on the performanceof the SUs. Our analytical and numerical results demonstratedthe significant improvements in the successful free spectrumutilization and throughput achieved by the two-hop cooperativetransmission as compared to the direct transmission. Basedon this efficient way of utilizing the available free spectrum,

we proposed our cooperation framework between a secondaryuser and its relay. The cooperation is modeled as a resourceexchange process where the secondary user vacates part of itsdedicated free access time to the secondary relay in return forits relaying power. The interaction between a primary user,a secondary user and a secondary relay is modeled using adiscrete time Markov chain to obtain different transmissioncharacteristics like efficiency and throughput. The obtainedcharacteristics are used to calculate a node utility function thatcombines both the achieved throughput and consumed energy.Based on this utility, Nash Bargaining Solution (NBS) is usedto determine the secondary user and the relay free spectrumaccess shares in case of cooperation. We derived the conditionsunder which cooperation improves the performance of bothcooperating nodes. Finally, considering a multi-channel multi-SU secondary infrastructure network, by using the bargaining-based free spectrum time shares, we proposed two optimaljoint channel allocation and node pairing schemes. The firstscheme aims at maximizing the total network throughput,whereas the second scheme minimizes the maximum (amongSUs) difference between the throughput and the rate demand.Our results showed that the cooperation gains are more notice-able when (i) the PU is highly active or (ii) the node density ishigh. In the future, we aim to optimize each secondary nodes’free spectrum share jointly with node pairing and channel

12

allocation.We will also consider designing distributed resourceallocation schemes and compare them with the centralizedschemes proposed in this paper.

APPENDIX

PU Stand-alone Model

In this appendix, we develop the PU stand-alone DTMCmodel that used to calculate the PU transition probabilitiesfor a given value for PU activity level ρ. The state space ofthe stand-alone DTMC consists of one idle state (denoted byI) and M active states (denoted by A1, A2, . . . , AM ), whereM is the number of time slots required to transmit a certainpacket. In Figure 19, we depict the stand alone DTMC for Mstates. For simplicity, we assume a fixed packet size and thereis no new arrival during the ongoing transmission.

Fig. 19: Stand-alone Markov chains for PU transmission consumesM time slots.

The steady-state occupancy distribution, denoted by π, canbe derived from the transition diagram of the DTMC shownin Figure 19. The steady-state probability of being in statej ∈ {A1, A2, . . . , AM , I}, denoted by πj , represents thepercentage of time the PU stays in state j. Because the DTMCis irreducible, π is obtained by solving the following twoequations [21]:

π = π × P (43)1 = π × 1, (44)

where π = [πA1, . . . , πAM

, πI ], P is the (M + 1)× (M + 1)transition probability matrix, and 1 = [1, 1, . . . , 1](M+1)×1.

Let πAdef=∑Mi=1 πAi , then πI = 1−πA, and M = (N−1),

the values of PPUAand PPUI

are calculated by solvingequations (43) and (44) giving that (πI = 1−πA). The valuesof PPUA

and PPUIare calculated as follows:

By referring to Figure 19, for a stand-alone DTMC of M+1states, (43) can be written as:

[πA1, . . . , πAM

, πI ] = [π1, . . . , πM , πI ]×0 1 0 . . . 00 0 1 . . . 0...

. . . . . . . . ....

PPUA· · · · · · · · · (1− PPUA

)(1− PPUI

) · · · · · · · · · PPUI

.

(45)

By solving the first or the last equation, we obtain thefollowing equation:

πAM(1− PPUA

) = πI (1− PPUI). (46)

As the transition probabilities between different active statesequal to 1, we have equal state occupancy for all active statessuch that πAM

=πAM

. Given that πA = 1− πI , PPUIcan be

written as:PPUI

= 1− πA(1− PPUA)

M(1− πA). (47)

To ensure that both PPUIand PPUA

values are in the rangefrom 0 to 1, we set PPUA

in the following range:

1 ≥ PPUA≥ 1− M(1− πA)

πA. (48)

For the PU, we define the PU activity level ρ as thepercentage of time the PU is active. The desire value of ρis obtained by changing the PU stand-alone probabilities suchthat:

ρ = πA =

M∑i=1

πAi . (49)

The value of the chosen transition probabilities affects theSU performance as it changes the interruption rate caused bythe PU. Figure 20 shows an example of three different PUactivity patterns (different values of PPUA

) at, approximately,the same value of ρ. The figure shows the effect of the PUactivity pattern on the availability and the width of the whitespaces at the same channel utilization level. At low value ofPPUA

, the probability that the PU, immediately, starts a newtransmission after the current one is low compared to highervalues of PPUA

where the PU is more likely to transmit aseries of continuous packets without time gaps. That means,for the same channel utilization level, at low value of PPUA

thePU interruptions to the SU’s transmissions will be higher thanat higher values of PPUA

. Figure 21 shows the performance ofthe SU’s transmission efficiency for different values of PPUA

and for the averaged efficiency when PPUAchanges over the

range from 0.2 to 0.8. As shown in the figure, and as describedbefore, for the same value of PU activity level ρ, at low valuesof PPUA

, the SU has a lower transmission efficiency as it ismore prone to the PU interruption than at the higher values.

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Mohamed AbdelRaheem (S13-M16) is an assis-tant professor of Electrical Engineering at AssiutUniversity, Egypt. He received his B.Sc. and M.Sc.in Electrical Engineering from Assiut University in2004 and 2010 respectively and his Ph.D. in Elec-trical Engineering from Virginia Tech in 2015. Hisresearch interests include wireless networking, es-pecially spectrum sharing, cognitive radio network,cooperative communication and LTE-U.

Mohammad J. Abdel-Rahman (S12-M15) re-ceived the PhD degree in electrical and computer en-gineering from The University of Arizona, Tucson,AZ, in 2014. He is currently a research associatewith the Department of Electrical and ComputerEngineering, Virginia Polytechnic Institute and StateUniversity, Blacksburg, VA. His research interestsinclude the areas of wireless communications andnetworking, with emphasis on resource management,adaptive protocols, and security issues. He serves asa reviewer for several international conferences and

journals. He is a member of the IEEE.

Mustafa El-Nainay (M13) is an Associate Pro-fessor of the Computer and Systems Engineeringdepartment at Alexandria University, Egypt. He isalso the associate director of the Virginia Tech-Middle East and North Africa (VT-MENA) programfor administration and research and adjunct facultyat Virginia Tech. He received his B.Sc. and M.Sc.in Computer Science from Alexandria Universityin 2001 and 2005 respectively and his Ph.D. inComputer Engineering from Virginia Tech in 2009.His research interests include wireless and mobile

networks, cognitive radio and cognitive networks, and software testing au-tomation and optimization.

Scott F. Midkiff (S82-M85-SM92) is a Professorand the Vice President for Information Technologyand the Chief Information Officer with VirginiaTech, Blacksburg, VA, USA. From 2009 to 2012, hewas the Department Head of the Bradley Departmentof Electrical and Computer Engineering, VirginiaTech. From 2006 to 2009, he served as the ProgramDirector with the National Science Foundation. Hisresearch interests include wireless and ad hoc net-works, network services for pervasive computing,and cyber-physical systems.