ACCEPTED FOR PUBLICATION IN IEEE TRANSACTIONS ON … · communications. Another driving factor for increasing energy Another driving factor for increasing energy efﬁciency of communications

ACCEPTED FOR PUBLICATION IN IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, OCTOBER 2012 1

Scheduling in Centralized Cognitive RadioNetworks for Energy Efficiency

Suzan Bayhan and Fatih Alagoz

Abstract—With growing concern on environmental issues andemerging green communications paradigm, cognitive radio (CR)networks have to be considered from energy efficiency perspec-tive. In this work, we focus on scheduling in CR networks (CRNs)in which cognitive base station (CBS) makes frequency allocationsto the CRs at the beginning of each frame. A cognitive schedulermust consider the diversity among CRs’ queues and channelcapacities in terms of number of bits as well as the channelswitching cost from one frequency to another. Taking all theseinto account, we formulate the scheduling problem as energyefficiency maximization problem which is a nonlinear integerprogramming (NLP) problem and thereby hard to solve. We seekfor alternate computationally easier solutions. To this aim, wepropose a polynomial time heuristic algorithm, energy-efficientheuristic scheduler, which allocates each idle frequency to theCR that attains the highest energy efficiency at this frequency.Next, we reformulate the original problem first as throughputmaximization problem subject to energy consumption restrictionsand next, as energy consumption minimization problem subjectto minimum throughput guarantees. These two schedulers havealso the power to provide fairness in resource allocation. Weanalyze the energy efficiency and successful transmission prob-ability of the proposed schedulers under both contiguous andfragmented spectrum scenarios. Performance studies show thatcompared to a pure opportunistic scheduler with a throughputmaximization objective, proposed schedulers can attain almostthe same throughput performance with better energy efficiency.

Index Terms—Cognitive radio (CR), energy efficiency, channelswitching, fragmented spectrum.

I. INTRODUCTION

Cognitive radio networks (CRNs) enable the radio spec-trum to be utilized effectively owing to their opportunistictransmission and dynamic spectrum access (DSA) capabilities.Moreover, CRs promise advanced functionalities which willrequire advanced information processing capabilities. On theother hand, CRs need powerful energy sources to afford allthese functionalities. However, there is a lag between the ad-vances in battery technology and semiconductor technologies;the former being significantly slower than the latter. As aresult, current battery technology cannot meet the tremendousincrease in power consumption related to the increasing trafficflow resulting from the improvement in fast semiconduc-tor technologies [1]. Thus, energy efficiency may becomea limiting factor in the development of advanced wireless

Copyright (c) 2012 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

Suzan Bayhan is with Helsinki Institute for Information Technology HIIT,Aalto University, Helsinki, Finland, e-mail: {[email protected]}. Fatih Alagoz iswith the Department of Computer Engineering, Bogazici University, Istanbul,Turkey, e-mail: {[email protected]}.

communications technologies which makes energy efficiencya crucial issue for wireless networks.

Quest for higher energy efficiency is primarily due tothree reasons: cost-effectiveness, longer battery lifetime andenvironmental concerns. Energy costs are constantly increas-ing and energy expenditure of a wireless network is a sig-nificant fraction (20 to 30 per cent [2]) of total operatorexpenditures (site rental, licensing etc.). Hence, energy shouldbe consumed effectively for cost-effective systems. Reducingenergy consumption and energy-efficient operation are therebyat the interest of the operators. From the user viewpoint,energy efficiency means longer battery lifetime. It is a factthat short durations between two battery charging annoy theusers and reduce the practicality of wireless communications.Thus, energy efficiency is vital for both actors of wirelesscommunications. Another driving factor for increasing energyefficiency of communications is the environmental concerns.Emissions due to Information and Communication Technolo-gies (ICT) is estimated to be around 2% of the worldwideCO2 emissions [3], [4]. Regarding wireless communicationsas a principal component of ICT, CO2 emissions are expectedto increase with the exponential growth in wireless traffic andfast penetration of smart mobile devices. Therefore, analysisof energy efficiency and design of energy-efficient systems inwireless communications have become more essential.

In the CRN literature, limited work has been done to addressenergy efficiency. Most of the prior research is on the energyefficiency of spectrum sensing and accordingly on spectrumaccess [5]–[8]. Since spectrum sensing is mostly treated asa task required to ensure a certain degree of primary user(PU) detection reliability and during this period transmissionis paused, mostly this period is desired to be minimized forboth throughput efficiency and energy consumption concerns.However, as the throughput attained in transmission durationis a function of the total discovered spectrum opportunities andcollision rate with the PU traffic, achieved throughput is af-fected by the sensing duration. Therefore, most of the researchconsidered this tradeoff between sensing and transmissionto design throughput-efficient CR systems with low energyconsumption. Works in [9]–[11] focus on cooperative sensingand devise energy-efficient solutions by trading-off betweenenergy consumption and cooperative detection performance.

Centralized resource allocation in CRNs, also referred to asscheduling, has been well-investigated mostly under through-put efficiency perspective [12], [13]. Besides, fairness andquality-of-service (QoS) issues are also considered in someof the works [13], [14]. To the best of our knowledge, energyefficiency is neglected as a design criteria in CRN scheduling.


Ri,r

CRi

RN,F

1 2 3 4 ... F

Ri,M

Ri,1

CRN

......

CR1

CRkCR

Cognitive

Scheduler (CS)

Frequency

channels

Fig. 1. Each CRi maintains a link with the CBS for each frequency fdenoted by li,f , i ∈ {1, .., N} and f ∈ {1, .., F}.

As CRs are expected to possess operation capability withina wide range of spectrum owing to power-intense spectrumsensing tasks, they are expected to operate with high energyefficiency. Furthermore, with the emerging green commu-nications paradigm, CRs are desired to be greener. Hence,cognitive protocols must also be designed with an energyefficiency perspective. In this sense, a cognitive schedulerlocated at the cognitive base station (CBS) should considerthe energy efficiency while determining a schedule.

Contributions of our work can be summarized as follows:we formulate the scheduling problem in CRNs as an energyefficiency maximization problem which is a nonlinear pro-gramming (NLP) problem. To overcome this computationalcomplexity, we propose a polynomial time heuristic algorithm,energy-efficient heuristic scheduler (EEHS), as a solution tothis problem. Next, we study scheduling problem not onlyfrom an energy efficiency perspective but also from throughputefficiency perspective. We revise our problem formulation andpresent two approaches: (1) maximization of throughput in aframe while meeting energy consumption restriction and (2)minimization of energy consumption in a frame while ensuringa desirable throughput performance. The first scheduler isreferred to as TMER and the second as EMTG. Both TMERand EMTG incorporate the ratio of traffic successfully sentby a CR as a fairness criteria in their objective functions. Wecompare performance of EEHS, TMER and EMTG with thethroughput maximizing scheduler that only aims to increasethe total throughput of the CRN. Numerical analysis showthat all the proposed schemes improve energy efficiency ofthe CRN while not sacrificing drastically from the throughputperformance. As EEHS has no consideration of fairness, itmay lead to starvation in some CRs. On the contrary, EMTGand TMER can support a fair, throughput and energy-efficientspectrum allocation. Different from previous works in theliterature, we also consider a realistic scenario where thewireless spectrum is fragmented into various frequency bandswhich are spectrally distant from each other. To the best ofour knowledge, our work is the only work in the literaturethat considers a fragmented spectrum rather than spectrum asa collection of contiguous bands.

The rest of this paper is organized as follows. Section IIpresents the system model and assumptions. Next, Section IIIintroduces the problem formulation and proposed solutions

Frame (T)

Channel

switching

Transmission

(ttx)

Tcs T-Tcs-t

Control

messaging

t

Idle

(a) CRs selected for transmission, i.e, CRi ∈ A,switch to the related channel and transmit throughthat channel.

IdleControl

messaging

(b) CRs stay in idle mode if not assigned afrequency.

Fig. 2. Frame organization.

for the formulated NLP problem. Section IV demonstratesthe performance analysis of each scheduler derived from thesimulations. For each scheduling scheme, energy efficiency,throughput, bandwidth of channel switchings, and energyconsumption are analyzed. Finally, Section V concludes thepaper.

II. SYSTEM MODEL AND ASSUMPTIONS

We consider a centralized CRN serving N CRs as in Fig. 1.The primary network (PN) has F non-overlapping orthogonalfrequencies. Occupancy state of each primary channel is mod-eled as a two-state Markov chain [15], two states representingthe idle and busy state of the channel. The probability ofa channel’s being idle is pidle. Both PN and CRN operatein a time-synchronized manner, the latter being synchronizedwith the former. We assume that PU spectrum occupancy isretrieved by cognitive base station (CBS) from an externalentity such as a white space database [16]. With the latestregulations [17], such database based CR systems have gainednoticeable interest due to its higher potential for turning CRsinto practical networks. The retrieved information is assumedto be reliable, and CRs access the assigned frequency withoutperforming spectrum analysis.

Let li,f denotes the channel between CRi and CBS atfrequency f . At the beginning of each frame, each CR sendsits state to the CBS as [Ri, Qi]. Ri = [Ri,f ] is the vectordenoting the number of bits that can be transmitted in a framethrough each li,f , and Qi is the number of bits in CRi’sbuffer. As all information is gathered at CBS, it determinesa transmission schedule applying its scheduling policy andbroadcasts it to the CRs. All these transactions are completedin control messaging period which takes t units of time. Weassume that control messaging period is significantly shortercompared to other periods. Hence, for the sake of simplicity,we trait it as if t = 0. Let A denotes the set of CRs thatare assigned a frequency. CRs in A tune their antennas tothe assigned frequencies and begin transmission while othersstay in idling state till the end of frame. CRs switch to idlingstate after completion of transmission. Fig. 2 depicts frameorganization for these two cases.

A. Link Capacity Calculation with Channel Switching Cost

Capacity of li,f depends on the bandwidth of the channel(W ) and signal-to-noise ratio (SNR) of the link. In addition,


number of bits that can be sent through this link in a frameis determined by the time spent for tuning the CR’s RF front-end to this frequency. In the literature, total time spent duringall these necessary RF front-end hardware configurations isreferred to as channel switching latency and it is consideredas a linear function of total frequency distance between theformer (f ′) and the latter frequencies (f ) [18]–[21]. Accord-ingly, channel switching latency denoted by Tcs is calculatedas follows:

Tcs = tcs|f − f ′| (1)

where tcs represents the delay for switching unit bandwidth.Let Bi,f be the channel capacity of li,f calculated by

Shannon’s formula and Ri,f be the maximum number of bitsthat can be sent by CRi at link li,f during a frame. Bi,f andRi,f are calculated as follows:

Bi,f = W log2(1 + SNRi,f ) bits/second, (2)

Ri,f = Bi,f (T − T i,fcs ) bits (3)

where W is the channel bandwidth, SNRi,f is the signal-to-noise ratio of li,f , T is the frame duration, and T i,f

cs isthe channel switching time for CRi to switch to frequency f .However, CRi cannot transmit more than the number of bitsin its buffer. Hence, effective rate of li,f denoted by Ci,f isrestricted by both Ri,f and number of bits in CRi’s buffer.Ci,f is calculated as follows:

Ci,f = min(Ri,f , Qi) bits. (4)

We calculate total CRN throughput as follows:

R =F∑

f=1

N∑i=1

Xi,fCi,f bits (5)

Xi,f standing for the binary decision variable that representsthe allocation state of CRi at frequency f , i.e. Xi,f = 1 if fis assigned to CRi, and Xi,f = 0 otherwise.

B. Energy Consumption Modeling

Considering the frame organization depicted in Fig. 2,we can model energy consumption of a CRN. If CRi isassigned a frequency (CRi ∈ A), first it tunes its antennato the assigned frequency which takes Tcs time units. Next,CR begins transmission. As the transmission is completed, itswitches to the idling state and keeps idle till the end of theframe. If CRi is not assigned a frequency (i.e., CRi ∈ A), CRi

waits idle in this frame.Since wireless interfaces are the dominant sources of energy

consumption in a wireless device [22], we ignore energy con-sumption due to information processing. Energy consumptionof a CR in such a CRN setting is due to various tasks andcomponents:

1) Transmission (Etx): The CRs that are scheduled fortransmission consume transmission energy while thosethat are not assigned any frequencies stay in idlingstate. The transmission power (Ptx) is assumed to beconstant. Energy consumption during transmission (Etx)is proportional to the transmission duration and Ptx.

Transmission duration of CRi at frequency f denotedby ti,ftx is calculated as follows:

ti,ftx =Ci,f

Bi,fseconds. (6)

Consequently, Etx is calculated as Etx = Ptxti,ftx .

2) Circuitry (Ec): Power consumed by electronic circuits(e.g. digital-to-analog converters, mixers, filters, etc.) ofa mobile device during transmission is referred to ascircuit power (Pc). It is almost constant and assumedto be independent of the transmission rate. Energyconsumption due to circuitry equals to Pct

i,ftx .

3) Channel switching (Ecs): Ecs represents the energyconsumed for configuring the hardware from currenttransmission frequency (f ′) to the assigned transmissionfrequency (f ). We model total energy consumption dueto channel switching (Ecs) as follows:

Ecs = PcsTi,fcs Joules (7)

where Pcs is the power dissipation for switching andT i,fcs = tcs|f − f ′|. Due to channel switching, transmis-

sion duration is decreased to T − T i,fcs seconds.

4) Idling (Ed): As mentioned above, CRs that are notselected for transmission stay idle. Hence, they consumeidling power (Pd) for a duration of T which results inenergy consumption Ed = PdT . Moreover, the CRsselected for transmission switch to idling state till theend of the frame once they complete transmission ofall the bits in their buffers. In this case, idling time isT − T i,f

cs − ti,ftx seconds.Taking all the above states into account, energy consumption

of CRi at frequency f is formulated as follows:

Ei,f = (Ptx + Pc)ti,ftx + Pd(T − T i,f

cs − ti,ftx ) + PcsTi,fcs .

(8)

In the above formulation, the first term is due to transmission,whereas the second is due to idling and the third due to channelswitching. Consequently, total energy consumption of a CRNin a frame is calculated as follows:

E =∑∀i,

CRi∈A

F∑f=1

Ei,fXi,f +∑∀i,

CRi ∈A

PdT Joules. (9)

In the above formula, the first term is due to CRs that areassigned a frequency and the second term is due to CRs thatdo not transmit.

III. ENERGY-EFFICIENT SCHEDULING IN CRNS

Formally, energy efficiency is defined as the throughputobtained per unit energy consumed in an observation periodT . Directly derived from this formal definition, bits-per-Joule capacity [23] serves as a metric for measuring energyefficiency of a network. Using (5) and (9) to compute totalCRN throughput (R) and total CRN energy consumption (E)


respectively, we can calculate the energy efficiency of the CRNas follows:

η =R

Ebits/Joule. (10)

Subsequently, we formulate the energy efficiency maximiza-tion problem as follows:

P1: maxx

η (11)

s.t.F∑

f=1

Xi,f 6 1 , i ∈ {1, .., N} (12)

N∑i=1

Xi,f 6 1 , f ∈ {1, .., F} (13)

Xi,f ∈ {0, 1} (14)

where x = [Xi,f , i ∈ {1, .., N} , f ∈ {1, .., F}] is theallocation vector with elements Xi,f . Constraint (12) ensuresthat each CR is assigned to at most one frequency dueto our assumption that CRs all have a single antenna. Weconsider an overlay model in which only one CR is active ata frequency at a specific time. Constraint (13) guarantees thisby preventing simultaneous transmissions in a frequency band.Constraint (14) denotes Xi,f is a binary variable.

The scheduler solves P1 (11) at the beginning of eachframe and broadcasts the scheduling decision x. In sequel,CRs tune their antennas to the assigned frequencies if theyare selected for transmission. However, P1 is not computa-tionally easy to solve due to the nonlinear objective function.The optimal solution of P1 can be discovered by exhaustivesearch for small instances of the problem. However, such asolution approach is inappropriate for practical networks withmany CRs and frequencies. For example, for F = 20 idlefrequencies and N = 40 CRs with a transmission request,the search space consisting of all possible assignments has∑F

i=0F !

(F−i)!i!N !

(N−i)! elements. Scheduling should be both effi-cient and computationally easy. Therefore, we propose Energy-Efficient Heuristic Scheduler (EEHS) which is a polynomialtime heuristic algorithm for P1. Furthermore, it may be subjectto low throughput performance since it does not explicitlyaim to ensure high throughput performance. Therefore, wecan reorganize the problem in (11) such that throughput ismaximized with some restrictions on energy consumption perframe, and alternatively we can define an energy consumptionminimization problem with minimum throughput guarantees.In the following subsections, we define these schedulingschemes.

A. Energy-Efficient Heuristic Scheduler (EEHS)

Let Cidle denotes the set of idle frequencies, R = {Ci,f}be the set of effective rate of each link li,f , and Ntx be theset of CRs with a transmission request (i.e., CRi with Qi >0). Let E = {Ei,f} denotes the set of energy consumptionvalues if CRi is assigned to frequency f and transmits at thisfrequency. The cardinality of Cidle denoted by |Cidle| equalsto the number of idle frequencies. Number of CRs with atransmission request is Ntx = |Ntx|.

Let ηi,f be the resulting energy efficiency of CRi’s trans-mission through f . ηi,f is formulated as:

ηi,f =Ci,f

Ei,f. (15)

The energy-efficient heuristic scheduler (EEHS) greedilyassigns each idle frequency to the CR that can attain themaximum energy efficiency at this frequency, i.e. highestηi,f . EEHS operates applying the steps listed in Algorithm 1.Briefly, if there are more CRs than the number of idle frequen-cies (Line 1), then the best CR denoted by CRi∗ for each idlefrequency is selected in channel assignment. We call the CRachieving the highest energy efficiency at a frequency the bestCR for f (i.e., CRi∗ where i∗ = argmaxi ηi,f in Line 4). Incase of ties, CR with higher effective rate, i.e., larger Ci,f , isselected for this frequency. If there are plenty of frequencies(Line 8), then the best frequency denoted by f∗ is selectedfor each CR in Ntx. The frequency at which CRi maintainsthe highest energy efficiency is the best frequency for this CR.After a frequency is assigned to a CR, it is removed from theset of idle frequencies (Line 13). Likewise, if CRi is assigneda frequency, it is removed from Ntx (Line 6).

Algorithm 1 Energy-efficient heuristic scheduler: EEHSRequire: Cidle, R, E .Ensure: Assignment vector x : [(f, CRi)], f ∈ Cidle and

CRi ∈ Ntx.1: if |Cidle| < Ntx then2: for all f ∈ Cidle do3: ηi,f =

Ci,f

Ei,f, ∀ CRi ∈ Ntx

4: i∗ ← argmaxi ηi,f5: Add (f, CRi∗) to the assignment vector6: Ntx ← Ntx \ CRi∗

7: end for8: else9: for all CRi ∈ Ntx do

10: ηi,f =Ci,f

Ei,f, ∀f ∈ Cidle

11: f∗ ← argmaxf ηi,f12: Add (f∗, CRi) to the assignment vector13: Cidle ← Cidle \ f∗

14: end for15: end if

The above algorithm operates in polynomial time for a con-stant F . More particularly, it is in the order of O(FpidleNtx)complexity where Fpidle is the expected number of idlechannels. As Ntx is a function of number of CRs (N ),complexity of EEHS can be written as O(FN).

B. Throughput Maximizing scheduler with an Energy con-sumption Restriction (TMER)

Instead of formulating the centralized resource allocationproblem as an energy efficiency maximization problem, wecan formulate it as a throughput maximization problem witha restriction on energy consumption (TMER). Let assume thatEmax is the maximum allowed energy consumption for aframe. It is a constant value determined by the scheduler at


each frame and can be tuned for the desired operation point.Let K be the number of CRs in transmission, α the averagenumber of channel switchings per user, and Td be the averageidling time of CRs after transmission. Accordingly, Emax iscalculated as follows:

Emax = β(K[(Ptx + Pc)(T − αtcs − Td) + PdTd + Pcsαtcs]

+ (N −K)PdT ) (16)

In the above formula, β ∈ (0, 1] is the energy-throughputtradeoff parameter. Number of CRs in transmission is simplythe minimum of number of CRs with a transmission request(Ntx) and number of idle channels (|Cidle|):

K = min(Ntx, |Cidle|). (17)

Next, average idling time of CRs after transmission (Td) iscomputed as follows:

Td = T − αtcs − Tavg (18)

where Tavg is the average transmission time of a CR. Tavg isthe time required for transmitting all bits in the CR’s buffer.However, as this time may be greater than the effective timeavailable for transmission, i.e., T−αtcs, we take the minimumof these values as below:

Tavg = min(Qavg

Ravg, T − αtcs) (19)

Qavg =

∑i Qi

Ntxi, CRi ∈ Ntx (20)

Ravg =

∑i

∑f Bi,f

|Cidle|Ntxf ∈ Cidle. (21)

Qavg in (20) and Ravg in (21) denote the average queue sizeof CRs with transmission request and average rate of idlechannels, respectively.

As a scheduler is desired to be fair in resource allocation, wedefine a metric called satisfaction ratio (ωi) which is simplythe ratio of CRi’s transmitted traffic to its total generatedtraffic up to current time. We use satisfaction ratio as a kindof fairness criteria in our scheduler. Therefore, (1−ωi) in theobjective serves to ensure a notion of fairness and favor theCRs with lower ωi. TMER can be formulated as below:

P2: maxx

N∑i=1

F∑f=1

(1− ωi)Xi,fCi,f (22)

s.t.∑∀i,

CRi∈A

F∑f=1

Ei,fXi,f +∑∀i,

CRi ∈A

PdT 6 Emax (23)

K1 6N∑i=1

F∑f=1

Xi,f 6 K (24)

and subject to Constraints (12), (13) and (14). Constraint (24)ensures that at least K1 CRs are allocated an idle frequency.Setting K1 = K, we can ensure that all idle channels areallocated to CRs, or all CRs with a transmission requestare assigned a frequency if Ntx < |Cidle|. Recall K =min(Ntx, |Cidle|). Otherwise, this scheduler may leave some

channels unused although being idle. P2 is a variant of P1which is a linear integer programming (LP) problem, and canbe solved using an optimization software such as CPLEX [24].

C. Energy consumption Minimizing scheduler with a Through-put Guarantee constraint (EMTG)

Similar to P2, we can formulate an energy consumptionminimization problem with minimum throughput guarantees(EMTG) as follows:

P3: minx

N∑i=1

F∑f=1

ωiXi,fEi,f (25)

s.t. Rmin 6N∑i=1

F∑f=1

Xi,fCi,f (26)

Rmin = βKTavgRavg (27)

K2 6N∑i=1

F∑f=1

Xi,f 6 K (28)

and subject to Constraints (12), (13) and (14). Constraint (26)ensures at least Rmin throughput is attained in a frame whileenergy consumption is minimized. Similar to Emax, Rmin isa constant value determined by the scheduler as in (27). ByConstraint (28), at least K2 CRs are assigned a frequency ina frame.

Both TMER and EMTG schedulers can be changed intoschedulers ignoring fairness by setting ωi = 0 for TMER, andωi = 1 for EMTG. Regarding computational complexity ofTMER and EMTG, both solve an LP problem. If we modelthe frequency assignment problem using bipartite graphs (CRsas vertices in V1 and frequencies in the other vertex groupV2, V1 ∩ V2 = ∅), throughput maximization corresponds tomaximum weighted matching in this bipartite graph. In thismodel, (1−ωi)Ci,f is the weight of the edge between vertexi and vertex f . Likewise, frequency assignment in EMTGcan be modeled using minimum weighted bipartite matching.However, we have additional energy consumption (Constraintin 23) and minimum throughput constraint (Constraint in26). In the literature, there are various algorithms running inpolynomial time for maximum/minimum weighted bipartitematching, e.g. O(|F |3) as in Hungarian algorithm [25]. Usingthe solutions in the literature and dealing with the additionalconstraints, EMTG and TMER optimization problems can besolved efficiently.

IV. PERFORMANCE EVALUATION

Basic performance metrics are probability of success (Ps),energy consumption, and energy efficiency (η). Probabilityof success represents the fraction of the generated CR traf-fic that is delivered successfully. We use it as a means toevaluate throughput performance. First, we deactivate fairnessin TMER and EMTG schedulers by appropriately setting ωvalues. In the last set of scenarios, we evaluate the fairnessof each scheduler. Simulations are performed on our discreteevent simulator developed in Java while ILOG CPLEX [24]is used for solving optimization problems P2 and P3.


TABLE ISUMMARY OF SYMBOLS AND BASIC SIMULATION PARAMETERS

Symbol Description Value/metricXi,f Binary decision variable denoting whether

CRi is assigned to frequency f{0, 1}

Bi,f Achievable rate of li,f if used by CRi bits/secondRi,f Number of bits that can be transmitted at

li,f in a frame if used by CRi

bits/frame

Ci,f Effective rate of li,f if CRi transmits at f bitsQi Number of bits in CRi’s buffer bitsT Frame duration 100 msW Channel bandwidth 5 MHzF Number of frequencies [5,50]N Number of CRs [5,40]Ptx Transmission power 1980 mWPd Idling power 990 mWPc Circuit power 210 mWPcs Channel switching power 1000 mWtcs Channel switching latency 0.1 ms/MHzλ Average number of packets generated by a

CR in a frame4.7 packets

α Average number of channel switching F /10β Energy-throughput tradeoff parameter (0,1]Emax Maximum allowed energy consumption in a

framemJ

Rmin Minimum throughput to be achieved in aframe

bits

f1

W

fi fF

(a) Contiguous spectrum.

Spectrum band that is open to CRsSpectrum band that is close to CRs

W1W2 W3

(b) Fragmented spectrum.

Fig. 3. Spectrum organization.

As benchmark, we also present performance of maximumrate heuristic scheduler (MRHS) in the following scenarios.MRHS is a well-known and commonly applied heuristicscheduler that aims to maximize total throughput of the CRNin a frame. Simply, MRHS assigns each idle frequency f tothe CR with maximum effective rate (Ci,f ) as opposed toEEHS which assigns frequency f to the CR which will attainmaximum energy efficiency (Ci,f

Ei,f) at frequency f . Similar

to EEHS, MRHS has polynomial time complexity, i.e. linearin N and F . Performance improvement in energy efficiencyachieved by a scheduler S over the reference scheduler (i.e.,MRHS) can be computed as energy saving ratio (ESR). It iscalculated as follows:

ESRS = (ηS

ηMRHS) (29)

where ηS is the energy efficiency achieved by S.Two spectrum occupancy scenarios are analyzed. In the

first (Fig. 3(a)), CRN operates on a contiguous spectrum ofF bands all with equal bandwidth, whereas in the second(Fig. 3(b)) frequency bands are fragmented. The second sce-

nario is more realistic: since some of the spectrum is forthe exclusive use of PUs such as military bands, that part ofthe spectrum is closed for CR access. Moreover, spectrum isdivided into bands with various bandwidths, e.g. GSM has 200kHz bands while WLAN has 22 MHz channels. Thus, spec-trum for CRN’s use becomes collection of various frequencybands with non-identical bandwidth and spectrally separatedfrom each other. Actual location of an opportunity is importantsince channel switching is a function of spectral separation oftwo frequencies. In our analysis, we only consider fragmentedspectrum of identical bandwidth channels for analyzing theeffect of spectral distance in the fragmented scenario andignore any other factors.

We assume CR traffic follows a batch Bernoulli process.In the literature [18], generally CRs are assumed to haveinfinite queue backlogs, i.e. they can transmit as much as thelink capacity lets. This approach simplifies the analysis andfacilitates the mechanisms to be assessed under full capacitywithout being restricted by the CR traffic process, however it isnot realistic. In our simulations, each CR probabilistically gen-erates i packets with probability pi which makes λ =

∑i ipi

packets in a frame on the average.In the following, results are collected from ten independent

runs for scheduling performed over 200 consecutive frames. Inour runs, we set λ = 4.7 packets/frame for each CR and eachpacket is assumed to be 60 Kb. We set α = F/10. In all sce-narios, channel switching latency tcs is set to 0.1ms/1MHz.SNR of a link is assumed to follow an exponential processwith mean SNR=2.5dB. Table I summarizes the symbols andbasic simulation parameters. Note that relationship amongpower values is as follows: Pd < Pcs < Ptx. We utilizethe power consumption profile of a WLAN interface [1] todetermine these power consumption components. To the bestof our knowledge, there is not any specification denotingthe power consumption of channel switching. Therefore, weassume that Pcs is larger than idling power and smaller thantransmission power. In order to avoid infeasible solutions, weset K1 = K − 2 and K2 = K for contiguous spectrum andK1 = K/2 and K2 = 0 for fragmented spectrum.

A. Contiguous Spectrum

In this scenario, first we set N = 20 and analyze the effectof increasing F . Next, we set F = 20 and analyze the effectof increasing N .

Fig. 4 illustrates the effect of increasing number of fre-quencies on the performance of schedulers. The CR trafficload changes from 2.2 (for F = 5) to 0.22 (for F = 50).As shown in Fig. 4(a), increase in F also leads to anincrease in success probability. TMER and EEHS performas good as MRHS almost for all F values while EMTGschedulers are close to MRHS in throughput performance forF > 20. For F > 20, although all schedulers achieve similarthroughput performance (i.e., Ps = 1), they differ in totalenergy consumption. As Fig. 4(b) depicts, EMTGs have thelowest energy consumption while MRHS always consumesthe highest energy. For increasing F , energy consumptionincreases for a while which is caused by more CRs having


5 10 15 20 25 30 35 40 45 50

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of frequencies (F)

Pro

babi

lity

of s

ucce

ss

MRHSEEHSTMER β=0.9

EMTG β=0.9

TMER β=0.7

EMTG β=0.7

(a) Probability of success.

5 10 15 20 25 30 35 40 45 50110

115

120

125

130

135

140

145

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Fig. 4. Performance figures of scheduling schemes with increasing F under contiguous spectrum.

chance to transmit. After some point (e.g. F = 20 forEEHS), energy consumption of proposed schedulers decreaseswith increasing F . Since there exists a huge amount ofavailable resources, proposed schedulers assign the frequencythat will lead to lower energy consumption. Moreover, sincemore frequencies are available, CRs’ queues are shorter ingeneral. That is, CRs can transmit quickly and switch tolow-energy-consuming idling state. On the other hand, energyconsumption in MRHS does not change significantly as itlacks an energy consumption perspective. Regarding ESR inFig. 4(c), EEHS has always better performance than MRHSand it attains significant improvement in energy efficiency forF > 25. To be more exact, for F = 25 EEHS transmits9% more bits with the same energy consumption compared toMRHS. Its ESR changes from -0.002 to 0.23. For high load(low F ), EMTGs have low throughput performance leading tolow energy efficiency. However, as there are more resourcesavailable in the system, EMTGs become more favorable owingto their lower operation energy costs. ESR changes from -0.53(significantly lower energy efficiency) to 0.24 for EMTG. Weobserve that Ps values for TMER and EMTG with β = 0.9 arehigher than their counterparts with β = 0.7 only for low F .For F > 10, TMER with β = 0.9 and β = 0.7 have the samethroughput performance. Similarly, for F > 20, EMTG withβ = 0.9 and β = 0.7 attain similar throughput. On the otherhand, achieved improvement in energy efficiency by TMERwith β = 0.9 is lower than TMER with β = 0.7 while there isnot a significant difference between EMTG with β = 0.9 and

β = 0.7. Hence, CBS can set β = 0.7 for TMER in order toattain higher energy efficiency. However, β parameter does notsignificantly affect EMTG scheduler for F > 20. Performanceof TMER and EMTGs directly depend on our estimate ofexpected energy consumption and expected throughput, i.e,Emax and Rmin, respectively. Hence, appropriate estimationof Emax and Rmin is paramount. Considering the throughputperformance in Fig. 4(a), it is seen that our estimations areappropriate for F > 20.

Time and energy spent on channel switching depends onthe number of frequencies in the system. Channel switch-ing bandwidth increase with increasing F for the proposedschedulers. For F = 50, average channel switching distanceis around 75 MHz. While it follows the same trend for MRHSfor F < 25, channel switching bandwidth begins to decreaseafter that point. This is caused by the fact that for N = 20and F > 25 each CR can be assigned a frequency fortransmission without switching to very distant frequencies.Given that tcs = 0.1ms/MHz, total channel switching time isaround 7.5 ms (Tcs = 75MHz × 0.1ms/MHz) for TMERs,EMTGs and EEHS, and shorter for MRHS. For T = 100ms, 92.5% of the frame is effectively useable. Since spectrumis contiguous and tcs is small, channel switching does notnoticeably affect the performance of the schedulers.

Given the fact that CR operators ensure a certain degree ofsuccess rate by various admission control techniques, a typicaloperation scenario is that CR load is kept at reasonable values.Therefore, in such scenarios, e.g. F > 20 corresponding to


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Fig. 5. Performance figures of scheduling schemes with increasing F under contiguous spectrum.

0.56 CR load, success rates attained by EEHS, EMTG andTMERs are the same as that of MRHS and energy efficienciesare higher. Hence, any of EEHS, TMER or EMTG shouldbe the choice for energy-efficient CRN scheduling. For smallF , in case a slight throughput sacrifice is tolerable, EEHSand TMER schedulers can be the choice since they consumelower energy compared to MRHS. Performance of EEHSis also compared to the optimal solution of problem P1 in[26]. We showed that EEHS has comparable performance tothat of the optimal solution. As EEHS has low complexity,we consider it as an efficient solution for maximum energy-efficiency scheduling problem.

Fig. 5 demonstrates the performance of schedulers withincreasing number of CRs for F = 20. This scenario is similarto the previous scenario in a way that increase in N representsthe increase in CR traffic load (and corresponds to decreasein F ). For low number of CRs (as in high F ), all schedulershave higher energy efficiency performance than that of MRHSwhile EMTGs consume the lowest energy. Throughput andenergy efficiency performance of EMTG drastically decreasewith increasing N . However, note that for N = 40 traffic loadis 1.1 which is much more higher than that would be allowedin operational networks. A typical operation point would beN = 20 for F = 20 corresponding to load of 0.56. At thispoint, EMTGs are more energy-efficient and have the samethroughput performance as MRHS. In all schemes, averagechannel switching bandwidth decreases with increasing N .

This is not surprising since there are many CRs requestingfrequency, and the ones which will require lower channelswitching are in general more favorable in terms of throughputand energy efficiency. ESR of EEHS changes from 0.20 to 0.06while it changes from 0.21 to -0.12 for EMTGs and 0.18 to0.06 for TMERs.

B. Fragmented Spectrum

In the previous scenarios, we have contiguous block ofspectrum bands. As an example, for F = 20 and W = 5 MHz,there is totally 100 MHz bandwidth as spectrum resourcefor CRN’s use. In this scenario, let us have the same totalbandwidth but in a fragmented way. Let assume CRN can useten channels at 470-520 MHz, five channels at 600-625 MHzand thirty channels at 2400-2575 MHz bands. We refer eachblock of channels as spectrum fragment in the following. Weassume all channels have 5 MHz bandwidth. Moreover, allchannels have exactly the same two-state model leading toidentical probability of being idle values (pidle=0.7).

Fig. 6 summarizes the performance figures of schedulersunder fragmented spectrum for increasing F . The results agreewith the previous runs in which contiguous spectrum is con-sidered. MRHS has lower energy efficiency than that of EEHSand TMERs. Average channel switching bandwidth is around20-30 MHz for EMTGs and MRHS whereas it is around 50MHz for TMERs and EEHS, lower than the contiguous case.Comparing these results with the contiguous spectrum case,


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we conclude that each scheduler tries to allocate the CRs to itsclose frequency bands in the same fragment. Therefore, despitethe spectrum being fragmented, average channel switchingbandwidth is lower than the contiguous spectrum case. Fig. 7corroborates this explanation.

We randomly select a CR and record its antenna configura-tion, i.e., the frequency it is tuned to, through the simulationduration for each frame for F = 50 under EEHS. Fig. 7 depictsthe frequencies for both contiguous and fragmented spectrum.Minimum and maximum operation frequencies are also writtenon the figures. The scheduler behaves as if CRs are partitionedin three classes, and each CR in a class is usually assigneda frequency in the corresponding spectrum fragment. For thefragmented spectrum scenario (Fig. 7(b)), this CR operates inthe first and second fragment, and never hops to the 2400 MHzfragment. This CR mostly switches to the frequencies in thesame fragment which are only tens of MHz distant. As weset tcs = 0.1ms/MHz and perform channel switching onlybefore transmission, CRs cannot hop between fragments ofthe spectrum due to infeasibility of switching. For F = 50,spectrum consists of 470-520 MHz (ten channels), 600-625MHz (5 channels) and 2400-2575 MHz (35 channels) bands.Switching from the first fragment to the second is feasiblewhereas it is not to switch to the 2400 MHz bands. Frequencyseparation is around [2400-625 MHz, 2425-600 MHz] and itrequires channel switching time in the interval [177.5 ms,182.5 ms] which is much longer than the frame duration.Hence, such assignments are accepted as infeasible and are

avoided by the scheduler.With the developments in the hardware technologies, chan-

nel switching cost may become negligible. However, currentsystems incur channel switching cost that may sometimesbe comparable to other energy consumption costs. Therefore,it is vital to implement scheduling schemes, especially foroperation in the fragmented spectrum, that combats this cost.For instance, if CRs have the ability to tune their antennas inan intelligent way during their idling periods, this switchingdelay can be hidden with careful scheduling and subsequentlyoperation in all parts of the spectrum becomes possible.However, it still incurs the energy consumption overhead.

To sum up, spectrum fragmentation does not noticeably af-fect the CRN performance if considered from a network-wideperspective since scheduling schemes tackle fragmentation viacareful frequency allocation. If considered from the viewpointof a single CR, spectrum resources a CR can use is decreasedto a smaller portion which may deteriorate the performanceof this CR. On the other hand, the set of CRs competingwith this CR may be reduced to a smaller set as some CRsare restricted to another portion of the spectrum. Consideringthese two points, we can conclude that fragmentation, on theaverage, does not affect the individual CR performance.

C. Fairness in Scheduling

In this section, we analyze each scheduling scheme in termsof fairness criteria. Ensuring a degree of fairness is desirableeven if fairness objective may conflict with the objective of


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Fig. 7. A CR is randomly selected and frequency to which its antenna is tuned is recorded for each frame, F = 50, EEHS scheme.

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throughput maximization. Otherwise, some users starve whileothers may be over allocated. As in opportunistic scheduling,MRHS and EEHS favor CRs leading to higher throughputand higher energy efficiency, respectively. However, ωi inTMER and EMTG schedulers enable fairness in resourceallocation. We interpret fairness in our system in terms of meansatisfaction ratio. In an informal way, we can say that a schemeis more fair than the other if it can keep satisfaction ratios ofCRs closer to each other. Formally, we evaluate fairness interms of Gini index. Gini index computes how much resourceallocation deviates from the ideal fair allocation [27]. Hence, itcan be considered as a measure of inequality. A perfectly fairallocation scheme has Gini index 0 whereas a highly unfair

allocation has high Gini index. Let FGini denotes this index,and it is calculated as follows:

FGini =1

2N2ω

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∑Ni=1 ωi

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For a clear understanding of the behavior of schedulers, wefocus on a scenario where CRs have non-homogenous trafficdensity and non-uniform SNR conditions [27]. Assume thathalf of the CRs are close to the CBS and therefore have good


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Fig. 9. Satisfaction ratios of CRs under various scheduling schemes.

channel conditions. We reflect this by setting mean SNR = 5dB for these CRs. In addition, these CRs generate high traffic.The other half (say CRs with identities ⌊N/2⌋,⌊N/2⌋+1,. . .,N ) have lower SNR (SNR=0 dB) and generate low traffic. Weassume CRs in the first group generates four-fold traffic thatof the second group. There are 40 CRs and 20 frequencies inthis setting. For low traffic, each scheme can satisfy a certaindegree of fairness since non-served CRs have longer queues(i.e. Qi) leading to higher Ci,f values. Therefore, these CRsare also served. However, for high, non-identical traffic, andnon-identical link conditions, scheduling schemes may fallshort of providing fairness.

Fig. 8 illustrates the change of satisfaction ratios of twoCRs; CR1 from the first group and CR2 from the secondgroup. Since CR2 has bad channel conditions, MRHS andEEHS never allocate frequency to this CR. On the other hand,TMER and EMTG assign a frequency to the CR when itssatisfaction ratio decreases for a while. Therefore, satisfactionratios of CRs are close to each other in TMER and EMTG.The unfairness of MRHS and EEHS can also be seen in Fig. 9.CRs in the first group are always favored in MRHS and EEHSwhereas TMER and EMTG distribute resources more fairly.

Table II includes TMER and EMTGs both with and withoutfairness notion and summarizes the performance of all sched-ulers for N = 10, N = 30 and N = 40. Please recall thatmean satisfaction in the first column is not a metric evaluatingthe user perceived quality but is simply a representation ofthe average satisfaction of all CRs and a representation ofthe throughput performance. For low N , all schedulers havethe same throughput and fairness performance (i.e., Ps = 1

and FGini = 0). Nevertheless, they differ in energy efficiencyprofiles. EMTGs yield the highest energy efficiency amongall schedulers. Furthermore, we also observe that there isa marginal decrease in energy efficiency when fairness isenabled in TMERs. For N = 30, energy efficiencies are lowerin general compared to the performance for N = 10. This isdue to the CRs that stay in idling mode which only contributeto the energy consumption but have no throughput. In this case,TMER Fair schedulers have slightly higher energy efficienciescompared to their counterparts with no fairness notion. AsF < N , some CRs cannot be assigned frequencies. FGini

values are higher compared to N = 10. For N = 40, regardingthe probability of success results, it can be seen that enablingfairness in TMERs and EMTGs also has a positive effect onthroughput performance. Fair schemes compared to the unfaircounterparts have higher probability of success and energyefficiency performance for this particular setting. This resultconflicts with the general expectation that enabling fairnessmay deteriorate the throughput performance. On the otherhand, the dynamic operation of TMER and EMTGs whichdepends on both satisfaction ratios (ωi) and effective channelrates (Ci,f ) challenges such a straightforward conclusion. Forinstance, TMER tries to maximize weighted sum of the CRthroughput but at the same time it has to meet the constraint onenergy consumption. Hence, it is not trivial to have a directgeneralization that fairness has a positive or negative effecton throughput and energy efficiency performance of TMERsand EMTGs. Since MRHS and EEHS cannot serve CRs in afair way, FGini is very high for these schemes. However, forTMERs with fairness enabled it is a perfectly fair system with


TABLE IISUMMARY OF SIMULATION RESULTS FOR CONTIGUOUS SPECTRUM, HETEROGENOUS CR TRAFFIC AND NON-UNIFORM LINK SNRS, F = 20.

N = 10 N = 30 N = 40Ps η FGini Ps η FGini Ps η FGini

MRHS 1.00 2680.21 0.00 0.99 2495.72 0.03 0.85 2350.89 0.40

EEHS 1.00 3027.54 0.00 0.92 2541.96 0.21 0.83 2460.90 0.46

TMER β = 0.9 1.00 2789.00 0.00 1.00 2622.23 1.00 0.87 2449.94 0.36

TMER Fair β = 0.9 1.00 2714.28 0.00 1.00 2702.92 0.00 1.00 2720.82 0.00

EMTG β = 0.9 1.00 3042.45 0.00 0.85 2527.02 0.22 0.68 2066.76 0.34

EMTG Fair β = 0.9 1.00 3042.23 0.00 0.94 2528.81 0.02 0.78 2117.01 0.02

TMER β = 0.7 1.00 2945.82 0.00 1.00 2691.24 0.00 0.87 2481.05 0.36

TMER Fair β = 0.7 1.00 2854.80 0.00 1.00 2733.90 0.00 1.00 2801.39 0.00

EMTG β = 0.7 1.00 3042.41 0.00 0.75 2212.48 0.21 0.60 1825.42 0.34

EMTG Fair β = 0.7 1.00 3042.31 0.00 0.89 2364.02 0.03 0.75 2037.88 0.02

FGini = 0. For EMTGs, FGini is higher than TMER, but stillvery close to zero.

V. CONCLUSIONS

In this work, we have formulated an energy efficiencymaximizing scheduler for cognitive radio networks. First,we have presented EEHS, a heuristic algorithm running inpolynomial time, for energy-efficient resource allocation. AsEEHS may fall short of throughput efficiency, we have re-formulated resource allocation as throughput maximizationproblem subject to energy consumption restrictions (TMER)and as an energy consumption minimization problem subjectto throughput guarantees (EMTG). TMER and EMTG alsohave the power to provide fairness among the CRs owing to thesatisfaction parameter in their objective functions. Satisfactionratio of a CR represents the fraction of traffic transmittedby this particular CR up to current time. CRs with lowersatisfaction are favored in frequency allocation resulting intheir satisfaction ratio to increase, and in turn facilitating lesssatisfied CRs to be favored in the subsequent frames.

We have evaluated the performance of these schedulersand compared them with the commonly-known throughputmaximizing scheduler (MRHS). Moreover, we have focusedour attention on the spectrum organization. Spectrum avail-able for CRN’s use may consist of either contiguous bandsor it may be a composition of spectrally distant frequencybands (also called fragments). Frequency separation in thesecond case determines the range of frequencies that can beassigned to a CR since channel switching time and energyconsumption depend on frequency separation between thetwo frequency bands. MRHS has lower energy efficiencyperformance compared to EEHS, TMER and EMTG. Besides,throughput performance of our proposals under practical op-eration conditions (e.g. sufficient number of frequencies) aresimilar. Therefore, schedulers with energy efficiency or energyconsumption concerns should be the preferred schedulingscheme for energy-efficient CRNs. Considering fairness, forlow traffic load and homogeneous conditions, all schemesserve CRs almost equally as expected. On the other hand,under non-homogeneous traffic and link quality conditions,EEHS and MRHS as opportunistic schedulers cannot provide

fairness among CRs. On the contrary, EMTG and TMERprovide a good balance in resource allocation among CRs.We have also showed that the proposed schedulers can combatthe spectrum fragmentation by considering the cost of channelswitching and avoiding hopping between distant frequencybands.

In this work, we have focused on a CRN that acquires sens-ing information from a white space database considering thelatest trends on geolocation databases. However, as spectrumsensing is the principal step for real autonomous CRNs, weplan to work on the energy-efficient scheduling problem fora CRN that performs spectrum sensing internally. Moreover,we will incorporate transmission power adaptation into ourscheme in our future work.

ACKNOWLEDGMENT

This work is supported by the State Planning Organizationof Turkey (DPT) under the TAM Project with grant numberDPT-2007K 120610, and the Scientific and TechnologicalResearch Council of Turkey (TUBITAK) with grant number109E256.

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Suzan Bayhan received her PhD, MS and BSdegrees in Computer Engineering department fromBogazici University, Istanbul, Turkey in 2012, 2006,and 2003, respectively. Currently, she works asa post-doctoral researcher at Helsinki Institute forInformation Technology (HIIT), Aalto University,Helsinki, Finland. Her current research interests in-clude cognitive radio networks, small cells, greencommunications and analytical modeling.

Fatih Alagoz is an Associate Professor in the De-partment of Computer Engineering, Bogazici Uni-versity, Turkey. From 2001 to 2003, he was withthe Department of Electrical Engineering, UnitedArab Emirates University, UAE. In 1993, he wasa research engineer in a missile manufacturing com-pany, Muhimmatsan AS, Turkey. He received theB.Sc. degree in Electrical Engineering from MiddleEast Technical University, Turkey, in 1992, andM.Sc. and D.Sc. degrees in Electrical Engineeringfrom The George Washington University, USA, in

1995 and 2000, respectively. His current research interests are in the ar-eas of satellite networks, wireless networks, sensor networks and UWBcommunications. He has contributed/managed to ten research projects forvarious agencies/organizations including US Army of Intelligence Center,Naval Research Laboratory, UAE Research Fund, Turkish Scientific ResearchCouncil, State Planning Organization of Turkey, BAP, etc. He has edited fivebooks and published more than 100 scholarly papers in selected journalsand conferences. Dr. Alagoz is the Satellite Systems Advisor to the KandilliEarthquake Research Institute, Istanbul, Turkey. He has served on severalmajor conferences technical committees, and organized and chaired manytechnical sessions in many international conferences. He is a member ofthe IEEE Satellite and Space Communications Technical Committee. He hasnumerous professional awards.

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