1

Cooperative Adaptive Spectrum Sharing in CognitiveRadio Networks

Haythem Bany Salameh Marwan Krunz Ossama YounisDept. of Telecomm. Eng. Dept. of Electrical and Computer Eng. Applied Research, Telcordia Techn., Inc.Yarmouk Univ., Irbid, Jordan Univ. of Arizona, Tucson, AZ Piscataway, NJEmail: haythem@ece.arizona.edu Email: krunz@ece.arizona.edu Email: oyounis@research.telcordia.com

Abstract— The cognitive radio (CR) paradigm calls for openspectrum access according to a predetermined etiquette. Underthis paradigm, CR nodes access the spectrum opportunistically bycontinuously monitoring the operating channels. A key challengein this domain is how the nodes in a CR network (CRN)cooperate to access the medium in order to maximize the CRNthroughput. Typical multi-channel MAC protocols assume thatfrequency channels are adjacent and that there are no constraintson the transmission power. However, a CRN may operate over awide range of frequencies, and a power mask is often enforcedon the transmission of a CR user to avoid corrupting thetransmissions of spectrum-licensed primary-radio (PR) users. Toavoid unnecessary blocking of CR transmissions, we proposeanovel distance-dependent MAC protocol for CRNs. Our protocol,called DDMAC, attempts to maximize the CRN throughput. Ituses a novel probabilistic channel assignment mechanism thatexploits the dependence between the signal’s attenuation modeland the transmission distance while considering the trafficprofile.DDMAC allows a pair of CR users to communicate on a channelthat may not be optimal from one user’s perspective, but thatallows more concurrent transmissions to take place, especiallyunder moderate and high traffic loads. Simulation results indicatethat compared to typical multi-channel CSMA-based protocols,DDMAC reduces the blocking rate of CR requests by up to30%,which consequently improves the network throughput.

Index Terms— Cognitive radio networks, spectrum access,distance-awareness, traffic-awareness, MAC protocols.

I. I NTRODUCTION

Spectrum measurements by FCC and other organizations(e.g., XG DARPA initiative) indicate significant temporal andgeographical variations in the utilization of the licensedspec-trum, ranging from15% to 85% [1]. These measurementsmotivated the need for a new technology that improves spec-trum utilization without degrading the performance of licensedprimary radio networks (PRNs). To cope with the rising demandin unlicensed wireless services, cognitive radio (CR) technologyhas been proposed. This technology allows an open access tothe spectrum subject to a predetermined etiquette. In a cognitiveradio network (CRN), users are aware of the radio frequenciesused by existing legacy networks, and they opportunisticallyadapt their communication parameters to be able to communi-cate without affecting active PR users.

A CRN has unique characteristics that distinguish it fromtraditional multi-channel wireless networks. Unlike tradi-tional wireless networks, which typically occupy contiguousbands [2]–[4], a CRN is expected to operate over a set ofwidely-separated non-contiguous frequency bands. Communi-cation on such bands exhibits different RF attenuation andinterference behaviors. It is well known that signal attenuation

An abridged version of this paper was presented at theIEEE SECON’08 Con-ference, June 2008. This research was supported in part by NSF (undergrantsCNS-0721935, CNS-0627118, CNS-0325979, and CNS-0313234), Raytheon,and Connection One (an I/UCRC NSF/industry/university consortium).

increases with the distance between the two communicatingusers and also with the carrier frequency used for communica-tion [5]. Therefore, when assigning transmission channelsin aCRN, it is necessary to consider the signal attenuation modeland the interference conditions to improve spectrum utilization.Another characteristic of a CRN is that users must operate usinga relatively low transmission power (i.e., abide by a powermask) to avoid degrading the performance of the PR users [4].These peculiar characteristics call for new MAC protocols thatefficiently utilize the available spectrum while improvingtheoverall network throughput.

A. Motivation

Channel assignment mechanisms in traditional multi-channelwireless networks typically select the “best” channel, or setof channels, for a given transmission (e.g., [3], [6], [7]).Inthese mechanisms, thebest channel is often defined as theone that supports the highest rate. We refer to this approachas thebest multi-channel(BMC) approach. When the BMCapproach is employed in a CRN, the blocking probability forCR transmissions, defined as the percentage of CR packetrequests that are blocked due to the unavailability of a feasiblechannel assignment, can increase, leading to a reduction inthenetwork throughput. To illustrate, consider an environment inwhich two PRNs and one CRN coexist. PRN1 operates overa low-frequency band (CH1), while PRN 2 operates over ahigh-frequency band (CH2). Suppose that PRN2 introducesa higher average PR-to-CR interference. Consequently, a CRreceiver experiences a higher average signal-to-interference-plus-noise ratio (SINR) overCH1 than overCH2. Assumethat two CR usersA andC need to send data to CR usersB andD, respectively (see Figure 1). Also assume that the distancebetweenA and B (dAB) is less than that betweenC and D(dCD). Figure 1(a) shows that when the CR users employ theBMC approach, the transmissionA → B usesCH1, whereasthe transmissionC → D usesCH2. A → B is allowedto proceed because it operates over a low carrier-frequencychannel with low PR-to-CR interference for a short transmis-sion distance. On the other hand,C → D requires relativelyhigher transmission power to overcome the high attenuationassociated with the high-frequency/high-interference channeland the long transmission distance. If the required transmissionpower exceeds the specified power mask,C → D cannotproceed. However, bothA → B andC → D have much betterchances of proceeding simultaneously if each CR transmitterselects channels while keeping in mind the constraining powermask of the other transmitter (Figure 1(b)).

As a numerical example, assume that PRN 1 and PRN 2operate in the900 MHz and 2.4 GHz bands, respectively.Assume thatdAB = 10 meters anddCD = 50 meters. Alsoassume that a CR transmission is successful if the received

2SINR over the selected channel is greater than the SINRthreshold. For both channels, we set the SINR threshold and theinterference mask to5 dB and60 mW, respectively. Assumethat CR receiversB andD experience the same level of totalinterference over both channels (0.05 µW). Given the aboveparameters and using the propagation model in [8] with pathloss exponent of2, the required transmit powers overCH1and CH2 for A → B are 2.2 mW and16 mW, respectively.For C → D, these powers are56.18 mW and 399.5 mW.According to the BMC scheme (Figure 1(a)),A → B canproceed overCH1 (the power mask is not violated), whereasC → D cannot proceed overCH2 (the required transmit powerexceeds the power mask). On the other hand, ifA → B usesCH2 andC → D usesCH1, both transmissions can proceedsimultaneously (Figure 1(b)).

A B

C D X

CH 1

CH 2

(a) BMC channel assignment

A B

C D

CH 2

CH 1

(b) Distance-dependent chan-nel assignment

Fig. 1. Scenarios in which two CR transmissions can/cannot proceedsimultaneously.

It is worth mentioning that in a given (one-hop) neigh-borhood, theoptimal channel assignment that maximizes thenumber of simultaneous CR transmissions can be formulatedas an integer linear programming (ILP) problem [9], [10].Since computing the optimal solution for the ILP problemgrows exponentially with the size of the network [9], heuristicalgorithms with suboptimal performance are needed. Suchalgorithms should attempt to compute channel assignment withreasonable computational/communication overhead.

B. Contributions

In this work, we develop a novel CSMA-based MAC protocolthat aims at enhancing the throughput of the CRN subject toa power mask constraint. The proposed protocol (DDMAC)employs an intelligent stochastic channel assignment schemethat exploits the dependence between the RF signal attenuationmodel and the transmission distance while taking into con-sideration the local traffic conditions. The channel assignmentscheme accounts for the interference conditions and the powerconstraints at different bands. In particular, the scheme assignschannels with lower average SINR to shorter transmissiondistances, and vice versa. In addition, our scheme associatesmore preferable channels to the most frequent transmissiondistances and less preferable channels to the less frequentdistances. In other words, the assignment process identifiesa “preferable” channel list for each CR user. Such a listindicates which channels are preferable to use depending ontheestimated distance between the transmitter and the receiver. Wepropose two variants for the channel assignment scheme. Thefirst variant is suitable for offline planning of spectrum sharing

in networks with known deployment and traffic patterns. In thiscase, there is no need for distance-traffic pattern prediction. Thesecond variant is suitable for online dynamic network operationwith unknown traffic patterns. To estimate the distance-trafficpattern in a given neighborhood, the second variant employsastochastic learning technique that adapts to network dynamics(i.e., mobility, interference conditions, and traffic conditions).The primary advantage of our assignment scheme is that it isbased on passive learning. This is because in DDMAC, CRusers always listen to the control channel in order to overhearcontrol-packet exchanges, including those not destined tothem.CR users use the control information to identify the preferablechannels.

DDMAC has the following attractive features:• It does not make any assumptions about the activity pat-

terns of the underlying networks or about user distribution.• It is easy to implement in practical settings and its pro-

cessing overhead is small.• It is transparent to PR users, i.e., does not require coordi-

nation with them.• It inherently improves the fairness among CR users, com-

pared to typical multi-channel CSMA-based protocols.• Under low load and several available channels, DDMAC

gracefully degrades to the BMC approach.To evaluate the performance of DDMAC, we conduct simula-tions over a dynamic CRN with mobile users. Our simulationresults show that by being distance- and traffic-aware, DDMACsignificantly improves network throughput while preservingfairness. The results also indicate that compared with typicalmulti-channel CSMA-based protocols, DDMAC decreases theconnection blocking rate in a CRN by up to30%. By injectingartificial errors into the estimated distances, our evaluationreveals that DDMAC is robust against estimation errors.

It should be noted that selecting a preferable channel list wasalso proposed in the MMAC protocol [11]. However, MMACdoes not support multiple-channel assignment (it is limitedto one channel per user). Specifically, the channel selectioncriterion in MMAC is to use a channel with the lowest countof source-destination pairs that have selected the channel. InDDMAC, the preferable channel list per node is constructedby accounting for the challenges associated with CRs (i.e.,lowtransmit power, presence of PR users, widely-separated non-contiguous available bands). Unlike DDMAC, the objective inMMAC was not to address spectrum sharing while improvingthe overall throughput, but rather to handle multi-channelhidden terminals using a single transceiver and to balancethe channel usage over all available channels. In addition,MMAC requires global network synchronization, which is nota requirement in DDMAC.

C. Organization

The rest of this paper is organized as follows. Section IIgives an overview of related work. In Section III-A, weintroduce our system model and state the main assumptions.The SINR analysis is presented in Section III-B. Section III-Cillustrates the effect of the carrier frequency and transmissiondistance on the path loss. In Section IV, we formulate theoptimal channel assignment problem. Section V introducesour proposed distance- and traffic-aware channel assignmentalgorithm. Section VI describes the proposed DDMAC protocoland outlines its benefits and associated overhead. We evaluateDDMAC in Section VII. Finally, Section VIII gives concludingremarks.

3II. RELATED WORK

Recently, several attempts were made to develop MACprotocols for CRNs (e.g., [6], [12]–[16]). In [6], the authorsdeveloped a CRN MAC protocol with a common control chan-nel. This protocol jointly optimizes the channel/power/rate as-signment, assuming a given power mask on CR transmissions.DC-MAC [12] is a cross-layer distributed scheme for spectrumallocation/sensing. It provides an optimization framework basedon partially observable Markov decision processes, assumingthat PR and CR users share the same slotted transmissionstructure. In [13], the authors investigated continuous-timeMarkov models for dynamic spectrum access in open spectrumwireless networks. Using such models, a distributed randomaccess protocol is proposed to achieve airtime fairness betweendissimilar unlicensed users.

The FCC defined theinterference temperature model[17],which provides a metric for measuring the interference ex-perienced by licensed receivers. In [14], the authors studiedthe issue of spectrum sharing among a group of spread-spectrum users subject to constrains on the SINR and on theinterference temperature. In [18], the interference temperaturemodel was used for optimal selection of spectrum and trans-mission powers for CR users. In [16], the authors proposeda decentralized channel-sharing mechanism for CRNs basedon a game-theoretic approach for both cooperative and non-cooperative scenarios. In [19], the concept of a time-spectrumblock is introduced to model spectrum reservation in a CRN.Based on this concept, the authors presented centralized anddistributed CRN protocols with a common control channel forspectrum allocation.

The above protocols were designed without exploiting thedependence of the number of allowable CR transmissions onthe carrier frequency and the transmission distance. They arelimited to the analytical aspects of MAC design, with nocomplete operational details. To the best of our knowledge,DDMAC is the first CRN MAC protocol that aims at improvingthe CRN throughput by exploiting the dependence on the RFsignal’s attenuation model and the transmission distance whileconsidering the prevailing traffic and interference conditions.

III. PRELIMINARIES

CR

CR CR

Users in PRN1

Users in PRN2

Fig. 2. Example of an opportunistic CRN that coexists with two PRNs.

A. Network Model

We consider a CRN with decentralized control (i.e., an ad hocnetwork). This CRN coexists geographically withM differentPRNs. PR users are legacy radios that cannot be controlled bythe CRN. Figure 2 shows a conceptual view of the scenariounder consideration withM = 2. The PRNs are licensed to

Fig. 3. Operating spectrum in the hybrid network.

operate over non-overlapping frequency bands. We assume thatall the PRN bands have the same bandwidth (BW ). In reality,a PRN may occupy multiple, non-contiguous, frequency bands.Such a PRN can be easily represented in our setup by usingmultiple equal-bandwidth virtual PRNs, each operating over itsown carrier frequency. For theith PRN, we denote its carrierfrequency byfi. As shown in Figure 3, the available bandwidth(BW ) of a PRN is divided intoL adjacent but non-overlappingfrequency channels each of Fourier bandwidthW (in Hz). SuchL channels are collectively referred to as a band. LetN denotethe total number of channels in all bands;N = LM .

Without loss of generality, we assume thatBW is sufficientto support at least one CR transmission. This is an acceptableassumption in many wireless systems that are built to operatein the unlicensed bands, including IEEE 802.11/a/b/g-compliantdevices. Each CR user is equipped withnt radio transceivers,1 ≤ nt ≤ L, that can be used simultaneously. In theory, a CRuser can transmit over an arbitrary segment of the availablebandwidth by using tunable filters. In practice, however, a CRtypically implements a bank of fixed filters, each tuned to agiven carrier frequency with fixed bandwidth, allowing the CRuser to choose from a fixed number of channels. In our setup,we assume the latter (more practical) capability, which canbeused to approximate the tunable filter scenario.

To avoid corrupting the transmissions of licensed users, amask is enforced on the transmission power of a CR userover each band, i.e,P (i)

t ≤ P(i)mask, i = 1, 2, . . . , M . The

determination of an appropriate power mask is an importanttopic, which has been investigated under certain simplifyingassumptions (e.g., [18], [20]). The spectrum sharing proto-cols in [18] and [20] were designed such that the maximumtransmission powers of CR users over various bands are dy-namically computed based on the PR’s interference margins(set by the FCC) and local traffic conditions. In [20], theauthors provided aneighborhood-dependentadaptive powermask on CR transmissions that ensures a statistical (soft)guarantee of the outage probability of PRNs (the probabilitythat the total interference power at a PR receiver exceedsthe maximum tolerable interference). The authors providedclosed-form expressions for the resulting power mask. For ourpurposes, we assume that a similar mechanism for determiningthe power mask is in place. A CR user transmits data toother CR users using the maximum allowable power vectorPmask. When not transmitting, a CR user is capable ofmeasuring the total noise-plus-interferenceI(i) over all bandsi = 1, 2, . . . , M1. This requires a wideband sensing capabilitywith a narrowband resolution. The technology to support such

1The quantityI(i) includes the PR-to-CR interference as well as the thermalnoise.

4M Number of PRNsL Number of channels in a PRN

N , N N is the total number of channels,N = 1, . . . , NBW , W Bandwidth of a band and a channel, respectively

nt Number of transceivers per CR userPt

(i) CR transmit power

P(i)mask

Interference power mask on channeli

I(i) Noise-plus-interference over channeli

SINR(i)j Measured SINR over bandi at receiverj

PL(fi) Path loss associated with bandiPr(fi) Received power at a CR receiver over bandi

d Transmitter-receiver distanceJ Set of all CR transmission requests in a locality

c(i)j

ith selected channel’s data rate for transmissionj

Cj Rate demand of thejth CR transmissionµ∗

i SINR threshold over channelimj Number of selected channels for thejth transmissionMj Mj is the set ofmj selected channels for thejth transmissionR Random variable represents the distance to the intended receiver

Rc , rc RC is the transmission region,Rc = πr2c

Ri ith ring around a CR in static channel assignmentri, ri−1 Radii that defineRi, i = 1, . . . M

Di ith ring around a CR in dynamic channel assignmentdi, di−1 Radii that defineDi

m Number of non-overlappingDi ringsTwin Observation window timepi(t) Probability ofDi at timetpi(t) Weighted average ofpi(t)

α Forgetting factorΩi(A), K CR A’s preferable channel list for regioni, i = 1, ..., K

CCL(A,B) Common channel list available forA → B transmissionΦ(A, B) Preferable available channels forA → B transmission

TABLE I

SUMMARY OF NOTATIONS USED IN THE PAPER.

capability is readily available through a wideband antenna, apower amplifier, adaptive filters, and a DSP technique calledcyclostationary feature detection [21], [22]. Thus, a CR user cansimultaneously sense several GHz-wide bands and estimate theinstantaneous interference over each band [22]. Alternatively, asequential partial sensing approach can be employed at the costof negligible switching/sensing overhead [21], [23]. It isworthmentioning that off-the-shelf wireless cards can readily serve asa fully functional wideband multi-channel CR interface. Suchan interface enables a CR user to perform analysis of the RFspectrum (i.e., sensing) in real time.

B. Analysis of the Average SINR

Based on the aforementioned characteristics of the CRN, theaverage measured SINR (SINR) at a CR receiver at a given timeover bandi is mainly determined by: (1) the path loss associatedwith that band (PL(fi)); (2) the average interference over that

band (I(i)

), which can be estimated based on the sensing historyand the spectrum occupancy statistics (e.g., using the techniquesin [12], [24]; and (3) the enforced power maskP

(i)mask. Formally,

SINR(i)

(dB) is given by:

SINR(i)

(dB) = P(i)mask(dB) − PL(fi)(dB) − I

(i)(dB). (1)

Note that in [25] and [26], it was shown that for a given CRNand due to PRN’s activity, CR users that are far away from eachother can experience different average interferenceI

(i), which

may vary with time. On the other hand, CR users in closeproximity typically share the same view of the surrounding RFenvironment.

Table I summarizes the main notation used in the paper.

C. Carrier Frequency and Distance Effects on Path Loss

In this section, we discuss the effect of the carrier frequencyand transmission distance on the path loss. For a given carrierfrequencyf , let do(f) be the close-in distance, i.e., the distancefrom the transmitter after which the RF channel can be approx-imated by the free-space model;do(f) can be determined frommeasurements or can be estimated by [8]:

do(f) = max

2D2

a f

c, Da,

c

f

(2)

whereDa is the antenna length of the transmitter andc is thespeed of light. LetPo(f) and Pt(f) respectively denote thereceived power at the close-in distance and the CR transmitpower. Then,Po(f) can be estimated as follows [8]:

Po(f) =c2Gt(f)Gr(f)

(4πdo(f))2f2Pt(f) (3)

whereGt(f) and Gr(f) are the transmit and receive antennagains, respectively. LetPr(f) denote the received power atdistanced from the transmitter,d ≥ do(f). Then,

Pr(f) = Po(f)

(do(f)

d

)n

(4)

where n is the path loss exponent (typically,2 ≤ n ≤ 6).Note that, in practice,do(f) is of the same order of magnitudeas the node’s dimensions. For example, for a mobile phoneoperating in the900 MHz band withDa = 5 cm, do(f) = 33cm. For an 802.11 WLAN card operating in the2.4 GHz bandand the same antenna size,do(f) = 12 cm. Accordingly, it isreasonable to assume that the probability thatd is less thando(f) is very small (i.e., Pr(d < do(f)) ≈ 0).

Using (2), (3), and (4), the path lossPL(f) can be expressedas:

PL(f) = 10 logPt(f)

Pr(f)= −10 ×

logc2γDn−2

a

f2dn , ∀ f s.t. Da ≥ max

cf,

2D2af

c

log cnγfndn , ∀ f s.t. c

f≥ max

Da,

2D2af

c

logc4−nγ(2D2

a)n−2

f4−ndn , ∀ f s.t. 2D2af

c≥ max

Da, c

f

(5)

where

γdef=

Gt(f)Gr(f)

(4π)2. (6)

Note that the dependence ofPL(f) on d (i.e., 1dn ) is the same

for any given carrier frequency.Figure 4 depicts the path loss for a wide range of carrier

frequencies and two values ofn at a distanced = 1 meter.This figure and equation (5) reveal that the signal attenuationincreases as the distance between the two communicatingusers increases, and as the frequency used for communicationincreases. These observations provide the motivation for ourdistance-dependant channel assignment, discussed in Section V.

IV. OPTIMAL CHANNEL ASSIGNMENTPROBLEM

Our objective is to maximize the number of simultaneous CRtransmissions, and consequently the overall network through-put. Toward this end, we define the termlocal spectrum utiliza-tion as the total number of simultaneous CR transmissions thatcan be supported in a given (one-hop) locality while meetinga predefined power mask. Before formulating the problem, wediscuss the requirements for a successful CR transmission.

5

0 1 2 3 4 5 6

x 109

20

30

40

50

60

70

f (Hz)

Pa

th L

oss (

dB

)

n = 4n = 2

Fig. 4. Path loss vs. carrier frequency for two path loss exponents (Da = 5cm, Gt(f) = Gr(f) = 1).

A. CRN Transmission Requirements

Within a given neighborhood, multiple CR users may con-tend for access to one or more of the available channels. LetNandJ denote the set of allN channels and the set of all CRtransmission requests in the local neighborhood at a given time,respectively. We assume that thejth CR transmission (j ∈ J )is successful if both of the following two conditions are met:

• It is possible to findmj available channels from the setN such that

∑mj

i=1 c(i)j ≥ Cj , wherec

(i)j is the data rate of

the ith selected channel andCj is the total rate demandfor the jth CR transmission.

• Let Mj be the set ofmj selected channels. Then, thereceived SINR of everyi ∈ Mj (SINR(i)

j ) must be greaterthan the SINR threshold (µ∗

i ) that is required at the CRreceiver to achieve a target bit error rate over channeli.

B. Maximizing the Utilization of Local Spectrum

Let δ(i)j be a binary variable denoting whether or not channel

i is assigned for transmissionj. Formally,

δ(i)j =

1, if channeli is assigned for transmissionj0, otherwise. (7)

Similar to [10], [27], the problem of maximizing the totalnumber of simultaneous CR transmissions in a given neighbor-hood can be formally stated as follows:

maxδ(i)j

∈0,1

∑j∈J 1

[∑i∈N δ

(i)j c

(i)j ≥ Cj

](8)

∑j∈J δ

(i)j ≤ 1, ∀i ∈ N (9)

∑i∈N δ

(i)j ≤ nt, ∀j ∈ J (10)

SINR(i)j ≥ µ∗

i , ∀j ∈ J , s.t. δ(i)j = 1 (11)

where 1[.] is the indicator function. The constraint in (9)ensures that a channel cannot be assigned to more than one CRtransmission in the same vicinity. The constraint in (10) ensuresthat at mostnt channels can be assigned to a CR transmission.For an ad hoc CRN, the above optimization problem mustrun in a distributed manner at each CR user in the network.This implies that each CR user must exchange instantaneousSINR and rate demand information with neighboring CR usersbefore selecting channels, which incurs high control overheadand delay (i.e., information may not be up-to-date). Even ifperfect knowledge of the SINR of each link and the rate

demands are available, the above ILP problem belongs to theclass of NP-hard problems [9]. In this paper, we develop aheuristic channel assignment scheme that provides a suboptimalsolution with low complexity and good spectrum utilization.Our heuristic exploits distance and traffic awareness. The keyidea behind it is to assign channels with lowSINR to short-distance transmissions. Also, local traffic information isusedto assign more channels to more likely transmission distances.

V. D ISTANCE-DEPENDENTCHANNEL ASSIGNMENTALGORITHM

In this section, we describe our proposed channel assignmentmechanism. The assignment process identifies a “preferable”channel list for each CR user. Such a list indicates whichchannels are preferable to use depending on the estimateddistance between the transmitter and the receiver. It is worthmentioning that many techniques for estimating the transmitter-receiver distance in wireless networks have been proposed inthe literature, including the Received Signal Strength Indicator(RSSI), the Time of Arrival (ToA), and the Time Difference ofArrival (TDoA) [28]. For our purposes, any of these schemescan be used. In Section VII, we investigate the robustnessof our scheme under inaccurate distance estimation, which ismainly caused by mobility, multi-path propagation, reflection,and fading effects.

Two variants of the channel assignment mechanism areproposed. The first variant is suitable for offline planningof spectrum sharing in networks with known traffic patterns,whereas the second variant is for online spectrum allocation indynamic (mobile) networks with unknown traffic patterns.

A. Spectrum Assignment for Known Traffic Profiles

Given a CR user with a packet to transmit, letr be theestimated distance to the intended receiver;r ≤ rc, whererc

is the maximum transmission range.rc represents the largestdistance from a CR transmitter over which the transmissionat maximum power can be correctly decoded over all selectedchannels in the absence of interference from other terminals(CR or PR users). LetFR(r)

def= PrR ≤ r. The functional

form of FR depends on both node distribution as well as thedistance traffic profile, which for now we assume to be given.Given FR, the channel assignment process is conducted asfollows:

• The available bands are divided according to their mea-suredSINR (given in (1))2 into M setsS1, S2, . . . , SM ,where each band consists of multiple channels. The setS1

contains the frequency channels of the band that has thehighestSINR, S2 contains the next highestSINR, and soon.

• A CR user, sayA, divides its maximum transmissionregion Rc

def= πr2

c into M non-overlapping “rings”R1, . . . , RM . The ith ring contains the CR users whosedistances toA fall in (ri−1, ri], wherei = 1, . . . , M and0 = r0 ≤ r1 ≤ r2 ≤ . . . ≤ rM = rc. The rings aredivided such that the probability of communicating witha CR receiver that falls within any of theM rings is thesame, i.e.,

FR(ri) − FR(ri−1) =1

M, i = 1, . . . , M. (12)

2Note thatPL’s dependence ond is the same for all bands. Thus, for thepurpose ofSINR comparison, we setd = 1 meter.

6UserA computes the radiiri, i = 1, . . .M , by substitutingfor FR(ri) in (12) and solving forri.

• Finally, A constructs a preferable channel list for eachring by assigning channels with lowerSINR to shortertransmission distances and channels with higherSINRto longer transmission distances, i.e., assignSM to R1,SM−1 to R2, . . ., andS1 to RM .

To illustrate the idea, we consider a uniformly distributedCRN and assume that a CR transmitter randomly chooses adestination for its data from withinRc. Therefore,FR(r) isgiven by:

FR(r) =

r2

r2c, r ≤ rc

1, r ≥ rc

. (13)

Using (12) and (13), and noting thatr0 = 0, we arrive at thefollowing expression forri:

ri =

√(1

M+

r2i−1

r2c

)rc =

√i

Mrc. (14)

Figure 5 illustrates the non-overlapping rings around a CRtransmitter whenM = 4. Within these rings, other CR and PRusers may exist. Assumerc = 100 meters. Then,r1, . . . , r4 aregiven by50, 70.71, 86.6, 100 meters, respectively.

Fig. 5. Four regions around a CR transmitter for assigning channels.

B. Spectrum Assignment for Unknown Traffic Profiles

For offline spectrum planning, we assumed in the previoussection a fixed network and prior knowledge of the distance-traffic pattern (i.e., the form ofFR). During network operation,however, the distance-traffic pattern may change with time,depending on network dynamics and user mobility. Becauseusers only possess local knowledge of their neighborhoods,itis difficult to maintain the optimal network performance. Nev-ertheless, we can develop a stochastic learning algorithm thatperforms well and uses only localized information. Stochasticlearning techniques have been widely used in wireless networksfor online traffic prediction, tracking, and power control [29],[30]. Our proposed learning approach is a distributed algorithmthat runs at each CR user in the network. A CR user, sayA,evenly divides its maximum transmission regionRc into m non-overlapping regions, wherem ≫ M . Theith region,Di, formsa ring, defined by the area(x, y) : d2

i−1 < x2 + y2 ≤ d2i ,

where di = i rc

m, and di−1 < di i = 1, . . . , m. CR userA

maintains anm-entry transmission distance table. Theith entryin that table corresponds to the regionDi, and contains thenumber of overheard CR packet requests during the recentobservation windowTwin for which the transmitter-receiver

distances fall in the range(di−1, di] (how to convey transmitter-receiver distance information will be discussed later). Note thatthe proper setting ofTwin depends on the dynamics of thenetwork. The effect ofTwin is studied in Section VII.

Fig. 6. Time diagram of pmf’s updating process.

To initialize the assignment algorithm, all CR users employthe BMC scheme discussed in Section I. At any timet, CR userA constructs its transmission distance table based on controlpackets it overheard during the observation window[t−Twin, t].Using the transmission distance table,A estimates the currentprobability mass functionpi(t) of the distancer at timet (seeFigure 6). It then computes an exponentially weighted averageof pi(t) :

pi(t) = αpi(t) + (1 − α)pi(t − Twin), (15)

where α is a forgetting factor,0 < α ≤ 1. Once pi(t) iscomputed,A computes the preferable channel list for each ring.Let Ωi(A) denote the preferable channel list for ringDi at CRuserA (how to constructΩi(A) will be given later). The newpreferable channel lists will be used during the next observationwindow time. The proposed channel assignment process mergesthe Di’s into K regions according topi(t), whereK ≤ M . Itthen assigns preferable channels for each region. The processis now described in detail:

1) UserA determines the integerk such that|∑k−1

i=0 pi(t)−∑mi=k pi(t)| is minimized, i.e., it divides the regions

into two groups; short-distance and long-distance groups.The probabilities of the short-distance and long-distancegroups are given by:

Pshort =

k−1∑

i=0

pi(t) (16)

and

Plong =

m∑

i=k

pi(t). (17)

2) User A divides theM bands into two frequency sets:low SINR frequency set and highSINR frequency set. Itassigns the lowSINR frequency set to the short-distancegroup and the highSINR frequency set to the long-distance group. The numbers of bands in the high (nH )and low (nL) frequency sets depend onPshort andPlong,as follows:

nH =

⌈Pshort

Pshort + Plong

M

⌉

nL = M − nH (18)

where⌈.⌉ is the ceiling function.3) Step1 and 2 are repeated for every group until either

only one band is assigned to that group or the groupcontains only one region. Note that when repeating the

7above process for a group,m in (17) andM in (18) arereplaced by the number of regions in that group and thenumber of channels assigned to that group, respectively.

Using this recursive procedure, the preferable channel listΩi(A), for all i, is computed for one observation window.

C. Complexity

Claim 1: The worst-case complexity for selecting the preferablechannel listΩi(A), for all i, may be obtained using the aboverecursive procedure inO(mK) time, whereK ≈ min[N, m].Proof: In the worst case, our proposed algorithm requiresO(m) comparisons to perform one iteration (steps1 and2). Inaddition, it requires at mostK = min[N−1, m−1] iterations toobtainΩi(A), for all i. Hence,Ωi(A), for all i, may be obtainedusing the proposed algorithm with a complexity ofO(mK),whereK ≈ (m min[N, m]). For N ≥ m, K ∼ O(m). On theother hand, forN < m, K ∼ O(N).

D. Illustrative Examples

We illustrate the previously discussed channel assignmentprocess using the following examples.

1) Example 1: Consider four PRNs and one CRN. EachPRN occupies two adjacent non-overlapping channels. ThePRNs are labeled such thatf1 < f2 < f3 < f4. Considera CR userA with SINR

(1)> SINR

(2)> SINR

(3)>

SINR(4)

. Suppose thatA divides its transmission regionRc

into 8 rings, D1, D2, . . . , D8. At a given timet, assume thatthe weighted average pmfpi(t) : i = 1, . . . , 8 is givenby 0.25, 0.1, 0.15, 0.05, 0.05, 0.15, 0.05, 0.2. Figure 7 showshow the proposed channel assignment process is conducted.The outcome of this process is as follows:

• Band4, which includes two channels, is assigned to all CRtransmissions whose distances are inD1 (i.e., Ω1(A) =4).

• Band 3, which includes two channels, is assigned to allCR transmissions whose distances are inD2 andD3 (i.e.,Ω2(A) = Ω3(A) = 3).

• Band 2, which includes two channels, is assigned to allCR transmissions whose distances are inD4, D5, andD6

(i.e., Ω4(A) = Ω5(A) = Ω6(A) = 2).• Band 1, which includes two channels, is assigned to all

CR transmissions whose distances are inD7 andD8 (i.e.,Ω7(A) = Ω8(A) = 1).

D i 1 0.25 2 0.1 3 0.15 4 0.05 5 0.05 6 0.15 7 0.05 8 0.2

0.5

0.5 0.25 f4, f3

f4

f3 0.25

f2, f1 0.25

0.25

f2

f1

i p ~

Fig. 7. Example that illustrates the channel assignment process in a dynamicCRN.

2) Example 2:Consider8 PRNs and one CRN. The PRNsare labeled such thatf1 < f2 < . . . < f8. Suppose thatAdivides its transmission region into2 rings. At a given timet, assume that the weighted average pmfpi(t) : i = 1, 2is given by0.25, 0.75. Then, the outcome of our preferablechannel assignment is as follows:

• Channels1 and2 (total of 2 channels are assigned to allCR transmissions whose distances are inD1).

• Channels3, . . . , 8 (total of 6 channels are assigned to allCR transmissions whose distances are inD2).

The above example reveals that our algorithm assigns morepreferable channels (total of6 channels) to the more frequentlyused transmission distances (D2, p2(t) = 0.75).

VI. DDMAC PROTOCOL

Based on the channel assignment process presented in Sec-tion V, we now propose a distributed, asynchronous MACprotocol for CRNs. The proposed DDMAC is a CSMA/CA-based scheme that uses contention-based handshaking for ex-changing control information. It is worth mentioning that themost common configuration for upcoming CRNs is to useCSMA/CA-like MAC access [6], [19], [20], [23], [25], [26],[31]. Thus, in designing the channel access in DDMAC, wefocus on extending the CSMA/CA scheme due to its maturityand wide deployment in many wireless packet networks. Notethat the handshaking procedure is essential in multi-channelsystems. Besides mitigating the hidden-terminal problems, thereare two other main objectives for the use of RTS/CTS: (1)conducting and announcing the channel assignment, and (2)prompting both the transmitter and the receiver to tune to theagreed on channels before transmission commences. Beforedescribing our protocol in detail, we first state our mainassumptions.

A. Assumptions

In designing DDMAC, we make the following assumptions:• For each frequency channel, the channel gain is stationary

for the duration of three control packets and one data andACK packet transmission periods. As explained in [32],this assumption holds for typical mobility patterns andtransmission rates.

• Channel gains between two CR users are symmetric. Thisis a typical assumption in any RTS/CTS-based protocol,including the IEEE 802.11 scheme.

• CR transmissions use the maximum allowable powervector (Pmask). The key idea behind this choice is asfollows. It is well-known that using as many channels aspossible for a transmission reduces the CR-to-PR inter-ference [6] due to the reduction in transmission power.However, because DDMAC enforces an exclusive channeloccupancy, which prevents two neighboring CR users fromusing common channels3, such a channel assignment pol-icy may lead to channel over-assignment, which reducesthe opportunity for finding available channels by otherneighboring CR transmitters (thus reducing the CRN’sthroughput). Therefore, in DDMAC, we tackled the CR-to-PR interference problem by assuming a given power maskto protect PR users while trying to use the least possiblenumber of selected channels per transmission. This can be

3The exclusive channel occupancy excludesCR-to-CRinterference althoughit still allows for the typical co-channel PR-to-CR interference, thus largelysimplifying theCR-to-PRinterference management process.

8done by transmitting at the highest possible transmissionpower over each selected channel, which results in lessnumber of assigned channels per CR transmission. Thisincreases the opportunity for finding available channelsby other neighboring CR transmitters.

• The total rate demand of a CR userA (denoted byCA)is met by aggregating the transmission rates of severalselected channels. Note thatCA can vary from one packetto another.

• A prespecified control channel with Fourier bandwidthBc

is available, whereBc ≪ B. This channel does not needto be reserved for the CRN. It can, for example, be oneof the subchannels in an ISM band.

• Contending CR users follow similar interframe spacingsand collision avoidance strategies of the 802.11 protocol(over the control channel) by using physical-carrier sens-ing and backoff before initiating control packet exchanges.We also assume that data packet sizes are significantlylarger than control packets, and therefore, the use of theRTS/CTS handshake is justified.

B. Channel Access in DDMAC

The channel access mechanism allows the CR transmitterand receiver to agree on the set of channels to use forcommunication and to allocate their rates. Rate is allocatedin a manner that ensures that the power mask and the ratedemands are met. A CR userA views its transmission regionasK non-overlapping regions, where each region is associatedwith a preferable channel listΩi(A), i = 1, . . . , K, determinedaccording to Section V. This user maintains anN -entry channellist and anm-entry transmission distance table (as describedin Section V). Thejth entry of the channel list indicatesthe status of thejth channel;1 if the channel is availableand 0 if the channel is occupied or reserved by any ofA’sCR neighbors. Recall that each CR user is equipped withnt

transceivers. One of these transceivers is tuned to the controlchannel, while the othernt−1 transceivers can be tuned to anydata channels. As a result, CR users can always hear controlmessages over the common control channel even when theyare transmitting/receiving data over other data channels.Thus,every CR user listens to the control channel, and accordinglyupdates its channel list and transmission distance table.

Suppose that CR userA has data to transmit to another CRuser B at an aggregate rate demandCA. Then, A reacts asfollows:

• If userA does not sense a carrier over the control channelfor a random duration of time, it sends an RTS messageat the maximum (known) powerPmax. This Pmax is con-strained by the power mask imposed on the prespecifiedcontrol channel. The RTS includesCA, the packet size(in bytes), and the list of all available channels atA (seeFigure 8).

• The neighbors ofA (other thanB) that can correctlydecode the RTS refrain from accessing the control channeluntil they receive one of two possible control packets,denoted by EPCA and ENCA (explained below).

• Upon receiving the RTS packet,B estimates the distancebetweenA and B (dAB) (using one of the techniquesdescribed in Section V). It identifies the preferable channellist Ωi(B) that corresponds todAB. Based on the availablechannels atA and B, and the instantaneous interferencelevel over these channels as measured atB, user Bremoves any channel that has a received SINR less thanits threshold SINR and determines thecommon channel

Transmitter ID

Receiver ID

Rate demand

(C A )

Available channel

list

Packet size RTS

Transmitter ID

Receiver ID

Distance (d)

Assigned channel

list

TX duration

PCA/ EPCA

Transmitter ID

Receiver ID

NCA/ ENCA

Distance (d)

Fig. 8. Formats of DDMAC control packets.

list that is potentially available forA → B transmis-sion, denoted byCCL(A, B). UserB then computes theintersection betweenΩi(B) and CCL(A, B) to identifya preferable set of channels forA → B (Φ(A, B)). Toachieve good throughput,B sorts the channels inΦ(A, B)in a descending order of their maximum possible data rate(calculated according to Shannon’s formula4). Then, userB appends the rest of the common available channels thatare not inΦ(A, B)

(i.e., CCL(A, B)

⋂Φ(A, B)

), also

listed in a descending order of their maximum possibledata rate, to the bottom of the sorted preferable channels.User B cumulatively adds channels from the top of thenew sorted list until either the aggregate rateCA issatisfied or the list is exhausted, i.e., no feasible channelassignment is found.

• If there is no feasible channel assignment, thenB respondsby sending a Negative-Channel-Assignment (NCA) mes-sage that includes the distancedAB (see Figure 8). Thepurpose of this packet is to helpB’s neighbors estimatethe network distance-traffic pattern and promptA to backoff and retransmit later. IfB can find a set of availablechannels that can support a total demandCA, it sends aPositive-Channel-Assignment (PCA) message toA, whichcontains the assigned channels for the transmissionA →B, the distancedAB , and the duration needed to hold theassigned channels for the ensuing data transmission andcorresponding ACK packet. The PCA packet implicitlyinstructsB’s CR neighbors to mark the set of assignedchannels as unavailable for the indicated transmissionduration. It also helps these neighbors estimate the networkdistance-traffic pattern.

• Depending on which control message is received, userAreacts as follows:

– If A receives an NCA message, it responds by sendingan Echo-NCA (ENCA) message, which includes thedistancedAB . The purpose of this packet is to helpA’s neighbors estimate the network distance-trafficpattern.

– If A receives a PCA message, it replies back with anEcho-PCA (EPCA) message, informing its neighborsof the selected channel list, the distancedAB, and thetransmission duration. This EPCA also announces thesuccess of the control packet exchange betweenA andB to A’s neighbors, which may not have heardB’sPCA.

• Once the RTS-PCA-EPCA exchange is completed, thedata transmissionA → B proceeds. Once completed,B

4Other rate-vs-SINR relationships, such as a staircase function, can be usedfor calculating the achievable data rates.

9sends back an ACK packet toA over the best assignedchannel, i.e., the channel that has the highest rate. A timediagram of the RTS-PCA-EPCA-DATA-ACK exchange isdepicted in Figure 9.

R T S

P C A

E P C A

A B A R T S

P C A

E P C A

C D C

DATA C->D

ACK

ACK

DATA A->B

.

.

.

………..

Data TX 1

Data TX 2

Fig. 9. RTS-PCA-EPCA-DATA-ACK packet exchange.

It is worth mentioning that there is no interference betweendata and control packet transmissions because the two areseparated in frequency. Therefore, a CR user that hears the RTSpacket fromA defers its attempt to access the control channeluntil it receives an EPCA or an ENCA packet fromA. Inaddition, a CR user that receives only a PCA or an NCA shoulddefer its attempt to access the control channel for the expectedtime of the EPCA/ENCA packet (to avoid a collision betweencontrol packets). This allows for more parallel transmissions totake place in the same neighborhood (see Figure 9).

Remark: DDMAC’s channel assignment is performed on aper-packet basis, with the channels assigned to different inter-faces dynamically changing. This type of channel assignmentrequires channel switching to occur at a very small time scale,which is in the range of micro-seconds5.

C. Spatial Reuse and DDMAC

We consider a CSMA/CA-based multi-hop CRN environ-ment, which consists of multiple contention regions (neighbor-hoods) that permit spatial reuse. Specifically, non-neighboringCR users may access the same channel on different contentiondomains. To illustrate the idea of spatial reuse, Figure 10depicts two scenarios for the operation of DDMAC. In thefirst scenario (Figure 10(a)), the two transmittersA and Ccannot hear each other’s control packets. So, according toCSMA/CA, the transmissionsA → B and C → D canoverlap in their data channels, i.e., the assigned channelsforA → B transmission are reserved only within the area ofA’sand B’s control range (spatial reuse case). In Figure 10(b),nodeC falls in the control region of nodeA (and vice versa).The exclusive channel occupancy policy preventsA and Cfrom using common channels. However, the two transmissionscan proceed simultaneously ifA and C can find two non-intersecting sets of channels to support their rates.

D. Worst-Case Scenarios for DDMAC

We illustrate two extreme scenarios under which theDDMAC protocol gracefully degrades into the BMC scheme.Recall that a CR receiverA divides its transmission range intom regions.

5Current radio technology allows channel switching to be done in a fewmicroseconds (i.e.,< 10 µs [23], [33])

A B

C D

*

*

*

* *

*

*

*

*

* *

(a) Allowed channel reuse

A B

C

D +

* *

CR user

* Users in PRN 1

*

*

*

*

*

*

* *

Users in PRN 2

(b) Unallowed channel reuse

Fig. 10. Scenarios in which a CR transmitterC can/cannot reuse the channelsassigned toA. Solid circles indicate data-transmission ranges, whereas dashedcircles indicate control-transmission ranges.

• Scenario I: At a given timet, assume that the weightedaverage pmfpi(t) : i = 1, . . . , m has a value of1at i = m and 0 otherwise (i.e., most likely, transmissiondistances are withinDm). This scenario represents the casewhen all ofA’s neighbors are located near the border ofA’s transmission range (Figure 11(a)). According to thechannel assignment algorithm, the preferable channel listis identified as follows:

Ωi(A) = φ : i = 1, . . . , m − 1.

Ωi(A) = N : i = m.

Recall thatN denotes the set of available channels. Inother words, no channels will be assigned to ring,i, i =1, 2, . . . , m − 1, and all channels will be assigned to themth ring.

A d m-1

d 1 r c

(a) Scenario I

A

d m-1

d 1 r c

(b) Scenario II

Fig. 11. Illustration of two worst-case scenarios in DDMAC.

• Scenario II: At a given timet, assume that the weightedaverage pmfpi(t) : i = 1, . . . , m has a value of1 at i =1 and0 otherwise (i.e., most likely, transmission distancesare within D1). This scenario represents the case whereall A’s neighbors are located close toA (Figure 11(b)).According to the proposed channel assignment algorithm,the preferable channel list is identified as follows:

Ωi(A) = N : i = 1.

Ωi(A) = φ : i = 2, . . . , m.

10According to DDMAC, the sorted channel list from which a

CR user assigns channels to its transmission is constructedbyappending the common sorted available channels that are notin the sorted preferable channels to the bottom of the sortedpreferable channels list. Thus, for the above two scenariosand depending on the transmitter-receiver distance, the sortedchannel list of DDMAC is as follows:

• If the distance falls in the range(dm−1, dm = rc] or(0, d1], the preferable channel list is the set of all availablechannels. Therefore, the sorted channel list of DDMACis the same as that of the BMC scheme. Consequently,DDMAC gracefully degrades into the BMC scheme.

• If the distance falls within the transmission rangeRc butnot in the range(dm−1, dm] or (0, d1], the preferablechannel list is empty whereas the available channel listcontains all the available common channels. Therefore, thesorted channel list of DDMAC is the same as that of BMC.Consequently, DDMAC gracefully degrades into the BMCscheme.

Protocol Overhead

Claim 2: DDMAC and BMC have comparable overheads.Proof: Both DDMAC and BMC use a three-way handshake tosend one data packet. Thus, DDMAC does not introduce anyadditional control message overhead.

VII. PROTOCOL EVALUATION

We now evaluate the performance of the DDMAC viasimulations and compare it with CSMA/CA variants. Ourresults are based on simulation experiments conducted usingCSIM (a C-based, process-oriented, discrete-event simulationpackage [34]). Each CR user generates packets according toa Poisson process with rateλ (in packet/time slot), which isthe same for all users. For simplicity, data packets are assumedto be of a fixed size (2 Kbytes). Each CR user requires anaggregate transmission rate of5 Mbps. We divide time intoslots, each of length3.3 ms. A time slot corresponds to thetransmission of one CR packet at a rate of5 Mbps. We setthe CRN SINR threshold to5 dB and the thermal noise toP

(i)th = 10−21 Watt/Hz for all channels. Because DDMAC

and the compared with CSMA/CA-based protocols have thesame maximum transmission ranges and use the same channelaccess mechanism, it is reasonable to assume that all protocolsachieve the same forward progress per hop. Consequently,our performance metrics are: (1) one-hop throughput, i.e.,thedestination of a packet is restricted to one hop from the source,(2) connection blocking rate, and (3) the fairness index [35].The connection blocking rate is defined as the percentage of CRpacket requests that are blocked due to the unavailability of afeasible channel assignment. We use Jain’s fairness index [35]to quantify the throughput fairness of a scheme6. Fairnessindex values closer to1 indicate better fairness. The signalpropagation model in (4) is used withn = 4, the antennalength (D) is 5 cm, andGt(f) = Gr(f) = 1 for every carrierfrequencyf .

6For our simulation setup, CR user demands are uniform. The destination CRuser is uniformly selected from the one-hop neighbors and the packet generationrate are the same for all CR users. Thus Jain’s fairness indexprovides ameaningful metric for comparing the fairness of DDMAC and BMC.

A. Single-hop Scenarios

1) Simulation Setup:We first simulate a small-scale networkfor the purpose of highlighting the advantages and operationaldetails of DDMAC. DDMAC is compared with three multi-channel CSMA-based protocols that use different channel se-lection schemes: an optimal scheme (which uses exhaustivesearch), the BMC scheme [3] (which is based on agreedystrategy that selects the best available channels for a giventransmission), and a naive scheme (which always tries to selecthigh-frequency channels if available for a given transmission,while leaving low-frequency channels for other users). Specifi-cally, we consider a single-hop CRN, where all users can heareach other. This CRN coexists with two PRNs in a100 meter× 100 meter field. The PRNs operate in the600 MHz and2.4 GHz bands. Each PRN band consists of one channel ofbandwidth1.5-MHz. The number of PR users in each PRN is50. Each user in theith PRN acts as an ON/OFF source, whereit is ON while transmitting and OFF otherwise. We define the“activity factor” αi as the fraction of time in which theithtype PR user is ON (i.e., the probability that the source isin the ON state). The source is further characterized by thedistribution of its ON and OFF periods, which are both takento be exponential. We set the average ON period to be theduration of one time slot. In other words, traffic correlations arecaptured using a two-state Markov model. The appropriatenessof the 2-state ON/OFF model has been demonstrated in severalprevious works, e.g., [6], [13], [20], [36], [37]. In essence, theON/OFF behavior is attributed to the bursty nature of manytypes of network traffic, including voice traffic and VBR videostreaming. Note that one potential PRN is a cellular networkthat transports voice traffic. We set theαi probabilities for thetwo PRNs to0.5 and0.3, respectively. The transmission powerfor each PR user is0.5 Watt.

For the CRN, we consider40 mobile users. The randomwaypoint model is used for mobility, with the speed of a CRuser uniformly distributed between0 and 2 meters/sec. Thisresults in dynamic, time-varying topologies. We assume that aCR user can use up to two data channels simultaneously. Weset the interference mask toP (1)

mask = P(2)mask = 50 mW. We

also set the forgetting factorα to 0.6, the observation windowTwin = 0.5 second, and the number of rings around a CR userm = 12. For a fair comparison, we let all schemes use themaximum allowable power vectorPmask.

2) Results: Under the above setup, Figure 12 shows thatDDMAC improves the one-hop throughput by up to25%(compared to BMC) and34% (compared to the naive ap-proach). More importantly, its throughput is within7% ofthe optimal throughput, obtained via exhaustive search. Notethat the exhaustive search implies that the instantaneous SINRvalues, location information, and rate demands are known tothe decision-making entity that assigns channels to CR users(i.e., such search requires global information). Even if perfectknowledge of the SINR of each link and the rate demands areavailable, for large-scale networks, finding the optimal solutionrequires exhaustive search over a large state space, which growsexponentially with the number of CR users and the availablechannels.

B. Multi-hop Scenarios

1) Simulation Setup:We now evaluate the performance ofDDMAC in more realistic (large-scale) network scenarios andcontrast it with a typical multi-channel CSMA-based protocolthat uses BMC for channel selection [3]. We consider four

11

0 10 20 30 400

0.25

0.5

0.75

1

1.25

1.5

λ (Packet/sec)

Th

rou

gh

pu

t (P

acke

t/tim

e s

lot)

OptimalDDMACBMCNaive approach

Fig. 12. Throughput vs.λ for a small-scale network (comparison with theoptimal scheme).

PRNs and one CRN. Users in each PRN are uniformly dis-tributed over a500 meter× 500 meter area. The PRNs operatein the 600 MHz, 900 MHz, 2.4 GHz, and5.7 GHz bands,respectively. Each PRN band consists of three non-overlapping1-MHz channels. The number of PR users in each PRN is300.The αi probabilities for the four PRNs are0.5, 0.3, 0.3, 0.1,respectively. The transmission power for each PR user is0.5Watt.

For the CRN, we consider arandom-gridtopology7, where225 mobile CR users are placed within the500 meter× 500meter field. The field is split into225 smaller squares, one foreach CR user. The location of a mobile user within the smallsquare is selected randomly. For each generated packet, thedestination is selected randomly from the one-hop neighbors.Within each small square, the random waypoint model is usedfor CR mobility, with the speed of a CR user uniformlydistributed between0 and2 meters/sec. We assume that a CRuser can use up to three data channels simultaneously. We setthe interference mask toP (1)

mask = P(2)mask = . . . = P

(12)mask = 50

mW. The reported results are the average of100 experiments. Inour design, we assume an exclusive channel occupancy policyon CR transmissions (i.e., no CR-CR interference). However,hidden-terminal problem can still occur in this scenario due toimperfect control. Our simulations relax these assumptions andaccount for all sources of interference, including those that arefar away from a receiver and use common channels.

Remark: Our simulations only address the MAC layeraspects and assume that route computations have already beencarried out. Taking the destination from a node’s one-hopneighbors is intended only to convey the need for channelaccess. A “destination” in this context could be the next hopwhere a packet is to be forwarded to or the final packetdestination. Randomly selecting a neighbor as a destinationis realistic in terms of packet forwarding, especially whenmultiple flows (like file transfers, messaging, or VoIP) passthrough a node.

2) Results:We first compare the performance of DDMACto that of the BMC scheme. For a fair comparison, we let bothschemes use the maximum allowable power vectorPmask.We setα to 0.6, Twin to 0.5 second, andm to 12. Figures13(a) and (b) show that under moderate and high traffic loads,DDMAC significantly reduces the connection blocking rate andimproves the overall one-hop throughput by up to30%. This

7Random-grid is a realistic topology that models constrained scenarios. Forexample, a building could have various offices, where each office may containseveral wireless devices.

0 0.1 0.2 0.3 0.4 0.5

0.3

0.35

0.4

0.45

Packet genaration rate

Blo

ckin

g r

ate

(%

)

BMCDDMAC

(a) Blocking rate vs.λ.

0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

25

30

35

40

Packet generation rate (Packet/sec)S

ing

le h

op

th

rou

gp

ut (P

acke

t/tim

e s

lot)

BMCDDMACBMC−Raleigh DDMAC−Raleigh

(b) Throughput vs.λ (with and without aRaleigh fading component).

Fig. 13. Performance of a CRN.

improvement is attributed to the increase in the number ofsimultaneous transmissions in DDMAC. Note that under lowtraffic load, the throughput of DDMAC gracefully degrades tothat of BMC due to the availability of a sufficient numberof channels. The system performance under Raleigh channelmodel (i.e., varying channel conditions) is also investigatedin Figure 13(b). We consider normalized random variables tocapture the fading processes [8]. The results show that, undersuch varying channel conditions, the same trends that werenoticed for the AWGN channel are observed here. Figure 13(b)shows that the impact on throughput is almost the same underAWGN and Raleigh channel models. Similar observations havealso been reported in an experimental study in [38] for IEEE802.11b wireless LAN. In [38], the authors showed that theimpact on throughput and packet error rate were virtuallyidentical under AWGN and Raleigh channel models.

In Figure 14(a), we focus on the per-user throughput per-formance under DDMAC8. As shown in this figure, althoughDDMAC requires a pair of CR users to communicate over aset of channels that may not be optimal from one user’s per-spective, theper-userthroughput of DDMAC under moderateand high traffic loads is still greater than that of the BMCscheme. This is because DDMAC attempts to serve a given CRtransmission first using the preferable channel list and preserves

8This figure shows the average worst-case throughput performance amongall CR users.

12

0 0.1 0.2 0.3 0.4 0.50

0.02

0.04

0.06

0.08

0.1

0.12

Packet generation rate

Sin

gle

−h

op

th

rou

gh

pu

t (p

acke

t/ t

ime

slo

t)

BMCDDMAC

(a) Per-user single-hop throughput.

0 0.1 0.2 0.3 0.4 0.50.5

0.6

0.7

0.8

0.9

1

Packet generation rate

Fa

irn

ess In

de

x

BMCDDMAC

(b) Fairness index vs.λ.

Fig. 14. Per-user throughput and fairness Performance.

the “better” channels for other transmissions. However, iftheaggregate rate of this transmission cannot be satisfied usingthe preferable list, DDMAC attempts to serve this transmissionusing the remaining available channels.

Next, we compare the fairness index of DDMAC to that ofBMC. Compared to BMC, Figure 14(b) shows that DDMACslightly improves the network fairness and preserves long-term fairness properties. This improvement occurs becauseDDMAC motivates cooperation among neighbors to maximizetheir network-wide benefit.

The effect of dividing the transmission range of a CR useris depicted in Figure 15(a) for different values ofλ. As mincreases, the throughput increases up to a certain point. Form ≥ 12, no significant improvement is observed in the networkthroughput. This is because the preferable-channel assignmentmechanism merges them regions intoK ≤ m regions, i.e.,over-splittingRc is not useful.

In Figure 15(b), we study the impact ofα andTwin on theperformance of DDMAC. We setλ = 0.3 packet/slot. Thenetwork throughput versusα for different values ofTwin isshown in the figure. It is clear that the throughput depends onthe choice ofα andTwin. As Twin increases,α should increaseto give much more importance to recent observations withoutentirely discarding older observations. Table II shows thebestthroughput performance and the associated optimal value ofα(α∗), obtained from simulation, for different values ofTwin. Itis clear that ifTwin is too small or too large, the throughputreduces significantly.

5 10 1520

25

30

35

40

m

Sin

gle

−h

op

th

rou

hp

ut (P

acke

t/tim

e s

lot) λ = 0.2

λ = 0.25λ = 0.3

(a) Throughput vs. number of rings (m)around a CR user.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 122

24

26

28

30

32

34

36

38

Forgitting factor α

Sin

gle

−h

op

th

rou

pu

t (P

acke

t/tim

e s

lot)

λ = 0.3

Twin

= 0.03 s

Twin

= 0.3 s

Twin

= 1 s

Twin

= 4 s

(b) Throughput vs.α for different Twin

values.

Fig. 15. Performance of DDMAC.

Scheme α∗ Best throughput (packet/slot)

BMC - 25DDMAC(Twin = 0.03 s) 0.1 26DDMAC(Twin = 0.3 s) 0.6 33.6DDMAC(Twin = 0.4 s) 0.6 33.85DDMAC(Twin = 1 s) 0.8 33.89DDMAC(Twin = 4 s) 1.0 28

TABLE II

PERFORMANCE OFDDMAC AT THE OPTIMAL α AS A FUNCTION OFTwin .

We also investigate the robustness of DDMAC under inac-curate distance estimation, which is mainly caused by mobility,multi-path propagation, reflection, and fading effects. The es-timated distanced is given by(1 + ξ) d, whereξ is a uniformestimation error (ξ ∼ Uniform[−ǫ, ǫ]). Figure 16(a) shows theeffect of inaccurate distance estimation on throughput as afunction ofǫ under different traffic loads. It can be observed thatthere are no significant changes in the throughput for differentvalues of ǫ. Figure 16(b) gives the percentage reduction inthroughput due to inaccurated as a function ofλ for differentvalues ofǫ. This figure shows that the maximum percentageof reduction in throughput due to inaccurate estimation ofd isless than6%.

The results in Figure 16 indicate that channel assignment

13in DDMAC is quite robust to distance estimation errors. Thisis because DDMAC requires only rough estimates of userdistribution, distances among users, and local traffic conditionsin order to dynamically adapt channel assignments to currentnetwork traffic.

0.05 0.1 0.15 0.2 0.250

5

10

15

20

25

30

35

40

ε

Sin

gle

−h

op

th

rou

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pu

t (P

acke

t/tim

e s

lot)

Low load

Moderate load

High load

(a) Throughput vs.ǫ.

0 0.1 0.2 0.3 0.4 0.50

1

2

3

4

5

6

Packet generation rate

Pe

rce

nta

ge

of re

du

ctio

n in

th

rou

gh

pu

t

ε = 5%

ε = 15%

ε = 25%

(b) Percentage of reduction in throughputvs. λ.

Fig. 16. Impact of inaccurate distance estimation in DDMAC.

Finally, we study the end-to-end throughput for both BMCand DDMAC. Specifically, for each generated packet, the desti-nation node is randomly selected to be any node in the network.We use a min-hop routing policy, but we ignore the routingoverhead. For both schemes, the next-hop candidates are nodesthat are within the transmission range of the transmitter. Figure17 shows that under moderate and high traffic loads, DDMACsignificantly improves the overall network throughput (inlinewith the results in Figure 13(b)).

VIII. C ONCLUSIONS

In this paper, we proposed an opportunistic distance-dependent MAC protocol for CRNs (DDMAC). DDMACimproves the CRN throughput through cooperative channelassignment, taking into consideration the non-adjacency offrequency channels and the imposed power masks. We pre-sented a heuristic stochastic channel assignment scheme thatdynamically exploits the dependence between the signal at-tenuation model and the transmission distance. Our schemeaccounts for traffic dynamics. It assigns channels with loweraverage SINR to shorter transmission distances to increasethe number of simultaneous transmissions. We integrated the

0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

10

Packet generation rate

En

d−

2−

en

d T

hro

ug

hp

ut

(Pa

cke

t/tim

e s

lot)

BMCDDMAC

Fig. 17. End-to-end throughput vs.λ

channel assignment process in the design of DDMAC. Wecompared the performance of DDMAC with that of a referencemulti-channel MAC protocol that is designed for typical multi-channel systems (BMC). We showed that, under moderate andhigh traffic loads, DDMAC achieves about30% increase inthroughput over the BMC scheme, with manageable processingoverhead. Although DDMAC requires a pair of CR users tocommunicate on a channel that may not be optimal froma user’s perspective, we showed that the average per-userthroughput of DDMAC under moderate and high traffic loadsis greater than that of the BMC scheme. Furthermore, DDMACpreserves (even slightly improves) throughput fairness relativeto BMC. In summary, DDMAC provides better spectrum uti-lization by reducing the connection blocking probability andincreasing the system throughput. To the best of our knowledge,DDMAC is the first CRN MAC protocol that utilizes theradio propagation characteristics to improve the overall networkthroughput.

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Haythem A. Bany Salameh received the Ph.D.degree in electrical and computer engineering fromthe University of Arizona, Tucson, in 2009. He is cur-rently an Assistant Professor of electrical engineeringwith the Hijawi Faculty for Engineering Technology,Yarmouk University (YU), Irbid, Jordan. He joinedYU in August 2009, after a brief postdoctoral positionwith the University of Arizona. His current researchinterests are in system architecture and communica-tion protocol designs for cognitive radio networkswith emphasis on spectrum access and channel/power

assignment. In Summer 2008, he was a member of the R&D LTE (Long TermEvolution) Development Group, QUALCOMM, Inc., San Diego. He serves asa reviewer for many IEEE conferences and journals.

Marwan Krunz is a professor of electrical andcomputer engineering at the University of Arizona.He directs the wireless and networking group and isalso the UA site director for Connection One, a jointNSF/state/industry IUCRC cooperative center thatfocuses on RF and wireless communication systemsand networks. Dr. Krunz received his Ph.D. degree inelectrical engineering from Michigan State Universityin 1995. He joined the University of Arizona inJanuary 1997, after a brief postdoctoral stint at theUniversity of Maryland, College Park. He previously

held visiting research positions at INRIA, HP Labs, University of Paris VI,and US West (now Qwest) Advanced Technologies. His researchinterestslie in the fields of computer networking and wireless communications. Hiscurrent research is focused on cognitive radios and SDRs; distributed radioresource management in wireless networks; channel access and protocol design;MIMO and smart-antenna systems; UWB-based personal area networks; energymanagement and clustering in sensor networks; media streaming; QoS routing;and fault monitoring/detection in optical networks. He haspublished more than150 journal articles and refereed conference papers, and isa co-inventor onthree US patents. M. Krunz is a recipient of the National Science FoundationCAREER Award (1998). He currently serves on the editorial boards for theIEEE Transactions on Mobile Computing and the Computer CommunicationsJournal. He previously served on the editorial board for theIEEE/ACMTransactions on Networking (2001-2008). He was a guest co-editor for specialissues in IEEE Micro and IEEE Communications magazines. He served asa technical program chair for various international conferences, includingthe IEEE WoWMoM 2006, the IEEE SECON 2005, the IEEE INFOCOM2004, and the 9th Hot Interconnects Symposium (2001). He hasserved andcontinues to serve on the executive and technical program committees of manyinternational conferences and on the panels of several NSF directorates. He gavekeynotes and tutorials, and participated in various panelsat premier wirelessnetworking conferences. He is a consultant for a number of companies in thetelecommunications sector.

Ossama Younis is a senior research scientist inApplied Research at Telcordia Technologies, Inc. Hereceived his B.S. and M.S. degrees in computerscience from Alexandria University, Egypt. Then, hereceived his Ph.D. degree in computer science fromPurdue University, USA in August 2005. He hasserved as the web chair of IEEE ICNP 2008 and onthe Technical Program Committee of several inter-national conferences. His research interests are in thearchitecture and experimentation of network protocolsand applications, especially wireless sensor networks,

cognitive-radio networks, and Internet tomography. distributed systems, secureprotocol design, and cross-layer optimization. He is a member of the ACM andthe IEEE.