1

Optimal Resource Allocation in Random AccessCooperative Cognitive Radio Networks

Mani Bharathi Pandian, Mihail L. Sichitiu, Huaiyu Dai

Abstract—Cooperative Cognitive Radio Networks (CCRNs) incorporates cooperative communication into cognitive radio networks,in which, primary users lease their spectrum to secondary users, and in exchange, the primary users leverage secondary users ascooperative relays to enhance their own throughput. Mobile operators offload their Internet traffic to privately owned WiFi access points(APs), much to the inconvenience of non-cellular users served by the APs. However, by employing the CCRN scheme, the mobileoperator can lease a licensed channel to the AP, effectively doubling its capacity. In this paper, we propose an implementation of theCCRN framework applied to IEEE 802.11 WLANs. The cooperation is cast as a two-player bargaining game where the two playersare the primary users (users of the mobile operator) and the secondary users (users of the AP before spectrum leasing) who bargainfor either throughput share or channel access time share. The optimal resource allocation that ensures efficiency as well as fairnessamong users is provided by the Nash solution. Simulation results show that the users achieve higher throughput via the proposedCCRN scheme, thus providing the mobile operator (e.g., AT&T) and the private WiFi provider (e.g., a Starbucks coffee shop) withincentives for cooperation.

Index Terms—Cooperative Cognitive Radio Networks, WLAN Optimization, WiFi, spectrum leasing, Game theory.

F

1 INTRODUCTION

MObile data offload to small cell technology such asWiFi or femtocell provides a compelling solution

for mobile operators who want to relieve the strain ontheir core networks. Compared to cellular macrocells,small cells provide increased spectrum reuse in the cov-erage area, higher signal to noise ratio in the cell (hencesuperior link bit rate for its users), and are highly costeffective even for large scale deployments. Furthermore,the reduced transmission times enabled by the superiorlink bit rates in the small cells directly translate intobattery power saving for the user devices. WiFi hotspotsoperate in the unlicensed bands and suffer from severeinterference due to scarce spectrum availability. On theother hand, macrocells and femtocells require the use ofthe same costly and scarce licensed spectrum and sufferfrom co-site interference problems.

To unlock new spectrum for small cell technology, anew regulatory spectrum sharing framework [1] is beingproposed by the Federal Communications Commission(FCC), where non-mobile incumbent owners, such asmilitary who do not use their spectrum at all timesand locations are allowed to grant exclusive access oftheir spectrum to mobile operators in regions wherethere is no incumbent activity. Recently, FCC and theUS Federal government have identified the 3550-3650MHz band [2] (3.5 GHz Band), currently utilized formilitary and satellite operations localized to the U.S.coastline, as an ideal spectrum band for shared use with

• Mani Bharathi Pandian, Mihail L. Sichitiu, Huaiyu Dai are withthe Department of Electrical and Computer Engineering, North Car-olina State University, Raleigh, NC, USA. E-mails: {mpandia, mlsichit,hdai}@ncsu.edu.

mobile operators for small cell operations. The EuropeanCommission is working on a similar proposal in the 2.3-2.4 GHz band that has very localized incumbent militarytelemetry use. Such a spectrum sharing approach regimecan potentially unlock more than 100 MHz of high-quality spectrum, specially in higher spectrum bands (>2 GHz) that are ideal for small cells.

To expedite spectrum sharing in small cells, FCC inits recent ruling [3] has eliminated spectrum sensingas a requisite for cognitive radio devices. Instead, FCCmandates that devices learn of spectrum availability attheir respective locations from an external source such asa location-based query to the database of the incumbent,for example the Google Spectrum Database [4]. Deviceswith such “cognitive” or “frequency-agile” transceiversare regarded as the main enabler of spectrum sharingin small cell technology. Although, spectrum leasingsimplifies commercial deployment and promotes bet-ter spectrum utilization, developing a workable pricingmodel between the primary network (owner of thespectrum) and the secondary network (beneficiary ofthe leased spectrum) is not trivial. To expedite spectrumleasing in real-world deployments, researchers have re-cently advocated for schemes that employ spectrumleasing, not necessarily on the basis of fees or charge, butin return for improved quality-of-service of the primarynetwork via cooperation with secondary network. Onesuch proposal is the new cognitive radio paradigm in [5]termed Cooperative Cognitive Radio Networks (CCRNs). InCCRNs, the primary users select a set of secondary users(which have better channel conditions) to relay the pri-mary traffic cooperatively, and in return the secondaryusers are granted channel access opportunities in thelicensed (leased) spectrum. CCRNs exploit cooperative

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diversity in cognitive radio networks by combining coop-erative communication [6], a physical layer technology, andthe spectrum leasing feature enabled by cognitive radios.

Consider the scenario in Fig. 1-(a) where the primaryusers initially connect to their cellular base station (BS)using cellular technology such as LTE in the licensedspectrum, while the secondary users connect to theIEEE 802.11 WiFi AP and use the standard 802.11 DCFprotocol for channel access in the unlicensed bands. Theprimary users along with the BS form the primary net-work, while the secondary users along with the AP formthe secondary network. If all primary users offload theirtraffic to the WiFi AP, although they might connect to theAP at superior link bit rate, the corresponding increasein contention can significantly degrade throughput of allthe users (both primary and secondary). Instead, assumethat spectrum leasing is enabled via the CCRN schemefor the network in Fig. 1. The primary network (i.e.,the mobile operator) leases an additional channel fromthe licensed spectrum to the secondary AP. In exchange,the secondary AP adds the extra channel to its auxiliaryinterface and reassigns both the primary and secondaryusers in the two resulting WLAN cells - the original cellthat continues to operate in the unlicensed channel andthe new cell operating in the newly leased channel asshown in Fig. 1-(b). With the capacity of the AP noweffectively doubled, both primary and secondary userscan expect significant improvements in their achievablethroughput, as well as power savings (owing to reducedtransmission time). Hence the CCRN scheme offers awin-win scenario for both the cellular network opera-tor (e.g., AT&T) as well as the WLAN owner (e.g., aStarbucks coffee shop).

INTERNET

SU

PU

SU

Licensed Spectrum (LTE)

Unlicensed

Spectrum

(WLAN)

BS AP

PU

(a)

INTERNET

SU

PU

PU

SU

Leased

Spectrum (WLAN-1)

Unlicensed

Spectrum

(WLAN-2)

BS AP

(b)

Fig. 1: Network diagram showing the base station (BS) ofthe primary network, the access point (AP) of the secondarynetwork, and the primary and secondary users (PUs and SUs)in the range of the AP (a) before, and (b) after spectrum sharingunder CCRN scheme.

Much of the existing CCRN schemes in the lit-erature assume that the users access the spectrumusing TDMA [5], [7], [8], frequency division multi-ple access (FDMA) [9], space division multiple access(SDMA) [10], orthogonal frequency division multipleaccess (OFDMA) [11], or using other special orthogonalschemes [12]. A random access scheme is presentedin [13], where secondary users access the spectrum us-

ing slotted Aloha. In contrast, WLANs have adopteda contention-based medium access control such as theIEEE 802.11 Distributed Coordination Function (DCF).To leverage cooperative transmission and spectrum leas-ing in WLANs, such as the scenario in Fig. 1-(b), existingCCRN schemes are no longer applicable.

In our work, we propose an implementation of theCCRN framework for primary network that supportsany current cellular standard, such as LTE, and anIEEE 802.11 multi-rate WLAN based secondary network.When served by the secondary AP, all users (either pri-mary and secondary) employ an IEEE 802.11 DCF basedchannel contention mechanism. As shown in Fig. 1,both the AP and the BS are connected to the Internetover wireline channel (backhaul), as is common in thepresent-day deployments. No backhaul capacity limita-tion is assumed for the wireline channel. The primarynetwork owns bandwidth in the form of “channels” ofcertain size (e.g., 20 MHz channels in the 3.5 GHz band),which it is willing to lease to the secondary network; inexchange, the AP of the secondary network offloads datatraffic for the primary (cellular) users in its range. To en-able spectrum leasing, the AP of the secondary networkis equipped with an auxiliary radio (shown in Fig. 1-(b))that can be tuned to the frequency of the leased channel(licensed spectrum). All the user equipments (primaryand secondary) are also equipped with radios that canbe tuned to the unlicensed frequency as well as theleased channel and support dual-mode (WiFi + Cellular,common in today’s smartphones). The setup in Fig. 1-(b)resembles the cooperative communication scheme in amixed wireline/wireless network [6] where the source-to-relay (Internet/BS-to-AP) is a wireline channel, andthe relay-to-destination (AP-to-users) is a wireless chan-nel. The problem formulation for the proposed CCRNscheme is discussed in Section 2.

2 SYSTEM MODEL

In the proposed CCRN scheme, the primary networkagrees to lease the channel to the AP only if the APis offering a bargain that improves the primary networkthroughput. The user devices are assumed to supportservice differentiation (readily available for 802.11 de-vices implementing 802.11e). The AP has the freedomto reassign any user in either of the two WLAN cells(Fig. 1-(b)), and to assign different service weights todifferent users. As a result, depending on the distri-bution of the users in the two cells and the serviceweight of each user, different throughputs for the usersin the primary and secondary networks are achievable.If we denote with Xp and Xs the aggregate throughputsfor the primary and secondary users respectively, wecan define the bargaining set (Xp, Xs) ∈ B. Fig. 2-(a)depicts the bargaining set B of achievable throughputsas well as the disagreement point (Xd

p , Xds ) representing

the throughputs of the two networks in the absence ofcooperation (i.e., when the cellular users communicate

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with the BS in the licensed channel, and the AP usersare all in the unlicensed channel). A bargaining point isa recommended solution for the two players given thebargaining set, the disagreement point and a bargainingsolution, which is a rule for finding the bargaining point.A thorough treatment of various bargaining solutionscan be found in [14]; however, we restrict our discussionto the well-known Nash bargaining solution [15].

N

◮

(Xdp , X

ds )

(Xbp, X

bs)

Xs

Xp

B

(a)

N

◮

(Xdp , X

ds )

(Xbp, X

bs)Xs

Xp

Bւ

(b)

Fig. 2: The bargaining set B, bargaining point (Xbp, X

bs) and

disagreement point (Xdp , X

ds ) for the CCRN problem without

(a), and with (b) fairness constraint (time or throughput)coupled with the use of the optimized contention window.

Achieving fairness and efficient use of resources(channel time or achievable throughput) are essentialin WLANs. For this reason, in the proposed CCRNscheme, we impose either a weighted time or a weightedthroughput fairness constraint in the WLAN. Whenserved by the WLAN AP, the primary and secondaryusers are assigned separate service classes, classp andclasss respectively, with wp and ws representing theweights for the service classes. Under the weighted timefairness constraint, users share their channel occupancytime in proportion to their assigned weights; whileunder weighted throughput fairness constraint, the usershare their achievable throughput in proportion to theirassigned weights. Our CCRN algorithm attempts to findthe

1) service weights (wbp, wbs) and,2) the distribution of the users in the two WLAN cells,

that will achieve the aggregate network throughputs(Xb

p, Xbs) at the Nash bargaining solution.

Our CCRN scheme requires an IEEE 802.11 DCF likecontention based channel access mechanism that willachieve the chosen fairness constraint (weighted timeor weighted throughput) in the WLAN. The proposedWLAN model for our CCRN scheme is built on therecent work in [16] that calculates an optimal fixedcontention window for each contending station in anIEEE 802.11 multi-rate WLAN to jointly achieve aggre-gate WLAN throughput maximization and time fairness(equal channel occupancy time for all stations). To fitour CCRN needs, the WLAN model in [16] is extendedin the following directions in Section 3:

1) to support weighted time or weighted throughput

fairness constraint among stations in the WLAN,and

2) to support both uplink as well as downlink traffic.Although the extended WLAN models are able to findthe optimal contention window, they however requiresolving an order n polynomial where n is the number ofstations in the WLAN. To reduce the computation com-plexity, we derive a computationally inexpensive closed-form approximation for the optimal contention windowin Section 3. Using the closed-form approximation, weshow that under a chosen fairness constraint (time orthroughput), when all stations adopt optimal contentionwindow sizes, the aggregate throughputs of the twoservice classes, Xp and Xs, evaluated for all feasibleweights, wp and ws, closely follow a straight line of theform:

cpXp + csXs = 1, (1)

where cp and cs are constants that are only a function ofthe bit rates of the links in the WLAN. The expressionsfor cp and cs are different under weighted time andweighted throughput fairness constraints. In Section 4,we take advantage of the result in (1) to show thatwhen all users in the WLAN use optimized contentionwindow under a fairness constraint (time or through-put), the bargaining set of the CCRN problem can beapproximated by a straight line (as shown in Fig. 2-(b)).The expression for the approximate linear bargaining setis only a function of bit rates of the participating users(primary and secondary users which are being servedby the AP) and hence easily calculated. Also, a closed-form expression for the network aggregate throughputs(Xb

p, Xbs ) and their service weights (wbp, wbs) at the Nash

bargaining solution exists and is a function of the dis-agreement point and the bit rates of users. Finally, amethod to find an effective user distribution in thetwo WLAN cells is proposed that will achieve aggre-gate network throughputs close to the Nash solution(Xb

p, Xbs ), while maintaining the weights wbp and wbs for

the service classes. Section 3 introduces the necessaryWLAN models, while Section 4 discusses the proposedCCRN scheme under both the time and throughputfairness constraints.

3 WLAN OPTIMIZATION

The recent work in [16] proposes a MAC algorithmfor IEEE 802.11 multi-rate WLAN that computes anoptimal contention window for every contending stationin the network to jointly achieve network throughputmaximization and time fairness among stations. The timefairness constraint requires each competing station toreceive approximately equal channel occupancy time. Webuild on the work in [16] and extend their WLANmodel to support service differentiation in terms ofweighted time and weighted throughput fairness wherethe stations share the available channel occupancy timeand achievable throughput respectively in proportion

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to their assigned weights. The proposed WLAN modeladopts a medium access mechanism very closely relatedto 802.11 DCF access mechanism, but which, instead ofthe binary exponentially backoff mechanism in DCF usesa fixed contention window for every access attempt. Thisapproach improves short-term fairness1 and has beenadopted in several works on WLAN optimization [16]–[20].

Consider a typical 802.11 multi-rate WLAN with oneAP and n competing stations. We assume a saturatednetwork where each competing station always has pack-ets to transmit. Each station uses the same packet pay-load size, sd (in our numerical results we use sd = 12000bits), although, our work can be easily extended toaccommodate heterogeneous payloads. Also, an idealchannel is assumed where packet losses are only dueto packet collisions. Notations are defined in Table 1.

pi channel access probability of station iCWi contention window of station iPti successful transmission probability of station i

Pidle probability that a slot is idlePc probability of collision in a slot timeTc average collision durationTti transmission duration for station i

Tslot duration of an empty slotsd packet payload size in bitsn total user stations in the network

TABLE 1: Notations used throughout the paper.

Consider the event where station i is attempting totransmit a packet of size sd in a given time slot. Theattempt probability can be calculated as in [19] whenthe exponential binary backoff is disabled:

pi =2

CWi + 1. (2)

The expression for Pti , Pidle, Pc can be calculated as [19]:

Pti = pi∏j 6=i

(1− pj), (3)

Pidle =

n∏i=1

(1− pi), (4)

Pc = 1− Pidle −n∑i=1

Pti . (5)

The per station throughput [19] of station i is:

xi =Ptisd∑n

j=1 PtjTtj + PcTc + PidleTslot, (6)

and the aggregate throughput of the WLAN, X , is:

X =

n∑i=1

xi =

∑ni=1 Ptisd∑n

i=1 PtiTti + PcTc + PidleTslot. (7)

In Section 3.1, the WLAN model in [16] is extended

1. With binary exponential backoff the collided stations choose longbackoffs with higher probability, thereby benefiting other stations fromincreased channel access.

to support weighted time fairness constraint. Howeverthe extended optimal WLAN model is computationallyexpensive, and therefore, a computationally inexpensiveapproximate WLAN model is developed in Section 3.1.1.The optimal and the approximate WLAN model arefurther extended in Section 3.1.2 to support downlinktraffic as well. In Section 3.1.3, we derive the closed-formexpression for constants cp and cs in (1) and show thatthey are only a function of the bit rates of the links in theWLAN. Using (1), the closed-form expression for the lin-ear bargaining set B on the Xp−Xs plane (see Fig. 2-(b))in the CCRN problem is easily obtained. In Section 3.2,we repeat the same analysis as in Section 3.1 but for theweighted throughput fairness constraint.

3.1 Time Fairness in WLANs

Under weighted time fairness constraint, the stationsshare the channel occupancy time in proportion to theirassigned weights. Therefore, any two stations i and jmust satisfy the condition:

PtiTtiPtjTtj

=wiwj, (8)

where wi and wj are the weights assigned to station i andj respectively. The relationship between contention win-dows of station i and j is obtained by combining (2), (3)and (8):

TtiTtj

=wiPtjwjPti

=wipj(1− pi)wjpi(1− pj)

=wi(CWi − 1)

wj(CWj − 1). (9)

It can be shown that maximizing the network through-put X in (7) for the weighted time fairness constraintin (8) is equivalent to minimizing the following costfunction:

C(pi) =TcPti

+1− pipi

(Tslot − Tc). (10)

When all stations use the same weight, i.e., w1 = w2 =. . . = wn = 1, the WLAN model in [16] computes theoptimal contention window for every contending stationin the WLAN so that they share the channel occupancytime equally and also simultaneously maximize the ag-gregate WLAN throughput. The optimized contentionwindow for station i is obtained by solving [16]:

λ2(CWi − 1)2

+2λ3

(CWi − 1)3+ · · ·+ (n− 1)λn

(CWi − 1)n=TslotTc

,

(11)

where hj =2Tti

Ttjis used to compute

λk =∑

l1<l2<···<lk1≤l1,l2,···,lk≤n

hl1hl2 · · · hlk , k = 1, 2, · · ·, n. (12)

Uniqueness of CWi is shown in [16]. The work in [16]can be easily extended to support weighted time fairnessconstraint, where the optimal contention window is ob-tained by the same expression (11) with λk, k ∈ {1, .., n},

5

defined in (12) but with a new definition for hj given by:

hj =2wjTtiwiTtj

. (13)

3.1.1 Approximate WLAN Model

Computing the optimal contention windowusing (11), (13) is relatively computationally expensiveas it requires finding the roots of an order n polynomial.To overcome this constraint, we provide a simplifiedequivalent solution that calculates the same optimalcontention window as in (11), (13) but at a greatlyreduced computation cost. Since the access probabilityof any station pi � 1, the following approximationholds:

1− pi1− pj

≈ 1. (A1)

Using (A1) in (9),

pj = piwjTtiwiTtj

. (14)

The first derivative (w.r.t pi) of the cost function in (10)is

C ′(pi) = −1−∑n

j=1 pj

p2i∏nj=1(1− pj)

Tc −1

p2i(Tslot − Tc). (15)

When n −→∞,n∏j=1

(1− pj) −→ e−∑n

j=1 pj = e−pi

∑nj=1

wjTtiwiTtj = e−τipi ,

(16)

where

τi =Ttiwi

n∑j=1

wjTtj

. (17)

The transmission duration Tti depends on the bit rate ofstation i, the parameters of MAC and PHY layers (802.11a/b/g) and the data packet size sd. Consequently, thetransmission duration for all supported bit rates of thechosen 802.11 variant can be precomputed and storedin a lookup table. Then, calculating τi only requires theknowledge of bit rates of all the links in the network. Tominimize the cost function, we set its derivative (15) tozero, resulting in:

1− τipi = ηe−τipi , (18)

where η = 1 − Tslot

Tccan be calculated for a given

variant of 802.11 from the parameters of the MACand PHY layers (Table 2). Solving (18) results in theoptimal channel access probability pi that maximizesthe network throughput under time fairness condition,however, (18) is a transcendental equation involvingexponential whose closed form solution is given in termsof the Lambert W function (W ) [21]:

pi =W(−ηe)

+ 1

τi. (19)

Since −1/e < −η/e < 0 and W (−η/e) > −1 because theaccess probability pi > 0 and τi > 0, we have:

pi =W0

(−ηe)

+ 1

τi, (20)

where W0(·) is the principal branch of W and is asingle-valued function. The value of W0(−η/e) is a fixedconstant for a given 802.11 variant since it takes ηand e as its arguments (Table 2). Hence the optimalaccess probability pi in (20) is unique and its calculationonly requires performing an addition and a division asopposed to solving the order n polynomial in (11).

a b g nTslot [µs] 9 20 9 9Tc [µs] 861.06 5.7×103 855.06 1.6×103

η 0.9895 0.9965 0.9895 0.99431+W0

(−ηe)

0.1380 0.0816 0.1385 0.1035

TABLE 2: Parameters Tslot, Tc, η and 1+W0

(− ηe

)for 802.11

a/b/g/n.

By denoting

ζ = W0

(−ηe

)+ 1, (21)

we have, from (16), (20):n∑i=1

pi = τipi = ζ. (22)

Furthermore using (22) in (3), (4), (5), we obtain thefollowing approximations which we will use later in ourdiscussion:

Pidle ≈ e−ζ , (23)n∑i=1

Pti ≈ ζe−ζ , (24)

Pc ≈ 1− ζe−ζ − e−ζ . (25)

3.1.2 Support for Downlink

The analysis to this point only considers uplink traffic.However, in a WLAN with n active stations and an AP,there are n uplinks and n downlinks. The bit rates onthe uplink and downlink are determined by the rateadaptation algorithm at the sending end, and can beasymmetric. In this sub-section, we extend the WLANmodel to also support downlink traffic. Let qi denotethe access probability the AP assigns to station i for itsdownlink traffic. We refer to AP as station n+ 1. Theaccess probability of the AP is:

pn+1 =

n∑i=1

qi. (26)

6

The condition for weighted time fairness becomes:

PtiTtiwi

=PtjTtjwj

=QtkT

′tk

wdwk=QtlT

′tl

wdwl, (27)

where T ′ti is the downlink transmission time of station i,wd is the weight for downlink traffic relative to uplinktraffic, wi is the weight of station i for both its uplinkand downlink traffic, Pti follows expression (3) with i ∈{1, . . . , n}; j ∈ {1, . . . , n + 1}, and Qti is the successfultransmission probability for AP to transmit a packet tostation i:

Qti = qi

n∏j=1

(1− pj), i = 1, . . . , n. (28)

Using (27) and (28), it can be shown that the AP withchannel access probability pn+1 is in a separate serviceclass with a service weight of:

wn+1 = wd

n∑i=1

wi, (29)

and transmission time defined by:

Ttn+1 =

∑ni=1 wi∑ni=1

wi

T ′ti

. (30)

The access probabilities p1, . . . , pn+1 can be computedusing (11), (13) or (20), (17). Internally, the AP assumesthat there are n individual virtual stations contending fora transmission opportunity each with access probability:

vi =qipn+1

=wj∑nj=1 wi

× Ttn+1

T ′ti=

wi

T ′ti∑n

j=1wj

T ′tj

. (31)

3.1.3 Closed-form expression for the bargaining set

Consider a multi-rate WLAN with two service classes,class1 and class2, and weights w1 and w2 respectively.Using the approximate WLAN model, we show thatwhen all stations in the service classes use optimizedcontention window, the aggregate throughputs of theservice classes, (X1, X2), when evaluated for all feasibleweights w1 and w2 and plotted on an X1-X2 plane,closely follow a straight line whose slope is independentof the weights and is only a function of the bit rates ofthe links. We take advantage of this result in the CCRNscheme where separate service classes are assigned tothe primary and secondary networks, and as a result,the bargaining game has a linear bargaining set.

Assume only uplink traffic in the WLAN. Let thesize and weights of class1, class2 be n1, n2 and r, 1respectively. Under weighted time fairness, the channelutilization is the same for every station within a class. Wefirst show that there exists a linear relationship betweenthe channel utilization of class1 and class2. The channeloccupancy time is approximated using (17), (22), (23):

PtiTti ≈ e−ζpiTti = ζe−ζwi∑nj=1

wj

Ttj

. (32)

The approximate channel utilization of a station in class1and class2 using (8), (25), (23) and (32) is then:

u1 =PtiTti∑n1+n2

j=1 PtjTtj + PcTc + PidleTslot, i ∈ class1 (33)

≈ r

rn1 + n2 + κ(rα1 + α2), (34)

u2 ≈1

rn1 + n2 + κ(rα1 + α2), (35)

where αj =∑i∈classj

1Tti

and

κ =(1− ζe−ζ − e−ζ)Tc + e−ζTslot

ζe−ζ, (36)

is a constant for an 802.11 variant (Table 2). Eliminatingr from (34) and (35):

(n1 + κα1)u1 + (n2 + κα2)u2 = 1. (37)

The aggregate throughput of classi, is Xi = uiαisd, i ∈{1, 2}, and by expressing ui in terms of Xi in (37), wehave the linear equation in X1, X2 that is independentof the weight ratio r and a function of α1, α2; where αidepends on the bit rates of the links in classi:

n1 + κα1

α1sdX1 +

n2 + κα2

α2sdX2 = 1. (38)

With both uplinks and downlinks traffic in the WLAN,the corresponding expression for (37) is:

[(1 + wd)n1 + κα1]u1 + [(1 + wd)n2 + κα2]u2 = 1, (39)

where αj = αj + wdαj , αj =∑i∈classj

1Tti

,αj =

∑i∈classj

1T ′ti

, j ∈ {p, s}. The correspondingexpression in (X1, X2) is

(1 + wd)n1 + κα1

sdαpX1 +

(1 + wd)n2 + κα2

sdαsX2 = 1. (40)

3.2 Throughput Fairness in WLANs

Under weighted throughput fairness constraint, the sta-tions share their achievable throughput in proportion totheir assigned weights. Therefore, any two stations i andj satisfy the condition:

xixj

=PtiPtj

=pi(1− pj)pj(1− pi)

=wiwj, (41)

where wi and wj are the assigned weights to stationsi and j respectively. Comparing (41) and (8), weightedtime fairness and weighted throughput fairness areequivalent upon rescaling the weights with the trans-mission time, i.e.,

PtiPtj

=wiwj⇐⇒ PtiTti

PtjTtj=wiTtiwjTtj

, i, j ∈ {1, . . . , n}. (42)

Therefore, by replacing wi with wiTti in (13), the optimalcontention window under weighted throughput fairnessis obtained by the same expression in (11) with λk, k ∈

7

{1, .., n}, defined in (12) but with hj defined by:

hj =2wjwi

. (43)

3.2.1 Approximate WLAN Model

By replacing wi with wiTti in (17), the closed form ex-pression for the approximate access probability pi is (20)with:

τi =1

wi

n∑j=1

wj , (44)

The closed form expression in (44) is identical to the ex-pression for the optimal access probability in [18] whoseWLAN model supports weighted throughput fairnessfor idle sense access method [17]. The only differenceis that in [18] the value of ζ in (21) is calculated forthe highest bit rate of the chosen 802.11 variant while ζin our model applies for all the bit rates of the 802.11variant.

3.2.2 Support for Downlink

The condition for proportional throughput allocation is:

Ptiwi

=Ptjwj

=Qtkwdwk

=Qtlwdwl

. (45)

Using (28) and (45), the AP (station n+1) is in a separateservice class with a service weight wn+1 defined in (29)and transmission time defined by

Ttn+1=

∑ni=1 wiT

′ti∑n

i=1 wi. (46)

The access probabilities p1, · · ·, pn+1 is computed us-ing (11), (43) or (20), (44). Internally, the AP assigns thefollowing probability to each station for their downlinktraffic:

vi =qipn+1

=wi∑nj=1 wj

. (47)

3.2.3 Closed-form expression for the bargaining set

As in Section 3.1.3, we derive the linear relationshipbetween the aggregate throughputs of class1 and class2.Under weighted throughput fairness constraint, the per-station throughputs are equal within a class. Using (41)and (24), we have:

Pti =

∑nj=1 Ptj∑nj=1

wj

wi

≈ ζe−ζ∑nj=1

wj

wi

, (48)

With only uplink traffic in the WLAN, the per-stationthroughput for class1 and class2 using (6) is approxi-mated by:

x1 ≈rsd

rβ1 + β2 + κ(rn1 + n2), (49)

x2 ≈sd

rβ1 + β2 + κ(rn1 + n2), (50)

where βj =∑i∈classj Tti . Eliminating r from (49)

and (50):

κn1 + β1sd

x1 +κn2 + β2

sdx2 = 1. (51)

The aggregate throughput of classi, is Xi = nixi, i ∈{1, 2}, and by expressing xi in terms of Xi in (51), wehave the linear equation in X1, X2 that is independentof r and a function of the bit rates of the links.

With both uplink and downlink traffic in the WLAN,the counterpart expression for (51) is:

κ(1 + wd)n1 + β1sd

x1 +κ(1 + wd)n2 + β2

sdx2 = 1, (52)

where βj = βj+wdβj , βj =∑i∈classj Tti , βj =

∑i∈classj T

′ti

and the resulting expression in (X1,X2) is

κ(1 + wd)n1 + β1(1 + wd)n1sd

X1 +κ(1 + wd)n2 + β2

(1 + wd)n2sdX2 = 1, (53)

where Xi = (1 + wd)nixi, i ∈ {1, 2}.

4 CCRN SCHEME

In this section we apply the models we developed inSections 3 to the CCRN problem we consider. Under theCCRN scheme, a cellular operator acts as the primarynetwork and offloads traffic to a secondary network thatowns an AP. In exchange, the cellular operator leasesan additional (licensed) channel to the AP, effectivelydoubling the capacity of the AP. We assume that thereare ns secondary users associated with the AP, and npprimary users that are initially cellular users, but whichare in the range of the AP and will be offloaded to the APif a suitable arrangement for both parties is found (Fig. 1-(b)). In the rest of the section, we first determine a closed-form expression for the bargaining set. We then findthe connected closed-form expression for the bargainingpoint (Nash solution). Finally, we give the closed-formexpression for the service weights of the user classes atthe bargaining point and present a method to determinea user distribution in the two WLAN cells that willresult in aggregate throughput of primary and secondarynetwork close to the bargaining point.

4.1 CCRN under Time FairnessThe aggregate throughput of the individual networks be-fore cooperation is the disagreement point, d = (Xd

p , Xds ).

Let cell1 and cell2 denote the two WLAN cells (Fig. 1-(b)) operating in the leased and the unlicensed spectrumrespectively. A user, primary or secondary, can be in-structed by the AP to associate to one of the two cells.The primary and secondary users in a cell belong to twodifferent service classes; we name them classp and classsrespectively. Note that under time fairness, the channeloccupancy time of any two users within a service classare the same and so are their channel utilization2. We

2. fraction of the time the station occupies the channel for a success-ful transmission of a packet.

8

place the following constraint on the channel utilizationof the classes in the two cells:

C1: The channel utilization of a primary user (secondaryuser) in cell1 is equal to the channel utilization of aprimary user (secondary user) in cell2.

This is the condition for cell fairness: two user havingsame bit rate (we assume equal payload for all users) andbelonging to the same class but placed in different cellswill achieve same throughput3. If we denote the targettime ratio between classp and classs by r and the chan-nel utilization of primary and secondary users by up andus respectively, then constraint C1 requires up : us = r : 1in each cell (cell1 and cell2). In Section 3.1.3, (39) givesthe linear relationship between the channel utilization oftwo service classes in a WLAN cell. Rewriting (39) foreach cell, cell1 and cell2, and the two classes, classp andclasss, we have:

[(1 + wd)n1p + κα1

p]up + [(1 + wd)n1s + κα1

s]us = 1, (54)

[(1 + wd)n2p + κα2

p]up + [(1 + wd)n2s + κα2

s]us = 1, (55)

where nij is the number of users of classj incelli, i∈{1, 2}, j∈{p, s}, αij = αij + wdα

ij where

αij =∑k∈celli∩classj

1Ttk

is the sum of the reciprocal ofuplink transmission times of all users of classj in celliand αij =

∑k∈celli∩classj

1T ′tk

is the sum of the reciprocalof downlink transmission times of all users of classjin celli, wd is the predetermined weight for downlinktraffic relative to uplink traffic and κ is a fixed constantgiven by (36) for the parameters defined in Table 2. Thetransmission duration, Tti or T ′ti , depends on the bit rateof the link between the AP and station i, the parametersof MAC and PHY layers (802.11 a/b/g) and the datapayload size sd. Hence expression in (54) and (55) areonly a function of bit rates of the users, sd, and theWLAN variant employed (802.11a/b/g/n). Adding (54)and (55):

[(1 + wd)np + καp]up + [(1 + wd)ns + καs]us = 2. (56)

where αj = αj + wdαj , αj =∑i∈classj

1Tti

,αj =

∑i∈classj

1T ′ti

, j ∈ {p, s}. The aggregate throughput

of the primary and secondary networks are3 :

Xp = upsdαp, (57)Xs = ussdαs. (58)

Combining (57), (58) and (56):

(1 + wd)np + καpsdαp

Xp +(1 + wd)ns + καs

sdαsXs = 2. (59)

By denoting

ap =(1 + wd)np + καp

sdαp, (60)

3. throughput of user i is ui× sdTti

where ui and Tti are the channelutilization and transmission time of user i and sd is payload in bytes.

as =(1 + wd)ns + καs

sdαs, (61)

the Nash bargaining problem is:

maximize (Xp −Xdp )(Xs −Xd

s )

subject to apXp + asXs = 2,

Xp ≥ Xdp ,

Xs ≥ Xds .

(62)

Since the bargaining set B defined in (59) is a straightline, the Nash bargaining solution will be the mid-pointof the bargaining range, Bd = {(Xp, Xs) ∈ B | Xp ≥Xdp , Xs ≥ Xd

s }, which is the line segment joining points(Xdp ,

2−apXdp

as

)and

(2−asXd

s

ap, Xd

s

). The bargaining point

(Xbp, X

bs) is then:

Xbp =

1

2

(Xdp +

2− asXds

ap

), (63)

Xbs =

1

2

(Xds +

2− apXdp

as

). (64)

From (57) and (58), r =up

us=

Xpαs

Xsαp. Hence the target

ratio between the classes at the bargaining point is:

rb =

(Xdp +

2−asXds

ap

)αs(

Xds +

2−apXdp

as

)αp. (65)

The ratio rb is the solution of the bargaining problemand can be computed using only the disagreement pointand the bit rates of all users in the WLAN. The nextstep is to find a distribution of primary and secondaryusers in each cell that will result in an operating point ofthe system close to the Nash solution. At the bargainingpoint, using (54) and (55):

[(1 + wd)n1p + κα1

p]rb + [(1 + wd)n1s + κα1

s] =1

ubs, (66)

[(1 + wd)n2p + κα2

p]rb + [(1 + wd)n2s + κα2

s] =1

ubs, (67)

where ubs is the channel utilization of a secondary userat the bargaining point. Hence, finding the user distri-bution is equivalent to solving the following partitionproblem: partition the np + ns users into two subsetscorresponding to each cell such that the sum of theweights in first subset equals the sum of weights inthe other subset, where the weight for a primary user iis rb

(1 + wd + κ

(1Tti

+ wd

T ′ti

))and for a secondary user

i is(

1 + wd + κ(

1Tti

+ wd

T ′ti

)). The partition problem is

NP complete, but there are efficient pseudo-polynomialalgorithms for solving it [22]. We implemented the dy-namic programming based algorithm in C and foundthe execution time to be less than 0.25 seconds for 40users with a precision of 2 decimal digits. Algorithm 1summarizes the steps for finding the distribution of usersin each cell and their channel access probabilities (line

9

4) that would result in the operating point of the systemclose to the Nash solution.

Algorithm 1 CCRN ApproachInputs: 〈Rp,Rs〉 are the uplink and downlink bit rates of theprimary and secondary users respectively; w is the preassignedweight of the downlink traffic relative to the uplink traffic;(Xd

p , Xds ) is the disagreement point.

1: calculate rb using (65) for the inputs {Rp, Rs, Xdp , Xd

s };2: using {Rp, Rs, rb, w} in the pseudo-polynomial algorithm,

find the distribution, 〈Cb1, Cb2〉, of the primary and sec-ondary users in cell1 and cell2, at the bargaining point.

3: find the corresponding optimal access probabilities,〈Pb1 ,Pb2〉, for the users in cell1 and cell2 using the WLANmodel in Section 3.

4: return 〈Cb1,Pb1〉, 〈Cb2,Pb2〉; . operating point.

4.2 CCRN under Throughput FairnessFor throughput fairness, we follow a similar approachas for the time fairness covered in Section 4.1. Thecorresponding throughput fairness constraints within aclass is:C2: The throughput of a primary user (secondary user)

in cell1 is equal to the throughput of a primary user(secondary user) in cell2.

With this constraint, two users belonging to the sameclass, but placed in different cells, will achieve equalthroughputs. As in the previous section, using C2, wecan show that the relative weights between the classesin each cell are equal, and the corresponding linearrelationship between the aggregate throughput of theprimary and secondary networks, Xp and Xs, is:

βp + κ(1 + wd)np(1 + wd)npsd

Xp +βs + κ(1 + wd)ns

(1 + wd)npsdXs = 2, (68)

where βj = βj + wdβj , βj =∑i∈classj Tti ,

βj =∑i∈classj T

′ti . The method to compute the

bargaining point (Xbp, X

sp), throughput ratio between

classes rb, and the corresponding user distribution whileusing C2 and (52) instead of (54) and (55) is similar tothe method presented in Section 4.1.

4.3 Protocol DesignIn this section we show how to integrate the proposedCCRN scheme with a WLAN similar to current 802.11systems. The AP first collects the bit rates of all the links(for both primary and secondary users) in its WLAN4.The AP then calculates the aggregate throughput forthe primary and secondary network at the bargainingpoint using (63) and (64). It then queries the BS for

4. The bit rate of a user on its uplink and downlink can be obtainedfrom the SINR or the rate adaptation algorithm at the respectivesender end. This information is then communicated to the AP by lever-aging the provisions provided in IEEE 802.11 for Wireless NetworkManagement such as the 802.11v amendment to 802.11a/b/g/n. Theamendment also allows configuration of client devices and can be usedto configure the frequency channel and the contention window size ofthe client.

the aggregate throughput it provides to the cellularusers in WLAN coverage. The AP and BS will agree tocooperate only when there is an improvement in theiraggregate throughput with respect to their disagreementpoint. Algorithm 1 is then invoked and the AP broad-casts4 the user assignment information along with theaccess probabilities of the users at the Nash solution.All users move to their assigned cell and operate attheir assigned contention window size. The mechanismis repeated periodically thereby allowing the protocol todynamically maintain the operating point of the systemclose to the Nash solution under varying user activitiesand channel conditions. All the the message exchangesduring the bargaining process between the AP and theBS occurs over the wireline channel that connects themto the Internet (Fig. 1).

5 PERFORMANCE EVALUATION

In this section we evaluate the performance of ourproposed WLAN model in Section 3 and the CCRNscheme in Section 4.

5.1 WLAN Model ValidationFor the simulation experiments, we developed a discrete-event simulator that implements the standard 802.11DCF (no RTS/CTS) for each independently transmittingstation. The simulator uses the MAC and PHY parame-ters of IEEE 802.11b standard for a packet size of 1500bytes and each experiment is run for a simulation timeof 200 seconds. The support for the other channel accessmechanisms under consideration in the section are alsobuilt in this simulator.

In Section 5.1.1, we evaluate the performance of theproposed approximate WLAN model for time fairnessby considering the first simulation scenario from Sec-tion V in [16]. In Sections 5.1.2 and 5.1.3, we comparethe performance of the approximate WLAN model andthe optimal WLAN model under both weighted timeand weighted throughput fairness constraints. In Sec-tion 5.1.4, the correctness of the closed-form linear ex-pression in X1 and X2 ( (40) and (53) derived in Sec-tions 3.1.3 and 3.2.3 respectively) are validated using thesimulator.

5.1.1 Time FairnessIn this section we consider a 802.11b WLAN with nstations where one slow station at 1 Mbps competes withn− 1 fast stations all at 11 Mbps and with time fairnessconstraint (all n stations receive equal channel occupancytime) imposed on the WLAN. The performance of ourapproximate WLAN model is compared with:

(i) the optimal WLAN model in [16];(ii) The default 802.11 DCF backoff algorithm;

(iii) the proportional fair throughput allocation algo-rithm proposed by Banchs et al in [20];

(iv) the idle sense algorithm in [17].

10

The following parameters are compared in Fig. 3:(i) the aggregate WLAN throughput;

(ii) the average Jain fairness index [23] (or the short-term fairness) of the channel occupancy time com-puted using the sliding window method5 in [24],[25].

2 3 4 5 10 20

1.5

2.5

3.5

4.5

5.5

6.5

Total Stations

Ag

gre

ga

te T

hro

ug

hp

ut

(Mb

ps

)

Approximate OptimalDCFIdle SenseBanchs

(a)

2 3 4 5 10 20

0.4

0.5

0.6

0.7

0.8

0.9

1

Total Stations

Jain

Fair

ne

ss I

nd

ex

Approximate OptimalDCFIdle SenseBanchs

(b)

Fig. 3: Performance comparison of the five MAC algorithmsunder time fairness: (a) aggregate throughput of the WLAN,(b) short-fairness of the channel occupancy time.

The experiment is same as scenario I in Section Vof [16]. Fig. 3 confirms that the approximate WLANmodel can achieve the same level of performance ob-served using the optimal WLAN model in [16] but at agreatly reduced computation cost (note that Fig. 3 andFigures 1a and 2a in [16] are similar). Our approximateWLAN model is similar in nature and complexity to thework in idle sense [17] but applies to multi-rate WLANs.The access method proposed in idle sense [17] achievesthroughput enhancement in multi-rate 802.11 WLANs,but compromises fairness as shown in Fig. 3 because theoptimization is performed for an equivalent single-ratenetwork.

5.1.2 Weighted Time Fairness

4 12 20 28 36 440

0.5

1

1.5

2

2.5

3

Total Stations

Ag

gre

gate

Th

rou

gh

pu

t (M

bp

s)

Class 1 − Approximate Class 2 − Approximate Class 1 − OptimalClass 2 − Optimal

(a)

4 12 20 28 36 440.93

0.95

0.97

Total Stations

Jain

Fair

ness In

dex

Approximate Optimal

(b)

Fig. 4: (a) Aggregate throughput per class vs. number ofstations and, (b) short-term fairness of the channel occupancytime under weighted time fairness.

In this section we consider two service classes in a802.11b WLAN of size n with weights w1 = 1 and

5. We fix the sliding window size to 20×n so that the window sizevaries with the WLAN size, n.

w2 = 0.5. Only one class is active in a station: halfof the stations send class1 traffic, while the other halfsends class2 traffic; and within each class, half of thestations use 1 Mbps bit rate to send packets whileother half use 11 Mbps. Figures 4a and 4b show theaggregate WLAN throughput of the two service classesand the short-term fairness of channel occupancy timemeasured using the modified sliding window methodof Jain fairness index in [26]. The results for the optimalWLAN model (Section 3.1) for n > 20 is not shown dueto the intractability of solving the polynomial in (11) forn > 20. Fig. 4 shows that the approximate WLAN modelagrees with the optimal WLAN model and that both themodels achieve the desired time ratio 1 : 0.5.

5.1.3 Weighted Throughput Fairness

4 12 20 28 36 440.1

0.3

0.5

0.7

0.9

1.1

Total Stations

Ag

gre

ga

te T

hro

ug

hp

ut

(Mb

ps

)

Class 1 − Approximate Class 2 − Approximate Class 1 − OptimalClass 2 − OptimalClass 1 − 802.11eClass 2 − 802.11e

(a)

4 12 20 28 36 44

0.95

1

Total Stations

Ja

in F

air

nes

s I

nd

ex

Approximate Optimal 802.11e

(b)

Fig. 5: (a) Aggregate throughput per class vs. number ofstations and, (b) short-term fairness of the channel accessopportunities under weighted throughput fairness.

Consider the same WLAN in Section 5.1.2 withweights w1 = 1 and w2 = 0.5 for the service classes(this experiment is similar to the scenario in Figure 3of [18]). In this experiment, the 802.11e EDCA modelin idle sense [18] is compared with both our WLANmodels (optimal and approximate) in Section 3.2. With802.11e, a throughput ratio of 1:0.5 between the classescan be obtained by setting CW1 ∈ [16, 48] for class1and CW2 ∈ [31, 93] for class2 (from [18]) in the sim-ulator. In Fig. 5, the aggregate WLAN throughput foreach service class and short-term fairness of channelaccess opportunities is computed. The results show thatthe approximate WLAN model agrees with the optimalWLAN model and that the models achieve the desiredthroughput ratio 1:0.5. The results also show that theaggregate throughput of the classes does not depend onthe number of stations when using our WLAN models,while with 802.11e the aggregate throughput decreaseswith an increase in the number of stations.

5.1.4 Linear Bargaining SetIn this section, we use the simulator to compute the ag-gregate throughputs (X1, X2) for the classes at differentweights (w1, w2), and show that the aggregate through-puts on the X1-X2 plane are well approximated bythe linear expression (1). Consider a multi-rate 802.11b

11

WLAN with 8 stations each in class1 and class2. Ineach service class, exactly two users use the same bitrate from the supported set of {1, 2, 5.5, 11} Mbps.For simplicity, symmetric bit rates are assumed on theuplink and downlink of a user and the downlink touplink traffic ratio is set to wd = 3. Consider 30 differentlogarithmically spaced values between 0.1 and 10 for theweight ratio r = w1

w2. For each r, the contention window

for the AP and the stations are computed using theapproximate WLAN model. The aggregate throughputof the classes calculated using (7) and from the simulatorare plotted in Fig. 6. With the bit rates of all the linksknown, the constant coefficients in (40) and (53) arecalculated and the corresponding straight line expressionin X1 and X2 is shown in Fig. 6. As shown in Fig. 6,the realistic aggregate throughput of the classes obtainedfrom the simulator is well approximated by the straightline in (40) and (53) (within < 5% margin of error).

0 1 2 3

1

2

3

X1 (Mbps)

X2 (

Mb

ps

)

ApproximateLineAnalyticalSimulator

(a)

0 1 2

1

2

X1 (Mbps)

X2 (

Mb

ps

)

ApproximateLineAnalyticalSimulator

(b)

Fig. 6: Comparison of the optimal aggregate throughput ofclass1 and class2 with the approximated linear equation under(a) time fairness, and (b) throughput fairness constraints.

5.2 CCRN SchemeIn Section 5.2.1, we verify the optimality of the operat-ing point obtained using our approach in Algorithm 1with the operating point obtained using the exhaustivesearch (brute-force) method. Through the experiment weshow that the optimality of the Nash solution obtainedusing our approach in Algorithm 1 is largely unaffecteddespite the approximations used in the approximateWLAN model, closed-form expression for the linearbargaining set, and the pseudo-polynomial algorithmfor finding the user distribution. Section 5.2.2 quantifiesthe resulting improvement in the throughputs of theprimary and secondary networks under the proposedCCRN scheme.

For the experiments, we assume primary and sec-ondary users are equipped with 2 antennas supportingtwo spatial streams. The AP of the secondary networkis equipped with 4 antennas and uses 2 of them percell (or WLAN). The transmission power for a user is17 dBm and for the AP is 20 dBm. The users and theAP use the following 802.11n PHY settings in 5 GHzband: bandwidth 20 MHz, Long Guard Interval (800 ns),MAC Service Data Unit Aggregation (A-MSDU) scheme,aggregation size of 5 frames per A-MSDU with 1500

bytes payload data per frame, and supported physicalbit rates of {13, 26, 39, 52, 78, 104, 117, 130} Mbps [27].The discrete event simulator is modified to support the802.11n PHY settings.

5.2.1 CCRN Solution ValidationConsider a CCRN network with 8 primary and 8 sec-ondary users in a IEEE 802.11n WLAN. For simplicity,symmetric bit rates are assumed on the uplink anddownlink of each user. In each service class (classp andclasss), the users use a unique bit rate from the set {13,26, 39, 52, 78, 104, 117, 130} Mbps. For the disagreementpoint, (Xd

p , Xds ), the initial aggregate throughput of the

primary network is set to 15 Mbps. The initial aggregatethroughput of the secondary network is calculated usingboth the optimal and the approximate WLAN model inSection 3.1.1. For the operating point obtained in line4 of Algorithm 1, the aggregate throughput of the pri-mary and secondary networks are calculated analyticallyusing (6) and shown in Fig. 7. Also, to replicate thereal-time behavior of the CCRN, the operating pointin line 4 of Algorithm 1 is used as the input to thediscrete event simulator. The aggregate throughput ofthe primary and secondary networks at the end of 200seconds of simulation time is shown in Fig. 7.

20 30 40 50

60

70

80

90

Xp (Mbps)

Xs (

Mb

ps)

Points in the Bargaining Set Brute Force − Analytical Brute Force − SimulatorCCRN − AnalyticalCCRN − SimulatorDisagreement Point

33.1 33.9

73.1

73.7

details atbaragining point

(a)

20 30 40 50

60

70

80

90

Xp (Mbps)

Xs (

Mb

ps)

Points in the Bargaining Set Brute Force − Analytical Brute Force − SimulatorCCRN − AnalyticalCCRN − SimulatorDisagreement Point

32.9 33.5

72.7

72.9

details atbaragining point

(b)

Fig. 7: Graphical representation of the bargaining problemalong with the Nash solution when (a) the optimal WLANmodel and, (b) the approximate WLAN model in Section 3are used to calculate the channel access probabilities for theusers (line 3 of Algorithm 1 and 2).

The exhaustive search approach necessitates iteratingthrough all possible distributions of primary and sec-ondary users in the two cells. For each user distribution,the aggregate throughput of the primary and secondarynetworks, (Xp, Xs), are calculated for the target ratio rthat satisfies the cell fairness constraint C1. The aggregatethroughput of the networks that maximizes the Nashproduct, (Xp − Xd

p )(Xs − Xds ), ∀ Xp ≥ Xd

p , Xs ≥ Xds , is

the bargaining point. The target ratio r that maintainsthe constraint C1 between the cells can be obtainedusing (54) and (55):

r =(1 + wd)(n

1s − n2s) + κ(α1

s − α2s)

(1 + wd)(n2p − n1p) + κ(α2p − α1

p). (69)

12

The steps in the brute-force approach are detailed in Al-gorithm 2 and the algorithm is run for the primary andsecondary network under study in Fig. 7. As shownin Fig. 7, the aggregate throughput of the networks,(Xp,Xs), calculated for all user distributions in the twocells forms the bargaining set and has a straight lineappearance ((59) is the corresponding straight line equa-tion). The operating point in line 10 of Algorithm 2 isused in the simulator and the aggregate throughput ofthe primary and secondary networks at the end of 200seconds of simulation time is shown in Fig. 7 along withthe analytically obtained bargaining solution in line 7of Algorithm 2. Fig. 7 shows that the loss in optimalityby using our approach (Algorithm 1) over the brute-forceapproach (Algorithm 2) is negligible6.

Algorithm 2 Brute Force ApproachInputs: Same inputs as for Algorithm 1.

1: for each combination of users in cell1 and ce112, 〈C1, C2〉,do

2: calculate r using (69) for the inputs {C1, C2, Rp, Rs};3: find the corresponding optimal access probabilities for

the users in each cell, 〈Pb1 ,Pb2〉, using either the optimalor the approximate WLAN model in Section 3.

4: find the optimal aggregate throughput of primary andsecondary users, (Xp, Xs), using (6).

5: if Nash product is maximized then6: 〈Cb1,Pb1〉=〈C1,P1〉, 〈Cb2,Pb2〉=〈C2,P2〉;7: Xb

p=Xp, Xbs=Xs;

8: end if9: end for

10: return 〈Cb1,Pb1〉, 〈Cb2,Pb2〉; . operating point.

5.2.2 Performance Evaluation of CCRN SchemeTo gain insight in the expected performance of theproposed CCRN solution, we evaluate the resulting im-provement in throughputs of the primary and secondarynetworks while varying the number of primary users,as well as the initial throughput of the primary users(before cooperation). The applicable bit rate for eachuplink-downlink pair is derived based on the RSSI,which in turn is calculated according to the log distancepath loss model with shadow fading (Model D) definedby the Task Group n (TGn) [28]. Under this model, a usermust be within 80 meters (on the average) from the AP toreceive the minimum bit rate of 13 Mbps on their uplinkand downlink. Consider a circular coverage region withthe AP at the center and radius of the coverage set R setto 80 meters. Assume all the users in the coverage areareceive at least the minimum bit rate on their uplink anddownlink. Two types of user placements are consideredin the coverage area:(i) uniform: users are randomly positioned uniformly

within the circular coverage area (probability densi-ties are: r ∼ 2r

R2 , 0 ≤ r ≤ R, and θ ∼ 12π , θ ∈ (0, 2π]).

6. Note that there are significant gains in execution time when theapproximate WLAN model is used in Algorithm 1 over the optimalWLAN model when the number of users is large (n > 20).

(ii) clustered: similar to uniform but half of the userpopulation is within the inner circle of radius R

2(probability densities are: r ∼ 1

R , r ∈ [0, R], andθ ∼ 1

2π , θ ∈ (0, 2π]).

2 5 8 11 14 17 200

40

80

120

160

200

npP

erc

en

tag

e t

hro

ug

hp

ut

imp

rovem

en

t

Primary NetworkSecondary Network

(a)

2 5 8 11 14 17 200

40

80

120

160

200

npP

erc

en

tag

e t

hro

ug

hp

ut

imp

rovem

en

t

Primary NetworkSecondary Network

(b)

Fig. 8: Percentage improvement in the aggregate throughputof the primary and secondary users while varying the numberof primary users and holding the number of secondary usersconstant (ns=10) for (a) uniform, and (b) clustered placements.

Using the simulator, we show the average and 90%confidence intervals in the throughput improvement ofthe networks after performing 1000 simulation runs forthe uniform and clustered user placement types. Weassume an aggregate throughput of 15 Mbps for the pri-mary users when served by its BS (before cooperation).This is consistent with the average throughput of LTEmacrocells (instead of the peak rates). The downlink touplink traffic ratio is set to wd = 3.

In this section we present the results for time fairness.The results for throughput fairness are very similaronly with a slightly lower value for the improvementas throughput fairness trades some cell capacity forincreased fairness. Due to space limitations and thesimilarity of the results we do not present the throughputfairness results. The improvement in throughput for boththe primary and secondary users when the number ofcellular (primary) users np changes from 2 to 20 whilethe number of secondary users ns is held constant at 10users is shown in Fig. 8. The percentage of improve-ment is considerably higher for the cellular users, asthey start with a relatively low aggregate throughput of15 Mbps. On average, the cellular users approximatelydouble their throughput (on the average by 100%) un-der the uniform placement type while their throughputimproves by 150% on the average under the clusteredplacement type. The comparatively higher throughputimprovement in the clustered placement is due to thepresence of more primary users in close proximity to theAP (and therefore having superior bit rates). While notas spectacular as for the primary users, the secondary(WLAN) users also increase their throughput by ap-proximately 40% under both placement types. The 90%confidence intervals show that the primary users expe-rience a higher variability in the improvement because

13

their bit rate after the agreement depends considerablyon the quality of their link to the AP. In contrast, forthe secondary users, if they have a good link to theAP before agreement, they will maintain that good linkafter the agreement (the converse is also true). Finally,the throughput improvement is relatively insensitive tothe number of primary users. In fact the improvementis insensitive to the number of primary and secondaryusers. The explanation for this fact is that the bargainingpoint is chosen as a function of the aggregate throughputfor both the primary and the secondary users. Those ag-gregate throughputs are, however, almost independentof the number of users. Fig. 9 shows the percentage

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Fig. 9: Percentage improvement in the throughputs of the pri-mary and secondary users while varying the initial aggregatethroughput of the primary users for (a) uniform, and (b)clustered placements.

of improvement as a function of the initial aggregatethroughput of the primary users. For this graph tenprimary users and ten secondary users were considered,although, as mentioned before, the results are insensitiveto the number of users. From Fig. 9 it is clear that asthe initial aggregate throughput of the cellular usersincreases, the improvement resulting from cooperationbecomes smaller and smaller, until, at about 40 Mbpsunder uniform placement type, the networks decide tooperate at the disagreement point, i.e., they choose notto cooperate. The lack of an agreement (due to reducedthroughput after cooperation) can only happen if the pri-mary users are better served by the cellular base stationthan by the access point. While this may happen fora particular combination of technologies (e.g., a legacy802.11b AP for WLAN and LTE advanced for the cellularnetwork with a relatively close base station), in generalWLAN data rates are often higher than cellular datarates due to the reduced cell size and higher signal tonoise ratio for WLANs.

6 RELATED WORKResource allocation and spectrum trading are treated astwo separate problems in the spectrum sharing model

of cognitive radios [29]. Optimal resource allocation offrequency channels, channel access time, transmissionpower, throughput etc. between primary and secondaryusers hold the key to efficient spectrum sharing. Spec-trum trading is the economic aspect of spectrum sharing,where secondary users pay for the leased channel. Exist-ing literature used a combination of game theory, markettheory and price theory to model the problems in opti-mal resource allocation and economic interactions [29].CCRNs combine the spectrum sharing scheme with thephysical layer cooperative communication technique inwhich one or more relay terminals are recruited to assistin the communication when the direct link suffers fromsevere signal fading [6].

The CCRN scheme in [5] uses Stakelberg games for op-timal resource sharing between the primary link (Stakel-berg leader) and the secondary ad hoc network (Stakel-berg follower). The primary link optimizes its strategy(lease time and amount of cooperation in terms of dis-tributed space-time coding) to maximize its transmissionrate, being aware that its decision will influence thestrategy adopted by the secondary network, namely thetransmission power expended for relaying the primarytraffic. The work in [7] extends [5] to include a rev-enue/payment mechanism and a Stakelberg game isadopted to solve the joint problem of resource alloca-tion and spectrum trading. The restriction of only oneprimary link in the system model of [5], [7] is addressedin [8], which extends the work in [7] to two co-locatedinfrastructure based primary and secondary networks.The work in [5], [7], [8] employs a three phase TDMAbased scheme for cooperation, where the primary trafficis broadcasted in phase 1, one or more secondary usersare recruited to relay the traffic to the destination inphase 2 and the secondary users access the leased chan-nel using TDMA in phase 3. The work in [13] proposes aCCRN scheme based on Stakelberg games for secondaryusers that employ slotted Aloha access method in phase3. The work in [10] extends [5] to equip secondary userswith multiple input multiple output (MIMO) antennas.Since MIMO allows concurrent transmission of multi-ple independent data streams, the need for phase 3 iseliminated where now the secondary users cooperativelyrelay the primary traffic in phases 1 and 2 while obtain-ing spectrum access opportunities for their own traffic.While [10] leverages the degrees of freedom (DoFs)offered in the spatial domain, [12] exploits the DoFsprovided by the orthogonal dimensions in quadraturephase shift keying (QPSK). The secondary users employin-phase binary phase shift keying (I-BPSK) to relaythe primary traffic and use the quadrature BPSK (Q-BPSK) to transmit their own traffic. A two-phase FDMAscheme is proposed in [9], where the primary users grantsecondary users exclusive access to a portion of theirspectrum in exchange for cooperation. To the best of ourknowledge, the current work is the first to propose aCCRN scheme for WLANs employing contention basedaccess schemes such as IEEE 802.11 DCF.

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7 CONCLUSION

In this paper, we have investigated and proposed animplementation of the CCRN framework for IEEE 802.11WLANs. In the proposed CCRN scheme, the mobileoperator leases a channel from the licensed spectrumband to a privately owned WiFi AP, and in return, themobile operator leverages the AP as cooperative relaysto offload its Internet traffic. The cooperation betweenthe primary (cellular) and secondary (WLAN) networksis analyzed using a two-player bargaining game wherethe utility function for the players are their respectiveaggregate network throughputs. We show that underfairness and optimal throughput constraints, the bar-gaining set for the bargaining game is a straight linewhose slope only depends on the bit rates of the users.Calculating the Nash bargaining solution for a linear bar-gaining set is trivial, and the proposed CCRN algorithmdetermines the corresponding distribution of the usersin the two WLAN and the service weights for the usersat the Nash solution. The proposed computationallyinexpensive WLAN model then calculates the contentionwindow for each user that results in the operating pointof the system close to the Nash solution. The simulationresults verify the optimality of the operating point aswell as quantify the benefits of employing the CCRNscheme in WLANs.

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Mani Bharathi Pandian is currently a Ph.D.candidate in the Department of Electrical andComputer Engineering at North Carolina StateUniversity under the supervision of Dr. MihailSichitiu and Dr. Huaiyu Dai. He received an M.S.degree from the same department in 2011. Hisresearch focuses on cooperative cognitive radionetworking in wireless local area networks.

Mihail L. Sichitiu was born in Bucharest, Roma-nia. He received a B.E. and an M.S. in ElectricalEngineering from the Polytechnic University ofBucharest in 1995 and 1996 respectively. InMay 2001, he received a Ph.D. degree in Elec-trical Engineering from the University of NotreDame. He is currently employed as an associateprofessor in the Department of Electrical andComputer Engineering at North Carolina StateUniversity. His primary research interest is inWireless Networking with emphasis on ad hoc

networking and wireless local area networks.Huaiyu Dai (M’03, SM’09) received the B.E.and M.S. degrees in electrical engineering fromTsinghua University, Beijing, China, in 1996 and1998, respectively, and the Ph.D. degree inelectrical engineering from Princeton University,Princeton, NJ in 2002. Currently he is an As-sociate Professor of Electrical and ComputerEngineering at NC State University, Raleigh.His research interests are in the general areasof communication systems and networks, ad-vanced signal processing for digital communica-

tions, and communication theory and information theory.