MObile data offload to small cell technology such as

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1 Optimal Resource Allocation in Random Access Cooperative 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 as cooperative 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 mobile operator can lease a licensed channel to the AP, effectively doubling its capacity. In this paper, we propose an implementation of the CCRN framework applied to IEEE 802. WLANs. The cooperation is cast as a two-player bargaining game where the two players are the primary users users of the mobile operator) and the secondary users users of the AP before spectrum leasing) who bargain for either throughput share or channel access time share. The optimal resource allocation that ensures efficiency as well as fairness among users is provided by the Nash solution. Simulation results show that the users achieve higher throughput via the proposed CCRN scheme, thus providing the mobile operator e.g., AT&T) and the private WiFi provider e.g., a Starbucks coffee shop) with incentives for cooperation. Index Terms Cooperative Cognitive Radio Networks, WLAN Optimization, WiFi, spectrum leasing, Game theory. INTRODUCTION MObile data offload to small cell technology such as WiFi or femtocell provides a compelling solution for mobile operators who want to relieve the strain on their core networks. Compared to cellular macrocells, small cells provide increased spectrum reuse in the coverage area, higher signal to noise ratio in the cell hence superior link bit rate for its users), and are highly cost effective even for large scale deployments. Furthermore, the reduced transmission times enabled by the superior link bit rates in the small cells directly translate into battery power saving for the user devices. WiFi hotspots operate in the unlicensed bands and suffer from severe interference due to scarce spectrum availability. On the other hand, macrocells and femtocells require the use of the same costly and scarce licensed spectrum and suffer from co-site interference problems. To unlock new spectrum for small cell technology, a new regulatory spectrum sharing framework [] is being proposed by the Federal Communications Commission FCC), where non-mobile incumbent owners, such as military who do not use their spectrum at all times and locations are allowed to grant exclusive access of their spectrum to mobile operators in regions where there is no incumbent activity. Recently, FCC and the US Federal government have identified the MHz band [2] 3.5 GHz Band), currently utilized for military 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 with the Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC, USA. s: {mpandia, mlsichit, hdai}@ncsu.edu. mobile operators for small cell operations. The European Commission is working on a similar proposal in the GHz band that has very localized incumbent military telemetry use. Such a spectrum sharing approach regime can potentially unlock more than 00 MHz of highquality spectrum, specially in higher spectrum bands > 2 GHz) that are ideal for small cells. To expedite spectrum sharing in small cells, FCC in its recent ruling [3] has eliminated spectrum sensing as a requisite for cognitive radio devices. Instead, FCC mandates that devices learn of spectrum availability at their respective locations from an external source such as a location-based query to the database of the incumbent, for example the Google Spectrum Database [4]. Devices with such cognitive or frequency-agile transceivers are regarded as the main enabler of spectrum sharing in small cell technology. Although, spectrum leasing simplifies commercial deployment and promotes better spectrum utilization, developing a workable pricing model between the primary network owner of the spectrum) and the secondary network beneficiary of the leased spectrum) is not trivial. To expedite spectrum leasing in real-world deployments, researchers have recently advocated for schemes that employ spectrum leasing, not necessarily on the basis of fees or charge, but in return for improved quality-of-service of the primary network via cooperation with secondary network. One such proposal is the new cognitive radio paradigm in [5] termed Cooperative Cognitive Radio Networks CCRNs). In CCRNs, the primary users select a set of secondary users which have better channel conditions) to relay the primary traffic cooperatively, and in return the secondary users are granted channel access opportunities in the licensed leased) spectrum. CCRNs exploit cooperative

2 2 diversity in cognitive radio networks by combining cooperative communication [6], a physical layer technology, and the spectrum leasing feature enabled by cognitive radios. Consider the scenario in Fig. - where the primary users initially connect to their cellular base station BS) using cellular technology such as LTE in the licensed spectrum, while the secondary users connect to the IEEE 802. WiFi AP and use the standard 802. DCF protocol for channel access in the unlicensed bands. The primary users along with the BS form the primary network, while the secondary users along with the AP form the secondary network. If all primary users offload their traffic to the WiFi AP, although they might connect to the AP at superior link bit rate, the corresponding increase in contention can significantly degrade throughput of all the users both primary and secondary). Instead, assume that spectrum leasing is enabled via the CCRN scheme for the network in Fig.. The primary network i.e., the mobile operator) leases an additional channel from the licensed spectrum to the secondary AP. In exchange, the secondary AP adds the extra channel to its auxiliary interface and reassigns both the primary and secondary users in the two resulting WLAN cells - the original cell that continues to operate in the unlicensed channel and the new cell operating in the newly leased channel as shown in Fig. -. With the capacity of the AP now effectively doubled, both primary and secondary users can expect significant improvements in their achievable throughput, as well as power savings owing to reduced transmission time). Hence the CCRN scheme offers a win-win scenario for both the cellular network operator e.g., AT&T) as well as the WLAN owner e.g., a Starbucks coffee shop). Licensed Spectrum LTE) BS PU SU INTERNET AP PU SU Unlicensed Spectrum WLAN) BS INTERNET Leased Spectrum WLAN-) SU PU AP SU PU Unlicensed Spectrum WLAN-2) Fig. : Network diagram showing the base station BS) of the primary network, the access point AP) of the secondary network, and the primary and secondary users PUs and SUs) in the range of the AP before, and after spectrum sharing under CCRN scheme. Much of the existing CCRN schemes in the literature assume that the users access the spectrum using TDMA [5], [7], [8], frequency division multiple access FDMA) [9], space division multiple access SDMA) [0], orthogonal frequency division multiple access OFDMA) [], or using other special orthogonal schemes [2]. A random access scheme is presented in [3], where secondary users access the spectrum using slotted Aloha. In contrast, WLANs have adopted a contention-based medium access control such as the IEEE 802. Distributed Coordination Function DCF). To leverage cooperative transmission and spectrum leasing in WLANs, such as the scenario in Fig. -, existing CCRN schemes are no longer applicable. In our work, we propose an implementation of the CCRN framework for primary network that supports any current cellular standard, such as LTE, and an IEEE 802. multi-rate WLAN based secondary network. When served by the secondary AP, all users either primary and secondary) employ an IEEE 802. DCF based channel contention mechanism. As shown in Fig., both the AP and the BS are connected to the Internet over wireline channel backhaul), as is common in the present-day deployments. No backhaul capacity limitation is assumed for the wireline channel. The primary network owns bandwidth in the form of channels of certain size e.g., 20 MHz channels in the 3.5 GHz band), which it is willing to lease to the secondary network; in exchange, the AP of the secondary network offloads data traffic for the primary cellular) users in its range. To enable spectrum leasing, the AP of the secondary network is equipped with an auxiliary radio shown in Fig. -) that can be tuned to the frequency of the leased channel licensed spectrum). All the user equipments primary and secondary) are also equipped with radios that can be tuned to the unlicensed frequency as well as the leased channel and support dual-mode WiFi + Cellular, common in today s smartphones). The setup in Fig. - resembles the cooperative communication scheme in a mixed wireline/wireless network [6] where the sourceto-relay Internet/BS-to-AP) is a wireline channel, and the relay-to-destination AP-to-users) is a wireless channel. The problem formulation for the proposed CCRN scheme is discussed in Section 2. 2 SYSTEM MODEL In the proposed CCRN scheme, the primary network agrees to lease the channel to the AP only if the AP is offering a bargain that improves the primary network throughput. The user devices are assumed to support service differentiation readily available for 802. devices implementing 802.e). The AP has the freedom to reassign any user in either of the two WLAN cells Fig. -), and to assign different service weights to different users. As a result, depending on the distribution of the users in the two cells and the service weight of each user, different throughputs for the users in the primary and secondary networks are achievable. If we denote with X p and X s the aggregate throughputs for the primary and secondary users respectively, we can define the bargaining set X p, X s ) B. Fig. 2- depicts the bargaining set B of achievable throughputs as well as the disagreement point X d p, X d s ) representing the throughputs of the two networks in the absence of cooperation i.e., when the cellular users communicate

3 3 with the BS in the licensed channel, and the AP users are all in the unlicensed channel). A bargaining point is a recommended solution for the two players given the bargaining set, the disagreement point and a bargaining solution, which is a rule for finding the bargaining point. A thorough treatment of various bargaining solutions can be found in [4]; however, we restrict our discussion to the well-known Nash bargaining solution [5]. X s X d p, X d s ) B X p X b p, Xb s ) X s B ւ X d p, X d s ) X b p, X b s) X p Fig. 2: The bargaining set B, bargaining point X b p, X b s) and disagreement point X d p, X d s ) for the CCRN problem without, and with 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 essential in WLANs. For this reason, in the proposed CCRN scheme, we impose either a weighted time or a weighted throughput fairness constraint in the WLAN. When served by the WLAN AP, the primary and secondary users are assigned separate service classes, class p and class s respectively, with w p and w s representing the weights for the service classes. Under the weighted time fairness constraint, users share their channel occupancy time in proportion to their assigned weights; while under weighted throughput fairness constraint, the user share their achievable throughput in proportion to their assigned weights. Our CCRN algorithm attempts to find the ) service weights w b p, w b s) and, 2) the distribution of the users in the two WLAN cells, that will achieve the aggregate network throughputs X b p, X b s) at the Nash bargaining solution. Our CCRN scheme requires an IEEE 802. DCF like contention based channel access mechanism that will achieve the chosen fairness constraint weighted time or weighted throughput) in the WLAN. The proposed WLAN model for our CCRN scheme is built on the recent work in [6] that calculates an optimal fixed contention window for each contending station in an IEEE 802. multi-rate WLAN to jointly achieve aggregate WLAN throughput maximization and time fairness equal channel occupancy time for all stations). To fit our CCRN needs, the WLAN model in [6] is extended in the following directions in Section 3: ) 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 find the optimal contention window, they however require solving an order n polynomial where n is the number of stations in the WLAN. To reduce the computation complexity, we derive a computationally inexpensive closedform approximation for the optimal contention window in Section 3. Using the closed-form approximation, we show that under a chosen fairness constraint time or throughput), when all stations adopt optimal contention window sizes, the aggregate throughputs of the two service classes, X p and X s, evaluated for all feasible weights, w p and w s, closely follow a straight line of the form: c p X p + c s X s =, ) where c p and c s are constants that are only a function of the bit rates of the links in the WLAN. The expressions for c p and c s are different under weighted time and weighted throughput fairness constraints. In Section 4, we take advantage of the result in ) to show that when all users in the WLAN use optimized contention window under a fairness constraint time or throughput), the bargaining set of the CCRN problem can be approximated by a straight line as shown in Fig. 2-). The expression for the approximate linear bargaining set is only a function of bit rates of the participating users primary and secondary users which are being served by the AP) and hence easily calculated. Also, a closedform expression for the network aggregate throughputs X b p, X b s) and their service weights w b p, w b s) at the Nash bargaining solution exists and is a function of the disagreement point and the bit rates of users. Finally, a method to find an effective user distribution in the two WLAN cells is proposed that will achieve aggregate network throughputs close to the Nash solution X b p, X b s), while maintaining the weights w b p and w b s for the service classes. Section 3 introduces the necessary WLAN models, while Section 4 discusses the proposed CCRN scheme under both the time and throughput fairness constraints. 3 WLAN OPTIMIZATION The recent work in [6] proposes a MAC algorithm for IEEE 802. multi-rate WLAN that computes an optimal contention window for every contending station in the network to jointly achieve network throughput maximization and time fairness among stations. The time fairness constraint requires each competing station to receive approximately equal channel occupancy time. We build on the work in [6] and extend their WLAN model to support service differentiation in terms of weighted time and weighted throughput fairness where the stations share the available channel occupancy time and achievable throughput respectively in proportion

4 4 to their assigned weights. The proposed WLAN model adopts a medium access mechanism very closely related to 802. DCF access mechanism, but which, instead of the binary exponentially backoff mechanism in DCF uses a fixed contention window for every access attempt. This approach improves short-term fairness and has been adopted in several works on WLAN optimization [6] [20]. Consider a typical 802. multi-rate WLAN with one AP and n competing stations. We assume a saturated network where each competing station always has packets to transmit. Each station uses the same packet payload size, s d in our numerical results we use s d = 2000 bits), although, our work can be easily extended to accommodate heterogeneous payloads. Also, an ideal channel is assumed where packet losses are only due to packet collisions. Notations are defined in Table. p i CW i P ti P idle P c T c T slot s d n channel access probability of station i contention window of station i successful transmission probability of station i probability that a slot is idle probability of collision in a slot time average collision duration transmission duration for station i duration of an empty slot packet payload size in bits total user stations in the network TABLE : Notations used throughout the paper. Consider the event where station i is attempting to transmit a packet of size s d in a given time slot. The attempt probability can be calculated as in [9] when the exponential binary backoff is disabled: p i = 2 CW i +. 2) The expression for P ti, P idle, P c can be calculated as [9]: = p i p j ), 3) P ti P idle = j i n p i ), 4) i= P c = P idle n P ti. 5) i= The per station throughput [9] of station i is: x i = P ti s d n j= P t j T tj + P c T c + P idle T slot, 6) and the aggregate throughput of the WLAN, X, is: n n i= X = x i = P t i s d n i= P. 7) t i + P c T c + P idle T slot i= In Section 3., the WLAN model in [6] is extended. With binary exponential backoff the collided stations choose long backoffs with higher probability, thereby benefiting other stations from increased channel access. to support weighted time fairness constraint. However the extended optimal WLAN model is computationally expensive, and therefore, a computationally inexpensive approximate WLAN model is developed in Section 3... The optimal and the approximate WLAN model are further extended in Section 3..2 to support downlink traffic as well. In Section 3..3, we derive the closed-form expression for constants c p and c s in ) and show that they are only a function of the bit rates of the links in the WLAN. Using ), the closed-form expression for the linear bargaining set B on the X p X s plane see Fig. 2-) in the CCRN problem is easily obtained. In Section 3.2, we repeat the same analysis as in Section 3. but for the weighted throughput fairness constraint. 3. Time Fairness in WLANs Under weighted time fairness constraint, the stations share the channel occupancy time in proportion to their assigned weights. Therefore, any two stations i and j must satisfy the condition: P ti P tj T tj = w i w j, 8) where w i and w j are the weights assigned to station i and j respectively. The relationship between contention windows of station i and j is obtained by combining 2), 3) and 8): T tj = w ip tj w j P ti = w ip j p i ) w j p i p j ) = w icw i ) w j CW j ). 9) It can be shown that maximizing the network throughput X in 7) for the weighted time fairness constraint in 8) is equivalent to minimizing the following cost function: Cp i ) = T c + p i T slot T c ). 0) P ti p i When all stations use the same weight, i.e., w = w 2 =... = w n =, the WLAN model in [6] computes the optimal contention window for every contending station in the WLAN so that they share the channel occupancy time equally and also simultaneously maximize the aggregate WLAN throughput. The optimized contention window for station i is obtained by solving [6]: λ 2 CW i ) 2 + 2λ 3 CW i ) n )λ n CW i ) n = T slot, T c where h j = 2Tt i T tj λ k = l <l 2< <l k l,l 2,,l k n is used to compute ) h l h l2 h lk, k =, 2,, n. 2) Uniqueness of CW i is shown in [6]. The work in [6] can be easily extended to support weighted time fairness constraint, where the optimal contention window is obtained by the same expression ) with λ k, k {,.., n},

5 5 defined in 2) but with a new definition for h j given by: 3.. Approximate WLAN Model h j = 2w j w i T tj. 3) Computing the optimal contention window using ), 3) is relatively computationally expensive as it requires finding the roots of an order n polynomial. To overcome this constraint, we provide a simplified equivalent solution that calculates the same optimal contention window as in ), 3) but at a greatly reduced computation cost. Since the access probability of any station p i, the following approximation holds: p i. A) p j Using A) in 9), p j = p i w j w i T tj. 4) The first derivative w.r.t p i ) of the cost function in 0) is C p i ) = n j= p j p 2 n i j= p j) T c p 2 T slot T c ). 5) i When n, n p j ) e n w j n j= pj = e pi j= w i T tj = e τ ip i, j= where τ i = T t i w i n j= 6) w j T tj. 7) The transmission duration depends on the bit rate of station i, the parameters of MAC and PHY layers 802. a/b/g) and the data packet size s d. Consequently, the transmission duration for all supported bit rates of the chosen 802. variant can be precomputed and stored in a lookup table. Then, calculating τ i only requires the knowledge of bit rates of all the links in the network. To minimize the cost function, we set its derivative 5) to zero, resulting in: τ i p i = ηe τipi, 8) where η = T slot T c can be calculated for a given variant of 802. from the parameters of the MAC and PHY layers Table 2). Solving 8) results in the optimal channel access probability p i that maximizes the network throughput under time fairness condition, however, 8) is a transcendental equation involving exponential whose closed form solution is given in terms of the Lambert W function W ) [2]: p i = W η ) e +. 9) τ i Since /e < η/e < 0 and W η/e) > because the access probability p i > 0 and τ i > 0, we have: p i = W ) 0 η e +, 20) τ i where W 0 ) is the principal branch of W and is a single-valued function. The value of W 0 η/e) is a fixed constant for a given 802. variant since it takes η and e as its arguments Table 2). Hence the optimal access probability p i in 20) is unique and its calculation only requires performing an addition and a division as opposed to solving the order n polynomial in ). a b g n T slot [µs] T c [µs] η ) W 0 η e TABLE 2: Parameters T slot, T c, η and +W 0 η e ) for 802. a/b/g/n. By denoting ζ = W 0 η ) +, 2) e we have, from 6), 20): n p i = τ i p i = ζ. 22) i= Furthermore using 22) in 3), 4), 5), we obtain the following approximations which we will use later in our discussion: P idle e ζ, 23) n P ti ζe ζ, 24) i= 3..2 Support for Downlink P c ζe ζ e ζ. 25) 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 on the uplink and downlink are determined by the rate adaptation algorithm at the sending end, and can be asymmetric. In this sub-section, we extend the WLAN model to also support downlink traffic. Let q i denote the access probability the AP assigns to station i for its downlink traffic. We refer to AP as station n +. The access probability of the AP is: n p n+ = q i. 26) i=

6 6 The condition for weighted time fairness becomes: P ti w i = P t j T tj w j = Q t k T t k w d w k = Q t l T t l w d w l, 27) where T t i is the downlink transmission time of station i, w d is the weight for downlink traffic relative to uplink traffic, w i is the weight of station i for both its uplink and downlink traffic, P ti follows expression 3) with i {,..., n}; j {,..., n + }, and Q ti is the successful transmission probability for AP to transmit a packet to station i: n Q ti = q i p j ), i =,..., n. 28) j= Using 27) and 28), it can be shown that the AP with channel access probability p n+ is in a separate service class with a service weight of: w n+ = w d n i= w i, 29) and transmission time defined by: n i= T tn+ = w i n w i. 30) i= T t i The access probabilities p,..., p n+ can be computed using ), 3) or 20), 7). Internally, the AP assumes that there are n individual virtual stations contending for a transmission opportunity each with access probability: v i = q i w = j p n n+ j= w T t n+ i T t = i w i T t i n j= w j. 3) T t j 3..3 Closed-form expression for the bargaining set Consider a multi-rate WLAN with two service classes, class and class 2, and weights w and w 2 respectively. Using the approximate WLAN model, we show that when all stations in the service classes use optimized contention window, the aggregate throughputs of the service classes, X, X 2 ), when evaluated for all feasible weights w and w 2 and plotted on an X -X 2 plane, closely follow a straight line whose slope is independent of the weights and is only a function of the bit rates of the links. We take advantage of this result in the CCRN scheme where separate service classes are assigned to the primary and secondary networks, and as a result, the bargaining game has a linear bargaining set. Assume only uplink traffic in the WLAN. Let the size and weights of class, class 2 be n, n 2 and r, respectively. Under weighted time fairness, the channel utilization is the same for every station within a class. We first show that there exists a linear relationship between the channel utilization of class and class 2. The channel occupancy time is approximated using 7), 22), 23): P ti e ζ p i = ζe ζ w i n w j. 32) j= T tj The approximate channel utilization of a station in class and class 2 using 8), 25), 23) and 32) is then: P ti u = n+n 2, i class 33) j= P tj T tj + P c T c + P idle T slot r rn + n 2 + κrα + α 2 ), 34) u 2 rn + n 2 + κrα + α 2 ), 35) where α j = i class j and κ = ζe ζ e ζ )T c + e ζ T slot ζe ζ, 36) is a constant for an 802. variant Table 2). Eliminating r from 34) and 35): n + κα )u + n 2 + κα 2 )u 2 =. 37) The aggregate throughput of class i, is X i = u i α i s d, i {, 2}, and by expressing u i in terms of X i in 37), we have the linear equation in X, X 2 that is independent of the weight ratio r and a function of α, α 2 ; where α i depends on the bit rates of the links in class i : n + κα α s d X + n 2 + κα 2 α 2 s d X 2 =. 38) With both uplinks and downlinks traffic in the WLAN, the corresponding expression for 37) is: [ + w d )n + κα ]u + [ + w d )n 2 + κα 2 ]u 2 =, 39) where α j = ˆα j + w d ˇα j, ˆα j = i class j, ˇα j = i class j T t i, j {p, s}. The corresponding expression in X, X 2 ) is + w d )n + κα s d α p X + + w d)n 2 + κα 2 s d α s X 2 =. 40) 3.2 Throughput Fairness in WLANs Under weighted throughput fairness constraint, the stations share their achievable throughput in proportion to their assigned weights. Therefore, any two stations i and j satisfy the condition: x i x j = P t i P tj = p i p j ) p j p i ) = w i w j, 4) where w i and w j are the assigned weights to stations i and j respectively. Comparing 4) and 8), weighted time fairness and weighted throughput fairness are equivalent upon rescaling the weights with the transmission time, i.e., P ti P tj = w i w j P t i P tj T tj = w i w j T tj, i, j {,..., n}. 42) Therefore, by replacing w i with w i in 3), the optimal contention window under weighted throughput fairness is obtained by the same expression in ) with λ k, k

7 7 {,.., n}, defined in 2) but with h j defined by: 3.2. Approximate WLAN Model h j = 2w j w i. 43) By replacing w i with w i in 7), the closed form expression for the approximate access probability p i is 20) with: τ i = w i n j= w j, 44) The closed form expression in 44) is identical to the expression for the optimal access probability in [8] whose WLAN model supports weighted throughput fairness for idle sense access method [7]. The only difference is that in [8] the value of ζ in 2) is calculated for the highest bit rate of the chosen 802. variant while ζ in our model applies for all the bit rates of the 802. variant Support for Downlink The condition for proportional throughput allocation is: P ti w i = P t j = Q t k = Q t l. 45) w j w d w k w d w l Using 28) and 45), the AP station n+) is in a separate service class with a service weight w n+ defined in 29) and transmission time defined by n i= T tn+ = w it t i n i= w. 46) i The access probabilities p,, p n+ is computed using ), 43) or 20), 44). Internally, the AP assigns the following probability to each station for their downlink traffic: v i = q i w = i p n n+ j= w. 47) j Closed-form expression for the bargaining set As in Section 3..3, we derive the linear relationship between the aggregate throughputs of class and class 2. Under weighted throughput fairness constraint, the perstation throughputs are equal within a class. Using 4) and 24), we have: n j= P ti = P t j n w j ζe ζ n w j, 48) j= w i j= w i With only uplink traffic in the WLAN, the per-station throughput for class and class 2 using 6) is approximated by: rs d x rβ + β 2 + κrn + n 2 ), 49) s d x 2 rβ + β 2 + κrn + n 2 ), 50) where β j = i class j. Eliminating r from 49) and 50): κn + β s d x + κn 2 + β 2 s d x 2 =. 5) The aggregate throughput of class i, is X i = n i x i, i {, 2}, and by expressing x i in terms of X i in 5), we have the linear equation in X, X 2 that is independent of r and a function of the bit rates of the links. With both uplink and downlink traffic in the WLAN, the counterpart expression for 5) is: κ + w d )n + β s d x + κ + w d)n 2 + β 2 s d x 2 =, 52) where β j = ˆβ j +w d ˇβj, ˆβ j = i class j, ˇβ j = i class j T t i and the resulting expression in X,X 2 ) is κ + w d )n + β + w d )n s d X + κ + w d)n 2 + β 2 + w d )n 2 s d X 2 =, 53) where X i = + w d )n i x i, i {, 2}. 4 CCRN SCHEME In this section we apply the models we developed in Sections 3 to the CCRN problem we consider. Under the CCRN scheme, a cellular operator acts as the primary network and offloads traffic to a secondary network that owns an AP. In exchange, the cellular operator leases an additional licensed) channel to the AP, effectively doubling the capacity of the AP. We assume that there are n s secondary users associated with the AP, and n p primary users that are initially cellular users, but which are in the range of the AP and will be offloaded to the AP if a suitable arrangement for both parties is found Fig. - ). In the rest of the section, we first determine a closedform expression for the bargaining set. We then find the connected closed-form expression for the bargaining point Nash solution). Finally, we give the closed-form expression for the service weights of the user classes at the bargaining point and present a method to determine a user distribution in the two WLAN cells that will result in aggregate throughput of primary and secondary network close to the bargaining point. 4. CCRN under Time Fairness The aggregate throughput of the individual networks before cooperation is the disagreement point, d = X d p, X d s ). Let cell and cell 2 denote the two WLAN cells Fig. - ) operating in the leased and the unlicensed spectrum respectively. A user, primary or secondary, can be instructed by the AP to associate to one of the two cells. The primary and secondary users in a cell belong to two different service classes; we name them class p and class s respectively. Note that under time fairness, the channel occupancy time of any two users within a service class are the same and so are their channel utilization 2. We 2. fraction of the time the station occupies the channel for a successful transmission of a packet.

8 8 place the following constraint on the channel utilization of the classes in the two cells: C: The channel utilization of a primary user secondary user) in cell is equal to the channel utilization of a primary user secondary user) in cell 2. This is the condition for cell fairness: two user having same bit rate we assume equal payload for all users) and belonging to the same class but placed in different cells will achieve same throughput 3. If we denote the target time ratio between class p and class s by r and the channel utilization of primary and secondary users by u p and u s respectively, then constraint C requires u p : u s = r : in each cell cell and cell 2 ). In Section 3..3, 39) gives the linear relationship between the channel utilization of two service classes in a WLAN cell. Rewriting 39) for each cell, cell and cell 2, and the two classes, class p and class s, we have: [ + w d )n p + κα p]u p + [ + w d )n s + κα s]u s =, 54) [ + w d )n 2 p + κα 2 p]u p + [ + w d )n 2 s + κα 2 s]u s =, 55) where n i j is the number of users of class j in cell i, i {, 2}, j {p, s}, αj i = ˆα j i + w d ˇα j i where ˆα j i = k cell i class j T tk is the sum of the reciprocal of uplink transmission times of all users of class j in cell i and ˇα j i = k cell i class j T is the sum of the reciprocal t k of downlink transmission times of all users of class j in cell i, w d is the predetermined weight for downlink traffic relative to uplink traffic and κ is a fixed constant given by 36) for the parameters defined in Table 2. The transmission duration, or T t i, depends on the bit rate of the link between the AP and station i, the parameters of MAC and PHY layers 802. a/b/g) and the data payload size s d. Hence expression in 54) and 55) are only a function of bit rates of the users, s d, and the WLAN variant employed 802.a/b/g/n). Adding 54) and 55): [ + w d )n p + κα p ]u p + [ + w d )n s + κα s ]u s = 2. 56) where α j = ˆα j + w d ˇα j, ˆα j = i class j, ˇα j = i class j T t i, j {p, s}. The aggregate throughput of the primary and secondary networks are 3 : Combining 57), 58) and 56): X p = u p s d α p, 57) X s = u s s d α s. 58) + w d )n p + κα p X p + + w d)n s + κα s X s = 2. 59) s d α p s d α s By denoting a p = + w d)n p + κα p s d α p, 60) 3. throughput of user i is u i s d where u i and are the channel utilization and transmission time of user i and s d is payload in bytes. the Nash bargaining problem is: a s = + w d)n s + κα s s d α s, 6) maximize X p X d p )X s X d s ) subject to a p X p + a s X s = 2, X p X d p, X s X d s. 62) Since the bargaining set B defined in 59) is a straight line, the Nash bargaining solution will be the mid-point of the bargaining range, B d = {X p, X s ) B X p Xp d, X s Xs d }, which is the line segment joining points ) Xp d, 2 apxd p a s and 2 asx d s a p, X d s ). The bargaining point Xp, b Xs) b is then: Xp b = Xp d + 2 a sx d ) s, 63) 2 a p ) X b s = 2 X d s + 2 a px d p a s. 64) From 57) and 58), r = up u s = Xpαs X sα p. Hence the target ratio between the classes at the bargaining point is: r b = ) Xp d + 2 asxd s a p α s ). 65) Xs d + 2 apxd p a s α p The ratio r b is the solution of the bargaining problem and can be computed using only the disagreement point and the bit rates of all users in the WLAN. The next step is to find a distribution of primary and secondary users in each cell that will result in an operating point of the system close to the Nash solution. At the bargaining point, using 54) and 55): [ + w d )n p + καp]r b + [ + w d )n s + καs] = u b, 66) s [ + w d )n 2 p + καp]r 2 b + [ + w d )n 2 s + καs] 2 = u b, 67) s where u b s is the channel utilization of a secondary user at the bargaining point. Hence, finding the user distribution is equivalent to solving the following partition problem: partition the n p + n s users into two subsets corresponding to each cell such that the sum of the weights in first subset equals the sum of weights in the other subset, where the weight for a primary user i is r b + w d + κ i is + w d + κ + w d T t i )) and for a secondary user + w d T t i )). The partition problem is NP complete, but there are efficient pseudo-polynomial algorithms for solving it [22]. We implemented the dynamic programming based algorithm in C and found the execution time to be less than 0.25 seconds for 40 users with a precision of 2 decimal digits. Algorithm summarizes the steps for finding the distribution of users in each cell and their channel access probabilities line

9 9 4) that would result in the operating point of the system close to the Nash solution. Algorithm CCRN Approach Inputs: R p, R s are the uplink and downlink bit rates of the primary and secondary users respectively; w is the preassigned weight of the downlink traffic relative to the uplink traffic; X d p, X d s ) is the disagreement point. : calculate r b using 65) for the inputs {R p, R s, X d p, X d s }; 2: using {R p, R s, r b, w} in the pseudo-polynomial algorithm, find the distribution, C b, C b 2, of the primary and secondary users in cell and cell 2, at the bargaining point. 3: find the corresponding optimal access probabilities, P b, P b 2, for the users in cell and cell 2 using the WLAN model in Section 3. 4: return C b, P b, C b 2, P b 2 ; operating point. 4.2 CCRN under Throughput Fairness For throughput fairness, we follow a similar approach as for the time fairness covered in Section 4.. The corresponding throughput fairness constraints within a class is: C2: The throughput of a primary user secondary user) in cell is equal to the throughput of a primary user secondary user) in cell 2. With this constraint, two users belonging to the same class, but placed in different cells, will achieve equal throughputs. As in the previous section, using C2, we can show that the relative weights between the classes in each cell are equal, and the corresponding linear relationship between the aggregate throughput of the primary and secondary networks, X p and X s, is: β p + κ + w d )n p + w d )n p s d X p + β s + κ + w d )n s + w d )n p s d X s = 2, 68) i class j, where β j = ˆβj + w d ˇβj, ˆβj = ˇβ j = i class j T t i. The method to compute the bargaining point Xp, b Xp), s throughput ratio between classes r b, and the corresponding user distribution while using C2 and 52) instead of 54) and 55) is similar to the method presented in Section Protocol Design In this section we show how to integrate the proposed CCRN scheme with a WLAN similar to current 802. systems. The AP first collects the bit rates of all the links for both primary and secondary users) in its WLAN 4. The AP then calculates the aggregate throughput for the primary and secondary network at the bargaining point using 63) and 64). It then queries the BS for 4. The bit rate of a user on its uplink and downlink can be obtained from the SINR or the rate adaptation algorithm at the respective sender end. This information is then communicated to the AP by leveraging the provisions provided in IEEE 802. for Wireless Network Management such as the 802.v amendment to 802.a/b/g/n. The amendment also allows configuration of client devices and can be used to configure the frequency channel and the contention window size of the client. the aggregate throughput it provides to the cellular users in WLAN coverage. The AP and BS will agree to cooperate only when there is an improvement in their aggregate throughput with respect to their disagreement point. Algorithm is then invoked and the AP broadcasts 4 the user assignment information along with the access probabilities of the users at the Nash solution. All users move to their assigned cell and operate at their assigned contention window size. The mechanism is repeated periodically thereby allowing the protocol to dynamically maintain the operating point of the system close to the Nash solution under varying user activities and channel conditions. All the the message exchanges during the bargaining process between the AP and the BS occurs over the wireline channel that connects them to the Internet Fig. ). 5 PERFORMANCE EVALUATION In this section we evaluate the performance of our proposed WLAN model in Section 3 and the CCRN scheme in Section WLAN Model Validation For the simulation experiments, we developed a discreteevent simulator that implements the standard 802. DCF no RTS/CTS) for each independently transmitting station. The simulator uses the MAC and PHY parameters of IEEE 802.b standard for a packet size of 500 bytes and each experiment is run for a simulation time of 200 seconds. The support for the other channel access mechanisms under consideration in the section are also built in this simulator. In Section 5.., we evaluate the performance of the proposed approximate WLAN model for time fairness by considering the first simulation scenario from Section V in [6]. In Sections 5..2 and 5..3, we compare the performance of the approximate WLAN model and the optimal WLAN model under both weighted time and weighted throughput fairness constraints. In Section 5..4, the correctness of the closed-form linear expression in X and X 2 40) and 53) derived in Sections 3..3 and respectively) are validated using the simulator. 5.. Time Fairness In this section we consider a 802.b WLAN with n stations where one slow station at Mbps competes with n fast stations all at Mbps and with time fairness constraint all n stations receive equal channel occupancy time) imposed on the WLAN. The performance of our approximate WLAN model is compared with: i) the optimal WLAN model in [6]; ii) The default 802. DCF backoff algorithm; iii) the proportional fair throughput allocation algorithm proposed by Banchs et al in [20]; iv) the idle sense algorithm in [7].

10 0 The following parameters are compared in Fig. 3: i) the aggregate WLAN throughput; ii) the average Jain fairness index [23] or the shortterm fairness) of the channel occupancy time computed using the sliding window method 5 in [24], [25]. Aggregate Throughput Mbps) Approximate Optimal 2.5 DCF Idle Sense.5 Banchs Total Stations Jain Fairness Index Approximate Optimal DCF Idle Sense Banchs Total Stations Fig. 3: Performance comparison of the five MAC algorithms under time fairness: aggregate throughput of the WLAN, short-fairness of the channel occupancy time. The experiment is same as scenario I in Section V of [6]. Fig. 3 confirms that the approximate WLAN model can achieve the same level of performance observed using the optimal WLAN model in [6] but at a greatly reduced computation cost note that Fig. 3 and Figures a and 2a in [6] are similar). Our approximate WLAN model is similar in nature and complexity to the work in idle sense [7] but applies to multi-rate WLANs. The access method proposed in idle sense [7] achieves throughput enhancement in multi-rate 802. WLANs, but compromises fairness as shown in Fig. 3 because the optimization is performed for an equivalent single-rate network Weighted Time Fairness Aggregate Throughput Mbps) Class Approximate Class 2 Approximate Class Optimal Class 2 Optimal Total Stations Jain Fairness Index Approximate Optimal Total Stations Fig. 4: Aggregate throughput per class vs. number of stations and, short-term fairness of the channel occupancy time under weighted time fairness. In this section we consider two service classes in a 802.b WLAN of size n with weights w = and 5. We fix the sliding window size to 20 n so that the window size varies with the WLAN size, n. w 2 = 0.5. Only one class is active in a station: half of the stations send class traffic, while the other half sends class 2 traffic; and within each class, half of the stations use Mbps bit rate to send packets while other half use Mbps. Figures 4a and 4b show the aggregate WLAN throughput of the two service classes and the short-term fairness of channel occupancy time measured using the modified sliding window method of Jain fairness index in [26]. The results for the optimal WLAN model Section 3.) for n > 20 is not shown due to the intractability of solving the polynomial in ) for n > 20. Fig. 4 shows that the approximate WLAN model agrees with the optimal WLAN model and that both the models achieve the desired time ratio : Weighted Throughput Fairness Aggregate Throughput Mbps) Class Approximate Class 2 Approximate Class Optimal Class 2 Optimal Class 802.e Class e Total Stations Jain Fairness Index 0.95 Approximate Optimal 802.e Total Stations Fig. 5: Aggregate throughput per class vs. number of stations and, short-term fairness of the channel access opportunities under weighted throughput fairness. Consider the same WLAN in Section 5..2 with weights w = and w 2 = 0.5 for the service classes this experiment is similar to the scenario in Figure 3 of [8]). In this experiment, the 802.e EDCA model in idle sense [8] is compared with both our WLAN models optimal and approximate) in Section 3.2. With 802.e, a throughput ratio of :0.5 between the classes can be obtained by setting CW [6, 48] for class and CW 2 [3, 93] for class 2 from [8]) in the simulator. In Fig. 5, the aggregate WLAN throughput for each service class and short-term fairness of channel access opportunities is computed. The results show that the approximate WLAN model agrees with the optimal WLAN model and that the models achieve the desired throughput ratio :0.5. The results also show that the aggregate throughput of the classes does not depend on the number of stations when using our WLAN models, while with 802.e the aggregate throughput decreases with an increase in the number of stations Linear Bargaining Set In this section, we use the simulator to compute the aggregate throughputs X, X 2 ) for the classes at different weights w, w 2 ), and show that the aggregate throughputs on the X -X 2 plane are well approximated by the linear expression ). Consider a multi-rate 802.b

11 WLAN with 8 stations each in class and class 2. In each service class, exactly two users use the same bit rate from the supported set of {, 2, 5.5, } Mbps. For simplicity, symmetric bit rates are assumed on the uplink and downlink of a user and the downlink to uplink traffic ratio is set to w d = 3. Consider 30 different logarithmically spaced values between 0. and 0 for the weight ratio r = w w 2. For each r, the contention window for the AP and the stations are computed using the approximate WLAN model. The aggregate throughput of the classes calculated using 7) and from the simulator are plotted in Fig. 6. With the bit rates of all the links known, the constant coefficients in 40) and 53) are calculated and the corresponding straight line expression in X and X 2 is shown in Fig. 6. As shown in Fig. 6, the realistic aggregate throughput of the classes obtained from the simulator is well approximated by the straight line in 40) and 53) within < 5% margin of error). X 2 Mbps) 3 2 Approximate Line Analytical Simulator X Mbps) X 2 Mbps) 2 Approximate Line Analytical Simulator 0 2 X Mbps) Fig. 6: Comparison of the optimal aggregate throughput of class and class 2 with the approximated linear equation under time fairness, and throughput fairness constraints. 5.2 CCRN Scheme In Section 5.2., we verify the optimality of the operating point obtained using our approach in Algorithm with the operating point obtained using the exhaustive search brute-force) method. Through the experiment we show that the optimality of the Nash solution obtained using our approach in Algorithm is largely unaffected despite the approximations used in the approximate WLAN model, closed-form expression for the linear bargaining set, and the pseudo-polynomial algorithm for finding the user distribution. Section quantifies the resulting improvement in the throughputs of the primary and secondary networks under the proposed CCRN scheme. For the experiments, we assume primary and secondary users are equipped with 2 antennas supporting two spatial streams. The AP of the secondary network is equipped with 4 antennas and uses 2 of them per cell or WLAN). The transmission power for a user is 7 dbm and for the AP is 20 dbm. The users and the AP use the following 802.n PHY settings in 5 GHz band: 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 500 bytes payload data per frame, and supported physical bit rates of {3, 26, 39, 52, 78, 04, 7, 30} Mbps [27]. The discrete event simulator is modified to support the 802.n PHY settings CCRN Solution Validation Consider a CCRN network with 8 primary and 8 secondary users in a IEEE 802.n WLAN. For simplicity, symmetric bit rates are assumed on the uplink and downlink of each user. In each service class class p and class s ), the users use a unique bit rate from the set {3, 26, 39, 52, 78, 04, 7, 30} Mbps. For the disagreement point, X d p, X d s ), the initial aggregate throughput of the primary network is set to 5 Mbps. The initial aggregate throughput of the secondary network is calculated using both the optimal and the approximate WLAN model in Section 3... For the operating point obtained in line 4 of Algorithm, the aggregate throughput of the primary and secondary networks are calculated analytically using 6) and shown in Fig. 7. Also, to replicate the real-time behavior of the CCRN, the operating point in line 4 of Algorithm is used as the input to the discrete event simulator. The aggregate throughput of the primary and secondary networks at the end of 200 seconds of simulation time is shown in Fig. 7. X s Mbps) Points in the Bargaining Set Brute Force Analytical Brute Force Simulator CCRN Analytical CCRN Simulator Disagreement Point details at baragining point X p Mbps) X s Mbps) Points in the Bargaining Set Brute Force Analytical Brute Force Simulator CCRN Analytical CCRN Simulator Disagreement Point details at baragining point X p Mbps) Fig. 7: Graphical representation of the bargaining problem along with the Nash solution when the optimal WLAN model and, the approximate WLAN model in Section 3 are used to calculate the channel access probabilities for the users line 3 of Algorithm and 2). The exhaustive search approach necessitates iterating through all possible distributions of primary and secondary users in the two cells. For each user distribution, the aggregate throughput of the primary and secondary networks, X p, X s ), are calculated for the target ratio r that satisfies the cell fairness constraint C. The aggregate throughput of the networks that maximizes the Nash product, X p X d p )X s X d s ), X p X d p, X s X d s, is the bargaining point. The target ratio r that maintains the constraint C between the cells can be obtained using 54) and 55): r = + w d)n s n 2 s) + κα s α 2 s) + w d )n 2 p n p) + κα 2 p α p). 69)

12 2 The steps in the brute-force approach are detailed in Algorithm 2 and the algorithm is run for the primary and secondary network under study in Fig. 7. As shown in Fig. 7, the aggregate throughput of the networks, X p,x s ), calculated for all user distributions in the two cells forms the bargaining set and has a straight line appearance 59) is the corresponding straight line equation). The operating point in line 0 of Algorithm 2 is used in the simulator and the aggregate throughput of the primary and secondary networks at the end of 200 seconds of simulation time is shown in Fig. 7 along with the analytically obtained bargaining solution in line 7 of Algorithm 2. Fig. 7 shows that the loss in optimality by using our approach Algorithm ) over the brute-force approach Algorithm 2) is negligible 6. Algorithm 2 Brute Force Approach Inputs: Same inputs as for Algorithm. : for each combination of users in cell and ce 2, C, C 2, do 2: calculate r using 69) for the inputs {C, C 2, R p, R s}; 3: find the corresponding optimal access probabilities for the users in each cell, P b, P b 2, using either the optimal or the approximate WLAN model in Section 3. 4: find the optimal aggregate throughput of primary and secondary users, X p, X s), using 6). 5: if Nash product is maximized then 6: C b, P b = C, P, C b 2, P b 2 = C 2, P 2 ; 7: X b p=x p, X b s=x s; 8: end if 9: end for 0: return C b, P b, C b 2, P b 2 ; operating point Performance Evaluation of CCRN Scheme To gain insight in the expected performance of the proposed CCRN solution, we evaluate the resulting improvement in throughputs of the primary and secondary networks while varying the number of primary users, as well as the initial throughput of the primary users before cooperation). The applicable bit rate for each uplink-downlink pair is derived based on the RSSI, which in turn is calculated according to the log distance path loss model with shadow fading Model D) defined by the Task Group n TGn) [28]. Under this model, a user must be within 80 meters on the average) from the AP to receive the minimum bit rate of 3 Mbps on their uplink and downlink. Consider a circular coverage region with the AP at the center and radius of the coverage set R set to 80 meters. Assume all the users in the coverage area receive at least the minimum bit rate on their uplink and downlink. Two types of user placements are considered in the coverage area: i) uniform: users are randomly positioned uniformly within the circular coverage area probability densities are: r 2r R, 0 r R, and θ 2 2π, θ 0, 2π]). 6. Note that there are significant gains in execution time when the approximate WLAN model is used in Algorithm over the optimal WLAN model when the number of users is large n > 20). ii) clustered: similar to uniform but half of the user population is within the inner circle of radius R 2 probability densities are: r R, r [0, R], and θ 2π, θ 0, 2π]). Percentage throughput improvement Primary Network Secondary Network n p Percentage throughput improvement Primary Network Secondary Network n p Fig. 8: Percentage improvement in the aggregate throughput of the primary and secondary users while varying the number of primary users and holding the number of secondary users constant n s=0) for uniform, and clustered placements. Using the simulator, we show the average and 90% confidence intervals in the throughput improvement of the networks after performing 000 simulation runs for the uniform and clustered user placement types. We assume an aggregate throughput of 5 Mbps for the primary users when served by its BS before cooperation). This is consistent with the average throughput of LTE macrocells instead of the peak rates). The downlink to uplink traffic ratio is set to w d = 3. In this section we present the results for time fairness. The results for throughput fairness are very similar only with a slightly lower value for the improvement as throughput fairness trades some cell capacity for increased fairness. Due to space limitations and the similarity of the results we do not present the throughput fairness results. The improvement in throughput for both the primary and secondary users when the number of cellular primary) users n p changes from 2 to 20 while the number of secondary users n s is held constant at 0 users is shown in Fig. 8. The percentage of improvement is considerably higher for the cellular users, as they start with a relatively low aggregate throughput of 5 Mbps. On average, the cellular users approximately double their throughput on the average by 00%) under the uniform placement type while their throughput improves by 50% on the average under the clustered placement type. The comparatively higher throughput improvement in the clustered placement is due to the presence of more primary users in close proximity to the AP and therefore having superior bit rates). While not as spectacular as for the primary users, the secondary WLAN) users also increase their throughput by approximately 40% under both placement types. The 90% confidence intervals show that the primary users experience a higher variability in the improvement because

13 3 their bit rate after the agreement depends considerably on the quality of their link to the AP. In contrast, for the secondary users, if they have a good link to the AP before agreement, they will maintain that good link after the agreement the converse is also true). Finally, the throughput improvement is relatively insensitive to the number of primary users. In fact the improvement is insensitive to the number of primary and secondary users. The explanation for this fact is that the bargaining point is chosen as a function of the aggregate throughput for both the primary and the secondary users. Those aggregate throughputs are, however, almost independent of the number of users. Fig. 9 shows the percentage Percentage throughput improvement Primary Network Secondary Network d X p Mbps) Percentage throughput improvement Primary Network Secondary Network d X p Mbps) Fig. 9: Percentage improvement in the throughputs of the primary and secondary users while varying the initial aggregate throughput of the primary users for uniform, and clustered placements. of improvement as a function of the initial aggregate throughput of the primary users. For this graph ten primary users and ten secondary users were considered, although, as mentioned before, the results are insensitive to the number of users. From Fig. 9 it is clear that as the initial aggregate throughput of the cellular users increases, the improvement resulting from cooperation becomes smaller and smaller, until, at about 40 Mbps under uniform placement type, the networks decide to operate at the disagreement point, i.e., they choose not to cooperate. The lack of an agreement due to reduced throughput after cooperation) can only happen if the primary users are better served by the cellular base station than by the access point. While this may happen for a particular combination of technologies e.g., a legacy 802.b AP for WLAN and LTE advanced for the cellular network with a relatively close base station), in general WLAN data rates are often higher than cellular data rates due to the reduced cell size and higher signal to noise ratio for WLANs. 6 RELATED WORK Resource allocation and spectrum trading are treated as two separate problems in the spectrum sharing model of cognitive radios [29]. Optimal resource allocation of frequency channels, channel access time, transmission power, throughput etc. between primary and secondary users hold the key to efficient spectrum sharing. Spectrum trading is the economic aspect of spectrum sharing, where secondary users pay for the leased channel. Existing literature used a combination of game theory, market theory and price theory to model the problems in optimal resource allocation and economic interactions [29]. CCRNs combine the spectrum sharing scheme with the physical layer cooperative communication technique in which one or more relay terminals are recruited to assist in the communication when the direct link suffers from severe signal fading [6]. The CCRN scheme in [5] uses Stakelberg games for optimal resource sharing between the primary link Stakelberg leader) and the secondary ad hoc network Stakelberg follower). The primary link optimizes its strategy lease time and amount of cooperation in terms of distributed space-time coding) to maximize its transmission rate, being aware that its decision will influence the strategy adopted by the secondary network, namely the transmission power expended for relaying the primary traffic. The work in [7] extends [5] to include a revenue/payment mechanism and a Stakelberg game is adopted to solve the joint problem of resource allocation and spectrum trading. The restriction of only one primary link in the system model of [5], [7] is addressed in [8], which extends the work in [7] to two co-located infrastructure based primary and secondary networks. The work in [5], [7], [8] employs a three phase TDMA based scheme for cooperation, where the primary traffic is broadcasted in phase, one or more secondary users are recruited to relay the traffic to the destination in phase 2 and the secondary users access the leased channel using TDMA in phase 3. The work in [3] proposes a CCRN scheme based on Stakelberg games for secondary users that employ slotted Aloha access method in phase 3. The work in [0] extends [5] to equip secondary users with multiple input multiple output MIMO) antennas. Since MIMO allows concurrent transmission of multiple independent data streams, the need for phase 3 is eliminated where now the secondary users cooperatively relay the primary traffic in phases and 2 while obtaining spectrum access opportunities for their own traffic. While [0] leverages the degrees of freedom DoFs) offered in the spatial domain, [2] exploits the DoFs provided by the orthogonal dimensions in quadrature phase shift keying QPSK). The secondary users employ in-phase binary phase shift keying I-BPSK) to relay the primary traffic and use the quadrature BPSK Q- BPSK) to transmit their own traffic. A two-phase FDMA scheme is proposed in [9], where the primary users grant secondary users exclusive access to a portion of their spectrum in exchange for cooperation. To the best of our knowledge, the current work is the first to propose a CCRN scheme for WLANs employing contention based access schemes such as IEEE 802. DCF.

14 4 7 CONCLUSION In this paper, we have investigated and proposed an implementation of the CCRN framework for IEEE 802. WLANs. In the proposed CCRN scheme, the mobile operator leases a channel from the licensed spectrum band to a privately owned WiFi AP, and in return, the mobile operator leverages the AP as cooperative relays to offload its Internet traffic. The cooperation between the primary cellular) and secondary WLAN) networks is analyzed using a two-player bargaining game where the utility function for the players are their respective aggregate network throughputs. We show that under fairness and optimal throughput constraints, the bargaining set for the bargaining game is a straight line whose slope only depends on the bit rates of the users. Calculating the Nash bargaining solution for a linear bargaining set is trivial, and the proposed CCRN algorithm determines the corresponding distribution of the users in the two WLAN and the service weights for the users at the Nash solution. The proposed computationally inexpensive WLAN model then calculates the contention window for each user that results in the operating point of the system close to the Nash solution. The simulation results verify the optimality of the operating point as well as quantify the benefits of employing the CCRN scheme in WLANs. REFERENCES [] 000x: More Spectrum Especially for Small Cells, in Presentation by QUALCOMM Inc., 203. [Online]. Available: [2] Enabling Spectrum Sharing and Small Cell Wireless Broadband Services in the 3.5 GHz Band, 203. [Online]. Available: [3] FCC Frees Up Vacant TV Airwaves for "Super WI-FI" Technologies, 202. [Online]. Available: [4] Google s Spectrum Database. [Online]. Available: com/get/spectrumdatabase/ [5] O. Simeone, I. 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Stamatakis, Optimal CWmin Selection for Achieving Proportional Fairness in Multi-Rate 802.e WLANs: Test-bed Implementation and Evaluation, in ACM WiNTECH, [27] H. Lee, Advanced Wireless LAN. InTech, 202, ch. 2: A MAC Throughput in the Wireless LAN. [28] T. Paul and T. Ogunfunmi, Wireless LAN Comes of Age: Understanding the IEEE 802.n Amendment, [29] S. Maharjan, Y. Zhang, and S. Gjessing, Economic Approaches for Cognitive Radio Networks: A Survey, Wireless Personal Communications, 20. Mani Bharathi Pandian is currently a Ph.D. candidate in the Department of Electrical and Computer Engineering at North Carolina State University under the supervision of Dr. Mihail Sichitiu and Dr. Huaiyu Dai. He received an M.S. degree from the same department in 20. His research focuses on cooperative cognitive radio networking in wireless local area networks. Mihail L. Sichitiu was born in Bucharest, Romania. He received a B.E. and an M.S. in Electrical Engineering from the Polytechnic University of Bucharest in 995 and 996 respectively. In May 200, he received a Ph.D. degree in Electrical Engineering from the University of Notre Dame. He is currently employed as an associate professor in the Department of Electrical and Computer Engineering at North Carolina State University. His primary research interest is in Wireless 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 from Tsinghua University, Beijing, China, in 996 and 998, respectively, and the Ph.D. degree in electrical engineering from Princeton University, Princeton, NJ in Currently he is an Associate Professor of Electrical and Computer Engineering at NC State University, Raleigh. His research interests are in the general areas of communication systems and networks, advanced signal processing for digital communications, and communication theory and information theory.