A Pricing-Based Cooperative Spectrum Sharing Stackelberg Game

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1 A Pricing-Based Cooerative Sectrum Sharing Stackelberg Game Ramy E. Ali, Karim G. Seddik, Mohammed Nafie, and Fadel F. Digham? Wireless Intelligent Networks Center (WINC), Nile University, Smart Village, Egyt. Electronics Engineering Deartment, American University in Cairo, AUC Avenue, New Cairo 835, Egyt.? National Telecom Regulatory Authority (NTRA), Egyt Abstract In this aer, we study the roblem of cooerative sectrum sharing among a rimary user (PU) and multile secondary users (SUs) under quality of service (QoS) constraints. The SUs network is controlled by the PU through a relay which gets a revenue for amlifying and forwarding the SUs signals to their resective destinations. The relay charges each SU a different rice deending on its received signal-to-interferenceand-noise ratio (SINR). The rimary relay controls the SUs network and imize any desired PU utility function. The PU utility function reresents its QoS, which is affected by the SUs access, and its gained revenue to allow the access of the SUs. The roblem of imizing the rimary utility is formulated as a Stackelberg game and solved through three different aroaches, namely, the otimal, the heuristic and the subotimal algorithms. Index Terms Differentiated ricing, sectrum sharing, Stackelberg game. I. INTRODUCTION Cognitive radio (CR) is a romising technology which can enhance the sectrum utilization efficiency by allowing the secondary usage of the under-utilized licensed sectrum held by rimary users (PUs) [], [2]. To utilize the sectrum holes, cooerative sectrum sharing allows the secondary users (SUs) to make use of the PU licensed sectrum as long as their interference to the PUs does not exceed a redefined threshold set by the PU. In return, the PUs would earn some money or use the SU as a cooerative relay to imrove their transmission, so a win-win situation can be achieved. Game theory is a owerful tool which can be used to study and analyze the cometition between the users willing to access the sectrum [3], [4]. In [5], a cooerative sectrum sharing aroach was roosed in which the PU selects a set of SUs as the cooerative relays for its transmission. In return, the PU leases ortion of channel access time to the selected SUs for their own transmission. The access time of each SU is roortional to its contribution in the PU transmission. The SUs game is investigated as a non-cooerative game. In [6], a Stackelberg game [3] was considered, in which the PU lays the role of the leader and SUs are the followers. The rimary transmitter (PT) may select a secondary transmitter This work was suorted by a grant from the Egytian National Telecommunications Regulatory Authority (NTRA). Mohamed Nafie is also affiliated with the EECE Det., Faculty of Engineering, Cairo University. (ST) as a cooerative relay or not deending on the PT desired rate. The PU allows the access of the SUs to its sectrum art of the time in a random access manner. A ST should make a ayment to the PU deending on the robability with which it attemts to access the channel. The ST which is selected as a cooerative relay ays less than the other SUs. Thus a win-win situation can be achieved. In [7], a cognitive radio network of one PU, a relay and one SU was considered. A relay assisted sectrum sharing scheme based on the mixed sharing strategy was roosed, in which the ST adats its ower according to the sensing results of the PU sectrum. If the PT is sensed to be OFF, the ST transmits with a higher ower which imizes its rate. If the PU is sensed to be ON, the ST transmits with a ower below the interference threshold of the PU to the relay then the relay decodes and forwards the the ST signal to the SD. In [8], a cognitive radio network with multile SUs and one PU is considered. The SUs ower control roblem is formulated as a sum-rate imization roblem under PU and SU quality of service (QoS). A convex aroximation aroach is introduced through an iterative algorithm which aroximates this non-convex rate imization roblem as a geometric rogram. In this model the PU always transmits its data with a fixed ower and the SUs are assumed to be non-selfish, so they transmit their data according to the ower allocation vector which imizes the overall sum-rate. In [9], a traditional (non-cognitive) wireless relay network consisting of one relay node and multile source-destination airs was considered. Each user acts as a self-interested layer, which aims at imizing its own benefit by choosing the otimal transmit ower. The cometition among the users is modelled as a non-cooerative game. The relay can set rices to imize either its revenue or any desirable system utility, and the ayment of each user to the relay deends on the received signal-to-interference-and-noise ratio (SINR). In this model, the relay does not ensure a certain QoS to any of the users and the relay is mainly concerned about its revenue. In this aer, we consider relay-assisted cognitive radio with one PU, one rimary relay, and a network of N selfish SUs. The transmission of the SUs is established through the rimary relay which adots the Amlify and Forward (AF) [] relaying technique. The PU adats its transmit ower, the relay ower and control the SUs ower allocation through

2 PT ST ST2 STN g g g2 gn g Relay Fig. : System Model h h h2 hn PD SD SD2 SDN the relay to imize its utility function. Secifically, the relay adots the differentiated ricing technique roosed in [9] to enforce all SUs to transmit with some desired ower levels that imize the PU utility. The PU utility function is defined such that it catures the interest of the PU to imize its QoS and the gained revenue from allowing the SUs to access its sectrum. The main contributions of this work are summarized as follows: We formulate the cooerative sectrum sharing ower control roblem as a Stackelberg game between the PU and the SUs. We roose a combinatorial otimal ower control solution for the roblem of imizing the PU utility under a minimum SUs QoS requirements. We also roose a simle heuristic real-time algorithm, which allows the access of a imum of one SU. Finally, we roose a low comlexity subotimal scheme which may allow more than one SU to access the sectrum. The rest of this aer is organized as follows. In Section II, we resent the system model. In Section III, we formulate the roblem of imizing the PU utility function as a Stackelberg game. Simulation results are resented in Section IV. Finally, concluding remarks are drawn in Section V. II. SYSTEM MODEL We consider a rimary network comosed of a PT, its intended destination (PD) and a relay (R). In addition, we consider a secondary network with N source-destination airs (ST, SD). Fig. deicts the system under consideration. Transmission is divided into two slots (one frame). The first slot is used by all STs to transmit their signals to the relay. The i- th ST, denoted by ST i, transmits with a ower i, while in the second slot, the relay amlifies and forwards the received signals from all STs with a ower R to their destinations. The PU transmits with ower in the first slot and with ower in the second slot in which its transmission is subjected to the relay interference. We assume a Rayleigh flat-fading channels, which means that the channel gain of a link remains constant during one frame (two time slots). Secifically, we denote the coefficients for PT-PD channel by g, PT-R and the R-PD channels by g and h, the ST i -R and the R-SD i channels by g i and h i, resectively. The direct links between ST i -SD i, ST i -PD and PT-SD i are neglected due to shadowing and the too large searation [9], []. We assume that each SU i has a imum ower of i. We also assume that the relay has a variable ower R and a imum ower of R, unlike the assumtion in [9] which assumes that the relay always transmits with a fixed ower level. We also assume that the relay has comlete information about the network, i.e., channel gains and imum ower constraints. The received signal at the relay can be exressed as y R = g x + g j j x j + n R, () j= where x is the unit-ower transmit signal from PT to PD in the first slot, x j is the unit-ower transmit signal from ST j to SD j and n R is zero-mean additive white Gaussian noise (AWGN) with variance N. The received signal at the i-th SU s destination (SD i ) can be exressed as y i = h i y R + n i i =,,N (2) where n i is zero-mean AWGN with variance N and is the amlification factor and is given by s R = P N j= g. (3) j 2 j + N o We can exress the received SINR at the i-th SU destination, i(), as i() = g i 2 h i 2 R i PN, g i 2 N o i +( h i 2 R + N o ) j=,j6=i g j 2 j + N o where is the ower allocation vector, which is defined as =[,,, N, R ] T. The rate at which the i-th SU transmits is given by (4) R i = 2 log( + i) nats/sec (5) where the scaling factor /2 is due to the fact that each SU transmits its data to the relay and remains silent in the next slot while the relay forwarding its data to the corresonding In the second time slot, the PU must transmit using its imum ower to imize its rate.

3 destination. We can also define the SUs s sum rate R as follows R = R i nats/sec. (6) i= The received signal at the PD in the first time slot can be exressed as y = g x + n, where n is zero-mean AWGN with variance N. The SINR at the PD in the first slot,, is then given by = g 2 N o. (7) The received signal at the PD in the second time slot can be exressed as y 2 = g x 2 + h y R + n, (8) where x 2 is the unit-ower transmit signal from PT to PD in the second slot. Similarly, the SINR at the PD in the second slot, 2, is given by The PU rate can be averaged as follows. 2 = g 2 N o + R h 2. (9) R = 2 (log( + ) + log( + 2 )) = 2 log(( + )( + 2 )) = 2 log( + e ) nats/sec, where e is the PU effective SINR and is given by The imum SINR of the PU, () e = (), is defined as = g 2. (2) N Thus, we can also define the PU rate when all SUs are inactive, which is an uer bound for R as R = log + g 2 nats/sec. (3) N III. STACKELBERG GAME ANALYSIS The roblem of imizing the PU cost function can be addressed as a Stackelberg game. The PU, which owns the licensed sectrum, lays the role of the leader and the SUs are the followers of this game. The PU selects the value of a weight arameter (w ),, R and the rices vector ( ), which contains the rice that each SU i will charge to access the sectrum, then each SU i selects its transmit ower i accordingly in a non-cooerative game. Our objective is to get the Nash Equilibrium (NE) for this Stackelberg game, where neither the PU nor any of the SUs have incentive to deviate unilaterally from this NE oint (Stackelberg Equilibria). The PU may be concerned with its QoS rather than its gained revenue from the secondary network or vice versa. Hence, the PU utility function, U, can be defined as U = w ( + )( + 2 )+R v, (4) where w is a weight arameter that converts the term ( + )(+ 2 ) into currency. The term (+ )(+ 2 ) can be interreted as e 2R or as (+ e ).The arameter w controls the PU trade-off between its QoS and its gained revenue, and it ranges from zero, where the PU only cares about the revenue it gets from the secondary network, to infinity, where the PU only cares about its QoS. The SUs ayment is a reimbursement of the PU SINR or QoS degradation caused by the SUs. The term R v is the PU revenue gained from the secondary network and can be exressed as R v = i= i i, (5) where i is the rice for SU i set by the PU. The non-cooerative SUs level game, G SUs is defined as G SUs =, {P i } i2, {U si } i2, (6) where is the set of all SUs and P i is the allowable ower strategies of the SU i which is defined as P i = { i :ale i ale i }. The term U si is the SU i cost function which is defined as U si = w s R i i i, (7) where w s is a factor that converts the rate units to currency. For simlicity, it is assumed that w s =in the following analysis. The term i i reresents the secondary ayment to the PU for allowing this SU i to access the sectrum, which is a function of the received SINR, i. In [9], it is roved that the relay can set its rices according to equation (8), to enforce the NE [4] of G SUs to any desired NE, i.e, obligate all SUs to send according to any desired ower allocation vector. i = 2( + i ( )) i =,,N, (8) where =[,,, i,, N, R ] T. In our analysis, we select as the solution of the rimary utility imization roblem, i.e; is the PU ower level that imizes U, i is the ower of the SU i that imizes U and finally R is the rimary relay ower level which imizes U. Based on the above definitions, the rimary utility can be written as U = w ( + )( + 2 )+ i= i() 2( + i ()) = w ( + g 2 N )( + g 2 N + h 2 ) R g i 2 h i 2 i R + 2(N + h i 2 R )(N + P N j= g j 2 j ) i= (9)

4 and the roblem of imizing the PU utility function can be formulated as follows. subject to U This roblem can be rewritten as i ale i,i=,...,n i i th, i =,...,N R ale R. min /U subject to i / i ale, i=,...,n i th / i ale, i =,...,N R / R ale. (2) (2) After some simlifications, we can write the objective function as a osynomial over osynomial. We can aroximate the osynomial in the denominator into a roduct of monomials, hence, the roblem can be converted in to a geometric rogram [2], [3]. We will erform this convergence using the iterative algorithm roosed in [8]. If the roblem is infeasible, the rimary relay can ban all SUs from accessing the PU sectrum. In this case, the PU will transmit with a fixed ower deending on the assumtion made in [8] which is not always otimal for the PU utility function to be imized as will be exlained later. To ban SU j from accessing the sectrum, the relay can simly set its rice to j 2, so the best resonse of SU j is to send with a zero ower level as has been roved in [9]. Next, we roose three different aroaches, namely, the otimal, the heuristic and the subotimal algorithms to imize the rimary user s cost function. A. The Otimal Scheme: Instead of banning all SUs from accessing the sectrum, we can allow a subset of them to access the sectrum. This subset is selected so as to imize the PU utility function. We should note that it may not be ossible to find a subset of SUs to allow their access such that all constraints are satisfied, i.e., emty set case and in this case no SU will access the sectrum. The new otimization roblem can be written as s 2S min /U subject to i / i ale, i2{ [ s} i th / i ale, i 2 s R / R ale, (22) where S is the set of all subsets of SUs, including the emty set { }, which means that the PU will access in the absence of any SU transmission. Each SU has a QoS constraint and if it cannot be satisfied the rimary relay will ban this SU from accessing the channel. Moreover if the access of the i-th SU contradicts with imizing the rimary user utility, the relay will also ban this SU by setting a high rice i 2 for this SU. Hence, this SU i best resonse in this case is to not access the channel, i.e, i =. Otimization over s can be accomlished combinatorially. Each user is reresented by a binary value which indicates its state, i.e., active or inactive. Active SU will be indicated by and inactive SU will be indicated by zero. The ossible states are the combination of N binary values with a imum of 2 N ossibilities. Otimization over is done using the same technique used in roblem (2). It is clear that the otimal scheme comlexity grows exonentially as N increases. The solution of this roblem is the desired ower allocation vector and then the otimal rices can be calculated through equation (8). We denote the imum value of U calculated through roblem (22) as u, which is the imum utility that can be achieved by any scheme. B. The Heuristic Scheme: The otimal scheme, which we have discussed above, becomes more comlicated as N increases. Here, we resent a simle heuristic scheme which is suitable for real time imlementation. In this scheme, the relay chooses only the best SU to access the PU sectrum and bans all other SUs. The best SU is defined as the SU with the imum harmonic mean (µ H ) 2 of the instantaneous channel gains g i 2 and h i 2 which can be defined as [4]: µ Hi = 2 g i 2 h i 2 g i 2 + h i 2. (23) The PU utility when all the SUs are inactive, dented by u P, can be exressed as follows. u = w ( + ) 2. (24) The PU imum utility in case that the best SU j is the only SU that accesses the channel (u ) can calculated through the following otimization roblem. subject to U ale j ale j j j th R ale R. (25) Hence, we can use Algorithm. to calculate the imum PU utility, (u H ), for the roosed heuristic aroach. Define the relative PU utility achieved by the heuristic scheme with resect to the otimal scheme, which indicates how near is the heuristic scheme from the otimal scheme as follows. r H = u H u. (27) 2 The subscrit H is used throughout this aer to indicate the heuristic scheme.

5 Algorithm : Calculate u using (24). 2 Calculate µ Hi for each SU i using (23). 3 Find the SU with the imum harmonic mean, j. 4 Calculate u through (25). 5 Calculate u H as follows u H = (u,u o ). (26) the PU to access the sectrum, also define the vector â as follows â =[â, â 2,, â N ]. Without loss of generality, we assume that the vector â is sorted in descending order, i.e, â â 2 â N. After finding the vector â using (29), we can use Algorithm. 2 to find the subotimal imum value of the PU utility, u S. 3 : C. The Subotimal Scheme: Here, we resent a simle subotimal algorithm. The comlexity of this subotimal scheme is a linear function of N, unlike the otimal scheme which has an exonential comlexity. Moreover, the erformance of the roosed subotimal scheme lies between that of the otimal and the heuristic schemes as will be shown in Section IV. Unlike the heuristic scheme, the subotimal scheme may allow more than one SU to access the sectrum. The subotimal scheme can be described as an incremental admission olicy, in which the PU gradually adds the SUs one after one according to a certain list rovided that adding more SUs will cause an increase in the rimary utility. The roblem of imizing U can be reformulated as follows.,a w ( + )( + 2 )+ i= subject to i / i ale, i =,...,N a i ( ith / i ()) ale, i =,...,N a i (a i ) =, i =,...,N i(a) 2( + i (A)) R / R ale, (28) where =[,, 2,, N, R ] T is the ower allocation vector, a i is a binary variable and the matrix A is a diagonal matrix with diag(a) =[, a,,a i,, ]. The binary variable a i controls the SU i QoS constraint; if a i =this means that SU i will access the sectrum and its QoS is guaranteed, otherwise it will not access. Unfortunately, the binary constraint is a non-convex constraint. This roblem can be relaxed into the following rogram which can also be solved using the algorithm roosed in [8]:, w ( + )( + 2 )+ i= subject to i / i ale, i =,...,N â i ( ith / i ()) ale, â i ale i =,...,N i =,...,N i(â) 2( + i (Â)) R / R ale, (29) where  is the aroximate value of A calculated after the relaxation (29). Define the set Ŝ as the SUs selected set by Algorithm 2: Initialize Ŝ = {;}. 2 Calculate u using (24). for k=,..,n do o Solve (3) for S = nŝk [ k and find u k imum value of the objective function. if u k <u k then u S = u k break; end if Ŝ k = S u S = u k end for U subject to i ale i,i2{[ S} i() i th, i 2 S R ale R. which is the (3) Similarly, we define the relative utility of the subotimal scheme with resect to the otimal scheme, which indicates how near is the subotimal scheme from the otimal scheme, as follows r S = u S u (3) IV. SIMULATION RESULTS In this section, we resent some numerical simulation results related to the erformance of the roosed schemes. Simulations are done using the GGPLAB simulator [5]. We assume a secondary network of three users (i.e., N = 3), =2Watt, R = Watt, i =Watt, N = Watt, E[ g 2 ]=.8, E[ g i 2 ]=E[ h i 2 ]=.8 8i =,,N and E[ g 2 ]=E[ h 2 ]=ce[ g 2 ], where c is a arameter that indicates the relation between the distance between the PT and the relay and the distance between the PT and the PD. The minimum SU QoS requirement th = db for all SUs. We investigate the following interference scenarios ) Weak Interference Case (c =.) This means that the distance between the PT and the relay is 3 times the distance between the PT and the PD. 3 The subscrit S is used throughout this aer to indicate the subotimal scheme.

6 .35 PU Rate R H R R S Sum Rate R R S R H.3 R w Fig. 2: Primary User Rate as a function of w,(c =5) w Fig. 4: SUs sum rate as a function of w,(c =5) PU Revenue w R vh R v R vs Fig. 3: Primary User Revenue as a function of w,(c =5) Relative Utility r H (c =.) r S (c =.) r H (c =5) r S (c =5) r H (c = ) r S (c = ) w Fig. 5: Relative Utility as a function of w 2) Moderate Interference Case (c =5) This means that the distance between the PT and the relay is 2 times the distance between the PT and the PD. 3) Strong Interference Case (c =) This means that the distance between the PT and the relay is the same as the distance between the PT and the PD. In Fig. 2, we show that the PU rate is an increasing function of w. Clearly, as w increases, the PU utility function sets more weight to the term ( + )( + 2 ) and hence, the PU rate will increase. It should be noted that as w increases the PU rate converges to the imum PU rate achieved when all SUs are inactive, R. In Fig. 3, we show the rimary revenue as a function of the arameter w, which is a decreasing function of w. As w increases the PU becomes more concerned with its rate rather than its secondary network revenue. It is clear that there is a trade-off between the PU rate and PU revenue and this trade-off can be controlled by the arameter w. In Fig. 4, we show that the SU sum rate is decreasing of w. As w increases, the robability of allowing the SUs access decreases since the PU cares more about its achieved rate; this will result in a decrease of the SU sum rate as w increases. In Fig. 5, the relative utilities, r H and r S, are shown as function of w for different values of the arameter c. From that figure, it is clear that the subotimal scheme outerforms the heuristic scheme because the subotimal scheme may allow more than one SU to access the sectrum, unlike the heuristic scheme, which allows a imum of one SU to access the medium. It is also obvious that the closeness of the subotimal and heuristic schemes to the otimal scheme

7 w = w = w = w = Fig. 6: The Histogram as a function of w, (c =5) Fig. 7: The Histogram, (w =) c =. c = is almost not affected by the variation of the arameter c. In Fig. 6, the occurrence of the different states under the otimal scheme with different values of w is shown, where a state is defined by the number of SUs allowed to access the medium. At low values of w, the PU ermits the access of more SUs since again in this case the PU cares more about it secondary network revenue, whereas at high values of w, nearly all the SUs are not allowed to access the sectrum most of the time as the PU cares more about its rate. In Fig. 7, the occurrence of the different states under the otimal scheme for different values of c is shown. It is clear that when the arameter c equals (Strong Interference) the robability that PU will allow the access of the SUs decreases, as their access in this case significantly affects the PU s transmission. The secondary transmission is also significantly affected by the rimary transmission in this case. V. DISCUSSION In this aer, we have studied a cognitive radio system with one PU, one rimary relay and N SUs, in which the PU can control the secondary network through its relay to imize its desired utility function. Each SU has a QoS constraint and if it cannot be satisfied or it is not beneficial for the PU to allow the access of this SU, this SU will not access the channel. We have investigated the PU trade-off between its achieved QoS and its gained revenue to allow the access of the SUs to its licensed sectrum. We have roosed an otimal ower control scheme, which has an exonential comlexity in terms of the number of secondary users; therefore, we have also roosed a simle heuristic scheme and a subotimal scheme which has a linear comlexity in terms of the number of the secondary users which achieves a erformance that is very close to the otimal scheme. Finally, we have investigated the erformance of these schemes relative to the otimal scheme under various interference scenarios, we have concluded that the closeness of these schemes to the otimal scheme is almost the same regardless of the interference scenario. REFERENCES [] I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty, Next generation/dynamic sectrum access/cognitive radio wireless networks: a survey, Comuter Networks, vol. 5, no. 3, , 26. [2] S. Haykin, Cognitive radio: brain-emowered wireless communications, IEEE Journal on Selected Areas in Communications, vol. 23, no. 2,. 2 22, 25. [3] M. J. Osborne, A course in game theory. Cambridge, Mass.: MIT Press, 994. [4] M. Felegyhazi and J.-P. Hubaux, Game theory in wireless networks: A tutorial, Technical Reort LCA-REPORT-26-2, EPFL, Tech. Re., 26. [5] H. Wang, L. Gao, X. Gan, X. Wang, and E. Hossain, Cooerative sectrum sharing in cognitive radio networks: A game-theoretic aroach, in IEEE International Conference on Communications (ICC). IEEE, 2,. 5. [6] X. Hao, M. H. Cheung, V. W. Wong, and V. C. Leung, A stackelberg game for cooerative transmission and random access in cognitive radio networks, in Proceedings of IEEE, PIMRC, 2, [7] Z. Wang, W. Zhang, and K. Ben Letaief, Relay assisted sectrum sharing in cognitive radio networks, in 22 IEEE International Conference on Communications (ICC). IEEE, 22, [8] S. Singh, P. D. Teal, P. A. Dmochowski, and A. J. Coulson, Interference management in cognitive radio systemsa convex otimisation aroach, in 22 IEEE International Conference on Communications (ICC). IEEE, 22, [9] S. Ren and M. van der Schaar, Pricing and distributed ower control in wireless relay networks, IEEE Transactions on Signal Processing, vol. 59, no. 6, , 2. [] J. N. Laneman, D. N. Tse, and G. W. Wornell, Cooerative diversity in wireless networks: Efficient rotocols and outage behavior, IEEE Transactions on Information Theory, vol. 5, no. 2, , 24. [] B. Rankov and A. Wittneben, Sectral efficient rotocols for halfdulex fading relay channels, IEEE Journal on Selected Areas in Communications, vol. 25, no. 2, , 27. [2] S. P. Boyd and L. Vandenberghe, Convex otimization. Cambridge university ress, 24. [3] S. Boyd, S.-J. Kim, L. Vandenberghe, and A. Hassibi, A tutorial on geometric rogramming, Otimization and engineering, vol. 8, no., , 27. [4] M. D. Sringer, The algebra of random variables. Wiley New York, 979. [5] A. Mutacic, K. Koh, S. Kim, L. Vandenberghe, and S. Boyd, Gglab: a simle matlab toolbox for geometric rogramming, web age and software: htt://stanford. edu/boyd/gglab, 26.