IEEE International Workshop on Recent Advances in Cognitive Communications and Networking

Reciprocal Spectrum Sharing Game and Mechanism in Cellular Systems with Cognitive Radio Users Pin-Yu Chen, Weng Chon Ao, Shih-Chun Lin, and Kwang-Cheng Chen, Fellow, IEEE Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan Email : {r98942052, r97942044, r97942056}@ntu.edu.tw, and [email protected] Abstract—To fully exploit Cognitive Radio (CR) techniques as secondary transmissions in exiting primary systems (PSs), especially cellular systems, we propose a cooperative spectrum sharing mechanism where CR users serve as relay nodes to enhance PS’s performance, and PS leases some portion of resources for CR users’ networking services by granting them radio access. Moreover, for CR users exposed to multiple licensed wireless service providers (WSPs), a further complicated spectrum sharing market is formed because not only WSPs compete for relay nodes, but also CR users compete for the released resources. We formulate such reciprocal behaviors as a threetier game and specify the additional configurations of control channel protocol to achieve the game equilibrium, where WSPs and CR users focus on maximizing their own utility functions. The results show a win-win solution that CR users are able to acquire radio access while enhancing PS’s performance, which offers the opportunities and incentive for CR deployments.

Fig. 1. System model. Solid lines are transmissions in the first phase and dashed lines are transmissions in the second phase.

I. I NTRODUCTION In recent years, cognitive radio (CR) [1], [2] has attracted tremendous attention as a promising technology to cope with inefficient spectrum usage due to its capability of dynamic adaptation to environmental changes. Since the unlicensed public spectrum such as WiFi band fails to support the proliferating wireless devices with the rapidly growing demand on networking services, mechanism for accommodating CR users to utilize licensed spectrum while guaranteeing primary system’s (PS’s) quality-of-service (QoS) is a must for nextgeneration wireless networking paradigms [3], [4]. To bridge the gap, we propose a novel cooperative mechanism for cellular systems with CR users by introducing a spectrum sharing market composed of wireless service providers (WSPs) (e.g. operators) and CR users. Originally, only licensed users, or primary users (PUs), are authenticated for spectrum access, but PUs may suffer from severe performance degradation due to channel fading, urging the incentive for cooperative transmission via CR users for performance enhancement. Therefore WSPs are willing to grant CR users radio access and lease some portion of resources to trade for cooperative relay, and CR users benefit from the cooperation for spectrum access from WSPs (e.g. Internet services). Consequently, the incentive for spectrum sharing resides in the reciprocal behaviors instead of payments or punishments, which is intuitively more feasible for CR deployments. The interactions among WSPs and CR users are investigated via game-theoretical approach [5], one of the most popular mathematical model for multiple entities aiming to maximize their own utility functions [6]. In this paper we formulate

the interactions as a three-tier game according to the service strategy of WSP and the relay strategy of CR user. The noncooperative game among WSPs avoids monopoly or oligopoly market leading to unfair spectrum sharing, the non-cooperative game among CR users guarantees optimal utility functions of CR users, and the Stackelberg game among the two parties ensures maximum payoff of WSPs. Note that the proposed mechanism is not only totally backward-compatible to existing cellular systems but also applicable to future system standards [7]–[9] with slight modification of control channel protocol. Cooperative spectrum sharing scheme has been discussed in [10], [11] to deal with relay node selection in a centralized manner, where the CR users are passively manipulated by PUs in a different networking paradigm consisting of one PS and secondary ad hoc networks, and it may provide no incentive for cooperative relay at the cost of power consumption. In [12], both PS and secondary network are infrastructure-based networks and the relay decisions are not involved. A three-tier game has also been formulated in [13], [14] among spectrum broker, WSPs and end users, however, the end users offer payments instead of cooperative relay for spectrum access. Note that distinct from the above scenarios, in this paper, a reciprocal spectrum sharing mechanism is firstly proposed for cellular systems embraced with emerging CR techniques, where the incentive for spectrum sharing is investigated and each CR user autonomously makes the relay decision by evaluating the power consumption and the released resources. The rest of this paper is organized as follows. We illustrate

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the system model and control channel protocol configuration in Sec. II. The three-tier spectrum sharing game is formulated in Sec. III. The game equilibrium is analyzed in Sec. IV. The results are shown in Sec. V regarding heterogeneity of WSPs. Finally, we conclude our contributions in Sec. VI. II. S YSTEM M ODEL AND P ROTOCOL C ONFIGURATION We assume there are NS CR users coexisting with NP WSPs depicted in Fig. 1, and both CR users and WSPs are rational and selfish in the sense that they manage to maximize their own utility functions. Without further specification the utility functions of WSPs and CR users are their achievable rates in the unit of bits/Hz per transmission. We consider the inter-system interference limited regime where WSPs possess separate spectrum bands. We divide the transmission period into three phases as illustrated in Fig. 2 (a). In the first phase, WSP transmits data to PUs and relay nodes, consuming α portion of time. Within the remaining 1 − α portion of time, 1 − β portion is required for relay transmission and the lasting β portion is released for spectrum access of CR users, which defines the second phase and the third phase, respectively. Throughout this paper, we consider slow flat Rayleigh fading and path loss for channel model. To facilitate the cooperative mechanism, additional control signal exchange is required between WSPs and CR users as illustrated in Fig. 2 (b). In the sequel we address the additional configurations of control channel protocol. Subscription. Leveraging CR techniques, CR users first listen to the reference signals broadcasted by all WSPs and subscribe to every WSP with information profiles including the transmitting power from ith CR user to jth WSP (denoted by Qij ) and channel status to neighboring PUs. WSPs estimate the channel gain between base station (BS) and possible relay nodes (denoted by |hjP S,i |2 ), and the channel gain between ith relay node and PU of jth WSP (denoted by |hjSP,i |2 ). Service announcement. After subscription, WSPs then announce the corresponding service strategies αj and βj as well as the necessary information for CR users’ relay strategies, namely NS , QjP , Qij , Wj , |hjP S,i |2 and |hjSP,i |2 , where QjP is the transmission power of jth WSP and Wj is the bandwidth of jth WSP. Relay decision. At the last step, each CR user autonomously decides an optimal relay strategy to transmit for a WSP according to the given information from all WSPs, and then CR user feedbacks the decision to all WSPs. In the third phase, CR users are authenticated to access the spectrum for networking services, where the resources are allocated by the corresponding WSP via time-sharing approach. Note that the third phase can be either in uplink (BS listens) or downlink (BS broadcasts) configuration. III. P ROBLEM F ORMULATION In this section, game theory is applied to characterize the spectrum sharing mechanism described in Sec. II. The complicated interactions of CR users and WSPs are formulated

Fig. 2.

(a) Frame structure. (b) Additional control channel signaling.

by a three-tier game with complete information since the information for strategy decision are available through control channel, which is the unique advantage of cellular systems. A. Non-cooperative game among WSPs We refer NP WSPs as irrelevant WSPs so that no coalitions occur, which thereby introduces a non-cooperative game among WSPs. The utility function of every WSP is defined as the achievable rate in a band-limited additive white Gaussian relay channel with noise power spectral density N0 . The utility function of jth WSP is the minimum transmission rate of the first and second phases, i.e., uW ¯ j β¯j RSP (Sj )}, j = min{αj RP S (Sj ), α

(1)

where RP S (RSP ) is the maximum transmission rate in the first (second) phase, Sj is the set including all relay nodes of jth WSP, and α ¯ j = 1 − αj (β¯j = 1 − βj ) is the complement of αj (βj ). Under the inter-system interference limited regime and cooperative relay scheme, we write   mini∈Sj |hjP S,i |2 QjP RP S (Sj ) = Wj log2 1 + , (2) N0 Wj ⎛ ⎞  |hjSP,i |2 Qij ⎠. RSP (Sj ) = Wj log2 ⎝1 + (3) N0 Wj i∈Sj

Note that RP S (Sj ) in (2) is confined by the relay node possessing the worst channel gain and transmission power so that every relay node is ensured to receive the data successfully. B. Non-cooperative game among CR users After the announcement of service parameters, each CR user simultaneously makes a relay decision and compete with other CR users for the released spectrum. The utility function of ith CR user relaying for jth WSP is the achievable rate of the third phase minus the the cost for transmitted energy uCR =α ¯ j βj Rji (Sj ) − c · α ¯ j Qij , i

(4)

where Rji (Sj ) is the achievable rate when αj = 0 and βj = 1, and c is the cost per unit transmission energy. Considering the time-sharing mechanism in the third phase, we have   j 2 i | Q |h W j j P S,i Rji (Sj ) = (5) log 1 + |Sj | 2 N 0 Wj because the spectrum is shared by |Sj | CR users who decide to relay for jth WSP, which leads to a non-cooperative game.

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C. Stackelberg game between WSPs and CR users In our proposed spectrum sharing mechanism, each CR user autonomously decides an optimal relay strategy based on the announced service strategies and other information provided by WSPs, which resembles a multiple-seller and multiplebuyer market. The interactions can be modeled by a Stackelberg game (also known as leader-follower game) where followers (CR users) take actions (relay strategies) after leaders’ (WSPs’) actions (service strategies). Denoting Ai as the action set of ith CR user in the coverage of NP WSPs, a strategic game NS , (Ai ), (uCR i ) among CR users is formed where uCR is a function of service strategies and actions of other i CR users (denoted by a−i ), namely, uCR i (ai , a−i , α, β, Sj ), where α, β ∈ RNP are the service strategies announced by NP WSPs. Similarly, a strategic game is also formed among WSPs with utility function uW j (αj , α−j , βj , β −j , Sj ). Note that Sj is also a function of αj , α−j , βj and β −j .

¯ j βj Wj log2 1 + Substituting Aj = α  N S pij into (6), cα ¯ j Qij and |Sj | = i=1 = uCR i

Theorem 1. (Existence of NE) [5] A strategic game N, (Ai ), (ui ) has a NE if, for all i ∈ N , the action set Ai of player i is a nonempty compact convex set of an Euclidian space, and the utility function ui is continuous and quasi-concave on Ai . Without loss of generality, we assume every CR user has the same action set, i.e., all CR users are exposed to NP WSPs. It is obvious that NE does not exit if every CR user adopts pure relay strategy. One CR user would benefit if other CR users determine to relay for specific WSPs for sure. However, for a finite strategic game, there exits an NE in mixed strategy by extending the strategic game. The existence of mixed strategy NE guarantees stable operating point(s) of a strategic game. Theorem 2. (Existence of mixed strategy NE) [5] Every finite strategic game has a mixed strategy NE. To solve the three-tier game, we first prove that the utility function of ith CR user is a strictly concave function with respect to pi ∈ RNP , the vector of the assigned probability for each relay strategy. Proposition 1. (Concavity of uCR i ) uCR is a strictly concave function with respect to pi , ∀ i. i Proof: From (4) and (5), we have   NP  |hjP S,i |2 Qij CR i Wj ui = α ¯ j βj pj log 1 + |Sj | 2 N0 Wj j=1 −

NP  j=1

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α ¯ j pij Qij .

(6)

NP NP   Aj pij Bj pij . NS i − p i=1 j j=1 j=1

For an element pij in pi , the first derivative is  NS i Aj i =1,i  =i pj ∂uCR i = 

2 − Bj , ∂pij NS i p  i =1 j

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(7)

(8)

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 NS i −2Aj i =1,i  =i pj ∂ 2 uCR i = < 0, 

3 ∂ 2 pij NS i p  i =1 j

∂ 2 uCR i = 0. ∂pij ∂pik j=k

IV. T HREE - TIER G AME A NALYSIS We analyze the Nash equilibrium (NE) of the three-tier game since NE is a fixed point of the best responses of all players in a non-cooperative game, i.e., no player can improve his/her utility function by a unilateral deviation from the NE.

|hjP S,i |2 Qij N0 W j

(9)

(10)

Regarding the Hessian matrix of uCR i , the entries on the diagonal are all less than zero while the entries off the diagonal are all zero, rendering uCR a strictly concave function with i respect to pi . To maximize CR user’s utility function, the optimal relay strategy is the solution of an optimization problem [15] in nonnegative orthant with equality constraint i maximize uCR i (p )

(11)

subject to p  0, 1 p = 1. T i

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From Proposition 1, due to the concavity the unconstrained solution is obtained by setting (8) = 0 and solving NS simultaneous equations, where   NS NS i ∗  Aj i =1,i  =i pj ∗ ∗ − pij , ∀ i. (12) pij = Bj   i =1,i =i

Regarding the axioms of probability, we further define ⎧ A 0, if θj > Bjj ⎪ ⎪  ⎨ Aj θj ∗ κij , if pij = Bj > 1 + θj (13) 

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NS i ∗ i i where θj = i =1,i  =i pj , κj and ψj are the normalization factors. It is easy to show that (13) satisfies the KarushKuhn-Tucker (KKT) condition [15] so that the optimal relay strategy is a feasible solution of (11), and hence the maximum transmission rate of a CR user is attainable. In addition to the existence of NE, we are interested in the uniqueness of NE in order to prevent the unappropriate operating points in the proposed spectrum sharing mechanism. Proposition 2. (Uniqueness of optimal relay strategy) The optimal relay strategies among NS CR users, p ∈ RNS ×NP is the unique NE.

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Proof: From Proposition 1, the utility function of every CR user is a strictly concave function, therefore p is the unique mixed strategy NE [5]. The uniqueness of NE can also be ∗ proved by verifying pij to be a standard function [16].

Fig. 6. Optimal service strategies of asymmetric case with W1 = 1M Hz, W2 = 2M Hz, W3 = 3M Hz, η = 4 and NS = 10.

In order to obtain β¯j∗ , we solve it by substituting the optimal relay strategy in (13) into uW j , a backward induction method which is often used to analyze the Stackelberg game. With ∗ (14), pij is a function of β¯j∗ , and β¯j∗ is hence the solution of the combinatorial optimization problem

∂ 2 uCR

Remark 1. Rigorously speaking, in extreme cases ∂ 2 pi i = 0 j  NS i if and only if i =1,i  =i Pj = 0, indicating that only ith CR user has the chance to relay for jth WSP. Without loss of generality, we consider the case NS  NP so that uCR is a i strictly concave function. We proceed to solve the optimal service strategies of WSPs. From [10], it is proved that uW = αj ∗ RP S (Sj ) = j ∗ ¯∗ α ¯ j βj RSP (Sj ), the condition that the first term and second term in (1) are equal to maximize transmission rate. We have β¯j∗ RSP (Sj ) , (14) αj∗ = RP S (Sj ) + β¯j∗ RSP (Sj ) β¯j∗ RP S (Sj )RSP (Sj ) uW . (15) j = RP S (Sj ) + β¯j∗ RSP (Sj )

¯ β¯j∗ = arg maxβ¯j ∈[0,1] uW j (βj ).

(16)

Consequently, we obtain the optimal service strategies αj∗ ∗ and βj∗ of WSPs and the optimal relay strategies pij of CR users. Moreover, to ensure the cooperative mechanism, the achievable rate of the proposed spectrum sharing mechanism must be larger than the direct transmission rate (αj = 1) to trigger the incentive for spectrum sharing, i.e, uW j > Rdir , where   2 |hjP | QjP (17) Rdir = Wj log2 1 + N0 Wj 2

and |hjP | is the channel gain between the BS of jth WSP and PU. We utilize (17) to evaluate the performance and the incentive of the proposed cooperative mechanism in Sec. V.

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To sum up, since uCR is a function of αj and βj , WSP first i announces optimal service parameters in order to maximize ∗ its payoff. CR user then decides an optimal relay strategy pij ∗ ∗ given service strategies αj and βj . Proposition 1 states that such relay strategy renders CR user maximum transmission rate while Proposition 2 guarantees the stability of operation. V. N UMERICAL R ESULTS The performance of our proposed spectrum sharing mechanism is evaluated for symmetric and asymmetric cases, where WSPs possess homogeneous and heterogeneous configurations, respectively. There are many configurations which lead to asymmetric case, here we specifically investigate the configuration that WSPs have different bandwidth but the same transmission power, while other parameter settings are consistent with that of symmetric case for comparison. We set c = 0.1, NP = 3 with identical BS coverage, and consider the case where NS CR users have normalized equal distances to the BSs. PU is located on the line between BS and CR user to simplify the analysis. The slow flat Rayleigh fading channel power gain is an exponential random variable with unit mean. The distance between PU and CR user (BS) is d (1−d) normal distance away, and regarding path loss exponent η we have E|hjP S |2 = 1, E|hjSP |2 = d−η and E|hjP |2 = (1 − d)−η . A. Symmetric case For symmetric case we have Wj = W , QjP = QP and = QCR due to homogeneity of WSPs and CR users. The transmission power is 46 dBm for BS and 10 dBm for relay node, and the noise power level is −102 dBm. In Fig. 3 we observe that all WSPs have the same achievable rates because they are identical, and the achievable rate decreases with the increase of d due to the marginal benefit from (1). When d ≈ 0.12, the direct transmission rate transcends the cooperative transmission rate, which is quite plausible because PU is far away from the cell edge, reducing the incentive for cooperative transmission. In case of severe path loss (larger η) or picocell (smaller QP ), the two lines intersect at larger d (d ≈ 0.2) due to severe performance degradation as shown in Fig. 4. In addition, when PU moves closer to the cell edge, WSP tends to require more cooperation (larger α) for higher transmission rate. Increasing α lessens β, and hence it contributes to lower transmission rate for CR users. Note that the optimal service strategies are identical for all WSPs due to symmetry. Qij

B. Asymmetric case The results in Fig. 5 reveal that WSP with larger bandwidth attains higher transmission rate, and both WSPs and CR users benefit from our proposed mechanism, especially at cell edges. The performance of PU is greatly enhanced via cooperative relay, and CR users are able to acquire networking resources in return. Note that in Fig. 6 the optimal service strategies are invariant of bandwidth, suggesting a stable economic market that the WSP with larger bandwidth is willing to release more resources. The intuitive interpretation is that our mechanism avoids the monopoly or oligopoly of WSPs by introducing the

competition among WSPs for relay nodes so that heterogeneity of WSPs does not distort the market, providing a fair and promising approach for CR deployments in cellular systems. VI. C ONCLUSION Our main contributions are twofold. First, we propose a reciprocal spectrum sharing mechanism between CR users and WSPs, where WSPs grant CR users radio access for cooperative relay in return. Additional configurations of control channel protocol are addressed to realize the cooperative mechanism. Second, we formulate the mechanism as a threetier game and analyze the game equilibrium. We prove the existence and uniqueness of the relay strategy that maximizes CR user’s achievable transmission rate, and we show that the incentive for the cooperative mechanism indeed exists since the PS’s performance can be greatly enhanced, especially for PUs suffering from severe performance degradation. This paper therefore offers novel avenues to practical spectrum sharing mechanism and protocol design toward CR deployments in next-generation wireless networking paradigms. R EFERENCES [1] J. Mitola, “Cognitive radio: An integrated agent architecture for software defined radio,” Ph.D. dissertation, KTH, Stockholm, Sweden, Dec. 2000. [2] S. Haykin, “Cognitive radio: brain-empowered wireless communications,” IEEE J. Sel. Areas Commun., vol. 23, no. 2, pp. 201–220, Feb. 2005. [3] S.-Y. Lien, C.-C. Tseng, K.-C. Chen, and C.-W. Su, “Cognitive radio resource management for QoS guarantees in autonomous femtocell networks,” in Proc. IEEE ICC, May 2010, pp. 1–6. [4] P.-Y. Chen, S.-M. Cheng, W. C. Ao, and K.-C. Chen, “Multi-path routing with end-to-end statistical QoS provisioning in underlay cognitive radio networks,” in Proc. IEEE INFOCOM Workshops, Apr. 2011, pp. 7–12. [5] M. Osborne and A. Rubinstein, A Course in Game Theory. MIT press, Cambridge, MA, 1999. [6] B. Wang, Y. Wu, and K. J. R. Liu, “Game theory for cognitive radio networks: An overview,” Comput. Netw., vol. 54, no. 14, pp. 2537–2561, Oct. 2010. [7] 3GPP TS 36.300 V10.0.0., “Evolved universal terrestrial radio access (E-UTRA) and evolved universal terrestrial radio access network (EUTRAN)”, Jun 2010. [8] K. Doppler, M. Rinne, C. Wijting, C. Ribeiro, and K. Hugl, “Deviceto-device communication as an underlay to LTE-advanced networks,” IEEE Commun. Mag., vol. 47, no. 12, pp. 42–49, Dec. 2009. [9] S.-Y. Lien, K.-C. Chen, and Y. Lin, “Toward ubiquitous massive accesses in 3gpp machine-to-machine communications,” IEEE Commun. Mag., vol. 49, no. 4, pp. 66–74, Apr. 2011. [10] O. Simeone, I. Stanojev, S. Savazzi, Y. Bar-Ness, U. Spagnolini, and R. Pickholtz, “Spectrum leasing to cooperating secondary ad hoc networks,” IEEE J. Sel. Areas Commun., vol. 26, no. 1, pp. 203–213, Jan. 2008. [11] J. Zhang and Q. Zhang, “Stackelberg game for utility-based cooperative cognitive radio networks,” in Proc. ACM MobiHoc, May 2009, pp. 23– 32. [12] Y. Yi, J. Zhang, Q. Zhang, T. Jiang, and J. Zhang, “Cooperative communication-aware spectrum leasing in cognitive radio networks,” in Proc. IEEE DySPAN, Apr. 2010, pp. 1–11. [13] J. Jia and Q. Zhang, “Competitions and dynamics of duopoly wireless service providers in dynamic spectrum market,” in Proc. ACM MobiHoc, May 2008, pp. 313–322. [14] S. Sengupta and M. Chatterjee, “An economic framework for dynamic spectrum access and service pricing,” IEEE/ACM Trans. Netw., vol. 17, no. 4, pp. 1200–1213, Aug. 2009. [15] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, Mar. 2004. [16] R. D. Yates, “A framework for uplink power control in cellular radio systems,” IEEE J. Sel. Areas Commun., vol. 13, no. 7, pp. 1341–1347, Sep. 1995.

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