Primary User Enters the Game: Performance of Dynamic Spectrum Leasing in Cognitive Radio Networks

Transcription

1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO., DECEMBER 365 Primary User Enters the Game: Performance of Dynamic Sectrum Leasing in Cognitive Radio Networks Gonzalo Vazquez-Vilar, Student Member, IEEE, Carlos Mosquera, Member, IEEE, and Sudharman K. Jayaweera, Senior Member, IEEE Abstract Dynamic sectrum leasing DSL) is one of the schemes roosed for dynamic sectrum sharing DSS) in cognitive radio networks. In DSL, sectrum owners, denoted as rimary users, dynamically adjust the amount of secondary interference they are willing to tolerate in resonse to the demand from secondary transmitters. In this corresondence we investigate how much can be gained by rimary users if this limited interaction with secondary system is allowed, comared to a scheme in which the interference ca allowed by rimary users is fixed arioriby a regulatory authority. To that end, we define erformance metrics for both rimary and secondary systems based on the theoretically achievable multiuser sum-rate of the secondary system and analyze both schemes behavior with resect to different system arameters. This analysis shows that i) in dynamic environments DSL based schemes may resent an imortant advantage over other schemes with fixed interference constraints, and ii) DSL schemes are robust against inaccurate arioriinformation that may degrade system erformance. Index Terms Cognitive radio, DSL, dynamic sectrum sharing, dynamic sectrum leasing, game theory, multiuser decoding. I. INTRODUCTION RECENT studies [], [] have showed that the aradox of aarent scarcity of radio sectrum while most of the bands are underutilized occurs mainly due to the inefficiency of traditional static sectrum allocation olicies. This has romted roosals for various dynamic sectrum sharing DSS) aroaches, such as dynamic sectrum leasing DSL) [3] [5]. As oosed to assive sectrum sharing by the rimary users considered in many revious DSS roosals, leasing, as roosed in [3] [5], means that the rimary users have an incentive e.g. monetary rewards as leasing ayments) to allow secondary users to access their licensed sectrum. Therefore, the rimary user lays an active role in interference management and dynamically controls how much interference Manuscrit received June 7, ; revised Setember, ; acceted Setember 5,. The associate editor coordinating the review of this letter and aroving it for ublication was C. Cordeiro. G. Vazquez-Vilar and C. Mosquera are with the Deartamento de Teoría de la Señal y Comunicaciones, Universidad de Vigo, 363 Vigo, Sain {gvazquez, mosquera}@gts.tsc.uvigo.es). S. K. Jayaweera is with the Deartment of Electrical and Comuter Engineering, University of New Mexico, Albuquerque, NM 873-, USA jayaweera@ece.unm.edu). This research was suorted in art by the Sanish Government and the Euroean Regional Develoment Fund ERDF) under rojects SPROACTIVE ref. TEC C-/TCM) and COMONSENS CONSOLIDER- INGENIO CSD8-). University of New Mexico s contribution was suorted by the Air Force Research Laboratory AFRL) Sace Vehicles Directorate. Digital Object Identifier.9/TWC /$5. c IEEE must be allowed from the secondary system. In DSL the rimary user is assumed to adat its interference ca IC), denoted by Q [, Q ], which is the maximum total interference the rimary user is willing to tolerate from secondary transmissions at any given time. While in [4], [5] we roosed a game theoretical framework in order to model and analyze a ractical DSL scheme, in this work we are interested in the best erformance achievable by a general DSL scheme. Hence, we investigate the erformance imrovement that can be exected by a DSL based aradigm with resect to assive sectrum sharing schemes which do not allow dynamic rimary-secondary network interaction based on roactive rimary systems. The roosed analysis results into a Stackelberg game formulation of the interactions between rimary and secondary systems. Stackelberg games have been reviously used to model cognitive radio systems. A cooerative scheme in which secondary users actively collaborate with the rimary user transmissions was roosed in [6]. However a high degree of awareness and global synchronization is required by the two in rincile heterogeneous systems. A Stackelberg game formulation is also used in [7], [8] to describe the high level interactions within the network. However these works do not consider hysical layer issues such as modulation used or imact of the rimary / secondary interference in the attainable rates of the system. As oosed to revious works, in the resent corresondence we use erformance metrics based on the multiuser sum-rate attainable by the secondary system. We choose this erformance metric because it is a fundamental limit against which ractical schemes can be comared, while it is indeendent of articular DSL imlementations. Most information theoretic work on the cognitive radio channel assumes a certain amount of knowledge by the secondary system on the transmitted rimary codeword that allows the use of dirty aer coding by the secondary system see i.e. [9]). In this work, however, we relax this assumtion and treat rimary transmission urely as noise. The rest of this aer is organized as follows: In Section II we introduce a signal model and the assumed decoding strategies emloyed by rimary and secondary users. Next, in Section III we roose a general family of erformance metrics for both rimary and secondary users and quantitatively show the erformance gain of a DSL based scheme In ractical systems strict causality hinders the arioriknowledge of the rimary user s codeword at secondary transmitters. On the other hand, at secondary receivers rimary signals cannot be reliably decoded due to SNR considerations or synchronization issues.

2 366 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO., DECEMBER over schemes in which the amount of interference tolerated by the rimary system is fixed. A ractical examle with two concrete erformance metric functions is resented in Section IV. Finally, Section V concludes this aer. II. SYSTEM AND SIGNAL MODEL In this work, for simlicity of exosition, we assume uncorrelated block fading channels and the existence of a single rimary link and a single secondary receiver of interest. K secondary transmitters are interested in accessing this sectrum band to the maximum ossible extent. While Matched filter MF) decoding is a oular decoding structure due to its simlicity and erforms reasonably well in systems with weak cross-channels, in an interference limited regime it is clearly subotimal and it is outerformed by joint decoding of multile users. We will consider here the otimal joint maximum likelihood multiuser decoder ML MUD) []. Note that multile schemes exist today for the ractical imlementation of multiuser decoding, such as successive interference cancellation hard) or multiuser turbo decoding soft). We require a limited awareness by the rimary receiver of the secondary system. Therefore secondary transmissions are considered as noise in the rimary decoding rocess. On the other hand, the base station of the secondary system is assumed to have a MUD for the K secondary transmissions while the rimary signal is assumed to be undecodable and thus treated as noise. A. Signal model The rimary user is denoted as user while the secondary transmitters are labeled as users through K. Adiscretetime reresentation of the received signals at the rimary and secondary receivers can be written as r [n] =h s [n]+ h k [n] s k [n]+σ n [n]; ) r s [l] =h s s [l]+ h sk [l]s k [l]+σ s n s [l] ) where n and l reresent the discrete samling times at rimary and secondary receivers resectively, h k and h sk are the effective channels from k-th transmitter to the rimary and secondary receivers resectively. If s k t) denotes the signal transmitted by the k-th user, then s k [n] denotes a synchronously samled and s k [n] an asynchronously samled version of s k t). Finally n [n] and n s [n] are iid Gaussian rocesses normalized to have variance so that σ and σ s reresent the noise ower levels at the rimary and secondary receivers, resectively. We denote the transmit ower of the k-th user as k. = E{ s k [n] }. = E{ s k [n] } for k =,,...,K. Note that this assumes that any deviations on the received ower due to front-end and bandwidth differences are absorbed into the effective channel coefficients. Then it is straightforward to see While in the schemes resented in [4], [5] more comlex set-us were emloyed, here we consider a simlified scenario to better illustrate the theoretical advantage of DSL over schemes that emloy fixed interference ca levels. R s) Q = Q =8 Q =6 Q =4 Q = R s) Saturation due to ower constraint Fig.. Secondary system -user rate region for different values of Q. that the actual interference ower generated by the secondary system at the rimary user is given by. K = h k k. 3) I B. Decoding strategy Primary user. The maximum achievable rate er channel use assuming secondary interference as noise at the rimary system is given by R W log + h ) I + σ 4) where W reresents the bandwidth emloyed by rimary transmissions and the transmitted ower is determined by the required quality of service QoS) and the interference ca selected. Secondary user. If otimal multiuser decoding is used in the secondary system with bandwidth W s, the maximum achievable sum rate at the secondary receiver treating rimary transmissions as noise is, see e.g. Sec in [], ) K R s <W s log + h sk k h s + σs 5) for each of the allowed secondary ower assignments k with k =,...,K, which are determined by the maximum interference allowed at the rimary user I Q and secondary user individual ower constraints k < k. The rate region obtained with this scheme is similar to the one obtained in a Gaussian Multile Access Channel, with the eculiarity that on to of having individual ower constraints, secondary users have a weighted global ower constraint. The individual rates achieved by each secondary user will deend on the articular coding/decoding strategy used. From the constraint I Q and given the definition of I we have that the term K h sk k in 5) is uer bounded by a monotonically increasing affine function of Q.Then it is aarent from 5) that while the uer bound on the secondary sum-rate is monotonically increasing with Q,the growth rate decreases with Q due to the logarithmic relation

3 VAZQUEZ-VILAR et al.: PRIMARY USER ENTERS THE GAME: PERFORMANCE OF DYNAMIC SPECTRUM LEASING IN COGNITIVE RADIO NETWORKS 367 with K h sk k. Figure shows an examle of the rate region obtained in a two user secondary system where the channel from user to rimary is much weaker than the one from user for different values of Q. While in general the region is increasing with Q, the effect of the individual ower constraints of the secondary nodes translates into the artial saturation of the achievable rate region. III. PERFORMANCE COMPARISON Although erformance evaluation of cognitive radio systems is imortant in comaring and ranking different aradigms, it has received only a limited attention in current literature []. Even for the relatively simle model considered in this work, there exist several ossible evaluation metrics: maximum achievable sum-rates at rimary and secondary systems R and R s resectively, ower dissiated by a given user k, interference generated at the rimary user I, robability of rimary outage rob{i > Q }, fairness among users, and sectral efficiency, among others. Therefore, an adequate utility function must first be defined in order to comare DSL based aradigms with other schemes. A. Performance metric While in our model a natural erformance metric for the secondary system should be an increasing function of the attained sum rate R s, the rimary user s utility needs further considerations. Since the rimary user suffers from a ermitted) interference I from the secondary system, in order to maintain its QoS the rimary user transmitted ower is increased with resect to an exclusive use of the frequency band I =). We denote this increment in the transmitted ower by Δ. Hence the rimary user needs an incentive to allow secondary users to use its managed sectrum. We assume here that the secondary system comensates the rimary user with a ayment monetary or of other nature) related to the generated interference I. As a result, the utility functions for rimary and secondary systems can be written as: U = u I, Δ ), 6) U s = u s R s,i ) 7) where rimary utility u ) is growing with I and decreasing with Δ, while secondary utility u s ) grows with R s.we additionally assume that when the interference constraint is violated, that is when I >Q, the enalization imosed by the rimary system to the secondary system imlies U =, U s =. This enalty discourages the secondary system from violating the allowed interference ca. B. Performance gain For a given interference ca Q the secondary utility U s is maximized for the secondary ower vector =[. K ] T rovided that Q ) = arg max {u sr s,q ),I ))} 8) subject to I ) Q, where we defined. = [ K ] T and the oerator denotes element by element comarison. Here we have exlicitly shown the deendence of R s on Q. We define the corresonding rimary and secondary utilities as U Q ) =. U Q ),Q ) and Us Q ) =. U s Q ),Q ), resectively. If the rimary user fixes ariorithe interference ca Q in a time varying environment its exected utility is given by E[U Q )] where the exectation is taken with resect to the channel realizations. On the other hand, in a DSL scheme we allow the rimary system to dynamically adjust the allowed interference ca Q. We can now comute the maximum achievable utility for both tyes of schemes: Schemes with fixed Q : If the rimary user chooses the value of Q that maximizes the exected utility and uses it for all channel realizations, its utility is given by U fixed =max Q {E[U Q )]}. 9) DSL schemes: On the other hand, in a DSL-based system, the rimary will choose the interference ca Q to maximize its own utility for each channel realization. The best exected rimary utility achievable in this dynamic environment is U dsl = E[max{U Q )}]. ) Q dsl fixed It is easy to see from 9) and ) that U U, with equality if and only if the otimal Q is constant for all channel realizations. In the next section we will use a simle examle to show that indeed the gain obtained by a DSL scheme can be significant. Remark: In deriving ) we imlicitly formulated the interaction between the rimary and secondary systems as a Stackelberg game [3], in which the rimary user acts as Stackelberg leader and the secondary system acts as follower. While this is a natural model for cognitive radio systems in which the rimary can always act unilaterally while secondary users have to adat their actions to the imosed constraint [4], ractical imlementations that achieve this behavior are a toic of further research. C. Practical considerations While in the revious analysis we did not discuss how a ractical scheme could achieve the derived erformance, we resent here some ractical issues that need to be taken into account. In the roosed Stackelberg game we assumed that both rimary and secondary systems have erfect knowledge of all system arameters, and thus they can otimize their erformance by maximizing their own utilities. However, even for classical schemes with fixed interference ca it is difficult for a secondary system to determine how much interference it causes to a rimary receiver. A ractical imlementation would require secondary users to estimate their channels to the rimary receivers. This could be erformed in dulex rimary systems with recirocal ulink and downlink channels by monitoring the rimary signal levels. On the other hand, DSL based schemes could achieve the oerating oint redicted by the Stackelberg equilibrium without requiring full knowledge of the system arameters. For examle, if the utilities are such that the Stackelberg equilibrium coincides with the unique Nash equilibrium of the

4 368 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO., DECEMBER game, it can be achieved via an iterative game between the rimary and secondary systems. The ractical DSL scheme roosed in [4] only requires the rimary system to broadcast the values of I and Q. Even though this aroach requires a certain degree of awareness about the secondary network by the rimary system, it results in a ractical scheme that can easily be imlemented in ractice. Due to sace limitations, in the following we will focus on theoretically achievable erformance and disregard ractical imlementation considerations. IV. EXAMPLE For illustration uroses, in this section we assume that the utilities associated with rimary and secondary users are resectively U = I μ P Δ, ) U s = μ R R s I ) with the additional restriction that I Q. That is, the rimary system obtains a reward roortional to the suffered interference I through the corresonding charge to the secondary system. Without loss of generality we assume here the ayoff er unit of interference equal to. The rimary user has a cost associated to the extra ower Δ required to maintain its desired QoS, riced at the rate of μ P. The reward for the secondary system is roortional to the achievable sum rate R s riced at the rate of μ R. Note that whereas these utilities kee the sirit of 6) and 7), they are also simle enough to obtain analytical results. A. Analysis Assuming equality in 5) we may rewrite ) as K h sk h U s = μ R W s log + k k σs + h s k 3). wherewehavedefined k = hk k >. In order to maximize U s with resect to k we first note that for fixed K k = I, U s is growing with resect to a convex combination of the ositive) ratios h sk /I h k ). Hence, for a fixed I, U s is maximized when all the allowed secondary interference I is allocated to the secondary transmitters with the largest ratios h sk / h k u to their individual ower constraints. Formally, if we define the indexes of the sorted effective channels as {i,i,...,i K } such that h si h i h si h i h si K h ik, 4) the otimal ower assignment is given by h ik ik, δ k <I,. i k = I δ k, δ k I δ k, 5), elsewhere,. k where we defined δ k = l= h i l il. Then we may define the instantaneous channel ratio η as η. = K h sk h k k I. 6) Note that when the secondary individual ower constraints are not active I h i i, hence η reduces to the largest channel ratio air: η =max k { h sk / h k }.Otherwiseη is a convex combination of the strongest channel ratio airs. Remark: While the simle utility ) leads to an oortunistic access scheme that does not take into account fairness among secondary users, in the general setting U s could take a more comlex form in order to guarantee fairness. However this analysis lies out of the scoe of the resent work. Using 6) and substituting 5) in 3) we have that U s = μ R W s log + ηi σ s + h s ) I. 7) Equating the derivative of 7) with resect to I to zero, we obtain the global U s maximizer. Taking into account the additional constraint I <Q, one obtains that the otimal I is given by I Q )=min Q,W s μ R +σ s + h s )/η ). 8) As in [4], we will assume here that = γq +σ )/ h where γ is the target rimary SINR to assure a required QoS. Then it follows that U Q )=I μ P Δ and 9) Us Q ηi ) )=μ R W s log + σs + h s I, ) where we omitted the deendence of I on Q. The maximal rimary utility is achieved by a DSL system maximizing U Q ). Given the restriction I Q and since U is growing with I and decreasing with Q it can be shown that U Q ) is maximized when I = Q. Hence the otimal instantaneous Q is given by Q = ηw sμ R h s h γσ σs. ) η + hs h γ Note that, as can be seen from ) above, the otimal strategy for the rimary user is heavily deendent on the scenario and thus cannot be fixed a riori. In order to comute the exected gain in a dynamic environment for a DSL based scheme over dsl fixed a aradigm with fixed Q,givenby U U,wefurther need to define a channel model and comute the average of 9) with resect to all channel realizations. Although, in general, the exected gain cannot be comuted in a closed form, it can easily be evaluated numerically for any given set of arameters. B. Numerical results We assume that channels to secondary receiver h k and h sk are Rayleigh distributed with E{ h k } = E{ h sk } =. The remaining system arameters are K =3, k =, Q =, σ = σ s =while the transmitters are considered fixed with h = h s =. We emloy normalized bandwidth W = W s =,targetsinr γ =and resource rizes initially set to μ P =. and μ R =. Figure shows the comarison between a DSL based scheme and a scheme in which the allowed interference ca Q is fixed for the given set of system arameters. In Fig. a)

5 VAZQUEZ-VILAR et al.: PRIMARY USER ENTERS THE GAME: PERFORMANCE OF DYNAMIC SPECTRUM LEASING IN COGNITIVE RADIO NETWORKS 369 U Us a) Q DSL Fixed Q b) Q DSL Fixed Q Fig.. Primary/secondary users average erformance in a time varying environment. a) Primary user erformance. b) Secondary user erformance. we can see that even if a fixed system were to use the otimal Q.5, the rimary utility attainable by a DSL based scheme is about 5% larger than the one of the fixed scheme. On the other hand, if we look at the secondary utility obtained by a DSL based scheme comared to a scheme with fixed Q, as shown in Fig. b), we can see that while fixed schemes erform better than DSL for a small range of Q values, for the otimal oerating oint of the fixed scheme Q.5) DSL erforms slightly better than the fixed scheme. That is, in this setting both rimary and secondary users can benefit from the use of a DSL scheme. Moreover in a DSL based scheme the allowed interference at the rimary is comuted on line, and thus it does not need to be fixed ariori. Hence, DSL schemes can be robust against inaccurate knowledge of the system arameters that may degrade both rimary and secondary erformance at the exense of the extra comlexity required for dynamically setting the value of Q. Note from Fig. that a small change in the Q value for the fixed scheme can significantly degrade the global system erformance. However, as we ointed out above the advantage of DSL based schemes vanishes if the otimal rimary user action Q is indeendent from the channel realization. If we assume high reward for the secondary system sum rate, that is μ R =, the best resonses for both rimary and secondary users turn to be I = Q = Q, not deending on the channel realization. In this case DSL and fixed schemes with Q = Q turn out to be equivalent achieving U 8.99 and U s 35. V. CONCLUSIONS In this corresondence we analyzed the erformance gain that a rimary user can exect by allowing a limited interaction with secondary systems. For a family of erformance metrics based on the secondary user sum-rate we showed that DSL based schemes can outerform classical schemes in dynamic environments. Moreover, since the allowed interference at the rimary is comuted on-line, DSL schemes are robust to inaccuracies on the arioriknowledge on system arameters that can degrade both rimary and secondary erformances. These results advocate the design of ractical dynamic sectrum sharing schemes based on DSL tye architectures with a limited interaction between rimary and secondary systems, as oosed to reviously roosed fixed interference ca frameworks. REFERENCES [] FCC, Reort of the sectrum efficiency working grou," FCC Sectrum Policy Task Force, Tech. Re., Nov.. [], ET docket no 3-3 notice of roosed rulemaking and order," Tech. Re., Dec. 3. [3] S. K. Jayaweera and T. Li, Dynamic sectrum leasing in cognitive radio networks via rimary-secondary user ower control games," IEEE Trans. Wireless Commun., vol. 8, no. 6, , June 9. [4] S. Jayaweera, G. Vazquez-Vilar, and C. Mosquera, Dynamic sectrum leasing: a new aradigm for sectrum sharing in cognitive radio networks," IEEE Trans. Veh. Technol., vol. 59, no. 5, , June. [5] K. Hakim, S. K. Jayaweera, G. El-howayek, and C. Mosquera, Efficient dynamic sectrum sharing in cognitive radio networks: centralized dynamic sectrum leasing C-DSL)," IEEE Trans. Wireless Commun., vol. 9, no. 9, , Se.. [6] J. Zhang and Q. Zhang, Stackelberg game for utility-based cooerative cognitiveradio networks," in Proc. th ACM International Sym. Mobile Ad Hoc Netw. Comut., 9, [7] A. Ercan, J. Lee, S. Pollin, and J. Rabaey, A revenue enhancing Stackelberg game for owners in oortunistic sectrum access," in Proc. 3rd IEEE Sym. New Frontiers Dynamic Sectrum Access Netw. 8, Oct. 8,. -8. [8] A. Al Daoud, T. Alcan, S. Agarwal, and M. Alanyali, A Stackelberg game for ricing ulink ower in wide-band cognitive radio networks," in Proc. IEEE Conf. Decision Control 8, Dec. 8, [9] P. Cheng, G. Yu, Z. Zhang, H.-H. Chen, and P. Qiu, On the achievable rate region of Gaussian cognitive multile access channel," IEEE Commun. Lett., vol., no. 5, , May 7. [] S. Verdu, Multiuser Detection. Cambridge University Press, 998. [] T. M. Cover and J. A. Thomas, Elements of Information Theory, nd edition. Wiley-Interscience, 6. [] Y. Zhao, S. Mao, J. Neel, and J. Reed, Performance evaluation of cognitive radios: metrics, utility functions, and methodology," Proc. IEEE, vol. 97, no. 4, , Ar. 9. [3] D. Fugenberg and J. Tirole, Game Theory. MIT Press, 99. [4] O. Simeone, I. Stanojev, S. Savazzi, Y. Bar-Ness, U. Sagnolini, and R. Pickholtz, Sectrum leasing to cooerating secondary ad hoc networks," IEEE J. Sel. Areas Commun., vol. 6, no.,. 3-3, Jan. 8.