A toy-model for the regulation of cognitive radios

Transcription

1 A toy-model for the regulation of cognitive radios Kristen Woyach and Anant Sahai Wireless Foundations Deartment of EECS University of California at Berkeley {kwoyach, Abstract With the develoment of frequency agile radios comes a new otion for using wireless sectrum: cognitive radio. Under this scheme a hierarchical aroach is emloyed in which legacy rimary users may use the band as they wish, while secondary users may take advantage of any unused sectrum. However, as of yet the question of enforcement in cognitive radio is unaddressed, esecially in the context of cooerative sectrum sensing. Unfortunately, it cannot be assumed that secondaries will not cheat as there is no hysical limitation to sto them. Therefore, enforcement mechanisms and models to evaluate these mechanisms are required. This aer considers the roblem of enforcement in terms of incentives available to encourage secondaries to lay by the rules. It develos a toy game-theoretic model to cature the dynamics of the rimary and secondary users and evaluates what this model can tell us regarding the overall tradeoff between enforcement mechanisms, cheating behavior and channel utilization. In articular we find that in order to guarantee that there is no incentive to cheat, it is not enough to unish cheaters simly by denying them access to the band. Also, we find that it is imortant to catch the individual cheater: no amount of unishment can incentivize laying by the rules when collective unishment is emloyed. I. INTRODUCTION As wireless technology becomes more ubiquitous, sectrum availability becomes an increasingly imortant concern. However, desite full allocation by the FCC, emirical measurements suggest sectrum is in fact vastly underutilized [] [3]. The real question becomes why is this recious resource being wasted and how can we correct the situation? We discuss some related ersectives on this roblem in Section II and then decide that any solution to this roblem must involve regulation that involves some form of exlicit or imlicit olicing at runtime. This aer focuses on the case of oortunistic sectrum users that want to use a band in which a rimary is only intermittently active. Ideally, we want to be able to answer questions such as the following: How should regulation be artitioned between device certification, standards, and incentives? How easily is this enforced? At what level is the regulation erformed (FCC, standards body, individual run-time decisions)? Does this regulation scheme encourage innovation and technological imrovement? In the comanion aer, [4], the enforcement of cognitive radios is considered to understand the overhead required and the tradeoffs involved to detect interference and catch culrits reliably. However, that story must be comlemented with a quantitative argument that bounds what is realistic from an incentive ersective. Otherwise, the arameters of any code could never be set. This aer begins the rocess of understanding these incentives and the tradeoffs in enforcement and utilization. This is done by defining a toy model to cature the enforcement dynamics in the cognitive-radio scenario. Obvious tradeoffs exist between utilization, the enforcement mechanism, and the cheating behavior of the secondary users. Consider the extreme cases: if no enforcement were emloyed, there is no accountability and therefore no incentive to follow the rescribed hierarchy. Secondaries would choose to transmit with no regard for interference to the rimary. Although utilization would be high, the rimaries would be severely affected, negating the original hierarchy concet entirely. On the other hand, if the unishment for cheating is that the secondary user is forever denied access to the band, the enalty is so severe that the secondaries would have to be very conservative in their use in order to avoid it. They must be so conservative, in fact, that the overall utilization would be essentially the same as if there were no cognitive users at all. In this aer, we seek to understand this tradeoff. To that end, in Section III we identify the imortant dynamics and resent a simle model to cature them. Sections IV and V investigate what this model can tell us about the tradeoffs of interest, and Section VI resents some concluding remarks on where we go from here. II. BACKGROUND The roblem of sectrum underuse naturally lies with the current allocation system and so regardless of technological imrovements, regulatory questions are unavoidable. When the FCC was designed, wireless use was synonymous with broadcast and interference was something to be feared [5]. The allocation system was designed on scales aroriate for broadcast. The allocation time was considered on the order of ten years: the order of device lifetimes. Geograhic scales were considered in the hundreds of square kilometers, or the order of a broadcast service area. At the time, this model worked well because the number of layers was relatively small and interference was the rimary concern. However, this original model is no longer aroriate because it roduces a mismatch between the scales of allocation and scales of use. Many of the current develoments in wireless networks are geared toward smaller, more decentralized

2 2 concets which simly do not oerate at the large scales assumed for broadcast systems. The effect is the existence of holes [6] in sectrum usage. In time these aear as legacy networks move to acketized, service uon demand schemes that do not constantly require sectrum use. Time holes also exist when legacy systems no longer have the ability or incentive to oerate and simly sit idle on their allocated band. In sace, these holes occur as the legacy systems oerate in a service area that does not cover the entire allocated area. If the FCC had the information and the seed to adat aroriately, it could dynamically allocate sectrum to the best users in real time. Unfortunately, as a centralized regulation authority that defines even the location and height of transmit antennas for every iece of sectrum in the United States, the FCC is not hysically caable of having all the necessary information and oerating at the aroriate seed. It seems that utilization would imrove if more flexibility were allowed, but this is only half the story. When sectrum is heavily regulated, the rules of use are clear, and anyone not following the rules is easily caught and unished. The current FCC actually reresents an extreme osition in which a high degree of regulation roduces very simle enforcement. If you know where and how all the transmit antennas are oerating, it is very simle to weed out illegal arties with a directional antenna. At the other extreme, consider a case in which there is no regulation. [7] suggests through gametheoretic arguments that the system would self-regulate so that everyone has some oerational ability. The outcome would look qualitatively similar to the internet: the QOS would be best effort. It would be only as good as the worst layer is willing to accet and it would be very difficult to effectively contain malicious users. The otimal solution in trying to rethink the rules, then, must lie somewhere in the middle. Ideally we want a lighthanded regulation in which oerational rules and means of enforcement are defined to maintain eaceful coexistence. The rules must also be general enough to rovide flexibility and encourage innovation. When considering sectrum use, regulating either only a riori with equiment or only at run time with usage rules and olicing seems insufficient. However, the correct mix of regulation scales is yet unclear. Solutions to the allocation roblem have been roosed, but differ widely in their aroaches. The first is sectrum rivatization, introduced by Coase in [5] and elaborated on by de Vany in [8]. The idea here is to assign roerty rights to sectrum much like they exist for land. This would include a time, geograhic area, and sectrum band. Correct usage is defined as not exceeding a ower threshold at the boundary of one s region. Beyond this stiulation, users are ermitted to use the band however they wish. With roerty rights, the sectrum could be sold, divided, merged, and otherwise renegotiated between individuals instead of by a central authority. Instead of a regulatory body making decisions, market forces determine the overall utilization. The argument is that this aroach would converge to the most efficient use of sectrum because those most able to effectively use the sectrum are recisely those who are most able to urchase the roerty rights. Note that the scales of allocation would begin on the order of the original FCC allocation scheme, but these too would resumably converge to the correct scales of use that most effectively utilize available sectrum. The ability to enforce in this scheme comes down to distinguishing when and who is at fault. But, this is not necessarily simle. As Hatfield oints out in [9], the wireless medium is variable and roagation deends on many factors including even the current state of the ionoshere. So, it is not sufficient to simly determine maximum ower levels a riori and assume they will always work. From the regulatory ersective, it is much easier to agree on a roagation model and then have users rove their models are in comliance. But this too raises difficult questions. Even if a good model could be develoed, it is not obvious that it would even be ossible to determine who is at fault. It is also not clear how to treat interference claims: should interference be considered as tresass or nuisance []? On the one hand, tresass seems aroriate because interference is one user oversteing their roerty and infringing on someone else. This is nice because litigation here is relatively straightforward. However, this treatment can encourage sectrum troll [9] behavior in which owners can simly sit idle on their sectrum, wait for someone to transmit too loudly, and sue them. Perhas a more aroriate concet is nuisance, which evaluates the degree to which one is affecting the other and can weigh the relative utility of the users to determine who is at fault. Unfortunately, although this allows flexibility which will hel maximize utilization, actually resolving nuisance cases is subjective and difficult. A second school of thought is characterized by Benkler [] which treats sectrum as a commons. Here, the concet is to lace the regulation burden solely on the equiment instead of distributing it between equiment and use, so that users are naturally able to coexist when using the sectrum in whatever manner they choose. The market, then, is ushed from the sectrum itself to the equiment and will favor those technologies more able to coexist effectively. Here we do not have to worry about usage scales as oerators may use their devices however the wish. But it is not clear how long device certification should last or if the standards could evolve effectively. The flexibility and adatability of this route is obvious: users are free to innovate with no more risk than the initial hardware investment. Enforcement is concerned with original certification of devices and finding malfunctioning units. Again, this becomes a technical question: can the equiment be certified to guarantee that coexistence is ossible and how do we recognize offending arties in this sea of users who are relatively unconstrained? Cognitive radio emerges as a third regulatory otion built like a hybrid of the revious two. It seeks to solve the allocation roblem through a hierarchy of oeration regimes. The legacy rimary systems, with rights to the sectrum either through allocation or market transaction, may continue to use the sectrum and oerate on the scale defined by the regulation scheme. However, secondary users may then oerate at a much smaller scale, observing holes in sectrum usage and filling them as long as their oeration does not interfere with the rimary users. Here, again, the otential

3 3 for higher utilization and innovation is obvious. We reclaim unused ortions of sectrum, increasing utilization. Innovation is encouraged as rimaries imrove their services from cometition with secondaries, and the secondaries have the freedom to exeriment so long as they conform to the hierarchy. Many aers exist on what the secondary must be able to do, technically, to oerate under these constraints (see for examle [2]), but the question of enforcement is largely ignored. It is generally assumed that the secondaries will imlicitly follow the rules. This is unfortunately not a fair assumtion. There are no hysical device constraints that limit cheating, so if one wants to regulate cheating behavior directly with standards it would require sifting through thousands of lines of code for every certified device. As this is not feasible, we must therefore consider enforcement from a ersective of how to incentivize secondaries to not cheat. Again, a game-theory aroach seems aroriate to cature these dynamics. With this in mind, we can question how to meet the goal of light handed regulation. Unfortunately, the answer is not obvious because all of these aroaches treat the roblem in very different ways. Although all resent obvious ways of increasing utilization and encouraging innovation, they also leave large technical questions unanswered, rimarily in the realm of enforcement. But, even if the mechanisms for enforcement were clear, we have no metrics to define what is good nor an understanding of the fundamental tradeoffs involved. It could be argued that defining metrics is unnecessary as we could simly design an exeriment where each roosal was itted against the others and market forces would decide the most efficient solution. However, with unused sectrum already at a remium, such an exeriment may be infeasible and certainly could not be erformed blindly. Even if we could erform such an exeriment, what works in one case is not necessarily alicable to another band and usage scenario. What are really needed are models that cature the dynamics of interest and give a qualitative and quantitative sense of the tradeoffs involved. With these tradeoffs in hand, aroriate metrics can be defined to comare different ideas against the ideal. This motivates the need for the idealized toy model in the next section. III. MODEL The goal of our roosed model is to cature the basic dynamics of the rimary and secondary users to get a handle on some of the tradeoffs involved. Secifically, a good model of this situation should hel us: Understand what needs to be regulated and what does not Understand the burden on the regulator Comare different enalties Understand the effect of different technologies We are concerned here rimarily with arameter choices and resonses, so we will make simlifying assumtions that remove comlications. First, we assume that the rimary and secondary users exist at a single oint in sace. This allows the Primary Use Secondary Use S S TX S 2 : Wait S 3 : Illegal TX q No TX S : FA S : Legal TX S : Pen. Box S : Pen. Box S S 2 S 3 S 3 Fig.. Markov chain for modeling secondary cheating dynamics in cognitive radio system. The rimary use is modeled as the two-state chain at the to, which determines the horizontal movement through the secondary chain. The secondary chain resonds to the rimary s use by transmitting or waiting on either side. Illegal use of the band romts a enalty, which is sitting in the enalty box for a secified amount of time. suression of any roagation effects so that interference can be treated as a binary quantity: if both rimary and secondary are transmitting, it qualifies as interference. We also suress overlas that would normally occur between the time the rimary turns on and the time the secondary notices. Likewise, the time lag between the rimary turning off and the secondary noticing is also suressed. We will assume three ossible layers in this game: the rimary determines channel use and cares about whether it is exeriencing interference. However, the rimary usage is assumed fixed, and so the rimary is a silent, oblivious layer. The secondary is assumed to always have something to transmit, and so it cares only about maximizing its transmit time. The regulator is able to determine the level of enforcement and cares about overall channel utilization. The dynamics of the game are modeled by movement in the Markov chain deicted in Fig.. The rimary, which can be transmitting or not, moves according to fixed arameters and q. When the rimary is not transmitting, the secondary can either be legally transmitting (S ) or registering a false alarm (S ). When the rimary is transmitting, the secondary may be waiting as it should (S 2 ), or illegally transmitting (S 3 ). The enalty boxes (S 4 and S 5 ) reresent the unishment for cheating: if a secondary is caught cheating, it must sit in the enalty box for a secified amount of time. Horizontal movement through the secondary chain is determined by the rimary s channel usage, so it deends on and q. Vertical movement is determined by the regulator and secondary setting individual arameter values to maximize resective utility functions. The regulator s goal is to maximize utilization while suressing cheating. Therefore, it uses the utility function: U R = S S max π + π 2 () catch, en,β where π i is the stationary robability of being in state S i. The secondary cares only about being able to transmit, and so its

4 4 MD 2 3 cheat FA Fig. 2. FA vs MD tradeoff curves for an energy detector. Bold lines are at SNR = 6dB with number of samles N = 4 and N = utility function is U S = max π + π 3 β(π 4 + π 5 ) (2) cheat, F A where β is a variable factor that determines how much the enalty boxes hurt the secondary beyond simly not being allowed to transmit (this case corresonds to β = ). The hysical meaning and imlications of this factor will be discussed later in Section IV-C. To maximize their utility functions, the users set arameters. The regulator controls arameters related to catching cheaters and unishing them. This includes catch, the robability that a cheating secondary will be caught, en, which determines the average length of stay in the enalty boxes, and β, the variable extra unishment for sitting in the enalty boxes. catch and β include external constraints which will be discussed later in Section IV-C, while en can be freely set. The secondary controls arameters related to cheating. This includes cheat, the robability of choosing to cheat given you know the rimary is transmitting. This is the secondary s free arameter with no external constraint. The secondary also controls FA and MD, the robabilities of false alarm and missed detection, resectively. These two arameters are not indeendent. Indeed, we can assume that they lie on a curve determined by the secondary s sensing mechanism. For all simulations here, the detector is assumed to be an energy detector which has the aroximate test statistic [2] T(Y ) H N (σ 2, N ) 2σ4 T(Y ) H N (P + σ 2, N ) 2(P + σ2 ) 2 This roduces the family of curves shown in Fig. 2 where the shae of the curve is determined by the energy detector itself and the sloe of the curve is determined by the SNR and number of samles N. The middle bold curve is the nominal one used for most of the simulations. When a better curve is required for comarison, the other bold curve is used. (3) (4) Fig. 3. cheat against channel use, characterized by the stationary robability the rimary is transmitting and, the robability the rimary will move from transmitting to not transmitting in the next ste. In this low enalty regime where catch =.8, en =.6, and β =, the cheating behavior always takes a binary form, with more cheating occurring when the channel is less available. To determine vertical state transitions, the arameters work together as follows: To enter S, the secondary must not exerience a false alarm ( FA ) A false alarm ( FA ) determines transitions into S. To enter S 2, the secondary must know the rimary is transmitting and choose not to cheat (( cheat )( MD )). To enter S 3, the secondary must know the rimary is on but cheat anyway (( MD ) cheat ) or not know the rimary is talking ( MD ). To be sent to the enalty box, the secondary must already be in S 3 and get caught ( catch ). Once in the enalty box, the secondary can leave if it is not forced to stay ( en ). IV. TRADEOFFS OF INTEREST We exlore how this model answers the desired questions by first qualitatively understanding the behavior of the secondary with resect to the channel usage of the rimary, and how it affects the overall utilization. We then take a quantitative look at the effect of the regulator s enforcement arameters, and the effect of changing secondary technology. A. Effect of rimary channel use In considering usage of the rimary, we want to get a sense of whether one size fits all : can we set the enforcement arameters once for any channel, or do they need to adat based on channel usage? To answer this question, we fix the enforcement arameters and let the secondary adjust its arameters to maximize its utility function. This results in two modes of oeration. In the first, shown in Fig. 3, the enalty is not bad comared to the oortunity to claim extra transmission time. So, the FA is ushed as low as the simulation will allow and cheat is a binary quantity which is determined by the enforcement

5 5 FA (a) FA Fig. 5. Channel utilization if only the rimary is resent. MD (b) MD Fig. 4. FA and MD against channel use when catch =.8, en =.6, and β = 3. When the enalty is high enough, the secondary begins to avoid it by raising its own FA. arameters and channel use. In this figure, the z-axis is the robability that the secondary will cheat, either imlicitly with MD or exlicitly with cheat. Cheating is visualized for different values of, the robability that the rimary transmitting in the current state will be not transmitting in the next, and the steady state robability that the rimary is transmitting (q/( + q)). The steady state robability is used as a natural general arameter because even if the rimary had a more comlicated usage attern, it still has some sort of duty cycle. The deendence on the steady state robability of transmitting is intuitively leasing as we would exect the secondary to cheat more when the channel is less available. is used to directly see the effect of choosing between cheating now with ossible enalty or legally transmitting in the near future. In all lots, the allowed range of the robability the rimary is transmitting and is outlined at the bottom for reference. Note that this region is a result of defining the model as a discrete Markov chain. If the model were continuous, the region would not be restricted. Fig. 4 shows the second mode of oeration in which the enalty is so high that the secondary actively avoids getting caught. In this case, cheat is always zero, and FA rises to ush MD as low as ossible. Notice again the deendence on the robability that the rimary is transmitting. When this value is high, there is greater oortunity to get caught, so the measures taken to reduce this robability are greater, i.e. FA is higher. B. Overall channel utilization From a regulatory ersective, the metric of interest is the overall utilization of the channel: we want to know whether the current enforcement scheme allows the secondary to effectively fill sectrum holes. So here we will discuss the effect of different modes of oeration on the overall utilization. All the cases that follow can be comared to Fig. 5, which shows the utilization when only the rimary is resent. It is equivalent to the steady state robability of the rimary transmitting. For all other utilization figures, two definitions are used: The first is total utilization, defined as = π + π 2 + π 3 + π 4 (5) which is the ercentage of time anyone is using the channel. The second definition, utility with collisions, is defined as U collide = π + π 2 + π 4 (6) which does not count interference as utilization. Fig. 6 shows the utilization for the cheating behavior observed in Fig. 3. Note in this figure that when the secondary is always cheating, the utilization follows more closely the curve in Fig. 5. When the secondary is not cheating, it more effectively fills sectrum holes. This effect is magnified when considering collisions; here the cheating drags the utilization down significantly when the rimary is usually transmitting. Fig. 7 shows the overall utilization when the secondary is avoiding unishment, with FA as shown in Fig. 4. When the rimary is always transmitting, it dominates utilization even when discounting collisions. When the rimary is rarely talking, the utilization is good because the secondary has a low FA in this region. The middle, however, shows relatively oor utilization as the secondary is still actively avoiding getting caught even though the rimary is not fully using the band.

6 6 (a) Overall Utility (a) Overall Utility U collide U collide (b) Utility with full collisions Fig. 6. Overall utility (ercentage of time either the rimary or secondary is using the channel, without collision) and utility with full collision (if both rimary and secondary are transmitting, not counted toward utility) in a low enalty regime with catch =.8, en =.6, and β =. Fig. 7. β = 3 (b) Utility with full collisions Effect of conservative FA on utility catch =.8, en =.6, and Fig. 8 shows the utilization in between the last two cases: the secondary is not cheating, but it is not actively avoiding the enalty either. Notice that qualitatively this curve looks much like that in Fig. 7, but it gets better utilization in the middle, where before the secondary had an inflated FA. This is the sweet sot for which any regulation should be aiming because it is the oint of maximum utilization. Fig. 9 shows the case where MD is held fixed at.5. The utilization is aroximately equal to our incentive scheme, so we lose little with light-handed regulation. The difference then is in simlicity of enforcement. [3] and [4] suggest that to achieve a good MD, cognitive radio systems will have to emloy some kind of cooeration. This means that in order to regulate a fixed MD, one would have to certify software by sifting through thousands of lines of code. With an incentive system, however, one simly has to correctly define the enforcement arameters. C. The effect of enforcement arameters In our model, the regulator has access to three arameters that determine enforcement: catch, β, and en. We want to get a sense of what these hysically mean and what effect each has on the secondary cheating behavior. We would also like to get a sense of how much of a burden enforcement is on the regulator. To do this, we will isolate the effects of different arameters and give hysical interretations of the results. catch catures the enforcement mechanism itself by reresenting the chance a enalty will be emloyed. The robability of catching cheaters deends on how the catching is done and the deloyment of catching nodes. Because secondary cheating always exhibits a binary behavior, we can evaluate the effect of catch by tracing how the boundary between always and never cheating moves when en and β are held fixed (Fig. ). catch determines the location of the boundary with resect to the robability of the rimary transmitting, but it does not affect the shae much. β is a factor that, in conjunction with en, affects the tye and severity of the unishment. Physically, β could reresent a number of things. It can be thought of as an extra fine imosed when in the enalty box. It can also be used to reresent a cost of missed oortunity if we were to consider a multiband scenario in which being in the enalty box in one band denies use in any band. As such, β could be a highly constrained

7 7 (a) Overall Utility (a) Overall Utility U collide (b) Utility with full collision U collide Fig. 8. Utilization with no cheating or extra false alarms catch =.8, en =.6, and β = arameter. If it is considered in the multiband sense, it is affected by the usage of the rimaries in other bands as well as how interested articular secondaries are in using those bands. So, β could even be different for different secondaries. If a value is assigned, the effect of this arameter on behavior is to give a relative weight between the rofit gained by using the band and the enalty incurred from using it imroerly. In regimes where the secondary is cheating, the effect of β is the shift shown in Fig. which looks much like that of catch. en determines the length of stay in the enalty box, effectively determining the deendence of cheating on. All examles thus far have en at a moderate value. To get a better sense of its effect on behavior, consider the extremes. When en = as in Fig. 2, the secondary will stay in the enalty box for only one time ste. So, whether it cheats is based on two things: the cost of cheating and whether the next time ste will be an oortunity for legal transmission. The first is determined by catch and β as before, but the second is determined solely by the transition robability and does not deend on channel usage. Therefore, the boundary between cheating and not in this case is a function only of. When en is very high, as in Fig. 3, the secondary will (b) Utility with full collision Fig. 9. Utilization when MD is fixed at.5. Overall utilization is not much better than with a urely incentivized scheme. A catch =.9 catch =.8 catch =.7 catch =.6 Fig.. While keeing en =.6 and β = fixed, the boundary between cheating (region A) and not cheating (region B) migrates with different values of catch, but the shae does not change. B

8 8 A B β =.5 β =.4 β =.3 β =.2 β =. β catch =.2 catch =.4 =.6 catch = catch Fig.. While keeing catch =.4 and en =.3 fixed, the boundary between cheating (region A) and not cheating (region B) migrates with different values of β, but the shae does not change. cheat Fig. 2. When en is very low ( en = here), with catch =.8 and β =, the boundary between cheating and not cheating is determined only by the chance of legally transmitting in the next time slot, en Fig. 4. Bounding β values vs. en where no more cheating occurs. Plotted for different values of cheat have to send a long time in the enalty box, so the time to return to legal transmission does not matter as much as a long term average of channel availability. Therefore in this case, the deendence is almost entirely on whether the rimary is transmitting and not on. In a real system, these enforcement arameters can be chosen in several ways. If the rimary usage is known a riori, they could be minimally set so that there is no incentive for the secondary to cheat. However, as usage may be less redictable or unknown, we could instead use bounding values that ensure the secondary has no incentive to cheat regardless of the rimary usage. These bounding values were found emirically and are lotted in Fig. 4. As catch is the technology-limited arameter, it is used to determine which β- en tradeoff curve is needed. These lines follow exactly an intuitive mathematical argument: if we define the total enalty as K = β en (7) which is the extra β factor times the exected amount of time in the enalty box, then the secondary would be temted to cheat if cheat Fig. 3. When en is very high ( en =.99 here), with catch =.2 and β =, the choice to cheat or not cheat deends on the long term average channel availability, so it is determined almost entirely by the steady state robability of the rimary transmitting K catch < (8) β catch en < (9) or the secondary is temted to cheat if the cost of the enalty is less than the utility gained by transmitting in that time slot. Equality in (8) determines the boundary between cheating and not; the boundaries found in Fig. 4 closely follow this exression. Note that this assumes a articular kind of traffic and QOS for the secondary. It will fit well the case when the secondary does not have time constraints, so the choice to cheat is based solely on the relative utility. If the secondary has time-sensitive data, however, the model will change as the secondary will have greater incentive to cheat to maintain a constant connection.

9 9 FA (a) FA (a) Total Utility MD U collide (b) MD Fig. 5. With catch =.8, en =.6, and β = 3, a better FA - MD curve means that the secondary does not have to increase its FA (and decrease MD ) much to avoid enalty. D. The effect of secondary technology We can model the effect of better secondary detection technology by simly relacing the FA - MD curve with a better one from Fig. 2. Under the same conditions that roduced the levels of FA and MD in Fig. 4, the better tradeoff curve roduces Fig. 5. Notice that while the original tradeoff curve requires the secondary to actively avoid the enalty, this one does not because the MD is already low enough so that the enalty is not incurred too often. With the imrovement in FA comes an imrovement in overall utility, shown in Fig. 6. Note that another tradeoff is suressed here. The better FA - MD tradeoff can also be achieved by simly sensing the channel longer. However, the better curve achieved by sensing longer must be traded off against the oortunity to use the available channel and may not always be worthwhile. So, it is ossible that the detector curve should be a function of the channel usage as well which is not yet catured here. If the secondary has a erfect detector, regardless of the strength of the enalty, FA and MD will never increase above zero, and the utility will be maximized as soon as (b) Utility with full collisions Fig. 6. With catch =.8, en =.6, β = 3, and a better FA - MD curve, the overall utility is increased. the enalty is greater than a threshold. This threshold was emirically found for a erfect detector to be the same as it was with the original detector, shown in Fig. 4. So to remove incentive to cheat, regardless of the detector, the enalty simly has to exceed this threshold. However, it may be of interest to intentionally far exceed the threshold: better FA means better utility for the secondary, so by simly setting the enalty very high, we can encourage better secondary-sensing technology. This means that regulation does not have to set a articular standard FA and MD that all users must meet, and it is ossible to simly incentivize better technology instead of having to certify every device and then recertify when the standard needs to be adjusted. V. THE EFFECT OF WRONGFUL PUNISHMENT Thus far we have considered only a single cognitive user and erfect detection by the rimary. However, when many users or less than erfect interference detection are considered, identifying the articular cheating user may be difficult. So, in this section we want to get a sense of how the incentives must change when a user can be wrongfully unished. Still assuming a single band, a user can be falsely accused only when the rimary is transmitting and another user is

10 The circled oints are emirically determined values, and the connecting lines corresond to cheat Fig. 7. With catch =.8, en =.6, β =, a wrong =.2 (the robability of false accusation) causes the secondary to cheat more often than the original case in Fig. 3 β wrong catch =.2 catch =.4 catch =.6 catch =.8 catch = Fig. 8. The relationshi between β and wrong to assure there is no incentive to cheat for any channel usage characteristic. Here en =.4 and different lines corresond to different values of catch. The circled oints are emirically determined; the lines are drawn from an emirically determined equation. Note that as wrong aroaches catch, the β required to assure no incentive to cheat goes to infinity. cheating. We will assume for simlicity that there is always a malfunctioning unit. We can then model the robability of being falsely accused as a transition from S 2 (in Fig. ) to the enalty boxes, controlled by a robability wrong. Intuitively, the secondary will be temted to cheat more often if there is a chance of wrongful unishment because if it will be unished anyway, it may as well use the channel. Fig. 7 shows the same arameters as in Fig. 3 but with a.2 robability of going to the enalty box without actually cheating. Indeed, with the chance of wrongful accusation, the secondary will cheat in a larger set of channel usage scenarios. To understand the incentives required to control cheating with wrongful unishment, we again find the bounding arameter values required to guarantee no incentive to cheat for any channel usage characteristic. These are lotted in Fig. 8. For illustration uroses, en is fixed at.4, and the rest of the arameters are varied. Different lines corresond to different values of catch and show the β required for different wrong. β = en +.9 wrong catch wrong () which was emirically determined. Note that if wrong =, this reverts back to (8) found reviously. Also, as wrong aroaches catch, the β required to assure no incentive to cheat goes to infinity.if the regulator unishes everyone when interference is detected, as soon as one user begins to cheat no amount of unishment will incentivize the other users not to cheat as well. VI. CONCLUDING REMARKS This aer has introduced a very simle toy model for cognitive radio oeration. Even with such a simle model, we can see some imortant effects: To incentivize cognitive users not to cheat, there must be a robability that they are caught and forced to undergo a enalty. It is not sufficient to enalize the cognitive user only by denying it access to the band that it is violating; some form of additional enalty is needed to deter cheating if we want a rule that works universally over rimary usage characteristics. Banning the user from cognitive access to other bands as well can serve as such an additional enalty. The duration of the enalty must be set aroriately to incentivize roer behavior. Setting the enalty high enough gives rational cognitive users an incentive to develo aroriately sensitive detection algorithms. There is no need to regulate at the level of sensitivity itself. If the regulator unishes all cognitive users when one of them cheats, as soon as one cheats no level of unishment can incentivize the others not to cheat This reresents the start of an investigation. Much more should be exlored, and the results of this model should be combined with a calculation of the overheads required to achieve the required level of enforcement. REFERENCES [] Sectrum olicy task force reort, Tech. Re. 2-35, Federal Communications Commision, Nov 22. [2] R. W. Broderson, A. Wolisz, D. Cabric, S. M. Mishra, and D. Willkomm, White aer: CORVUS: A Cognitive Radio Aroach for Usage of Virtual Unlicensed Sectrum, tech. re., 24. [3] M. A. McHenry and K. Steadman, Sectrum occuancy measurements, location of 6: Riverbend ark, great falls, virginia, tech. re., 25. [4] G. Atia, A. Sahai, and S. Venkatesh, Sectrum Enforcement and Liability Assignment in Cognitive Radio Systems, Submitted to DySAN, 28. [5] R. H. Coase, The Federal Communications Commission, Journal of Law and Economics, vol. 2,. 4, October 959. [6] R. Tandra, S. M. Mishra, and A. Sahai, What is a sectrum hole and what does it take to recognize one?, submitted to Proceedings of the IEEE, 28. [7] R. Etkin, A. Parekh, and D. Tse, Sectrum sharing for unlicensed bands, IEEE DySAN, Nov

11 [8] A. S. de Vany, R. D. Eckert, C. J. Meyers, D. J. O Hara, and R. C. Scott, A Proerty System for Market Allocation of the Electromagnetic Sectrum: A Legal-Economic-Engineering Study, Stanford Law Review, vol. 2, , June 969. [9] D. Hatfield and P. Weiser, Toward Proerty Rights in Sectrum: The Difficult Policy Choices Ahead, CATO Institute, August 26. [] E. Goodman, Sectrum Rights in the Telecosm to Come, San Diego Law Review, vol. 4, no. 269, 24. [] Y. Benkler, Overcoming Agorahobia: Building the Commons of the Digitally Networked Environment, Harvard Journal of Law and Technology, vol., , Winter 998. [2] R. Tandra and A. Sahai, SNR walls for signal detection, IEEE Journal of Selected Toics in Signal Processing, vol. 2,. 4 7, February 28. [3] S. M. Mishra, A. Sahai, and R. W. Broderson, Cooerative sensing among Cognitive Radios, ICC, June [4] S. M. Mishra, R. Tandra, and A. Sahai, The case for Wideband Sensing, Allerton Conference on Communication, Control, and Comuting, Set