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Limits on Communicationsin a Cognitive Radio Channel

Natasha Devroye, Patrick Mitran, and Vahid TarokhHarvard University

Abstract— In this article, we review FCC secondary marketsinitiatives and how smart wireless devices could be used toincrease spectral efficiency. We survey the current proposalsfor cognitive radio deployment, and present a new, potentiallymore spectrally efficient model for a wireless channel employingcognitive radios; thecognitive radio channel. This channel modelsthe simplest scenario in which a cognitive radio could be used andconsists of a 2 Tx, 2 Rx wireless channel in which one transmitterknows the message of the other. We obtain fundamental limitson the communication possible over such a channel, and discussfuture engineering and regulatory issues.

I. I NTRODUCTION

Recent FCC measurements have indicated that 90% of thetime, many licensed frequency bands remain unused [7]. Asuser demands for data services and data rates steadily increase,efficient spectrum usage is becoming a critical issue.

In order to better utilize the licensed spectrum, the FCChas recently launched a Secondary Markets Initiative [13],whose goal is to “remove regulatory barriers and facilitatethedevelopment of secondary markets in spectrum usage rightsamong Wireless Radio Services.” This proposal introduces theconcept of “dynamic spectrum licensing”, which implicitlyrequires the use of cognitive radios to improve spectral ef-ficiency. Cognitive radio, a term first coined by Mitola [11],is a low cost, highly flexible alternative to the classic singlefrequency band, single protocol wireless device. By sensingand adapting to its environment, a cognitive radio is ableto cleverly avoid interference and fill voids in the wirelessspectrum, dramatically increasing spectral efficiency.

Although the gains to be made by the combination ofcogni-tive radios and secondary spectrum licensing seem intuitive,the fundamental theoretical limits of the gains to be madeby this coupling have only recently been explored [3], [5].This motivates the writing of this article, where we review thebasics of cognitive radio, and the FCC initiatives which theyopportunistically exploit. Furthermore, the current state of theart on the theoretical limits of wireless channels employingcognitive radios will be laid out, as well as a novel ideafor an achievable rate region that more fully exploits thecapabilities of cognitive radios. In short, the question ofhowmuch data can be reliably transmitted over the newly definedcognitive radio channel is posed in information theoretic

N. Devroye, P. Mitran, and V. Tarokh are with the Divisionof Engineering and Applied Sciences, Harvard University.(e-mail: {ndevroye, mitran, vahid}@deas.harvard.edu)This material is based upon research supported by the National ScienceFoundation under the Alan T. Waterman Award, Grant No. CCR-0139398.

terms, in order to conclusively explore the limits of this newchannel. This channel is modeled as a 2 sender, 2 receiverinterference channel, with one twist: thegenie. Suppose a(possibly non-cognitive) radio is transmitting. A cognitiveradio that wishes to transmit may listen to the wireless channel,and can obtain the signal of the currently transmitting user. Thegenie idealizes message knowledge, and non-causally givesthe incumbent cognitive radio full, non-causal knowledge ofthe existing transmitters’ messages. We will argue why thisis a viable model to explore, and what conclusions may bedrawn from these results. Approaching the problem from aninformation theoretic angle is novel, as the limited research oncognitive radios tends to come from a more practical, protocol-oriented perspective. We finally explore some of the regulatoryand engineering aspects that must be addressed in order torealize these gains.

II. COGNITIVE RADIO : THE SMART APPROACH

Over the past few years, the incorporation of software intoradio systems has become increasingly common. This hasallowed for faster upgrades, and has given these wirelesscommunication devices more flexibility and the ability totransmit and receive using a variety of protocols and mod-ulation schemes (enabled by reconfigurable software ratherthan hardware). Furthermore, as their name suggests, suchradios can even become “cognitive”, and, as dictated by thesoftware, adapt their behavior to their wireless surroundingswithout user intervention. According to the FCC softwaredefined radios (SDR) encompasses any “radio that includesa transmitter in which operating parameters such as frequencyrange, modulation type or maximum output power can bealtered by software without making any changes to hardwarecomponents that affect the radio frequency emissions.” Mitola[11] took the definition of an SDR one step further, andenvisioned a radio which could make decisions as to thenetwork, modulation and/or coding parameters based on itssurroundings, and called such a “smart” radio acognitiveradio. Such radios could even make decisions based on theavailability of nearby collaborative nodes, or on the regulationsdictated by their current location and spectral conditions.

One of the main players in the early development of soft-ware defined radios was the US Department of Defense’s JointTactical Radio System (JTRS) Program. The JTRS developed asoftware architecture known as the Software CommunicationsArchitecture (SCA), into which different hardware componentsmay be integrated. SCA was later adopted by commercial

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industry through a non-profit, international organizationaimedat promoting SDR technology, called the Software DefinedRadio Forum. In an alternative and parallel approach, the opensource GNU radio project hopes to encourage research anddevelopment of SDRs, allowing anyone to contribute theirown code to the already existing openly available software.In the EU, the End-to-End Reconfigurability (E2R) Project[6] aims at realising the full benefits of the diversity withinthe radio eco-space, composed of a wide range of systemssuch as cellular, fixed, wireless local area and broadcast. Thesystems they intend to develop will provide common platformsand associated execution environments for multiple air inter-faces, protocols and applications, which will yield to scalableand reconfigurable infrastructure that optimise resource usagethrough the use of cognition based methods. Other SDRresearch efforts include the collaboration of Tektronix withVirginia Tech’s Mobile and Portable Radio Research Group,DARPA’s Next Generation (XG) program, Rutger’s WINLAB,as well as a new National Science Foundation “Research inNetworking Technology and Systems” (NeTS) program.

Cognitive radio technology is perfectly suited to oppor-tunistically employ the wireless spectrum. Theirfrequencyagility, dynamic frequency selection, adaptive modulation,transmit power control, location awareness, and negotiateduse– meaning ability to incorporate agreements into theirbehavior– all allow for very flexible spectrum use. In essence,cognitive radios could skillfully navigate their way throughinterference, and greatly improve spectral efficiency. TheFCC,very enthusiastic about these possibilities, is now vigorouslyaltering their regulations to allow for more flexible use of thelicensed wireless spectrum.

III. SECONDARY MARKETS: ENCOURAGING EFFICIENCY

Since 2000, the FCC has actively been developing a Sec-ondary Markets Initiative, as well as various rulemaking re-leases regarding the use of cognitive radio technologies. Theyare interested in removing unnecessary regulatory barriers tonew, secondary market oriented policies such as:

• Spectrum leasing:allowing non-licensed users to leaseany part, or all of the spectrum of a licensed user.

• Dynamic spectrum leasing:temporary and opportunisticusage of spectrum rather than a longer-term sub-lease.

• “Private commons”: a licensee could allow non-licensedusers access to his/her spectrum without a contract,optionally with an access fee.

• Interruptible spectrum leasing: would be suitable fora lessor that wants a high level of assurance that anyspectrum temporarily in use, or leased, to an incumbentcognitive radio could be efficiently reclaimed if needed.A prime example would be the leasing of the generallyunoccupied spectrum alloted to the US government orlocal enforcement agencies, which in times of emergencycould be quickly reclaimed. Interruptible spectrum leas-ing methods resemble those ofspectrum pooling. Thework [14] provides a nice overview of spectrum poolingand solutions to some of the associated technical aspects.

In current FCC proposals on opportunistic channel usage,the cognitive radio listens to the wireless channel and deter-mines, either in time or frequency, which part of the spectrumis unused [7]. It then adapts its signal to fill this void inthe spectrum domain, by either transmitting at a differenttime, or in a different band, as shown in Fig 1. Thus, adevice transmits over a certain time or frequency bandonlywhen no other user does. Another potentially more flexible,general, and spectrally efficient approach would be toallowtwo users to simultaneously transmit over the same time orfrequency. Under this scheme, a cognitive radio will listentothe channel and, if sensed idle, could proceed as in the currentproposals, that is, transmit during the voids. On the other hand,if another sender is sensed, the radio may decide to proceedwith simultaneous transmission. The cognitive radio need notwait for an idle channel to start transmission. Some questionsthat arise with this new model are: is this really spectrallymore efficient than time sharing the spectrum? What are theachievable rates at which two users could transmit, and howdoes this compare to when the devices are not cognitive radios,yet still proceed in the same fashion? What regulatory issueswill be faced? What engineering problems will need to besolved for this to enter into the mainstream?

IV. COGNITIVE RADIO CHANNELS: EXPLOITING FLEXIBLE

SPECTRUM USAGE

Cognitive radios have the ability to listen to the surroundingwireless channel, make decisions on the fly, and encode usingavariety of schemes. In order to fully exploit this, first considerthe simplest example, shown in Fig. 2 of a channel in whicha cognitive radio device could be used in order to improvespectral efficiency. As shown on the left, suppose senderX1

is transmitting over the wireless channel to receiverY1, andthat a second, incumbent user,X2, wishes to transmit to asecond receiver,Y2. In current secondary spectrum licensingproposals, the incumbent userX2, a cognitive radio that is ableto sense the presence of other transmitting users, would eitherwait until X1 has finished transmitting before proceeding,or possibly transmit over a different frequency band. Ratherthan forcingX2 to wait, in [3] we have suggested allowingX2 to simultaneously transmit with the userX1 at the sametime in the same band of frequencies. The wireless natureof the channel will make interference between simultaneouslytransmitting users unavoidable. However, by making use ofthe capabilities of a cognitive radio, we have shown that thecognitive radio is able to potentially mitigate the interference.The question we pose is thus: what are the fundamentalcommunication limits of such a 2 sender, 2 receiver schemein which at least one user, the incumbent transmitter, is acognitive radio? To more precisely define the problem, as wellas to solve it from a theoretical perspective, we translate it intothe language of information theory.

A. Cognitive Radio Channels: Capacity versus AchievableRegions

One of the many contributions of information theory is thenotion of channel capacity. Qualitatively, it is the maximum

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rate at which information may be sentreliably over a channel.When there are multiple simultaneous information streamsbeing transmitted, we can speak of capacity regions as themaximum set of all rates which can be simultaneously reliablyachieved. For example, the capacity region of the channeldepicted in Fig 2 is a two-dimensional region, or set of rates(R1, R2), whereR1 is the rate between(X1 → Y1) and R2

is the rate between(X2 → Y2). For any point(R1, R2) insidethe capacity region, the rateR1 on the x-axis corresponds to arate that can be reliably transmitted at simultaneously, over thesame channel, with the rateR2 on the y-axis. There exist manychannels whose capacity regions are still unknown. For suchchannels, tight inner and outer bounds on this capacity regionare research goals. An inner bound is also called anachievablerate/region, and consists of suggesting a particular coding(often random coding) scheme and proving that the claimedrates can be reliably achieved, that is, that the probability of adecoding error vanishes with increasing block size. Noticethatthis guarantees the existence of schemes which can reliablycommunicate at these rates. Random coding does not constructexplicit practical schemes, and does not guarantee that betterschemes do not exist. We will demonstrate our achievableregion [3], [5] for the 2 sender 2 receiver case in which atleast one sender is a cognitive radio.

B. The Genie: message knowledge idealization

What differentiates the cognitive radio channel from abasic 2 sender, 2 receiver interference channel is themessageknowledge of one of the transmitters. This message knowledgeis possible due to the properties of cognitive radios. IfX2 isa cognitive radio, and is geographically close toX1 (relativeto Y1), then the wireless channel(X1 → X2) could be ofmuch higher capacity than the channel(X1 → Y1). Thus, in afraction of the transmission time,X2 could listen to, and obtainthe message transmitted byX1. It could then employ thismessage knowledge – which translates into exact knowledgeof the interference it will encounter – to intelligently tryto mitigate it. Although we have used transmitter proximityto motivate the message idealization assumption, and haveproposed a particular transmission scheme for this scenario,different relative distances between transmitting and receivingnodes could dictate different schemes, as is investigated in [8].Important to note is that our scheme is beneficial mostly in theweak interference case, as the strong [9], [12], and very strong[1] interference channels have known capacity regions andknown ways of achieving them. The relative node positionswill determine what type of interference channel results.

We introduce thegenie so as to idealize the messageknowledge of senderX2. That is, we suppose that ratherthan causally obtaining the messageX1 is transmitting, afictitious genie handsX2 this message. Notice thatX1 isnot given X2’s message, and so we have an asymmetricproblem. This idealization will provide an upper bound to anyreal-world scenario, and the solutions to this problem mayprovide valuable insight to the fundamental techniques thatcould be employed in such a scenario. We also expect thatunder suitable proximity of the two transmitters, this bound is

nearly achievable. The techniques used in obtaining the limitson communication for the channel employing a genie could beextended to provide achievable regions for the case in whichX2 obtainsX1’s message causally. We have suggested causalschemes in [4].

C. Achievable Region of the Cognitive Radio Channel

A cognitive radio channel [3] is a 2 transmitter,2 receiverclassical information theoretic interference channel in whichsender2 (a cognitive radio) obtains, or is given by agenie themessage senders1 plans to transmit. The scenario is illustratedin Fig. 2. The cognitive radio may then simultaneously trans-mit over the same channel, as opposed to waiting for an idlechannel as in a traditional cognitive radio channel protocol.Although the capacity region of the formulated cognitive radiochannel at first glance seems to be a simple problem, it isalso still an open one. Thus, an intuitively pleasing achievableregion for the rates(R1, R2) at whichX1 can transmit toY1,andX2 to Y2, simultaneously, was constructed in our previouswork in [3] and improved in [5]. This construction mergesideas used in dirty-paper (or Gel’fand-Pinsker) coding [2]withthe Han and Kobayashi achievable region construction [9] forthe interference channel, as well as the relay channel. WhenX2 hasa-priori knowledge of whatX1 will transmit, or theinterference it will encounter, one can think of two possiblecourses of action:

1. Selfishly try and mitigate the interference. This can be doneusing a dirty paper coding technique [2]. In this case,X2 islayering on his own independent information to be transmittedto Y2. This strategy yields points of higherR2, lower R1 inthe cognitive channel region of Figure 3.

2. Selflesslyact as a relay to reinforce the signal of userX1.Such a scheme, although it does not allowX2 to transmit itsown independent information, seems intuitively correct froma fairness perspective. That is, sinceX2 infringes onX1’sspectrum, it seems only fair thatX1 should somehow benefit.This strategy yields points of highR1 and lowerR2 in thecognitive channel region of Figure 3.

In [5] we demonstrate an achievable region that smoothlyinterpolates between these two schemes. The resulting achiev-able region, in the presence additive white Gaussian noisecase, is plotted as the “cognitive channel region” in Figure3. There, we see 4 regions. The “time-sharing” region (1)displays the result of pure time sharing of the wireless channelbetween usersX1 andX2. Points in this region are obtainedby letting X1 transmit for a fraction of the time, duringwhich X2 refrains, and vice versa. These points would beamenable to the current proposals on secondary spectrumlicensing. The “interference channel region” (2) corresponds tothe best known achievable region of the classical informationtheoretic interference channel. In this region, both sendersencode independently, and there is no message knowledge byeither transmitter. The “cognitive channel region” (3) is theachievable region proposed in our prior work [5] and describedhere. In this caseX2 received the message ofX1 non-causallyfrom a genie, andX2 uses a coding scheme which combinesinterference mitigation with relaying the message ofX1. As

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expected, the region is convex and smooth. One can think ofthe convexity as a consequence of time sharing: if any two(or more) schemes achieve certain rates, then by time-sharingthese schemes, any convex combination of the rates can beachieved. The region is smooth since our scheme actuallyinvolves power sharing at the coding level, which tends toyield rounder edges. We see that both users, not only theincumbentX2 which has the extra message knowledge, benefitfrom using this scheme. This is as expected, as the selfishstrategy boostsR2 rates, while the selfless one boostsR1 rates,and so gracefully combining the two will yield benefits to bothusers. The presence of the incumbent cognitive radioX2 canbe beneficial toX1, a point which is of practical significance.This could provide yet another incentive for the introductionof such schemes. The “modified MIMO bound” region (4)is an outer bound on the capacity of this channel: the 2x2Multiple Input Multiple Output Gaussian Broadcast Channelcapacity region, where we have restricted the form of the

transmit covariance matrix to be of the form

(

P1 c

c P2

)

,

to more closely resemble our constraints, intersected withthecapacity bound onR2 for the channel forX2 → Y2 in theabsence of interference fromX1.

V. EXTENSIONS: COGNITIVE RADIO NETWORKS

The simple2×2 wireless channel employing, and exploitingcognitive radios, can be generalized to largercognitive net-works, where we abstract the asymmetric form of transmittercooperation to a general type ofcognitive behavior. In our pre-vious work [5], we noticed that cognitive transmitter behavioris one of three fundamental types of transmitter cooperativebehavior that can be seen in wireless networks containingcognitive radios. At any given point in time, certain nodes ina wireless network wish to transmit to other nodes, indicatedby directed arcs. The wireless network can be partitioned intoclusters, as shown in Fig. 4, and different levels of transmittercooperation within, and between clusters can be investigated.The inter/intra-clustercompetitive, cooperative, andcognitivebehavior in wireless networks, as shown in Fig. 5 is definedin [5]. These represent three types of transmitter cooperationand encompass a wide range of classical information theoreticchannels. We defineinter-cluster cognitive behavior as simul-taneous transmission of messages by two or more clusters inwhich some clusters know (given by agenie) the messagesto be transmitted by other clusters, and so can selfishly use adirty paper coding-like technique to mitigate interference, orselflessly relay the messages. Similarly,intra-cluster behavioris when nodes within one cluster obtain the messages of othernodes within that same cluster and simultaneously transmit. Anachievable region for the inter-cluster behavior of two multipleaccess channels is constructed in the authors’ prior work [5].

VI. PRACTICAL CONSIDERATIONS ANDFUTURE

DIRECTIONS

As demonstrated by Fig. 3, when two users must share achannel, there is an incentive for both the cognitive and non-cognitive users of a wireless channel to employ a scheme

other than time-sharing. Better rates can be achieved byboth users. However, for such acognitive scheme to becomea reality, many practical engineering aspects must first beovercome. First, an efficient coding scheme that combines adirty-paper like scheme with a relay-like scheme will haveto be constructed. Practical coding schemes for channelswith known side-information at the transmitter have recentlyreceived a great deal of attention [15]. Such schemes couldpotentially be modified for the current needs. The achievableregion calculated requires full channel knowledge, an idealisticassumption. The construction of good codes, that perform welleven if partial or noisy channel state information is available, isanother hurdle to overcome. In addition, the genie idealizationmust be removed. In our extended work on cognitive radiochannels [4] we provide two phase protocols (listening phase,cognitive transmission phase) for which the cognitive userX2

may causally obtain userX1’s message. Although this is astart, other causal protocols will need to be developed. As thegenie represents an idealization, causal schemes may use thegenie-aided achievable region as an outer bound. Theoreticalbounds on what can be achieved in the causal case could alsobe developed. Another interesting engineering aspect wouldbe to see the intuitive tradeoff between (partial) messageknowledge and achievable rates. Then, a cognitive radio coulddecide when it has obtained a sufficient portion of the message(or with sufficient reliability) to operate at the desired pointin the region. The transmission scheme derived here assumedasymmetry in the capability of the two transmitting devices.However, in a future in which all devices are smart, newpossibilities for simultaneous transmission arise. Should bothexchange messages then transmit, or should one layer on topof the other in the currently proposed cognitive fashion? Dobetter schemes become possible when the problem becomessymmetric?

Once the basic 2 sender, 2 receiver case is solved from apractical perspective, scaling this behavior to large networksof cognitive radios must also be considered. Given a generalnetwork with cognitive nodes, we must determine which, howmany, and how the nodes should best collaborate to transmittheir respective messages. Finding protocols that performand scale well under both cognitive radio capabilities andregulatory constraints will be of vital importance.

VII. R EGULATORY CONSIDERATIONS

The FCC is trying to make the process of secondaryspectrum licensing as painless as possible. In addition, theyare aggressively working on encouraging the development anduse of cognitive radio technology. The proposed secondaryspectrum licensing, some of which lies in the VHF and UHFtelevision bands has caused some controversy [10], and theFCC is welcoming comments on issues relating to secondarylicensing of spectrum. In the EU, the E2R [6] project isalso considering the associated regulatory issues. The FCCenvisions at least 4 possible scenarios in which cognitiveradio technologies could be used to improve spectral efficiency[7]. First, a licensee would use cognitive radios internallyto increase efficiency within its own spectrum. Second, they

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could be used in easing secondary spectrum licensing, betweena licensee and a third party. Thirdly, they could facilitateautomated frequency coordination among licensees of a co-primary license. Finally, in the situation mostly consideredhere, a cognitive radio could act as an unlicensed deviceopportunistically employing the spectrum in time. Our pro-posal would require clarification of this final use: rather thanrestrict cognitive radios to time-sharing the channel, theymust obtain the right toconcurrent spectrum use, a moredelicate regulatory question. Since choice of the modulationand coding parameters would allow operation anywhere insidethe (R1, R2) achievable rate region, measures must be takento ensure that the incumbent cognitive radio, who will havepermission to simultaneously transmit, will not abuse thisrightand adversely affect the current users.

The FCC is also currently investigating what kind thetechnology in cognitive radios could guarantee the immediaterelease of any borrowed spectrum, forinterruptible spectrumleasing, or spectrum pooling [14]. This is particularly relevantin the context of governmental emergency bands, which forthe most part remain unused, and would be prime candidatesfor secondary licensing or dynamic spectrum sharing. Suchagencies will be reluctant to proceed with secondary licensingunless such a guarantee can be made. These issues havebeen addressed in [7], and could be extended to controllingincumbent cognitive radios in other scenarios as well.

VIII. C ONCLUSION

In this article, we reviewed the basics of cognitive radiosand recent FCC secondary spectrum licensing initiatives forincreasing the spectral efficiency of wireless channels. Weproposed an alternate scheme for exploiting both the cognitiveradio capabilities and the new, more flexible licensing agree-ments. This motivated the definition of thecognitive radiochannel, a 2 Tx, 2 Rx interference channel in which one userknows the message to be transmitted by the other. Fundamentallimits on communication were established for such channels,and engineering and regulatory aspects in order to approachthese limits were discussed.

REFERENCES

[1] A.B. Carleial, “Interference channels,”IEEE Trans. on Inf. Theory, vol.IT-24, pp.60-70, Jan., 1978.

[2] M.H.M. Costa, “Writing on dirty paper,”IEEE Trans. on Inf. Theory,vol. IT-29, pp. 439-441, May 1983.

[3] N. Devroye, P. Mitran, and V. Tarokh, “Achievable Rates in CognitiveRadio Channels,”39th Annual Conf. on Information Sciences andSystems (CISS), March 2005.

[4] N. Devroye, P. Mitran, and V. Tarokh, “Achievable Rates in CognitiveRadio Channels,” to appear inIEEE Trans. on Inf.Theory.

[5] N. Devroye, P. Mitran, and V. Tarokh, “Cognitive Multiple AccessNetworks,” Proc. IEEE Int. Symp. Inf. Theory, September 2005.

[6] End-to-End Reconfigurabiityhttp://phase2.e2r.motlabs.com/

[7] Federal Communications Commission Spectrum Policy Task Force,“FCC Report of the Spectrum Efficiency Working Group,” November2002.http://www.fcc.gov/sptf/files/SEWGFinalReport_1.pdf

[8] C. T. K. Ng and A. Goldsmith, “Capacity Gain from Transmitter andReceiver Cooperation,”Proceedings: IEEE International Symposium onInformation Theory (ISIT), September 2005.

[9] T.S. Han, and K. Kobayashi, “A new achievable rate regionfor theinterference channel,”IEEE Trans. on Inf. Theory, vol. IT-27, no.1, pp.49-60, January 1981.

[10] M.J. Marcus, “Unlicensed Cognitive Sharing of the TV Spectrum:the Controversy at the Federal Communications Commission,” IEEECommunications Magazine, May 2005.

[11] J. Mitola III, “Cognitive Radio: an Integrated Agent Architecture forSoftware Defined Radio.” Ph.D Thesis, KTH Royal Institute ofTech-nology, Stockholm, Sweden, 2000.

[12] H. Sato, “The capacity of Gaussian interference channel under stronginterference, ”IEEE Trans. on Inf. Theory, vol.IT-27, no. 6, November1981.

[13] Secondary Markets Initative:http://wireless.fcc.gov/licensing/secondarymarkets/.

[14] T. A. Weiss, F. K. Jondral, “ Spectrum Pooling: An Innovative Strategyfor the Enhancement of Spectrum Efficiency,”IEEE CommunicationsMagazine,Radio Communications Supplement, pp. S8 - S14, March2004.

[15] R.Zamir, S.Shamai, and U. Erez, “Nested linear/lattice codes for struc-tured multi-terminal binning, ”IEEE Trans. on Inf. Theory, vol. 48, no.6, June 2002.

PLACEPHOTOHERE

Natasha Devroye (S’01) received the Bachelor’sdegree in electrical engineering in 2001 from McGillUniversity, Montreal, PQ, Canada. She received herMaster’s degree in 2003 from the Division of Engi-neering and Applied Sciences at Harvard University,Cambridge, MA, where she is currently workingtowards her Ph.D degree. In 2005, she interned as aresearch scientist for Intel Corporation in the RadioCommunications Lab.

Her research interests include multi-user informa-tion theory, wireless networks, as well as cognitive

radio communications.

PLACEPHOTOHERE

Patrick Mitran (S’01) received the Bachelor’s andMaster’s degrees in electrical engineering, in 2001and 2002, respectively, from McGill University,Montreal, PQ, Canada. He is currently workingtoward the Ph.D. degree in the Division of Engi-neering and Applied Sciences, Harvard University,Cambridge, MA. In 2005, he interned as a researchscientist for Intel Corporation in the Radio Commu-nications Lab.

His research interests iterative decoding, dis-tributed/joint source-channel coding, cooperative

and cognitive communications as well as information theory.

PLACEPHOTOHERE

Vahid Tarokh (M’95, SM’03) is a Perkins Professorof Applied Mathematics and a Vinton Hayes Se-nior Research Fellow of Electrical Engineering atHarvard University, where he defines and supervisesresearch in the general areas of signal processing,communications and networking.

He has received a number of awards includingGold Medal of the Governor General of Canada1995, IEEE Information Theory Society Prize PaperAward 1999, The Alan T. Waterman Award 2001and was selected as one of the Top 100 Inventors of

Years (1999-2002) by the Technology Review Magazine. He holds honourarydegrees from Harvard University (2002) and the University of Windsor (2003).

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X 2 Y 2Y 1X 1W I S H E S T OT R A N S M I T T R A N S M I T I NA D I F F E R E N TB A N D

B E F O R EW A I T U N T I LO T H E R I S D O N E T H E NT R A N S M I T

A F T E RX 1 Y 2Y 1X 2 X 1 Y 2Y 1X 2X 1 Y 2Y 1X 2

Fig. 1. Current proposals for dynamic spectrum leasing involve twoschemes: when a cognitive radioX2 wishes to transmit toY2 anda possibly non-cognitiveX1 is already transmitting toY1, it caneither wait untilX1 has completed its transmission (time division,as in the top figure), or possibly transmit at a different frequencyband (frequency division, as in the bottom figure). In eithercase,time or frequency division is employed, rather than sharingthetime/frequency spectrum.X 1W I S H E S T OT R A N S M I T G E N I E I N T E R F E R E N C EB E F O R E A F T E RY 2Y 1X 2 X 1 Y 2Y 1X 2Fig. 2. The cognitive radio channel is defined as a 2 sender (X1, X2),2 receiver (Y1, Y2) interference channel in which the cognitive radiotransmitterX2 is non-causally given, by agenie the messageX1

plans to transmit.X2 can then either mitigate the interference it willsee, or aidX1 in transmitting its message, or as we propose, a smoothmixture of both.

0 0 . 5 1 1 . 5 2200 . 511 . 51 . 5

R 1R 2 ( 1 ) T i m e W s h a r i n gr e g i o n( 2 ) I n t e r f e r e n c ec h a n n e lr e g i o n ( 3 ) C o g n i t i v ec h a n n e lr e g i o n ( 4 ) M o d i fi e dM I M Ob o u n dFig. 3. Rate regions(R1, R2) for different 2 sender, 2 receiverwireless channels. Region (1) is the time-sharing region oftwoindependent senders. Region (2) is the best known achievable regionfor the interference channel, as calculated by Han and Kobayashi[9]. Region (3) is the achievable region described here and in [5]for the cognitive radio channel. Region (4) is an outer boundon thecognitive radio channel capacity. All simulations are in AWGN, withsender powers6, and noise powers1. The cross-over parameters inthe interference channel are 0.55 and 0.55.

Fig. 4. A wireless network at a given instance in time can bepartitioned into clusters.

I N T E R F E R E N C E G E N I E I N T E R F E R E N C E G E N IE I N T E R F E R E N C E( a ) ( b ) ( c )Fig. 5. Wireless clusters of nodes can behave in 3 fashions: (a) theycan compete for the wireless resources (competitive), (b) partiallycooperate (cognitive), and (c) fully cooperate during transmission(cooperative). Hereinter-cluster, or transmitter behavior betweenclusters is demonstrated.