Cooperative Spectrum Sensing in Cognitive Radio Networks

Transcription

1 Cooperative Spectrum Sesig i Cogitive Radio Networks Ghurumuruha Gaesa ad Ye (Geoffrey) Li School of Electrical ad Computer Egieerig Georgia Istitute of Techology, Atlata, Georgia Abstract I cogitive etworks, cogitive (ulicesed) users eed to cotiuously moitor spectrum to detect the presece of primary (licesed) users I this paper, we illustrate the beefits of cooperatio i cogitive radio We show that by allowig the cogitive radios operatig i the same bad to cooperate we ca reduce the detectio time ad thus icreasig their agility We first cosider the case of two cogitive users ad show how the iheret asymmetry i the etwork ca be exploited to icrease the probability of detectio We the exted our work to multiple cogitive user etworks We also propose a practical algorithm which allows cooperatio i radom etworks Idex Terms cogitive radio, cooperative diversity, agility gai, detectio time I INTRODUCTION Recetly there has bee tremedous iterest i the field of software defied radio (SDR) ad its relatively ewer versio cogitive radio (CR) SDR, which has bee itroduced i [1], achieves sigificat improvemets over services offered by curret wireless etworks With SDR, the software embedded i a radio cell phoe, for example, would defie the parameters uder which the phoe should operate i real-time as its user moves from place to place CR is eve smarter tha SDR CR is desiged to be aware of ad sesitive to the chages i its surroudigs Thus it lears from its eviromet ad performs fuctios that best serve its user This is a very crucial feature of CR etworks sice, curretly, the Federal Commuicatios Commissio (FCC) is reviewig its policies regardig the usage of licesed bads by ulicesed users [2] I this cotext, the greatest advatage of CR is that it ca be operated i licesed bads without a licese Sice the cogitive (ulicesed) users are utilizig the licesed bad, they must detect the presece of licesed (primary) users i a very short time ad must vacate the bad for the primary users Thus oe of the major challeges that cofrots this techology is: how do the cogitive (ulicesed) radios sese the presece of the primary (licesed) user? Oe may expect this to be trivial but as show i [3], there are fudametal limits to the detectio capabilities of CR etworks I this paper, we show improvemet i spectrum sesig capabilities through cooperatio betwee idividual cogitive users Cooperative schemes with orthogoal trasmissio i a TDMA system have bee recetly proposed i [4] ad [5] Correspodig Author: guru@ecegatechedu, phoe/fax : / It has bee show i [4] that two user sigle hop etworks i which oe of the user acts as a relay for the other, result i lower outage probabilities I particular, it is show that the amplify-ad-forward (AF) protocol [4], i which the relay trasmits the sigal obtaied from the trasmitter without ay processig, achieves full diversity I this paper, we study the effect of the AF cooperatio protocol o the spectrum sesig capabilities of multi-user sigle-carrier cogitive radio etworks Aalysis of multi-user sigle carrier etworks ca be foud i [6] I [6], we describe a cooperatio scheme where the relay user is assumed to have o power costrait However i practice all relay users have power costrait I this paper, we describe a power costraied cooperatio scheme The paper is orgaized as follows: I Sectio II, we describe the system model ad formulate the problem of the primary user detectio i a simple two user cooperative etwork We also propose a practical cooperatio scheme to detect the primary user To show that cooperatio leads to reduced detectio time, i Sectio III, we cosider a simple two-user asymmetric cogitive radio etwork ad derive expressios for agility gai I Sectio IV, we aalyze multiuser sigle-carrier cogitive etworks with ad without cetralized schedulig ad derive precise coditios uder which agility gai is achieved Fially, i Sectio V, we preset our coclusio We first itroduce a few otatios we shall be usig throughout the paper Cosider ay two o-egative fuctios fuctios f(x) ad g(x) The followig are stadard otatios [7]: 1) We say f(x) =Ω(g(x)), if there exists a costat C 2 > 0 such that f(x) >C 2 g(x) for sufficietly large x 2) We say f(x) =Θ(g(x)) if there exists costats C 3,C 4 > 0 such that C 3 g(x) f(x) C 4 g(x) for sufficietly large x The followig are the symbols used throughout the paper: U 1,U 2 : Cogitive (ulicesed) users : Received power at U 1 due to the primary user P 2 : Received power at U 2 due to the primary user G 12 : Chael gai betwee U 1 ad U 2 θ : Primary user idicator; θ =1implies presece of the primary user ad θ =0implies its absece II COOPERATION SCHEME I this sectio, we describe the chael model that will be used throughout the paper, formulate the primary user detectio problem ad propose a practical cooperatio scheme to improve the agility US Govermet Work ot protected by US Copyright 137

2 A System Model I this paper, we assume that all chaels experiece Rayleigh fadig Moreover, chaels correspodig to differet cogitive users are assumed to be idepedet If a sigal x is set, the received sigal y is give by y = fx+ w, where the fadig coefficiet f ad the additive oise w are modelled as idepedet complex Gaussia radom variables Uless otherwise metioed, the oise i this paper is assumed to be of zero mea ad uit variace We also assume that each user has access to its chael state iformatio This is facilitated by allowig the base statio to trasmit pilot symbols at regular itervals B Detectio Problem A importat requiremet of a cogitive radio architecture is to detect the presece of primary or licesed users as quickly as possible For this reaso cogitive users should cotiuously sese the spectrum Cosider a etwork with two cogitive radio users U 1 ad U 2 operatig i a fixed TDMA mode for sedig data to some base statio Suppose that a primary (licesed) user starts usig the bad The the two cogitive users eed to vacate the bad as soo as possible to make way for the primary user However, the detectio time becomes sigificat if oe of the users, say U 1 is i the boudary of decodability as illustrated i Figure 1 The sigal received from the primary user is so weak that the cogitive user U 1 takes a log time to sese its presece We show that cooperatio betwee the cogitive users ca reduce the detectio time of the weaker user thereby improvig the agility of the overall etwork We shall defie these terms more precisely i Sectio III Throughout the paper, we allow the cogitive users, U 1 ad U 2, to cooperate, with U 2 actig as a relay for the U 1 Figure 1 describes a sceario where two cogitive users U 1 ad U 2 are egaged i trasmittig data to a commo receiver i a particular frequecy bad Slotted trasmissio is used wherei U 1 ad U 2 trasmit i successive slots followig the AF protocol [4] as show i Figure 2 Accordigly i time slot T 1, U 1 trasmits ad U 2 listes I time slot T 2, U 2 relays the iformatio of the previous slot Ukow to both these users, there is a primary user who has higher priority i occupyig the bad It is crucial that presece of this primary user be detected as soo as possible I time slot T 1, the sigal received by U 2 from U 1 is give by, ỹ = θh p2 + ah 12 + w, (1) where h pi deotes the istataeous chael gai betwee the primary user ad U i, h 12 deotes the istataeous chael gai betwee U 1 ad U 2, ad w is the additive Gaussia oise We assume that h p2, h 12, ad w 2 are zero-mea complex Gaussia radom variables which are pairwise idepedet Also we assume that the chaels are reciprocal, ie, h 12 = h 21 I (1), a deotes the sigal set from U 1 such that E{a} =0ad θ deotes the primary idicator; θ =1implies presece of the primary user ad θ =0implies its absece If the trasmit power costrait of U 1 is P the, E{ ah 12 2 } = PG 12, where G 12 = E{ h 12 2 } refers to the chael gai betwee the users U 1 ad U 2 Sice h p2,h 12 ad w are assumed pairwise idepedet, we have from (1) that E{ ỹ 2 } = θ 2 P 2 + PG where P 2 = E{ h p2 2 } refers to the received power at U 2 due to the primary user I time slot T 2, the relay user U 2 relays the message from U 1 to a commo cogitive receiver The relay user has a maximum power costrait P Hece it measures the average received sigal power [8] ad scales it appropriately so that its power costrait P is satisfied I slot T 2, whe U 2 is relayig the message of U 1, we allow U 1 also to liste to its ow message The the sigal received by U 1 from U 2 is give by y = βỹh 12 + θh p1 + w = βh 12 (θh p2 + ah 12 + w)+θh p1 + w, where h p1 is the istataeous chael gai betwee the primary user ad U 1, w is additive Gaussia oise ad β is the scalig factor [4] used by U 2 to relay the iformatio to the commo receiver I fact β is give by [4] [8] P β = E{ ỹ 2 } = P θ 2 P 2 + PG After the message compoet is cacelled, the user U 1 is left with the sigal Y = θh + W, where H = h p1 + βh 12 h p2 ad W = w + βh 12 w The detectio problem ca be ow stated as: Give the observatio the detector decides o or Y = θh + W, H 1 : θ =1 H 0 : θ =0 I [6], we describe a variat of the above algorithm where there is o power costrait o the relay user U 2 However i practice all users have power costrait The detectio problem for the costraied cooperatio scheme described above is idetical to the ucostraied cooperatio scheme i [6] (see Eq(3) i [6]) As i [6], we use the eergy detector (ED) [9] to detect the presece of primary user Sice the derivatio of the detectio probability is very similar to the ucostraied cooperatio scheme i [6], we skip the details i this paper ad preset the fial result The details ca be foud i [6] Defiig ϕ(t; a, b) = e h t a+bh dh 0 138

3 for positive t, a, ad b, we have the followig propositio: Propositio 1: Let c ad deote the detectio probabilities of U 1 with ad without cooperatio from U 2 respectively We have c = ϕ(λ; +1, β(p 2 + 1)) (2) ad where β = = α 1 +1, (3) PG 12 θ 2 P 2 + PG ad λ is uiquely determied by ( ) PG 12 ϕ λ;1, = α PG I Figure 3, we have plotted ad c as a fuctio of P 2 for P = P = 1 For a path-loss expoet of 35, we have plotted ad c for three differet values of : =1, 25, ad 6 For each value of, we ote that the costraied cooperatio scheme is beeficial ( c > ) oly for a certai rage of the power level at U 2,P 2 Also the maximum achievable probability gai is depedet o the positio of the cogitive user U 1 From Figure 3, we see that the maximum gai is achieved whe U 2 is optimally placed betwee the primary user ad U 1 Whe P = P =1, we have extesively evaluated (2) ad (3) for various values of false alarm probability α ad path loss expoet δ Usig umerical calculatio, we ca easily cofirm the followig fact: Observatio 1: IfP 2 = G 12, the c > This is supported by Figure 4 where we have plotted c as a fuctio of for differet values of δ betwee 3 ad 6 This Observatio is useful i Sectio IV, whe we discuss optimal pairig schemes for radom etworks III AGILITY OF THE TWO USER COGNITIVE RADIO NETWORK So far, we have devoted ourselves to improvemet i detectio probabilities through cooperatio The fial goal, however, is to reduce the overall detectio time To show the effect of cooperatio o the overall detectio time, we shall defie two types of protocols employig differet degrees of cooperatio We assume that there is a commo base statio (capable of both receivig ad sedig) with which all the cogitive users commuicate 1) No Cooperative (NC) Protocol : All the users detect the primary user idepedetly However the first user to detect the presece of the primary user iforms the other users through the commo receiver 2) Totally Cooperative (TC) Protocol : This employs the costraied cooperatio scheme described i Sectio II Thus two users operatig i the same carrier, if placed sufficietly ear to each other, cooperate to fid the presece of the primary user The first user to detect the presece of the primary user iforms the others through the commo base statio Let T ad T t deote the average time take by the two user etwork described i Sectio II to detect the primary user uder NC ad TC protocol, respectively As before, let c ad be give by (2) ad (3) We have the followig propositio Propositio 2: Ifp (2) = α 1 P 2 +1, the we have, ad T = T t = 2 p(1) +p(2) 2, + p (2) p (2) 2 p(1) c +p(2) 2 c + p (2) c p (2) We defie the agility gai of the TC protocol over the NC protocol as T µ /t = T t I Figure 5, we have plotted the agility gai µ /t uder the costraied cooperatio scheme We fid that as U 1 is farther from the primary user, the maximum agility gai icreases Whe = 1, the maximum agility gai is see to be approximately 15 This implies a decrease i the detectio time by approximately 34% Sice the cogitive users eed to cotiuously moitor spectrum, a decrease of 34% i the detectio time is very useful i the log term IV MULTIUSER COGNITIVE NETWORK Throughout the sectio, we have cosidered the simple case of two user etwork What happes whe there are more tha two users? How ca we cooperate the users to achieve agility gai? I this sectio, we shall cosider the presece of more tha two cogitive users Ideally sice there are may users, we would like to fid a optimal cooperatio algorithm (possibly) ivolvig more tha two users that would achieve eve more gai tha a simple two-user etwork However, this leads to complex detectio algorithms which perform better oly at the cost of great computatioal complexity We kow from Sectios II ad III that groupig the users ito pairs leads to icreased detectio probability if i each pair, oe user acts as a relay for the other Thus a alterative solutio would be to fid a relay for each user who seeks help ad to hope that the overall detectio time is reduced Ca we fid a relay user for each user who eeds help? Ca we still achieve agility gai over o-cooperatio? Let {U k } m k=1 deote the set of users iside the boudary of decodability of the primary user Further let P k deote the received power from the primary user at cogitive user U k If P low deotes the received power due to the primary user at the boudary of decodability, the all the cogitive users with power level P k >P low have to be vacated as soo as possible for the primary user Sice the cogitive users caot be arbitrarily close to the primary user, we assume P k <P upp for some fiite P upp For ay two power levels P A ad P B, defie U(P A,P B )={U k : P A P k P B } 139

4 I the costraied cooperatio scheme of Sectio II, we fid that for a particular cogitive user U 1 to be beefitted by cooperatio, it is essetial that the relay user U 2 is closer to the primary user tha U 1 (see Figure 3) I geeral, it is practically difficult to assig a relay user for each cogitive user I such a case, we defie the critical power P of a detectio scheme i the followig way: If a particular cogitive user U k U(P low,p ), we allow the user U k to search for a relay user If o the other had U k U(P,P upp ) the U k does ot seek help from ayoe The ratioale behid this is that users close to the primary user already have good detectio probabilities So they ca help the users far away from the primary user to improve their detectio probabilities We ca visualize the above procedure the followig way: Ay cogitive user U k U(P low,p upp ) causes iterferece to the primary user ad must be vacated We have divided the user set U(P low,p upp ) ito two subsets A = U(P low,p ) ad B = U(P,P upp ) such that users i A seek help from users i B Let ad ñ be the umber of users i A ad B respectively ad let m = +ñ I geeral, there ca be may ways to determie the critical power, P For example, we ca fix a threshold probability of detectio p such that if the detectio probability of a cogitive user is greater tha p without cooperatio the it does ot search for ay relay user From (3), we fid that P is uiquely determied by α 1 P +1 = p, yieldig ( l (α/p P ) ) = l p where α is the tolerable false alarm probability Throughout this paper we discuss oly sigle-carrier multi-user etworks Discussio of multi-carrier multi-user etworks ca be foud i [6] A Cetralized Networks I this sectio, we shall assume that all the m = +ñ users are i U(P low,p upp ) ad operate i the same frequecy bad Cosider two users U 1 U(P low,p ) ad U 2 U(P,P upp ) with G 12 beig the chael gai betwee them Further let U 2 act as a relay for U 1 ad let the positio of U 1 be fixed, ie, let be fixed We search through the (P 2,G 12 ) space to fid a optimal relay user for U 1 As before, let c ad give by (2) ad (3) deote the detectio probabilities of U 1 with ad without cooperatio from U 2, respectively Defie P( )={(P 2,G 12 ): c > } to be the critical regio for the user U 1 It is obvious that U 1 ca beefit from cooperatio oly if the relay user U 2 is iside its critical regio P( ) Without loss of geerality, we let U(P low,p )={U k } k=1 ad U(P,P upp )={U k } m k=+1 I this sectio, we assume that there is a cetralized scheduler that implemets the cooperatio protocol described below If all the users i U(P low,p upp ) follow the cooperatio protocol, we say that the users follow the TC protocol If Algorithm 1 Multi-user Cooperatio Protocol (Cetralized) 1: A = {U k } k=1 = U(P low,p ) 2: B = {U k } m k=+1 = U(P,P upp ) 3: for k =1to do 4: for j = +1 to m do 5: if (P j,g jk ) P(P k ) the 6: Cogitive user k is assiged cogitive user j as a relay user 7: k = k +1 8: ed if 9: ed for 10: Cogitive user k detects the primary user by itself 11: ed for o the other had, all the users detect the primary user by themselves with o cooperatio, they are said to follow the NC protocol Sice all users are operatig i a sigle carrier, we allow them to operate i a TDMA mode I that case, the order i which the users operate becomes a importat issue Let p k deote the detectio probability of the k th cogitive user Suppose ow that the detectio probabilities satisfy p 1 p 2 p m ad we follow the orderig (m, m 1,, 1) The the detectio time is the least amog all permutatios of the users sice the cogitive user with the best chace of detectig the primary user operates first However this is always ot guarateed I geeral, followig a suboptimal orderig ca result i more time for detectio Whe there are m users there are m! ways to arrage their operatio cycle Ay orderig S is a elemet of T m Give a orderig S T m, let T (m S) ad T t (m S) deote the time take to detect the primary user whe all the m users are uder NC protocol ad TC protocol respectively We have the followig result: Propositio 4: Letmbe the umber of cogitive users operatig i a sigle carrier The for ay give orderig S T m, we have 1 <T t (m S) T (m S) However, as argued before, there is a possibility that the users with the best chace of fidig the primary user operate after a log time i a cycle To improve the detectio capability, we allow users to operate i a time-hoppig fashio Hece after every cycle ivolvig the operatio of all the m users, we choose a orderig radomly from T m Note that i this sectio, we assume that there exists a cetralized scheduler to pair the users Thus oe ca argue that the scheduler ca select the optimal orderig S opt T m where S opt = arg mi{t t (m S)} S T m However our ultimate goal is to develop decetralized cooperatio schemes With this i mid, we adopt the radom orderig strategy Sice all the orderigs are equally likely, we get that the average detectio time i case of TC ad NC protocol are 140

5 give, respectively, by ad T t (m) = 1 T t (m S) m! S T m T (m) = 1 T (m S) m! S T m We defie the agility gai i this case to be ad also let µ m = T (m) T t (m) µ = lim m µ m if it exists The followig result summarizes the behaviour of asymptotic agility gai Propositio 5: Letm be the total umber of users operatig i a sigle carrier The (a) For ay m, we have, (b) Whe µ m µ, we have 1 µ m < 1 µ < Sice there is a possibility of µ =1, we wish to kow whe there is agility gai Cosider two users U 1 U(P low,p ) ad U 2 U(P,P upp ) with U 2 actig as a relay for U 1 As before, give by (2) ad (3) deote the detectio probabilities of U 1 with ad without cooperatio from U 2 respectively Defiitio: We say that cogitive user U 1 U(P low,p ) is a happy user if let c ad c ɛ 0 (4) for some ɛ 0 > 0 ad idepedet of,p 2 ad G 12 Let c() deote the umber of happy users out of the users i U(P low,p ) The followig theorem gives a simple sufficiet coditio for the agility gai to be greater tha oe Theorem 1:(Agility Gai Theorem) Let ad ñ deote the umber of users i U(P low,p ) ad U(P,P upp ) respectively The as m = +ñ, we have (a) If ñ 0, the µ m 1 (b) If =Ω(ñ) ad c() =Ω() the µ m = 1 + Ω(1) Sice c(), the previous theorem implies that we get agility gai from cooperatio if c() =Θ() The worst case occurs whe all users i U(P low,p ) are scheduled to trasmit first Though the primary user will evetually be detected, the time take will be greatly reduced i case of cooperative etworks sice each user i U(P low,p ) is liked with a user i U(P,P upp ) whose help ca greatly improve the detectio probability ad hece the overall agility B Decetralized Networks The results of Sectio IVA ca be used to desig practical pairig schemes whe the locatio of users are radom ad there is o cetralized scheduler Let us assume that the locatio of the primary user is kow to all the cogitive users Thus each user kows its positio from the primary user We assume that the power level P k of the cogitive user U k is uiformly distributed i [P low,p upp ] Let a particular cogitive user U 1 be i U(P low,p ) I the previous sectio, we assumed that there was a cetralized scheduler which assiged a relay user for U 1 iside its critical regio P( ) However ow there is o cetralized scheduler ad i geeral P( ) may ot be eve of regular shape Also all the cogitive users have limited trasmissio rage Thus G 12 G low for some positive G low Sice the distace betwee ay two cogitive users is strictly positive, G 12 G upp for some fiite G upp I such a practical situatio, how does the user U 1 fid a relay such that (4) is satisfied A ad-hoc solutio would be the followig: (1) For some iteger N, partitio [P low,p ] ito N subitervals {I l } N l=1 where each I l is of width P P low N (2) Partitio [P,P upp ] ito N subitervals {J l } N l=1 where each J l is of width Pupp P N (3) Partitio [G low,g upp ] ito N subitervals {G l } N l=1 where each G l is of width Gupp Glow N (4) For each I l determie a regio J l ad G l with the followig property: If a cogitive user U 1 is i I l ad is able to fid a relay user U 2 i J l ad G 12 G l, the U 1 is a happy user, ie, (4) is satisfied (5) Assig label l to users i I l ad J l Thus i effect we have discretized the search space for each cogitive user This allows practical implemetatio Also for auseru k i U(P low,p upp ) let l(k) deote its label We say that a cooperative detectio scheme has a pairig protocol if we are able to do steps (1)-(5) metioed above We ow ask the questio: Does there exist a pairig protocol for our cooperatio scheme? The followig theorem aswers the questio: Theorem 2: Suppose Observatio 1 holds, ie, for ay two users U 1 ad U 2, if P 2 = G 12 the c > The the costraied cooperatio scheme of Sectio II has a pairig protocol We describe the decetralized pairig protocol below: Algorithm 2 Multi-user Cooperatio Protocol (Decetralized) 1: A = {U k } k=1 = U(P low,p ) 2: B = {U k } m k=+1 = U(P,P upp ) 3: for k =1to do 4: Cogitive user U k trasmits a request for relay statig its label l(k) 5: if j with P j J l(k) ad G jk G l(k) the 6: Cogitive user U j replies to U k 7: else 8: Cogitive user k detects the primary user by itself 9: ed if 10: ed for 141

6 I step (5) of the above protocol, if more tha oe user respods back to a cogitive user U 1 seekig help, the U 1 chooses oe of the users radomly As before, let ñ deote the umber of users i U(P,P upp ) ad = m ñ deote the umber of users i U(P low,p ) We kow from the Agility Gai theorem, that whe ñ 0 there is o agility gai Let us the assume that =Ω(ñ) ad let c() be the umber of happy users i U(P low,p ) If we ca esure that P U 2 Boudary of decodability of P P : Primary user U 1 : User 1 U 2 : User 2 c() =Ω(), (5) our scheme is defiitely beeficial Ca we esure (5) with probability 1? The followig theorem tells whe that is possible Theorem 3: Uder the hypothesis of Theorem 2, as m, U 1 Ordiary lik Relay lik c() =1 with probability 1 if ad oly if ñ Thus we have esured that µ m = 1 + Ω(1) with probability 1 I essece, we have developed a practical algorithm for pairig i radom etworks which is asymptotically optimal ad thus has reduced detectio time The algorithm is very importat i practical systems because the cogitive users eed to cotiuously sese the spectrum ad shift bads to avoid iterferece with the primary users I this cotext, algorithms which reduce detectio time eve by a small amout are very useful Fig 1 Fig 2 Cooperatio i cogitive etwork U 1 Tx U 2 Relay U 2 Tx U 1 Relay Relay protocol used time V CONCLUSION AND FUTURE WORK I this paper, we have show the beefits of cooperatio i icreasig the agility of cogitive radio systems We have take a asymmetric two user cooperative cogitive etwork ad show improvemet i probability of detectio leadig to ehaced agility We have the cosidered the geeral user sigle carrier cogitive etwork ad derived a simple sufficiet coditio for asymptotic agility gai We have also cosidered the case whe the users are radomly distributed ad stated coditios uder which agility gai ca be achieved I this paper, we have assumed the locatio of the primary trasmitter I future, we wish to develop cooperative protocols whe the primary trasmitter locatio is ukow to the cogitive users Also, we wish to cosider other practical issues like mobility of the cogitive users, effect of shadowig ad the presece of more tha oe cogitive cluster [6] G Gaesa ad Y G Li, Agility improvemet through cooperative diversity i cogitive radio etworks, i GLOBECOM 2005, St Louis, Missouri, accepted for publicatio [7] C E L T H Corme ad R L Rivest, Itroductio to Algorithms, 1st ed MIT Press, 1990 [8] I Hammerstrom, M Kuh ad A Wittebe, Cooperative diversity by relay phase rotatios i block fadig eviromet, i Fifth IEEE Workshop o Sigal Process Advaces i Wireless Commu, July 2004 [9] H V Poor, A Itroductio to Sigal Detectio ad Estimatio, 2d ed Spriger-Verlag, 1994 REFERENCES [1] I J Mitola, Software radios: Survey, critical evaluatio ad future directios, IEEE Aerosp Electro Syst Mag, vol 8, pp 25 31, Apr 1993 [2] FCC, Spectrum policy task force report, ET Docket No , Nov 2002 [3] A Sahai, N Hove ad R Tadra, Some fudametal limits i cogitive radio, i Proc Allerto Cof o Commu, Cotrol ad Computig, Oct 2004 [4] J N Laema ad D N C Tse, Cooperative diversity i wireless etworks: Efficiet protocols ad outage behaviour, IEEE Tras Iform Theory, vol 50, pp , Dec 2004 [5] J N Laema ad G W Worell, Distributed space-time coded protocols for exploitig cooperative diversity i wireless etworks, IEEE Tras Iform Theory, vol 49, pp , Oct

7 Cooperatio No cooperatio = 1 probability of detectio by U = 25 = measure of assymetry (log (P )) 10 2 Fig 3 Cooperatio improves probability of detectio δ = 55 δ = 45 δ = p c (1) p (1) power at U, (P ) 1 1 Fig 4 Icrease i detectio probability whe U 2 is placed optimally betwee U 1 ad the primary user = 1 = 25 = agility gai (µ /c ) measure of assymetry (log (P )) 10 2 Fig 5 Agility gai i two user etworks uder the costraied scheme 143