A Return and Risk Model for Efficient Spectrum Sharing in Cognitive Radio Networks

Transcription

1 A eturn and sk Model for Effcent Spectrum Sharng n Cogntve ado Networks Mao Pan,HaoYue, Yuguang Fang and Phone Ln Department of Electrcal and Computer Engneerng, Unversty of Florda, Ganesvlle, FL 326, USA Department of Computer Scence and Informaton Engneerng, Natonal Tawan Unversty, Tape, 06, Tawan Abstract Cogntve ado technology releases the spectrum from shackles of authorzed lcenses and facltates the tradng of spectrum bands. In the spectrum market, prmary users PUs set prces for ther vacant bands and sell them for monetary gans, and secondary users SUs buy the bands and opportunstcally use them to satsfy ther servce demands when the PUs are not actve. However, when there are multple bands avalable for the SUs to access, the SU confronts the challenges of how to choose bands and how to splt hs traffc over them consderng both the contenton from peer SUs as well as the unpredctable actvtes of the PUs. In ths paper, we propose a return and rsk model to represent these concerns of the SU, and help the SU to make approprate decsons of traffc dstrbuton over avalable spectrum bands, ether the bands belongng to SU tself or the bands shared wth PUs. The smulaton and analyss show that our spectrum sharng scheme s effcent n terms of maxmum return for gven rsk or mnmum rsk for gven return, and s also effectve n mprovng the spectrum utlzaton and SUs satsfactory degrees. Index Terms Cogntve ado, eturn, sk, Mx of Bands I. INTODUCTION ecent years has wtnessed the boomng growth of wreless networks and floursh of varous wreless servces. In parallel wth that, current statc spectrum allocaton polcy of Federal Communcatons Commsson FCC [] results n the exhauston of avalable spectrum, whle many lcensed spectrum bands are extremely under usage. As one of the most promsng solutons to mprove spectrum utlzaton, cogntve rado technology allows the SUs to opportunstcally access to vacant bands belongng to PUs n ether temporal or spatal doman [2], [3]. The dea of openng up the lcensed spectrum bands n cogntve rado networks ntates the market of spectrum tradng, and promotes a batch of nterestng research on related topcs. Specfcally, n [4], Grandblase has generally descrbed the possble scenaros and ntroduced some mcroeconomcs nspred mechansms of dynamc spectrum access; from the PUs aspect, Xng [5] and Nyato [6] have well nvestgated the spectrum prcng ssues n the spectrum market where multple PUs compete wth each other to offer spectrum access to the SUs; from the SUs aspect, people are nterested n how the SU chooses to dstrbute hs traffc over the spectrum The work of Pan, Yue and Fang was partally supported by the U.S. Natonal Scence Foundaton under grant CNS-09639, CNS and CNS The work of Ln was partally sponsored by the Natonal Scence Councl NSC, OC, under contract numbers NSC E MY2, NSC E and NSC E , and the Mnstry of Educaton, OC, under contract numbers and bands when there s more than one unoccuped lcensed band. Motamed [7] has formulated ths problem as a multarmed bandt problem and proposed a renforce learnng algorthm to consstently track the best band n terms of band condton. However, f the SU ontly consders the contenton among the SUs and the actvtes of PUs n cogntve rado networks, the concept of the best band tends to be ambguous snce he can nether dentfy the band wth least competton among SUs as the best band, nor regard the one wth most possblty of PU s absence as the best band. In ths paper, we propose to leverage SU s expected return to model the contenton among SUs and the varance of return to represent the potental rsk of PUs comng back. Instead of swarmng all the traffc over the best band, we make the SU splt hs traffc on a dversfed mx of bands. In partcular, we llustrate how the SU effcently dstrbutes hs traffc over the rsk free band of hs own and rsky bands shared wth PUs, and how the SU effcently selects the mx of rsky bands belongng to PUs. Smulaton results show that the proposed spectrum sharng scheme s effcent n the sense that the SU s able to obtan maxmum return for gven rsk or carry on mnmum rsk for gven return, except for t s effectve n mprovng the spectrum utlzaton and SUs satsfacton. II. SYSTEM MODEL A. Overvew We consder a wreless system wth multple PUs operatng on dfferent spectrum bands and multple SUs who can take opportunstc use of these frequences. That s to say, consderng the constrants of geographcal locaton, SUs are able to access to dfferent spectrum bands belongng to dfferent PUs when the PUs servces are not on; SUs must dsconnect and move out of PU s spectrum bands mmedately when PUs become actve. For example, as shown n Fg.a, the leftmost SU can opportunstcally access to the spectrum bands owned by {PU,PU 2,,PU } snce he s n the coverage of these PUs The grey part of PU s spectrum represents the currently vacant spectrum bands whch the SUs can access to. A PU may own more than one avalable spectrum band at a gven tme pont.. Smlarly, the rghtmost SU has to opportunstcally The process of selectng a mx of bands may be dvded nto two stages. The frst stage starts wth samplng and observaton, and ends wth statstcal values about the future performances of avalable spectrum bands [8]; the second stage starts wth the relevant values about future performances, and ends wth the selecton of the band mx. In ths paper, we are only concerned wth the second stage /0/$ IEEE

2 Prce p Spectrum F Prce p Prce p a System archtecture t 0 t t 2 t τ Spectrum F N Seller-layer Prce pn Buyer-layer b Perodcal spectrum sellng t n Prmary User Secondary User tme Fg.. System model for spectrum sharng use the spectrum bands of {PU,PU +,,PU n } because of hs locaton. From the vew of PUs, they allow unlcensed SUs to opportunstcally use ther bands for monetary purposes. In ths case, a PU wll set reasonable prces for hs unoccuped bands consderng the band condton as well as competton among the PUs n the spectrum market [5], [6], and sell those bands perodcally to enlarge hs revenue as shown n Fg.b. On the other hand, the SUs need to decde how to access to, or say how to buy, those vacant spectrum bands wth dfferent characterstcs. Intutvely, the decson-makng process of the SU must take the contenton from the other SUs.e., the competton for the transmsson opportuntes among the SUs, ust the same as n the pure Ad-hoc networks and prce of the avalable spectrum bands nto consderaton. Besdes, the SUs are also concerned wth qualty of the bands, and worred about the unpredctable comng back of PUs traffc. B. Qualty of the Spectrum Bands As for a SU, the characterstcs of the avalable bands shared by the PUs are not dentcal. The qualty of those bands may be evaluated qute dfferently by dfferent SUs regardng the locaton of the SUs, the frequency of the unoccuped bands, the contguty of bands provded, etc.; Table.I quoted from [5] roughly shows the change n terms of receved power when the transmsson s swtched from one frequency to another. When dong the computaton, we suppose the antenna gan both G t and G r to be, and the dstance d to be the same. As we can see, for nstance, when the transmsson frequency s swtched from 3000 MHz to 300 MHz, for the same transmsson power, the receved power wll ncrease by 20 db 2. To model these phenomena, spectral effcency q of transmsson of the SUs can be summarzed as [5], [6], qw,d W log 2 + y b d 2. N 0 2 Here, we gnore the effect of nterference and mult-path effects. TABLE I GAIN WITH DIFFEENT FEQUENCIES Intal Frequency Target Frequency ato Gan MHz MHz db where y b s sgnal power, W s the bandwdth of the spectrum band, and d s the dstance between the PU and the SU. Wth the help of spectrum effcency q, dfferent spectrum bands can be ranked accordng to the SU s preferences. III. ETUN AND ISK But, n cogntve rado networks, qualty s not the only crteron for the SUs to evaluate the condton of spectrum bands, especally the ones bought from the PUs. Snce the PUs can become actve at any tme, the SU must carry on the rsk of sharng spectrum bands wth PUs f we assume the payment for the spectrum s non-refundable. It s necessary for a SU to take the PUs actvtes nto account when he makes choce of the spectrum bands. To formulate all SU s concerns, we let a random varable r 0 r represent the contenton stuaton for a SU n band,.e., r denotes the tme that the SU can use for hs transmsson durng a unt sellng/buyng tme perod consderng the competton from the peer SUs. Thus, when the SU s usng band bought from PUs, hs monetary revenue for one perod s r q v p, 2 where q s the spectral effcency of band as descrbed n Secton II-B, v s the revenue the SU attans for satsfyng the traffc demands per Mbps, p s the unt prce for sharng band wth PUs, and s the monetary gans the SU obtans by usng band. Gven a specfc band, s a random varable dependng on r snce v, q and p can be regarded as constants. Wthout loss of generalty, we use the expected value 3, E, to represent the expected return of the SU, and the varance, σ σ > 0, to represent the rsk of return,.e., the SU s potental worry about PUs traffc comng back on band. Smlarly, f the SU s usng hs own bands, hs return can be expressed as, s r s q s v c s, 3 where s s the rsk-free return σ s 0per Mbps, r s s a random varable reflectng the contenton status, q s s the 3 These values can be abstracted from the hstory record of the prevous m or drectly from database of whte space [8].

3 low retrun s low rsk s Fg. 2. hgh retrun s 2 hgh rsk s 2 eturn vs sk. spectrum effcency coeffcent, and c s s the nherent cost of the SU s own band. We assume there are n dfferent bands denoted by N {, 2,,n} owned by PUs, and can be opportunstcally accessed by the SUs. Then, there wll be an nterestng queston for the SU,.e., how does a SU choose hs way to share the bands wth PUs, or say, how to dstrbute hs traffc over all the bands ncludng both rsk-free band of hs own and rsky bands from PUs. The problem can be mathematcally expressed as the follows, and E ηe s + ηe p, 4 E p n ω E, 5 where s the overall monetary return per Mbps, s s the rsk-free return per Mbps from dstrbutng traffc on the SU s own band, and p s the rsky return per Mbps from dstrbutng traffc on the PUs bands. The value of 0 η< ndcates that the SU takes opportunstc use of PUs vacant bands, whle η s s the return from the SU s own band. p s a weghted average of wth ω as non-negatve weghts, where s ndependent of ω. Intutvely, we fnd that the SU s able to maxmze hs expected return by pourng all hs traffc over the band k wth the maxmal expected return,.e., k argmax E. N However, the rsk of usng the chosen band k may be qute hgh, whch means the maxmum return s not guaranteed wth regard to the PU s actvtes, e.g., for the SU, the return E 2 s larger than E, but the rsk σ 2 s also greater than σ, as shown n Fg.2. Consequently, a ratonal or rsk-averse SU s not lkely to gamble all hs traffc on ths band snce the return may be extraordnarly low. On the other hand, f a SU dversfes hs traffc over a mx of dfferent bands, he may obtan gven return wth the correspondng mnmal rsk or maxmum return wth the gven rsk. So, the spectrum sharng s consdered to be effcent f the SU chooses a mx of PUs spectrum bands wth maxmum E for gven σ or less and mnmum σ for gven E or more, whch can be abbrevated as E σ crteron. As for the SU, the effcent spectrum sharng nvolves two ssues:. How to splt the traffc over the rsk-free band belongng to the SU and the rsky bands belongng to PUs; 2. How to choose the mx of the PUs bands. IV. THE EFFICIENT TAFFIC DISTIBUTION OVE ISKY AND ISK-FEE BANDS A. Traffc Splttng over the Mx of Bands In last secton, we establsh the relaton between the SU s traffc dstrbuton over arbtrary mx of spectrum bands and hs total expected return E as llustrated n equaton 4. Wth smple dervaton, we rewrte E and σ of the return of the band mx as, { E E s + η E p E s σ 2 6 η2 σp. 2 After elmnatng η between these two equatons above, we fnd that the drect relaton between the expected value of the SU s return of the traffc per Mbps and the rsk parameters of hs traffc splttng s: { E E s + θσ θ E p E s /σ p. In terms of any arbtrarly selected mx of spectrum bands, therefore, the SU s expected return on hs traffc dstrbuton over these bands s lnearly related to the rsk of return, as measured by the standard devaton of hs return. Gven any selected mx, the ntercept of ths lnear functon s the rskfree return s and ts slope s gven by θ, whch s determned by the parameters p and σ p of the partcular band mx of PUs beng consdered. Moreover, let us consder all possble mxes of spectrum bands. Those mxes wth the same θ value le on the same Opportunstc Spectrum Utlzaton Lne OSUL, but those have dfferent θ values wll produce dfferent OSULs between return and rsk for the SUs as shown n Fg.3. The SU s problem s to decde whch OSUL to choose the proper value of η, and how ntensvely to use t the proper value of ω. A ratonal SU adherng to the proposed effcent sharng crteron wll mnmze the varance of hs overall return σ 2 assocated wth any expected return E he may choose by confnng all hs selecton n bands to the mx wth the largest θ value. After choosng the band mx by maxmzng θ, the SU can complete hs effcent sharng choce and determne a unque best value of η,.e., the rato of the SU s traffc dstrbuton on the rsky bands and the amount of traffc on hs own rsk-free band. B. The Geometry of the Effcent Traffc Splttng The algebrac analyss gven above can be represented graphcally as n Fg.3. Any avalable mx of spectrum bands from PUs s characterzed by a par of values σ p, p whch can be represented as a pont n a plane wth σ as the horzonal axs and as the vertcal axs. Our assumptons nsure that the ponts representng all avalable band mxes le n a fnte regon, all parts of whch le to the rght of the lne σ 0, and that ths regon s bounded by a closed curve. All the σ, pars wth any partcular mx le on a seres of lne segments from the pont 0, f, where η 0,to the ponts on the boundary of attanable set, where η. Each possble band mx thus determnes a unque OSUL. Thus, 7

4 s m Effcent Set for the Band Mxes from PUs S a s Effcent Set for the Band Mxes from PUs S As for the SU, the effcent mx s the one whch maxmzes θ as we dscussed n the Secton IV. Therefore, we examne the partal dervatves of θ wth respect to the ω and fnd, θ σ p [ x λω σ x + ω σ x ], 3 ω s 2 s 0 σa σp σ Fg. 3. a Gven σ a 0 σp σ b Gven a Geometry of traffc splttng between rsk free and rsky bands the optmal band mx s determned by two factors: the SU s selecton of s and hs selecton of θ. Accordng to the -σ rule, the optmal s selecton strategy for the SU s to make full use of hs own band. As shown n Fg.3a, for gven rsk σ a, the total return of the SU wth the maxmum s.e., s m n Fg.3a s greater than that wth less rsk-free return.e., s, s 2,, s m. Then, the second factor s θ, the slope of OSUL. Note that shfts from one possble mx to another, rotatng the assocated OSUL counter clockwse, move the SU to preferred postons. The lmt of the favorable rotaton s OSUL wth the maxmum attanable θ, whch dentfes the effcent mx of spectrum bands. V. THE EFFICIENT MIX OF PUS SPECTUM BANDS Now, the problem left s how to select the effcent mx of PUs spectrum bands,.e., how to determne the proper value of ω. We see that f ω s assgned to the th band for servce provdng, the return of the th band wll be ω, whch can also be wrtten n the form ω ω s +ω s. 8 By usng the constrant ω, the expected return per Mbps for any mx of PUs bands can be expressed as E p [ ω E E s + ω E ] s E s + ω E E s. 9 Thus, the expectaton and varance of the return on any mx of PUs bands s { E p E s + ω E E s σ p ω 0 ω σ. where σ represents the varance σ when, and covarances when. By defnng x s,the notatons n the rght-hand expressons are able to be further smplfed : { E p E s + ω x σ p ω ω σ x. By substtutng equaton nto equaton 7, θ defned n Secton IV-A can be wrtten as θ E p E s ω ˇx σ p /2 ω. 2 ω σ x /2 where λ x σ 2 p ω x ω. 4 ω σ x The necessary and suffcent condtons on the relatve values of the ω for a statonary and the unque maxmum are obtaned by settng the dervatves above equal to zero, whch gve the set of equatons ζ σ x + ζ σ x x, N 5 where ζ λω. Note that the set of equatons are lnear n terms of the own-varances, σ x, pooled covarances, σ x, and excess returns, x, of the respectve spectrum bands from PUs. Snce the covarance matrx s postve defnte and hence nonsngular, there s a unque soluton to ths system of equatons, ζ σ x x, 6 where σ x represents the th element of the nverse of the covarance matrx. Ths soluton may also be expressed n terms of the prmary varables as ω λ σ x s, N. 7 Moreover, ζ λω mples ζ λ ω. 8 When we leverage the constrant ω, λ s readly evaluated as ζ λ ω λ. 9 The optmal ζ can consequently be scaled to the effcent traffc splttng over the band mx ω, whch s ζ λ x σ 2 x. 20 It s also nterestng to note that f we represent the rato of the expected excess return to ts varance for the th band at the effcent sharng, we have x ω λ λ ω, where λ x. 2 σ x σ x The fracton of traffc dstrbuted n each band n the effcent band mx of PUs s equal to the rato of ts λ to λ of the entre mx mnus the rato of ts pooled covarance wth other bands to ts own varance. As a result, f the SU acts on the assumpton that all the covarances were zero, he s able to pck hs optmal band mx of PUs smply by determnng the λ rato of the expected excess return x s of each

5 AND AV AND AV ato Spectrum Utlzaton ato SUs Satsfactory Degree AND AV a The rato of return and rsk b Spectrum utlzaton c SUs satsfactory degrees Fg. 4. Performance comparson of dfferent traffc splttng schemes over spectrum bands spectrum band to ts varance σ x σ, and settng each ω λ / λ. Consder the case of no covarances, we fnd λ λ x /σx 2. Wth ths smplfed assumpton, the λ ratos of each band s enough to determne the effcent mx 4. VI. SIMULATION AND ANALYSIS In ths secton, we compare the proposed E σ based traffc splttng wth random splttng AND and averaged splttng AV over the bands to demonstrate ts effcency n spectrum sharng n terms of E σ rato, spectrum utlzaton and SUs satsfactory degrees. We set up the smulaton wth a smlar settng to that shown n Fg., modelng a SU to choose hs traffc dstrbuton over a mx of hs own band and bands of PUs. For llustraton purpose, we suppose that the rsk free return f s equal to 5 and the number of PUs bands n s 0. Wthout loss of generalty, we assume the return of the band belongng to PUs > 5 monotoncally ncreases wth the rsk of that band σ σ > 0. As depcted n Fg.4a, when the number of spectrum bands ncreases, the E σ rato ncreases n all these three schemes. But the proposed spectrum sharng s more effcent than AND and AV because t dstrbutes traffc to the th band wth ω λ λ, whch makes t acheve the maxmal θ and guarantee the maxmum wth gven σ or mnmum σ wth gven. In Fg.4b, we evaluate the performance of spectrum utlzaton. Note that no matter the band s used by the PU or used by the SU, the spectrum band tself should be consdered as utlzed one. The spectrum utlzaton should be calculated as the rato of the number of utlzed bands to the number of total bands. Accordng to ths defnton, we fnd that the E σ based traffc splttng s stll slghtly better than the other two schemes. The reason s that the SU wll dstrbute less traffc on the more rsky band f he shares the spectrum accordng to E σ rule. In ths way, although the SU cannot releve hs servces from mpact of the PUs comng back to 00%, he s able to take more opportunstc use of the lcensed bands of 4 In the more general case wth non-zero covarances, a sngle set of lnear equatons must be solved n the usual way, but no lnear or non-lnear programmng s requred. PUs. By contrast, the spectrum utlzaton n both AND and AV are more lkely affected by the PUs actvtes. Smlar analyss also apples to the SUs satsfactory degrees, whch can be defned as the rato of satsfed demands to overall demands of the SU. Compared wth AND and AV, the satsfactory degrees of E σ based spectrum sharng s hgher when the vacant spectrum of PUs s not abundant. VII. CONCLUSION In ths paper, we propose a return and rsk model for spectrum sharng n cogntve rado networks. Consderng the rsk of gatherng all the traffc on one band, we elaborate on how to choose a effcent band mx consstng of rsky and rsk free bands, and gude the SUs to dstrbute hs traffc over them. By numercal smulatons, we show that our spectrum sharng scheme s effcent n terms of E σ crteron, and t mproves the spectrum utlzaton and SUs satsfactory degrees as well. EFEENCES [] FCC, Spectrum polcy task force report, eport of Federal Communcatons Commsson, Et docket No , November [2] IEEE P802.22/D0. Draft Standard for Wreless egonal Area Networks Part 22: Cogntve Wreless AN Medum Access Control MAC and Physcal Layer PHY specfcatons: Polces and procedures for operaton n the TV Bands, IEEE Workng Group on Wreless egonal Area Networks, IEEE doc: P D0., May [3] I. Akyldz, W. Lee, M. Vuran, and M. Shantdev, Next generaton/ dynamc spectrum access/ cogntve rado wreless networks: a survey, Computer Networks Elsever Journal, vol. 50, no. 4, pp , September [4] D. Grandblase, P. Bag, P. Levne, K. Moessner, and M. Pan, Mcroeconomcs nspred mechansms to manage dynamc spectrum allocaton, n Proc. of IEEE Internatonal Symposum on New Fronters n Dynamc Spectrum Access Networks, DySPAN 07, Dubln, Ireland, Aprl [5] Y. Xng,. Chandramoul, and C. Cordero, Prce dynamcs n compettve agle spectrum access markets, IEEE Journal on Selected Areas n Communcatons, vol. 25, no. 3, pp , Aprl [6] D. Nyato and E. Hossan, Compettve prcng for spectrum sharng n cogntve rado networks: Dynamc game, neffcency of nash equlbrum, and colluson, IEEE Journal on Selected Areas n Communcatons, vol. 26, no., pp , January [7] A. Motamed and A. Baha, Optmal channel selecton for spectrumagle low-power wreless packet swtched networks n unlcensed band, EUASIP J. Wrel. Commun. Netw., vol. 2008, pp. 0, [8] D. Gurney, G. Buchwald, L. Ecklund, S. Kuffner, and J. Grosspetsch, Geo-locaton database technques for ncumbent protecton n the tv whte space, n Proc. of IEEE Internatonal Symposum on New Fronters n Dynamc Spectrum Access Networks, DySPAN 08, Chcago, Illnos, October 2008.