Spectrum Assignment with Non-deterministic Bandwidth of Spectrum Holein Cognitive Radio Networks

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1 MAEC We of Cofereces 56, DOI:.5/ ateccof/6565 Spectru Assiget with No-deteriistic Badwidth of Spectru Holei Cogitive Radio Networks Huag Jie, He Yua, Zeg Xiaopig, a Xiaoheg ad Miao Liua College of Couicatio Egieerig, Chogqig Uiversity, Chogqig, Chia Astract.he spectru allocatio for cogitive radio etworks (CRNs) has received cosiderale studies uder the assuptio that the adwidth of spectru holes is static. However, i practice, the adwidth of spectru holes is tievaried due to priary user/secodary user (PU/SU) activity ad oility, which result i o-deteriacy. his paper studies the spectru allocatio for CRNs with o-deteriistic adwidth of spectru holes. We preset a ovel proaility desity fuctio (PDF) odel through order statistic to descrie the o-deteriistic adwidth of spectru holes ad provide a oud to approiate it. After that, a statistical spectru allocatio odel ased o stochastic ultiple kapsack prole (MKP) is estalished for spectru allocatio with o-deteriistic adwidth of spectru holes. o reduce the coputatioal copleity, we trasfor this stochastic prograig proleito a costat MKP though eploitig the properties of cuulative distriutio fuctio (CDF), which ca e solved via MHG algorith y usig auiliary variale. Siulatio results illustrate that the proposed statistical spectru allocatio algorith ca achieve etter perforaces copared to the eistig algoriths whe the adwidth of spectru holes istie-varied. Keywords-cogitive radio; tie-varied; spectru allocatio; o-deteriistic adwidth of spectru holes; stochastic prograig.. Itroductio Radio spectru is ecoig oe of the ost iportat ad scarcest resources i wireless couicatio syste. However, ecause of the curret spectru allocatio policies, the spectru utilizatio efficiecy i licesed spectru is very low [], which geerates ay o-cotiuous vacat frequecy ads, referred to as spectru holes []. Cogitive radio (CR) which allows secodary users (SUs) to opportuistically utilize the frequecy spectru origially assiged to licesed priary users (PUs) is a proisig approach to alleviate spectru scarcity. Cosiderale achieveethave ee ade for spectru allocatio i CRNs y adoptig gae theory [3]-[4], graph theory[5]-[6] ad liear prograig[7]-[9], which assue that the paraeters of radio eviroet are static. However, i practice, due to the iperfect spectru sesig, trasissio delay ad tie-varied spectru eviroet etc, it is difficultforthe secodary etwork to have theaccuratereal-tieparaetersi CRNs, which will ake the paraeters o-deteriistic. herefore, i fact, static spectru allocatioalgorith without cosiderig odeteriistic paraeters ay result i frequet spectru collisio ad poor perforace. Recetly, dyaic resource allocatio with o-deteriistic paraeters i CRNs has received cosiderale iterest fro acadeia, which aily focus o o-deteriistic chael gai ad utual iterferece []-[]. [] studies the resource allocatio for CRNs uder o-deteriistic sigal-to-iterferece-plusoise ratio (SINR) ad propose a power cotrol schee y usig water fillig algorith ad stochastic prograig. O the other had, [] studies the distriuted resourceallocatio prole i CRNs y cosiderig the odeteriistic chael gaiad the authors propose aroustdistriutedpowercotrol algorith y applyig secodorder coe prograig (SOCP).[] proposes a roust distriuted uplik power allocatio algorith y usig worst case roust optiizatio ethod, which cosider chael gais fro SUs to PUs ase statio, ad iterferececaused y PUs to the SUs ase statio are odeteriistic. Iadditio,ost eistig works aily focus o o-deteriistic chael gai ad utual iterferece. However, due to PU/SU activity ad oility, spectru eviroet will chage frequetly, which result i tie- he Authors, pulished y EDP Scieces. his is a ope access article distriuted uder the ters of the Creative Coos Attriutio Licese 4. (

2 MAEC We of Cofereces 56, DOI:.5/ ateccof/6565 variedadwidth of spectru holes. herefore, eplorig a spectru allocatio algorith y cosiderig odeteriistic adwidth of spectru holes is ecessary for future CRNs, which will reduce spectru collisio ad greatlyiprove spectru efficiecy. o the est ofour kowledge, o-cotiuous spectru allocatio i CRNs y cosiderig o-deteriistic adwidth of spectru holeshas ot eestudied i previous works. his paper studies the o-cotiuous spectru allocatio prole i CRNs where the adwidth of spectru holes iso-deteriistic due to PU/SU activity ad oility. We preset a ovel PDF odel through order statistic to descrie the o-deteriistic adwidth of spectru holes ad provide a oud to approiate it. his PDF odel is differet fro eistig researches which aily focus o the tie duratio of spectru holes[3][4]. After that, a statistical spectru allocatio odel ased o stochastic MKP is estalished for spectru allocatio with o-deteriistic adwidth of spectru holes. o reduce the coputatioal copleity, we trasfor this stochastic prograig proleito a costat MKP though eploitig the properties of CDF, which ca e solved via MHG algorith y usig auiliary variale. Siulatio results illustrate that the proposed statistical spectru allocatio algorith ca achieve etter perforaces copared to the eistig algoriths whe the adwidth of spectru holes istie-varied. he reaider of this paper is orgaized as follows. he layout prole is isectio II.ISectio III, the statistical odel for adwidth of spectru holes is preseted. I Sectio IV, the statistical spectru allocatio algorith ased o stochastic MKP ethodisproposed. Nuerical results are provided i Sectio V to deostrate theadvatages of the proposed schees.we coclude this paper isectio VI.. Layout of Prole I this CRNs syste, the spectru occupacy over frequecy doai at a certai tie is o-cotiuous, as depicted i Fig. he totally frequecy ad is, ad the uer of spectru holes is. i () ad yi () are used to deote the start poit of spectru occupacy ad the occupied adwidth. he adwidth of spectru hole are deoted y. o descrie the o-deteriistic adwidth of spectru holes, we estalish a PDF odel for adwidth of spectru holes ad ased o this,a statistical spectru allocatio algorith is proposed. () y () () y () i () yi () ( ) y ( ) Figure. Spectru occupacy over frequecy doai 3. Statistical Modelfor Badwidth ofspectruholes f I this sectio, the o-deteriistic adwidth of spectru holes has ee forulated i a atheatic way. We cosider the adwidth of spectru holes as a part of iterval etwee two adacet order statistics ad represet it through a rado variale. he, ase o the properties of two adacet order statistics, the PDF of adwidth of spectru holes ca e derived. heore : he PDF of adwidth of spectru holes whe i () follows a uifor distriutio U(, ) ad yi () follows a coditioal uifor distriutio U (, ( i) ( i)) is give y y Where for f () is f E () () ( ), ad the upper ad lower ouds e l( ) f( ) e l( ) () (his derivatio ethod ca also e used whe i () ad yi () follow other distriutios) Proof: Let zi () i ( ) i (), where zi () represets the iterval etwee two adacet order statistics. he the adwidth of spectru holes ca e achieved y i () zi () yi (). Accordig to [5], the oit proaility distriutio fuctio of two order statistics ca e otaied as! fi (), ( ) ( u, v) f( u) ( i)!( i)!( )! i i f( v)[ F( u)] [ F( v) F( u)] (3) [ F ( v)] u v Whe i () follows uifor distriutio, f ( ), F ( ),the proaility distriutio fuctio z ca e epressed as fz( z) f(), i ( i) ( u, uz) du (4)! z i i ( ) t ( t) dt ( i)!( i)! Sustitutig ( ) ( ) B(, ) i (4) yields ( ) B(, ) u ( u) du z fz () z ( ) e ad z (5)

3 MAEC We of Cofereces 56, DOI:.5/ ateccof/6565 Sice yi () follows a coditioal uifor distriutio, uiforly distriuted i (, z ), accordig to Bayes' theore, the oit proaility distriutio fuctio fyz, ( y, z ) ca e otai as z fyz, ( y, z) e (6) z he proaility distriutio fuctio of ca e give as u e y, z (7) u f () f (, y y ) dy du Sustitutigepoetial itegral fuctio, a ( ) e E a d, i (7), result i f ( ) [E ( ) E ( )] (8) Let, sice the value of E( ) is iial, (8) ca e approiated as E( ). Based o the properties of epoetial itegralfuctio[6], we otai the upper ad lower ouds for f () is give as e l( ) f( ) e l( ) (9) 4. StatisticalSpectruAllocatioAlgorith Based o StochasticMKP 4. Spectru allocatio odel ased o stochastic MKP We assue that the CRNs cosist of SUs ad spectru holes, where SUs data rate requireets ad the adwidth of spectru holes are idicated as R{ r..., r} ad C { c,..., c } respectively. Aog this, each SU i (,3,, ) ca utilize ay spectru hole (,,3,, ), which eas the o-cotiuous spectru allocatio prole ca e trasfored ito a kid of MKP to achieve aiu trasissio rate. aiize z r () i i i () i st.. c N {,..., } im {,..., } () or im N (3) Let i e the ecessary adwidth that satisfieddata rate requireet r i ad represet SU i ca allocated ito spectru hole. Moreover, y adoptig AMC schee, SUs with differet positios ca achieve differet data rate i sae chael due to eviroet differeces. Accordig to G.J.Foschii s iferece[7], the adwidth eeds for SU i o spectru hole ca e give as ri (4) log ( ) P l 3 Where P deotes aiu tolerale error rate ad i, idicates the SINR whe SU i trasits o spectru hole. Sustitutig (4) ito (), we otai a special MKP odel, where each SU requires differet adwidth whe allocated ito differet spectru holes. he () ca e epressed as c i, cau N {,..., } (5) i cab chb Where ca B is the sucarrier adwidth, chb deotes the chael adwidth, ca u idicates the uer of sucarriers i each chael. o cosider o-deteriistic adwidth of spectru holes, we take previous statistical odel ito this MKP odel. Let c t, e the availale adwidth of spectru hole detected ysus ase statio at tie t ad C { c, tk, c, tk... c, t} represets the record of adwidth of spectru hole i recet k ties spectru sesig. We ca deterie the paraeter of the statistical odel y applyig poit estiatio ethod. he epectatio of previous PDF ca e writte as () E () E ( d ) ( ) (6) Hece, ased o the ethod of oet[5], the PDF paraeter of adwidth of spectru hole ca epress as / EC ( ). We assue c is a rado variale i (5) ad follows the PDF (), which trasits the MKP spectru allocatio odel aove ito a stochastic prograig odel. he ukow rado variale itroduces ucertaity to (5) ad akes the costrait quit coplicated. hus, to reduce the copleity, we tackle this issue y usig chace-costrait prograig ethod which fids the optiu solutio uder the coditio that the costraits is feasile with proaility greater tha the threshold. he costrait (5) aove ca e rewritte as c st.. Pr{ i, cau} N (7) ca ch i B B 3

4 MAEC We of Cofereces 56, DOI:.5/ ateccof/6565 his idicates the costrait ust e feasile with the proaility greater tha ad this odel aiizes the trasissio rate y satisfyig the costrait with high proaility. 4. Siplificatio ad solutio o reduce the coputatioal copleity, we siplify the stochastic prograig odel aove y the usage of the properties of CDF. For (7), sice c follows the CDF F () c, there ust eist a K for each threshold satisfies Pr{ K c}. herefore, (7) will e satisfied oly if chb K i cab cau (8) Furtherore, as Pr{ K c} F( K), K ca e represeted y F ( ). We ca trasit (7) as chb F ( ) N {,..., } (9) i cab cau Sice the odel proposed is a NP-hard prole, the eistig algorith otais the solutio y ehaustive search which will ecouter cople coputatioswhe ad have large values. Hece, we covert the odel ito a Geeralized Assiget Prole (GAP) y usig auiliary variale ad solve it via MHG algorith[7] which will get the suoptial solutio. Let ca B ch ca B u w, c F ( ), p r, N i ad addig auiliaryvariales pi,, c ad w i M. he, the odel ca e rewritte as i,, aiize z p () i st.. w c N {,...,, } () i im {,..., } () or im N (3) his GAP odel eas each SU ust e allocated i a uique c ad c cotais the SUs which have ot e allocated due to lack of spectru resource. he GAP odel ca e solved y usig MHG algorith, where iteratively cosider all the uassiged SUs, ad assig the SU i * havig the aiu differece etwee the largest ad secod largest p to the spectru hole * for which p is a * * i, aiu ( p * * a{ p, : N }). i 5. Siulatio Results I this sectio, the perforace of proposed statistical spectru allocatio algorith has e studied thoughuericalsiulatios.we assue that all SUslocated aroud SUs ase statio with the distace radoly raged fro 5 to ad the siulatio paraeters are set as alei. I order to siulate the tie-variedadwidth of spectru holes caused y PU/SU activity ad oility, we radoly geerate spectru holes with the adwidth chaged through chage rate p (the proaility of adwidth of spectru hole chaged et oet) over the frequecy ad W. he, we copare the perforace of proposed statistical MKP spectru allocatio algorith with static MKP spectru allocatio algorith i [8]. ABLE I. Paraeters SU output power Pa SIMULAIONPARAMEERS Values 45dB Maiu tolerale error rate P 6 SU uer SMUN 3 Spectru hole uer SH 36 Noise power NB -db Chace prograig threshold.5 Badwidth of spectru hole chage rate p. otal frequecy ad W MHZ Fig. illustrates the CDF of SU spectru efficiecy usig the two algorithswith differet situatio ( p.5 ad p ). As show i Fig., statistical MKP algorith ad static MKP algorith occupy 6% ad 5% respectively whe the spectru efficiecy is large tha.8, which eas statistical MKPalgorith has larger percetage of high spectru efficiecy tha the static MKP algorith. his case is ecausestatistical MKP algorith which takes the statistical properties of adwidth of spectru holes ito cosideratio ca achieve dyaic optial ad reduce adwidth collisios caused y spectru holes chages. Moreover, as p icreased to, statistical MKP algorith eceeds static MKP algorith ore, which eas statistical MKP algorith ca etter adapt to the sceario with frequecy tie-varied adwidth of spectru holes ad achieve high spectru efficiecy. Figure. CDF of spectru efficiecy 4

5 MAEC We of Cofereces 56, DOI:.5/ ateccof/6565 I Fig.3, we evaluate the etwork utility with differet adwidth chage rate p. he etwork utility is defied as[8] U l R(k) (4) k Where R(k) is the throughput for SU k. I thefig. 3, as p icreased, the etwork utility is reduced due to adwidth collisio. he static MKP algorith suffers lower etworkutility thastatistical MKP algorith, ecause it oly cosiders curret static optial ad use costat allocatio paraeters, which ay lead to ore adwidth collisio. I additio, whe the uer of spectru holes icrease, the etwork utility of statistical MKP algorith icrease ore tha the static MKP algorith, which eas statistical MKP algorith ca otai a good perforace uder the coditio of o-cotiuous spectru. I this paper, we study the prole of o-cotiuous spectru allocatio i CRNs where the adwidth of spectru holes is o-deteriistic due to PU/SU activity ad oility.we preset a ovel PDF odel through order statistic to descrie the o-deteriistic adwidth of spectru holes ad provide a oud to approiate it.after that, a statistical spectru allocatio odel ased o stochastic MKP is estalished for spectru allocatio with o-deteriistic adwidth of spectru holes. o reduce the coputatioal copleity, we trasfor this stochastic prograig proleito a costat MKP though eploitig the properties of CDF, which ca e solved via MHG algorith y usig auiliary variale. Siulatio resultsverify that the proposedstatistical spectru allocatio algorith ca achieve etter perforaces copared to the eistig algoriths whe the adwidth of spectru holes istie-varied. Ackowledget hisworkwassupportedytheraiigprograofthemaor ResearchPlaoftheNaturalScieceFoudatioofChia(Grat No.94384)adtheGraduateStudetsResearchPrograofC hogqig(gratno.cys45). Figure 3. Network utility with differet adwidth of spectru holes chage rate p Fig. 4 shows the average spectru collisio rate with differet adwidth chage rate p. Fro Fig. 4, we ca see that as p icrease, the spectru collisio rate icreased draatically ad statistical MKP algorith achieve lower collisio rate tha the static MKP algorith. It is ecausestatistical MKP algorith ca rela the adwidth collisio through assigig spectru resource with cosiderig the statistical properties of spectru holes. he result shows that statistical MKP algorith ca effectively reduce the spectru collisio whe spectru holes chages. Figure 4. Average spectru collisio rate with differet adwidth of spectru holes chage rate p 6. Coclusio Refereces. C.KC.Lee,S.Kag, Policy ad techology of dyaic spectru access i Korea, 8 3rd Iteratioal Coferece o Cogitive Radio Orieted Wireless Networks ad Couicatios, pp. -4, 8, doi:.9/crowncom M. Mchery,E.Livsics,.Nguye, XG dyaic spectru access field test results, IEEE Couicatio Magazie,pp. 5-57,Ju J. Revathy,M. Sethil, Resource allocatio i et geeratio etworks usig gae theory, 4 Iteratioal Coferece o Iforatio Couicatio ad Eedded Systes (ICICES), pp Z. Wu, P. Cheg, X. Wag, Cooperative spectru allocatio for cogitive radio etwork: a evolutioary approach, IEEE Iteratioal Coferece o Couicatios (ICC), pp Y. L L. Zhao, C. Wag, Aggregatio-ased spectru allocatio algorith i cogitive radio etworks, Network Operatios ad Maageet Syposiu (NOMS), IEEE, pp A. Pluer, S. Biswas, Distriuted spectru assiget for cogitive etworks with heterogeeous spectru opportuities, Wireless Couicatios ad Moile Coputig, pp , Sep.. 7. F.Wu,Y.Mao,S.Leg, A carrier aggregatio ased resource allocatio schee for pervasive wireless etworks, IEEE Nith Iteratioal Coferece o Depedale, Autooic ad Secure Coputig (DASC), IEEE, pp C.LW.Liu,Q.Liu, Spectru aggregatio ased spectru allocatio for cogitive radio etworks, Wireless Couicatios ad Networkig Coferece (WCNC), IEEE, pp Y. Sog, C. Zhag, Y. Fag, Multiple ultidiesioal kapsack prole ad its 5

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