Subcarrier and Power Allocation in OFDM-based Cognitive Radio Systems

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1 I.J. Computer etwork ad Iformatio Security 4-3 Published Olie ovember i MECS ( Subcarrier ad Power llocatio i OFDM-based Cogitive Radio Systems Pei Zhag ogxiag Yag Xu iu Wirele Commuicatios ey ab of Jiagsu Provice ajig Uiversity of Posts ad Telecommuicatios ajig Jiagsu P. R. Chia 3; Widebad Wirele Commuicatios ad Sesor etworks Techology ab Miistry of Educatio of Chia ajig Jiagsu P. R. Chia 3 bstract For CR systems where primary ad CR users coexist i adjacet bads it is importat to keep e iterferece itroduced to e primary user (PU) bad wii a tolerable rage. I is paper we ivestigate e subcarrier ad power allocatio problem i CR systems where primary ad CR users co-exist i adjacet bads while keepig e total iterferece itroduced to e PU bad below a certai reshold ad e total power allocated to e CR users uder a costrait. First accordig to e differet purposes of e resource allocatio several suboptimal subcarrier allocatio algorims are ivestigated which are termed as Max-Rate Mi-Iterferece ad Fair-Rate subcarrier allocatio algorim separately. Furer for a give subcarrier allocatio ree suboptimal power allocatio algorims which have le complexity are proposed ad compared to e optimal power allocatio algorim. umerical results are obtaied for e behaviors ad performace of our proposed algorims. Idex Terms cogitive radio OFDM subcarrier allocatio power allocatio I. ITRODUCTIO Wi e rapid developmet of wirele commuicatios techology radio spectrum resource is icreasigly scarce. Cogitive radio (CR) [] is a popular techology which ca dyamically acce to e vacat radio spectrum resource effectively solve e problem of resources shortage ad icrease e frequecy spectrum efficiecy. Orogoal Frequecy Divisio Multiple (OFDM) techology [] has bee cosidered as a appropriate modulatio cadidate for CR system. I OFDM system e frequecy bad is divided ito a large umber of small bads called subcarriers at use specific frequecies so as to be completely orogoal to each oer which ca ot oly reduce e mutual iterferece betwee e subcarriers but also improve e spectral efficiecy. I e cogitive radio etwork bo CR user ad PU exist i side-by-side bads so mutual iterferece is e limitig factor for e performace of bo systems. Therefore bo e total iterferece itroduced to e PU bad ad e total power allocated to e CR users should Correspodig uor: ogxiag Yag. This work is supported by e atural Sciece Foudatio of Chia(679) 973 project(7c367) of Chia atioal be take ito accout durig e resource allocatio to esure at all users ca be effectively coexistece. Figure. Distributio of primary ad CR users i e spatial domai The claical water fillig algorim [3] for allocatig power to subcarriers i OFDM systems is ot suitable i e CR cotext because it does ot take ito cosideratio of e protectio of primary users operatig i earby bads. The basic idea i e water fillig algorim is to aig more power to subcarriers at experiece higher chael gai while aigig little or o power to subcarriers sufferig from low chael gai. However i e cotext of CR a set of subcarriers experiecig favorable chael quality may be adjacet to a primary user bad. Thus if e water fillig algorim is employed ose subcarriers will typically be aiged higher power levels which i tur will cause severe iterferece to e adjacet primary users. Cosiderig at joit subcarrier ad power allocatio i OFDM system is a complex problem us e problem is usually simplified by separatig subcarrier allocatio ad power allocatio. I [4] power time slots ad subcarriers are joitly optimized by two separate optimal algorims i ree steps while keep faire amog users ad maximizatio of total capacity. However e existece of primary user has ot bee take ito cosidered. I [5] two ovel algorims are preseted for subcarrier ad power allocatio i OFDM-based CR etworks which are costat power subcarrier allocatio ad heuristic joit subcarrier ad power allocatio respectively. o of em are aimig at maximizig e sum capacity while maitaiig e iterferece power itroduced i e primary etwork bad below a Copyright MECS I.J. Computer etwork ad Iformatio Security 4-3

2 Subcarrier ad Power llocatio i OFDM-based Cogitive Radio Systems 5 predefied reshold. I [6] a optimal ad two suboptimal power loadig algorims Figure. Distributio of primary ad CR users i e frequecy domai for a OFDM-based cogitive radio system are ivestigated while keepig e iterferece itroduced to e primary user wii a tolerable rage oly. This paper ivestigates e subcarrier ad power allocatio problem i CR systems where primary ad CR users co-exist i adjacet bads while keepig e total iterferece itroduced to e PU bad below a certai reshold ad e total power allocated to e CR users uder a costrait. I e first part accordig to e differet purposes of e resource allocatio several suboptimal subcarrier allocatio algorims are ivestigated. First we ivestigate Max-Rate subcarrier allocatio algorim (MaxR-S) which ca achieve maximum trasmit rate of e CR system. I is algorim iterferece itroduced to e PU bad is kept uder e costrait but it is still very high. esides faire amog all e secod users (SU) is ot take ito cosideratio. The focusig o e fact at e le iterferece itroduced to e PU bad e better e PU ca work; we proposed a Mi-Iterferece subcarrier allocatio algorim (MiI-S). Furer aimig at achievig faire amog all e SUs we propose a subcarrier allocatio algorim which is termed as Fair- Rate subcarrier allocatio algorim (FairR-S). I e secod part for a give subcarrier allocatio ree suboptimal power allocatio algorims which have le complexity are proposed ad compared to e optimal power allocatio algorim [7]. The orgaizatio of is paper is as follows. Sectio II describes e system model ad e problem is formulated. I Sectio III several suboptimal subcarrier allocatio algorims are ivestigated which are termed as Max- Rate Mi-Iterferece ad Fair-Rate subcarrier allocatio algorim. The algorim for optimal ad suboptimal power allocatio for e give subcarriers is preseted i Sectio IV. umerical results are give i Sectio V ad fially Sectio VI cocludes e paper. II. SYSTEM MODE D PROEM FORMUTIO We cosider e side-by-side CR radio acce model as show i Fig.. The total frequecy badwid is aumed to be o which badwid... are occupied by e PU(s)... respectively ad are sesed by e CR system cosistig of users. The uoccupied bad sesed by e CR system for poible trasmiio is located o bo sides of primary user bads ad e PU ca be located aywhere of e frequecy bads. It is aumed at e available badwid for CR trasmiio is divided ito subcarriers each of which has a badwid of Δf Hz as show i Fig.. sp ps It is aumed at chael gai h h h ca be perfectly kow at e CR user s trasmitter where h deotes e chael gai betwee e k CR sp user trasmitter ad receiver hk deotes e chael gai betwee e k CR user ps trasmitter ad e PU receiver ad h deotes e chael gai betwee PU trasmitter ad e k CR user receiver as show i Fig.. The e trasmiio rate for e k CR user for e subcarrier ca be expreed as [6] R k. h Pk = log ( + ) J + σ l = () where Pk is e trasmiio power allocated to e k CR user for e subcarrier σ is e WG variace ad J is e iterferece itroduced to l= k CR user s subcarrier by all e PU bads. Uder e ifluece of e side lobe of e spectrum electromagetic sigal may experiece some radiatio ad leak of spectrum. Sice bo CR user ad PU exist i side-by-side bads mutual iterferece is e limitig factor for e performace of bo systems which is determied by e trasmiio power ad e spectrum distace betwee e CR user ad e primary user.. Iterferece itroduced by CR user s sigal Uder e situatio of a ideal yquist pulse e power desity spectrum of e subcarrier which is allocated to e k CR user ca be writte as [9] siπ fts φ k = Pk Ts () π fts where T s is e symbol duratio. The iterferece itroduced by e subcarrier to e l PU bad is e itegratio of e power desity spectrum of e subcarrier acro e l PU bad ad ca be writte as sp d si l + π fts l / I = h Pk Ts df dl l / (3) π fts where d l deotes e spectrum distace betwee e subcarrier ad e l PU bad. The Equatio (3) ca be writte as ( l) ( l) k * I = P F (4) sp d si l + π fts l / where F = h Ts df dl l / which π fts is deoted as e iterferece factor betwee e k CR user for e subcarrier ad e l PU bad. Copyright MECS I.J. Computer etwork ad Iformatio Security 4-3

3 6 Subcarrier ad Power llocatio i OFDM-based Cogitive Radio Systems. Iterferece itroduced by primary user s sigal The power desity spectrum of e primary user sigal after e M-fast Fourier trasform (FFT) proceig ca be expreed as [9] π jw si ( w ψ ) M / E{ I( w) } = φ PU( e ) dψ πm π si ( w ψ) / (5) where w represets e frequecy ormalized to e jw samplig frequecy ad φ PU( e ) is e power desity spectrum of e PU sigal. The e iterferece itroduced by e l PU to e k CR user for e subcarrier ca be writte as ps dl +Δf / dl Δf / { ( )} J = h E I w dw (6) C. Problem formulatio The optimizatio problem of resource allocatio is to maximize e total capacity of CR users while keepig e total iterferece itroduced to e PU bad below a certai reshold ad e total power allocated to e CR users uder a costrait. It ca be writte maematically as follows Pk ρ k hk Pk ρk + k= = σ + J l = max log ( ) k= = ρ Pk Pt P k k= = ρ k = k {} k = k Pk F I l= ρ = (7) where Pt deotes e total power budget which is ( l) allocated to e CR users I deotes e iterferece reshold of e l primary user ad ρ k = meas at e subcarrier is allocated to e k CR user. esides it is aumed at oe particular subcarrier ca be allocated to oly oe user while oe user ca occupy multi-subcarrier. This paper first ivestigates e subcarrier allocatio problem i a sub-optimal fashio. The for a give subcarrier allocatio ree suboptimal power allocatio algorims are proposed ad compared to e optimal power allocatio algorim. I e ext sectio we first preset e algorims for sub-optimal subcarrier allocatio. Ⅲ. SUCRRIER OCTIO Subcarrier allocatio e base of e bit ad power allocatio is to decide two problems. Oe is how may subcarriers should be allocated to each user; e oer is how to allocate em. I is sectio we propose ree subcarrier allocatio algorims which are Max-Rate subcarrier allocatio algorim (MaxR-S) Mi- Iterferece subcarrier allocatio algorim (MiI-S) ad Fair-Rate subcarrier allocatio algorim (FairR- S) separately. s [] is said as log as e subcarriers are allocated properly e smoo power desity spectrum will ot cause e debase of e roughput of e system. Therefore to predigest e aalysis it is aumed at equal power is allocated to every subcarrier accordig to [7]. For all e iterferece resholds ad power costrait to satisfy we allocate equal power as follows () ( ) Pt I I I Peq = mi... (8) () ( ) F F F k= = k= = k= = Cosiderig at a sigle user be scheduled o each subcarrier erefore e problem of subcarrier allocatio is eetially to choose a user for each subcarrier. We =... ad defie e set of all subcarriers as { } deotes e set of subcarriers aiged to e CR user k. Sice each subcarrier ca be oly allocated to oe CR user we ca draw at Ω I Ω = k j ad k j U Ω =. k =. MaxR-S I CR systems to improve e spectrum efficiecy CR users ca sese ad acce e vacat spectrum. Max-Rate subcarrier allocatio algorim aims at achieve maximum trasmit rate of e CR system while keepig e total iterferece itroduced to e PU bad below a certai reshold ad e total power allocated to e CR users uder a costrait. Therefore e MaxR-S problem i OFDM-based CR systems ca be formulated as hk Pk R = + k= Ω k k= σ + J l = max max log ( ) k=... k=... k= k P F I Pk Pt P k k= l= where ca be obtaied by followig steps: ) Iitializatio: a) R k = for k =... =... ; b) Ω k = for k =... ; ) for =... a) fid CR user k = arg max k =... ; k hk σ + l = J for b) allocate e foud subcarrier to e CR user k k k Ω =Ω U ; (9) Copyright MECS I.J. Computer etwork ad Iformatio Security 4-3

4 Subcarrier ad Power llocatio i OFDM-based Cogitive Radio Systems 7 c) update R accordig to ().. MiI-S Sice i a CR etwork where e CR users ad e PUs exist i side by side spectrum we should isure at e PU ca work wiout iterruptio. So e iterferece itroduced to e PU bad should be as little as poible. Therefore e MiI-S problem i OFDM-based CR systems ca be formulated as I = F Pk l= k= Ω k l= k= () mi mi * k=... k=... k= k P F I Pk Pt P k k= l= where ca be obtaied by followig steps: ) Iitializatio: a) R k = for k =... =... ; b) Ω k = for k =... ; ) for =... () l a) fid CR user k = arg mi F for k =... ; l = b) allocate e foud subcarrier to e CR user k k k Ω =Ω U ; c) update R accordig to (). C. FairR-S imig at achievig faire amog all e SUs first we propose a statistic as follows S k. = hk ( σ + J )* F l= l= () where bo e mutual iterferece betwee e CR user ad PU ad e capacity of e CR system are take ito accout. Therefore e FairR-S subcarrier allocatio algorim ca be described as follows: ) Iitializatio: a) R k = for k =... =... ; b) Ω k = for k =... ; c) {... } = ; ) for k =... a) fid subcarrier = arg max S for ; b) allocate e foud subcarrier to e CR user k = ; Ω k =U { } c) update R accordig to (). 3) while a) fid CR user k = arg mi Rk. ; b) for e foud CR user k fid subcarrier = arg max S k for ; c) allocate e foud subcarrier to e CR user k = ; Ω k =U { } d) update R accordig to (). I is sectio each subcarrier allocatio algorim has its ow advatage. For example e MaxR-S ca achieve e maximum trasmit rate e MiI-S itroduces e least iterferece to e PU bad ad e FairR-S ca almost achieve faire amog all e SUs. Durig e ext sectio we use e Fair-Rate subcarrier allocatio algorim which allocates subcarriers to CR users i a maer at ot oly e capacity of CR users is icreased but also e iterferece itroduced to e PU bad is decreased. Ⅳ. POWER OCTIO s e subcarrier allocatio is give we should allocate power to each subcarrier i order to maximize e total capacity of CR users while keepig e total iterferece itroduced to e PU below a certai reshold ad e total power allocated to e CR users uder a costrait. I is sectio we ivestigate e optimal power allocatio algorim ad propose ree suboptimal power allocatio algorims amed distace-based step power allocatio algorim iterferece-based step power allocatio algorim ad modified equal power allocatio algorim which have le complexity.. Optimal power allocatio For e give subcarrier allocatio algorim e optimal power allocatio problem is formulated as hk Pk maxlog ( + ) Pk k= σ + J l = () Pk F I (3) k= Ω k Pk Pt k k= P (4) y itroducig e agrage multiplier ad e arush-uh-tucker coditios we ca get e optimal solutio [7] as Copyright MECS I.J. Computer etwork ad Iformatio Security 4-3

5 8 Subcarrier ad Power llocatio i OFDM-based Cogitive Radio Systems σ + J * l = = wk k h P where w k = + β λf l = l Ω (5) ad β ad λl are agrage multipliers which ca be determied accordig to e subjectio coditios (3) ad (4).. Step power allocatio Scheme ( Distace-based ): I is scheme e step size is fixed ad is equal to e power level of e subcarrier which is earest to e primary user bad. Hece e power allocated to e subcarrier ca be writte as P = p* (6) where p is e step size. The accordig to e iterferece reshold of e primary user p ca be expreed as where = * P = I p = l = = I * (7) = F deotes e sum iterferece itroduced by e subcarrier allocated to e k CR user to all e primary users. The accordig to e costrait o e total power budget allocated to e CR users e step size p ca be expreed as = P Pt p = Pt = (8) Use e leer solutio calculated by (7) ad (8) as e fial step size ad substitute it to (5) to obtai e value of P. Scheme ( Iterferece-based ): I is scheme e step size of e ladder is iversely proportioal to. Hece e power allocated to e subcarrier ca be writte as P = p/ (9) where p is e step size. The accordig to e iterferece reshold of e primary user e step size p ca be writte as I * P = I p = () = The accordig to e costrait o e total power budget allocated to e CR users e step size p ca be writte as = P Pt p = ( / ) = Pt () Use e leer solutio calculated by () ad () as e fial step size ad substitute it to (9) to obtai e value of P. C. Modified equal power allocatio For e sake of faire we ca allocate equal power to each subcarrier. Durig e subcarrier allocatio i sectio III where we allocate equal power to all subcarriers we cosider at total iterferece itroduced to e l PU is k= = F however after e subcarrier allocatio each CR user ca oly occupy part of e subcarriers. So we eed to modify e total iterferece as k= F. Therefore e power which is equally allocated to e subcarriers should be writte as () ( ) ' PT I I I eq mi... () ( ) F F Fk k= Ω k k= Ω k k= P = () Ⅴ. UMERIC RESUTS For e umerical results preseted i is sectio we Δf use e values of Ts ad to be 4μs.35MHz ad 5MHz respectively. WG variace is aumed to be -6. The chael is aumed to be Rayleigh fadig wi a average chael power gai of d. Furer we aume at ere are oe primary user ad two CR users. The primary user has a frequecy badwi of MHz ad a cetral frequecy of.5mhz whose iterferece reshold is -6 W. total trasmiio rate of e CR users maxr fair mii total power budget for e CR system x -5 Figure 3. Total trasmiio rate of e CR users Copyright MECS I.J. Computer etwork ad Iformatio Security 4-3

6 Subcarrier ad Power llocatio i OFDM-based Cogitive Radio Systems 9 e total iterferece itroduced to e PU bad 7 x maxr fair mii total trasmiio rate of e CR users optimal power allocatio step power allocatio step power allocatio modified equal power allocatio.5 trasmiio rate of each CR user total power budget for e CR system x Figure 4. Total iterferece itroduced to PU bad maxr x -3 mii fair Pt/ - 4 Figure 5. Trasmiio rate of each CR user Fig.3 shows e total trasmiio rate of e CR users versus e total power budget for e CR system where as e total power budget icreases e total trasmiio rate of e CR users is icreasig at first ad will come to be steady. Furer as we expect e MaxR-S ca achieve e highest trasmiio rate amog e algorims we have proposed while e MiI-S achieves e lowest. However as we ca see from Fig.4 which shows e total iterferece itroduced to e PU bad versus e total power budget for e CR system e MaxR-S caused higher iterferece to e PU bad a e MiI-S ad obviously e MiI-S caused least iterferece to e PU bad. What is more e trasmiio rate of each CR user is observed i Fig. 5. We ca draw at oly e FairR-S ca almost obtai faire amog all e CR users which meas at e trasmiio rate of each CR user ca be almost e same. d from Fig.3 ad Fig.4 we ca draw at e FairR-S is a tradeoff betwee e MaxR-S ad MiI-S at e aspect of e total trasmiio rate of e CR users ad e total iterferece itroduced to e PU bad total power budget for e CR system Figure 6. Total trasmiio rate of e CR users I Fig.7 ad Fig.8 we ca draw at all e algorims i is paper ca satisfy bo e iterferece reshold ad e power budget costraits. I Fig.8 we ca see at e total trasmitted power is equal to e prescribed power budget reshold whe e power budget of e CR system is small. t is time e algorims are i e power-limit state. The as e power budget of CR system icreases e total trasmiio rate of e CR users is icreasig. Whe e power budget reaches a certai value as show i Fig.7 e total iterferece itroduced to e PU bad will come up to e iterferece reshold ad e algorims will eter ito e iterferece-limit state. fter e two states metioed above all e algorims will come up to e maximum trasmitted data rate ad remai steady while e power budget icreases. Furermore we ca see from Fig.7 for e give power budget of e CR system e optimal scheme achieves e highest trasmiio rate for CR users ad causes e least iterferece to PU bad. Performace of e suboptimal power allocatio algorims which have le complexity is much worse a e optimal scheme. esides it is also obvious at e step power allocatio algorim performs better a e step power allocatio algorim ad offers e best performace amog e suboptimal power allocatio algorims. Moreover ough e modified equal power allocatio algorim ca achieve partly faire amog e CR users it offers e worst performace. Ⅵ. COCUSIO I is paper we have ivestigated e subcarrier ad power allocatio problem i CR systems where primary ad CR users co-exist i adjacet bads while keepig e total iterferece itroduced to e PU bad below a certai reshold ad e total power allocated to e CR users uder a costrait. First accordig to e differet purposes of e resource allocatio Max-Rate Mi- Iterferece ad Fair-Rate subcarrier allocatio algorims are ivestigated separately. Furer for e give subcarrier allocatio algorim ree suboptimal Copyright MECS I.J. Computer etwork ad Iformatio Security 4-3

7 3 Subcarrier ad Power llocatio i OFDM-based Cogitive Radio Systems power allocatio algorims which have le complexity are proposed e total iterferece itroduced to e PU bad total power actually allocated to e CR system x -6 optimal power allocatio step power allocatio step power allocatio modified equal power allocatio I total power budget for e CR system 3.5 x Figure 7. Total iterferece itroduced to PU bad optimal power allocatio step power allocatio step power allocatio modified equal power allocatio total power budget for e CR system [3] Z. She J. G. drews ad.. Evas daptive resource allocatio i multiuser OFDM systems wi proportioal rate costraits i IEEE Tras. o Wirele Commu. vol. 4 o. 6 pp ov. 5. [4] Feg-Seg Chu wag-cheg Che Radio Resource llocatio i OFDM Cogitive Radio Systems Persoal Idoor ad Mobile Radio Commuicatios 7. IEEE 8 Iteratioal Symposium o Digital Object Idetifier:.9/PIMRC Page(s): 57. [5] Sami M. lmalfouh Gordo. Stüber Iterferece ware Subcarrier ad Power lloc atio i OFDM- ased Cogitive Radio etworks ecture otes i Electrical Egieerig Volume 4 Multi-Carrier Systems & Solutios 9 I Pages [6] G. asal Md. J. Hoai ad V.. hargava Optimal ad suboptimal power allocatio schemes for OFDMbased cogitive radio systems i IEEE Tras. o Wirele Commu. vol. 7 o. pp ov. 8. [7] G. asal Md. J. Hoai ad V.. hargava Subcarrier ad power adaptatio for multiuser OFDMbased cogitive radio systems Commuicatios (CC) atioal Coferece o Digital Object Idetifier:.9/CC Publicatio Year: Page(s): - 5 [8] u Tag Hua Wag Qiabi Che Guagmig iu Subcarrier ad power allocatio for OFDM-based cogitive radio etworks Commuicatios Techology ad pplicatios 9. ICCT '9. IEEE Iteratioal Coferece o Digital Object Idetifier:.9/ICCOMT Publicatio Year: 9 Page(s): [9] T.Wei J.Hillebrad.roh ad F..Jodral Mutual iterferece i OFDM-based spectrum poolig systems i Proc. IEEE Vehicular Techol. Cof. (VTC 4) vol.4 pp May 4 [] RHEE W. CIOFFI J M. Icrease i capacity of multiuser OFDM system usig dyamic subchael allocatio [C]. IEEE.Proceedigs of IEEE Iteratiosl Vehicular Techology coferece. Tokyo; IEEE : Figure 8. Total power actually allocated to CR system ad compared to e optimal power allocatio algorim. Simulatio results have show at all e algorims i is paper ca always maitai e iterferece reshold ad power costrait ad at amog e subcarrier allocatio algorims we proposed e MaxR-S ca achieve e maximum trasmit rate e MiI-S itroduces e least iterferece to e PU bad ad e FairR-S ca almost achieve faire amog all e SUs. Furermore e step power allocatio algorim offers e best performace amog e suboptimal power allocatio algorims. esides whe faire is take ito accout i e modified equal power allocatio algorim it will cost e capacity of e CR system. REFERECE [] S.Hayki Cogitive radio:brai-empowered wirele commuicatios Selected reas i CommuicatiosIEEE Joural ovol.3pp. Feb.5. [] T.Weiad F..Jodral Spectrum poolig: a iovative strategy for e ehacemet of spectrum efficiecy IEEE Commu.Mag.vol.43o.3pp.S8-S4Mar.4. Copyright MECS I.J. Computer etwork ad Iformatio Security 4-3

Adaptive Resource Allocation in Multiuser OFDM Systems

Adaptive Resource Allocation in Multiuser OFDM Systems Adaptive Resource Allocatio i Multiuser OFDM Systems Fial Report Multidimesioal Digital Sigal Processig Malik Meherali Saleh The Uiversity of Texas at Austi malikmsaleh@mail.utexas.edu Sprig 005 Abstract