Power and Subcarrier Allocation for Multicast Service in OFDMA Decode-and-Forward Relay Systems

Transcription

1 Power ad Subcarrier Allocatio for Multicast Service i OFDMA Decode-ad-Forward elay Systems Yi Wa, Xiafe Liu, Fuwe Pa, ad Bi Li Deartmet of Iformatio ad Sciece Techoloy, Dalia Maritime Uiversity, Dalia, Chia wayi@dlmu.edu.c liuxf8676@63.com, fwa@63.com, libi060@63.com Abstract Orthooal Frecy Divisio Multilexi Access (OFDMA) relay system is a romisi techique for icreasi the caacity ad the rae of wireless commuicatio systems. Dyamic resource allocatio for OFDMA relay systems lays a imortat role i imrovi the system erformace. However, most of the resource allocatio alorithms are desied for the uicast traffics, ad resource allocatio alorithm for multicast traffics i OFDMA relay systems has received little attetio. I this aer, the resource allocatio roblem for the decode-ad-forward relay assisted OFDMA multicast system is cosidered. Our oal is to maximize the sum rate of the multicast system uder the costraits of total ower limit ad exclusive subcarrier usae. The multicast resource allocatio roblem is formulated as a mixed iteer rorammi roblem. The roblem is firstly solved by usi Laraia dual decomositio method, resulti i a asymtotically otimal joit subcarrier ad ower allocatio alorithm with comutatioal comlexity bei liear with the umber of multicast rous ad subcarriers. Furthermore, a low comlexity subotimal resource allocatio alorithm is reseted to further reduce the comutatioal comlexity. Simulatio results show that both the roosed otimal ad subotimal alorithms ca siificatly imrove the system erformace ad the roosed subotimal alorithm ca achieve a ear otimal solutio. Idex Terms OFDMA, multicast, resource allocatio, decode-ad-forward. I. ITODUCTIO OFDMA system with relay has bee cosidered as a romisi techoloy for the ext eeratio wireless systems due to its resistace to frecy selective fadi, flexibility for resource allocatio, ad ability to rovide ubiquitous wide area coverae []. O the other had, wireless multicast is a attractive techique to efficietly deliver badwidth-itesive traffic loads to multile destiatios simultaeously by taki the advatae of the broadcast chael ature of wireless media []. Therefore, OFDMA multicast etworks ca be used to rovide ew additioal fuctioalities, icludi the multimedia alicatios, real time ami alicatios, Iteret Protocol Tele Visio (IPTV) alicatios, ad may others. Dyamic radio resource allocatio i OFDMA etworks aims to efficietly utilize the Mauscrit received Jauary 5, 03; revised February 8, 03. doi: 0.70/jcm subcarriers ad trasmissio ower amo multile mobile users, ad lays a imortat role i meeti the quality of service (QoS) riremets imosed by the broadbad services [3]. Therefore, radio resource maaemet strateies should be desied carefully. adio resource allocatio alorithm for relay-aided OFDMA systems is a challei tas ad has bee attracti much iterest i recet years [4]. However, most of the literatures deali with the resource allocatio roblem i relay-aided OFDMA systems focus o uicast cases [5]-[7], where each user has its idividual dowlik or ulik traffic flows. Curret researches [8]-[0] have cosidered the multicast radio resource allocatio roblems i OFDMA etworks without relay. I [8], low-comlexity subotimal alorithms are roosed for subcarrier ad ower allocatio to maximize the system throuhut with a total trasmissio ower costrait. I [9], a chuk-based subotimal resource allocatio alorithm for the dowlik of multicast OFDMA systems is ivestiated. The roosed alorithm is to maximize the total throuhut subject to costraits o total available ower ad averae bit error rate over a chuk uder the assumtio of uiform ower distributio amo subcarriers. I [0], a dual decomositio based otimal subcarrier ad ower allocatio for OFDMA coitive multicast etwork is carried out. However, to our best kowlede, little research has bee doe o the resource allocatio for multicast service i OFDMA relay systems. I this aer, the case where the base statio serves multile multicast rous with the assistace of a decodead-forward relay is cosidered. The resource allocatio roblem is formulated as a otimizatio roblem with the objective to maximize the system sum rate uder total ower ad exclusive subcarrier usae costraits. Firstly, the otimizatio roblem is solved by usi Laraia dual decomositio techique ad subradiet udate method to obtai a asymtotically otimal joit subcarrier ad ower allocatio alorithm whose comlexity is liear with the umber of subcarriers ad multicast rous. The, to further reduce the comutatioal comlexity, a subotimal resource allocatio alorithm is reseted. Fially, it is show throuh umerical simulatios that the roosed otimal resource allocatio alorithm ca covere fast, ad the roosed subotimal resource allocatio alorithm ca rovide a ear otimal solutio. The simulatio results also show that both the roosed otimal ad subotimal 77

2 resource allocatio alorithms ca siificatly outerform a fixed subcarrier assimet ad water filli ower allocatio scheme. The remaider of this aer is oraized as follows. I Sectio II, the system model is reseted ad the otimizatio roblem is formulated. I Sectio III, the otimal joit subcarrier ad ower allocatio alorithm is reseted. I Sectio IV, the low comlexity subotimal resource allocatio alorithm is ive. I Sectio V, some umerical examles to verify the erformace of the roosed resource allocatio alorithms are offered. Fially, Sectio VI cocludes the aer. II. SYSTEM MODEL AD POBLEM FOULATIO BS Traffic flow Traffic flow Traffic flow S Fiure. Block diaram for multicast DF-relayed OFDMA system The system is comosed of oe base statio (BS), oe relay statio (S), ad K mobile statios (MSs), as show i Fi.. The K MSs are oraized ito multicast rous, ad the users i the same rou receive the same messaes. Similar to [], it is assumed that there is o direct liks betwee the BS ad the MSs because of the distace or obstacles. The commuicatio betwee the BS ad MSs i each multicast rou should be assisted by the S. The BS trasmits traffic flows to the rous, ad each rou oly receives its ow traffic flow which is differet from the oe received by other rous. Let U, {,,} deote the set of users which belo to the -th multicast rou, ad U deote the umber of users i the -th rou. The S is assumed to be half-dulex, as a result, the commuicatio betwee the BS ad MSs is divided ito two staes. I the first stae, the BS seds oe modulated symbol to the S. I the secod stae, the relay decodes the received sials ad retrasmits them to the members of all multicast rous. It is also assumed that the S uses the same subcarrier as the oe used by the BS i the first hase to forward messaes, i other words, the fixed subcarrier ari stratey is used i this model. The total badwidth is divided ito al- badwidth subcarriers. Let h, h, deote the chael k coefficiets over the first ho betwee the BS ad the S, ad over the secod ho betwee the S ad MS k i subcarrier, resectively. The chaels are assumed to remai costat duri a two-slot scheduli iterval, ad vary ideedetly i the ext scheduli iterval. If subcarrier is allocated to the multicast rou, the trasmissio rate secod stae for MS exressed as k, at the first stae ad k, at the k U, ca be resectively B, l h lo 0, lk hk, lo 0 where, l reresets the ath loss betwee the BS ad the S, l reresets the ath loss betwee the S ad k B the MS k.,,, are the trasmit owers allocated to subcarrier for multicast rou at the BS ad the S, resectively. 0 deotes the ower sectrum desity of the additive white aussia oise at the S ad MSs. I this way, for decode-ad-forward relay stratey, the maximum achievable averae rate for MS k, k U, i subcarrier with the hel of the S is mi k,, () () (3) It is kow that the achievable rate i Eq. (3) at the MS k ca be maximized whe the coditio of is satisfied. Let l h k, ad l h 0 k 0, ad let, deote the total trasmissio ower allocated to the multicast rou o subcarrier. Uder the total ower costrait of B for the multicast rou i subcarrier,,,, to maximize, the trasmit ower at the BS ad S ca be exressed, resectively, as follows B,, (4),, (5) with Eq. (4) or Eq. (5), Eq. (3) ca be rewritte as: lo, (6) where k, is the ivalet chael ai for user k over subcarrier air (, ), which is defied as: (7) I the traditioal multicast sceario [8], whe subcarrier is allocated to multicast rou, the achievable rate over this subcarrier is the miimum oe i Eq. (6) which ca be exressed as, mi k, (8) ku Based o Eq. (8), a ivalet chael ai for each multicast rou ca be defied. The ivalet chael 78

3 ai of subcarrier for multicast rou is ive by, mi (9) ku Thus, the achievable data rate i subcarrier allocated to multicast rou is U lo, lo,, ku,, (0) The otimal resource allocatio roblem for the OFDMA multicast system with decode-ad-forward relay ca be formulated as max,π,, (.a) s.t.,, PT ; (.b),, 0, ; (.c), ; (.d), 0,, (.e),, where is a vector of trasmit ower allocatio for all multicast rous over the subcarriers, which is ive by,,,,,. π is a vector of subcarrier T,,,,, allocatio idicator variables, which is ive by T,,,,,,,,,,.,,, is the subcarrier allocatio idicator, ad if subcarrier is allocated, to multicast rou, ad 0 otherwise. I this aer,, it is also assumed that a subcarrier is exclusively allocated to oe multicast rou. As a result, we have the costraits i Eq. (.d) ad (.e). The costraits i Eq. (.b) ad (.c) uaratee that the sum trasmit ower i all subcarrier is smaller tha the system available total ower, ad the trasmit ower i ay subcarrier is oeative, resectively. ote that the otimizatio roblem i Eq. () is a mixed iteer rorammi roblem which is P-hard. If the roblem is solved by cosideri its dual roblem, the duality a betwee the rimal roblem ad its dual roblem will ot be zero due to the o-covexity of the rimal roblem. However, it has bee show that whe the umber of subcarriers i a multicarrier commuicatio system is sufficietly lare, the duality a teds to zero []. Therefore, the Larae dual decomositio method ca be used to desi a asymtotically otimal resource allocatio alorithm for the otimizatio roblem i Eq. (), as show i sectio III. III. OPTIMAL SUBCAIE AD POWE ALLOCATIO VIA LAAIA DUAL DECOMPOSITIO METHOD The Laraia fuctio of roblem Eq. () ca be formulated by relaxi the total ower costrait as follows L,, PT, L, P () T where is the Larae multilier. L,,,, which is the er-subcarrier Laraia fuctio. The costrait i Eq. (.d) is ot take ito accout i Eq. (), ad this costrait will take effect whe solvi er-subcarrier otimizatio roblem with dual decomositio method. Thus, the dual roblem is defied as: mi D s.t. 0 (3) where the dual objective fuctio is ive by max L, D (4.a) max,, PT (4.b) P maxl, (4.c) T P T max max,,,, 0, (4.d) where Eq. (4.c) follows the fact that the er-subcarrier Laraia fuctios are ideedet of each other. Eq. (4.d) ca be obtaied whe cosideri the subcarrier exclusive allocatio costraits i Eq. (.d), ad we allocate the subcarrier to rou which achieves the maximal value of the term,, i (4.d). For a ive, whe subcarrier is exclusively allocated to multicast rou, the otimal trasmit ower, ca be obtaied by usi Karush-Kuh-Tucker (KKT) coditios, ad is ive by, U, (5) where x maxx, 0,,, ad,, The, the rou idex ca be ive by ar. max U lo,,,,, (6) Ad the subcarrier allocatio idicator variables ca be determied by,,, (7) 0, otherwise Cosetly, the trasmit ower ca be udated by 79

4 ,,,,, (8) Based o Eq. (5) ad (6), the dual objective fuctio i Eq. (3) ca be determied. The dual roblem is always covex, therefore, radiet udate method ca be used to fid the otimal value of the dual variable. However, due to the exclusive subcarrier allocatio costraits, the dual objective fuctio may ot be differetiable, thus, the subradiet udate method [] should be used to solve Eq. (3) istead of radiet udate method, that is t t t PT, (9) t where t is the iteratio umber ad 0 is the udate ste size at the t-th iteratio. Accordi to [3], the t dimiishi rules t for some costat ca uaratee the coverece of the subradiet udate method. Combii Eq. (5) to Eq. (9), the alorithm to fid the otimal subcarrier assimet ad ower allocatio ca be desied. The seudocode of the roosed asymtotically otimal resource allocatio (AOA) alorithm is outlied i Alorithm A. ALOITHM A: Asymtotically OPTIMAL ESOUCE ALLOCATIO ALOITHM (AOA),, Ste Fid,, for, ad,, Ste Iitialize, ad let t Ste 3 for = to do Comute,,, usi t i (5) Comute,,, usi, i (7) Udate, usi ed for Ste 4 Udate t usi t,,,, i (9), ad t t, Ste 5 eeat ste 3 to 4 util coverece I ste 3, the subcarrier assimet ad otimal trasit ower allocatio are erformed with a ive dual variable. I ste 4, the dual variable is udated by meas of subradiet method. Ste 3 to 4 should be reeated util coverece. Let T be the umber of iteratio rired for the subradiet method i ste 4 of the joit subcarrier ad ower allocatio alorithm to covere. I each iteratio, it rires comarisos, ad T times of iteratio are eeded for coverece. I ste, it rires comarisos to obtai,,. Therefore, the total comutatioal comlexity of the reseted alorithm is O T. As oited i [], T is a olyomial fuctio of. So, comared with the comutatioal comlexity of the exhaustive search for the otimal solutio,.e.., O( ), the reseted alorithm ca siificatly reduce the comutatio burde., IV. LOW COMPLEXITY SUBOPTIMAL ESOUCE ALLOCATIO ALOITHM The joit subcarrier ad ower allocatio alorithm reseted i sectio III ca rovide otimal solutio for the system with a larer umber of OFDM subcarriers. However, the coverece of the dual decomositio based alorithm is sesitive to the iitial value of the Laraia multilier ad subradiet udate ste size, ad the alorithm may have a slow coverece behavior. I order to further imrove the efficiecy of the resource allocatio alorithm, isired by [8] we roose a two-ste subotimal resource allocatio alorithm with low comlexity for the relay assisted OFDMA multicast system i this sectio. The idea of the subotimal alorithm is to first assi subcarriers to multicast rous i a reedy maer to maximize the system throuhut with the assumtio of al trasmissio ower distributio o every subcarrier. After that, the alorithm erforms water filli ower allocatio amo the subcarriers to imrove the system caacity further. I the subotimal alorithm, after the subcarrier allocatio variables for all ad are determied,, the otimizatio roblem i Eq. () ca be rewritte as max,, (0.a) s.t.,, PT ; (0.b),, 0, (0.c) The otimal ower allocatio roblem i Eq. (0) is a covex rorammi roblem, ad it ca be solved by usi Laraia multilier techique ad KKT coditio. The resultat otimal ower allocated to the k user i subcarrier is, U,, (), where is the Laraia multilier, which ca be determied by usi, PT () It ca be oted that the ower allocatio across the subcarriers i Eq. () follows the stadard water filli scheme, excet that the water level may be ot a costat for subcarriers. The outlie of the low comlexity subotimal resource allocatio (LCSA) alorithm is summarized i alorithm B. It has a comutatioal comlexity of O(), therefore, the subotimal scheme is more efficiet tha the otimal scheme reseted i Sectio III. Alorithm B: Low Comlexity Subotimal esource 80

5 System Sum ate(mbs) Dual variable λ Allocatio Alorithm (LCSA) Ste Iitializatio : Fid,, ad let, 0,, : Set the al ower distributio as: P, Ste reedy Subcarrier Allocatio,, T : for = to do : Fid the best rou idex ( ) for subcarrier usi ( ) ar max U lo (,, ) {,... } 3: Let 4: ed for, Ste 3 Power Allocatio : Calculate ower allocatio usi Eq. () ad () : Calculate the sum rate of the system, U lo (,, ) V. SIMULATIO ESULTS I this sectio, we reset the simulatio results to show the erformace of the roosed subcarrier ad ower allocatio alorithms. We cosider a OFDMA decode-ad-forward relay system with a radius of km. The total badwidth is 5 MHz, which is evely divided ito 8 subcarriers. The total available trasmissio ower at the base statio ad the relay is 0W. The S is fixed with a distace of /3 km to the BS, ad all the MSs are uiformly distributed aroud the S with distaces rai from 0.03km to 0.3km to the S. The distace-deedet ath loss model used i the simulatio is ive by L lo 0( d ) db (3) where d is the distace betwee two statios i km. The shadowi comoet follows a loormal distributio with a mea value of 0dB ad stadard deviatio of 8dB. For the small scale fadi effect, the wireless chael is modeled as a frecy selective fadi chael cosisti of six ideedet ayleih multiaths. All the multiath comoets ideedetly exeriece idetical ayleih fadi, ad the corresodi ower delay rofile is exoetially decayi with e l, where l is the multiath idex. Fi. illustrates the evolutio of the dual variable i the dual decomositio based joit subcarrier ad ower allocatio alorithm uder differet oise ower desities. The simulatio arameters are cofiured as: =4, U = U =4, U 3 = U 4 =5, 0 {-55dBm/Hz, - 65dBm/Hz, -75dBm/Hz}. It ca be see that the roosed resource allocatio alorithm ca covere with a small iteratio umber. I our simulatio, it is foud that the dimiishi iteratio ste size should be selected carefully so that the alorithm ca reliably covere uder differet oise ower desity =-55dBm/Hz 0 =-65dBm/Hz 0 =-75dBm/Hz umber of iteratio t Fiure. Dual variable versus umber of iteratios with differet oise ower desity for =4, U = U =4, U 3 = U 4 = AOA alorithm LCSA alorithm FSA alorithm oise ower desity 0 (dbm/hz) Fiure 3. Comariso of system sum rate versus oise variace for =4, U = U =4, U 3 = U 4 =5. To evaluate the roosed asymtotically otimal ad subotimal resource allocatio alorithms, a fixed subcarrier assimet scheme is itroduced as a bechmark i the simulatio. I the fixed subcarrier assimet scheme which is deoted as FSA, the subcarrier airs are evely allocated to each multicast rou ad remai uchaed, ad oly the trasmissio ower is allocated amo subcarriers by usi water filli method. Fi. 3 shows the system sum rate versus the oise ower desity, ad the results are obtaied throuh averae over 000 times of chael realizatios. The umber of multicast rou =4, ad U = U =4, U 3 = U 4 =5. As exected, the system sum rate decreases with the icreasi of the oise ower desity. We further observe that the roosed asymtotically otimal joit subcarrier ad ower allocatio alorithm (AOA) outerforms the other schemes, but the erformace as betwee the roosed asymtotically otimal alorithm ad subotimal scheme (LCSA) is dimiutive, esecially whe the oise ower desity is small. I other words, the roosed subotimal resource allocatio alorithm ca achieve a ear otimal solutio. Sice the multiuser diversity is ot exloited i the fixed subcarrier assimet scheme, its system sum rate is siificatly lower tha that of the roosed asymtotically otimal ad subotimal alorithms. Fi. 4 shows the system sum rate comariso of AOA, LCSA ad FSA for the umber of multicast rous rai from to 8. The umber of MSs i each multicast rou is fixed with 4, ad the oise ower 8

6 System Sum ate(mbs) desity 0 is assumed to be 55dBm/Hz. It is show that the erformace of the AOA ad LCSA siificatly outerform that of the FSA. The erformace of the LCSA alorithm ca aroach that of the AOA alorithm whe the umber of multicast rous is small, whereas the erformace a becomes obvious with a lare umber of multicast rous AOA alorithm LCSA alorithm FSA alorithm 5 /4 /8 3/ 4/6 5/0 6/4 7/8 8/3 umber of users i each multicast rou / Total umber of users Fiure 4. System sum rate verse differet rou umbers for U = U =U 3 = U 4, 0 = -55dBm/Hz VI. COCLUSIO This aer has ivestiated the resource allocatio roblem for multicast service i a OFDMA decode-adforward relay system. The subcarrier ad ower allocatio is formulated as a costrait otimizatio roblem which maximizes the sum rate of the multicast system while satisfyi the total ower costrait ad exclusive subcarrier usae amo multicast rous. The otimizatio roblem is first solved by usi the Laraia dual decomositio techique to obtai a asymtotically otimal resource allocatio alorithm. I order to further imrove the efficiecy of the resource allocatio, a low comlexity subotimal alorithm is reseted. Simulatio results show that the iteratio umber of the asymtotically otimal resource allocatio alorithm is small, ad the roosed subotimal alorithm ca achieve a ear otimal solutio, ad outerforms the fixed subcarrier assimet ad water filli ower allocatio scheme uder various sial to oise ratio. ACKOWLEDEMETS This work is suorted by i art by the atioal atural Sciece Foudatio esearch Proram of Chia uder rat o EFEECES [] D. W. K. ad. Schober, Cross-layer scheduli for OFDMA amlify-ad-forward relay etworks, IEEE Trasactios o Vehicular Techoloy, vol. 59, , 00. [] S. W. Kim ad B. S. Kim, ate-adative MAC rotocol for wireless multicast over OFDMA-based MAETs, Wireless Persoal Commuicatios, vol. 56, , February 0. [3] P. Li, Y. Cha,. Fe, ad F. Ya, A cross-layer alorithm of acket scheduli ad resource allocatio for multi-user wireless video trasmissio, IEEE Trasactios o Cosumer Electroic, vol. 57,. 8-34, 0. [4] M. Salem, A. Adioyi, ad M. ahma, et al, A overview of radio resource maaemet i relay-ehaced OFDMA-based etworks, IEEE Commuicatio Surveys & Tutorials, vol., , 00. [5] C. Hsu, H. Su, ad P. Li, Joit subcarrier airi ad ower allocatio for OFDM trasmissio with decode-ad-forward relay, IEEE Trasactios o Sial Processi, vol. 59, , 0. [6] H. Boostaiehr ad V. K. Bharava, Selective subcarrier airi ad ower allocatio for DF OFDM relay systems with erfect ad artial CSI, IEEE Trasactios o Wireless Commuicatios, vol. 0, , 0. [7] W. Wa, S. Ya, ad S. Ya, Otimal joit subcarrier matchi ad ower allocatio i OFDM multiho systems, EUASIP Joural o Advaces i Sial Processi, vol. 008,. -8, Jauary 008. [8] J. Liu, W. Che, ad K. B. Letaief, Dyamic ower ad subcarrier allocatio for OFDMA-based wireless multicast systems, i Proc. IEEE Iteratioal Coferece Commuicatios, May 9-3, Beiji: Chia, 008, [9] V. D. Paoutsis ad S. A. Kotsooulos, Chuk-based resource allocatio i multicast OFDMA systems with averae BE costrait, IEEE Commuicatio Letters, vol. 5, , 0. [0] D. T. o, C. Tellambura, ad H. H. uye, esource allocatio for OFDMA-based coitive radio multicast etworks with rimary user activity cosideratio, IEEE Trasactios o Vehicular Techoloy, vol. 59, , 00. []. Zhou, X. Zhu, ad Y. Hua, et al, Adative resource allocatio for multi-destiatio relay systems based o OFDM modulatio, i Proc. IEEE Iteratioal Coferece Commuicatios, Jue 4-8, Dresde, ermay, 009,. -5. [] W. Yu ad. Lui, Dual methods for ocovex sectrum otimizatio of multicarrier systems, IEEE Trasactios o Commuicatios, vol. 54,. 30-3, 006. [3] S. Boyd ad L. Vadeberhe, Covex Otimizatio, Cambride, U.K.: Cambride Uiversity Press, 004. Yi Wa received the B.S. deree ad M.S. deree i 99 ad 995, resectively, from orth Chia Electric Power Uiversity, Chia, ad Ph.D. deree i 00 from Beiji Istitute of Techoloy, Chia. He is curretly with Dalia Maritime Uiversity. His research iterests iclude resource allocatio of OFDM etworks, MIMO techiques, ad wireless ad hoc etworks. He is a member of the IEEE. Xiafe Liu received the B.S. deree i Commuicatio Eieeri from Dalia Maritime Uiversity, Chia, i 0. She is also a M.S. cadidate i the Iformatio Sciece ad Techoloy Collee of the same istitute sice 0. Her research iterests iclude resource allocatio of OFDM etworks, ad wireless ad hoc etworks. Fuwe Pa received the B.S. deree i 975 from Dalia Maritime Uiversity, Chia, ad Ph.D. deree i 00 from Korea Maritime Uiversity, Korea. He is curretly with Dalia Maritime Uiversity. His curret research iterests iclude maritime mobile commuicatio, maritime Ad Hoc etworks. 8

7 Bi Li received his M.E. ad Ph.D. derees i commuicatio ad iformatio System from Dalia Maritime Uiversity, Dalia, Chia, at 996 ad 008, resectively. At reset, he is a Associate Professor at commuicatios deartmet, Dalia Maritime Uiversity. His research iterests iclude adative sial rocessi ad commuicatio system develomet. He is a member of the IEEE 83