Energy-Efficient Design in Wireless OFDMA

Transcription

1 Ths full text paper was peer revewed at the dreton of IEEE Communatons Soety subjet matter experts for publaton n the ICC 2008 proeedngs. Energy-Effent Desgn n Wreless OFDMA Guowang Mao, Nageen Hmayat, Ye (Geoffrey) L, and Davd Bormann Shool of ECE, Georga Insttute of Tehnology Atlanta, Georga , emal: gmao3@gateh.edu and lye@ee.gateh.edu Wreless Commun. Lab./Commun. Teh. Lab., Corp. Teh. Group, Intel Corp. Santa Clara, CA, emal: nageen.hmayat@ntel.om and davd.bormann@ntel.om Abstrat Energy-effent transmsson s an mportant aspet of wreless system desgn due to lmted battery power n moble deves. We onsder uplnk energy-effent transmsson n OFDMA systems sne moble statons are battery powered. We aount for both rut and transmt power when desgnng energy-effent ommunaton mehansms and emphasze energy effeny over peak rates or throughput. Both lnk adaptaton and resoure alloaton shemes are developed to optmze the overall bts transmtted per Joule of energy, whh allows for maxmum energy savngs n a network. Our smulaton results show that the proposed shemes sgnfantly mprove energy effeny. Index Terms energy effeny, OFDMA, bts per Joule, lnk adaptaton, resoure alloaton I. INTODUCTION Power effeny s beomng nreasngly mportant for wreless ommunaton systems due to lmted battery resoures n moble deves. Unfortunately, battery tehnology has not progressed as fast as slon tehnology []. Hene, reent energy-effent management shemes [2] [4] have foused on mnmzng energy onsumpton rather than throughput maxmzaton [5]. Addtonally, orthogonal frequeny dvson multple aess (OFDMA) has emerged as one of the prme multple aess shemes for next generaton mult-user broadband wreless networks. However, lmted researh has been done for energy-effent ommunaton n OFDMA systems. In ths paper, we onsder uplnk energyeffent transmsson n OFDMA systems to mprove battery onsumpton at the mobles. We aount for both rut and transmt power when desgnng lnk adaptaton and resoure alloaton shemes, and emphasze energy effeny over peak rates or throughput. We ntally fous on the ase of flat-fadng OFDMA hannels, and defer the frequeny seletve ase to future work. The rest of the paper s organzed as followng. In Seton II, we brefly desrbe the system model. Then we develop optmal energy-effent lnk adaptaton and network resoure alloaton shemes n Setons III and IV respetvely. Fnally, we onlude the paper n Seton V. II. SYSTEM DESCIPTION Multple aess s aheved n OFDMA by assgnng subhannels to ndvdual users based on qualty of serve (QoS) requrement and hannel ondton. Ths allows smultaneous data transmsson for several users. For smplty, we nvestgate energy-effent OFDMA ommunaton wth flat fadng hannels n ths paper. Consder uplnk transmsson n an OFDMA network wth one base staton (BS) and multple users,.e. moble statons. Denote N and K as the numbers of users and subhannels, respetvely. Denote as the number of subhannels assgned to User. Eah subhannel wll be assgned to one user exlusvely at eah frame slot. Hene, N K. () Denote r as the ahevable data rate on eah subhannel by User, then the data rate of User s r. (2) The BS alloates subhannels to mprove the overall network energy effeny, whh s measured by the number of bts transmtted per Joule. Addtonally, eah user also adjusts transmt power and modulaton order for further optmzaton. III. OPTIMAL ENEGY-EFFICIENT LINK ADAPTATION Ths seton onsders per lnk adaptaton shemes that wll result n mnmum energy onsumpton, or equvalently, maxmum energy-effeny. Throughout ths seton, assume subhannels are assgned. Sne we fous on per lnk energyeffent optmzaton, subsrpts ndatng dfferent users wll be dropped subsequently. A. Energy-Effent Transmsson ate Power onsumpton of a moble staton n transmsson mode onssts of two parts. The frst s rut power, denoted as P C, whh s ndependent of data rate and exsts whenever the user s n transmsson mode. The seond s transmt power, P T (), whh depends on data transmsson rate,. For example, we onsder an addtve whte Gaussan nose (AWGN) hannel wth sgnal bandwdth W, the ahevable data rate s gven by the Shannon apaty as W log( + P T g ), (3) N o W /08/$ IEEE 3307

2 Ths full text paper was peer revewed at the dreton of IEEE Communatons Soety subjet matter experts for publaton n the ICC 2008 proeedngs. where g s the hannel power gan, N o s the power spetral densty. Hene, P T () (e W )No W/g, (4) whh s monotonally nreasng and strtly onvex n. In general, we assume P T () to be monotonally nreasng and strtly onvex and P T (0) 0. The overall power used for data transmsson s P () P C + P T (). (5) The number of bts transmtted per Joule of energy, alled energy effeny, s used as a performane measure, and t s defned as U() P () P C + P T (). (6) The network s optmzed for the hghest energy effeny. Thus, the ntended data rate s arg max U() arg max P C + P T (). (7) The optmal transmsson data rate s gven by the followng theorem, whh s proved n Appendx A. Theorem. If P T () s monotonally nreasng and strtly onvex n, there exsts a unque globally optmal transmsson data rate for (7) gven by P C + P T ( ), (8) P T ( ) where P T ( ) s the frst dervatve of funton P T ( ). 2 Data Interval n 3 T s l- Sgnalng Interval Fg. : Frame struture l τ To llustrate the applaton of Theorem, we derve the optmal lnk settngs for unoded multple quadrature ampltude modulaton (M-QAM) n AWGN hannel. The frame struture of the system s shown n Fgure. Eah transmsson slot onssts of a data nterval, T s, and a sgnallng nterval, τ. Assume blok fadng, that s, the hannel state remans onstant durng eah data nterval and s ndependent from one to another. For M-QAM, the number of bts transmtted per symbol s b log 2 M, where M s the modulaton order. In eah data nterval, l symbols are transmtted on eah subhannel. The data rate on eah subhannel s r bl T s+τ, and the overall data rate s r bl T s + τ. (9) Consequently, for a gven data transmsson rate, the number of bts transmtted per symbol wll be b (Ts+τ) l. The bt-error rate (BE) for oherently deteted M-QAM wth Gray mappng over an AWGN hannel s approxmated by [8] ( P e (γ) 0.2exp.5γ ), (0) M where γ s the sgnal-to-nose rato (SN). Denote g to be the power gan of the hannel. The SN on eah subhannel wll be γ P T ()g N o W, () where N o s the power spetral densty and W s the sgnal bandwdth n eah subhannel. For a gven BE, P e, the requred SN an be determned by (0). Consequently, the requred transmt power wll be P T () γn ow g 2 ln(5pe)now 3g A( 2 B ), (2) where A for effetve transmsson, therefore, A<0. It an be seen that P T () s monotonally nreasng and strtly onvex n. P C haraterzes rut power onsumpton n both the data and sgnallng ntervals. Aordng to Theorem, the desred data rate s Correspondngly, b (T s+τ) l and B Ts+τ l. Usually, 5P e < A(2B ) P. (3) AB2 B ln 2 and M 2 (T s+τ) l. B. Charatersts of Energy-Effent Transmsson Theorems 2 and 3 desrbes the haratersts of energyeffent lnk transmsson and are proved n Appendes B and C respetvely. Theorem 2. For energy-effent transmsson, both the transmsson data rate, determned by modulaton order, and the energy effeny nrease wth hannel power gan. Theorem 3. For energy-effent transmsson, the modulaton order on eah subhannel dereases wth the nrease of the number of subhannels assgned to a user, whle the energy effeny nreases wth t. To demonstrate Theorem 2 and 3, we present energyeffent lnk transmsson for an unoded M-QAM system wth the frame struture as n Fgure. System parameters are lsted n Table I. Eah user s assgned 0 subhannels, unless otherwse spefed. Fgure 2(a) shows the energy effeny of users loated at dfferent dstanes from the BS. The lower axs shows the data rate aheved gven the modulaton order ndated by the top 3308

3 Ths full text paper was peer revewed at the dreton of IEEE Communatons Soety subjet matter experts for publaton n the ICC 2008 proeedngs. TABLE I: System Parameters Carrer frequeny.5 GHz Subhannel bandwdth 0 khz BE 0 6 bol number of data nterval, l 00 Tme duraton of data nterval, T s 0.0s Tme duraton of sgnallng nterval, τ 0.00s Thermal nose power, N o -4 dbw/mhz User antenna heght.6 m BS antenna heght 40 m Envronment Maro ell n urban area Crut power, P C 00 mw Maxmum transmt power 33 dbm Propagaton Model Okumura-Hata model Fadng Flat fadng Modulaton Unoded M-QAM axs. The fgure shows that by seletng an optmal modulaton sheme, energy effeny nreases as the user moves loser to the BS. Furthermore, the optmal modulaton for energyeffent transmsson vares wth the dstane between the user and BS. In general, for transmsson wth maxmum energy effeny, the loser the user s to the BS, the hgher the modulaton order should be. Fgure 2(b) shows energy effeny of a user loated km away from the BS wth dfferent numbers of assgned subhannels. From Fgure 2(b), the more the number of subhannels assgned to a user, the hgher the maxmum energy effeny s, and the more senstve to modulaton order the energy effeny s. Fgure 3 shows the energy onsumed for sendng one megabt. Fgure 3(a) ompares energy onsumpton for a system wth fxed modulaton and wth optmal modulaton order determned by the proposed energy-effent transmsson. For fxed modulaton, the transmt power s alloated suh that the BE s 0 6. Fgure 3(b) ompares the optmal energy-effent sheme wth tradtonal adaptve modulaton. In tradtonal adaptve modulaton, the transmt power s fxed to be 5 dbm, 20 dbm, 25 dbm, or 30 dbm. The energy values are normalzed wth those of the proposed optmal energyeffent sheme. From the fgures, the proposed sheme always aheves the lowest energy onsumpton. IV. ENEGY-EFFICIENT ESOUCE ALLOCATION The BS alloates subhannels to mprove overall network energy effeny. Subsrpts are added to dstngush users. A. esoure Alloaton wthout Farness Denote set {, 2,, N } to be the set of numbers of subhannels assgned to eah user. Wth subhannel assgnment, the total energy effeny aross the whole network should be maxmzed,.e., arg max arg max U ( ) (4a) P ( ) subjet to r, (4b) and N K. (4) Denote P T (r ) as the transmt power on eah subhannel when the supported data rate s r for User. P ( ) P C + P T (r ).Wehave, U ( ) P ( ) r P C + P T (r ) r P C + P T (r ). r (5) Let V ( ), whh s strtly onave n P C +P T (r ). Problem (4) s equvalent to arg max V ( ) (6a) subjet to N K. (6b) Sne V ( ) s strtly onave and therefore, unque globally optmal subhannel assgnment exsts. Lagrange multpler an be used to fnd the soluton of the above optmzaton problem. The Lagrange funton assoated wth problem (6) s N N L(,λ) V ( ) λ( K). (7) Let L V ( ) λ 0, the optmal assgnment for User s V (λ ), (8) where V ( ) s the nverse funton of V ( ), and λ s gven by V (λ )K. (9) The optmal soluton n (8) may produe fratonal subhannel assgnment, whh s not desred. If we searh ntegers, s, for problem (4), then t an be treated as a utlty based resoure alloaton, and has been thoroughly nvestgated n [9]. The pratal sortng-searh algorthm n [9] an be used to assgn subhannels for the purpose of energy effeny. B. esoure Alloaton wth Farness In ths seton, we onsder energy-effent shedulng wth proportonal farness onstrant [0]. The BS assgns subhannels to maxmze the produt of energy effeny of all users,.e., ( ) arg max arg max log P ( ) P ( ) (20a) 3309

4 Ths full text paper was peer revewed at the dreton of IEEE Communatons Soety subjet matter experts for publaton n the ICC 2008 proeedngs. Energy Effeny (Mbts/Joule) Modulaton Order (bts/symbol) km 0.7km 0.9km.km.3km Data ate (Mbts/s) Modulaton Order (bts/symbol) (a) elatonshp of energy effeny, dstane, modulaton and transmsson data rate ment (b) elatonshp of energy effeny, modulaton and subhannel assgn- Fg. 2: Energy-effeny relatonshp of per lnk transmsson Energy Effeny (Mbts/Joule) (a) Comparson wth fxed modulaton (normalzed energy) (b) Comparson wth adaptve modulaton (normalzed energy) Fg. 3: Energy onsumed for transmttng one megabt subjet to and r N K. (20b) (20) Denote W ( ) log(v ( )). Problem (20) s equvalent to arg max log(v ( )) arg max W ( ), (2a) subjet to N K. (2b) Sne V ( ) > 0 s strtly onave, 2 W ( ) 2 2 log(v ( )) 2 V ( ))V ( )) V 2 ( )) [ ] 2 V ( )) < 0. (22) Hene, W ( ) s strtly onave n. Problem (2) s strtly onave and unque globally optmal assgnment exsts. Smlar to (8), the optmal assgnment s gven by where λ satsfes W (λ )K. W (λ ), (23) 330

5 Ths full text paper was peer revewed at the dreton of IEEE Communatons Soety subjet matter experts for publaton n the ICC 2008 proeedngs. (a) Network energy effeny omparson Fg. 4: Comparsons of dfferent algorthms (b) Network throughput omparson C. Performane Comparsons In ths seton we present performane results for energyeffent resoure alloaton shemes. System parameters are the same as those n Table I. All the shedulers and orrespondng transmsson shemes are lsted n Table II. In PropTrad, we set the transmt power to be 5 dbm, 25 dbm, and 33 dbm respetvely. Users are randomly dropped wthn the ell and the hannels experene both log-normal shadowng wth standard devaton of 0 db, and aylegh fadng wth unt average power gan. There are 96 subhannels, eah wth 0 khz. Fgure 4 ompares energy effeny and the orrespondng throughput, respetvely. We note that the energy-effent sheduler wthout farness performs wth hghest energy effeny and wth smlar throughput to the proportonal sheduler wth 25 dbm transmt power for adaptve modulaton. Comparng the proportonal sheduler wth 25 dbm transmt power and the energy-effent sheduler wth proportonal farness, both of whh guarantee farness amongst users, we note that the energy-effent sheduler has around 20% less nstantaneous throughput than the proportonal sheduler, however, t transmts about 00% more data than the proportonal sheduler gven a fxed amount of energy. Or equvalently, gven a fxed amount of data, the energy-effent sheduler saves 50% energy. Comparng the two round-robn shedulers, we note that the one wth energy-effent transmsson always performs approxmately 50% better than the one wth fxed modulaton for both energy effeny and throughput and ths omes from the adaptvty of both modulaton and power by energy-effent transmsson to the hannel status. We note that whle energy-effent shedulng an optmze the energy utlzaton, overall throughput s not optmzed. Observng the performane of proportonal sheduler wth dfferent values of transmt power n Fgures 4(a) and 4(b), we note that TABLE II: Shedulng and Transmsson Shemes Legend Sheduler Modulaton OptEE energy-effent sheduler energy-effent transmsson wthout farness EE round-robn sheduler energy-effent transmsson Trad round-robn sheduler 2, 4, 8-QAM seleted wth equal probablty PropTrad proportonal sheduler adaptve modulaton wth fxed transmt power PropEE energy-effent sheduler energy-effent transmsson wth proportonal farness the throughput nreases as the transmt power, whle the energy effeny dereases. Energy effeny and throughput effeny do not neessarly agree. Fgure 5 ompares the umulatve dstrbuton funtons of energy effeny when 3 users are atve. Whle the energyeffent sheduler wthout farness has the most perentage of users at hgh energy effeny, the one wth proportonal farness aheves the best farness aross dfferent users wth lowest perentage at low energy effeny range. The energyeffent sheduler wth proportonal farness performs better than both round-robn shedulers, whh means that whle assurng better farness among all users, t also aheves hgher energy effeny. V. CONCLUSION In ths paper, we desgn lnk adaptaton and resoure alloaton shemes that emphasze energy effeny. Both rut and transmt power are taken nto aount. Shedulng poles are also desgned for BSs to mprove the overall network energy effeny. Smulaton results show that the proposed shemes sgnfantly mprove moble energy effeny per lnk as well as aross the network. Here, we foused on the ase of flat fadng OFDMA hannels. Extenson of energyeffent desgn for frequeny seletve OFDMA hannels, wll 33

6 Ths full text paper was peer revewed at the dreton of IEEE Communatons Soety subjet matter experts for publaton n the ICC 2008 proeedngs. be addressed n future work. Cumulatve Dstrbuton Funton OptEE EE Trad PropEE Energy effeny (Mbts/Joule) Fg. 5: Farness omparsons APPENDIX A POOF OF THEOEM Proof: arg max P C+P T () P arg mn C+P T () PC+PT (). Denote f(). Let t > 0, and g(t) f( t )P Ct+P T ( t )t. Then t and t arg mn t g(t). Sne 2 g(t) t 2 t P 3 T ( t ) > 0, g(t) s strtly onvex n t. Sne P T () s monotonally nreasng and strtly onvex n, the dervatve satsfes lm > P T (). Aordng to the L Hoptal s rule, lm t >0 g(t) lm t >0 P T ( t )t lm PT () > P T lm () >. Besdes, lm t > g(t). Sne g(t) < for 0 <t<, t unquely exsts and s globally optmal. By lettng g(t) t 0 and t, we have the soluton n Equaton (8). APPENDIX B POOF OF THEOEM 2 Proof: Denote P (r) to be the reeved power on a subhannel for relable deteton when the data rate on the subhannel s r. We have P T () P (r) g P ( ), (B.24) g where g s the hannel power gan. It s easy to see that P (r) s monotonally nreasng and strtly onvex, and P T (0) P (0) 0. Aordng to Theorem, we have P T ( ) P C + P T ( ), whh s equvalent to P ( ) P ( )P Cg. (B.25) By dfferentatng the left hand sde of (B.25) wth respet to, ( P ) ( ) P( ) P ( ) > 0. Hene, the left hand sde of (B.25) s strtly nreasng n. Therefore, hgher modulaton order should be used when the hannel has hgher power gan. Suppose g > g 2, and the orrespondng optmal modulatons and odngs result n data rates and 2 respetvely. Hene, U () > U (2). Besdes, U (2) U 2 (2). Hene, the energy 2 P C+ P ( 2 /) g > 2 P C+ P ( 2 /) g 2 effeny nrease wth hannel gan. APPENDIX C POOF OF THEOEM 3 Proof: r and P T () P T (r) P T ( ), where P T (r) s the transmt power on eah subhannel, and s monotonally nreasng and strtly onvex n r. Aordng to Theorem, we have P T ( )P C + P T ( ), whh s equvalent to r P T (r ) P T (r ) PC. The left hand sde s nreasng n r whle the rght hand sde s dereasng n. Hene, the modulaton order on eah subhannel should derease wth nreasng number of subhannels assgned. The proof that the energy effeny nreases wth the number of subhannels assgned s smlar to the proof n B and s omtted here. EFEENCES [] K. Lahr, A. aghunathan, S. Dey, and D. Pangrah, Battery-drven system desgn: A new fronter n low power desgn, n Pro. Intl. Conf. on VLSI Desgn, Bangalore, Inda, pp , Jan [2] Y. Xao, Energy savng mehansm n the IEEE 802.6e wreless MAN, IEEE Commun. Letters, vol. 9, no. 7, pp , July [3] F. Meshkat, H. V. Poor, S. C. Shwartz, and N. B. Mandayam, An energy-effent approah to power ontrol and reever desgn n wreless networks, IEEE Trans. Commun., vol. 5, no., pp , Nov [4] N. Feng, S. C. Mau, and N. B. Mandayam, Prng and Power Control for Jont Network-Centr and User-Centr ado esoure Management, IEEE Trans. Commun., vol. 52, no. 9, pp , Sep [5] G. Mao, and Z. Nu, Pratal Feedbak Desgn based OFDM Lnk Adaptve Communatons over Frequeny Seletve Channels, n Pro. IEEE Conf. Commun. 2006, Istanbul, Turkey, June 2006, pp [6] IEEE, IEEE 802.6e-2004, part 6: ar nterfae for fxed and moble broadband wreless aess systems - amendment for physal and medum aess ontrol layers for ombned fxed and moble operaton n lensed bands, Nov., [7] IEEE, IEEE 802.6e-2005, part 6: ar nterfae for fxed and moble broadband wreless aess systems - amendment2: physal and medum aess ontrol layers for ombned fxed and moble operaton n lensed bands, Feb., [8] A.J.Goldsmth and S. G. Chua Varable-rate varable-power MQAM for fadng hannels, IEEE Trans. Commun., vol. 45, no. 0, pp , Ot [9] G. Song, and Y. L, Cross-layer optmzaton for OFDM wreless networks-part II: algorthm development, IEEE Trans. Wreless Commun., vol. 4, no. 2, pp , Marh [0]. Mazumdar, L. G. Mason, and C. Doulgers, Farness n network optmal flow ontrol: optmalty of produt forms, IEEE Trans. Commun., vol 39, no. 5, pp , May