Regenerator vs. Simple-Relay with Optimum Transmit Power Control for Error Propagation

Transcription

1 MEL A MITSUBISHI ELECTIC ESEH LOATOY hp://wwwmrlcom gnraor vs Simpl-lay wih Opimum Transmi Powr Conrol for Error opagaion Zafr Sahinoglu and Philip Orlik T July 003 Absrac W sudy powr dissipaion in rlay assisd wirlss ransmissions Two yps of assisanc ar considrd: simpl rlaying and rgnraiv rpar W find minimum ransmi powr lvls o provision h sam bi rror ra (BE) in boh cass Th simpl-rlay cas considrs powr adjusmn for rror propagaion a h inrmdia rlay nod Powr consumpion comparisons ar mad and rsuls ar discussd This work may no b copid or rproducd in whol or in par for any commrcial purpos mission o copy in whol or in par wihou paymn of f is grand for nonprofi ducaional and rsarch purposs providd ha all such whol or parial copis includ h following: a noic ha such copying is by prmission of Misubishi Elcric sarch Laboraoris, Inc; an acknowldgmn of h auhors and individual conribuions o h work; and all applicabl porions of h copyrigh noic Copying, rproducion, or rpublishing for any ohr purpos shall rquir a licns wih paymn of f o Misubishi Elcric sarch Laboraoris, Inc All righs rsrvd Copyrigh c Misubishi Elcric sarch Laboraoris, Inc, Broadway, Cambridg, Massachuss 039

2 Publicaion Hisory: Firs prining, T , July 003

3 gnraor vs Simpl-lay wih Opimum Transmi Powr Conrol for Error opagaion Zafr Sahinoglu, Mmbr, IEEE, and Philip Orlik, Mmbr, IEEE Absrac W sudy powr dissipaion in rlay assisd wirlss ransmissions Two yps of assisanc ar considrd: simpl rlaying and rgnraiv rpar W find minimum ransmi powr lvls o provision h sam bi rror ra (BE) in boh cass Th simpl-rlay cas considrs powr adjusmn for rror propagaion a h inrmdia rlay nod Powr consumpion comparisons ar mad and rsuls ar discussd boom), C dos no prform any daa rcovry (g, rror corrcion c), bu coopras wih A such ha A adjuss is ransmi powr lvl o provision a rcivr C; and C adjuss is ransmi powr lvl o provision a rcivr B Hnc, assuming ha h bi rrors on hs wo pahs ar addiiv, h oal BE is consraind o Indx Trms Powr conrol, rror propagaion, rlayassisd ransmission I I INTODUCTION N snsor nworks and mobil ad-hoc nworks, minimizing ovrall powr consumpion in h nwork, and accordingly incrasing nwork lifim is currnly an aciv rsarch ara Som of h approachs o achiv powr fficincy ar o dcras ncodr and dcodr complxiis, o dsign low powr circuiris, and o dvlop low signalingcos rouing proocols c Thr ar also ohr chniqus ha ry o xploi nwork opology o rduc powr xpndiur lay assisd ransmission and powr combining mhods wih divrsiy chniqus []-[4] fall undr h lar Assum a ripl as illusrad in Fig In [], [] and [4], i is shown ha whn rminal A snds is daa o B hrough C, h ovrall powr consumpion compard o h cas whn A ransmis dircly o B is rducd This comparison is only valid providd ha wo scnarios provision h sam bi rror ra (BE) consrain,, a dsinaion B In []-[4], his consrain is provisiond Howvr, hir rsuls do no ak ransmi powr compnsaion du o rror propagaion ino accoun a h rlay nod This lr aims o fill his gap Inrmdia nod C may funcion in wo diffrn ways: a rgnraor or a simpl rlay In h rgnraor mod (Fig- op), C rcivs daa from A, a a powr lvl ha would saisfy, corrcs bis in rrors and forwards h rcovrd daa o B a a ransmi powr lvl ha would again saisfy a rcivr B In a simpl rlay mod (Fig- Manuscrip rcivd Fbruary 4, 003 Th associa dior coordinaing h rviw of his lr and approving i for publicaion was Dr Yu-Dong Yao Th auhors ar wih h Misubishi Elcric sarch Labs, Cambridg, MA 039, USA, (phon: (67) ; fax: (67) ; -mail: zafr@mrlcom, porlik@mrlcom ) Fig Illusraion of h rcivd signal powr lvls and bi rror ras a rciving rminals in wirlss ransmission ovr (op) h rgnraor (boom) simpl rlay inrmdia nod II ADIO MODEL W dno by α, h rquird rcivd signal powr a ra such ha h BE is W us a simpl radio modl analogous o h ons in [] and [3] o modl wirlss ransmission W assum ha h powr consumpion of a communicaions nod, P (in was), consiss of powr consumd by h x/rx radio circuiry, P circ, which is fixd; h powr consumd by h x amplifir powr, Pamp ( ), which is adjusd o achiv a dsird BE a ra ; and powr consumd o rciv h bis a h rcivr nd, c ( ) Also, diffrn lvls of clur on propagaion pahs ar modld as lognormal shadowing Th shadowing ffc bwn nods i and j, x (in db), is xprssd in h powr quaions as x /0 0 (in was)

4 P = P + P ( ) + P ( ) () circ amp rc x /0 P amp can b furhr xpandd as P 0 amp = α d γ, whr d is h disanc bwn nod pairs i and j, and γ is h pah loss xponn Annna gain is assumd o b uniy III POWE ANALYSIS In his scion, w quanify powr dissipaion in a communicaions ripl wih an inrmdia nod ha is usd as a rgnraor or a simpl-rlay (amplifir) Ths wo cass ar compard o h powr consumpion in dirc ransmission A Dirc Transmission L P amp dno h amplifir powr a ransmir i for sraming daa o rcivr j Whn daa ar dircly ransmid from A o B, h oal powr xpndd in h ' sysm, P, is ' A B P = Pcirc + Pamp ( ) + c ( ) + Pcirc () x /0 = ( Pc + c( )) + α 0 d γ In (), w hav mad an assumpion wihou loss of gnraliy A B C ha P = P = P = P circ circ circ c B Inrmdia gnraor Nod Assum ha A ransmis daa o B using C as an inrmdia rgnraor nod C would consum powr whil boh '' rciving daa from A and forwarding i o B L P dno h powr dissipaion in his ripl '' A C B P = Pcirc + Pamp ( ) + Pcirc + c ( ) + Pamp ( ) + Pcirc (3) x x = 3Pc + c( ) + α (0 d + 0 d) Th saisfacory condiion o hav powr savings wih " ' comparison o h dirc ransmission is P = P P < 0 x x P = α ( 0 d + 0 d (4) x + 0 d) + Pc + c ( ) Afr rarranging (4), h s condiion for powr savings is givn in (5) x /0 /0 /0 ( ) γ x γ x γ Pc + c 0 d + 0 d < 0 d (5) α C Inrmdia Simpl lay Nod In his scnario, C dos no prform any rcovry on h daa rcivd from A L α and α dno h rquird rcivd signal powr lvls o provision from A o C and from C o B Thn, h ovrall powr dissipaion, ''' P, is ''' A C B P = Pcirc + Pamp ( ) + Pcirc + c ( ) + Pamp ( ) + Pcirc (6) x x = 3Pc + c( ) + α 0 d + α 0 d Th diffrnc in powr xpndiur bwn simpl rlaying "' ' and dirc ransmission is P = P P x / 0 γ x / 0 γ P = α 0 d + α 0 d (7) x / 0 γ α 0 d Pc + c( ) To prov powr fficincy of simpl rlaying compard o dirc ransmission P < 0 mus b saisfid Eq7 lads o s condiion (8), which is slighly diffrn from (5) α x / 0 γ α x / 0 γ 0 d + 0 d α α (8) x / ( ) 0 γ Pc + c < 0 d α No ha h righ sids of (5) and (8) ar h sam In ordr o b abl o compar powr consumpion in h inrmdia simpl rlay scnario o ihr h dirc ransmission or o h inrmdia rgnraor scnario, α and α mus b opimally slcd such ha h lf sid of (8) is minimizd, undr h consrain ha + = Assuming a M- ary Quadraur ampliud modulaion (QAM) schm in dirc ransmission from A o B, can b approximad as in (9) [5] 4( / M ) 3α log M Q (9) log M ( M ) N 0 whr N 0 is h powr dnsiy of addiiv whi Gaussian nois (AWGN) In a similar way, w can formula and as in (0) and () rspcivly 4( / M ) 3α log M Q log M ( M ) N 0 (0) = (4/ β) Q α / α Q 05β ( ( )) 4( / M ) 3α log M Q log M ( M ) N 0 = (4/ β) Q α / α 05β ( Q ( )) () whr β = (log M) /( / M) Th goal is o find opimum rror ras * and * ha would minimiz objciv funcion (), and hn o compu opimum rcivd signal powr lvls * α and * α Q (05β ) x 0 d Q (05β ) arg min () Q (05β ) x 0 d + Q (05β ) Afr rarranging h drivaiv of () in rms of, w g (3) I is hn sraighforward o find *

5 ( Q ( β )) γ x /0 d 0 γ x /0 = d0 ln ln 05 ( ) ( rf ( 05 β( )) ( rf ( 05β )) ln ( Q ( 05β )) + (3) No ha * * = Finally, * α and * α ar drivd from (0) and (), and ar usd in (6) o compu h powr dissipaion in h simpl rlay ripl rsuls show ha rgnraing may xpnd up o 055dB lss powr han simpl rlaying, as h inrmdia nod gs closr o h midpoin of A-B sparaion, inuiivly which provs o b h opimum poin o achiv h highs powr savings in -hop assisd wirlss ransmission IV ESULTS Assum a grid ara of 00x00 mrs L us dno h Carsian coordinas of nods A, B and C as (0,0), (00,0) and (i,j) rspcivly, whr i,j [,99] In ordr o compar rlaiv powr savings bwn h rgnraor and h simpl-rlay, w dfin a nw mric η in (4) I is h avrag raio of h powr xpndiur in h rlay mod o h powr xpndiur in h rgnraor mod This avrag is akn only ovr h s of coordinas whr rlaying has powr savings, ha is P ''' ' < P Th I(x) is h indicaor funcion dfind such ha i rurns if x is TUE, and 0 ohrwis η = ''' '' ''' ' ( P ( i, j)/ P ( i, j)) Ι ( P ( i, j) < P ) i= j= ''' ' Ι ( P ( i, j) < P ) i= j= (4) Fig Powr savings of rgnraing wih rspc o simpl rlaying a inrmdia nod posiions ovr h dirc pah bwn A and B sparad wih 3 00m No: = 0, x, x, x = 0, M=64, and ( 3P + P ( ))/ α = 0 c rc Figur plos h numraor in (4) for only inrmdia nod posiions on h dirc pah bwn A and B Th

6 TLE I AVEAGE POWE SAVING DIFFEENCE BETWEEN SIMPLE- ELAYING AND EGENEATING (in db) No: M=64 On h ohr hand, h numrical rsuls givn in Tabl- for η prov ha for lowr and highr γ, h prformanc margin bwn h simpl rlay and h rgnraor gs qui narrow Noing ha rsuls in Fig and Tabl- ignor powr consumpion du o rgnraion procss a h inrmdia nod, simpl rlaying may b prfrrd o rgnraing For insanc, assum ha h rlay nod is locad on h dirc pah a 70 mrs from A and 30 mrs ''' '' from B In Fig, P < P corrsponds o 0 (db) for γ=4 a ha posiion This lls us ha if h powr dissipaion for rgnraion procss xcds 0 (db), simpl rlaying is favord KNOWLEDGMENT Th auhors hank Dr Anhony Vro for hlpful discussions and criical rading of h manuscrip W also hank h anonymous rviwrs for hlpful suggsions EFEENCES [] W Hinzlman, A Chandrakasan, H Balakrishnan, Enrgy-fficin Communicaion oocol for Wirlss Microsnsor Nworks, oc of IEEE Hawaii In Conf on Sysm Scincs, pp , January, 000, Maui, Hawaii [] P Chn, B O Da, E Callaway, Enrgy Efficin Sysm Dsign wih Opimum Transmission ang for Wirlss Ad-hoc Nworks, oc of IEEE In Conf on Communicaions, ICC 0, pp , May, 00, Nw York Ciy, Nw York [3] A Caovic, S Tkinay, "ducing Transmi Powr and Exnding Nwork Lifim via Usr Coopraion in h Nx Gnraion Muli-hop Wirlss Nworks, J Communicaions and Nworks, Spcial Issu on Evolving from 3G dploymn o 4G dfiniion, vol 4, no 4, pp 35-36, Dcmbr 00 [4] V odoplu, T H Mng, Minimum Enrgy Mobil Wirlss Nworks, IEEE J Slc Aras Commun, vol 7, no 8, pp , Augus 999 [5] T S appapor, Wirlss Communicaions: incipls and acic, nd Ediion, pp 37, Uppr Saddl ivr, NJ: nic Hall PT, 00 V CONCLUSIONS W quanify powr savings prformancs of simpl rlaying and rgnraing a an inrmdia nod in rlayassisd wirlss ransmission Error propagaion is akn ino considraion for opimizing ransmi-powrs