Throughput maximization for full-duplex energy harvesting MIMO communications

Transcription

1 Loughborough Univrsiy Insiuional Rposiory Throughpu imizaion for full-duplx nrgy harvsing MIMO communicaions This im was submid o Loughborough Univrsiy's Insiuional Rposiory by h/an auhor. Ciaion: CHALISE,.K., SURAWEERA, H.A. and ZHENG, G., 06. Throughpu imizaion for full-duplx nrgy harvsing MIMO communicaions. Prsnd a h 7h IEEE Inrnaional workshop on Signal Procssing advancs in Wirlss Communicaions, SPAWC Edinburgh, 3-6h. July. Addiional Informaion: c IEEE. Prsonal us of his marial is prmid. Prmission from IEEE mus b obaind for all ohr uss, in any currn or fuur mdia, including rprining/rpublishing his marial for advrising or promoional purposs, craing nw collciv works, for rsal or rdisribuion o srvrs or liss, or rus of any copyrighd componn of his work in ohr works. Madaa Rcord: hps://dspac.lboro.ac.uk/34/386 Vrsion: Accpd for publicaion Publishr: c IEEE Plas ci h publishd vrsion.

2 Throughpu Maximizaion for Full-Duplx Enrgy Harvsing MIMO Communicaions au K. Chalis, Himal A. Surawra, and Gan Zhng Dparmn of Elcrical Enginring and Compur Scinc, Clvland Sa Univrsiy, USA Dparmn of Elcrical and Elcronic Enginring, Univrsiy of Pradniya, Sri Lanka Wolfson School of Mchanical, Elcrical and Manufacuring Enginring, Loughborough Univrsiy, UK Absrac This papr proposs mhods for opimizing bidircional informaion ras bwn a bas saion S and a wirlssly powrd mobil saion MS. In h firs phas, h MS harvss nrgy using signals ransmid by h S, whras in h scond phas boh h S and MS communica o ach ohr in a full-duplx mod. Th S-bamformr and h im-spliing paramr TSP of nrgy harvsing schm ar joinly opimizd o obain h S-MS ra rgion. Th join opimizaion is non-convx, howvr a compuaionally fficin opimum chniqu basd upon smidfini rlaxaion and linsarch is proposd o solv h problm. Morovr, a subopimum approach basd upon h zro-forcing ZF bamformr consrain is also proposd. In his cas, a closd-form soluion of TSP is obaind. Simulaion rsuls dmonsra h advanag of h opimum mhod ovr h subopimum mhod, spcially for smallr valus of S ransmi powr and numbr of ransmi annnas a h S. I. INTRODUCTION Currnly mos bi-dircional wirlss sysms hav bn dvlopd assuming half-duplx HD opraion []. As a way of improving h spcral fficincy of conmporary HD sysms, full-duplx FD communicaions can b usd. Alhough h concp of FD is no nw, i has bn considrd as impossibl o da du o larg loopback inrfrnc LI [], [3]. Howvr, FD is now bcoming fasibl hanks o promising analog and digial LI cancllaion chniqus ha can achiv high ransmi-rciv isolaion [4] [6]. In addiion o spcral fficincy, h issu of nrgy fficincy has gaind wid rsarch anion for h dsign of fuur wirlss nworks. For xampl, nrgy consrains impos an uppr limi on ransmi powr and associad signal procssing in wirlss dvics. To his nd, a nw communicaion paradigm ha can powr dvics by uilizing wirlss nrgy ransfr WET has mrgd [7] [9]. Som xising works in h liraur hav invsigad poin-o-poin PP bi-dircional FD wirlss sysms. Ths includ paprs ha hav focusd on informaioncommunicaion horic mrics such as achivabl sum ras and h symbol rror probabiliy. In [3], achivabl uppr and lowr sum-ra bounds of mulipl annna bi-dircional communicaion ha us pilo-aidd channl simas for ransmi/rciv bamforming and inrfrnc cancllaion wr drivd. Th bamforming prformanc of bi-dircional mulipl-inpu mulipl-oupu MIMO ransmission wih spaial LI miigaion was invsigad in [0]. Th capaciy of a bi-dircional MIMO sysm wih spaial fading corrlaion was prsnd in []. Th imizaion of h asympoic rgodic muual informaion for a MIMO bi-dircional communicaion sysm wih imprfc channl sa informaion CSI assumpions was h focus of []. Moivad by h advanags of FD and WET, som rcn works hav also invsigad h prformanc of wirlsspowrd PP bi-dircional FD [3] [5]. In [3], considring a hybrid FD accss-poin AP ha broadcass wirlss nrgy o a s of downlink usrs whil rciving informaion from a s of uplink usrs, a soluion o an opimal rsourc allocaion problm was prsnd. In [4], hardwar implmnaion of a wirlss sysm ha ransmis daa and powr in h sam frquncy was prsnd. Mor rcnly, in [5], a wighd sum ransmi powr opimizaion problm for a bi-dircional PP FD sysm wih WET was formulad and solvd. Howvr, i nglcd an imporan aspc of FD opraion, namly, prfc LI cancllaion was assumd a ach rminal. Inspird by wirlss-powrd FD communicaions, in his papr, w considr bi-dircional communicaion bwn an N-annna bas saion S and an mobil saion MS wih wo annnas. In our harvs-hn-ransmi sysm, h S firs ransmis nrgy o h MS which will b usd by h MS for subsqun uplink ransmission. A h nd of nrgy ransfr phas, boh S and MS simulanously ransfr informaion in h uplink and downlink. Th boundary of h S-MS informaion ra rgion is characrizd, which dscribs h rad-offs bwn S and MS informaion ras. W propos opimum and subopimum mhods for joinly opimizing h bamformr a h S and h im-spliing paramr TSP ha divids a givn im-slo ino nrgy harvsing and daa ransmission phass. A compuaionally fficin opimum mhod basd upon smidfini rlaxaion SDR and lin-sarch is proposd, whras h subopimum mhod uss h zro-forcing ZF cririon for dsigning h bamformr. In h lar cas, a closd-form soluion of TSP is also drivd. Simulaion rsuls dmonsra ha h proposd opimum mhod ouprforms h subopimum mhod, spcially whn S ransmi powr and numbr of ransmi annnas a h S assum low valus. Th rs of h papr is organizd as follows. Th sysm modl and problm formulaion ar prsnd in Scion II. Th proposd opimum and subopimum mhods ar solvd

3 in Scion III, whras in Scion IV simulaion rsuls ar prsnd. Finally, h conclusions ar drawn in Scion V. II. SYSTEM MODEL AND PROLEM FORMULATION W considr bidircional communicaions bwn an N- annna S and a MS wih wo annnas [5]. Spcifically, h S has ransmi annnas and N rciv annnas. This numbr,, oghr wih h associad ransmi/rciv chosn annnas could b opimizd, bu w kp hm fixd. A h MS sid, on annna is for ransmission and h ohr is for rcpion. Sinc h MS is usually powr limid and h uplink ra is h bolnck, w considr a cas whr h S firs ransmis nrgy o h MS, which will b usd by h MS for h subsqun uplink ransmission. Th communicaion aks plac in wo phass wih duraion α and α, rspcivly. In phas I, h S ransmis nrgy o h MS. Suppos h ransmi powr of S in his phas is P, hn h rcivd nrgy is E = αpλ H M H H M, whr h channl bwn h S and h MS is dnod as H M and λ rurns h imum ignvalu of a marix. In phas II, h S and h MS communica o ach ohr using FD opraion. Th MS s ransmi powr can b wrin as p m = αηpλ H M H H M, α whr η is h convrsion fficincy of wirlss nrgy ransfr. Assum ha h S s ransmi powr is no mor han P no ncssarily P in his phas. L h S MS channl b h H and h N MS S channl is h M. Th LI channls ar H C N N N and h M a h S and MS, rspcivly. Th rspciv ransmi and rciv bamformrs a h S ar w and r. A. Signal Modl Rcivd signals a h S and h MS, ar: y = r H p m h M s M +H w s +n, y M = h H w s + p m h M s M +n M. 3 Thn achivabl ras using h minimum man-squar rror rcivr a h S ar r = αlog + p m r H h M + r H H w = αlog +p m h H MI+H w wh H H h M, = αlog +p m h M hh M H w + H w 4 r M = αlog + hh w +p m h m. 5. Problm Formulaion W ar inrsd o find h MS-S ra rgion. This can b achivd by imizing h MS ra whil confirming ha h S-ra is qual o a crain valu R. y solving his opimizaion problm for all R whr R [0,R ] and is h imum valu of S ra, w obain h MS- S ra rgion. No ha R is drivd in closd-form in Appndix VI-A. As such, h opimizaion problm for a givn R is xprssd as αlog + hh w w P,0 α,p m +p m h m s.. αlog +p m h M hh M H w + H w = R, p m = αηpλ H M H H M. 6 α R Th opimizaion problm 6 is a complicad nonconvx opimizaion w.r.. w and α. Howvr, h problm can b solvd fficinly by finding opimum w for a givn α and vic-vrsa. Sinc α is scalar valud, h opimum soluion can b ascraind by using on-dimnsional sarch w.r.. α. III. PROPOSED JOINT OPTIMIZATION In his scion, w propos opimum and subopimum mhods for solving h join opimizaion of bamformr and h im-spliing paramr α. A. Opimum Mhod In his mhod, h opimum w is found for a givn α. Sinc α is a scalar, h joinly opimal soluion of w and α is obaind using on-dimnsional sarch w.r.. α. Th compuaional complxiy of lin sarch is minimizd by xploiing h naur of h opimizaion problm 6. Opimizaion of w : W firs considr a problm o opimiz w for a givn α. In his cas, h opimizaion problm 6 is xprssd as + αlog hh w w P +p m h m s.. 7 αlog +p m h M hh M H w + H w = R. Sinc log + x is a monoonically incrasing funcion of x and h dnominaor + p m h m of x hh w +p m h m is indpndn of w, 7 can b solvd via w P hh w s.. whr Γ h M h H M H w + H w = Γ, 8 [ p m R α ]. I is clar ha h objciv funcion in 8 is imizd wih w = P. This opimizaion problm is nonconvx du o h fac ha i is h imizaion of a quadraic funcion wih a quadraic qualiy consrain. Morovr, o h bs of our knowldg, 8 dos no admi a closd-form soluion. Howvr, i can b fficinly and opimally solvd using smi-dfini programming. For

4 his purpos, dfin V = w w H and rlax h rank-on consrain rankv =. Th rlaxd opimizaion is V fα,p m = rv h h H s.. rv H H h M h H MH = Γ +rv H H H, rv = P,V 0. 9 Th opimizaion problm 9 is a sandard SDR problm wih only wo qualiy consrains. Thrfor, according o Shapiro- arvinok-paaki SP rank rducion horm [6], hr xiss a rank-on opimum soluion of V for his rlaxd opimizaion problm. L V b h opimum soluion of 9. Sinc V is rank-on marix, h opimum soluion w is obaind w = Pũũ H, whr ũ is h ignvcor corrsponding o non-zro ignvalu of V. Opimizaion of w and α: In ordr o joinly opimiz w and α, w solv h SDR problm 9 using ondimnsional or lin sarch sarch ovr α whr 0 α. Howvr, his lin sarch can b limid o a small sgmn, and hrfor, h numbr of rquird SDR opimizaions can b significanly minimizd. To illusra his, l h objciv funcion in 7, for a givn w, b dfind as whr fα = αlog + β c+ αb α 0 β = hh w h m,c = h m,b = ηpλ H M H H M. Th drivaiv of fα w.r.. α is dfα dα = log gα bβgα αlog c+ αb α whr gα = + β 0, α [0,]. I is clar from c+ αb α ha dfα dα < 0 for all α, i.., fα is a monoonically dcrasing funcion of α. This mans ha imum of h objciv funcion is achivd whn α is minimum providd ha h qualiy consrain is fulfilld. Howvr, as α 0, Γ, i.., h infasibiliy of h SDR opimizaion problm 9 incrass. Consqunly, h opimum α is h minimum α for which 9 is fasibl. Th oupu V of such fasibl SDR provids h opimum w. In a nushll, h proposd opimum soluion can b summarizd as follows: Dfin a fin grid of α in sps of α. Solv 9 wih h smalls α. 3 If fasibl, sop and oupu α and V. 4 If no, rpa sp wih h incrmn of α.. Subopimal Mhod As a subopimal mhod of opimizing w and α, w considr ZF approach. This rquirs ha w H H H h M = 0. 3 Opimizaion of w : Subsiuing 3 ino 6, h rsuling opimizaion problm is xprssd as w P,0 α αlog + hh w +p m h m s.. αlog +p m h M = R, p m = αηpλ H M H H M 4 α wh H H h M = 0. For a givn α, h opimizaion of w bcoms w h H w s.. w P 5 w H H H h M = 0. Using a sandard Lagrangian muliplir mhod and skipping h corrsponding dails, h closd-form soluion of w is xprssd as w = P h h, = I HH h Mh H M H H H h M 6 which is indpndn of α. Consqunly, h corrsponding objciv funcion is h H w = P hh h h = P h. 7 Opimizaion of α: Dno h subopimal bamformr soluion of 6 by w. Th rmaining opimizaion problm w.r.. α is xprssd as β fα αlog + 0 α s.. αlog + α α c+ αb α = R. 8 whr γ = h M. No ha h opimum α would b zro if hr wr no qualiy consrain or h consrain wih R = 0. In h prsnc of qualiy consrain wih R > 0, i is clar ha h opimum α is h smalls α ha saisfis h qualiy consrain. Th following proposiion drivs h opimum α. Proposiion. Whn qualiy consrain is fasibl i.., R R, h opimum α is givn by α op R log W R log R log = R log W R log R log 9 whr Wy is h Lambr funcion, i.., y = x x = x = Wy. Proof. Th proof is givn in Appndix VI-.

5 MS-ra bpcu.5.5 N =4, Opimum N =4, Sub-opimum N =5, Opimum N =5, Sub-opimum =4, HD N =5, HD MS-ra bpcu =4, Opimum =4, Sub-opimum =5, Opimum =5, Sub-opimum =4, HD =5, HD S-ra bpcu Fig.. Comparison of ra rgions wih P = 0 d, and = 4, S-ra bpcu Fig.. Comparison of ra rgions wih P = 0 d, and = 4,5. IV. SIMULATION RESULTS In all simulaion rsuls, w ak N = 6 and chang h valu of. Th channl cofficins for all channls ar akn as zro-man indpndn and idnically disribud complx Gaussian random variabls wih uni varianc. All rsuls corrspond o avraging of 00 indpndn channl ralizaions. Th S ra is varid from 0 o R, whr R is compud as in Appndix VI-A. Th nois powrs a boh h S and MS ar s o uniy. Fig. shows h ra rgions obaind wih h opimum and subopimum mhods for = 4 and 5, whn P = 0 d, whras h corrsponding rgions for P = 0 d ar shown in Fig.. As a bnchmark, h achivd S-MS ra rgions ar also shown for h HD mod. I can b obsrvd from Figs. and ha h imum valu of h MS ra is obaind whn R is minimum, whras h minimum valu is obaind whn R aks imum valu. Morovr, as xpcd boh h S and MS ras incras whn P incrass from 0 d o 0 d. oh figurs show ha h opimum mhod prforms br han h subopimum approach. Howvr, h advanag of h opimum mhod ovr h subopimum mhod diminishs whn P incrass from 0 d o 0 d. Morovr, whn incrass, h obaind imum MS ra incrass, whras h obaind imum S ra dcrass. This can b xplaind from h fac ha incrasing improvs h ransmi bamforming a h S, which in urn is aribud for an incras in h MS ra. Howvr, incras in dcrass N r = N for a givn. This mans ha h LI rjcion capabiliy of h S dcrass which lads o a drop in h suppord S ra. All rsuls also show ha h FD opraion almos doubls h ra of h HD mod. Th ra rgions of h opimum and subopimum mhods wih diffrn valus of = and 3 ar shown in Fig. 3 and Fig. 4 for P = 0 d and P = 0 d, rspcivly. From hs figurs, similar obsrvaions can b mad as in Figs. and Fig.. Howvr, in conras o h lar figurs, Figs. 3 and 4 show a significan prformanc gains for h opimum mhod compard o h subopimum mhod. Mor spcifically, h advanag of h opimum mhod is mor pronouncd for smallr valus of and P. MS-ra bpcu =, Opimum =, Sub-opimum =3, Opimum =3, Sub-opimum =, HD =3, HD S-ra bpcu Fig. 3. Comparison of ra rgions wih P = 0 d, and =,3. V. CONCLUSIONS In his papr, compuaionally fficin opimum and subopimum mhods wr proposd o nlarg h boundary of h S-MS ra rgion for a bi-dircional FD communicaion sysm quippd wih an N-annna S and a wirlsspowrd MS quippd wih wo annnas. Simulaion rsuls dmonsra ha significan prformanc gains ar achivabl whn h S-bamformr and h im-spliing paramr, which splis h availabl im bwn nrgy harvsing MS-ra bpcu =, Opimum =, Sub-opimum =3, Opimum =3, Sub-opimum =, HD =3, HD S-ra bpcu Fig. 4. Comparison of ra rgions P = 0 d, and =,3.

6 and FD communicaion mods, ar joinly opimizd. Th advanags of muli-annna ransmission for LI supprssion wr also dmonsrad. VI. APPENDIX A. Drivaion of imum S ra R I is obvious ha h M hh M H w + H w h M 0 whr h qualiy is achivd wih h ZF consrain h H M H w = 0. Th imum S ra is hn obaind as R = αlog + α 0<α< α b h M whrb = ηpλ H M HM H. Dno b = b hm. Equaing h firs ordr drivaiv of R w.r.. α, w obain R = 0 = log + α b = α α b + α α α b which can b wrin in h form zlogz = z + b, whr z = + α b. α 3 Afr sraighforward manipulaion, w obain z z log = b z = log logz b =. 4 According o h dfiniion of Lambr-W funcion, h soluion of h quaion y = x x for a givn y is xprssd as x = Wy, whr W is h Lambr-W funcion. Thus, 4 is givn by b z = W +. 5 Subsiuing z ino 5, h opimum α is Thrfor, R b α Op = W W b+ is givn by + b +. 6 R = α Op log + αop α Opb h M. Proof of Proposiion. 7 Proof. Th qualiy consrain for h S ra is xprssd as log + α α α = R log α +. 8 Dfin y + α α. Thn 8 can b xprssd in rms of y as y = R log y R log 9 which afr simpl manipulaion is xprssd as R log y R log y = R log R log. 30 Using h Lambr-W funcion Wy i.., y = x x x = Wy, y in 30 is xprssd as y = R log W R log R log. 3 No ha R log R log is rquird o hav a ral valu of y. If no, h qualiy consrain is no fasibl for givn b, γ, and R whr R R. Subsiuing y in 3, w obain α α = R log W R log R log which yilds h opimum α Op givn in 9. REFERENCES [] A. Sabharwal al., In-band full-duplx wirlss: Challngs and opporuniis, IEEE J. Sl. Aras Commun., vol. 3, pp , Sp. 04. [] T. Riihonn, S. Wrnr, and R. Wichman, Miigaion of loopback slfinrfrnc in full-duplx MIMO rlays, IEEE Trans. Signal Procss., vol. 59, pp , Dc. 0. [3]. P. Day, A. R. Margs, D. W. liss, and P. Schnir, Full-duplx bidircional MIMO: Achivabl ras undr limid dynamic rang, IEEE Trans. Signal Procss., vol. 60, pp , Jul. 0. [4] M. Duar, Full-duplx wirlss: Dsign, implmnaion and characrizaion, Ph.D. Dissraion, Dp. Elc. and Compur Eng., Ric Univrsiy, Houson, TX, 0. [5] H. A. Surawra, I. Krikidis, G. Zhng, C. Yun and P. J. Smih, Lowcomplxiy nd-o-nd prformanc opimizaion in MIMO full-duplx rlay sysms, IEEE Trans. Wirlss Commun., vol. 3, pp , Fb. 04. [6] H. Q. Ngo, H. A. Surawra, M. Mahaiou and E. G. Larsson, Mulipair full-duplx rlaying wih massiv arrays and linar procssing, IEEE J. Sl. Aras Commun., vol. 3, pp , Sp. 04. [7] R. Zhang and C. Ho, MIMO broadcasing for simulanous wirlss informaion and powr ransfr, IEEE Trans. Wirlss Commun., vol., pp , May 03. [8] Z. Ding, C. Zhong, D. W. K. Ng, M. Png, H. A. Surawra, R. Schobr and H. V. Poor, Applicaion of smar annna chnologis in simulanous wirlss informaion and powr ransfr, IEEE Commun. Mag., vol. 53, pp , Apr. 05. [9] K. Huang and X. Zhou, Cuing las wirs for mobil communicaion by microwav powr ransfr, IEEE Commun. Mag., vol. 53, pp , Jun 05. [0] D. Snaran and C. Tllambura, amforming for spac division duplxing, in Proc. IEEE ICC 0, Kyoo, Japan, Jun 0, pp. -5. [] H. Ju, X. Shang, H. V. Poor and D. Hong, i-dircional us of spaial rsourcs and ffcs of spaial corrlaion, IEEE Trans. Wirlss Commun., vol. 0, pp , Oc. 0. [] A. C. Cirik, Y. Rong and Y. Hua, Achivabl ras of full-duplx MIMO radios in fas fading channls wih imprfc channl simaion, IEEE Trans. Signal Procss., vol. 6, pp , Aug. 04. [3] H. Ju and R. Zhang, Opimal rsourc allocaion in full-duplx wirlss powrd communicaion nwork, IEEE Trans. Commun., vol. 6, pp , Oc. 04. [4] K. Yamazaki, Y. Sugiyama, Y. Kawaharay, S. Saruwaari and T. Waanab, Prliminary valuaion of simulanous daa and powr ransmission in h sam frquncy channl, in Proc. IEEE WCNC 05, Nw Orlans, LA, Mar. 05, pp. -6. [5] Z. Hu, C. Yuan, F. Zhu, and F. Gao, Wighd sum ransmi powr minimizaion for full-duplx sysm wih SWIPT and slf-nrgy rcycling, [Onlin]. Availabl: hp://arxiv.org/abs/5.083 [6]. K. Chalis, W.-K. Ma, Y. D. Zhang, H. A. Surawra, and M. G. Amin, Opimum prformanc boundaris of OSTC basd AF- MIMO rlay sysm wih nrgy harvsing rcivr, IEEE Trans. Signal Procss., vol. 6, no. 7. pp , Sp. 03.