Beamforming towards regions of interest for multi-site mobile networks

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1 Itratoal Zurch Smar o Commucatos (IZS) March Bamformg towards rgos of trst for mult-st mobl twors Paul Hurly Matthu Smo IBM Zurch sarch Laboratory CH-3 üschlo Swtzrlad Écol Polytchqu Fédéral d Lausa (EPFL) CH-5 Lausa Swtzrlad Emal: pah@zurch.bm.com mo@zurch.bm.com Abstract W show how a bamformg tchqu for aalytcal spatal fltrg calld flxbam ca b appld to mobl pho mast broadcastg so as to rsult coctratos of powr whr most dvcs ar. To that d flxbam s trprtd as trasmsso bamformg. A aalytcally dscrbd radato pattr s xtdd from a sphr to Euclda spac. A cotuous bamformg fucto s th obtad by th Fourr trasform of th xtdd radato pattr. W th show how a Gaussa fltr ca b approxmatly achvd usg bamformg. Th mthod s th xpadd by mas of a xampl of a collcto of mobl pho masts covrg a ara of Zurch cty so as to coctrat rgy whr dvcs ar coctratd. I. INTODUCTION Bamformg has b dployd mobl pho stadards startg alrady wth G. Th tchqus hav bcom vr mor sophstcatd wth ach trato. G/LTE for xampl dploys MIMO-basd bamformg. I gral drct mult-usr bamformg [] [] cratg bams for ach dvdual dvcs from mobl pho masts s a gargatua tas. Thr ar smply too may usrs ad a stady stram of accurat chal fdbac [3] would b rqurd to accout popl ad vhcls movg aroud. Yt algorthms dployd to dat ar varatos o a thm wth th MIMO framwor: strg th bam towards a sgl pot [] [5] []. I practs o would l to b abl to coctrat rgy a way commsurat wth th locatos of dvcs amly targt aras of trst ot sgl pots all th whl buldg tolrac for movmt ad mprcs locato formato. To cras rcvd powr LTE dvcs ca rcv sgal from multpl bas statos. Ths s a complx coordato protocol gral ad o y compot to ts ffccy s to hav bas statos targt aras of mportac. I ths papr w apply a tchqu calld flxbam whch dtrms bamformg wghts that wh appld approxmat a optmal radato pattr so as to abl bas statos to jotly coctrat rgy whr most dvcs ar. Th aalytc framwor allows tractabl umrcally stabl dtrmato of bamformg wghts. Amg for aras rathr tha pots mmss th rqurd updat rat ad rducs th commucato rqurmt. To ths d Scto II drvs flxbam from a xplct trasmt bamformg prspctv. W th Scto III llustrat ts applcato usg a Gaussa approxmato to trac a objct th prsc of ucrtaty. Aftrwards Scto III w llustrat how rgy ca b coctratd aroud a crta ara. Thr w ta a xampl of dvcs coctratd aroud a ara of Zurch cty ad show how th targt radato pattr ca b approxmatd by a srs of Gaussa fltrs. W th llustrat how to dtrm ach bas stato s bamformg wghts so as to coctrat rgy whr most dvcs ar. II. FLEXIBEAM FOM THE TANSMIT PESPECTIVE I [7] w drvd th rcvg cas for flxbam. As a cosquc of th rcprocty thorm [] bam-shaps so dsgd ca b usd to rcv or trasmt. Howvr to ga sght to ts oprato ad applcato w ow drv th trasmsso cas drctly. Cosdr a array of L om-drctoal rcvg atas wth ut gas ad postos p...p L. Each ata mt a dtcal arrow-bad sgal s(t) C. Wthout loss of gralty lt th wavlgth of ths sgal b =. Th sgals orgatg from ach ata wll sum cohrtly producg a radato pattr also calld bam-shap of th ata array. To cotrol ths radato pattr dffrt dlays ad gas ar troducd at ach ata: x (t) = j s(t) () whr > ad [ ] ar rspctvly th ga ad phas dlay for ata. Th sgal s at a far fld targt wth posto r S s gv by [] [9] LX y(t r) =s(t) j j hrp = s(t) = LX w j hrp = = s(t)b (r) () whr b(r) = P L = w j hrp s th array bam-shap ad w = j C ar th bamformg wghts. W obsrv that bamformg s hr th rsult of th physcal summato of th sgals mttd by ach ata. For matchd bamformg (cf. Fg. ) th bamformg wghts ar chos by w = j hr p =...L 9

2 Itratoal Zurch Smar o Commucatos (IZS) March 9 3 x (a) Extdd radato pattr. Ovr th ut crcl t approxmats wll th targt radato pattr. 3 7 Fg. : Exampl bam-shap obtad wth matchd bamformg. (b) Magtud of ts D Fourr trasform. Th wht dots dot th bamformg wghts..5.5 whr r S s th strg drcto. Thus th gas ad dlays at ach ata ar rspctvly = ad = hr p. Now cosdr a otoal cotuous fld of atas covrg ovr whch w df a broadcast fucto x(t p) L ( C). Ths dscrbs th sgal that would b broadcastd by a ata locatd at posto p ad xtds () to covr all pots : x(t p) = (p)j (p) s(t) = w (p)s(t) whr w L ( C) s th bamformg fucto that gralss th cocpt of bamformg wghts ad dscrbs th gas ad dlays to b appld at ach posto p. Th sgals mttd by ths cotuous fld of atas grat costructv trfrc ad Eq. () bcoms Z y(t r) = s(t) w (p) j hrp dp = s(t)w (r). (3) Th bam-shap for th otoal ata fld s th w (r) L (S C). It dscrbs th radato strgth of th bamformd ata fld towards varous drctos ad as such acts as a spatal fltr. Th l to th bamformg fucto s as follows: Z w (r) = w(p)j hrp dp (c) Bam-shap obtad wth bamformg wghts (wht l) whch approxmats rlatvly wll th targt (d) Bam-shap obtad matchd bamformg. wth Fg. : Fltrg a rag of drctos wth flxbam for = ad 9 atas. Th bam-shap covrs a much wdr rag of drctos tha matchd bamformg. whch for a arbtrary targt radato pattr would b calculatd umrcally. Howvr th targt ad xtdd radato pattr ca b dsgd so that a aalytcal Fourr trasform xsts. I partcular ad rlvat for th xampl w show th xt scto th -dmsoal symmtrc Gaussa r r ˆ (r) = (5) ( )/ wth ma r S trasform ad stadard dvato w(p) = ( ) Th bamformg fucto was dfd thus far oly ovr th sphr S. To abl samplg at ay pot th pla ad to hav a ralsabl -dmsoal Fourr trasform rlatoshp th fltr ds to b xtdd to. Lt th ˆ : C b a fucto whos D Fourr trasform xsts ad o th hyprsphr S s qual to th targt radato pattr w would l to achv. W call ˆ (r) thus dsgd th xtdd radato pattr. Th actual choc of xtso s applcato dpdt ad part of th dsg. Th bamformg fucto ca ow b computd by th Fourr trasform Z w(p) = ˆ (r) j hrp dr. ().5.5 p j hpr has Fourr. () Cosdr ow L atas wth postos p =... L. Th bamformg wght for ata s th Hc th gas by = qp w(p ) w(p ) L = w(p ) = ad phas dlays w(p ). for ata ar gv = arg (w(p )) =... L. Th ormalsato prvts atas from havg too hgh dvrsty magtud whch would magfy thr rspos to chal os. 95

3 Itratoal Zurch Smar o Commucatos (IZS) March dg dg dg 9 dg 9 dg 5 dg 37 dg dg MB atas atas atas 3 atas 3 atas 37 atas 3 atas 5 atas (a) Fltrg a rag of drctos wth flxbam for varous agls ad 9 atas. (b) Fltrg a rag of drctos wth flxbam for = 35 wth varyg umbr of atas. Fg. 3: Evoluto of th flxbam bam-shap for varous agls ad umbr of atas. How closly th bamformg achvs th targt radato fltr ovr th sphr S dpds strogly o th umbr ad posto of th atas. Ths ffctvly s th ablty of a FI fltr to approxmat a II fltr usg a gv umbr of taps (atas). III. T ACKING WITH FLEXIBEAM Suppos w wsh to trac th drcto of a targt movg o th pla. W tally th t s locatd at ˆ = 5 but ar ucrta. If w try to targt t usg too arrow a bam w could mss th targt altogthr. W thus calculat bamformg wghts usg flxbam so as to obta a radato pattr wth a wd ough ma lob ctrd aroud our stmat ˆ = 5. Ths wdr bam prmts tracg for a logr prod of tm whch avods havg to rfrsh th bam too oft as th targt movs. From xprmtal codtos th optmal radato pattr w () was stmatd to b w () = p ( ˆ ) (7) whr s a agl o th ut crcl S masurd dgrs ad = s th dsrd wdth of th ma lob. For practcal purposs w propos to xtd w () to by p th D symmtrc Gaussa fucto (5) wth r = ( )/ S p = cos. Strctly spag ths s oly a approxmat xtso of Eq. (7). Howvr for rasoabl bam wdths ths approxmato s accurat ough (s Fg. a) ad covtly provds us wth a aalytcal xprsso for th bamformg fucto show o Fg. b. Th bamformg wghts ar dtrmd by samplg th bamformg fucto at th atas postos (s Fg. b). Th rsultat bam-shap Fg. c ca b s gral to b a good approxmato. I cotrast matchd bamformg would rqur strg towards may drctos to covr th sam ara ad hc would b mor lly to mss th movg targt f th rfrsh rat s ot hgh ough. For a fxd umbr of atas Fg. 3a shows that for vry small th bam-shap s sstally dtcal to th o Fg. : Dsty fucto of pdstras Bllvuplatz Zurch. Th blac dots ar sampld postos from whch th dsty has b frrd. Th colourd dots ar th trasmttrs. from matchd bamformg whl for largr th bamshap struggls to covr th whol rag (bcaus th D Gaussa xtso dos ot approxmat wll ough th targt radato fltr ovr th sphr). For fxd Fg. 3b shows that th bam-shap bcoms crasgly accurat as th umbr of atas crass. IV. E XAMPLE USING MOBILE BASE STATIONS W ow llustrat a xampl for bamformg a collcto of 3G/G trasmttrs ordr to covr optmally Bllvuplatz a porto of th cty of Zurch gv probabl clt postos. Bllvuplatz has a approxmat ara of. m ad wlcoms o of th bggst tram statos wth corrspodgly ds pdstra traffc. For ths xprmt w gathrd postos of pdstras ths ara (blac dots o Fg. ) ad frrd a cotuous dsty fucto (th colourd rgos). Ths dsty fucto s calld th prfrc fucto. It dscrbs whr th powr s most dd. Th goal s th to bamform from ach of th trasmttrs (th colourd dots) so that thy basd o pdstra dsty jotly covr th ara wll. W assum dvcs ar th far-fld ad that th chal has a arrow badwdth. For smplcty w glct sgal attuato. Each trasmttr has 7 atas arragd o thr coctrc crcls of rad 5 5 ad 5cm rspctvly. Morovr thy ar assumd to hav a msso rag of approxmatvly m. Hc ach trasmttr oly ss a crcular cut of a m radus of th dsty fucto whch dfs th dvdual trasmttr prfrc fucto f L ( ) =.... Th bam dtrmato problm for ach trasmttr cossts th of four stps: 9 ) Comput th targt radato pattr by tag th radal projcto of th dvdual prfrc fuctos from

4 Itratoal Zurch Smar o Commucatos (IZS) March Targt adato Pattr Bamformd adato Pattr Fg. 7: Comparso btw th targt radato pattr (colourd ls) ad th actual achvd bam-shap (dashd gry ls) for ach trasmttr Fg. 5: Crcular cuts of th dsty fucto Fg. basd o th rag of ach trasmttr Fg. : Th trasmttrs covr mor aras wth a hgh dsty of pdstra (compar wth Fg. 5). (a) Targt radato pattrs for ach trasmttr plottd ovr a sgmt of lgth (b) Approxmato of th targt radato pattrs by a sum of wghtd Gaussa fuctos. Fg. : Targt radato pattrs for ach trasmttr ad thr approxmato by a sum of wghtd Gaussa fuctos. Fg. 9: Th summato of th bam-shaps from ach trasmttr gvs th jot covrag. Jot covrag achvd by all th trasmttrs aftr choosg th bamformg wghts. Aras wth hgh pdstra dsty ar bttr covrd. 97

5 Itratoal Zurch Smar o Commucatos (IZS) March Fg. 5 ŵ () = Z f (r cos rs )dr wth [ ]. ) Approxmat ths targt fltr by a sum of wghtd Gaussa fuctos (s Fg. b) N X ŵ () ' = () p () µ () () whr N N () () > ad µ () [ ] ar rspctvly th last squars stmats of th umbr of Gaussa compots ad thr assocatd wghts stadard dvatos ad mas. 3) Extd ths fltr to th pla wth th sam tchqu as dscrbd Scto III ad comput ts Fourr trasform aalytcally usg Eq. (). W gt N X ˆ (x y) = = () x cos(µ () () ) ) y s(µ() () EFEENCES [].-T. Juag K.-P. Yar K.-Y. L ad P. Tg Dctralzd multusr bamformg for cllular commucato systms Wrlss ad Mobl Computg Ntworg ad Commucatos (WMob) IEEE 7th Itratoal Cofrc o Oct pp.. [] C. Jag ad L. Cm Ergy-ffct multusr mmo bamformg Iformato Sccs ad Systms (CISS) 5th Aual Cofrc o March pp. 5. [3] J. J C. L Q. Wag H. Yag ad Y. Wag Effct of mprfct chal stmato o mult-usr bamformg lt-advacd systm Vhcular Tchology Cofrc (VTC -Sprg) IEEE 7st May pp. 5. [] D. H. Johso ad D. E. Dudgo Array sgal procssg: cocpts ad tchqus. Smo & Schustr 99. [5] B. D. V. V ad K. M. Bucly Bamformg: a vrsatl approach to spatal fltrg ASSP Magaz IEEE vol. 5 o. pp. 9. [] Y.-S. Chg ad C.-H. Ch A ovl 3d bamformg schm for ltadvacd systm Ntwor Opratos ad Maagmt Symposum (APNOMS) th Asa-Pacfc Spt pp.. [7] P. Hurly ad M. Smo Flxbam: aalytc spatal fltrg by bamformg Itratoal Cofrc o Acoustcs Spch ad Sgal Procssg (ICASSP) IEEE March (to appar). []. J. Malloux Phasd array ata hadboo Bosto MA: Artch Hous [9] W.-Q. Wag ad H. Shao A flxbl phasd-mmo array ata wth trasmt bamformg Itratoal Joural of Atas ad Propagato vol.. [] A. Sbll C. Ostgs ad A. Zalla MIMO: from thory to mplmtato. Acadmc Prss. whr (x y) L q( ) s th stadard D Gaussa fucto ad () = cos( () ). ) Comput th wghts to b appld to ach ata composg th trasmttr by samplg th Fourr trasform at th locatos of th atas. Most of th trasmttr bam-shaps show Fg. 7 approxmat th assocatd targt fltr wll dspt uavodabl sd-lobs du to th ft umbr of atas. Fg. 9 shows that aras wth hghr pdstra dsty ar bttr covrd tha bfor gvg thm bttr sgal as lss powr s dsspatd ucssary aras. V. CONCLUSIONS W too th flxbam tchqu to dtrm bamformg wghts for a targt spatal fltr ad xplad t from th trasmt bamformg prspctv. W th showd o a xampl how t ca b usd by groups of mobl bas statos to coctrat rgy whr dvcs ar coctratd. W argud th cas for targtg rgos rathr tha sgl pots ad showd that ths could b achvd. O trstg ffct s that th MIMO optmsato tradoff btw (focusd) bamformg ad spatal dvrsty (multpl rplcas of th rado sgal from dffrt drctos) [] ca b crcumvtd. Of cours practs ral-lf data trasfr ad th rsultat commucatos protocol s far mor complcatd ad bamformg s just o compot th mx. Futur wor cluds corporatg ths togthr ad addg cooprato btw th statos to maxms throughput ad mms latcy. 9