Spatially Correlated 3-D HAP-MIMO Fading Channels

Transcription

1 ptilly Corrltd 3-D -MIMO Fding Chnnls Emmnoul Michilidis Gorg Efthymoglou nd Athnsios G Knts Dprtmnt of Digitl ystms Univrsity of Pirus Pirus Grc {michil gfthymo knts}@unipigr Abstrct his ppr proposs thr-dimnsionl (3-D) scttring modl for multi-input multi-output (MIMO) lnd mobil strtosphric multipth-fding chnnls Anlyticl nd closd-form xprssions for th sptil nd tmporl corrltion functions btwn two rbitrry sub-chnnls r drivd ssuming non-isotropic or isotropic scttring nvironmnts his modl cn b usd to stimt th rquird High Altitud Pltform () ntnn sprtion to chiv n uncorrltd -MIMO chnnl mtrix umricl clcultions hv bn crrid out to dmonstrt thorticl drivtions h proposd modl is usful to dsign nlyz nd tst futur -MIMO bsd 3G communiction systms with lin-of-sight (LO) nd non-lin-of-sight (LO) componnts Kywords- trtosphric tform multi-input multi output (MIMO) fding chnnls thr dimnsionl scttring nvironmnt sptil corrltion ntnn sprtion LO LO 3G communictions I IODUCIO High ltitud tforms (s) hv bn nw ltrntiv to trditionl trrstril nd stllit communictions infrstructurs tht cn xoit th bst fturs of both systms nd cn promis ccss to brodbnd modrn tlcommuniction srvics [] [2] h trm s dfins qusi-sttionry tforms flying t n ltitud rnging btwn 7 nd 22 Km bov th ground in th strtosphr h IU hs licnsd svrl frquncy bnds for communictions through s for th world wid 4G communictions systms [3] [4] nd for 3G communictions systms [5] Covrg zons of bsd systm dpnd on lvtion ngl of th rcivr High lvtion ngls imy th prsnc of prdominnt rdio wv pth of lin of sight [6] but lso multipth propgtion should b considrd whn vluting th tlcommuniction systm prformnc [7] h chllng nowdys is to invstigt th piction of Multi-Input Multi-Output (MIMO) tchniqus to th Lnd Mobil trtosphric communiction systms [8] [9] om modls using multi constlltions [] [] hv shown tht cpcity cn b significntly incrsd by using highly dirctionl usr ntnns to sptilly discrimint btwn s in diffrnt prts of th sky Morovr in [2] physicl sttisticl Lnd Mobil- propgtion chnnl modl ws dscribd tht cn prdict joint sttisticl tim sris nd powr-sptil-dly profil dt in multi-ntnn mobil multi- scnrio whrs th potntil gin of using vrious compct MIMO ntnn rry configurtions in conjunction with divrsity tchniqus ws studid in [3] his ppr focuss on th dsign of MIMO chnnl modl for 3G communictions (2 GHz frquncy bnd) bsd on strtosphric tform mobil usr nd th prsnc of infinit scttrrs round cylindr his imis tht th rdio propgtion nvironmnt is chrctrizd by 3-D scttring with lin-of-sight (LO) or non-lin-of-sight (LO) propgtion conditions btwn th fr of locl scttring nd th mobil usr tudis on th rrstril 3-D MIMO chnnl modling includ Aulin s 3-D cylindr modl [4] nd improvd IO IMO MIO [5] [6] nd MIMO fixd-to-mobil [7] or mobil-to-mobil vrsions [8] without th LO componnt h rst of th ppr is orgnizd s follows In ction II th 3-D gomtricl modl is dscribd From this modl th corrsponding spc-tim corrltion function is drivd in sction III ction IV prsnts numricl rsults for this modl rltiv to diffrnt prmtrs Conclusions r drwn in ction V II HE 3-D LAD MOBILE -MIMO CHAEL MODEL his ppr considrs downlink MIMO Lnd Mobil trtosphric communiction chnnl with L B trnsmit nd L rciv ntnn lmnts All ntnns r fixd omnidirctionl without bmforming nd r numbrd s M p q L nd l m L B M rspctivly h L B lmnts of th trtosphric Bs ttion (B) r situtd 7-22 Km bov th ground nd it is ssumd tht th L M lmnts of th rrstril Mobil ttion (M) r in motion /8/$25 28 IEEE Authorizd licnsd us limitd to: UIV OF PIAEU Downlodd on July 22 t 9:33:56 UC from IEEE Xor strictions py

2 Evn though s cn provid qusi-sttionry communiction tforms svrl points should b xmind crfully in th dsign of th modl [] Aircrfts usully fly on tight circl (bout 2km rdius or mor) whil irships cn thorticlly sty still nd thy only hv to compnst th winds or prssur vritions h IU hs spcifid tht should b kpt within circl of 4m rdius with hight vritions of ±7m [9] so tht srvics r vilbl lmost ll th tim In prctic s my mov in ny dirction t vrying spd nd th movmnts cn b horizontl/vrticl discmnt with rspct to x y nd z-xis s wll s yw pitch nd roll (6 dgrs of frdom) [2] Drift on th x or y-xis hv similr ffcts on th ground but vrticl discmnt roll nd pitch cn b bypssd bsd on study of th winds sttistics nd th rspctiv s instbility modl [2] which indicts tht th most importnt componnt is th horizontl discmnt nd th vrticl winds r lmost insignificnt For this work w considr tht th is kpt within circl of rdius h gomtricl chrctristics of our modl nd th dfinition of th Crtsin coordint systm r discussd in th following figurs Fig shows th LO pths of th 3-D modl for 2 2 MIMO chnnl with L = L = 2 B M ntnn lmnts Fig 2 shows th LO pths for th chnnl in Fig his lmntry 2x2 ntnn configurtion cn b usd to form Uniform Linr Arrys (ULA) with rbitrry numbr of ntnn lmnts As shown in th Figs nd 2 th y xis is th lin tht conncts coordint origin O (cntr of th projctions p nd q of th B ntnn lmnts p nd q to th X Y n) nd O (th cntr circl of th cylindr) o id our nlysis w dnot D s b th distnc btwn two points nd b hn th distnc btwn O nd O is D OO nd th lvtions of th B nd M ntnns r H = D OO nd D OO rspctivly Furthrmor th lvtion ngl of B rltiv to th O is h proposd modl ssums fixd mitting scttrd wvs tht imping on th M ntnn lmnts from rndom position round th cylindr (not insid it) hn th th n scttrr is dnotd by ( n ) h lvtion ngl of rltiv to th O is nd th zimuth ngl is ( n α ) It is ssumd tht rdius is much smllr thn th distnc D OO i D OO (Locl cttring Condition) h spcing btwn two djcnt ntnn lmnts t th B nd M is dnotd by δ nd δ rspctivly It is ssumd tht δ nd δ r much smllr thn th rdius i mx { δ δ } min Angls θ nd θ rprsnt th orinttion of th trnsmittr nd rcivr ntnn rrys rspctivly rltiv to th x-xis nd ngl ψ dscribs th lvtion ngl of th M ntnn rry q q y z O p θ p γ u O O m m O ψ LO α l Figur h LO pths of th 3-D gomtricl modl for MIMO chnnls q q z y O p θ p u γ O O m m O ψ l l θ l l θ Figur 2 h LO pths of th 3-D gomtricl modl for MIMO chnnls γ γ u x u x /8/$25 28 IEEE 2 Authorizd licnsd us limitd to: UIV OF PIAEU Downlodd on July 22 t 9:33:56 UC from IEEE Xor strictions py

3 h symbols LO n n α α nd α dnot th ngl of l rrivl (AoA) of th LO pths th ngl of dprtur (AoD) of th wv tht imping on th scttrr nd th AoA of th wv scttrd from ( n ) rspctivly Morovr w ssum tht B nd M r moving with spds u nd u in th dirctions dtrmind by th ngls γ nd γ rspctivly Bsd on th gomtricl modl dscribd bov th impuls rspons h () t of th sub-chnnl p l is suprposition of th LO nd LO rys nd cn b writtn s follows () () () h t = h t + h t () LO LO In th 3-D rfrnc modl th numbr of locl scttrrs is infinit ( ) Consquntly th impuls rspons h cn b modld s low pss zro mn comx LO Gussin procss nd thrfor its nvlop h is LO yligh distributd (cntrl limit thorm) [22] h impuls rsponss of th LO nd LO componnts r rspctivly K Ω h () t = LO K + LO ( ) jtf cos α mx l γ jtf LO cos( αl γ ) j ( D ) (2) p l mx Ω jϕ j ( D + D ) p l h () t = lim LO K + n = j2 t f cos mx f cos mx ( ) α γ + α γ (3) whr f = u / nd f = u / r th trnsmittr s mx mx nd rcivr s mximum Dopr frquncy rspctivly nd is th crrir wvlngth It is ssumd tht phs ϕ is rndom vribl uniformly distributd in th intrvl [ ) nd indpndnt from AoD nd AoA In (2) nd (3) K nd Ω dnot th icn fctor nd th trnsmittd powr of th subchnnl p l rspctivly h distncs D D nd D cn b xprssd s p l p l functions of th ngls Lo n α α nd D l Lo ( ) H δ cosθ δ cos α θ cosψ l (4) sin 2 cos 2 cos D p H δ cosθ δ Δ sin θ sin α (5) sin 2 cos 2 cos D 5δ sinψ sin l 5δ cosψ cos cosθ cos α 5δ cosψ cos sin θ sin α (6) whr rcsin ( / D ) / OO DOO sprd whn D ( δ δ ) OO α rcsin ( / D ) Δ is th nrrow ngl of mx hn from Fig 2 is smll ngl Drivtions of (4)-(6) O O r omittd for brvity Using (4)-(6) ssuming tht th totl trnsmit powr is unity nd pying th sin lw to th tringl O n O th impuls rsponss of th LO nd LO componnts bcom rspctivly whr K h () t LO K + LO H j j sin cos δ cosθ δ cos α + l θ cosψ j2 tf cos( LO l γ ) j2 tf LO cos( l γ ) (7) mx mx h t lim b l () LO p l K + n = p jϕ j2 t f mx ( sin sin cos ) f cos mx ( ) Δ γ α + γ + α γ (8) H δ cosθ δδ sinθ sinα j j j sin cos cos = (9) 2 j j δ sinψ sin j δ cosψ cos cosθ cosα b = j δ cos ψ cos sin θ sin α () III PACE-IME COELAIO FUCIO h spc-tim corrltion function btwn two subchnnls h () t και h () t is dfind s: E * ( δ δ τ) = E + τ = * * h () t h ( t τ) E h () t h ( t τ) LO LO LO LO h t h t Lo LO ( δ δ τ) ( δ δ τ) = + () whr ( ) * dnots comx conjugt oprtion E [ ] is th sttisticl xpcttion oprtor p q { L } B m { } l L M nd /8/$25 28 IEEE 3 Authorizd licnsd us limitd to: UIV OF PIAEU Downlodd on July 22 t 9:33:56 UC from IEEE Xor strictions py

4 Using (2) nd (7) spc-tim corrltion function of th LO componnt cn b writtn s * ( δ δ τ ) E ( τ) LO t h t h t LO LO K K K + K + = + = LO LO jτ f cos mx ( α γ ) f cos m mx ( α γ m ) j2 D D / + j 2 tf cos Lo ( α l ) Lo γ ( αm γ ) j 2 tf cos Lo ( α l ) Lo γ ( αm γ ) (2) mx mx mx δ δ w obtin tht Assuming tht { } D O O LO LO α α Bsd on this pproximtion qution (2) l m cn b simifid to LO ( δ δ τ) jτ [ f cosγ f cosγ ] mx mx = K K K + K + K K K + K + j cos ( δ cosθ δ cosθ cosψ) ( ) j2 D D / jτ [ f cosγ f cosγ ] mx mx (3) Morovr using (3) nd (8)-() spc-tim corrltion function of th LO componnt cn b writtn s * ( δ δ τ) E ( τ) LO h t h t LO LO lim K + K + n = j + jτ f mx ( Δ sin γ sin α + cos γ ) jτ f cos mx ( α γ ) = lim K + K + = + = n= E E [ D Dq D D ] p l m jτ f Δ sinγ sinα + cosγ mx δ cosθ δ Δ sinθ sinα j j j sin sin j2 f cos mx ( ) δ ψ τ α γ cos cos j δ cosψ cos cosθ cosα j δ cosψ cos sin θ sin α (4) inc th numbr of scttrrs is infinit th discrt AoA ( n ) α nd th lvtion ngl cn b rcd with continuous rndom vribls α nd with probbility dnsity functions qution (4) bcoms f α nd f ( ) rspctivly hus LO f f K + K + mx ( δ δ τ) = ( α ) ( ) + mx jtf cos( α γ ) jτ f ( Δ sin γ sinα + cosγ ) mx mx δ cosθ δ Δ sinθ sin j j j δ sinψ sin j δ cosψ cos cosθ cos cos cos j δ cos cos sin sin ψ θ d d (5) whr is rndom scttrr s mximum lvtion ngl mx Assuming tht th scttring nvironmnt is non-isotropic w f α nd Prson s dopt Von Miss distribution [23] for rcommndd pdf [5] for scttrr s lvtion ngl h Von Miss pdf is dfind s f α xp cos α μ - α (6) ( k) [ k ] I whr I ( ) is th zroth-ordr modifid Bssl function of th first kind μ [ ] is th mn ngl t which th scttrrs r distributd on th zimuth nd k controls th sprd round th mn tting k = incurs isotropic f α = / 2 Prson s pdf is dfind s scttring ( ) f ( ) = cos 4 2 mx mx (7) whr /2 Prmtr is th bsolut mx mx vlu of rndom scttrr s mximum lvtion ngl nd ccording to [24] cn tk vlus btwn nd 2 for th trrstril strt cnyon typ of propgtion nd btwn 2 nd 8 for ovr th roof propgtion whr th bs sttion is lvtd bov th roofs of th buildings Using th formntiond pdfs nd th intgrl sin( c ) + b cos( c ) dc = I 2 + b 2 [25 q ] spctim corrltion function of th LO componnt bcoms ( ) δ δ τ = LO 3 4 K + K + 2I k sin 2 2 ( ) 3 ( 2 ) + mx cos 5 I d (8) mx + whr δ Δ sinθ = jτ f sin γ jτ f Δ sin γ + j mx mx cos + j δ cos cos sin ksin ψ θ + μ (9) /8/$25 28 IEEE 4 Authorizd licnsd us limitd to: UIV OF PIAEU Downlodd on July 22 t 9:33:56 UC from IEEE Xor strictions py

5 = jτ f cosγ + j δ cosψ cos cosθ 2 mx + k cos μ (2) = /2 3 (2) mx δ cosθ = j jτ f cos γ (22) 4 mx cos 5 = j δ sin ψ (23) o obtin th spc-tim corrltion function of th LO componnt th intgrl in (8) hs to b vlutd numriclly sinc thr is no closd-form solution Finlly th spc-tim corrltion function btwn two subchnnls h () t nd h () t bcoms summtion of th spc-tim corrltion function of th LO componnt LO ( δ δ τ ) nd th spc-tim corrltion function of LO th LO componnt (8)-(23) rspctivly δ δ τ dfind in (3) nd h gnrl formuls of th Lnd Mobil trtosphric MIMO chnnl spc-tim corrltion function cn b furthr simifid for th css of IMO nd MIO chnnls In MIO chnnls w considr multi B ntnn lmnts δ = In tht cs th nd on M ntnn lmnt closd form of th sptil corrltion function ( τ = ) btwn two subchnnls () scttring ( k = ) is th following MIO δ = K + K + h t nd h () t with isotropic { ( )} 4 K K I θ + Δ tn (24) 4 In IMO chnnls w considr on B ntnn lmnt δ = nd multi M ntnn lmnts In tht cs th sptil corrltion function ( τ = ) btwn two subchnnls () ( k = ) is th following ( δ ) h t nd h () t with isotropic scttring = K K IMO pm K + K + cos θ 5 tnψ cos + mx 3 sin 5 5 cos( ) I cos d 3 (25) ψ mx + 2 tn IV UMEICAL EUL his sction provids numricl rsults of th 3-D - MIMO 2x2 cylindr modl h ffct of sptil corrltion is invstigtd s wll s th impct of th ntnn spcing nd rrngmnt is dmonstrtd in non-isotropic nd isotropic scttring nvironmnts In ll xms w usd th following modl prmtrs: B lvtion ws D 2 OO = Km B lvtion ngl ws = 6 th distnc btwn O nd O ws D /tn 5 OO = D Km th rdius of th cylindr OO ws = 8 m nd th nrrow ngl of sprd ws Δ= rcsin / D 4 Unlss indictd othrwis OO othr modl s prmtrs wr chosn to b θ = θ = 9 ψ = = 45 τ = nd k = Morovr in ordr to mx stimt th rquird intr-lmnt distnc to chiv n uncorrltd -MIMO chnnl mtrix w st icn fctor K = h ffct of non-isotropic scttring for -MIO chnnl with two B ntnns nd on M ntnn is obsrvd in Fig 3 for μ = 6 h corrltion incrss s th scttring bcoms mor non-isotropic which corrsponds to n incrs in k At 2 GHz ssuming n isotropic scttring nvironmnt ( k = ) th B ntnns rquir sprtion of round 4 mtrs which suggsts tht MIMO tchniqus r picbl in singl h corrltion functions of on B ntnn nd two uniformly nd vrticlly cd M ntnns for - IMO chnnl r ottd in Fig 4 for svrl vlus As chngs from to 45 mx mx th corrltions btwn th two subchnnls rducs drmticlly Whn M ntnns r horizontlly cd thir corrltion is significntly smll nd is lmost th sm with diffrnt mx Corrltion k=2 k= k= δ / Figur 3 h corrltion of -MIO chnnl with two B ntnns nd on M ntnn in trms of th dgr of locl scttring t th M k= /8/$25 28 IEEE 5 Authorizd licnsd us limitd to: UIV OF PIAEU Downlodd on July 22 t 9:33:56 UC from IEEE Xor strictions py

6 Corrltion ψ= mx =/4 ψ=/2 mx =/4 ψ=/2 mx =/9 ψ=/2 mx =/8 5 δ / Figur 4 h corrltion of -IMO chnnl with on B ntnn nd two M ntnns horizontlly or vrticlly cd in trms of diffrnt scttrr s mximum lvtion ngl vlus Corrltion δ / δ Τ / Figur 5 h corrltion of 2 2 -MIMO chnnl with horizontlly cd M ntnns Corrltion δ / δ / Figur 6 h corrltion of 2 2 -MIMO chnnl with vrticlly cd M ntnns Finlly th corrltion function for 2 2 -MIMO chnnl is prsntd in th figurs 5 nd 6 h corrltions of th uniformly nd horizontlly cd M ntnns r shown if Fig 5 nd thos of th uniformly nd vrticlly cd M ntnns in Fig 6 It is clr tht th corrltion functions of th MIMO chnnls r significntly ffctd not only by th spcing but lso by th rrngmnt of th ntnn lmnts his suggsts tht low corrltions cn b obtind if w crfully rrng th B nd M ntnn lmnts such tht thir corrltion flls in th vllys of th ots V COCLUIO In this ppr rfrnc modl for Lnd Mobil trtosphric icn MIMO chnnl is introducd ptil corrltion functions of this modl hv bn nlyzd undr 3-D cylindr fding nvironmnt Gnrl formuls s wll s spcific closd-form xprssions hv bn drivd for th sptil corrltion btwn two rbitrry sub-chnnls Extnsiv numricl clcultions hv bn crrid out to dmonstrt thorticl drivtions nd stimt th rquird intr-lmnt distnc for n uncorrltd -MIMO chnnl mtrix Our procdur provids usful frmwork for dsigning nd tsting futur -MIMO bsd 3G communiction systms nd studying th chnnl cpcity of -MIMO bsd chnnls with LO nd LO componnts EFEECE [] Krpntzis nd F Pvlidou Brodbnd communictions vi highltitud tforms: A survy IEEE Communictions ocity urvys & utorils vol 7 o First Qurtr 25 [2] C ozr nd D Grc High ltitud tforms for wirlss communictions IEE Elctronics & Communiction Enginring Journl vol3 o 3 pp27 37 Jun 2 [3] Prfrrd chrctristics of systms in th fixd srvic using high ltitud tforms oprting in th bnds GHz nd GHz Intrntionl lcommuniction Union Gnv witzrlnd IU- solution [4] chnicl nd oprtionl chrctristics for th fixd srvic using high ltitud tform sttions in th frquncy rng 8 32 GHz Intrntionl lcommuniction Union Gnv witzrlnd IU- f[9b/k ] 2 [5] Minimum prformnc chrctristics nd oprtionl conditions for high ltitud tform sttions providing IM-2 in th bnds MHz MHz nd 2 27 MHz in rgion nd 3 nd MHz nd 2 26 MHz in rgion 2 Intrntionl lcommuniction Union Gnv witzrlnd IU- commndtion F456 2 [6] D Grc E Dly C ozr A G Burr nd D A J Prc Providing Multimdi Communictions rvics from High Altitud Pltforms Intrntionl Journl of tllit Communictions o 9 pp ovmbr 2 [7] F Dovis Fntini M Mondin nd P vi "mll-scl fding for high ltitud tform () propgtion chnnls" IEEE Journl on lctd Ars in Communictions vol2 o3 pp April 22 [8] ltr E Cpcity of Multi-ntnn Gussin Chnnls Europn rnsctions on lcommunictions vol o 6 pp [9] G J Foschini nd M J Gns On Limits of Wirlss Communictions in Fding Environmnt whn Using Multi Antnns Wirlss Prsonl Communictions vol 6 o 3 pp [] D Grc J hornton G Chn GP Whit nd C ozr Improving th ystm of Brodbnd rvics Using Multi High Altitud Pltforms IEEE rnsctions on Wirlss Communictions vol 4 o 2 pp 7-9 Mrch 25 [] G Chn D Grc nd C ozr Prformnc of Multi s using Dirctiv nd Usr Antnns Intrntionl Journl of /8/$25 28 IEEE 6 Authorizd licnsd us limitd to: UIV OF PIAEU Downlodd on July 22 t 9:33:56 UC from IEEE Xor strictions py

7 Wirlss Prsonl Communictions pcil issu on High Altitud Pltforms vol 32 o 3-4 pp Fbrury 25 [2] P King B G Evns nd tvrou "Physicl-sttisticl modl for th lnd mobil-stllit chnnl pid to stllit/ MIMO" in Procdings of th th Europn Wirlss Confrnc vol pp icosi Cyprus April 25 [3] ommy Hult Abbs Mohmmd Compct MIMO Antnns nd Divrsity for Enhncd Dt t Communictions VC pring 27 pp [4] Aulin A modifid modl for th fding t mobil rdio chnnl IEEE rnsctions on Vhiculr chnology vol V-28 pp [5] JD Prsons nd AMD urkmni Chrctriztion of mobil rdio signls: modl dscription IEE Proc-I vol 38 o 6 pp Dcmbr 99 [6] AMD urkmni nd JD Prsons Chrctriztion of mobil rdio signls: bs sttion cross-corrltion IEE Proc-I vol38 o 6 pp Dcmbr 99 [7] -Y Long Y Zhng nd C Xio pc-im Fding Corrltion Functions of 3-D MIMO Chnnl Modl'' IEEE Wirlss Communictions tworking Confrnc (WCC) Atlnt Vol2 pp Mrch 24 [8] G Zjić nd G L tübr hr-dimnsionl modling simultion nd cpcity nlysis of spc-tim corrltd mobil-to-mobil chnnls to ppr in IEEE rnsctions on Vhiculr chnology My 28 [9] commndtion IU- F5 Prfrrd chrctristics of systms in th F using high ltitud tforms oprting in th bnds GHz nd GHz Intrntionl lcommunictions Union 2 [2] K Ktzis D A J Prc nd D Grc "Impct of high ltitud tform movmnts on cllulr hndovr" Intrntionl Workshop on High Altitud Pltform ystm Athns Grc ptmbr 25 [2] D I Axiotis nd M E hologou "Modling th positionl instbilitis of High Altitud trtosphric Pltform sttions" AIAA J Arospc Computing Inform Commun 25 [22] G L tubr Princi of mobil communiction 2nd Edition Boston MA:Kluwr 2 [23] Abdi nd M Kvh A spc-tim corrltion modl for multilmnt ntnn systms in mobil fding chnnls IEEE Journl on lctd Ars in Communictions vol 2 pp April 22 [24] Kuchr J P ossi nd E Bonk Dirctionl mcro-cll chnnl chrctriztion from urbn msurmnts IEEE rnsctions on Antnns nd Propgtion vol 48 o 2 pp Fbrury 2 [25] I Grdshtyn nd IM yzhik bl of Intgrls ris nd Products 5th dition Editd by A Jffry Acdmic Prss /8/$25 28 IEEE 7 Authorizd licnsd us limitd to: UIV OF PIAEU Downlodd on July 22 t 9:33:56 UC from IEEE Xor strictions py