MIMO principles. s1(t) y1(t) H(,t) ( t) s2(t) y2(t) Helka Määttänen. paper provides a general overview of this promising transmission technique.

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1 S Pograduae Coure n Rado Communcaon 1 IO prncple ela ääänen I. IRODUCIO e growng demand of mulmeda ervce and e grow of Inerne relaed conen lead o ncreang nere o g peed communcaon. e requremen for wde bandwd and flebl mpoe e ue of effcen ranmon meod a would f o e caracerc of wdeband cannel epecall n wrele envronmen were e cannel ver callengng. In wrele envronmen e gnal propagang from e ranmer o e recever along number of dfferen pa, collecvel referred a mulpa. Wle propagang e gnal power drop of due o ree effec: pa lo, macrocopc fadng and mcrocopc fadng. Fadng of e gnal can be mgaed b dfferen dver ecnque. o oban dver, e gnal ranmed roug mulple deall ndependen fadng pa e.g. n me, frequenc or pace and combned conrucvel a e recever. ulplenpu-mulple-oupu IO eplo paal dver b avng everal ranm and receve anenna a depced n Fg. 1. For eample n receve anenna dver, n rc caerng envronmen, eac receve anenna ee dfferen veron of e ranmed gnal and wen ee veron are combned n a proper manner e oucome a beer qual lower b-error-rae BER or ger daa rae an a ngle veron of e gnal. Specfcall, f e number of mulpa componen eceed a ceran value e cannel capac ncreae can be proporonal o e number of ranm and receve anenna and no addonal power or bandwd requred. IO effecvel ae advanage of random fadng and wen avalable, mulpa dela pread. Acuall, e abl o urn mulpa propagaon, wc convenonall condered a a drawbac of wrele ranmon, no a benef for e uer e e feaure of IO em. IO a emerged a one of e mo gnfcan ecncal brearoug n modern communcaon. paper provde a general overvew of promng ranmon ecnque. 1 Fgure 1 IO em A. IO, II. BASIC DEFIIIOS 1 Conder a IO cannel w ranm anenna and receve anenna a depced n Fg. 1. e gnal ranmed from e ranm anenna. e me-varng cannel mpule repone beween e ranm anenna and e receve anenna denoed a,,. e IO cannel repone can be epreed a an mar: 1,1,,1,,,1, 1,,,,,, 1,,,,,, 1 e gnal receved a e receve anenna gven b 1, n, 1,,...,, were denoe e convoluon and n e noe

2 S Pograduae Coure n Rado Communcaon added n e recever. e pao-emporal gnaure nduced b e ranm anenna acro e receve anenna arra gven b e vecor,,,. 1,,, B. ISO If e number of receve anenna reduced o 1, a mulple-npu-ngle-oupu ISO em aaned. ISO cannel can be decompoed no ngle-npungle-oupu SISO cannel. e ISO cannel mpule repone beween e ranm anenna and e receve anenna can preened b a 1 vecor 1 d 1,,,,. 3 e receved gnal can be repreened a 1, or n vecor noaon a n 4, n 5 were e npu gnal vecor a 1 1 vecor C. SIO If e number of ranm anenna 1 and e number of receve anenna e em called ngle-npumulple-oupu SIO em. I compre SISO cannel le e ISO cae. e SIO cannel can be repreened a an 1 vecor,,,, 6 1 e gnal receved a receve anenna gven b, n 7 or n a vecor form, 1, b, n 8 Fgure Scemac of wavefron mpngng on an anenna arra III. CAEL ODEL Equaon 1-8 ncorporae me varaon naure of e wrele envronmen bu for convenence we now uppre e me-varng naure of e cannel. Alo a narrowband arra aumpon decrbed brefl below made wen dervng a IO wrele cannel model from a mplc pcal caerng decrpon. Fg. ow e cemac of wavefron mpngng on an anenna arra. e mpngng wavefron avng a bandwd B denoed a, e gnal receved b e fr and econd anenna denoed b 1 and and e anenna eparaon d. mpngng a angle repreened a c e 9 were e comple envelope repreenaon of e gnal and c e carrer frequenc. Under e narrowband aumpon we ae e bandwd B o muc maller an e recprocal of e ran me of e wavefron acro e anenna arra,.e. B1/. ow can be repreened w 1, nce e gnal are dencal ecep for a pae f a depend on e arra geomer and e angle of arrval of e wavefron. n d / 1 e 10 were e waveleng of e gnal wavefron. oe a e narrowband aumpon doe no mpl frequenc

3 S Pograduae Coure n Rado Communcaon 3 fla cannel. Fg. 3 ow e IO cemac w a cannel of fne number of o-dela caerer. Under aumpon e gnal caered from dfferen caerer arrve a e recever a e ame me.e. e mulpa caracerc of e cannel are no modeled. In Fg. 3 a caerer locaed a angle, w repec o e ranmer and a angle and dela w repec o e recever. An wo of ee varable defne e rd one b vrue of e geomere n Fg.3. W ee aumpon a eerng vecor a recever and ranmer arra ma be defned, repecvel a a b n 1 n 1 e e 11 n 1 n 1 e e 1 e anenna eparaon d aumed o be /. e ranmed gnal vecor can be denoed a 1 and e receved conrbuon from e caerer a 1, wc can be epreed a a b 13 were e comple valued caerer amplude. e receved gnal e um of all conrbuon from all K caerer K K a b 14 Ran of mar ell e number of ndependen conrbuon a e recever de. of ze.e. a ran maller or equal o mn,. Ran of depend alo on e number of ndependen caere nce bul a a um of ran one marce n cae of onl one caerer e ran of obvoul 1. A a concluon e ran of e cannel mar maller or equal o mn,k,. 1 caerer 1 Fgure 3 IO cemac w a cannel of fne number of o-dela caerer IV. IO CAPACIY IO cannel eb fadng and encompa paal dmenon. e cannel 1 random and erefore e capac alo a random varable. e ergodc capac of e IO cannel C r 1 E ma E log de I R 15 R 0 were E e oal avalable average energ over a mbol perod avalable a e ranmer and R =E[ ] e covarance mar of. aumed o ave zero mean and e race of R mu be n order o conran e oal average energ ranmed over a mbol perod. Cannel nowledge a e recever aumed. Acqurng cannel nowledge a e ranmer n general ver dffcul n praccal em. If e cannel unnown o e ranmer and e cannel a no preferred drecon ma be coen o be acall non-preferenal wc mple a e gnal are ndependen and equ-powered a e ranm anenna. I.e. R=I and e capac n cae of no cannel nowledge a e ranmer read a C E 1 E log de I 16 0

4 S Pograduae Coure n Rado Communcaon 4 V. PERFORACE IPROVEE OF IO SYSE Arra gan, dver gan, paal mulpleng gan and nerference reducon are e e feaure a conue e performance mprovemen of IO em. A. Arra gan Arra gan refer o e average ncreae n e gnalo-noe rao SR a e recever wen e receved gnal ave been coerenl combned. e ranm/receve arra gan requre cannel nowledge n e ranmer and recever, repecvel, and depend on and. For eample, conder a ISO cannel w ranm anenna. oal ranm power E[ ]=P.e. /qr ranmed from eac anenna. Aume e noe power o be 0 and all cannel repone o be 1 non-pcal cannel model. e receved gnal ee eq. 4 =*/qr+n. e receved ueful gnal power E[ -n ]=*P.e. e SR *P/ 0. me e SR of a SISO ln ence e arra gan n cae. If one of e cannel repone for eample -1, e arra gan depend on weer e ranmer now a or no. If e ranmer a cannel ae nformaon CSI wll end /qr from e correpondng anenna n order o eplo e ame arra gan. [4] B. Dver gan A menoned n e nroducon dver a powerful wa o mgae fadng n wrele ln. e dea of dver baed on e fac a f we ave everal uncorrelaed cannel e are no lel o ave deep fade mulaneoul and u wen recevng e ame nformaon roug all ee uncorrelaed cannel e probabl a e gnal eperence a deep fade maller an n ngle cannel cae. IO eplo paal dver a doe no acrfce me or frequenc unle me and frequenc dvere. Onl comple added. e dver order e number of uncorrelaed cannel n e em and depend on e avalable cannel and e anenna confguraon. For eample conder a SIO cannel and aume a e anenna are eparaed b e coerence dance.e. e cannel are ndependen aume alo ndependen caerng. In SISO cannel e probabl a e gnal level goe below a reold p. In ISO cannel e probabl a e gnal level n ever cannel goe below e ame reold p. ence, n eample, a dver order aceved compared o e SISO cae. If e cannel are correlaed e dver order decreae. [4] e precedng eample ad onl one ranm anenna. In order o capalze of everal ranm anenna wou cannel nowledge a e ranmer e gnal mu be pre-proceed or pre-coded before e ranmon. In cae e cannel nown o e ranmer full dver can be eploed, for eample n ISO cae, b wegng e gnal approprael, o a e gnal arrve n pae a e receve anenna and add coerenl. In IO cae paal dver can be eraced roug a ecnque nown a domnan egenmode ranmon. A w ISO cae e ame gnal ranmed from all anenna n e ranm arra w an approprae weg vecor. C. Spaal mulpleng gan Spaal mulpleng gan e ncreae of capac. I can be decrbed w e followng formula, were r e paal mulpleng gan C r log SR. 17 e gan aceved wen more an one ndependen mbol can be ranmed durng e ame mbol duraon. In oer word e aceved paal mulpleng gan dependen on e number of ndependen daa ream a can be uppored relabl.e. e ran of. D. Inerference reducon A menoned n Sec. II e gnal end from anenna a a paal gnaure a can be ued n recognzng e gnal. Obvoul, e nowledge of e dered gnal cannel requred. e dfference beween paal gnaure of e dered gnal and e cocannel gnal can be eploed n o reduce cocannel nerference a are due o frequenc reue. Effcen cocannel nerference cancellaon gve prereque for aggreve frequenc reue. VI. COCLUSIO I a been een a IO a ver promng ranmon ecnque bu ould be noed a no all feaure menoned n Sec. IV can no be eploed mulaneoul due o dfferen demand on e paal degree of freedom or number of anenna. REFERECES [1] A. Paulra, R. abar, D. Gore: Inroducon o Space-me Wrele Communcaon, Publed a 003, ISB: [] D. Geber,. Saf, S. Da-an, P.J. Sm, A. agub, From eor o pracce: an overvew of IO pace-me coded wrele em, Seleced Area n Communcaon, IEEE Journal on, Volume: 1, Iue: 3, Aprl 003 Page:81 30

5 S Pograduae Coure n Rado Communcaon 5 [3] A.J. Paulra, D.A. Gore, R.U. abar,. Bölce, An overvew of IO communcaon - a e o ggab wrele Proceedng of e IEEE,Volume: 9, Iue:, Feb. 004 Page: [4] aeral of e coure Sgnal proeng n wrele communcaon p://wooer.u.f/ur/88175.ml VII. OEWORK We aumed a ver mplc cannel. Wa our opnon, ow would IO be worng n a real wrele communcaon cannel? Could IO be a praccal applcaon or onl a nce reearc opc? Gve our opnon w reaonng.