Analysis and Experimental Of 3-Dimentional AOA with Directional Antenna on Narrowband MIMO Capacity

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1 Vol., Issue. 6, Nov.-Dec. 0 pp ISSN: Aalyss ad Expermetal Of 3-Dmetoal AOA wt Drectoal Atea o Narrowbad MIMO Capacty Carsak Saetaw, Sakst Summart, Caca Togsopa 3 3 (Scool of Telecommucato Egeerg, Suraaree Uversty of Tecology, Talad) ABSTRACT: Recetly, may works ave cosdered a pyscal properly of atea MIMO cael models, suc as radato patter effectve for MIMO system. However, effect of atea for MIMO wt dfferet algortms s requred ad also wt dfferet evromets of sgal beavor at eac ed of te lk. Tus, a tradtoal atea suc as Om-drectoal atea geerally s used to desg MIMO systems. I ts paper, we aalyze te performace of drectoal atea dfferet evromet of sgal spread for multple-putmultple-output (MIMO). We corporate 3-dmesoal (3D) of sgal spread matcg wt drectoal atea to a arrow-bad MIMO cael model separately. Ts cael model allows us to vestgate effect of dstrbuto of sgal comg to atea combed wt atea radato patter to MIMO capacty varous propagato evromets. We perform MIMO capacty smulatos of a system wt varous ateas radato patter property. Uform ad peaky dstrbuto models of agle of arrval (AOA) azmut ad elevato plaes are used te smulatos. We ave sow tat drectoal ateas reduce te arrow-bad MIMO capacty we te AOA s uformly dstrbuted. If te AOA s peaky dstrbuted, suc as Laplaca dstrbuto or Gaussa dstrbuto, te arrow-bad MIMO capacty s mproved we te drectoal ateas wt proper algmet to te mea AOA. However, radato patter wll sow some lmtato of te atea propertes, suc as ga ad beam-wdt wll affect to te capacty. Ts wll trade off wt lmt a atea for dfferece evromet of propagato for MIMO by ga ad beam-wdt. Te proposed model s valdated by arrow-bad MIMO capacty measuremets. Om-drectoal moopole ad Yag-Uda wt dfferet ga ad beam-wdt s used te expermets. Te expermets are performed a aecoc camber for referece ad compared wt door ad outdoor scearo. Te result verfes tat te capacty wt drectoal atea s greater ta sotropc capacty proper scearos. Keywords: cael capacty, 3D-radato patter, multple-put multple-output (MIMO) system I. INTRODUCTION It as bee sow tat systems wt multple ateas at bot trasmtter ad recever, called MIMO systems, learly crease te capacty of a wreless lk wt te umber of ateas []. Te MIMO systems explot te cael ucertaty to create multple depedet pats betwee te trasmtter ad recever. Te ucertaty of te cael s sgfcatly flueced by fadg peomea of te wreless cael. Fadg correlato s cosdered to be a major factor tat reduces te MIMO capacty []. Te MIMO capacty also depeds O array elemet radato patters [3-6]. Ulke te fadg Correlato, te radato Patters do ot deped o a propagato evromet. Aalyss performace of atea desg a propagato cael for MIMO ad atea dversty systems as become may of publcatos. Te resultg uderstadg as led to te practce of desgg atea arrays wose elemet radato patters are early ortogoal, as suc a crtero leads to good performace mult-atea systems uder specfc assumptos suc as te propagato evromet. I practcally, desg of te atea s lkely to be used dfferet evromets, suc as door, outdoor, offce ad so o. Te questo s wc type of atea wll mprove tose evromets. However, may works ave recetly reported best atea caracterstcs for MIMO systems operatg a specfc propagato evromet [7], [8]. Furtermore, to compare ateas performace s ot a easy task, sce t s dffcult to replcate te same cael codtos for dfferet measuremets. Te soluto for atea propertes must be optmal for te specfc propagato cael tat tey cosdered. Wle tese reported tecques are usually dscovered, tey eed to cosder te trasmtted ad receved atea caracterstcs togeter but te desgs are terdepedet. Ts paper presets MIMO capacty results for drectoal atea arrays relevat evromets usg - ad outdoor evromet ad proposes a smplfy model for aalyze te atea radato caracterstcs based o stocastc caracterstcs of te propagato at recever. We geeralze te cael model so tat t ca take 3- dmeso or 3D atea property cludg atea patter effect o te system capacty to cosderato. Tere are two major cotrbutos ts paper. ) Ivestgate te effect of drectoal atea wt combed AOA dstrbuto o te MIMO capacty dfferece evromet by smulatos. ) Verfy te smulato results by measuremet te real propagato scearos compare wt a result from smulatos. Ts paper s orgazed as follow. Te ext secto, te proposed cael model of specal correlato wt drectoal atea ad propagato spread s dscussed for multple atea systems. Smulatos of te MIMO capacty varous propagato evromets are preseted secto tree. Secto four wll report te results from our MIMO cael measuremets ad fally, te smulatos comparg results wll be reported. II. ANALYSIS MIMO MODEL.. Narrow-bads MIMO model I ts secto, a bref revew of "oe-rg" cael model s gve. Te, te proposed model of te MIMO system wt te effect from patter of drectoal 43 Page

2 Vol., Issue. 6, Nov.-Dec. 0 pp ISSN: atea s dscussed. Te ed of ts secto presets a tecque for MIMO capacty calculato wt effect of bot atea patter property ad a spread of AOAs. Let x be a vector of te trasmtted sgals wt trasmt ateas ad y be a vector of te receved T sgals wt R receve ateas. Te te MIMO system model [],[],[9] s gve by y Hx () Were s a ( Rx ) addtve ose vector troduced at te recever ad H s a ( Rx ) cael matrx. T Te followg assumptos are made order to compute cael capacty for ts model. ) H Is a matrx of..d. zero mea Gaussa radom varables wt varace. j ) s a vector of..d. zero mea Gaussa radom varables wt varace. ) Te trasmtter as kowledge of cael statstcs ad te recever kows H. v) Te total trasmt power P s allocated uformly to total eac trasmt atea as P P total /. T However, we cosderato a model for a arrowbad wt a specfy bad of frequecy spectrum. Let x ad y be a trasmtted ad receved sgal respectvely. Te system model for a arrowbad wreless system wt sgle atea at te bot eds ca be wrtte as y x () Were ad are te cael mpulse respose ad addtve ose respectvely. However, to descrbe a cael spercal coordate tat wll be used for atea radato patter or atea ga ad cdet wave for eter atea wll sow Fg.. A comg sgal wll come over [0, 360] or [0, π] for azmut plae ( ) ad [0,80] or [0, π] for elevato plae ( ) respectvely. We ca be calculated atea ga from te far-feld radato patter 3D usg [0] we ave, 4U (, ) G(, ) (3) P Were G (, ) ad P are atea ga as a fucto of agle ad total power respectvely. U (, ) Is radato testy of atea gve by? U(, ) E (, ) E (, ) (4) Were E ad E s electrc fled compoet of atea. Substtutg (4) to (3) gves k E (, ) E (, ) (5) G(, ) Were k 4 / P. Te atea radato patter s determstc peomea wereas te cael mpulse resposes are stocastc process. Te comg electromagetc waves are stocastc process due to te radomess of te cael. Sce te atea s used for covertg statstcal electromagetc waves to a electrcal sgal, te output electrcal sgal wll be a stocastc process. However, te output stocastc process wll ot be te same wt te put process because te atea radato patter flueces te put process as a trasfer fucto. I oter words, te radomess of te cael s altered by te atea radato patter. Te radato patter drectly flueces te capacty. I a deal cael case, te atea patter s eeded to be Om-drecto. However, a certa propagato evromet, te Om-drectoal atea may ot be a optmal coce for maxmzg te capacty. A model for te cael cludg te effect of te radato patter s eeded. We propose a MIMO cael model wt atea radato patter 3-dmeto. I ts paper, te cael mpulse resposes, te agle of arrval ad te atea patter ca be modeled separately te proposed model. Fg. Spercal coordate system. For Om-drectoal atea, te drecto of comg sgal derved as closed-form expressos. Te dstrbutos of AOA ave a closed-form as a Uform, Gaussa ad Laplaca dstrbuto ave bee troduced [-3]. For tese tree dstrbutos wll usg te AOA as dexg varables. So, te modfed cael mpulse respose wt te effect of te drectoal atea ad spread of AOA for a arrowbad wreless system ca be ta wrtte as a G(, ) (6) Were s frequecy doma for arrowbad system model. Te ma advatage of te proposed model s tat te cael mpulse respose ad atea patter for dfferet evromets of AOA ca be treated as oe sgle fucto or separately deped o evromet selected. Te cael mpulse respose ca be obtaed from eter a wreless cael measuremet [7] or a aalytc model [6],[4-6]. Wereas eter a full wave electromagetc smulato or atea radato patter measuremet ca be used to obta radato or atea ga patter. By usg (6) for te modfed cael mpulse resposes wt atea patter ad a spread of AOA, eac row of te cael matrx s gve by a G ) (7) (, )... G (, T T Were G (, ) s te radato patter of -t receve atea. Hece, te cael matrx wt te effect of receve atea radato patters ad a spread of AOA ca be wrtte as T 43 Page

3 a a a... Iteratoal Joural of Moder Egeerg Researc (IJMER) Vol., Issue. 6, Nov.-Dec. 0 pp ISSN: a T T H (8) Te MIMO system model () wt te effect receved atea radato patter ad AOA ca be wrtte as y H a x (9) Te arrowbad MIMO capacty s a fucto of te cael matrx wll gve by P T C log det I HaH (0) T a Were P te sgal s power ad s te ose power. To calculate te capacty wt effect of drectoal atea ad a spread of AOA, radom matrces are geerated by usg (7) eac realzato of te cael matrx s obtaed by usg (9) ad (0) were te AOA for eac receve atea s geerated based o evromets scearos selected... Dstrbutos Fucto of AOA Fg. Laplaca dstrbuto. III. SIMULATIONS Te MIMO capacty (0) s evaluated usg Mote Carlo smulatos. Te, 0,000 staces of cael ad collect te statstcs of MIMO cael capacty were geerated. I te smulatos, 4 trasmts ad 4 receve ateas are used at te bot eds. Te sgal to ose rato ( P / ) s calculated from a result of measuremet tat wll dscuss for detal later. Te AOAs are geerated usg Uform, Gaussa ad Laplaca dstrbuto bot azmut ad elevato plae deped o scearos tat wll be descrbe as, Scearo I a measuremet as bee settg up a laboratory room tat as a desk ad partto. Te measuremet space s 5.00m. x 7.00m. x 3.00m., as sow Fg. 3. So, te dstrbuto azmut plae s used ad elevato wll be uformed o bot plaes. For 3D Model, te propagato dstrbuto for bot azmut ad elevato plaes are depedet ad detcally dstrbuted (..d.) radom varables. However, te dstrbuto of te propagato drectos are defed for azmut ad elevato plae. So, lterature measuremet results suggest tree caddates for AOA dstrbuto azmut plae, Uform, Gaussa ad double expoetal or Laplaca dstrbutos [7]. Te uform dstrbuto, wc assumes tat all te comg waves are come from all drecto te azmut plae, wt a depedet radom pase for eac azmut drecto wt equal probablty. Te oter dstrbuto fucto ca be wrtte as follows. ) Gaussa fucto: ( x ) ( x) A exp () b ) Double expoetal fucto: x A exp, x () ( x) b x A exp, x b If te spread parameters b ad b are equal, te double expoetal fucto become Laplaca fucto as sow Fg.. Were coeffcets A / b ad A / b. Fg. 3 Dagram of TX ad RX locato for door scearos. Scearo II a measuremet as settg up a parkg yard wt a wde area opeed. So, te dstrbuto azmut plae usg a peaky dstrbuto wt spread parameter s ormal dstrbuto. So, we wll use bot Gaussa ad a double-sded expoetal fucto wt equal spread parameters or Laplaca o bot plaes ts scearo. For AOA 3D model, we wll combe te AOA of te comg multpat at te recever bot spercal agles ad. Te jot pdf p (, ) s wrtte terms of te codtoal pdf of for a gve ; p ( ), ad te margal pdf f ( ) Tus, p(, ) p ( ) f ( ) (3) So, te result of dstrbuto of AOA bot azmut ad elevato plae ca be wrtte as, ) Gaussa fucto: (, ) ( ) ( ) B exp (4) b b ) Double expoetal fucto: B (, ) B exp,, b b exp,, b b (5) 433 Page

4 Vol., Issue. 6, Nov.-Dec. 0 pp ISSN: We coeffcets B A ad B A. Te ceter of dstrbuto ad drecto of atea must pot to te drecto of te ma lobe of atea. So, te dstrbuto wll sft a agle tat te dstrbuto maly dstrbuted tat matc to ma lobe of a atea we used. For smulato, a moopole atea s used as a referece scearo ad oter tree type of Yag-Uda are used to vestgate te effect of atea radato patter wt dfferece AOA dstrbuto to te cael capacty. Te 3D radato patters of ateas are obtaed from CST mcrowave studo 009. Te radato patter te smulatos, 5-elemet, 9-elemet, 3-elemet Yag- Uda ateas are sow Fg. 4 ad Fg. 5 for azmut ad elevato plae respectvely. Table. Atea property from CST for smulato. Atea Type Azmut- (Degree) Elevato- (Degree) Ga (db) Isotropc Yag-05E Yag-09E Yag-3E Table. Actual atea property used measuremet. Atea Type Azmut- Elevato- Ga (db) (Degree) (Degree) Moopole Yag-05E Yag-09E Fg. 4 Te radato patter for Yag-Uda o azmut plae. Yag-3E I order to access te capacty performace of drectoal ateas, te dowlk of a pot-to-pot arrowbad MIMO system s cosdered, operatg at te frequecy of.45 GHz. It s assumed te 3D scatterg evromet ca be represeted by a scearos selected as descrbe before. Fg. 5 Te radato patter for Yag-Uda o elevato plae. Te actual atea patter propertes suc as ga ad from measuremet compare to a result from CST s smlarly o bot azmut ad elevato plaes as sow table ad table. Were te gas are wt respect to Om-drectoal atea db ad s are degrees. Ateas at recever are equpped wt uform lear arrays (ULA) of te same type ateas. Furtermore, t s assumed tat atea spacg at bot sdes s te same at trasmtter ad recever, eac as four ateas. Te MIMO capactes were compared terms of te Complemetary Cumulatve Dstrbuto Fuctos (CCDF). Te performace of eac atea type s vared by dfferet scearos referrg to te dfferet AOA dstrbuto ad te outage capacty observato. Te cael capacty at a gve outage probablty q, deoted by C. Te 0% outage cael capactes wll be wrtte as q C. 0. a) Isotropc Atea b) Yag-Uda 5E Atea c) Yag-Uda 9E Atea b) Yag-Uda 3E Atea Fg. 6 Percet capacty outage wt dfferet spread parameter o 3D for scearos I wt Uform AOA. 3. Scearo I I ts scearo, a dstrbuto of AOA s uformed o bot plaes. We geerate cael wt a dstrbuto of AOA for 0000 stats. Te AOAs are cocetrated aroud te mea. Te spread parameter s a parameter to cotrol te radomess of te AOA. So, te result of te 0% outage cael capactes couted from CCDF wll be compare to deal case of sotropc atea 434 Page

5 Vol., Issue. 6, Nov.-Dec. 0 pp ISSN: wt dfferet spread parameter of AOA dstrbuto o azmut ad elevato plae wll be vestgated. vared wt a spread parameter bot plaes. We te spread creases, t decreases te capacty o bot ways. a) Isotropc Atea b) Yag-Uda 5E Atea IV. EXPERIMENTAL MEASUREMENTS I ts secto, te capacty of a drectoal atea, 5-elemets 9-elemet ad 3-elemets Yag-Uda, s measured. A Moopole atea s used te expermet for comparso wt tose tree Yag-Uda ateas. Te 4- moopole array s used te expermet as a trasmt atea. At te recever, 4-Yag-Uda array s used. Te system s 4x4 MIMO. c) Yag-Uda 9E Atea b) Yag-Uda 3E Atea Fg. 7 Percet capacty outage wt dfferet spread parameter o 3D for scearos II wt Gaussa AOA. Te spread parameter betwee 0 to 00 degree o azmut ad 5 to 50 degree o elevato plae as bee vestgated. Te 0% outage cael capactes for four types of atea sow Fg. 6. Te capacty s about 66%, 57% ad 55% for 5E 9E ad 3E Yag-Uda atea. All capacty s greater ta te deal case due to te ga of eac atea but ot affect a spread of AOA caged. Fg. 9 Dagram of arrowbad MIMO cael measuremet system. Te block dagram of te capacty measuremet system s sow Fg. 9. Te capacty measuremets are performed by usg te sgal sceme [8]. Ts sgal s loaded to te E4433 sgal geerator. Te receved sgals are store te sgal aalyzer MXA900A. Dstace(La mbda) Table 3. Mutual Couplg level (S). Moop Yag- Yagole 05E 09E Yag- 3E a) Isotropc Atea b) Yag-Uda 5E Atea d= d= d= d= c) Yag-Uda 9E Atea b) Yag-Uda 3E Atea Fg. 8 Percet capacty outage wt dfferet spread parameter o 3D for scearos II wt Laplaca AOA. 3. Scearo II I ts scearo, te atea s located so tat te drecto of maxmum drectvty s alged wt te mea of AOA of te Yag-Uda atea s used. Te 0% outage cael capactes (8) for all atea types are sow Fg. 7 ad 8 for Gaussa ad Laplaca AOA evromet respectvely. It ca be see tat te drectoal ateas maxmze te system capacty sow Fg. 7 for Gaussa AOA. of te Yag-Uda 5E, Yag-Uda 9E ad Yag-Uda 3E s about 56%, 6% ad 60% more ta te deal case. For Laplaca AOA Fg.8, Te result of Yag-Uda 5E, Yag-Uda 9E ad Yag-Uda 3E s about 56%, 6% ad 60% more ta te deal case. I ts scearo, te capacty mprovemet s d= d= d= d= Te atea separatos te array are determed by mutual couplg measuremets measurg a aecoc camber for moopole ad all type of Yag-Uda. Te mutual couplg wt varous atea separatos s sow table 3. Normally, te mutual couplg wll effect to capacty we atea space less ta /. So, te mutual couplg s less ta -40 db we te atea separato s greater ta. Fally, we coose te atea separato of te expermets to eglect te mutual couplg [9-0]. 435 Page

6 Vol., Issue. 6, Nov.-Dec. 0 pp ISSN: MIMO Capacty Calculato. A comparso of te MIMO capacty aceved by eac type of atea array must be made usg measuremets from varous scearos. Drectve ateas may crease SNR ad also reduce te multpat sgals tat ca be receved by te ateas at te same tme. To separate tese two effects we frstly quatfy weter tere s a MIMO capacty reducto wt drectve ateas at costat SNR. To make a far comparso sow smulato, a moopole atea closed to a sotropc atea all measuremet scearos s used to compare result wt a smulato. Average cael capacty of moopole s measured as referece for ormalzed as follows. A referece SNR measuremet s made at eac scearo usg moopole ULAs wt atea spacg of. Mutual couplg s assumed to ave eglgble effect o recever SNR for suc large spacg. Te referece measuremet s made usg te same grd postos ad frequeces used for all ste measuremets. A referece ose varace s computed as before wle te referece cael varace s computed as [] T R j T R j (7) Te ormalzed esemble average cael capacty s te computed as C N CH (8) C(, ), r Were C(, r, ) s te..d. Gaussa cael capacty correspodg to te referece SNR measuremet ad computed by Mote Carlo smulato of te system defed Secto 3. Te computed referece cael capacty s assumed to be able to aceve te best case scearo of o mutual couplg ad o cael correlato. Ts capacty ormalzato s a departure from te tradtoal metod wc te measured cael matrces are ormalzed ad SNR s scaled freely. 4. Feld Measuremet Procedure Table 4. Measuremet parameter for all scearos Parameter Value Trasmtter atea ga Recever atea ga (Yag-Uda 3E) Recever atea ga (Yag-Uda 09E) Recever atea ga (Yag-Uda 05E) Recever atea ga (Moopole) 4.3dB 0.55dB 9.7dB 8.58dB 4.3dB Dstace from TX. at. To RX. at. 3.0 m. Total trasmsso cable loss -.48dB A measuremet campag s performed by usg te QPSK sgal geerator tat broadcasts a 50 MHz IF exctato sgal at.45 GHz from eac trasmt atea. Te trasmtted sgal from eac atea s captured at eac receve atea by usg a maual-swtc. For far-feld measuremet, ts trasmtter ad recever wll ave 3 meter dstace. A MXA900A sgal aalyzer was used to measure a propagato ga tat s used ts paper. A complete calbrato of eac rado s ga, pase ose ad frequecy offset was performed pror to feld measuremets. It as bee sow tat te statstcal property of AOA outdoor propagato evromet as peaky caracterstc []. Te measuremet parameters are sow table Measuremet Results Ts secto presets te results from a door ad outdoor measuremet campag usg a measuremet strumet test-set wt te Yag-Uda ad moopole ateas. Measured cael capacty results from dfferece measuremet scearos are preseted to sow te effect of atea radato patter ad AOA dstrbuto evromet. Before usg te measuremet result, t must ormalze capacty as sow secto 4.. A average SNR at receve atea from all measuremet scearo as scearo I, scearo II ad aecoc camber are sow table 5. A referece SNR measure camber tat wll extremely ave drect le of sgt sgal. Tat result sow a dfferece scatterg effect to SNR for bot scearos. Table 5. Average receve power from measuremets. Atea Type Scearo I Scearo II Camber Moopole Yag-05E Yag-09E Yag-3E Table 6. Improvemet of 0% outage capacty from measuremets. Atea Type Scearo I Scearos II Camber Moopole 00% 00% 00% Yag-05E 6% 43% 3% Yag-09E 34% 56% 4% Yag-3E 36% 64% 47% However, a compreesve set of results s preseted for bot scearos. A far comparso of MIMO performace s made betwee te Yag-Uda ad te referece moopole from smulato result as sow table 6. A drectoal atea scearos ot be mproved MIMO capacty but scearos II, drectoal atea wll mprove MIMO 436 Page

7 Vol., Issue. 6, Nov.-Dec. 0 pp ISSN: capacty. Fally, drectoal atea tat as ga ad drecto matc to AOA spread wll mprove MIMO capacty codto as te drecto of atea s correctly. V. CONCLUSIONS Ts researc proposes proposed te cael model for MIMO capacty calculato. Te proposed model ca be used to calculate te MIMO capacty wt te presece of 3D atea radato patter. Te proposed model allows us to model te 3D atea patter. Te elemets spacg are for decrease effect of mutual couplg. However, ot oly radato patter of te elemet flueces te arrowbad MIMO capacty but also te statstcal property of AOA. We ave sow tat drectoal ateas are ot attractve for MIMO systems a scearo were te radomess of AOA s g. I a scearo wt AOA cocetratg o a sgle value, te atea posto s crucal to te capacty. If te atea s pot to te mea AOA, te te capacty s creased. Te results from measuremet sow tat te AOA ad atea radato patter fluece arrowbad MIMO capacty from smulato be cofrmed. O te oter ad, rc scatterg evromets, te power ga of drectoal ateas s o more elpful, sce te sgal power s dspersed over a large extet of drectos. Te lmted beam-wdt of drectoal ateas wll decrease te effectve agular spread wc severely creases te correlato. Terefore Om-drectoal ateas outperform tese stuatos. Tese results suggest te followg geeral gudeles for selecto of atea type. Our results sow tat coosg te sutable atea, operatg SNR ad atea spacg are oter factors tat sould also be cosdered togeter wt te spread of AOA. VI. ACKNOWLEDGEMENTS Ts work was supported by Suraaree Uversty of Tecology (SUT) ad advsed by Ms. Nattaa Summat o te paper report wrtg. REFERENCES [] G.J. Fosc ad M.J. Ga, O lmts of wreless commucatos fadg evromet we usg multple ateas, Wreless Persoal Commucatos, 6(3), 998, [] D.S. Su, G.J. Fosc, M.J. Gas ad J.M. Ka, Fadg correlato ad ts effect o te capacty of mult-elemet atea systems, Proc. IEEE 998 Iteratoal Coferece o Uversal Persoal Commucatos, 998, [3] K. Yu ad B. Otterste, Models for MIMO propagato caels: A revew, Wrel. Commu. Mob. Comput., (7), 00, [4] B. Wag, ad A.G. Burr, Effect of elemet radato patters o te capacty of MIMO system, Proc. IEEE It. Symp. o Mcrowave, Atea, Propagato ad EMC Tec. for Wreless Comms, 005, [5] C. Saetaw, A. Itrapac, C. Togsopa, Effect of Spatal Correlato wt Drectoal Atea o MIMO Capacty, Proc. of ISAP007, 007, [6] H.S. Rad ad S. Gazor, Te mpact of o-sotropc scatterg ad drectoal ateas o MIMO multcarrer moble commucato caels, IEEE Trasactos o Commucatos, 56(4), 008, [7] D. Czk, J. Lg, P.W. Wolasky, R.A. Valezuela, N. Costa, ad K. Huber, Multple-put-multple-output measuremets ad modelg Maatta, IEEE J. Sel. Areas Commu.,, 003, [8] K.I. Pederse, P.E. Mogese, ad B.H. Fleury, Power azmut spectrum outdoor evromets, Electro. Lett., 33(8), 997, [9] I.E. Telatar, Capacty of mult-atea Gaussa caels AT&T Bell Labs, Tec. Rep., 995. [0] C.A. Balas, Atea Teory: Aalyss ad Desg, 3rd Edto, Jo Wley & Sos Ic, 005. [] K.I. Pederse, P.E. Mogese, ad B.H. Fleury, A stocastc model of te temporal ad azmutally dsperso see at te base stato outdoor propagato evromets, IEEE Tras. Ve. Tecol., 49(), 000, [] Q.H. Specer, B.D. Jeffs, M.A. Jese, ad A.L. Swdelurst, Modelg te Statstcal Tme ad Agle of Arrval Caracterstcs of a Idoor Multpat Cael, IEEE Joural o Selected Areas Commucatos, 8, 000, [3] F. Adac, M. Feey, A. Wllamso, ad J. Parsos, Cross- Correlato betwee te Evelopes of 900 MHz Sgals Receved at a Moble Rado Base Stato Ste, IEE Proceedgs Pt. F, 33, 986, [4] W.C.Y. Lee, Effects o correlato betwee two moble rado base-stato ateas, IEEE Tras. Commu.,, 973, 4 4. [5] J. Salz ad J. Wters, Effect of Fadg Correlato o Adaptve Arrays Dgtal Moble Rado, IEEE Trasactos o Vecular Tecology, 43, 994, [6] C. Saetaw, A. Itarapac, C. Togsopa, Relatos Betwee 3-Dmesos Atea Patter ad Narrowbad MIMO Capacty, Proc. Mcrowave Coferece, APMC007, 007, 4. [7] K. Kallola, K. Suloe, H. Late, O. Kvek as, J. Krogerus, ad P. Vakae, Agular power dstrbuto ad mea effectve ga of moble atea dfferet propagato evromets, IEEE Trasactos o Vecular Tecology, 5(5), 00, [8] D.W. Browe, W. Zu, ad M.P. Ftz, A sgalg sceme ad estmato algortm for caracterzg frequecy selectve MIMO caels, Proc. IEEE Ve. Tecol. Cof., 005. [9] T. Svatesso ad A. Raem, Mutual couplg effects o te capacty of multelemet atea systems, Proc. IEEE ICASSP, 00, [0] I. Gupta ad A. Ksesk, Effect of mutual couplg o te performace of adaptve arrays, IEEE Tras. Ateas Propag., 3, 983, [] D.W. Browe, M. Mateg, M.P. Ftz, Y. Ramat-Sam, Expermets Wt Compact Atea Arrays for MIMO Rado Commucatos, Ateas ad Propagato, IEEE Trasactos o, 54(), 006, [] M. Alseal, S. Nogaa, D.A Bucaa ad A.R. Sebak, Agle-of-Arrval Statstcs of a Tree-Dmesoal Geometrcal Scatterg Cael Model for Idoor ad Outdoor Propagato Evromets, IEEE Ateas ad Wreless Propagato Letters, 9, 00, Page