PERFORMANCE OF MULTIBEAM MIMO FOR NLOS MILLIMETER WAVE INDOOR COMMUNICATION SYSTEMS CHAPTER 6

Transcription

1 PERFORMANCE OF MULTIBEAM MIMO FOR NLOS MILLIMETER WAVE INDOOR COMMUNICATION SYSTEMS CAPTER 6 1

2 PERFORMANCE OF MULTIBEAM MIMO FOR NLOS MILLIMETER WAVE INDOOR COMMUNICATION SYSTEMS CAPTER 6 igh data rate video stream usig MMW suffer data loss due to fadig effects. Multipath fadig beig pre-domiat i idoor, Multi Iput Multi Output (MIMO) techology is cosidered to be the ideal choice compared with the existig sigle lik systems. As spatial diversity i both trasmit ad receive ehaces the diversity gai, the performace of the system is further ehaced by itroducig trasmit beamformig based atea beam diversity. I classical x MIMO, a diversity gai of 4 is achieved, whereas i this work, Alamouti code ad dualbeam x MIMO with diversity gai 8 is cosidered. This chapter has bee formulated for a persoal commuicatio system i NLOS idoor eviromet. I order to compesate the path loss at 60 Gz, high gai atea array is proposed. This leads to achievig highly directive beam, requirig LOS coditio. LOS is ot suitable for idoor local eviromet. To overcome this problem, we have proposed multibeam MIMO to create rich scatterig eviromet. The proposed system cofiguratio may be highly suitable for MMW-MIMO i idoor local eviromet, where systems eed ot be aliged with LOS coditio. The chapter is orgaized with sectio 6.1 discussig survey of reported results, sectio 6. details the TSV chael No-Lie of Sight (NLOS) parameters, sectio 6.3 describes the MMW MIMO chael model, sectio 6.4 describes the three cases i Multibeam MIMO viz. sigle beam, dual beam ad N-beam, sectio 6.5 presets the performace compariso of classical MIMO ad Multibeam MIMO ad sectio 6.6 presets the observatios ad commets. 6.1 Itroductio Omidirectioal versus directive beams I recet years, cosiderable attetio has bee devoted to the desig ad stadardizatio of multi-gigabits per secod wireless systems operatig at 60 Gz bad for a large variety of low cost cosumer applicatios. Compared with the covetioal systems operatig i the lower frequecy bads like.4 Gz, a sigificat additive challege is the achievemet of 13

3 sufficiet lik budget. The mai reaso for this is the much lower performace of the RFsectios as well as the much higher propagatio losses. O the other had, it is easier to establish highly focused atea beams at both the eds (or oly oe ed) of the lik by meas of small atea structures. I this maer, the lower RF performace ad higher propagatio losses ca be compesated by a high atea gai. Cosequetly, i the cotext of 60 Gz radio desig, a paradigm shift has occurred from omidirectioal atea to beamformig atea. Spatial Multiplexig The millimeter wave commuicatio has the advatage of the availability of spatial multiplexig for MIMO liks with moderate atea spacig eve with less scatterig eviromet. This multiplexig helps to icrease the spectral efficiecy at millimeter wave frequecies (Torkildso, E. et al., 011). For a give liear array of costraied size, spatial degrees of freedom for millimeter wave lie-of-sight (LOS) eviromet based system architecture was proposed (Sheldo, C. et al., 008; Sheldo, C. et al., 009). The performace of the proposed architecture i terms of lik capacity was measured i a idoor eviromet. It was foud that the positioig of trasmit ad receive modes play a importat role i the performace ehacemet. Multipath ad MIMO capacity MIMO capacity icreases with rich multipath, i.e spatially ucorrelated chael offers multiple subchaels based o the atea cofiguratio (Kermoal, J.P. et al., 00). But more the umber of multipath, higher is the path loss that leads to reduced SNR. MIMO capacity as a fuctio of SNR, effective degree of freedom that defie the umber of multipaths was aalyzed i (Wallace, J.W. ad Jese, M.A. 003). Apart from the multipath stregth, the agle spread, atea spacig, array topology sigificatly improve the MIMO capacity (McKay, M.R. ad Colligs, I.B. 006; Foreza, B. ad eath, R.W. 005). Path loss compesatio Path loss icrease with icrease i frequecy. The path loss scales as the square of the wavelegth accordig to the Friis formula. Peetratio effects lead to reductio i sigal stregth. Icreasig the atea gai at the trasmitter or receiver compesates the loss. This 14

4 compels the use of highly directive ateae. Fortuately it is easy to sythesize directive ateae for millimetre waves. Lik reliability usig spatial diversity A simple trasmit diversity techique proposed by Alamouti for wireless commuicatio system achieved full trasmit diversity, uity code rate with badwidth efficiecy (Alamouti, S.M., 1998). A geeralised desig for space time block code with orthogoal code matrix facilitatig full trasmit diversity, code rate of ½ ad ¾ were extesively studied ad aalysed (Tarokh, V. et al., 1999). Code rate less tha uity were ot badwidth efficiet but were foud to be suitable i poor scatterig eviromet ad idoor eviromets where highly directive atea is used. Closed loop orthogoal space time block codes (OSTBC) proposed for MIMO systems with more receive atea compared to trasmit atea. This was suggested as a alterative to Alamouti code that holds good for x system yieldig full diversity gai. The closed loop OSTBC is based o the feedback of sigle phase term which is a fuctio of the chael gais. This family of chael orthogoalized STBC is foud to achieve full rate for N=3, 4 receive atea. Thus closed loop OSTBC outperforms the ope loop OSTBC at all SNRs (Milleth, J.K., et al., 004; Milleth, J.K., et al., 006). Depedig o the badwidth ad applicatio, various space time codig schemes have come ito deploymet. Aother variat of space time code was space time trellis code, which is foud to have better codig gai ad diversity gai (Tarokh, V. et al., 1998; Che, Z. et al., 00). Icreasig Multipath for MIMO Primarily multipath occur based o the eviromet, that is excited by the omidirectioal or directioal atea. Secodly, multipath is created by multiple beams radiated from atea array as show i Figure 6.1 below. Lik reliability ad capacity icrease with icrease i multipath ad this shows sigificat advatages over LOS with high SNR. I idoor eviromet sice the propagatio loss ad probability of LOS sigal beig blocked are high, the choice of omidirectioal ad directioal atea is ot cosidered. Atea array serves to address the problem by geeratig multiple beams. This reduces the probability of blockage by obstacles ad compesates for the propagatio losses due to icreased atea gai. 15

5 (a) Figure 6.1 (a) Sigle beam ad (b) Multibeam MIMO i NLOS (b) 16

6 Figure 6.1 shows a typical NLOS cofiguratio based o the siglebeam ad multibeam ateas employed for MIMO, for a idoor eviromet. Our proposed method, such as multibeam based MIMO improves the performace due to large umber of multipaths compared with sigle beam. Rich scatterig, improved atea directivity ad performace with multibeam atea array cofiguratio were cosidered (uag, K-C. ad Wag, Z., 011). The multibeam ateas are atea array that make use of beamformig etwork to produce multiple idepedet beams poitig to differet directios. By offerig idepedet beams, access poit will switch betwee these beams to select the chael that has the highest received power. This feature assists the atea system to maximize the power received i the desired directio (uag, K-C. ad Wag, Z., 011). The directivity of a atea scales iversely as the square of carrier wavelegth. As a result of these directive ateae, the multipath eviromet is much sparser compared to lower carrier frequecies. Directig the ateae at the trasmittig ad receivig ed ca be doe either maually or electroically. Trasmit ad receive beamformig is aother solutio, that aalyses the directio of maximum sigal stregth ad steers the beam i the desired directio. Space time block code (STBC) coupled with mea values of the uderlyig chael matrix serves as a eige beamformer with multiple beams poitig to orthogoal directios ad foud as a attractive choice over oe-directioal beamformig (Zhou, S. ad Giaakis, G.B. 00; Zhou, W. et al., 011). Iterative power method was used to fid the CSI which icreased the complexity (Sharma, V. ad Lambothara, S. 006). Iterative algorithm had slow covergece ad hece maximal orm combiig was used to fid the Chael State Iformatio (CSI) to steer the MIMO beam, which served as a good tradeoff betwee complexity ad performace (Lee,. et al., 009). To ease the receiver complexity i MIMO systems, space time codig with trasmit atea selectio was aalyzed (Coşku, A.F. et al., 01). Also a estimatio of the upper ad lower boud of symbol error rate for Nagakami-m fadig chael have bee performed i (Coşku, A.F. et al., 01). Idoor eviromet predomiate with LOS ad reflected paths, trasmit ad receive beamformig serves as a ideal choice to select a subset of atea elemets. This cosiderably reduces spatial processig (Dog, ke. et al., 011). The CSI fedback from the 17

7 receiver to the trasmitter, selects the trasmitter atea elemets with the help of beamformig etwork. This reduces the requiremet of multiple RF chais (Dog, ke. et al., 011). Time-varyig chaels are better estimated over specific frames by trasmit beamformig ad CSI kow to trasmitter (Martos-Naya, E. et al., 007). Orgaizatio of the work This work addresses the MIMO MMW propagatio i NLOS. Owig to the LOS issues, that do ot esure safe propagatio, atea array with multibeam is cosidered i this work. The multibeam atea sources multipath i additio to the oes geerated i the eviromet. The amplitude ad phase of the multibeam are aalyzed for three differet cases vis-a-vis (i) sigle beam (ii) dual beam ad (iii) geeral N-beam. I this research work, full rate Alamouti code ad uiform liear atea array with beamformig etwork based MIMO cofiguratio is cosidered. The complex weights of the beamformig etwork play a critical role i geeratig the beams with cotrolled iterferece (wag, S-S. ad Lee, Y-. 005). The performace is the compared with the classical x MIMO. 6. Idoor NLOS chael model Shoji, Sawada, Saleh (Triple S) ad Valezuela simply called as Triple SV (TSV) chael model is a cluster based model (Karedal, J. et al., 010; Rao, T. et al., 011). Each cluster is comprised of may rays. This model is cotributed by NICT Japa to the c chael model subgroup. This is a merger of the two-path model ad Saleh-Valezuela (S-V) model. This model was foud to be much suitable for the idoor eviromet because of its capability to describe both the LOS ad No-lie-of-sight (NLOS) compoets (Sato, K. et al., 007; Skafidas, E. et al., 005). The impulse respose of the S-V model takes ito accout oly the complex amplitude of each ray ad the Time-of-Arrival (ToA) iformatio of each ray i a cluster. The impulse respose of modified S-V model cotais AoA iformatio also alog with ToA iformatio (Sawada,. et al., 006; Maoja, S.D. et al., 011). The small scale fadig chael impulse respose of TSV assumig doppler spread to be egligible is give by 18

8 L1 M l 1 h( t) ( t T ) ( ) l0 m0 lm l l, m l l, m (6.1) where h(t) is a complex evelope expressio of impulse respose of received sigal, t ad are ToA ad AoA, respectively, (.) are give by l : cluster umber m : ray umber withi the l th cluster L : total umber of clusters M l : total umber of rays withi the l th cluster T l : arrival time of the first ray of the l th cluster l,m l,m meas delta fuctio. The parameters i CIR of TSV : delay time of the m th ray withi the l th cluster relative to the first ray arrival time T l l Uiform (0, ]: arrival agle of the first ray of the l th cluster : arrival agle of the m th ray withi the l th cluster relative to the first ray arrival time The amplitude i impulse respose is give by l, m 0 e T l e l, m k[1 ( m)] Gr ( 0, l l, m ) (6.) l, m Uiform(0, ] where Ω o is the mea value of amplitude of the first comig wave of the delayed wave, k is the coefficiet used to take the Ricia-factor for each cluster ito accout G t directivity fuctio of the trasmittig atea G r directivity fuctio of the receivig atea 19

9 Figure 6. Time dispersive characteristics of TSV chael model The Figure 6. shows the time dispersive TSV chael, where Λ is cluster arrival rate, λ is ray arrival rate, Г is cluster decay factor, ad γ is ray decay factor. The assumptios i modelig the chael are there will be limited scatterers, brick walls, widow paes, floor ad ceilig all of which cotribute to diffractio, scatterig ad reflectio. Clusters formed deped o the type of eviromet. The umber of clusters ad rays withi a cluster are limited to four ad te as the amplitude levels of these clusters are withi the receiver sesitivity. As the umber of reflectios per ray icreases, the correspodig amplitude of the ray decreases, due to reflectio loss ad free space loss. ece, the ray amplitude depeds o room dimesios ad the magitude of reflectio co-efficiet. Figure 6.3 shows the power delay profile for 10 chael realizatios. The PDP i Figure 6.3 idicates the cluster model of the TSV chael. The NLOS compoets with cluster power distributio limitig the umber rays to 10 i oe cluster is evidet i Figure 6.3. The maximum chael realizatios supported i TSV is 100, for computatioal simplicity the umber of rays was limited to 10. Each cluster has a expoetial decrease i power. The umber of clusters depeds o the superstructure of the room, floor ad ceilig material (Kirthiga, S. ad Jayakumar, M. 011). 130

10 Figure 6.3 Power delay profile for 10 chael realizatios Small scale fadig effects domiated by multipath delay spread is aalyzed i Figure 6.3. The aalysis icludes the estimatio of the time dispersive parameters i.e RMS delay spread (RDS), maximum delay spread ad mea excess delay. The estimated values serve as a referece to fix the trasmitted symbol period i order to realize frequecy flat fadig chael i.e trasmitted symbol period has to be much greater tha RDS. The power delay ad agle profile are depicted i Figure 6.4. The power of multipath compoets withi the cluster is the same with variatios i ToA ad AoA. ToA ad AoA statistics closely relate to the ature of the propagatio eviromet. PDP for a specific chael i idoor eviromet have bee studied extesively (olloway, C.L. et al., 1999). Figure 6.4 shows the PDP of te chaels with three clusters ad LOS. The decay characteristics of PDP ca be correlated to the effects of variable idoor values ad properties of the surfaces. 131

11 Figure 6.4 Power delay profile as a fuctio of ToA ad AoA iformatio. AoA iformatio provides immediate isight ito local area fadig characteristics, also the positio of the source ca be calculated. The LOS compoet i Figure 6.4 has power of -70 db with ToA 50 s ad AoA 90 o ad this compoet acts as a referece for the NLOS AoA computatio. The effect o spatial correlatio of multipath compoets (MPC) with AoA betwee 50 o ad 180 o that comprise oe cluster is the same as they have same sigal power but the effect o agle spread is differet. Agle spread rages betwee 0 ad 1, value 0 idicates the MPC come from sigle directio while value 1 idicates differet directios, that leads to reduced correlatio. igher the agle spread, lesser is the spatial correlatio (Tag, Z. ad Moha, A.S. 006). The agle spread depeds o the spatial separatio betwee the atea ad for NLOS idoor it varies betwee 0.63 ad 0.81 (Xu,. et al., 00). From Figure 6.4, the cluster power idicates the ifluece of ear ad far field scatterers, that cotribute to varyig AoA ad ToA with arrow ad wide agle spread. The path traced by the reflected rays is too log such that the overall power is reduced with icrease i ToA. The ToA from Figure 6.4 is foud to vary betwee 110 ad 90 s. 13

12 6.3 Millimeter Wave MIMO chael model The spatial isolatio due to oxyge absorptio at 60 Gz is beeficial for frequecy re-use i a idoor dese etworks, ehaces the safety ad security of the liks ad reductio i cochael iterferece. The uderlyig propagatio chael imparts blockages to the multipath sigal, to couter this effect MIMO spatial diversity is used. The classical x MIMO cofiguratio for NLOS is aalyzed. The classical MIMO for millimeter wave is aalyzed with TSV chael model. The capacity achieved with multiatea over the same badwidth ad costat trasmit power is compared to the sigle atea system. The trasmitter ad receiver show i Figure 6.5 has the iformatio source modulated ad ecoded usig space time block code (STBC) ito a code trasmissio matrix. The two trasmit atea with Alamouti STBC is used, as the scheme which achieves full trasmit diversity, full rate ad is badwidth efficiet (Alamouti, S.M., 1998). The orthogoal trasmissios esure full trasmit diversity of M T where M T is the umber of trasmit atea. The code trasmissio matrix S is give by the dot product of the rows is zero, where s 1 ad s are the modulated symbols, s S s 1 * s 1 ad * * 1 s s, * s are the complex cojugate of s 1 ad s. As the rows are orthogoal, full trasmit diversity is obtaied i.e. SS s1 s I MT, where I M is the idetity matrix of size M T T x M T. The code rate which is the ratio of umber of trasmit symbols to the total umber of time slots i.e R l m, where l is the umber of trasmit symbols ad m is the umber of time slots is uity. I Alamouti scheme, as l= ad m=, the code rate R equals uity, which idicates the code is badwidth efficiet (Jakirama, M. 004). I the receiver, chael estimatio usig TSV chael model is doe. Orthogoal traiig symbols are used to trai the receiver to perform better i faded chaels. The traiig based chael estimatio, traiig symbols are kow at both trasmitter ad receiver ad from the output at the receiver, chael estimatio is doe (Biguesh, M. ad Gershma, A.B. 006; Che, Y. ad Su, Y.T. 010). Block cotaiig both traiig symbols ad data are set (assibi, B. ad Areaochwald, B.M.. 003). 133

13 Desired Iterferece Iformatio source BPSK Modulatio ML Detector Zero Forcig Equalizer Chael estimatio (Least Squares) h 11 Alamouti Space time coder h 1 h 1 Combier h Figure 6.5 MIMO trasmitter ad receiver with spatial diversity Optimum umber of traiig symbols with eough data comprises a block. If more amout of traiig symbols are set, the oly less data ca be trasmitted leadig to spectrum iefficiecy so a tradeoff has to be maitaied which results i good estimate of chael ad also ot compromisig o data rate. Durig the trasmissio of the data the chael is assumed to be costat. The PDP of the TSV is used to calculate the delay spread. The delay spread serves as a referece to calculate the symbol time Calculatio of symbol period with delay spread parameter The PDP i Figure 6.3 is aalyzed to determie the symbol period. As the symbol period has to be greater tha the delay spread for flat fadig characteristic. RMS delay spread usig equatio (4.1) ad equatio (4.) is determied. The RMS delay spread is foud to be 10s. Sice the symbol period should be at least greater tha te times the RMS delay spread, the symbol period is take as 1ms ad hece block legth size is fixed as 1000 bits i.e 134

14 chael is assumed to be costat for this period. Based o this block size, the chael is estimated Combier The multiple copies of the same sigal are liearly combied to icrease the SNR of the received sigal. The three techiques amely selectio gai combiig, equal gai combiig ad maximal ratio combiig are the liear combier techiques. Selectio gai combiig selects the sigal with maximum SNR ad it is further processed by the receiver. Equal gai combiig, combies all the sigals with equal gai which is the processed. Maximal ratio combier weights the received sigal ad the combies for further processig. MRC is preferred as the phase shifts ecoutered by the sigals are co-phased before combiig operatio. This icreases the SNR. The chael estimatio of the combied sigal is performed later Chael estimatio Least Square chael estimatio The MMW MIMO chael is a frequecy flat with delay spread smaller tha the symbol period as discussed i sectio ad slow fadig with doppler spread smaller compared to trasmitted sigal badwidth as i equatio (6.1). Flat slow fadig chael are best estimated usig LS ad MMSE techiques. Traiig symbols formig part of the trasmissio are used for estimatig the chael. The complex received sigal vector is expressed as y = s+, where s is the traiig symbol of size M T x 1. To estimate the chael matrix, let N M T traiig sigal vectors [s 1, s,..s N] be trasmitted. The correspodig M R x N matrix Y = [y 1, y y N ] of the received sigal is expressed i equatio (6.3). The LS method does ot require kowledge of the chael parameters ad hece is a little less efficiet (Biguesh, M. ad Gershma, A.B. 006). I LS, chael estimates are foud by miimizig the followig squared error quatity ^ Y S (6.3) S Y S Y S Y S ^ S Y 135 S S Y Y Y

15 where Y is the received sigal, S is the traiig symbol matrix S= [s 1, s,..s N ] of size M T x N ad ^ is the estimate of, After differetiatig with respect to S ^ ^ ad equatig it to zero, is obtaied S S Y 1 S S S Y (6.4) The give solutio is further simplified to Where K = S S ^ 1 S K Y MMSE chael estimatio The chael estimate obtaied usig LS is used i MMSE, to calculate the chael correlatio R. A liear estimator that miimizes mea square error (MSE) of is expressed as MMSE =YA o (6.5) Where Y is the output whe traiig symbols are trasmitted ad A o has to be obtaied so that the MSE is miimized (Biguesh, M. ad Gershma, A.B. 006). A o ^ arg mi E F A arg mi E o YA F (6.6) From equatio (6.6) the estimatio error ca be expressed as E{ YA F } Differetiatig equatio (6.7) with respect to A, A ( S o R P M R I) 1 S R (6.7) (6.8) Usig equatio (6.8) i equatio (6.5), the liear MMSE estimator ca be writte as 136

16 where R is the chael correlatio matrix, Squared Frobeius orm. ^ MMSE Y( S R S M R (6.9) - Noise vector at the receiver,. F is the From the expressios of both the techiques it ca be foud that MMSE chael estimate takes both the chael correlatio matrix ad oise vector at the receiver which results i a better estimate whe compared to that of LS estimate. Equalizatio is performed o the chael estimate followed with decodig. BER ca be calculated for various values of SNRs. I) 1 S R Maximum Likelihood (ML) decoder The ML decoder computes the squared euclidea distace betwee the received sigal ad the various combiatios of the trasmitted sigal to estimate the trasmitted sigal (Alamouti, S.M., 1998). The ML priciple is give as ^ s arg s { s,... } mi 1 s s y s k k MT where y is the received sigal, is the chael matrix ad s is the trasmitted sigal. The search space beig 4 for x MIMO system with trasmitted data modulated usig BPSK. 6.4 Multibeam MIMO At MMW rage, multibeam atea systems are widely used with multibeam patters formig i space ad providig probig sigal trasmissio i the set of desired directios. This serves to address the MMW propagatio i NLOS coditios. Mathematically, the multibeam is realized by its weight vectors ad the directio varies accordig to the weight vectors. Multibeam MIMO is aalyzed for three special cases (i) Sigle beam MIMO (ii) Dualbeam MIMO ad (iii) Geeral N-beam MIMO Sigle beam MIMO For simplicity i performace aalysis, a x MIMO system is cosidered. The iformatio source is modulated ad ecoded usig Alamouti STBC that gives two symbols [x 1, x ] i a specific time slot (Jakirama, M., 004). 137

17 Iput Data Beamformig Network TSV Chael ML Detector Demodulator h 11 QPSK Modulatio w 11 w 1 Equalizer STBC Ecoder Liear Combier Chael Estimatio h w 1 w Data from STBC ecoder w 11 w Atea elemets Corporate feed Digital phase shifter Figure 6.6 (a) MIMO with sigle beam trasmitter ad sigle beam receiver ad (b) Atea array of λ\ spacig with same amplitude, same frequecy ad equal phase 138

18 The coded symbols are fed to the atea array that geerates sigle beam per array with the help of beamformig etwork (BFN) as show i Figure 6.6. The weight vectors of the BFN are of the same amplitude, frequecy ad equal phase, so as to geerate sigle beam. This aalysis is the same as the classical x MIMO, which has bee discussed i sectio 6.3. The radiatio patter obtaied with the atea array is show below gai (db) Figure 6.7 Sigle mai lobe ad back lobe obtaied usig weight vectors of the same amplitude, frequecy ad equal phase. Figure 6.7 shows the sigle beam geerated usig atea array i Figure 6.6b where the weight vectors w 11 ad w 1 are of the same amplitude, frequecy ad equal phase. 139

19 6.4. Dualbeam MIMO For simplicity i performace aalysis, a x MIMO system with dualbeam is studied. The system model for the proposed cocept is depicted i Figure 6.8a ad Figure 6.8b. The iformatio source is modulated ad ecoded usig Alamouti code geeratig two symbols [x 1, x ]. The basebad symbols are the processed by the RF module ad fially by the beamformig etwork. The iput data to the beamformer has to be esured zero degree phase shift. This is required to geerate two beams. The weight vector of the beamformig etwork is 180 degree out of phase as to reduce the iterferece betwee the beams. The weights are assumed out of phase so as iclude a ull betwee the two beams which also reduces the iterferece betwee the beams. Iput Data Beamformig Network TSV Chael ML Detector QPSK Modulatio w 11 w 1 h 11 Demodulator Equalizer STBC Ecoder q 11 h Liear Combier Chael Estimatio w 1 w q (a) The atea array show i dotted lies is expaded i Figure 6.8b. 140

20 Data from STBC ecoder w 11 w Atea elemets Corporate feed Digital phase shifter (b) Figure 6.8 (a) MIMO with dualbeam trasmitter ad siglebeam receiver ad (b) Atea array of λ\ atea spacig with out of phase feed cofiguratio (w 1 = -w 11 ) I Figure 6.8, the dualbeam of each atea pair is defied by weight vectors w 1 = [w 11, w 1 ] T for the first atea pair ad w =[w 1,w ] T for the secod atea pair ad the TSV chael co-efficiet are h 11, q 11, h, q. Geeratio of radom beams is cosidered where the multiple beams iterfere i a cotrolled level. Orthogoal beams do ot provide eough capacity gai so radom beam geeratio through multi-user diversity ad multiplexig (MUDAM) scheme is cosidered (wag, S-S ad Lee, Y-., 005). The radom weight vector w 1 is give by jm,1 m=1, (6.10) w m e,1 m,1 Where α Amplitude of the beam varies from 0 to 1 θ Agle of beam varies from 0 to π. The four atea elemets i Figure 6.8b, geerate two beams. RF sigal x 1 is fed to atea elemets 1,,3 ad 4. Weights of the atea elemets 1 ad are w 11 ad w 1 is the weight of the atea elemets 3 ad 4. w 1 is cosidered 180 o out of phase with respect to w 11. The weight vector W is also geerated usig equatio (6.10) ad this processes RF sigal x. As CSI is ukow at the trasmitter, equal power is allocated to all the atea elemets. The 141

21 dual beam radiatio patter obtaied usig beamformig etwork (BFN) ad atea array is show i Figure gai (db) Figure 6.9 Two mai lobes ad two back lobes obtaied usig out of phase weight vectors. Geerally, x MIMO systems have chael matrix with x elemets, so the output at the receiver is give by y = x + (6.11) Where x is the data trasmitted ad is the additive white Gaussia oise. I the proposed work with two sets of dualbeam, four paths exist betwee the trasmitreceive pair, hece chael matrix i dualbeam comprises of eight elemets [h 11, q 11, h 1, q 1, h 1, q 1, h, q ]. ere, h 11 is chael see by the first beam of the first trasmit atea array ad received by 1 st receive atea ad q 11 is chael see by the secod beam of the first trasmit atea array ad received by the first receive atea as show i Figure 6.8a. Similarly, h is chael see by the first beam of the secod trasmit atea array ad received by 1 st receive atea ad q is chael see by the secod beam of the secod 14

22 trasmit atea array ad received by the secod receive atea as show i Figure 6.8a. The remaiig chael co-efficiets h 1, q 1, h 1 ad q 1 act as iterferece co-efficiets. Thus the dualbeam MIMO has four desired paths ad four iterferece paths that icrease the diversity gai from four i classical x MIMO to eight i the proposed system. Cosiderig receiver i Figure 6.8a, the received sigal y 1 by the first receive atea is y 1 = h 11 x 1 w 11 + q 11 x 1 w 1 + h 1 x w 1 + q 1 x w + 1 (6.1) STBC ecoded data Iterferece from AWGN Noise secod trasmit atea array Where h 11, h 1 q 11, q 1 x 1, x w 11 w 1 w 1 w y 1 - Elemets of chael matrix - Elemets of chael matrix Q - RF sigal - Weight vector W 1 of first trasmit atea array - Weight vector W of secod trasmit atea array - Received sigal of first atea Thus the received sigals i dualbeam MIMO trasmitter with sigle beam receiver is as follows y 1 = h 11 x 1 w 11 + q 11 x 1 w 1 + h 1 x w 1 + q 1 x w + 1 y = h 1 x 1 w 11 + q 1 x 1 w 1 + h x w 1 + q x w + Puttig the above equatios i matrix form y y h11w h1w q q 11 1 w w 1 1 h h 1 w w 1 1 q q 1 w w x1 x1 1 x x Therefore, the received vector ca be expressed as y = Bx + (6.13) Where y is x1 vector, B = [ Q] is x4 chael matrix, x is 4x1 vector ad is x1 vector 143

23 So this gives a improved diversity gai to the system with multiple copies set at differet paths ad havig maximal ratio combier (MRC) ad chael estimatio implemeted at the receiver, the performace certaily ehaces at the decoder. Diversity gai for the proposed dualbeam MIMO is 8 obtaied from M T M R, where is the umber of atea elemets per array which is, M T umber of trasmit atea equal to ad M R is the umber of receive atea equal to (M T M R =4x=8). The diversity order of dualbeam x MIMO is two times greater tha that of the classical x MIMO. This sigificatly improves the power gai ad lowers the error rate. Selectio combiig is to the elemets what switched beamformig was to beams. As each elemet is a idepedet sample of the fadig process, the elemet with the greatest SNR is chose for further processig. I selectio combiig therefore, 1 max w 0 otherwise (6.14) Sice the elemet chose is the oe with the maximum SNR, the output SNR of the selectio diversity scheme is max, where γ is the SNR of idividual brach. Such a scheme would eed oly a measuremet of sigal power, phase shifters or variable gais are ot required. I the above formulatio of selectio diversity, the elemet with the best SNR is chose. This is clearly ot the optimal solutio as sigals with low SNR are igored. But, maximal ratio combiig (MRC) obtais the weights that maximize the output SNR, i.e., it is optimal i terms of SNR. MRC is applied to equatio (6.13) by weightig the received sigal ad its output is R. The weights take care of the SNR of the received sigal. R G Y G BX G N (6.15) where G is the weight of each brach of dimesio x4, the weights are chose i such a way that the MRC produces the largest possible value of istataeous output sigal-to-oise ratio (Jakirama. M. 004; ayki. S. ad Moher. M, 005). 144

24 145 The istataeous output SNR γ c of MRC is R R M M j o X c g e b g N E 1 1 (6.16) Where E x /N o is the symbol eergy to oise spectral desity ratio, the row vectors of the weight matrix G ad chael matrix B are idicated as g ad b, be jθ is the chael fadig compoet i.e. magitude ad phase. As γ c is to be maximized, which is carried out usig stadard differetiatio procedure, recogizig that the weightig parameter G is complex, a simpler procedure based o Cauchy Schwarz iequality is used. Applyig Cauchy-Schwarz iequality to istataeous output SNR i equatio (6.16) (ayki. S. ad Moher. M, 005). R R R M M M j x c g e b g N E (6.17) Cacellig commo terms i equatio (6.17) yields M R o x c b N E 1 (6.18) Equatio (6.18) proves that i geeral γ c caot exceed where o x b N E. The equality i equatio (6.18) holds for R j j M where e cb e b c g... 1, ) ( *, c is some arbitrary complex costat. Equatio (6.18) defies the complex weightig parameters of the maximal ratio combier. The weight values of G matrix are proportioal to the chael amplitude B ad a phase that cacels the chael phase to withi some value that is idetical for all M R braches. Thus permittig coheret additio of the M R receiver outputs by the liear combier. Equatio (6.18) with the equality sig defies the istataeous output sigal-to-oise ratio of the MRC which is writte as

25 M E R x MRC b (6.19) No 1 Thus the MRC produces a istataeous output sigal-to-oise ratio that is the sum of the istataeous sigal-to-oise ratios of the idividual braches M R (6.0) MRC 1 The MRC is the most optimal diversity combiig scheme at the receiver to improve the performace of the system. The combier output is the processed by the chael estimatio ad chael equalizatio. MMSE chael estimatio based o traiig symbols is performed. The secod order chael statistics ad oise are accouted i MMSE chael estimatio. Zero forcig equalizatio discussed i sectio 4.3 is used to equalize the chael effects. As the codes used for spatial diversity is liear, ML decoder is used. ML decoder computes the Euclidea distace betwee the received sigal ad the actual sigal (Jakirama, M. 004) Geeral N-beam MIMO The system model i Figure 6.8a ad Figure 6.8b is cosidered. The iformatio is space time ecoded usig Alamouti code ad fed to the RF module. The arbitrary phase of the RF sigal whe fed to the beamformer, leads to multibeam geeratio. Except for the arbitrary phase of the icomig RF sigal, the aalysis of N-beam is the same as that of dual beam. More the umber of beams, larger is the umber of multipaths. The probability of sigal loss due to blockages is reduced as the multibeam itroduces NLOS paths. As a tradeoff betwee trasmit power ad computatioal complexity, our aalysis was restricted to dualbeam. 146

26 gai (db) Figure 6.10 Multiple mai lobes ad multiple back lobes obtaied usig weight vectors of radom phase i.e 45 o Figure 6.10 shows the three beams geerated usig the atea array i Figure 6.6b with weight vectors of radom phase 45 o Relatio betwee scatterig eviromet ad atea spacig The chael matrix of the multibeam atea varies depedig o three cases (i) critically spaced (ii) desely spaced ad (iii) sparsely spaced. The atea spacig for idoor system depeds o the scatterig mechaism. If the scatterig eviromet is rich eough the scattered waves comig from all directios ca be easily resolved whe the atea spacig is λ\. If the scatterig is clustered i certai directios the the atea spacig has be greater tha λ\. Atea spacig less tha λ\ caters to directioal chaels i.e chael that use high gai directioal atea. The spatial degrees of freedom icrease with less spatial correlatio betwee the chaels. Spatial correlatio is miimum for atea spacig equal to λ\, hece this icreases the rak of the chael matrix ad equals the umber of receiver 147

27 atea. Thus the chael matrix achieves the full rak coditio i critically spaced case for idoor eviromet. 6.5 Results ad Discussio Classical ad Multibeam MIMO performaces are aalyzed for a idoor eviromet. More the umber of multipaths, better the system performace i.e fadig is completely mitigated i the presece of ifiite diversity (Paulraj, A., 003). I this work, multipath is itroduced i the form of spatial diversity ad multiple beams i additio to that provided by propagatio mechaisms such as scatterig, reflectio ad shadowig. The classical MIMO ad multibeam MIMO are simulated usig radom samples draw from the uiform distributio ad oise sigal is geerated usig ormal distributio of zero mea ad uit variace. The samples draw from the distributio are take to be equiprobable for simple ad efficiet decodig Classical x MIMO ad Sigle beam MIMO performace aalysis usig TSV A x MIMO of diversity gai 4 is aalyzed usig TSV chael. The parameters i Table 6.1 are cosidered for the simulatio. These parameters hold good for aalysis of oe case i multibeam MIMO amely sigle beam. Simulatio parameter Iput data Modulatio scheme Value Code rate of STBC 1 Trasmittig Atea Receivig Atea Separatio betwee the trasmit ad 3m receive ateas as per NICT stadard Tx ad Rx beamwidth 30 o 10 6 bits MPSK TSV Chael Realizatios 10 Combier MRC Chael estimatio LS ad MMSE Equalizer Zero Forcig Decoder ML Table 6.1: Simulatio parameters used i x MIMO usig TSV chael Table 6.1, specifies the parameters used to model the trasmitter ad receiver of classical MIMO ad sigle beam x MIMO ad 4x4 MIMO. BPSK is used sice spectral efficiecy 148

28 BER is ot matter of cocer as MMW has huge badwidth ad esures reduced probability of error. Alamouti code of code rate uity is cosidered to esure orthogoal space time code. The trasmit ad receive beamwidth of 30 o is maitaied to esure directioal beam. The te chael realizatios esure that the delay spread does t exceed the symbol period i order to realize flat fadig chael. The reaso behid cosiderig combier, chael estimatio, equalizatio ad detectio techique is explaied i sectio 6.3., sectio ad sectio LS MMSE Eb/No,dB Figure 6.11 x MIMO usig LS ad MMSE techiques employig BPSK modulatio usig TSV model. The orthogoal traiig symbols are used to trai ad track the chael. The chael characterisitics depicted i Figure 6.4 are estimated usig LS ad MMSE. The chael is assumed to be costat for a block of 1000 symbols, the block size was determied from the parameters obtaied i Figure 6.3. I Figure 6.11, at SNR greater tha db, 149 MMSE performs better compared to LS. This is due to the fact that the chael correlatio ad oise are accouted while computig the chael estimate usig MMSE, whereas i LS it is ot so, as expected i sectio

29 Diversity gai icreases with icrease i umber of atea, but the icrease i atea leads to iterferece. Tradig off iterferece with diversity gai, a optimum multiatea cofiguratio i.e 4x4 is cosidered. I Figure 6.1, the parameters i Table 6.1 are used except that the umber of trasmittig ad receivig atea is 4. This aalysis is performed for classical 4x4 MIMO system. Figure 6.1 4x4 MIMO usig LS ad MMSE techiques employig MPSK modulatio usig TSV model. Complex code matrix (Tarokh, V., 1999) is used for 4x4 cofiguratio. As the desig of the code matrix satisfies orthogoality criteria, the space time ecoder acheives full trasmit diversity, which is 4 equallig the umber of tramit atea. But the code rate R is 1/ with umber of trasmittig symbols equal to 4 ad umber of time slots equallig 8 ad hece badwidth is foud iefficiet. The above features eables liear processig i the receiver with MRC liear combier ad ML decoder computig the decisio metric usig the squared euclidea distace betwee the received sigal ad the weighted output versios of the combier. 150

30 6.5. MIMO dualbeam trasmitter ad siglebeam receiver usig TSV ad Rayleigh Multibeam MIMO special case dualbeam is aalysed. More the umber of beams, more is the umber of multipaths, but this leads to reductio i SNR ad icreased computatioal complexity. As a tradeoff betwee SNR ad computatioal complexity, dualbeam MIMO is studied. A MIMO x with dualbeam trasmitter of diversity gai 8 is cosidered ad its performace aalysed usig TSV ad Rayleigh chael models usig parameters i Table 6.. Simulatio parameter Value Iput data 10 6 bits Trasmit Atea Array ( atea elemets per array with λ/ spacig) Weight vector of the atea elemets (w 11,w 1 ad w 1, w ) Equal amplitude ad 180 degree out of phase Receivig Atea Separatio betwee the trasmit ad 3m receive ateas as per NICT Tx ad Rx beamwidth 30 o ad 60 o Modulatio BPSK Code rate of STBC 1 Chael TSV ad Rayleigh Chael Realizatios 10 Diversity Liear Combier MRC Chael Estimatio Equalizer Decoder LS Zero Forcig ML Table 6.: Simulatio parameters used i dualbeam MIMO usig TSV ad Rayleigh chael The parameters discussed as part of Table 6.1 is applicable to Table 6., except that each trasmit atea is replaced with atea array whose weight vectors are 180 o out of phase to reduce iterferece betwee the beams as discussed i sectio The directivity of the trasmit ad receive atea is esured sice the beamwidth are 30 o ad 60 o respectively. Sice Rayleigh chael is the most widely used model for NLOS eviromet, the performace of the dualbeam MIMO usig TSV ad Rayleigh is compared. 151

31 BER Dualbeam MIMO x usig Rayleigh Dualbeam MIMO x usig TSV Figure 6.13 x MIMO dualbeam trasmitter ad siglebeam receiver usig TSV ad Rayleigh chael. Figure 6.13 aalyses the performace of the proposed desig usig TSV ad Rayleigh chael model. I Figure 6.13, the performace of dualbeam MIMO usig TSV is better compared to dualbeam MIMO usig Rayleigh. Typically at high SNR, spatial correlatio betwee the atea elemets reduces the rak of the chael matrix ad leads to Iter Symbol Iterferece (ISI). TSV compared to Rayleigh is cluster based model, whose chael impulse respose takes ito accout the LOS ad NLOS alog with ToA ad AoA of ray ad cluster discussed i sectio 6.. The respective power delay ad power agle profiles are depicted i Figure 6.3 ad Figure 6.4. Eb/No (db) The agle spread i Figure 6.4 is a clear idicatio of well coditioed idoor chael. The smaller the agle spread, more is the spatial correlatio which teds to reduce the MIMO chael capacity (Jakirama, M. 004; Paulraj, A. et al., 003). The clusterig effect i TSV model spreads the AoA ad hece performace of dualbeam MIMO usig TSV is better 15

32 compared to dualbeam MIMO usig Rayleigh. This is evidet from Figure 6.13, BER of 10-3 at.5 db is achieved with TSV as agaist 4.5 db with Rayleigh. The correlatio effect ca be reduced with Rayleigh model with λ/ atea elemet spacig. Thus for high atteuatio, rich scatterig idoor eviromet, dualbeam MIMO usig TSV is foud to be a better choice compared to dualbeam MIMO usig Rayleigh Compariso of MIMO dualbeam ad Classical MIMO usig TSV The proposed dualbeam performace is compared with classical MIMO uder the assumptio that CSI is ukow to the trasmitter. The orthogoal space time code of uity code rate ad full trasmit diversity ad parameters i Table 6.3 are cosidered. Simulatio parameter Value Iput data 10 6 bits Trasmittig Atea Array ( atea elemets per array with λ/ spacig) for dualbeam MIMO cofiguratio. ateae for classical MIMO cofiguratio. Receivig Atea Separatio betwee the trasmit ad 3m receive atea as per NICT Tx ad Rx beamwidth 30 o ad 60 o Modulatio BPSK Code rate of STBC 1 Chael TSV Chael Realizatios 10 Diversity Liear Combier MRC Chael Estimatio LS Equalizer Zero Forcig Decoder ML Table 6.3: Simulatio parameters used i dualbeam MIMO ad Classical MIMO The parameters discussed i Table 6. is applicable for Table 6.3 except that the trasmit atea with ad without atea array usig TSV is aalyzed. 153

33 BER Classical MIMO x Dualbeam MIMO x Eb/No (db) Figure 6.14 Bit Error Rate of Dualbeam MIMO ad Classical MIMO usig TSV The dualbeam MIMO with trasmit atea array uses Alamouti code (Alamouti, S.M., 1998). The receiver decodes the trasmitted symbol after two trasmissio periods. The umber of idepedet paths betwee the trasmitter ad receiver for dualbeam MIMO is 8, as the elemets i the atea array have out of phase feed cofiguratio. This leads to geeratio of two beams from atea array. I the case of classical MIMO umber of idepedet paths is 4. The dualbeam exhibits a power gai of 1.6dB compared to classical sigle beam MIMO. It is oted i Figure 6.14, that at a BER of 10-3, the proposed dualbeam MIMO gais about 1.6 db relative to the classical MIMO, which ca be further improved if CSI is kow to the trasmitter. 154

34 MIMO cofiguratio x Classical MIMO usig TSV Sigle beam MIMO usig TSV Dual beam MIMO usig TSV Dual beam MIMO usig Rayleigh E b /N 0 5 db 8 db 5 db 8 db 5 db 8 db 5 db 8 db BER Table 6.4 Compariso of Classical ad Multibeam MIMO A simple x cofiguratio is cosidered for comparig classical ad multibeam MIMO with TSV chael model. Also, dualbeam MIMO usig TSV ad Rayleigh chael model is aalyzed. From Table 6.4, reductio i BER is observed i dualbeam because the two beams carryig the same data iterfere less with each other due to the ull betwee them. Ad the same fact cotributes to two paths from the trasmitter i the place of oe path as i the case of classical ad sigle beam trasmitter. Aalysis of x is performed owig to the fact of reduced complexity ad optimal trasmit power compared to other multibeam cofiguratios. 6.6 Coclusio ad Cotributio The dualbeam MIMO is the first of its kid proposed for MMW bad with simple modulatio scheme i.e BPSK is chose. As atteuatio ad huma blockages reduce the sigal stregth, either high gai atea or adaptive atea array were used to improve the sigal receptio. igh gai atea is suitable if LOS coditio is guarateed while adaptive atea array has propagatio delay issue which was of major cocer i high defiitio video streamig (Yog, S.K. ad Chog, C-C. 007). ece as a solutio to the above problems, trasmit beamformer based atea array was proposed with equal power allocatio for the atea elemets. I idoor eviromet, with the ifluece of strog LOS ad reflected paths usig directive atea is preferred. But sice the obstacles idoor provide rich scatterig eviromet, use of MIMO system with trasmit beamformig is cosidered. The trasmit diversity for x system is exploited with respect to STBC ad dualbeam geerated usig atea array with two elemets per array with out of phase feed 155

35 cofiguratio. The dualbeam with trasmit beamformig ad STBC has give diversity gai of 8 as agaist the diversity gai of 4 achieved usig classical MIMO. The performace of dualbeam x MIMO has a power gai of 1.6 db compared to classical MIMO. The performace study of dualbeam MIMO usig TSV ad Rayleigh was also carried out. I low E b /N 0 rage, with oly receiver havig the kowledge of CSI, the dualbeam performace usig TSV is better compared to Rayleigh with a power gai of db. This is attributed to the fact, that TSV beig cluster based model, cosiders wide agle spread clusters that geerates almost full rak chael matrix, reducig correlatio betwee the chael elemets. Also, with desig criteria of beams satisfyig out-of phase coditio, the receiver decouples the trasmitted streams ad better estimate of the trasmitted sigal is obtaied. This work fids applicatio i fixed wireless access (FWA). The aalysis ad the results idicate a low complex receiver with dualbeam trasmit atea achieves cosiderable improvemet i performace whe the idoor chael is modeled usig TSV. 156