Design and implementation of a testbed for indoor mimo systems

2.1.2 Rank and Condition number... Eigenvalues for 3x3 IMIMO system as a function of deviation factor in dB forpure LOS channel Figure 6.. The capacity of MIMO system... R ecent1 Selecti

V I E T N A M N A T I O N A L U N I V E R S I T Y H A N O I

C O L L E G E O F T E C H N O L O G Y

VU XUAN THANG

DJEDESIGN AND IMPLEMENTATION OF A TESTBED

FOR INDOOR MIMO SYSTEMS

A C K N O W L E D G E M E N T

I w o u l d like to g i v e a w a r m th a n k to Prof N g u y e n D in h T h o n g a n d Dr T rin h A n h V u,

m y s u p e r v is o r s , fo r th e ir c o n s id e r a b le h elp in m y ti m e s tu d y in g m y m a ste r 1 w o u ld like to t h a n k m y c o l le a g u e s , fa m ily and frie n d s for th e ir u n b e n d i n g s u p p o r t and

e n c o u r a g e m e n t

C O N T E N T S

A b s t r a c t

A b b r e v i a t i o n s

L ist o f F i g u r e

C h a p t e r 1 I n t r o d u c t i o n 1

C h a p t e r 2 M I M O m o d e l s a n d c h a r a c t e r i s t i c s .4

2.1 M a t h e m a t i c a l M I M O m o d e l .4

2.1.1 C a p a c i t y v ia S in g le V a l u e D e c o m p o s i t i o n 4

2 1 2 R a n k a n d C o n d i t i o n n u m b e r 6

2 2 P h y s ic a l M I M O m o d e l 7

2.2.1 L i n e o f s ig h t S I M O 8

2 2 2 L i n e o f s ig h t M 1 S O 9

2 2 3 A n t e n n a a r r a y s w ith o n ly L O S p a t h 10

2.3 K e y p a r a m e t e r s in M I M O c h a n n e l 1 1 2.3.1 A n t e n n a s e p a r a t i o n 1 1 2 3 2 R e s o lv a b ili ty in th e a n g u l a r d o m a i n 15

2 4 A n t e n n a S e le c tio n A l g o r i t h m s 16

C h a p t e r 3 M I M O T e s t b e d f o r i n d o o r e n v i r o n m e n t 21

3.1 A s u r v e y o f M I M O T e s t b e d d e s i g n 21

3.1.1 T h e M I M O T e s t b e d at V i e n n a U n i v e r s i t y .21

3 1 2 T h e M I M O T e s t b e d at B r i g h a m Y o u n g U n i v e r s i t y 21

3.1 3 T h e M I M O T e s t b e d at T h e U n i v e r s i t y o f B ris to l 22

3 1 4 T h e M I M O T e s t b e d at A l b e r t a U n iv e r s it y 22

3.2 D e s i g n T o o l s .22

3.2.1 X i l i n x X t r e m e D S P V ir te x - 4 K i t 22

3 2 2 S y s te m G e n e r a t o r 2 7 3 2.3 I S E S o f t w a r e 2 9 3.3 T e s t b e d D e s c r ip ti o n 30

3.3.1 R F M o d u l e 3 0 3 3 2 D ig it a l T r a n s m i t t e r 32

3 3.3 D ig ita l R e c e i v e r 35 3.3.3.1 T i m i n g S y n c h r o n i z a t i o n .3 6

3 3 3 2 C o r r e la tio n B l o c k .36

3 3 3 3 M a x i m u m S e l e c t o r 37

3 3 3 4 S ig n a l D e te c tio n B lo c k 38

3 3 3 5 S y n c h r o n i z a t i o n D e t e c t o r 39

C h a p t e r 4 I m p l e m e n t i n g R e s u l t s o f M I M O T e s t b e d .41

4.1 R F I m p l e m e n t i n g R e s u l t s 41

4 2 B a s e b e n d I m p l e m e n t i n g R e s u lt s 42

4 3 C o m p l e t e R e c e i v e r fo r M I M O s y s t e m .45

C o n c l u s i o n s 4 9 R e f e r e n c e s 50

R e l a te d P u b l i c a t i o n s .52

L I S T O F F I G U R E S

F ig 1 E q u i v a l e n t c h a n n e l o f MI M O c h a n n e l t h r o u g h S V D 6

F ig 2 A r c h i t e c t u r e o f M I M O w ith S V D 6

F ig 3 L in e o f s ig h t S I M O a n d L i n e o f s ig h t M I S O c h a n n e l s 9

F ig 4 A g e n e ra l M I M O s y s t e m w ith U l A s at b o th th e T x a n d R x 12

F ig 5 E i g e n v a l u e s fo r 3 x 3 M I M O s y s t e m as a fu n c tio n o f d e v i a tio n fa c to r in dB for p u r e I O S c h a n n e l .14

F ig 6 T h e c a p a c it y o f M I M O s y s t e m 14

F ig 7 T h e f u n c ti o n f r ( Q , ) p lo t e d as a f u n c tio n o f Q , for fixed L r = 8 and d if f e r e n t v a l u e s o f th e n u m b e r o f r e c e iv e a n t e n n a n r 16

F ig 8 A n i n d o o r M I M O s c e n a r i o c o m m u n i c a t i n g th r o u g h a s m a ll h o le in th e w a ll b e t w e e n t w o r o o m s 17

F ig 9 V a r ia t io n o f e i g e n v a l u e s w i t h th e w id th o f th e h o le .18

F ig 10 C a p a c ity v e r s u s h o le s iz e d u e to s e le c tio n o f th re e a n d t w o r e c e iv e a n t e n n a u s i n g n o r m - b a s e d in c r e m e n t a l a lg o ri th m .19

F ig 11 A c t u a l c a p a c it y lo ss f r o m F ig u r e 10 c o m p a r e d to th e u p p e r b o u n d L r in e q u a t i o n (5 1 ) 20

F i g 12 T h e p h y s ic a l la y o u t b o a r d 23

F ig 13 A D C to F P G A I n te r f a c e .24

F ig 14 D A C I n t e r f a c e 25

F ig 15 Z B T S R A M I n te r f a c e 26

F ig 16 X i l i n x D S P B l o c k s e t s 28

F i g 17 H a r d w a r e C o - s i m u l a t i o n .28

F i g 18 P r o je c t N a v i g a t o r 29

F ig 19 T h e T e s t b e d D i a g r a m 30

F ig 20: S tr u c t u r e o f R F IC M a x 2 8 2 9 31

F ig 21: B l o c k d i a g r a m o f R F t r a n s c e i v e r 32

F ig 22: D u a l - b a n d R F tr a n s c e i v e r m o d u l e 32

F ig 23: B a s e b a n d T r a n s m i t t e r D ia g r a m 33

F ig 24: D a t a G e n e r a t o r B lo c k 33

F ig 25: D a ta , 3 2 - l e n g t h W a l s h c o d e a n d C o d e d s i g n a l 34

F ig 26: B a s e b a n d S ig n a l, IF w a v e a n d IF s ig n a l 34

F i g 27: B a s e b a n d R e c e i v e r D i a g r a m .35

F i g 28: T i m i n g s y n c h r o n i z a t i o n 36

F ig 29: C o r r e la tio n B lo c k .36

F ig 30: C o r r e l a t i o n V a lu e .37

F ig 31: A b s o l u t o r .37

F ig 32: M a x i m u m s e l e c t o r 38

F ig 33 C o r r e la tio n s ig n a l A b s o l u t e s ig n a l a n d M a x i m u m t i m e 38

F ig 34 S ig n a l d e t e c t o r .38

F ig 35 S y n c h r o n i z a t i o n D e t e c t i o n B lo c k 39

F ig 36: T r a n s m i t t e d d a ta C o r r e l a t i o n a n d R e c e iv e d D a t a 4 0 F ig 37: R F c o n t r o l le r i n t e r f a c e .42

F ig 38: S p e c t r u m o f t r a n s m i t t e d s ig n a l w ith c e n tre f r e q u e n c y is at 2 4 3 7 G H z 42

F ig 39: C o r r e la tio n R e c e i v e I m p l e m e n t a t i o n W a ls h c o d e a n d D a t a 43

F ig 40: B a s e b a n d s ig n a l a n d IF s ig n a l .43

F ig 41: B a s e b a n d C o r r e l a t i o n R e c e i v e R e s u lts 43

F ig 42: Channel coefficients estim ated vs S N R 4 4 F ig 43: B E R o f Correlation Receiver for SISO 4 4 F ig 44: 2 x 2 M I M O M e a s u r e m e n t D i a g r a m 45

F ig 45: R e c o v e r e d D a ta in R X 1 4 6 F ig 46: R e c o v e r e d D a t a in R X 2 .47

F ig 47: R X D a t a a t A n t e n n a 1 w h e n D if f e r e n t T X D a t a a r e u s e d .47

F ig 48: C h a n n e l c o e f f i c ie n t s e s t i m a t e d o v e r S N R 4 8

CH A PT E R 1

IN T R O D U C T IO N

T h e d e v e lo p m e n t o f s e rv ic e s in c o m m u n ic a tio n s puts h e a v y p re s s u re on w ireless

c o m m u n ic a tio n s , n o t o n ly to e n h a n c e the q u ality o f serv ice but also to increase the

sp e c tru m e ffic ie n c y o f c o m m u n ic a tio n links T h e re h a v e been several solutions

p ro p o s e d a n d d e v e lo p e d T h e m u ltip le input- m u ltip le o u tp u t ( M I M O ) techn iq u e is

on e o f the m o s t p ro m is in g s o lu tio n s for the n ext g e n e ra tio n w ire le ss co m m u n ic a tio n s

w h ic h b e n e fits from m u lti-p a th p ro p a g a tio n By splitting a genera l data stream into several sm all, u n c o rre la te d parallel ones, a M I M O s y stem can a ch iev e significant

e n h a n c e m e n t in c a p a c ity as w ell as reliability T h e p e rfo rm a n c e o f a M IM O system

d e p e n d s g re a tly on h o w m a n y s u b -s tr e a m s it has and h o w c o rre la te d the sub-stream s are In g e n era l, the M I M O chan n e l is d e te rm in e d by m a n y p a ra m e te rs such as reflection, scatterin g , s h a d o w in g , a n te n n a s e p aratio n , and ang le o f arrival w aves

U n fo rtu n a te ly , a g iv e n M I M O s y ste m is best suited only to the set o f p ropagation

p a ra m e te rs it is d e s ig n e d for T his s tro n g ly req u ire s us to k n o w th e se p a ram eters well

b e fo re d e s ig n in g an indiv id u al M IM O s y ste m , as w ell as a p p ly in g algorithm s T here

h a v e been a n u m b e r o f m o d e ls for s im u la tin g M I M O chan n e ls H o w e v e r, those M IM O

m o d e ls c a n n o t a p p ly to all situ ations H e n c e the b e s t w a y to k n o w ac c u ra te ly about the

M I M O c h a n n e l is to m e a s u r e it in real c o n d itio n s by u s in g a M I M O testbed T hat is

w h y the a u th o r c h o o s e s the d e s ig n o f a M I M O testbed as the topic for his M asters thesis

In gen era l, m u lti-p a th is h o stile to w ire le ss p ro p a g a tio n that results in fading in

th e re c e iv ed signal In c o n tra st, M I M O m a k e s u s e o f m u ltip a th p ro p a g a tio n to im prove its d ata rate In ad d itio n , the use o f m u ltip le a n te n n a s at both tra n sm itter and rece iver

d e p lo y s c o n s id e ra b le spatial diversity R e c e n tly , M I M O c o m b in e d w ith O F D M

te c h n iq u e p ro m is e s a p o te n tia l s o lu tio n for 3G and the n e x t g e n e ra tio n w ireless

c o m m u n ic a tio n s

M I M O c h a n n e l c a p a c ity d e p e n d s m a in ly on the statistical properties o f the

c h a n n e l a n d on the a n te n n a s correlatio n A n te n n a co rrelatio n v arie s significantly as a

fu n c tio n o f the sc a tte rin g c o n d itio n , the tra n s m is s io n d ista n ce, the anten n a structures

a n d the D o p p le r sp read A s w e shall see, th e effect o f a n te n n a co rrelatio n on capa city

d e p e n d s on the c h a n n e l ’s c h a ra c te ristic s at the tra n s m itte r a n d receiver A dditionally,

c h a n n e ls w ith v ery lo w c o rre la tio n b e tw e e n an te n n a s can still ex hibit a “ k e y h o le ” effect w h e r e the c h a n n e l m a trix 's rank is defic ien t, leading to loss o f capacity gains

N u m e ro u s recent w o rk s have d ev e lo p e d both analytical and m e a su re m e n t-b a se d

M IM O channel m o d e ls w ith the co rre s p o n d in g capacity calculations for typical indoor and o u td o o r e n v iro n m e n ts [9,10,1 1,12],

D esig n in g h a rd w a re for M IM O channel m e a su re m e n t is a big ch allenge that requires expertise a n d k n o w le d g e o f both digital d esign and R F design T he testbed

T hanks to the d e v e lo p m e n t o f digital electronics, both b a s e b a n d and IF parts can be

im plem ented on F P G A b o ards w h ic h are s u p p o rted by high speed A D C s and D A C s A group o f re s e a rc h e rs at V ie n n a U n iv ersity built a M IM O T e s tb e d for the purpose o f rapid p ro to ty p in g a n d a lg o rith m testing for w ireless tran sm issio n [9], This design takes advantage o f the flexibility o f c o m p u te r so ftw are such as M atlab and the availability o f high speed D S P / F P G A chips O ne ad v a n ta g e o f this testb ed is that it supports m any types o f m o d u la tio n b e c a u se the b aseb an d signal p ro c e s s in g is p e rfo rm e d by M atlab

So algorithm ic re s e a rc h e rs do not need to have a d eep k n o w le d g e o f h ard w are design

A research te am at B rig h a m Y o u n g U n iv ersity has d e v e lo p e d a 4 * 4 M IM O

p rototyping te stb ed that o p erates at 2.45 G H z [10], Both the tra n sm itter and receiver stations are b a s e d on fixed p o in t digital signal p ro c e s s in g (D S P ) m ic ro p ro cesso r

d e v elo p m en t b o a rd s a n d use c u sto m fo u r-ch an n el radio fre q u e n c y (R F ) m odules The most c o m p le te te stb e d is a 4 x 4 M I M O d e v e lo p e d at the U n iv e rs ity o f A lberta [12]

T he testb ed o p e ra te s at 9 0 2 -9 2 8 M H z IS M fre q u e n c y band B a s e b a n d and IF processes are im p lem en ted o n a G V A 290 board: at its heart are tw o X ilinx V irtex -E 2 0 0 0

F P G A s, fo u r 12-bit A n a lo g to Digital C o n v e rte r A D 9 7 6 2 and fo u r 12-bit Digital to

A nalog C o n v e rte r A D 9 4 3 2 F o u r W alsh co d e seq u e n c e s w hich are the s am e as those

in the tran sm itter are g en era ted at the receiver T he signal from each receive antenna is correlated w ith the four W alsh codes in the re c e iv e r to e stim ate four channel coefficients H c n c e , in total, there are 16 correlators n eed e d to estim ate all 4x4 channel transfer functions T h e estim ated results are then input to a PC to perfo rm the singular value d e c o m p o s itio n to obtain the channel capacity

T h is thesis p re s e n ts the design and im p lem en tatio n o f both th e RF section and

b as eband section T h e im p lem en tatio n o f a c o m p le te S IS O system has been successfully c o m p le te d T he extension to build a c o m p le te M I M O testbed in an indoor

e n v ironm ent is u n d e rw a y T h e testbed s u p p o rts dual b an d o f 2.45 G H z and 5 G H z and

a num ber o f m o d u la tio n types RF part is built b as e d on IC M a x 2829 w h ich is a special IC for rad io fre q u e n c y transm ission T he o th e r parts o f the testbed are

im p lem en ted in a F P G A platform W e dep lo y the X ilinx X tr e m e D S P D e v e lo p m e n t

V i r e x - 4 K it for this design At the transm itter, data s e q u e n c e is m ultip lied to different

W a s h codes c o rre s p o n d in g to different tran sm it anten n as, before b ein g passed on to

th e m o d u la to r and the freq u en cy up-co n v erter The resulting IF signal is then passed

o n o the D A C to be c o n v e rte d into a n a lo g and u p -c o n v e rte d to the carrier frequency

T h t re ce iv er u ses the co rrelation te ch n iq u e to estim ate the chan n e l coefficients The

signal fro m each re c e iv e a n te n n a is p a s s e d th r o u g h th e 4 c o rre la to rs in o u r 4 x 4 testbed,

w h ich h a v e W a ls h arra y s the s a m e as in the tra n sm itte r T h e r e c e i v e r ’s d ata is then sent to M a tl a b to c o m p u te the c h an n e l m a trix , h e n c e e s tim a tin g the c h a n n e l capacity

T h e r e m a in d e r o f this th e sis is c o n s tru c te d as follow s: C h a p t e r 2 p re s e n ts s o m e

M IM O m o d e ls and th e ir c h a ra cteristics; C h a p t e r 3 is a b o u t the d e s ig n a n d s im u latio n

o f the in d o o r M I M O te stb ed , a n d the results and c o n c lu s io n s are s h o w n a n d a n a ly z e d

in C h a p t e r 4

C H A P T E R 2

M IM O M O D E L S AND CHARACTERISTICS

T h i s c h a p te r d e s c rib e s the M I M O model from tw o m ain po in ts o f view: the

m a th e m a tic a l v ie w a n d the ph y sical view In addition, the key p ara m e te rs w hich

d e te rm in e the p e r f o r m a n c e o f a M I M O channel are also presen te d T h e effects o f these

p a ra m e te rs will be p re s e n te d in te rm s o f sim u latio n results at the end o f this section

2.1 M a t h e m a t ic a l M I M O m o d e l

A flat fa d in g M I M O ch a n n e l w ith M rece iv e a n te n n a s an d N tran sm it antennas

can b e d e s c rib e d th ro u g h the relation below :

w h ere x is th e N x 1 tra n s m itte d signal vector, y is the M x 1 rece iv ed signal vector, n is

tra n s m it a n te n n a to /t h re ce iv e antenna

2.1.1 Capacity via Single Value Decomposition

T h e c a p a c ity o f a M I M O c h an n e l is as follows:

L e t us p re s e n t C in a s im p le r form to find out the key factors co n trib u tin g to the

o p eratio n s: a ro ta tio n o p e ra tio n , a sc a lin g operation and a n o th e r rotation operation

n o n -d ia g o n a l e le m e n ts are z e ro and diagonal ele m e n ts are n o n -n e g a tiv e real num bers

1=1

w e ig h te d input, a n d since the input signal v ector x in ( 1) has unit p o w e r, th e capacity

o f the “ w a te r-f ille d ” M I M O system in (5 ) b ec o m e s

{XWi) as p ro p o s e d in [ I ]

constraint

It can be seen from the w ater-filling alg o rith m ab o v e that the tra n sm itter allocates

T h e re is the q u e s tio n o f ho w to parallelize a M IM O c h a n n e l? T h e an s w e r is as

b elo w F rom S V D w e have:

y = Dx + n (12)

Figure 2 Architecture of MIMO with SVD

F igure 2 s h o w s th e a rc h ite c tu re for a M I M O c o m m u n ic a tio n sy stem using SV D

p o w e r to o th e r ones

2.1.2 Rank and Condition number

T h is section w ill s h o w w hat are the key factors co n trib u tin g to the capacity o f a

M 1M O channel It is s im p le r to focus on tw o s eparate low an d high S N R regim es At low S N R , the p o w e r p olicy will allocate all p o w e r to the stro n g est eig enchannel The

M I M O channel th e n p ro v id es o nly p o w e r gain:

[8], It e x p resses th e d im e n s io n o f rece iv ed signal through the M I M O channel, i.e

e n v iro n m e n t is n o t sc a tte rin g rich enough

2.2 P h y s ic a l M I M O m o d e l

In this sectio n , w e will look into physical e n v iro n m e n ta l factors co n trib u tin g to the M I M O c h a n n e l p e r fo rm a n c e in three main m od e ls: S IM O , M I S O and M IM O W e also find the re la tio n s h ip b etw een the key factors in the m a th e m a tic a l m odel and those

in the p h ysical m o d e l in the case o f M I M O channel In addition, w e only pay attention

to uniform antenna arrays in this section, that is, all a n te n n a s are alig n e d and equally

s ep a ra te d in the tra n s m it and rece iv e a n ten n a arrays

2.2.1 Line o f sight SIM O

T h e m o d e l o f this case is show n in figure 3, in w hich there is no obstacle b etw een the tra n s m itte r and rece iver, hence there is only direct path to the receiver T he antenna separatio n is AtA c, in w h ic h Ac is the rece iv e an ten n a s e p aratio n n o rm a liz e d to the

c arrier w a v e le n g th an d Xc is the w a v ele n g th o f the carrier

T h e c o n tin u o u s - tim e im p u ls e response /?,(t) betw ee n the tran sm it an te n n a and the /' rece iv e a n te n n a is g iv e n as:

L et h b e the ch a n n e l m atrix, h =[h, h 2 hM]', th e n the S IM O ch annel can be

w ritten as

c a u sed by th e tra n s m itte d signal on the receiver

B e c a u s e the d is ta n c e b etw ee n the tra n s m itte r and the rec e iv e r is m u c h larger than

the a n g le o f re c e iv e a n te n n a array and the incident d irec tio n o f tra n s m itte d signal The

s e c o n d term on the rig h t h and o f (21) stands for the d is p la c e m e n t o f the receive

tran sm it an te n n a s a n d only 1 rcceive antenna If <j) is the d iffere n ce angle b etw een the tra n s m it a n te n n a a rray an d the transm itted signal, and AtXc is the sp a c in g betw een anten n as, then the M I S O channel is given as:

and Q = cos <f>.

T h e m a x im u m c a p a c ity can be reached by p e rfo rm in g b e a m f o r m in g algorithm

a c c o rd in g to h T h e c a p a c ity is as given in (23) in w h ich the M I S O c h an n e l does not

s u p p ly any d e g re e - o f - fre e d o m gain

2.2.3 Antenna arrays with only I.OS path

D o e s the M I M O ch annel provide d eg ree - o f - fre e d o m w ith only direct path?

W e are n o w c o n s id e rin g the M IM O ch annel as in figure 4 In this m o d e l, let A, and Ar

be n o rm a liz e d tra n s m it an te n n a spacing and receive a n te n n a sp acin g , respectively Let

the d ista n ce b e tw e e n tw o an te n n a arrays is m u c h larger than the size o f each array, the

substitu tin g (27) into (26) w c have:

d ik — d + (z - 1 )ArAc cos cj)r - (A - 1 )A, Ac cos <t>t (27)

hlk = a e x p - exp( /2^(A' - l)A,i2, ) e x p ( / 2 ^ ( / - l ) A , Q r ) (28)

( 29 )

w h ere

e x p ( - /2 /rA ,Q ) e x p ( - / 2 ; r A , Q )

( 30)

and Q, = cos </>, Q { - cos (/>,.

S in ce the p r o p a g a tio n d is ta n c e is m u c h bigger than the a n te n n a a r r a y s ’ size, the cap a city o f this m o d e l is still as in (23) w hich states that an te n n a arrays w ith only LOS path an d a r r a y s ’s size b e in g m u c h sm aller than the tra n s m is sio n d ista n ce does not

p ro v id e any d e g re e o f freed o m

2.3 K e y p a r a m e t e r s in M I M O ch a n n e l

In the cases a b o v e , it is c lear that although there are m u ltip le an tennas at the transm itter, at the re c e iv e r o r at the both, w e ju s t obtain only the p o w e r gain w hich increases the c a p a c ity lo g a rith m ically This e m e rg e s a q u e s tio n that h o w to obtain

s o m e d e g re e - o f - freed o m , hen ce linear gain in the c a p a c ity ? A n d w hat is the

im p o rtan t factor to a c h ie v e this gain? This section will clarify w h ic h are the key factors in the M I M O c h a n n e l to a c h ie v e d eg ree - o f - fre e d o m gain

L ets look at th e p rim a ry fo rm u la for capacity o f the M I M O ch annel as in (2)

w h ich w o u ld b e c o m e (5) i f th e ch annel m atrix H has m o re than 1 eigen v alu e W e will

find o u t this c o n d itio n in the p h y s ic a l model

2.3.1 Antenna separation [4]

In this p art w e will s tu d y the effect o f a n ten n a sep a ra tio n on the capacity o f

M I M O channel T h e c h a n n e l m o d e l is as in figure 4 w ith a s s u m p tio n that there is only

are co n s ta n t but ca n be a d ju sta b le Tx a n ten n a is placed in the jrz-plane w ith the low er

B ec a u se w e fo cu s on a n te n n a sp a c in g , only L O S path is a n a ly z e d at this situation

Figure 4 A general MI1MO system with ULAs at both the Tx and Rx

U sin g ra y -tr a c in g m e th o d , the au th o rs in |3 | m odel the link as:

( x * \ ( - 2 n

(32)

F o r sim p lic ity , w e c o n s id e r that Tx and Rx an te n n a arrays are parallel T he

re c e iv e v e c to r fro m th e /7th T x an tenna is:

j2 ,T

I A M-ljt

(35)

an d the c h an n e l m a trix is:

T h e m a trix H will have a high rank if its c o lu m n s are u n c o rre la te d , i.e.

F ro m (38) w e see that there are several s o lu tio n s for high rank condition

H o w e v e r w e c h o o s e the one w hich has the sh o rtest an te n n a s p a c in g as in (39)

d e s ig n p a ra m e te r It is clear that A S P d e p en d s on the tra n s m it-re c e iv e distance, the

h o w s e n s itiv e the p e rf o r m a n c e is as the ratio o f the op tim al A S P to cu rren t one

F ig u re 5 b e lo w s h o w s the eig en v alu e s o f m atrix H versu s d iffere n t values o f r|

and fig u re 6 s h o w s the cap a city o f a 3x3 M IM O channel for d iffere n t valu es o f rj At r)=0dB, i.e A S P eq u a ls to A S P op[, three eig en v alu e s are the s a m e w h ic h c o rresp o n d s to the m a x im u m c a p a c ity condition T o o large or too sm all a n te n n a sp a c in g results in

d e g ra d a tio n in ch annel capacity

Figure 5 Eigenvalues for 3x3 IMIMO system as a function of deviation factor in dB for

pure LOS channel

Figure 6 The capacity of MIMO system

2.3.2 Resolvability in the angular domain |X]

T h e sep a ra tio n in d ire c tio n a l co sin e does not e n su re full-rank condition for the

ch annel m atrix H In fact, it can still be ill-conditioned if the a n g u la r condition is not satisfied In o th e r w o r d s , the less alig n ed the spatial s ig n atu res are, the better the condition o f H is T h e a n g le # b e tw e e n tw o spatial s ig n atu res is:

T his p a r a m e te r d e c id e s the co n d itio n o f the m atrix H F o r sim plicity, w e s u ppose

T o s u m up, the a n g le re so lu tio n has to be large en o u g h to e n su re the m a trix ch annel H

b e in g w e ll-c o n d itio n e d for w h a te v e r the a n ten n a sep a ra tio n is It m e a n s that the tra n s m it-re c e iv e d is ta n c e relative to the an tenna a r r a y s ’ size will d e cid e w h e th e r the

m a trix H is w e ll-c o n d itio n e d or not

2.4 A n t e n n a S e le c tio n A lg o r ith m

M I M O s y s te m s are not alw ay s well- co n d itio n ed an d the c h an n e l m atrix has low

w a s te d i f w e use all an alo g chains in a M IM O sy stem , e s p ecially in small

c o m m u n ic a tio n h a n d s e ts w h o s e p o w e r is limited T h e au th o r o f this thesis and his

c o lle a g u e s h a v e p ro p o s e d an antenna selection alg o rith m 17] to re m o v e those inactive

a n te n n a s in r a n k -d e fic ie n t indoor M IM O system s W e will n u m e rically , using sim u latio n , d e m o n s tr a te the c o rre s p o n d e n c e betw ee n rank d e fic ie n c y o f an indoor

M I M O and the e x te n t to w hich the n u m b e r o f receive a n te n n a s can be redu ce d

a n d the classical s in g le -sca tte rin g M IM O model c a n n o t a d e q u a te ly explain this

re ce iv e a n te n n a a rra y s are o bstructed by n e arb y scatterers), has b een p ro p o sed in

w h ic h the ch an n e l m a trix is c h a ra cterized by a p ro d u c t o f tw o statistically independent

c o m p le x G a u s sia n m a tric e s [15] This d o u b le -s c a tte rin g m odel can d e c o u p le (i.e can

c a p tu re s e p arately ) the effects o f ran k -d eficien c y an d spatial fad in g correlation in

M IM O c h a n n e ls M I M O channels with uncorrelated spatial fad in g at both the

keyhole’ c h a n n e ls [1 5], T h e double scattering M IM O c h an n e l m o d e l is

matrices, re s p e c tiv e ly , an d G K and G r are i.i.d R ayleigh fading m a trices on receive and tra n s m it sides, respectively For u n co rrelated fading at both tra n s m it and receive

v e c ( H) = (h[ \ h ‘ | | h\ , ) r

n y - trac in g m o d e l o f the scatterer, for no spatial correlation at both ends, the ra n d o m

instances o f H a b o v e is eq u iv a le n t to

v e c { W ) = Y H2v e c { G ) (48)

entries

Figure 8: An indoor M IM O scenario communicating through a small hole in the wall

between two rooms

T h e e ig e n v a lu e s o f the in-door M IM O channel in F ig u re 8 has been calcula ted in[5] as a fu n c tio n o f the hole dim ension Figure 9 sh o w s w h e n the hole is w id e enough

H ow ever, the rank o f the 4x3 M IM O ch annel d ecre ase s as the hole gets narro w er (toward th e left) an d e v e n tu ally d eg e n e ra te s to rank one

Đ Ạ I H Ọ C Q U Ố C G IA H À N Ọ I TRUNG TÂM TH Ô N G TIN THƯ VIẸN

In a g e n e ra liz e d div e rsity reception system , the rec e iv e r sees several v ersions o f the tra n s m it signal, each ex p eriencing a different c o m p le x -v a lu e d fading coefficient

hj{t) a n d noise n,(t). T o exploit diversity, these signals m ust be c o m b in e d in a gainful

from the selec ted path M a x im a l ratio c o m b in in g (M R C ) m a k e s d ec isio n s b ased on an

op tim al linear c o m b in a tio n o f all path signals

Eigenvalues ot 4,.J MlMG

ỡmđa 1 amda 2 arrtda 3

size of holt* (m)

2 5

Figure 9: Variation of eigenv alues with the width of the hole

Equal gain c o m b in in g (E G C ) sim p ly adds the path signals after they have been

chain H o w e v e r, to d a y a rece iv er n o rm ally has m ore than o n e R F ch ain and a subset

co m b inin g (G S C )

a s s u m in g equal p o w e r on all transm it antennas

C ( / / ; ) = log2 deti / +

co n su m in g

T w o a p p r o x im a tio n te c h n iq u es for an te n n a selection h av e b een p roposed: A t low

SNRs, by a p p ly in g T a y lo r e x p an sio n o f log ( l+.v) to (49) an d n e g le c tin g h ig h e r-o rd e r

a n te n n a s e lec tio n alg o rith m can sim ply m a x im iz e the n o rm o f the (selected) channel

te c h n iq u e ) an d a n te n n a selection for capacity both follow the n o r m -b a s e d strategy In

most c o m m o n b e c a u s e o f its low com p u tatio n al c o m p le x ity an d k n o w n statistics In

an a tte m p t to a c h ie v e near-o p tim a l selection for h ig h -S N R M IM O , G o ro k h o v [14]

d e c re m e n ta l o n e) leads to less c o m p lex ity and has a lm o s t the s am e cap a city as optim al

the p re v io u s ly c h o s e n v e c to rs , and ch o o se the one w h o s e p ro jec tio n has the largest

g re e d y a lg o rith m fo r m a x im iz in g capacity As a result, s u c c e s s iv e selection m ay not be strictly o p tim a l H o w e v e r, sim u latio n s sh o w that the ergo d ic c a p a c ity o f su ccessive selection is in d is tin g u is h a b le from the true o p tim u m A lso, it is s h o w n that successive selec tion p r o v id e s th e full div e rsity o f the original M I M O system

R ecent1 Selection out nf 4x3 MIMO SNR = 10JB 16

15 14 13

size of hole (m)

Figure 10: Capacity versus hole size due to selection of three and two receive antenna

using norm-based incremental algorithm.

A u s e fu l lo w e r b o u n d has been derived in [ 14] for the c a p a c ity o f the selected

N x N M I M O in (49), i.e w h e n Mr = /V, is

C ( H , ) > C( H) + log, det(UrU" ) (50)

side o f (50) is n o n p o s itiv e w h ic h represents the u p p er b o u n d o f the cap a city reduction

loss be

19

Receive S electio n on! uf 4x3 MIMO SNR = 10JB

Lr( H) = - tog: dct(L', U H ) (51)

F ig u re 10 s h o w s the capacity v ersu s hole size (in a w all) in the indoor M 1M O

s c e n a rio in [7] w h e n the full 4x3 M IM O is used (in red), also w h e n three receive

a n te n n a s are s e le c te d (in blue) (i.e //, is a 3x3 selected m a trix ),a n d w hen only two

re c e iv e a n te n n a s are selected (in green) (i.e /7, is a 2x3 selec ted m atrix) It is clear that

to w a rd s the left en d o f the capacity graphs w h ere the hole size is n arrow and the

sy s te m d e g e n e r a te s to rank one, one or even two receive a n te n n a s b e c o m e inactive

a n d th e re fo re can b e elim in a te d with o n ly a v ery small resu ltin g cap a city loss, being

a p p ro x im a te ly o n ly a fraction o f bps/H z As the hole size g ro w s larger allo w in g all three e i g e n m o d e s to survive, the red u ce d n u m b e r o f re ce iv e a n te n n a s is no longer

c a p a b le o f s u p p o r tin g all the e ig en m o d es, h en c e c a p a city loss g ro w s accordingly

1 6

1 2

I 1U n»

3 18 o

F ig u re 11 p lo ts the actual capacity loss due to s e lec tin g three receive antennas

c o m p a re d to the the ore tic al u p p e r b o u n d given in e q u atio n (51) It is im portant to

ob s e rv e fro m this fig u re that to w ard s the left end o f the c a p a city loss curves, the actual

beca u se the u p p e r b o u n d in (51) ass u m e s that the original M I M O has full rank w hile in the region o f n a rro w hole sizes the 4x3 M IM O is s ig n ifican tly ran k -d eficien t before

an tenna selection

C H A PT E R 3

M IM O TE STBE D FOR INDOOR ENVIRONM ENT

3.1 A s u r v e y o f M I M O T e s tb e d designs

T h e M I M O c a p a c ity can be en h a n c e d sig n ifican tly by d e p lo y in g diversity

te c h n iq u e in ric h -s c a tte r enviro n m en t T he capacity will increase linearly with the

n u m b e r o f a n te n n a s i f the channel matrix is full rank a n d w a ter-fillin g is applied to

p o w e r a llo c a tio n po licy So the channel state in fo rm atio n (C S I) b e c o m e s very

im p o rtan t a n d attracts m u c h attention from researchers

3.1.1 The M IM O Testbed at Vienna University

T h e a u th o rs in [9 | have d esigned and im p le m e n te d a M I M O T e stb ed for the

p u rp o s e o f rapid p ro to ty p in g and flexible testing o f alg o rith m s for w ireless tran sm issio n T h is d e s ig n takes a d v an tag e o f the flexibility o f c o m p u te r softw are such

as M a tla b a n d the a v ailab ility o f high sp eed o f D S P / F P G A chips T hus, it has m any

a d v a n c e s in c o m p a r is o n to m o s t p re v io u s designs O n e o f these a d v a n ta g e s o f this testbed is th a t it s u p p o rts m a n y types o f m o d u la tio n b e c a u se the b aseb an d signal

p ro c e s s in g is p e rfo rm e d in M atlab softw are So the alg o rith m ic research e rs do not need to h a v e d e e p k n o w le d g e o f hard w are design

T h e T e s t b e d h as three parts: softw are on PC, F P G A for IF p ro c e s s in g and RF part T h e T e s tb e d ca n su p p o rt up to 4 x 4 M IM O ch annel w ith an y ty p e o f m odulation

th anks to u s in g s o ftw a re to g enera te b aseb an d data on co m p u te r T h e m o d u lated signal after s a m p le d b y a 14-bit D A C at the rate o f up to 25 M s a m p le s /s is shifted to 70 M H z

in te rm e d ia te fre q u e n c y It is then u p -c o n v e rte d to 2 4 G H z frequ en cy At the receiver, arrival signal is d o w n -c o n v e rte d to IF fre q u e n c y to create 7 0 M H z ± 10kH z signal

w h ich th e n is p ro c e s s e d to re c o v e r b aseb an d signal to m e a su re channel T h e testbed

su p p o rts u p to 6.25 M H z o f b a n d w id th an d 50 M B p s o f d ata co in in g in PC

3.1.2 The M IM O Testbed at Brigham Young University

A re s e a rc h te a m at B rig h a m Y o u n g U niversity has d e v e lo p e d a 4 * 4 M IM O

p ro to ty p in g te stb e d that operates at 2.45 G H / [10], Both the tran s m itte r and receiver stations are b a s e d on fixed p o in t D S P m ic ro p ro c e s s o r d e v e lo p m e n t board s and use

c u s to m fo u r -c h a n n e l R F m od u les A c o m p u te r at the tran s m itte r station g en era tes the four d ata s tr e a m s an d passes the sam p led signals to the D S P board Each D SP

p ro c e s s o r p u ls e - s h a p e d filters each c o m p o n e n t o f the c o m p le x signal and sends the

b a s e b a n d sig n al to a digital u p -converter At ihe re c e iv e r station, eac h D S P processo r

p e rfo rm s m a tc h e d filtering and passes the filtered o u tp u ts to a co m p u te r T h e co m p u te r