MIMO Transceiver -II

8/14/2019 MIMO Transceiver -II

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2Outline

MIMO !ireless c"annelsMIMO transcei#er

MIMO preco$er


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%%

%Outline

MIMO !ireless c"annelsMIMO transcei#er

MIMO preco$er


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&&

&MIMO S'stem Mo$el

N() antennas an$ M*) antennas (flat-fading case)

: M x NMIMO c"annel matri+

: Nx T(ransmit matri+

: Mx T*ecei#e matri+


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MIMO (ec"nolo,'

MIMO transmitter an$ recei#erSpace (ime Co$e S(C.

1. High link ualit'due to $ual ()-*). $i#ersit'

2. Create multiple signal copies thru MIMO channels

Spatial Multiple+in, SM.

1. High spectral eicienc'due to spatial multiple+in,

2. Create spatial degrees of freedom for transmission of

multiple data streams simultaneousl


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(ransmission Sc"emes

2 x 2

(!"2 # $"2)

% x %

(!"% # $"%)

Matrix &('$C)

uasi-Orth.('$C)


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777(ransmission Sc"emes

2 x 1

(!"2 # $"1)

% x %

(!"% # $"%)

Matrix ('$C 'M)

Matrix C('M)


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888

Space

(ime Co$in, S(C.


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Space (ime Co$e

3re t"ere an' a$#anta,es or usin, space timeco$e4

& practical performance criterion is the pro5a5ilit' o

error*hich is particularl important *hen coding o+er a

small num,er of ,locs *here the 'hannon capacit is ero

Consi$er communications o#er *a'lei," a$in,

c"annels

/or 0' o+er a aleigh channel *ith +ariance 34

2

5"10e 16 (%3,6!7)

/or 80' 0e 16 (23,6!7)

/or coherent /' 0e 16 (23,6!7)

/or non-coherent /' 0e 16 (3,6!7)


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111111Space (ime Co$e

Ho! $o people usuall' $o to com5at a$in,4Di#ersit' techni9ues

Frequency diversitymaximal ratio combining(MRC)

For BPSK with MRC:

Temporal diversityInterleaving

Spatial diversityuing multi!le "# an$%or R#

antennaBeam&orming'ntenna election


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1%1%1%Space (ime Co$e

Is t"ere a ormal $einition or $i#ersit'4e loo at this from the sense of outa,e pro5a5ilit'

$o achie+e capacit; a coding is assumed to tae place

across fading ,locs; *hich entails large delas

e consider a coding scheme *hich is done


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1&1&1&Space (ime Co$e

W"en one use a !"ite 6aussian co$e5ook

3t "i," S* t"e outa,e pro5a5ilit' is t"e same ast"e rame error pro5a5ilit' 9*. in terms o t"e S*

e+ponent

-- ;< ="en, an$ D< < C< (se I-I( 200%


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111Space (ime Co$e

Def 2: 3 co$in, sc"eme !"ic" "as an a#era,e errorpro5a5ilit' >eor an outa,e pro5a5ilit' >out. as

a unction o S* t"at 5e"a#es as

is sai$ to "a#e a $i#ersit' o or$er d


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111Space (ime Co$e

3 s'stematic !a' to e+ploit space-time $i#ersit'-- (arok" et al. I-I(1999

Consider a code*ord se9uence +" =+$(7);>;+$(!)?;

*here +()"=x1();> xMt()?$

@i+en the perfect C'I; the pair-!ise error pro5a5ilit'

(>>) ,et*een +and ecan ,e ,ounded from a,o+e ,

*here m;nis the icean coefficient; Es"P 6 Mt


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iare the eigen+alues of &(+;e)"(+;e)H

(+;e); and

9or *a'lei," a$in, c"annels ?mn@0. !e "a#e


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;et q$enote t"e rank o 3xe. t"en !e "a#e

3ccor$in, to Def 2 or t"e $i#ersit' or$er t"e

$i#ersit' or$er usin, space-time co$in, is qMr

(+;e) has to ,e ull ro! rankfor an code*ords +and e

to achie+e the ma+imum $i#ersit' MtMr


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111Space (ime Co$e

3 natural uestion t"at arises is "o! man'co$e!or$s can !e "a#e t"at allo!s us to attain a

certain $i#ersit' or$er4

Def 3: 3 co$in, sc"eme !"ic" "as a transmissionrate oR(NR!as a unction o S* is sai$ to

"a#e a multiple+in, ,ain ri

!"ere t"e constellation siAe is also allo!e$ to

5ecome lar,er !it" S*


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("eorem 1:/or ! A MtB Mr-1; and " min(Mt; Mr); the optimal

tradeoff cur+e d(r) is gi+en , the piece!ise linearunctionconnecting points in (; d()); " 7;>;;*here d() " (MrD ) (MtD )

I r @ k is an inte,ert"is can 5e interprete$ asusin, MrB k. recei#e an$

MtB k. transmit antennasto pro#i$e $i#ersit' !"ileusin, kantennas to pro#i$emultiple+in, ,ain


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212121S(C Matri+ 3

(ransmit Matri+/or 2 x 2 MIMO sstem

/or % x % MIMO sstem


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222222S(C Matri+ 3

*ecei#er Desi,n 1

&t the recei+er:

Di#ersit' or$er is t!o E


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2%2%2%S(C Matri+ 3 1


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2&2&2&S(C Matri+ 3

'imilarl; for our$E antennas; *e ha+e

Di#ersit' or$er is onl' t!oE


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222S(C Matri+ 3 Simulation *esults.

2 x 2 '$CMatrix &. (2 x 2) II8 /ading Channel Model (/d$s" 7.771)


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2 x 2 '$CMatrix &. (2 x 2) II8 /lat /ading Channel Model (Code ate " 162)


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2 x 2 '$CMatrix &. (2 x 2) 'CM Channel Model (Fr,an; Marco; G7 mh)


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% x % '$CMatrix &. II8 /lat /ading Channel Model (/d$s" 7.771)


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% x % '$CMatrix &. II8 /lat /ading Channel Model (Code ate " 162)


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%0%0%0S(C Matri+ 3 Simulation *esults.

% x % '$CMatrix &.'CM Channel Model (Fr,an; Marco; G7 mh)


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%1%1%1S(C Fuasi-Ort"o,onal Sc"eme

(ransmit Matri+/or % x 1 MIMO sstem


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%2%2%2S(C Fuasi-Ort"o,onal Sc"eme

*ecei#er Desi,n 2

1.et and

*here is an unitar matrix

2.&t the recei+er:

%%


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%%%%%%S(C Fuasi-Ort"o,onal Sc"eme

*here and

%.et

%&


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%&%&%&S(C Fuasi-Ort"o,onal Sc"eme

&.8efine a filter

!ote that the t*o su,sstems can ,e com,ined as

%S(C Fuasi Ort" Simulation


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%%%S(C Fuasi-Ort"< Simulation*esults.

% x % '$Cuasi-Orthogonal. II8 /lat /ading Channel Model (/d$s" 7.771)

%S(C Fuasi Ort" Simulation


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%%%S(C Fuasi-Ort"< Simulation*esults.

% x % '$Cuasi-Orthogonal. II8 /lat /ading Channel Model (Code ate " 162)

%7S(C Fuasi Ort" Simulation


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%7%7%7S(C Fuasi-Ort"< Simulation*esults.

% x % '$Cuasi-Orthogonal.'CM Channel Model (Fr,an; Marco; G7 mh)


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%


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%%%S(C Matri+ G

*ecei#er Desi,n

&t the recei+er:

1.Consider the sm,olsX1 X% at first

&0


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&0&0&0S(C Matri+ G

*here ;


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&2


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&2&2&2S(C Matri+ G

%.'imilarl; considering the sm,olsXJ XK; *e ha+e

$herefore;XJ XK can ,e detected , the same algorithm

gi+en in step (1) and (2)

&%

&%


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&%&%&%S(C Matri+ G Simulation *esults.

% x % '$CMatrix . II8 /lat /ading Channel Model (/d$s" 7.771)

&&&&

&&


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&&&&&&S(C Matri+ G Simulation *esults.

% x % '$CMatrix . II8 /lat /ading Channel Model (Code ate " 162)

&&

&


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&&&S(C Matri+ G Simulation *esults.

% x % '$CMatrix .'CM Channel Model (Fr,an; Marco; G7 mh)

&&

&


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&&&Space (ime (rellis Co$e S((C.

Co$e construction e+ample8-state S((C !it" 2 transmit antennas 8->S?..

&ssuming that the input to the encoder at time #is the G

input ,its ; the output of the encoder at time # is

*here$1kand$2

kare the sm,ols transmitted at the first

and second transmit antennas respecti+el

&7&7

&7


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&7&7&7Space (ime (rellis Co$e S((C.

3l,orit"m

M; $eco$er

*here C : '$$C code ,oo # % : sample sie

M decoder is implemented as a iter5i al,orit"m*here the

trellis path *ith the smallest accumulated metric is chosen

3$#anta,e: S"orta,e:L @ood tradeoff ,et*een High decoding complexit

$i#ersit'and co$in, ,ain

L High code rate can ,e achie+ed

&8&8

&8


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&8&8&8Space (ime (rellis Co$e S((C.

+ample %:


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00

0S (i ( lli C $ S((C.


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000Space (ime (rellis Co$e S((C.

9* or t!o transmit antennas an$ one recei#eantenna

Diversity order = 2

11

1S (i ( lli C $ S((C.


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111Space (ime (rellis Co$e S((C.

9* or t!o transmit antennas an$ t!o recei#eantennas

Diversity order = 4


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%%

%S (i ( lli C $ S((C.


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%%%Space (ime (rellis Co$e S((C.

9* or t!o transmit antennas an$ one recei#eantenna

Diversity order = 2


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Spatial Multiple+in, SM.

SM M t i C


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SM Matri+ C

(ransmit matri+/or 2 x 2 MIMO sstem /or % x % MIMO sstem


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88

8SM Matri C


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888SM Matri+ C

CommentsMulti dimensional +ector se9uence search is re9uired3xhausti+e search method is e+ponentiall' comple+

educed complexit solutions:* Spherical decoding+* BLAST

SM Matri+ C Sp"ere Deco$in,.


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SM Matri+ C Sp"ere Deco$in,.

3 tec"niue or sol#in, ' @ 3+

Main i$ea o sp"ere $eco$in, is to re$uce

computational comple+it' o M; $etector

'earches o+er onl lattice points in that lies in a certainhpersphere of radius d around the recei+ed signal y

e9uires onl polnomial complexit

Sp"ere $etector e#aluates all&t"at satis':

00

0SM Matri+ C Sp"ere Deco$in,.


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("ere are t!o uestions or sp"ere $eco$er: Ho* to choose the radius d ?

Ho* to tell *hich lattice points are inside the sphere

C"oosin, d too lar,e lea$s to "i," comple+it' !"ilec"oosin, d too small results in an empt' sp"ere

& successi+e procedure ,ased on 5ack-su5stitution

(e.g.; ) is suggested

11



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Gack-su5stitution proce$ure:Gasic I$ea:

8etermine all lattice points in a sphere of dimension

N *ith radius d ,successi#el' $eterminin, all lattice

points in sp"eres o lo!er $imensions 12NJ1!it" ra$ius d

+ample

Step 1.8ecompose H " F*; *e ha+e

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*here 'is an unitar' matri+; and Ris an uppertrian,ular matri+

Step 2. 'tarts *ith the last la'er searc"

(1-$im) and successi#el'$etecte$from the lo*er to upper

laers

Step %.'tops until the first laer ( $imension) is detected

%%

%SM Matri+ C Sp"ere Deco$in,.


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%%SM Matri+ C Sp"ere Deco$in,.

G* perormance e#aluation o sp"ere $etector !it"our transmit an$ recei#e antennas

&&

&SM Matri+ C G;3S(.


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&SM Matri+ C G;3S(.

G;3S( (ranscei#er al,orit"m &

1. Ordering

2. Interference nullin, (e.g.; MM'3 or N/)

%.Interference cancellation(e.g.; 'IC or 0IC)

SM Matri+ C G;3S(.


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SM Matri+ C G;3S(.

1st Iteration Intererence ullin, (decoupling N transmitted signals)

a.8ecorrelating (N/) detector:

5.MM'3 :

S'm5ol Decision: &ssume that E1is the detected sm,ol

SM Matri+ C G;3S(.


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SM Matri+ C G;3S(.

Intererence Cancellation

2n$ Iteration

Intererence ullin,a.Nero /orcing :

5.MM'3 :

77

7SM Matri+ C G;3S(.


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7SM Matri+ C G;3S(.

S'm5ol Decision:&ssume thatX2

is the detected sm,ol

(ithout the interferenceX1More>recise)

Intererence Cancellation

%r$ &t" iterations are similar an$&%&&are $etecte$ E

88

8SM Matri+ C Simulation *esults.


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2 x 2 'M!it" P&'$recei#er Matrix C. II8 /lat /ading Channel Model (/d$s" 7.771)

SM Matri+ C Simulation *esults.


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SM Matri+ C Simulation *esults.

2 x 2 'M!it" P&'$recei#er Matrix C. II8 /lat /ading Channel Model (Code ate " 162)

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2 x 2 'M!it" P&'$recei#er Matrix C.'CM Channel Model (Fr,an; Marco; G7 mh)

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2 x 2 'M!it" Mrecei#er Matrix C. II8 /lat /ading Channel Model (/d$s" 7.771)

7272



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% x % 'M !it"P&'$recei#er Matrix C.

II8 /lat /ading Channel Model (/d$s" 7.771)

7%7%

7%SM Matri+ C Simulation *esults.


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7%SM Matri+ C Simulation *esults.


II8 /lat /ading Channel Model (Code ate " 162)

7&7&

7&SM Matri+ C Simulation *esults.


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7&SM Matri+ C Simulation *esults.


'CM Channel Model (Fr,an; Marco; G7 mh)

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% x % 'M !it"Mrecei#er Matrix C.

II8 /lat /ading Channel Model (/d$s" 7.771)

77

7


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Git Interlea#e$ Co$e$ Mo$ulation

7777

77S'stem Mo$el


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S'stem Mo$el

Glock $ia,ram

I O OFD

7878

78Con#olutional Co$e


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Con#olutional Co$e

nco$er Ginar' rate K con#olutional co$e. 7

6enerator pol'nomial

Glock $ia,ram

77

7Con#olutional Co$e


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Con#olutional Co$e

Deco$er iter5i $eco$er.

(rellis Mo$ule

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Con#olutional Co$e

(rellis $ia,ram

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Con#olutional Co$e

Deco$erLs (ask

eco+er length-code*ord from the gar,led

code*ord )

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Con#olutional Co$e

iter5i al,orit"m

'uppose there are Mcode*ords *ith

e9ual pro,a,ilit

@i+en the recei+ed se9uence ); is chosen as thedecoded output if

8%8%

8%Con#olutional Co$e


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Co o ut o a Co$e

&ssume the channel is memor)le**# *e ha+e

8&8&

8&Con#olutional Co$e


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Distance(Metric) ,et*een t*o ad


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is chosen , the trellis path from ato 5*ith the

smallest accumulate$ metric

88

8Con#olutional Co$e


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Sot-input iter5i al,orut"m

'oft inputto t"e iter5i $eco$er.:

*here *e defined the lo,-likeli"oo$ ratioas the metric:

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og-lielihood ratiocan 5e $eri#e$ 5' t"e $emo$ulator:

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Sli$in,-!in$o! $eco$in, !it" truncation len,t" ;

9i#e constraint len,t"s rule:

If the truncation length is larger enough ( 5m) then the

sur+i+ors *ill ,e of common tail (m: 1.(otal enco$er

memor' "2. o s"it re,ister)

88

8Con#olutional Co$e


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Sur#i#or (runcation

/inite memor sie

/inite decoding dela

("ree strate,ies or sur#i#or truncation:1< 9i+e$ state truncation

2< MaNorit'-#otetruncation

%< Gest state truncation

00

0Con#olutional Co$e


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+ample: ;@&

Deco$e t"e irst 5ranc":

11

1Con#olutional Co$e


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3pproac" 1: /ixed 'tate $runcation

egard a i+e$ stateas the start of the trace ,ac

8ecide the output ,it , a trace *ith minimum

accumulated distance

22

2Con#olutional Co$e


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3pproac" 2: Ma


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3pproac" %: est 'tate $runcation

egard a state *ith the minimum accumulate$ metric

(Gest state) as the start of the trace ,ac

8ecide the output ,it , a trace *ith minimum

accumulated distance

&&

&Con#olutional Co$e


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+ample: ;@&

Deco$e t"e irst 5ranc":

Con#olutional Co$e


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Deco$e t"e secon$ 5ranc":

Con#olutional Co$e


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Deco$e t"e k-t" 5ranc":

77

7Con#olutional Co$e


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Deco$e t"e (otal len,t" B ;1. to inal 5ranc"

88

8Simulation *esults


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Comparison 5et!een Sot $ecision Har$ $ecision

&@! Channel Model

Simulation *esults


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Comparison 5et!een $ierent truncation len,t"s

&@! Channel Model

100100

100Simulation *esults


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Comparison 5et!een $ierent truncation strate,ies

&@! Channel Model

101101

101Glock Interlea#er


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& ,loc interlea+er is defined , a t*o step permutations

7:

(1) $he first ensures that ad


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$he de-interlea+er; *hich performs the in+erse operation;

is also defined , t*o permutations:

(1) /irst permutation:

(2) 'econd permutation:

ote:

$he first permutation in the de-interlea+er is the in+erse of

the second permutation in the interlea+er; and con+ersel

10%10%

10%Glock Interlea#er


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>ermutation >arameters

Index of the coded ,it ,efore the first permutationk, j

Index of that coded ,it after the first and ,efore the second

permutation

mk

Index of that ,it after the first and ,efore the second permutationmj

Index after the second permutation;


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Operatin, parameters or 5lock interlea#er

1010

10Glock Interlea#er


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Glock siAes o t"e Git Interlea#er

1010

10*ate 3$aptation


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*ate a$aptationis a e functionalit to cope *ith time-

+aring channel conditions and to maximie the

throughput of point-to-point *ireless lins

8esign a channel code *ith code rate #6 n(e.9. (n;)

con+olutional code) is complex and impractical

$o generate code rates of 26G; G6%; J6Q; and R6K; the rate

162 channel encoder outputs shall ,e puncture$

107107

107*ate 3$aptation


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>uncturin, / Depuncturin,

+ample: Sot-input iter5i al,orit"m.

Sot metric lo,-likeli"oo$ ratio.for each ,inar input:

108108

108*ate 3$aptation


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>uncture patterns an$ serialiAation or con#olution

co$e 7

1010

10*ate 3$aptation


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Supporte$ mo$ulations an$ inner (CM. co$e rates

110110

110*ate 3$aptation


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ad*); there

exists a tradeoff ,et*een

Constellation 'ie (Modulation scheme)

Code ate

ecei+ed '!

111111



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2 x 2 '$CMatrix &.

(2 x 2) II8 /lat /ading Channel Model (Code ate " 162)


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11%11%

11%S(C Matri+ 3 Simulation *esults.


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% x % '$CMatrix &.

II8 /lat /ading Channel Model

11&11&

11&S(C Fuasi-Ort"< Simulation*esults.


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.

% x % '$Cuasi-Orthogonal.


1111

11S(C Matri+ G Simulation *esults.


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% x % '$CMatrix .


1111



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2 x 2 'M!it" P&'$recei#er Matrix C.

II8 /lat /ading Channel Model (Wit" C"annel Co$in,)

117117



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118118

118*eerence


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=1? '. M. &lamouti; S& simple transmit di+ersit techni9ue for

*ireless communications;S I333 T'&C; +ol. 1Q; no K; pp.1%J1-1%JK; Oct. 1UUK

=2? H. Tafarhani; S& uasi-Orthogonal 'pace-$ime loc Code;S

I333 $rans. on Communications; +ol. %U; no. 1; pp. 1-%; 2771

=G? P. $aroh; !. 'eshdri and &. . Calder,an; V'pace-time

codes for high data rate *ireless communication: 0erformance

analsis and code construction;W I333 $rans. Inform. $heor;

+ol. %%; no. 2; pp. R%%-RQJ; Mar. 1UUK

1111

11*eerence


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=%? @. T. /oschini; Vaered space-time architecture for *ireless

communication in a fading en+ironment *hen using multipleantennas;W ell a,s 'st. $ech. T.; +ol. 1; pp. %1-JU; &utumn

1UUQ

=J? 0. . olnains; @. T. /oschini; @. 8. @olden and . &.Palenuela; V8etection algorithm and initial la,orator results

using P-&'$ space-time communication

architecture;W3lectronic etters; +ol. GJ; no. 1; Tan. 1UUU

=Q? 3. Nimmermann; . a+e and @. /ett*eis; VOn the complexit

of sphere decoding;W in 0roc. 0MC 277%

120120

120*eerence


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=R? K72.1Q; I333 'tandard for ocal and metropolitan area

net*ors; 0art 1Q: &ir Interface for /ixed road,and ireless&ccess 'stems

=K? 8igga+i et al; V@reat expectations X $he +alue of spatial

di+ersit in *ireless net*ors;W 0roceeding of I333 277%

Documents

MIMO Transceiver -II