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22
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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171717Space (ime Co$e
iare the eigen+alues of &(+;e)"(+;e)H
(+;e); and
9or *a'lei," a$in, c"annels ?mn@0. !e "a#e
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181818Space (ime Co$e
;et q$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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202020Space (ime Co$e
("eorem 1:/or ! A MtB Mr-1; and " min(Mt; Mr); the optimal
tradeoff cur+e d(r) is gi+en , the piece!ise linearunctionconnecting points in (; d()); " 7;>;;*here d() " (MrD ) (MtD )
I r @ k is an inte,ert"is can 5e interprete$ 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$s" 7.771)
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222S(C Matri+ 3 Simulation *esults.
2 x 2 '$CMatrix &. (2 x 2) II8 /lat /ading Channel Model (Code ate " 162)
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272727S(C Matri+ 3 Simulation *esults.
2 x 2 '$CMatrix &. (2 x 2) 'CM Channel Model (Fr,an; Marco; G7 mh)
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282828S(C Matri+ 3 Simulation *esults.
% x % '$CMatrix &. II8 /lat /ading Channel Model (/d$s" 7.771)
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222S(C Matri+ 3 Simulation *esults.
% x % '$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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000SM Matri+ C Sp"ere Deco$in,.
("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$s to "i," comple+it' !"ilec"oosin, d too small results in an empt' sp"ere
& successi+e procedure ,ased on 5ack-su5stitution
(e.g.; ) is suggested
11
1SM Matri+ C Sp"ere Deco$in,.
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111SM Matri+ C Sp"ere Deco$in,.
Gack-su5stitution proce$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
22
2SM Matri+ C Sp"ere Deco$in,.
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22SM Matri+ C Sp"ere Deco$in,.
*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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8SM Matri+ C Simulation *esults.
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&'$recei#er Matrix C. II8 /lat /ading Channel Model (Code ate " 162)
7070
70SM Matri+ C Simulation *esults.
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70SM Matri+ C Simulation *esults.
2 x 2 'M!it" P&'$recei#er Matrix C.'CM Channel Model (Fr,an; Marco; G7 mh)
7171
71SM Matri+ C Simulation *esults.
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71SM Matri+ C Simulation *esults.
2 x 2 'M!it" Mrecei#er Matrix C. II8 /lat /ading Channel Model (/d$s" 7.771)
7272
72SM Matri+ C Simulation *esults.
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72SM Matri+ C Simulation *esults.
% x % 'M !it"P&'$recei#er Matrix C.
II8 /lat /ading Channel Model (/d$s" 7.771)
7%7%
7%SM Matri+ C Simulation *esults.
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7%SM Matri+ C Simulation *esults.
% x % 'M !it"P&'$recei#er Matrix C.
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.
% x % 'M !it"P&'$recei#er Matrix C.
'CM Channel Model (Fr,an; Marco; G7 mh)
77
7SM Matri+ C Simulation *esults.
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7SM Matri+ C Simulation *esults.
% x % 'M !it"Mrecei#er Matrix C.
II8 /lat /ading Channel Model (/d$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$ule
8080
80Con#olutional Co$e
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Con#olutional Co$e
(rellis $ia,ram
8181
81Con#olutional Co$e
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Con#olutional Co$e
Deco$erLs (ask
eco+er length-code*ord from the gar,led
code*ord )
8282
82Con#olutional Co$e
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Con#olutional Co$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:
8787
87Con#olutional Co$e
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og-lielihood ratiocan 5e $eri#e$ 5' t"e $emo$ulator:
8888
88Con#olutional Co$e
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Sli$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
111S(C Matri+ 3 Simulation *esults.
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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 % '$Cuasi-Orthogonal.
II8 /lat /ading Channel Model
1111
11S(C Matri+ G Simulation *esults.
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% x % '$CMatrix .
II8 /lat /ading Channel Model
1111
11SM Matri+ C Simulation *esults.
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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
117SM Matri+ C Simulation *esults.
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% x % 'M !it"P&'$recei#er Matrix C.
II8 /lat /ading Channel Model
118118
118*eerence
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=1? '. M. &lamouti; S& simple transmit di+ersit techni9ue for
*ireless communications;S I333 T'&C; +ol. 1Q; no K; pp.1%J1-1%JK; Oct. 1UUK
=2? H. Tafarhani; S& uasi-Orthogonal 'pace-$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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119/120
=%? @. 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%
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