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PERFORMANCE
OF
SOFT-OUTPUT EQUALIZATION AND
CONVOLUTIONAL CODING OVER FREQUENCY-SELECTIVE FADING
RADIO CHANNELS
An onio Valdo inos, An onio Na as, An oni Gelonch, Fe nando
J.
Casade all
Depa men
o
Signal Theo y and Communica ions
E.T.S. Ingenie os de Telecomunicaci6n
Uni e sidad Poli Ccnica de Ca aluiia
Apdo. 30002,08080 Ba celona, SPAIN
e-mail. [email p o ec ed]
Tel. 34 3 401
59
48 Fax. 34 3 401 72
00
Abs ac : This pape p esen s an analysis o so -ou pu
equaliza ion and codi ica ion echniques applied o
4
and
16-QAM TDMA adio sys ems o equency selec i e
ading channels. In pa icula , Typical U ban (TU) and
Hilly Te ain (HT) en i onmen s ha e been conside ed.
The use o he so in o ma ion p o ided by he equalize
enhances he sys em pe o mance conside ably.
Speci ically, an imp o emen o mo e han
4
dB can be
achie ed in ela ion o ha d decoding echniques. The
necessi y o in oducing some in e lea ing in o de o
des oy he channel memo y has also been s a ed. The
ac ual in es iga ed equalize s ha e been a So -Ou pu
Decision-Feedback equalize (SODFE) and a So -
Decision M-Algo i hm (SDMA) join ly wi h con olu ional
coding and bo h ideal and ini e in e lea ing.
I. INTRODUCTION
The g owing impo ance o wi eless digi al adio
sys ems has led o he de elopmen o high-pe o mance
echniques necessa y o compensa e o he se e e
equency-selec i e ading in oduced by he channel. In
o de o comba he In e symbol in e e ence caused by
he mul ipa h p opaga ion, he use o equaliza ion
echniques becomes manda o y. F om he poin o iew
o sys em pe o mance, non-linea equalize s a e mo e
e icien han linea ones since hey can compensa e o
deepe in-band nulls due o selec i e ading. Speci ically,
Decision-Feedback Equalize s
(DFE)
and he Maximum
Likelihood Sequence Es ima ion (MLSE) and Maximum
a Pos e io i (MAP) algo i hms can be conside ed
[l].
I
he channel memo y is oo long, he p obabilis ic
equalize s, ha is MLSE and MAP, become imp ac ical
due o hei compu a ional complexi y, which g ows
exponen ially wi h he channel memo y. The e o e,
simpli ied algo i hms ha e o be in oduced in spi e o a
mode a e loss in bi e o a e (BER) pe o mance. The
mos widely in oduced echniques a e he M-Algo i hm
(MA),
[2],
and he SDMA,
[3],
which ha e p o ed o be
app op ia e o eliable ope a ion wi h ela i ely low
compu a ional cos . Howe e , he only use o equaliza ion
echniques does no usually p o ide good enough
pe o mance o ope a e in p ac ical sys ems and some
coding and in e lea ing which des oys he channel
memo y a e equi ed. On he o he hand, he decode
usually ope a es on he ha d decisions made by he
demodula o , which leads o an in o ma ion and,
consequen ly, o a pe o mance loss. This d awback can
be ci cum en ed by making use o he addi ional
in o ma ion con ained in he unquan ized samples gi en
by he demodula o .
In his pape bo h DFE and SDMA echniques
ha e been in es iga ed join ly wi h con olu ional coding
and ideal and ini e in e lea ing in wo ealis ic
en i onmen s, namely Typical U ban (TU) and Hilly
Te ain (HT). The chosen modula ion schemes ha e been
M-QAM pa e ns because hey a e spec um e icien and
so, app op ia e o en i onmen s whe e a high densi y o
a ic is gene a ed. In pa icula ,
4
and 16-QAM
modula ion schemes ha e been conside ed. Pe o mance
esul s, in e ms o bi e o a e alues, ob ained by
means o compu e simula ion a e p esen ed.
II.
SYSTEM DESCRIPTION
The block diag am o he simula ed ansmission
sys em is shown in ig. 1. The ou pu sequence om he
sou ce is p o ec ed by a con olu ional code and passed o
an in e lea e wi h some ini e span and dep h. The
in e lea ed sequence is M-QAM modula ed and
ansmi ed o he channel a e being passed h ough he
ansmi e il e , hT( ), which
is
a oo - aised cosine il e
wi h a oll-o ac o equal o
0.5.
The e o e, he lowpass
@
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Figu e
1.
Lowpass equi alen
model
o
he
ansmission sys em.
equi alen M-QAM signal ansmi ed o he channel can
be exp essed as:
m
x( )
=
a,hJ -kT)
+
jb,.
hJ -kT)
(l)
k=-
whe e {ak} and {b,} a e independen da a sequences
o
du a ion T o he in-phase and quad a u e channels
espec i ely. They a e selec ed om he se
{&1,&3, ...,k(M"2-l)} wi h M=4 o 4-QAM and M=16 o
16-QAM.
A he ecei e a ma ched il e
H,(Q
is
inco po a ed, hen:
h,( )
=
F-'[H,(R]
3
h;(- )
(2)
whe e
+
deno es he conjuga e,
F1
is he in e se Fou ie
ans o m and hl( ) is he equi alen impulse esponse
p io o he ma ched il e :
(3)
The e o e, he global impulse esponse esul s:
(4)
h( )
=
hJ )*hc( )*h,( )
=
h,( )*h;(- )
=
h+(- )
Le us no ice as he ecei e il e is ma ched no only o
he oo - aised cosine ansmi ing il e bu also o he
en i e impulse esponse hl( ), which is a ec ed by he
channel impulse esponse a ia ions, and hus needs o be
con inually upda ed.
I
could be implemen ed in
acco dance wi h a FIR s uc u e om he es ima ed
impulse esponse. In his s udy, a ideal channel es ima ion
is assumed and,
so,
he ideal ma ched il e is always
a ailable. The unc ion h,( ) models he channel beha io
ha in oduces selec i e ading in he adio link. The
channel is assumed o be wide-sense s a iona y
unco ela ed sca e ing
(WSSUS)
and i is ep esen ed by
a unique co ela ion unc ion e e ed o as he Powe
Delay P o ile, P( ), and gi en by:
The mul ipa h phenomenon can be desc ibed in
e ms o ime delays and hei associa ed powe alues.
No
Dopple shi s ha e been conside ed. The models
adop ed co espond o hose p oposed by COST-207, [4],
o desc ibe ypical u ban (non-hilly) and hilly e ain
en i onmen s and is based on ep esen ing he channel by
a ini e numbe o aps, each one de e mined by i s ime
delay and a e age powe . The ampli ude o each ap is
Rayleigh dis ibu ed. This models is desc ibed by a
con inuous powe delay p o ile and app oxima ed h ough
a disc e e numbe o aps,
[4].
A he ou pu
o
he
channel model,
AWGN
wi h a double-sided powe
spec al densi y NJ2 is added.
The signal a he ma ched il e ou pu is
exp essed as:
-
( )
=
[
ak. h R( -kT) -bk. h
'(
-kT)]
+
k -m
-
+
jc [bk.hR( -kT) +ak.h'{ -kT)] +nx( )+j ny( )
(6)
k-a
whe e
wi h
*
he con olu ion ope a o .
G
is a gain ac o ha
ensu es a cons an a e age powe a he demodula o
inpu . I is in oduced
in
o de o conside he p esence o
au oma ic gain con ol (AGC) and is only necessa y o
16-QAM pa e ns since in 4-QAM we ha e ze o-c ossing
decision bounda ies.
A e he ma ched il e , we ha e conside ed wo
possible b anches co esponding o he SDMA and
SODFE equalize s. Fo he i s one, he global impulse
esponse p io he SDMA equalize is equi ed o be h(k)
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1
=
0
o k<O and
so,
a whi ening il e (WF) is necessa y.
This il e has been cons uc ed as a DFE o wa d il e
whose aps a e adjus ed ollowing he minimum mean-
squa e e o (MMSE) echnique because e en hough
ideally he
WF
shoud be adjus ed by means o he ze o
o zing c i e ion
[5],
una oidably he numbe o aps is
ini e and, he e o e, he esidual IS1 e ec is no
negligible. Fu he mo e, he SDMA mus wo k wi h a
ini e impulse esponse leng h, and
so
h(k)
=
0
o k>L.
We should ake a alue o L high enough o conside all
he signi ican IS1 componen s, bu no
so
high ha he
compu a ional complexi y becomes un easonable. The
de ailed SDMA algo i hm can be ound in [3]. On he
o he hand, a DFE s uc u e wi h symbol pe iod (T)
spacing be ween s ages has also been in es iga ed. The
MMSE echnique has also been adop ed o calcula e he
ap alues. In his case, he so ou pu is ob ained om
he unquan ized signal. Bo h equalize s deli e so
decisions o each symbol and, om hem, he espec i e
bi me ics a e calcula ed [3][6]. Finally, a e de-
in e lea ing, hese me ics a e ed o he decode
o
exploi he so in o ma ion. In o de o compa e so
e sus ha d-decision pe o mance, we ha e also
conside ed he ou pu sequence om he quan ize which
is ed di ec ly o he de-in e lea e .
III.
RESULTS
The pe o mance o so -ou pu equaliza ion and
con olu ional coding echniques in ou doo adio channels
ha e been in es iga ed using he bi e o a e (BER)
as
quali y c i e ion. The signal- o noise a io is gi en by:
Ell
No
SNR
=
-
+
1OlogM
whe e E, is he a e age bi ene gy and M=4 and M=16
o 4 and 16-QAM espec i ely.
We ha e conside ed bi a e alues o
1
Mbi ls
and
200
Kbi /s o
TU
and HT en i onmen s since hey
lead o he same no malized delay sp ead de ined as he
p oduc
z.R,,,
whe e Rb is he bi a e and
z
is he oo
mean-squa e delay sp ead, which is a mesu e o he wid h
o he Powe Delay P o ile and is equal o
1
ps
o TU
and
5
ps
o HT in he analyzed models[4].
The numbe o aps o he SODFE has been
chosen 6 o he o wa d and
5
o he eedback il e s.
Fo he SDMA equalize a channel memo y leng h
L=6
l@
10-'
10-2
gj
10-3
10-4
10-5
10"
1
4
7
10
13
16
EWNo
CdBl
Figu e
2.
BER
e sus
E;JN,.TU
and
4-QAM.
has been conside ed. Va ious echniques ha e been
compa ed. In pa icula , ha d-decision e sus so -decision
has been in es iga ed.
In ig.:! he e olu ion o he BER as a unc ion
o E,& o 4-QAM and
TU
en i onmen s is depic ed. A
con olu ional code wi h a e =3/4 and cons ain leng h
o
K=2
is used o p o ec he sou ce da a. We can obse e
ha he e is no app eciable di e ence be ween he
SODFE and SDMA s uc u es, no mo e han
0.5
dB,
al hough he la e is always slig hly be e . Howe e , he
pe o mance imp o emen ob ained when in oducing
decoding echniques is e y impo an , pa icula ly when
So me ics a e conside ed. Fo a BER o
lo2
So
me ics o e an imp o emen o 3 dB wi h e e ence o
ha d decoding and 4.5 dB wi h e e ence o no coding.
Fo inc easing alues o E& we can no ice ha he
di e ence be ween bo h so and ha d decoding
echniques a ies slowly and is o abou
3
dB o and
4 dB o In con as , he ela i e deg ada ion i no
coding is conside ed inc eases o highe E&, alues.
Fo
a
BER o his deg ada ion is
7.5
dB and o
could be
10.5
dB wi h e e ence o So me ics. A
simila compa ison can be ca ied ou om he
obse a ion o ig.3, which ep esen s he BER e olu ion
o HT en i onmen s and 4-QAM modula ion schemes. In
his case, o achie e a BER o he di e ence be ween
so and ha d decoding is abou 4 dB. I mus be
bo n
in
mind ha he delay sp ead in oduced by he channel in
HT en i onmen s is i e imes g ea e han
TU
channels,
and
so,
al hough igu es
2
and 3 p esen simila BER
alues o equal
E,
/
No,
in he la e
he
bi a e
is
i e
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108
10-1
18-2
10-3
1
0-4
18-5
10-6
_.
1
4
7
io
13
16
Eb/No
CdBl
Figu e
3.
BER e sus
E,,/NW
HT
and
4-QAM.
imes lowe .
Fig. 4 shows he sys em pe o mance o 16-
QAM and TU en i onmen s. In his case he di e ence
be ween SODFE and SDMA is sligh ly highe , bu ne e
mo e han 1 dB. F om his igu e we can no ice ha he
beha io is simila o ha o 4-QAM sys ems, bu i is
clea ha he E,/N, alue needed o gua an ee a ce ain
alue o BER is conside ably highe . Ac ually, a 16-QAM
sys em needs app oxima ely 6 dB mo e han 4-QAM o
achie e he same pe o mance. The e o e, highe le el
modula ion schemes
a e
use ul o inc ease he spec al
e iciency, bu no he maximum bi a e eached by he
sys em due o i s highe sensi i i y o
IS1
e ec s.
Fig.5 p esen s he e ec o conside ing ini e
ins ead o in ini e in e lea ing. We ha e ocused on TU
en i onmen s, 4-QAM and So me ics. I no in e lea ing
a all is in oduced, he deg ada ion due o he channel
memo y is as high as 4 dB o BER
=
lo-*, 6 dB o
BER=10-3 and
8
dB o BER=10-4. I a ini e in e lea ing
dep h o 4 is conside ed, he deg ada ion is
2,
3 and
4
dB
espec i ely o SDMA equaliza ion. In he case o
SODFE an addi ional deg ada ion o
1
dB is e ealed.
F om his igu e
we
can conclude ha some kind
o
in e lea ing is needed in o de o ake he mos ad an age
om he so in o ma ion deli e ed by he equalize .
O he wise he e ec o coding no only is no
ad an ageous, bu may in oduce a highe pe o mance
deg ada ion.
108
la-'
18-2
2
10-4
10-5
lad
...
...
.II
...
I..
I,.
...
...
.II
...
...
4
6
8 18 12
14
16 18
20
EWNo
CdBl
Figu e
4.
BER e sus E,,/N,.TU
and
16-QAM.
Finally, we ha e analyzed he e ec o a ying
he code a e om
=
314 o 213 and 112 when an
in e le ing dep h o 4 is conside ed. The esul s a e
p esen ed in ig.
6.
I
can be no iced ha passing om
-314 o 2 3 an imp o emen o abou
2
dB
is
achie ed,
and oughly 2.5 dB when passing om 213 o 112.
This
may no seem a g ea imp o emen aking in o accoun
he inc easing bandwid h equi ed when dec eases.
IV. CONCLUSIONS
In his pape we ha e in es iga ed he
pe o mance o equaliza ion and codi ica ion echniques
applied o 4 and 16-QAM TDMA adio sys ems in wo
ypical ou doo en i onmen s whe e he dispe si e na u e
o he channel in oduces bo h in e symbol in e e ence
and Rayleigh luc ua ions o he signal- o-noise a io. The
use o equaliza ion echniques which p o ide so
in o ma ion o he decode , namely
SODFE
and SDMA,
has p o ed o be e y e ec i e and leads o BER alues
conside ably lowe han hose achie ed by using he mo e
con en ional ha d-decision echniques. Mo eo e , we ha e
p esen ed a b ie compa ison be ween
4
and 16-QAM
modula ion schemes. F om he esul s ob ained we can
conclude ha he use o high-o de QAM pa e ns does
no o e any ad an age in e ms o maximum bi a e
achie able by he sys em, and i s use is only ad isable
when a high spec al e iciency is equi ed. We ha e also
s a ed he necessi y o in oducing some ini e
in e lea ing, as high as he da a delay equi emen s make
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l@
10-'
10-2
10-3
10-4
10-5
106
2
4
6
8 10
12
14 16 18
Eh/No
CdBl
Figu e
5.
BER
e sus
WN,.
TU
and
4-QAM.
possible, in o de o des oy he channel memo y, and we
ha e e alua e he esul s o h ee di e en cases. Finally,
he e ec o a ying he code a e, , has been analyzed,
bu , ob iously, he adeo be ween BER and bandwid h
has o be sol ed in each pa icula case.
V. REFERENCES
J.G. P oakis. "Adap i e Equaliza ion o TDMA
Digi al Mobile Radio". IEEE T ans. on Vehic.
Tech. Vol. 40.
NO
2. May 1991. pp. 333-341.
A. Baie and G. Hein ich. "Pe o mance o M-
Algo i hm MLSE Equalize in F equency-
Selec i e Fading Mobile Radio Channels". P oc.
IEEE
ICC'89, Bos on, MA, 1989, pp. 281-285.
R.
Mehlan and
H.
Mey . "So Ou pu M-
Algo i hm Equalize and T ellis-Coded
Modula ion o Mobile Radio Communica ions".
P oc. 42nd IEEE Vehic. Technol. Con ., Den e ,
CO, 1992, pp. 586,591.
COST 207: "Digi al Land Mobile Radio
Communica ions". Final Repo . Published by
he Commission o he Eu opean
Communi ies.Luxembou g, 1989.
pp.
135-
147.
E.A.
Lee
and D.G. Messe schmi . "Digi al
Communica ions". Kluwe Academic Publishe s.
Y.J. Liu, M. Wallace and J.W. Ke chum. "A
So -Ou pu Bidi ec ional Decision Feedback
Equaliza ion Technique o TDMA Cellula
1988. pp. 345-346.
l@
10-'
10-2
10-3
10-4
10-5
1
A6
--
2
4
6
8
10
12
14
16
EWNo
CdBl
Figu e
6.
BER
e sus
E&.TU
and
4-QAM.
Radio". IEEE Jou nal on Selec ed A eas in Comm.. Vol
11.
NO.
7. Sep embe 1993. pp. 1034-1045.