PERFORMANCE
OF
JOINT
DIVERSITY
AND
EQUALIZATION TECHNIQUES
IN M-QAM INDOOR RADIO SYSTEMS
Fe nando
J.
CASADEVALL
Depa amen de Teo ia del Senyal i Comunicacions
Uni e si a Poli kcnica
de
Ca alunya
Apdo.
30002.08080
Ba celona, SPAIN
In his pape we analyze he pe o mances o he join
di e si y and equaliza ion echniques in an indoo adio
en i onmen . 4, 16 and 64 QAM modula ion a e conside ed. The
sys em pe o mances a e desc ibed
in
e ms o he Ou age
P obabili y. The esul s show ha a sys em wi hou p o ec ion has
e y limi ed pe o mances. When he channel in oduces low le el
o dis o ion, he di e si y echnique p oduces be e pe o mances
han he equalize echnique, bu
i
he channel in oduces a high
deg ee
o
in e symbol in e e ence, hen he equalize echniques
a e sligh ly be e han he di e si y echniques. Mo eo e , he join
equaliza ion and di e si y echniques a e e y e ec i e ools o
comba he deg ading e ec in oduced by he indoo channel.
Imp o emen in he sys em pe o mances
,
wi h espec
o
a sys em
wi hou any p o ec ion, anging om
10
o
100
ha e been ob ained.
We will shown ha he sys em pe o mances emain almos
unchanged o alues o he co ela ion coe icien be ween
di e si y b anches lowe han 0.6
,0.7
app oxima ely.
E en hough some pa ial analysis abou
his
subjec ha e
been ca ied ou .[l],[2], o example aking in o accoun speci ic
bi a es, pa icula p opaga ion condi ions
ando
asymp o ic
app oaches
o
he equalize beha io , in
OUT
knowledge, he e is
no ye a gene al analysis o indoo adio channels ha p o ides
a global cha ac e iza ion o he beha io o he di e si y and
equaliza ion echniques wo king join ly when M-QAM modula ions
a e conside ed.
In his pape . we assess he pe o mances o M-QAM
indoo adio sys ems ha use join di e si y and equaliza ion
echniques. 4-QAM, 16-QAM and 64-QAM ha e been conside ed.
The in luences on he sys em pe o mances o a ious sys em and
channel pa ame e s, like he shape and .m.s. delay sp ead o he
Powe Delay P o ile ha cha ac e ize he p opaga ion condi ions,
he equalize s uc u e (linea and non-liiea )
as
well
as
he numbe
o aps e c... ha e
been
aken in o accoun . The sys em
pe o mances a e desc ibed in e ms o bo h a e aged Bi E o
Ra e an Ou age P obabili y.
INTRODUCTION TRANSMISSION MODEL
The use o adio in indoo da a communica ions
is
an
a ac i e p oposi ion because i gi es o al mobili y
o
he
inc easing numbe o e minal equipmen s in la ge buildings.
Howe e , indoo adio sys ems a e a ec ed by equency selec i e
ading caused by he mul ipa h ime delay sp ead ha p oduces
in e symbol in e e ence (ISI). hus esul ing in an i educible bi
e o a e @ER) and imposing an
upjw
limi on he da a symbol
a e. In o de
o
comba
his
si ua ion di e si y echniques and o
adap i e channel equalize s could be used.
Di e si y echniques a e e icien when low
o
medium
bi a e ansmission sys em a e conside ed because in hese cases
he signal ading can be assumed o be non-selec i e. Howe e , o
sys ems ope a ing a high bi a e, whe e he selec i e ading na u e
caused by he mul ipa h p opaga ion in oduces
ISI,
he
di e si y
echniques a en’ sui able because hey can’ cope wi h he abo e
men ioned ISI.
On
he o he hand, he equaliza ion echniques, ha
a e able o compensa e he IS1 in oduced by he mul ipa h
p opaga ion, ha e limi ed pe o mances due
o
he luc ua ions on
he signal
o
noise a io p oduced by he Rayleigh na u e o he
p opaga ion. Then, in o de o inc ease he sys em pe o mances i
could be con enien
o
conside he beha io o he join di e si y
and equaliza ion echniques.
228
Figu e 1 shows he low-pass equi alen model o he
ansmission sys em. The ansmi ed signal can be o mula ed
as:
-
S( )=
(a,+jb,).& -kT)
=E
d,.& - m,
k---
-
km
--
whe e
[
ak),
[
b)
a e da a sequences o du a ion T o he in-phase
and quad a u e channels. They a e kl,
3,
....
k(M”-I)
wi h
M=4
o 4-QAM, M=16 o 16-QAM,andM=64
o
64-QAM. Mo eo e ,
ak and
4,
a e independen andom a iables. The o e all il e ing
ans e unc ion
H-,-( ).H,( )
is
a aised-cosine
ype
wi h a oll-o
ac o equal
o
0.5.
The il e ing is spli equally be ween he
ansmi e and he ecei e . 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( ),[3].
A
measu e o he
wid h o P( ) is he oo mean-squa e delay sp ead,
T.
F om he
Powe Delay P o ile unc ion
,
a sample o he channel impulse
CH2944-7/91/0000/0228 $1
.OO
0
1991
IEEE
-__
-
-~
esponse can be cons uc ed by he ollowing o mula
:
whe e
kj
and hgn,i a e ze o mean gaussian andom a iables wi h
a iance P(n. ,,)/;! and
,,
is he ime be ween samples. The numbe
o samples,
L,
needed o ep esen he indoo mobile channel in an
accu a e o m, depends on he shape o he Powe Delay P o ile,
P( ). and on i s
ms
delay sp ead. Measu emen s om many
di e en buildmgs,[4],[5], allow
us
o
conside ha he mos
common shape o he Powe Delay P o ile is he one-side
exponen ial p o ile, gi en by:
In
he analyzed cases
i
is su icien o conside ed a ime
du a ion o he one-side exponen ial p o ile app oxima ely equal o
14. and
,,=~J2.
The ecei ed signal l( ) ( esp. ,( )) can be exp essed by:
m
j( )=
[a,.h” -~~)-b,.hl( -k~)l
+
k--m
m
+j
[bk.hF(
-KT)
+u,.h ( -KT)]
+
k---
+
n,W+j
ny( )
whe e, in gene al
wi h i=1,2
.
F’
deno es he in e se
con olu ion ope a o , and
G;
is a Fou ie ans o m,
*
is
he
gain ac o in oduced o
conside ed he p esence o au oma ic gin con ol (AGC). We ha e
aken in o accoun a ca ie eco e y ci cui ha minimizes he
ou pu mean squa e e o .[6]. Assuming ha he bandwid h o he
ca ie eco e y ci cui is much highe han he ading a e, i could
be
conside ed ha he ca ie phase can be acked
as
i he global
impulse esponse, h,( ). is ime-in a ian .
As
we ocus on he
e ec s o he delay sp ead, he phase ji e on he eco e ed ca ie
caused by he gaussian noise will no be aken in o accoun . The
op imum sampling
ins an
is ob ained om a classical squa ing
iming eco e y loop,[7].
Two
baseband equalize s uc u es a e
analyzed. Linea and Non-Linea equalize s bo h wi h baud pe iod
T
spacing be ween s ages.
In
all he cases, he minimum mean-
229
squa e e o (MMSE) echnique has been adop ed
o
calcula e he
ap alues.
RESULTS
We ha e examined he e ec i eness o he join adap i e
equaliza ion and di e si y echniques
in
igh ing he mul ipa h and
ading in oduced by he indoo adio channel. The objec i e is o
de e mine he
da a
a e limi a ion o indoo communica ion
sys ems. The c i e ium used
o
e alua e he sys em quali y
is
he
ou age.p obabili y, de ined
as
:
P,=P Ob.(P,>lo- )
whe e P, is he e o p obabili y and
y
is a cons an ha we ha e
aken equal o 2 o 6.
To
compu e he
e o
p obabili y in eg al we
ha e conside ed he LEVI’s me hodJ81.
In igu es
2
and
3
we show
he
e olu ion o he ou age
p obabili y, agains he no malized delay sp ead o he Powe
Delay P o ile,
. /T.
We can
see
ha a sys em wi hou any
p o ec ion has a e y limi ed pe o mances since o
. /T
>
0.1 he
ou age p obabili y
is
g ea e han 0.1 (10%). Mo eo e . o smalle
alues o
. /T,
he ou age p obabili y
goes
o an asymp o ic alue
(ma ked by he le e A on he igu es) ha
is
g ea e han 0,Ol
(1%). I is impo an o emphasize ha
his
alue shows he
beha io o he sys em pe o mances when a la ading channel
is
conside ed. I he di e si y echnique is conside ed we can
see
ha
o high alues o he a io
. /T
he sys em pe o mances a e only
sligh ly be e han he ob ained o a sys em wi hou p o ec ion,
bu when smalle alues a e aken in o accoun he alues o he
ou age p obabili y con e ge on he alue o a la ading channel.
On
he o he hand, o small alues o
he
no malized delay sp ead,
he sys em pe o mances inc ease by a ac o o en app oxima ely.
In conclusion. he di e si y echnique could be
used
in an e ec i e
way i a la channels o channels wi h low dis o ion a e
conside ed. When join equalize and di e si y echniques a e aken
in o accoun , he pe o mance o he sys em inc eases quickly. Fo
a BER o 1W2 and a linea equalize o 5 aps in each b anch
(ma ked
as
2+2 in he igu e) he sys em is able
o
gua an ee an
ou age p obabili y lowe han 0.001 (0.1%) o alues o he
no malized delay sp ead smalle han
0.8.
Howe e i a BER o
is conside ed he sys em is no able
o
gi e an ou age
p obabili y lowe han
0.01
(1%).
In o de o ob ain an ou age p obabili y lowe han
lo3
o bo h BER alues o
lo-’
and
lo6
a highe signal
o
noise a io
mus be conside ed. In pa icula we ha e chosen a signal o noise
a io o
30
dB.
Figu es 4 and
5
show he sys em pe o mances in
his
case. Conside ing a non-linea equalize wi h
3
aps (1 ap in
he non-linea pa ) and o a BER equal
o
lo2
he ou age
p obabili y is lowe han
(0.01%)
o alues o
T/T<
0.5
.
I
is
impo an o emphasize ha , when join equaliza ion and di e si y
echniques a e conside ed, he sys em pe o mances a e be e han
he ob ained o a la ading channel o alues o
. /T
anging
om 0.01
o
0.5
.
This could be explained because he sys em
uses
he mul ipa h
as
a addi ional edundan channels
o
inc ease he
di e si y gain. Howe e , o la ge alues o
T/T
he induced
in e symbol in e e ence .due
o
he mul ipa h, inc eases
conside ably and he equalize can no
cope
comple ely wi h i
,
and
as
he esul he sys em pe o mances deg ades quickly. Fo a
BER o an ou age p obabili y smalle han
10”
could be
ob ained o alues o
T/T
lowe han 0.3
.
I could also be no iced
ha o g ea alues o
T/T
he sys em pe o mances a e limi ed
by
he in enymbol in e e ence due
o
he limi ed numbe o equalize
aps (3 aps a e only conside ed in each b anch). Fo highe alues
o he
~ l
a io, be e sys em pe o mances could be ob ained
inc easing he numbe o aps.
Figu es 6 and
7
show he sys em pe o mances when 16
QAM
modula ion
is
conside ed. Again a signal o noise a io o 30
dB
is
aken in o accoun . The beha io o he linea and non linea
equalize
is
shown conside ing
3
and
5
aps in each di e si y
b anch (ma ked in he igu e by 1+1 and
2+2
espec i ely). Fo a
BER
o
lo-’
a
linea equalize could gua an ee an ou age
p obabili y lowe han 0.01 (1%) o alues o
~ l<
0.3
i
3 aps
a e aken in o accoun , and
~ l<
0.5
when
5
aps a e used.
An
ou age p obabili y lowe han could only be gua an eed o
~ l~0.1.
Howe e
i
a nonlinea equalize wi h
5
aps (ma ked by
2+2)
is conside ed he ou age p obabili y could be lowe han
i
~ l<0.55
and lowe han
lo-’
i
T/T<
0.7.
Fo a BER o a
non linea equalize wi h
5
aps is necessa y in o de o ob ain an
ou age p obabili y lowe han
lo-’
o ~/T<0.4
Finally, igu es
8
and
9
show he sys em pe o mances
when 64
QAM
modula ion
is
conside ed.
In
his case a signal
o
noise a io o
40
dB is aken in o accoun . Again, he beha io o
he linea and non linea equalize conside ing 3 and
5
aps in each
di e si y b anch (ma ked in he igu e by 1+1 and
2+2
espec i ely) is also analyzed. Fo a BER o
lo-’
a linea equalize
could gua an ee an ou age p obabili y lowe han 0.01
(1%)
o
alues o
T/T
<
0.2
i 3 aps a e
aken
in o accoun , and
~ k
0.5
when
5
aps a e used. I a nonlinea equalize wi h
5
aps (ma ked
by
2+2)
is
conside ed he ou age p obabili y could be lowe han
10-3 i
/T<O.4
and lowe han
IO-’
i
T/T<
0.55.
a non linea equalize wi h
5
aps is
necessa y in o de
o
ob ain an ou age p obabili y lowe han
lo-’
o T/T4.4
Fo a BER o
CORRELATED CHANNELS
We ha e also conside ed he in luence on he sys em
pe o mances o he impulse esponse co ela ion be ween bo h
di e si y channels.
Gi en a alue o he co ela ion coe icien ,p, de ied
as:
E[(X-X).(Y-Y)I
=
lsIY
P=
-,
/E[(x-m’l.E[(Y-n’l
/GG
p
=m
mu=m,=02
XY XY
wi h
02
he a iance, he wo complex impulse esponse o he
sys em a e ob ained by means o he ollowing p du e:
a-
b.-
C.-
whe e
X
and
Y
a e ze o mean a iables and:
230
Two unco ela ed complex gaussian impulse esponse,
h( ) and b( ), a e gene a ed, wi h
:
L
h( )=c.x
(h,+jhqn).8( -n n)
bO)=c.h
nil
(b,+jbq,,).& -n n)
n-
1
Fo each couple o andom a iables,
h,,,
and b, ( esp.
bqn and b
)
wo new co ela ed andom a iables a e
ob ained using he ollowing exp essions:
q?
U,
=U1
.hi,
in=uZ1
.h,
+uz2.bin
U
¶n
=ull.h,
qn=uZ1
.h,
+%.bqn
wi h:
mXY
a21
=-
J;;;;
The impulse esponse
o
he wo new co ela ed channels
a e ob ained
as
:
In igu e
10
we show he e olu ion o he ou age
p obabili y, o a BER o agains he co ela ion coe icien
p
o a 4-QAM modula ion and a signal
o
noise a io a I.F. o 20
dB.
Th ee di e en a io
l,
ela ed
o
channels wi h small,
medium and high le el o he in e symbol in e e ence, ha e been
conside ed.
F om
he
igu e we can conclude ha o co ela ion
coe icien s,
p.
lowe han 0.7 he sys em pe o mances emain
almos unchanged. Howe e when he co ela ion coe icien
inc eases i s alue he sys em pe o mances deg ades quickly.
Simila esul s we e ob ained o highe signal o noise a ios and
high le el M-QAM modula ion:
Fu he mo e,
in
each igu e we a e able
o
compa e he
beha io o h ee di e en sys ems. The poin deno ed by A in he
uppe cu e gi es he sys em pe o mance when an unp o ec ed
sys em
is
conside ed. The eason is ha i we conside a sys em
wi h only di e si y echnique when he co ela ion coe icien is
equal
o
one,
bo h
di e si y channels ha e he same impulse
esponse and
as
a esul he sys em pe o mances a e co esponding
o an unp o ec ed sys em. O e he same cu e, he
poin
B
indica es he sys em pe o mance when ideal di e si y echnique is
conside ed.
In
a simila o m, on he lowe cu e we can
dis inguish wo poin s. The poin deno ed by C ep esen s he
sys em pe o mances when join equaliza ion and di e si y
echniques a e conside ed. Finally he poin
D
deno es he sys em
pe o mances o an equalized sys em, because
as
he co ela ion
coe icien is equal
o
one bo h di e si y channels ha e he same
impulse esponse and
as
a esul only he equaliza ion echnique
becomes ope a i e. Compa ing he h ee igu es i can be
concluded
a.- When he impulse esponses p esen low le el o
dis o ion wi h, e.g. o
. / =0.05,
he di e si y echnique
p oduces be e pe o mances
han
he equalize
echniques.
b.- When he impulse esponses show a high deg ee o
in e symbol in e e ence, e.g. o
~/T=0.5,
he equalize
echniques a e sligh ly be e han he di e si y
echniques.
c.- The imp o emen on he sys em pe o mances due
o
use
join ly di e si y and equaliza ion echniques, wi h espec
o an unp o ec ed sys em, anges be ween
10
o 100.
CONCLUSIONS
In
his
pape we ha e analyzed he pe o mances o he
join di e si y and equaliza ion echniques in an indoo adio
en i onmen . 4,16 and 64 QAM modula ion ha e been conside ed.
F om he ob ained esul s we can conclude ha a sys em wi hou
p o ec ion has e y limi ed pe o mances. When he channel
in oduces low le el o dis o ion, he di e si y echnique p oduces
be e pe o mances han he equalize echnique, bu i he channel
in oduces a high deg ee o in e symbol in e e ence. hen he
equalize echniques a e sligh ly be e han he di e si y
echniques.
On
he o he hand he join equaliza ion and di e si y
echniques a e e y e ec i e
ools
o
comba he deg ading e ec
in oduced by he indoo channel. Imp o emen
in
he
sys em
pe o mances
,
wi h espec
o
a sys em wi hou any
p o ec ion,
anging om 10
o
100
ha e been ob ained. Mo eo e he sys em
pe o mances emain almos unchanged
i
he alue o he
co ela ion coe icien be ween di e si y b anches
is
lowe han
0.6
,0.7 app oxima ely.
REFERENCES
R.A. VALENZUELA,
Pe o munce o ADap i e
Equaliza ion o Indoo Radio Communica ions,
IEEE
T ans. on Communica ions, ol. COM-37,
pp.
291-293,
Ma ch 1989.
T.A. SEXTON and KPAHLAVAN,
Channel
Modelling
and Adap i e Equaliza ion
o
indoo Radio
Channels,
IEEE J. Selec ed A eas
in
Communica ions, Vol. SAC-7,
pp. 114-121, Janua y 1989.
J.C.
PROMS,
Digi al Communica ions,
Mc C aw Hill,
1983. Chap e 7.
D.M.J. DEVASIRVATHAM,
Time Delay Sp ead
Measu emen s
850
MHz
Radio Wa es in Building
En i onmen s,
IEEE T ans. An ennas and P opaga ion,
Vol.
AP-34, pp. 1300-1305, No embe 1986.
R.J.C. BULTlTUDE,
A
Compa ison o Indoo Radio
P opaga ion Cha ac e is ics
a
9IOMHz
and
1.75
GHz,
IEEE J. Selec ed A eas in Communica ions, Vol. SAC-I,
pp. 20-30. Janua y 1989.
S.
MORIDI, H. SARI,
Analysis o Decision-Feedback
Ca ie Reco e y
Loops
wi h applica ions o
16
QAh4
Digi al Radio Sys ems,
In e na ional Con e ence on
Communica ions (ICC’83), 1983,
pp.
671-675.
N. AMITAY, L.J. GREENSTEIN.
Mul ipa h Ou age
Pe o mance o Digi al Radio Recei e s Using Fini e-
aps Adap i e Equalize s,
IEEE T ans. on
Communica ions, Vol. COM-32,
NQ
5.
May 1984.
A. LEVI,
Fas E o Ra e E alua ion in
he
P esence o
In e symbol In e e ence,
IEEE T ans. on
Communica ions, Vol. COM-33, NQ5, May 1985,
pp.
479-481
AGREEMENTS
This wo k has been inanced by Spain CICYT TIC880543.
231
k
Figu e
1.-
LOU PASS EQUIVALENT MOOEL
OF
THE TRANSMISSION SYSTEM
N
w
m
LL
W
*
+--
-
=!
m
M
4
0
LL
(L
W
(3
4
0
5
Tau/ T
Figu e
2.-
OUTAGE PROBABILITY VERSUS NORMALIZED
DELAY SPREAD. $-PAM, SNR=ZOdB, BER=
lom2
1
N
w
m
E
W
,
....
,
,...
,
....
I
Tau/T
Figu e
4.-
OUTAGE PROBABILITY VERSUS NORMALIZED
DELAY SPREAD. 4-QAM. SNR=30dB, BER=10-2.
CD
w
m
=!
m
m
LL
W
-
4
0
LL
a
W
4
0
5
Tau/T
Figu e
3.-
OUTAGE PROBABILITY VERSUS NORMALIZED
DELAY SPREAD. 4-QAM, SNR=ZOdB, BER=10-6
Tau/T
Figu e
5.-
OUTAGE PROBABILITY VERSUS NORMALIZED
DELAY SPREAD. 4-QAM, SNRJOdB, BER=10-6.
232

......
10'
,
Tau/T
.....
.....
. .
,.,
I
...............
.....
.....
. .
,.,
.....
-ul hau
p o ecclon
.
-01 .
L
MIII[WR
EO.
104
10-4
I
Tau/T
Figu e
6.-
OUTAGE PROBABILITY VERSUS NORMALIZED
DELAY SPREAD. 16-PAM, SNR=30dB, BER=1Om2 Figu e
7.-
OUTAGE PROBABILITY VERSUS NORMALIZED
DELAY SPREAD. 16-QAM, SNR=30dB, BER=10-6
I
Tau/T
I
Figu e
8.-
OUTAGE PROBABILITY VERSUS NORMALIZED
DELAY SPREAD. &-PAM, SNR=40dB, BER=10-2
CORRELATION COEFFICIENT
(a)
-
CD
I
W
I,
CI
W
+
m
!
>
c
m
m
U
0
E
a
W
a
Q
c
3
0
10-1 109
Tau/T
Figu e
9.-
OUTAGE PROBABILITY VERSUS NORMALIZED
DELAY SPREAD. &-PAM, SNR=40dB, BER=10-6.
le.
!@L&Pl
Iau/T=E.
1
CORRELATION COEFFICIENT
(b)
CORRELATION COEFF [CIENT
(C)
Figu e
10.-OUTAGE PROBABILITY VERSUS CORRELATION COEFFICIENT. SNR=20 dB,
4-QAM,
T/T
=
0.05,
0.1,
0.01