CORRELATION EFFECTS OF FREQUENCY HOPPING
DIVERSITY SYSTEMS IN INDOOR MOBILE COMMUNICATIONS
ENVIRONMENTS
R.AGUSTI
and
P.DIAZ
Depa men
o Signal
Theo y
and
Communica ions
Uni e si a Poli&nica
de
Ca alunya
Absuac - F equency-Hopping (FH) echniques in
conjunc ion wi h coding ha e been p oposed o indoo
adio sys ems based on he ac ha FH beha es
as
an
in insic equency di e si y echnique. In his pape
we assess he pe o mance o
a
FH-BPSK
o o he
si ua ions no p e iously conside ed in he li e a u e.
In pa icula , he e ec s o ha ing a non-null
co ela ion coe iiien
in
unc ion
o
he equency
sepa a ion as well
as
he p esence o coding schemes
ha e been conside ed.
1.
INTRODUCTION
The pe o mance o an indoo mobile adio sys em
ope a ing in
he
UHF
band is se e ely
a ec ed
by he
mul ipa h p opaga ion medium. To coun e ac he e ec s
o he ading one can
eso
o
coding, di e si y o
combined coding/di e si y schemes.
The mo e ecen s anda d sys ems o mobile
communica ions use
in
some ex en combined
coding/di e si y schemes by means o he F equency
Hopping
(FH)
echniques in
o de
o
ake ad an age
o
he
in insic equency di e si y
ha
he
FH
enable.
In
his
pape ,
we analyze
he
pe o mance o a
speci ically
FH
o ien ed sys em
p oposed
o
be
used
in
indoo communica ions. In pa icula , we ha e analyzed
he sensibili y o his sys em wi h espec
o
he hopping
equency
sepa a ion.
SI.
The
men ioned scheme is a
TDMA
cyclical slow FH
sys em p opxed in
[l]
o indoo applica ions and simila
o
he
GSM
scheme. To
ake
ull ad an age o i s in insic
equency di e si y,
FH
has
o
be
used
in conjunc ion wi h
coding and in e lea ing echniques.
In
his sense besides
he Reed-Solomon
(6.2)
coding e ained in
[I]
a Repe i ion
coding wi h he same edundancy
has
also
been
in oduced. In o de
o
assess
he
pe o mance o his
scheme we ha e conside ed a disc e e model wi h a Powe
Delay P o ile modeled as a double Poisson
P ocess
[2]
ha allows
us
o
analyze any ansmission a e.
2.
SIGNALING FORMAT
In
o de
o
ob ain some ep esen a i e esul s o he
e ccLq o
bo h
he hopping equency sepa a ion and
he
coding
u.scd
in he sys em pe o mance, a signaling o ma
as
p oposed
in
[
11
has
been e ained.
Fo
his pu pose da a
packe s
a e
o med acco ding
o
he
ollowing s eps:
1-
Da a en e ing
a
64
Kb/s
a e
collec ed
as
a
384
bi
block 6
ms.
long
118
shown
in Table 1.
Table
1.
2-
A
a e
1/3:
R46.2)
o
Repe i ion code is o med
gi ing a
384
symbol block 6
ns.
long.
3-
Ihe
symbols
a e
s o ed
in o
a
bu e
in
succesi e
columns
and
ead
ou
in ows
as
shown
in
Table
2.
Table
2.
4-
P eamble, sync
wo d
and
spa e
ime
a e
added
o
each
ow gi ing a slo
1
ms. long
as
shown
in Table
3.
To
make use o
he
FH
in insic di e si y in
he
sense
ha
some
equency channels
a e
be=
han
o he s
in e ms o
he ecei ed powe
and/o
dis o ion.
he
6 o med
slo s
a e
inally modula ed acco ding
o
6
assigned hopping
eouencies.
192
8
I
Table
3.
5-
The
ml
TDMA
FH
o ma esul s
om
sha ing each
1
ms. ame du a ion among
n
use s.
The
esul ing
ai
bi
a e
is
hen
Rkn.256
KWs.
3.
SYSTEM ANALYSIS
Each
onc
o he
6
ca ie s
abo e
men ioned is used o
CH29645/91/0000-0712$01.00
01991
IEEE
712
pe o m
a BPSK modula ion. Then, wi h espec
o
he
ansmission poin o iew, he base band model sys em
is
simply o mcd by a cascade
o
a ansmi lc il e , he
mobile channel and hc ccci c ille , so ha , he o e all
impulse esponse complex en elope in absence o channel
dis o ion is a aisedcosine wi h a
0.5
Roll-o pa ame e
equally spli ed be ween ansmi e and ecei e . The
complex en elope o
he
channel impulse esponse,
hN( ).
is modcled acco ding
o
121
as
whc c
bk,,
and
Elk,,
a e Rayleigh and uni o mly dis ibu ed
espec i ely. Fu he mo e,
in
his model he ecei ed
signal ays a i e in clus e s,
so
ha , he a i al imes o
he ays wi hin he clus e ,
Tk,i,
and he clus e s
hemsel es, Ti,a e
bo h
dis ibu ed acco ding wo Poisson
a i al
p ocesses
wi h
pa ame e s
h
and
A
espec i ely.
The modcl pa ame c s a e
=6om.
y=2(k s
1
1
1
Mean
Time
Bnween
Rays:-=Sns
(2)
Mean
lime
Be ween
C1u e s:-
=3QQm
In
he abo e FH-BPSK sys em he hopping-
equency sepa a jon be ween he di e en ca ie s
dc c mine he deg ee o co ela ion ha he six coded
symbols cn e ing he decode p esen . Fu hc mo e,
he
symbol e o p obabili y a he inpu o he decode is
posi ion dependen due
o
he ac ha each g oup o h ee
bi s ha make up a symbol
is
ansmi ed h ough a
di c cn i- h equency channel cha ac e ized by a
di e en complex
en elope
impulse csponse
h,( )=hl( )el p02x
i
S,O
(3)
whe e h,( ) is a sample o h( ),
S,
is he hopping-
cquency sepa a ion and
i
a ies om
1
o
6.
To
obuin hc
BER
a he ou pu o he decode , he
Bl:R
;i
dic
ou pu
o hc BPSK dc cc o is li s cqui c l.
Fo
Ihis
pu posc
a
combina ion o analy ical and Mon e
Ca lo simula ion echniques ha c bccn cn isagcd
acco ding
o
he ollowing wo
s eps
p ocedu e:
1.
A
sample o h( ), deno ed h,( ),
is
gene a ed
acco ding
o
i s s a is ical p ope ies. Only ays wi h
ampli udes g ea e han
0.01
mul iplied by he ampli ude
co esponding
o
he i s ay a e aken in o accoun .
Conside ing ays wi h g ea e ampli udes hey do no1
change he esul s signi ican ly.
A
squa ing iming
loop
is used o clock cco c y.
The sampling
ins an
is
[3]
(4)
A
loop ha elimina es he c oss- alk is adop ed o
ca ie
eco e y.
Then
[4]
A
as
bi e o a e, deno ed he e
~b,~,~.
compu a ion
me hod is hen used o
each
i- h equency channel.
In
he simple
case
ha la ading had
been
assumed, ha
is
11
R
=-e-
’
Tb
OS
whe e R, deno es he da a bi a e. The bi e o a e
co esponding
o
he
i- h
equency channcl o he m- h
impulse
esponse
sample would hen
be
(7)
713
2-The bi e o a e,pb,m, a
he
decode ou pii ,
co esponding
o
he
m- h sample, is calcula ed om he
symbol e o p obabili y a he decode inpu gi cn by
This is shown in he ollowing o
bo h
Reed-Solomon
coding
and
Repe i ion coding.
3.1.
REED-SOLOMON
CODING
The em p obabili y o he decoded
symbols
o
a
gi en h,( ) sample is
6
6
6
6
(9
)
I.1
66
I k
I4
The pb,,, can be ob ained
as
[SI
1
-Pe,mn iPb, P,,
2
I
In o de
o
ob ain nume ical esul s, he
uppe
bound
o
he
h,,,
has been e ained.
3.2.
REPETITION
CODING
Inpu X,,X2
Le he inpu and he ou pu o he decode
be
ou p~~:~,,~.x,~,,~,x~
Then, we ha e
pb=,pEm
1
3- The inal BER esul s om a e aging
Pb,,,
o
a
g ea numbe o
h,,,( )
samples.
In he abo e calcula ions he signal
o
noise
a io
in
he ecei e inpu depends on he m- h channel impulse
esponse pa ame e s. Tha is, gi en he complex en elope
o he ansmi ed signal
as
whe e cn=+l
o
-1 and hd ) is he ansmi e impulse
esponse, i can be shown ha
equal
o
m
Mhz.,
10
MHz.,~
MHz.
and 2.5
Mb.
ha e
been conside ed. The co esponding
BER
o hese cases
a e displayed in Figu es 1,2,3,4 espec i ely. I can
be
no iced ha no signi ican a ia ions appea when
compa ing
SF-
and S,=lO
MHz.
So
inc easing
S,
beyond
10
MHz.
i
is
no con enien . Ano he conclusion ha
could be
also
ex ac ed om he obse a ion o he
Figu es 2,3 and 4 is ha Reed-Solomon coding
ou pe o ms
he Repe i ion coding o S,Ds g ea e han
0.05 app oxima ely.
Rb alues o 2.56
Mb/s,
5.12
Mb/s
and 10.24
Mb/s
ha e been also conside ed and simila igu es
o
hose
shown o he 256Kb/s case ha e been ob ained.
S,
alues
g ea e han 10
Mhz
a e
no conside ed because he
changes a e no signi ican . Fo he obse a ion o
he
esul s ob ained i can
be
concluded, o all Rb alues, ha
Reed-Solomon coding ou pe o ms he Repe i ion coding
o S,Ds g ea e han
0.05
app oxima ely. Wha e e Rb is
conside ed, S,.Ds g ea e han abou 0.1 and
0.2
o he
R-
S
and Repe i ion codes espec i ely does no imp o e he
sys em pe o mance signi ican ly. This can
be
be e
app ecia ed in Figu es
5
and 6 o 256 Kb/s and 5.12 Mb/s
espec i ely. This di e en beha io
o
bo h codes could
be explained because he R-S ecei ed symbols p esen a
g ea e co ela ion han he co esponding epe i ion
symbols in ol ed in he in e lea ing p ocess. Finally
a
igu e o me i
o
he sys em could be gi en by saying
ha Ou age Ra es lowe han 0.01 o BER=10-3 seems
possible o Rb=5.12h4b/s. In pa icula , in he case o
using Repe i ion Coding, i is in e es ing
o
poin ou ha
he ecei e could
be
implemen ed wi h low powe
consump ion echnologies as needed o ealis ic po able
ope a ion.
AGREEMENTS
TIC880543.
(14)
This wo k
has
been inanced by Spain CICYT
REFERENCES
[l]
A.A.M. Saleh, A.J.Rus ako,
J .,
L.J.Cimuni, J .,
"A
TDMA indoo adio communica ions sys em using cyclical
slow equency hopping and coding-expe imen al
esul s
and implemen a ion issues", Globecom
88.
[2] A.A.M. Saleh, R.A. Valenzuela,
"A
s a is ical modcl
o
indoo mul ipa h p opaga ion", IEEE SAC, Feb ua y
whc c
E,
is he bi enc gy a he ecei ed inpu and U( )
is
he s ep unc ion.
The ou age p obabili y o g ea in e es in quasi-s a ic
indoo en i onmen s is also e alua ed o he wo coding
schemes. I is gi en by
Ou age
P ob&li y=P ob.[BER BER
J
(15)
whe e BER, is a h eshold bi e o a e.
4.
RESULTS
Some esul s ha e been ob ained in o de o de ine a
p ope design alue
o
S,
as well
as
o
assess
he coding
sys em pe o mance
o
inc easing Rb alues, in he
p esence
o
bo h R-S(6,2) and Repe i ion coding.
A i s , Rb=256 Kb/s has been e ained and
S,
alues
1987.
[3]
J.C-I
Chuang, " he e ec s o mul ipa h delay sp ead on
iming eco e y", IEEE T ans. on Vehicula Technology,
Augus 1987.
[4] S.Mo idi, H.Sa i, "Analysis o decision- eedback
ca ie eco e y
loops
wi h applica ion
o
16 QAM digi al
adio sys ems", ICC 1983.
[5] D. To ie i, "The in o ma ion bi a e.
o
block codes",
IEEE T ans. on Comm.. Ap il 1984.
714
I
I4
n
I1
m
EblNa
Figu e
1.
BER o Rb=256Kb/s and S~2.5Mhz
Rb=5.12Hbps
Eb/No=lSdB
In-'
L
,
-
-.-
-.
'
.-:_
-
'
:.
..
:
.
.-
'._
..
I
lg-l
-.
..
.:*.
.........
.A..
_.A..
......
.:.
........
.........
.'"'...
............
w
b-
U
0:
B
6
;
m
Eblk
Figu e 2. BER
o
Rb=256Kb/s and S,=5Mhz
Eblk
Figu e
3.
BER o Rb=256Kb/s and S,=lOMhz
71
5
..
:....:..:.
.....
:
.......
:
3
:
'p
--no *
...
-- qdi i
code
0
5
10
.i @i-"[&
j
I
**.
..
i
'
.
.;F
.
'A'
'
'"A'
'
*
l .
EblNa
Figu e
4.
BER o Rb=256Kb/s and S in ini y
E,
m
Figu e
5.
BER e sus no malized FH sepa a ion
o Rb=256Kbls
w
6
LI
a
0
CL
LI
w
....
.......
S O5
Figu e 6. BER e sus no malized FH sepa a ion
o Rb=5.12Mb/s