he p o ile exhibi s wo dis inc 'slow e ching' c ys al planes:
(Oil) and (lll)B. This obse a ion is consis en wi h he wo k
o Cold en e a/.4 on he sensi i i y o he e ch a e o InP in
HC1 o he c ys al o ien a ion.
The p o ile in Fig. 2 was ob ained using a mix u e o 1(HC1):
3(H3POJ (again he g a ing o ien a ion is (Oil)), In his case
he p o ile is ec angula wi h a dep h o c*2000 A. He e, he
e ched dep h is no limi ed by he o ma ion o in e sec ing
slow-e ching planes, and he ec angula p o ile p oduced is
pa icula ly a ac i e o use in second-o de DFB lase s
since a s aigh o wa d Fou ie analysis shows i o con ain
=s:
1270 A o he desi ed 0-23 jum pe iod ha monic componen
( he ma k/space a io was aken o be =* 1/3). By compa ison
he commonly used iangula p o ile3 con ains only 666 A o
his componen .
Fig. 3 As Fig. 1, e ched in 1{HCI): l(CH3C00H)
Dep h =a 2000 A
A ec angula p o ile was also achie ed using 1(HC1):
1(CH3COOH) as he e chan . Fig. 3 shows he c oss-sec ion o
a g a ing o med in his e chan —again he dep h is ^2000 A.
A pa icula ad an age o he use o elec on-beam-exposed
g a ings is ha , by a ying he exposu e dose, di e en g oo e
ma k/space a ios can be ob ained. Toge he wi h con olled
o e -e ching o he SiO2, his has allowed us o ab ica e
nea ly saw oo h g a ings, con aining i ually no second-
ha monic Fqu ie componen (Fig. 4). The e chan used was
l(HB ):l(CH3COOH) and in his case he g a ings we e
aligned in he (Oil) di ec ion. The g a ing dep h, which is
limi ed by he o ma ion o (111)A planes, is ^3200 A.
IA12/4I
Fig. 4 As Fig.
1,
e ched in l(HB ):(CH3COOH)
Dep h a 3000 A
in conclusion, we ha e demons a ed a submic ome e
bile el p ocess o he p oduc ion o semiconduc o di ac ion
g a ings and ha e ab ica ed a ange o new g a ing p o iles in
InP using his echnique. These p o iles, ha ing a ied Fou ie
ha monic spec a, should pe mi he p oduc ion o mo e e i-
cien op oelec onic g a ing de ices.
Acknowledgmen s: The au ho s hank C. Dix o elec on-
beam exposu e o he g a ing pa e ns, P. Rodge s o assis -
ance wi h he d y e ching and B. Wake ield o SEM
e alua ion. They also acknowledge he Di ec o o Resea ch,
B i ish Telecom, o pe mission o publish his le e .
L. D. WESTBROOK 9 h No embe 1983
A. W. NELSON
P.
J. FIDDYMENT
B i ish Telecom Resea ch Labo a o ies
Ma lesham Hea h, Ipswich, Su olk IP5 7RE, England
Re e ences
1
UTAKA,
K.,
AKIBA,
S.,
SAKAI,
K., and MATSUSHIMA, Y.:
'Room-
empe a u e CW ope a ion o dis ibu ed- eedback bu ied*
he e os uc u e InGaAsP/InP lase s emi ing a 1-57 (mC,
Elec on. Le ., 1981,17, pp. 961-962
2
TANBUN-EK, T., ARM, S., KOYAMA, F.,
KISHINO,
K., YOSHIZAWA, S.,
WATANABE,
T., and
SUEMATSU, Y.:*
'Low- h eshold
cu en
CW
ope a ion o GalnAsP/InP bu ied-he e os uc u e dis ibu ed*
B agg- e lec o lase emi ing a
1-5-1-6
.im
ibid.,
1981, 17, pp.
967-968
3 WESTBROOK, L. D.,
NELSON,
A. w., and
DIX,
c: 'High-quali y InP
su ace co uga ions o 1-55 /Am InGaAsP DFB lase s ab ica ed
by elec on-beam li hog aphy',
ibid.,
1982,18, pp. 863-865
4
COLDREN,
L. A., FURAYA, K., MILLER, B. I., and RBNTSCHLER, J. A.:
'Combined d y and we e ching echniques o o m plana (011)
ace s in InGaAsP/InP double-he e os uc u es',
ibid.,
1982, 18,
pp.
235-237
PERFORMANCE OF FH-MFSK CELLULAR
MOBILE RADIO IN THE PRESENCE
OF NONSYNCHRONOUS USERS
Indexing e ms: Telecommunica ion, Synch onisa ion, Mobile
adio sys ems
Mon e Ca lo simula ion o an FH-MFSK sp ead«spec um
cellula mobile adio sys em in he p esence o nonsyn-
ch onous use s is p esen ed. Impai men s such as sho - e m
and shadow ading a e in oduced. Pe o mance cu es
showing he numbe o simul aneous use s he sys em can
accep a e gi en. Bo h clus e ing and no-clus e ing s a egies
a e conside ed.
In oduc ion: A mul ile el equency-shi -keying (FH-MFSK)
sp ead-spec um communica ion sys em has been ecen ly
p oposed1 o cellula mobile- adio elephony. This sys em
appea s o pe o m be e han o he FH-DPSK sys ems, i s
p oposed in Re e ence 2, when only one isola ed cell is con-
side ed. Howe e , a mo e ealis ic assessmen o he
FH-MFSK sys em calls o an analysis o i s pe o mance in a
m-ul icell con ex . An a emp o e alua e he numbe o simul-
aneous use s ha could be handled a a bi e o a e o 10"3
was unde aken in Re e ence 3. In his pape 3 a mobile- o-
base ansmission model was p oposed and sys em impai -
men s such as in acell in e e ence om nonsynch onous
use s and adjacen equency channels in he p esence o
ma ched uned ecei e il e s we e analysed. Fo in e cell
in e e ence, a Gaussian app oxima ion was used and only
quali a i e esul s we e gi en wi hou any quan i a i e assess-
men being p esen ed so a .
In his le e we p esen a compu e simula ion o he
FH-MFSK ansmission model men ioned3 abo e, allowing a
mo e p ecise e alua ion o he numbe o simul aneous use s
ha he sys em can ole a e when in e cell in e e ence is con-
side ed.
Mon e Ca lo simula ion: I was shown in Re e ence 1 ha he
sys em bi e o a e Pb could be eadily ob ained om he
inse ion p obabili y P, and miss p obabili y PM ss. These
alues we e o mula ed in Re e ence 3 as
P,
= p ob (| ( )n/x)
> Co)
and
(| Re-jeS0( )
ELECTRONICS
LETTERS
8 h Decembe 1983 Vol. 19 No. 25/26
)
< Co)
1077
whe e
x is he
sampling ime,
( ) is he
in acell in e e ence
signal,
n ( ) is he
ecei ed Gaussian noise,
Co is a
h eshold
decision alue, Re~jeS0{ )
is he
desi ed signal,
10
S0( )
0 < <
X
-
+ 2x
x< <2x
R
and 0 a e
andom a iables, namely
he
Rayleigh
and
uni o m dis ibu ions, espec i ely,
and
//c( )
is he
in e cell
in e e ence. De ails abou
he
na u e
o ( ) and
IIC( )
a e
gi en
in
Re e ence
3.
The abo e o mulas
a e
main ained
i
clus e ing
is
used,
bu
in his case
he
bandwid h a ailable
o
each cell
is he
whole
bandwid h a ailable di ided
by he
numbe
o
hexagonal cells
which compose
a
single clus e (see Fig.
1).
Fig.
1
Hexagonal
cell
layou
wi h
clus e s
o
se en
cells
The beha iou
o P and
PMISS
can be
eadily de e mined
by Mon e Ca lo ials.
I is
me ely necessa y
o
gene a e inde-
penden uni o mly dis ibu ed a iables; hen,
by
using
he
adequa e ans o ma ions, samplings
o ( ),
M/T),
//C(T)
and
Re~jeS0(x)
can be
ob ained. This p ocess
is
epea ed
N
imes,
and ul ima ely we ha e
N
P'**W
whe e
1 i
|
{x)
+
//C(T)
+ n/x)
|
> Co
|0 o he wise
N
MlSS — N
whe e
{ Re-»SQ{x)
+
{x)
0 o he wise
n (x)
|
< Co
1
id1
I
bi
<
10
M=20
o =3
5
^>>%((^
40
^-^^^
35
"^^^
30
}-&
Fig.
3 Bi
e o a e
in a
mul icell sys em
assuming
Gaussian
in e -
e ence
(do s
ep esen
Mon e
Ca lo simula ion
poin s)
N
=
10000
was
aken. Inc easing his alue p oduced
a
negli-
gible change
in he
esul s
bu
ma kedly inc eased
un
ime.
I
can
be
obse ed ha he e
may be
some ques ion ega ding
he accu acy
o
hese esul s, pa icula ly
o Pb
alues smalle
han
10"3.
Fo una ely hese
Pb
alues
a e no
usually
handled
in
mobile- adio elephony.
Resul s:
Fig. 2
shows
he
FH-MFSK sys em pe o mance
in
he p esence
o
six adjacen in e e ing cells. E e y hexagonal
cell con ains
M
simul aneous use s,
he
ansmission a e
pe
use
is 32
kbi /s,
and he
bandwid h conside ed
in
each cell
is
he whole
20 MHz
a ailable. Powe con ol
in he
mobileSj
a
mean pa h loss exponen
a o
—3-5
and a
logno mal dis ibu-
ion modelling
he
shadow ading wi h
8 dB
s anda d de i-
a ion ha e been aken in o accoun . Finally, op imum h es-
hold decision alues we e ound
a
each signal/noise a io.
Fig.
3
shows
he
esul s ob ained
in
Re e ence
3 by
using
he
Gaussian app oxima ion
o
he in e cell in e e ence. Compa -
ing Figs.
2 and 3
leads
o he
ealisa ion ha
he
Gaussian
app oach
is oo
pessimis ic
and a
be e pe o mance could
be
expec ed.
The
do ed line
o
Fig.
3
also shows
he
FH-MFSK
sys em pe o mance using
he
Mon e Ca lo simula ion
and
he Gaussian app oxima ion
o he
in e cell in e e ence
o
M
= 20
simul aneous use s
pe
cell. This analysis se es
as a
check
on he
alidi y
o
he Mon e Ca lo echniques.
In Re e ence
3
clus e ing
was
sugges ed
as a
s a egy
o
imp o e
he
mul icell pe o mance.
In
o de
o
gain insigh
on
1
1030
c<
=3 5
2530
15
20 25^ 30 5 1Q 15 20
|371/2|
Ec/N0.dB
Ec/N0.dB
Fig.
2 Bi
e o a e
in a
mul icell sys em
om
Mon e
Ca lo simula ion
Fig. 4 Bi
e o a e
in a
mul icell sys em
wi h
a
clus e
o
se en
cells
1078 ELECTRONICS LETTERS 8 h Decembe 1983 Vol.19 No. 25/26
i s e ec s, he desi ed cell and
i s
six adjacen ones we e con-
side ed
o be a
clus e
o
basic cell
o
epe i ion. The o he
clus e s appea ing
in
he mul icell sys em we e no aken in o
accoun because
in a
i s app oach
he
in e cell in e e ence
a ising wi h
he
clus e ing s a egy was supposed negligible.
The esul s plo ed
in
Fig.
4
show ha clus e ing wo sens
he
mul icell e iciency
and
consequen ly
i s
p esence
in he
FH-MFSK sys em
is
appa en ly no
o be
ecommended. The
indica ion
is
ha
he
gains om sp ead-spec um p ocessing
a e o se by inc eased in acell in e e ence, when his ac o
is
aken in o accoun .
R. AGUST1-COMES 31s Oc obe 1983
F.
CASADEVALL-PALACIO
G. JUNYENT-GIRALT
ETS1 Telecomunicacibn
Apdo.
30 002, Ba celona, Spain
Re e ences
1
GOODMAN,
D. J.,
HENRY,
p. s., and
PRABHU,
. K.: 'F equency-
hopped mul ile el FSK
o
mobile adio', Bell Sys . Tech. J., 1980,
59,
pp.1257-1275
2
COOPER,
G. R., and
NETTLETON,
R.
W.
:
'A sp ead spec um echnique
o high-capaci y mobile communica ions', IEEE T ans.,
1978,
VT-27,
pp. 264-275
3
AGUSTI,
R., and
JUNYENT,
G.: 'Pe o mance o FH mul ile el FSK
o mobile adio
in an
in e e ence en i onmen ',
ibid.,
1983,
•JOM-31,
pp. 840-846
using he a e age alue and he a iance o he ecei ed signal
3
as
MODE PARTITION NOISE CAUSED
BY
WAVELENGTH-DEPENDENT ATTENUATION
IN LIGHTWAVE SYSTEMS
Indexing e ms: Lase s and applica ions, Lase diodes, Op ical
ansmission
Powe luc ua ions among
he
longi udinal modes
o
lase
diodes cause noise
in he
ecei ed signal a e being il e ed
by
a
wa eleng h-dependen a enua ion mechanism. We ha e
de eloped
a
heo e ical model
o
cha ac e ise his noise and
s udied deg ada ion
in
ligh wa e sys em pe o mance. Powe
penal ies obse ed
in a 432
Mbi /s wa eleng h di ision
mul iplexing sys em expe imen ag eed wi h heo e ical p e-
dic ions.
Mode pa i ion noise (MPN)
in
ligh wa e sys ems
is
caused
by
a
combina ion
o
ins an aneous luc ua ion
o
he powe
dis ibu ed among he lase modes and spec al il e ing
in
he
ansmission pa h.
MPN
associa ed wi h ib e dispe sion
causing phase delay
in
each pulse
has
been ex ensi ely
dis-
cussed
in he
li e a u e1
and
ound
o se one o he pe -
o mance limi a ions in high-bi - a e ligh wa e sys ems.
In his le e
we
desc ibe
MPN
caused
by
wa eleng h-
dependen a enua ion
in
he ansmission pa h.2 MPN o his
kind
is
especially impo an
in
designing
WDM
sys ems,
whe e ansmission cha ac e is ics nea cu o wa eleng hs
o
mul iplexe s
and
demul iplexe s
a e
highly wa eleng h-
dependen . Wa eleng h-dependen ib e a enua ion
in
long-
haul sys ems also can cause his ype
o
MPN
in
addi ion
o
he MPN associa ed wi h ib e dispe sion, especially in sys em
channels ope a ing nea he OH abso p ion peaks.
Le a( and/- ep esen he ins an aneous powe
in
he lase 's
i h mode and mode-dependen a enua ion
in
he ansmission
pa h
a
wa eleng h A,, espec i ely. Then he signal ampli ude
o each pulse a i ing
a
he ecei e can be gi en by
=
L
ai i
(!)
Assuming ha
he
powe
is
no malised such ha £,-
a, = 1
and ha he pa i ioning is cons an o e he du a ion o each
pulse bu andom om pulse
o
pulse, MPN can be desc ibed
(2)
whe e as ep esen s ime-a e aged powe
o
he
i h
mode and
mode pa i ion coe icien
k
ep esen s
a
measu e o he powe
which luc ua es. The coe icien
k is
assumed
o be
cons an
o
all
modes. The noise- o-signal a io due
o
MPN can
be
gi en by
N/S
= a2 =
<T2JP
(3)
The powe penal y AP, which
is
de ined
as he
inc ease
in
ecei ed powe necessa y
o
main ain
an
e o a e equal
o
he one wi hou MPN, is hen gi en by
(4)
whe e Qc
=
l/< p
and Q
is
he Q- alue associa ed wi h
a
gi en
bi e o a e.4
Al hough eqns.
2-4 can be
calcula ed nume ically
o a
gi en lase spec um and il e ing cha ac e is ic,
i is
use ul
o
ob ain
an
analy ical o mula
o
e alua e sys em pe o mance
by making he ollowing assump ions.
The ime-a e aged en elope o he lase spec um is app ox-
ima ed wi h
a
Gaussian cen ed
a
wa eleng h Xc and
o
hal -
wid h AX:
1exp[-(/l-Ac)2/2(AA)2](5)
The wa eleng h-dependen a enua ion is assumed
o
be linea
wi h wa eleng h a ound Xc:
(6)
whe e
A
ep esen s a e
o
a enua ion change
in
dB/nm. Sub-
s i u ing eqns.
5
and
6
in o eqns.
2
and
3
and app oxima ing
he sums wi h in eg als yields
<x2
=
e2(exp [04 AA/4-34)2]
- 1)
(7)
and om eqn.
4
he powe penal y is gi en by
AP
= -5
log.o {1
-
e2 c2(exp [(A AA/4-34)2]
-
1)}
(8)
T ansmission deg ada ion
due o MPN was
in es iga ed
expe imen ally as he op ical signal was sen h ough
a
g a ing
demul iplexe used
o a
single-mode wo-channel
WDM
sys em expe imen .5'6 The powe penal ies due
o
MPN we e
de e mined om
bi
e o a e (BER) agains ecei ed powe
measu emen s wi h
and
wi hou
he
demul iplexe . Bu ied-
he e os uc u e
(BH)
InGaAsP/InP lase s we e modula ed
wi h
432
Mbi /s
NRZ
o ma .
Fig. 1
shows
he
spec al
a enua ion
o he
g a ing demul iplexe
and he
ope a ing
wa eleng hs o lase ansmi e s.
Table
1
summa ises lase spec a and ansmission il e ing
cha ac e is ics. Also gi en
a e MPN
penal ies measu ed
a
10
ACB
1200
1300 1
wa eleng h
,nm
[577/il
Fig. 1 Spec al a enua ion o g a ing demul iplexe and lase ope a ing
wa eleng hs
ELECTRONICS
LETTERS
8 h
Decembe 1983 Vol.
19
No. 25/26 1079