Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
8
,
No.
6
,
D
ece
m
ber
201
8
, pp.
4334
~
43
42
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v8
i
6
.
pp
4334
-
43
42
4334
Journ
al h
om
e
page
:
http:
//
ia
es
core
.c
om/
journa
ls
/i
ndex.
ph
p/IJECE
Avera
ge Ch
annel
Ca
p
ac
i
t
y of Am
pli
fy
-
an
d
-
forward
MIMO/
FSO Sys
tems O
ver Atm
osp
heric
Turbu
lence Chan
nels
Duon
g
H
uu A
i
Facul
t
y
of Electr
onic
s a
nd
T
el
e
co
m
m
unic
at
ions, Korea
Vi
et
nam
Friendship
Infor
m
at
ion
T
ec
hnolo
g
y
Coll
e
ge
,
Vie
t
nam
Depa
rt
m
ent
o
f
A
ero
spac
e
E
le
c
tro
nic
s,
Schoo
l
of
El
e
ct
roni
cs
and
Te
l
ec
om
m
unic
ations,
Hanoi
Uni
ver
sit
y
of
Sci
ence
and
Te
chno
log
y
,
Vie
tna
m
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Oct
6
, 2
01
7
Re
vised
Ju
l
18
,
201
8
Accepte
d
Aug
1
, 2
01
8
In
amplif
y
-
and
-
forward
(AF
)
rel
a
y
ch
anne
l
,
wh
en
the
d
irect
l
i
nk
bet
wee
n
source
and
dest
i
nat
ion
t
erminal
s
is
dee
pl
y
f
ade
d
,
the
signa
l
from
the
source
te
rm
ina
l
to
th
e
desti
nation
t
erminal
prop
agate
s
through
the
re
l
a
y
te
rm
ina
ls
,
ea
ch
o
f
which
r
e
lay
s
a
sign
al
r
ecei
ved
from
th
e
p
rev
ious
te
rm
in
al
to
the
next
te
rm
ina
l
in
ser
ies
.
Thi
s
pape
r,
w
e
the
ore
ticall
y
a
naly
z
e
the
per
fo
rm
anc
e
of
m
ult
ipl
e
-
inpu
t
m
ult
ipl
e
-
outpu
t
(MIM
O)
A
F
fre
e
-
spa
ce
op
ti
c
al
(FS
O)
s
y
stems
.
Th
e
A
F
-
MIM
O/F
SO
ave
rag
e
ch
anne
l
ca
pa
ci
t
y
(ACC),
which
is
expr
essed
in
te
r
m
s
of
ave
rag
e
spec
tr
al
eff
i
cienc
y
(AS
E)
is de
rive
d
ta
king
int
o
ac
coun
t
the
at
m
ospheric
turbu
lence
eff
ec
ts
on
th
e
MIM
O/FS
O
cha
nnel.
T
h
e
y
are
m
odel
ed
b
y
l
og
-
norm
al
and
t
he
gamm
a
-
gamm
a
distri
buti
ons
for
the
c
ase
s
of
wea
k
-
to
-
str
ong
turbul
ence
condi
ti
ons.
W
e
ext
ract
clos
ed
form
m
at
hemati
c
al
ex
pre
ss
ion
for
the
eva
lu
at
ion
o
f
the
ACC
and
we
qu
ant
itati
v
e
l
y
discuss
the
infl
u
enc
e
of
turbul
en
ce
str
engt
h
,
l
ink
dista
n
ce,
diff
er
ent
num
ber
of
rela
y
st
at
ions
and
di
ff
ere
n
t
MI
MO
conf
igura
t
io
ns
on
it.
Ke
yw
or
d:
Am
plify
-
and
-
f
orward
Atm
os
ph
eric t
urb
ulence
Av
e
ra
ge
c
hann
el
capacit
y
Av
e
ra
ge
s
pectr
al
eff
ic
ie
ncy
Fr
ee
-
sp
ace
opti
cal
Copyright
©
201
8
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Duo
ng Hu
u Ai,
Faculty
of Elec
tro
nics and
Tel
ecom
m
un
ic
at
i
on
s
,
Korea
Viet
nam
Fr
ie
nd
s
hip I
nfor
m
at
ion
Tec
hnol
og
y C
ollege
,
136 Tra
n Dai
Nghia St.
, Dan
ang,
Viet
nam
.
Em
a
il
: ai
dh
@vi
et
han
it
.edu.
vn
1.
INTROD
U
CTION
The
nece
ssit
y
of
a
co
st
-
ef
fec
ti
ve,
li
cense
-
f
r
ee,
high
secu
ri
ty
and
high
ba
ndwidt
h
acce
s
s
te
chn
iq
ue
has
le
ad
to
a
con
ti
nu
ous
rese
arch
a
nd
com
m
ercial
interest
in
op
ti
cal
wireless
com
m
un
i
cat
ion
syst
e
m
s
[1
]
-
[
3].
On
e
of
m
ajo
r
deg
ra
datio
ns
to
the
per
f
orm
ance
of
F
SO
com
m
un
ic
at
ion
s
is
the
influe
nce
of
at
m
os
ph
e
ric
tur
bu
le
nce
cau
sed
by
va
riat
io
ns
in
the
r
ef
rac
ti
ve
ind
e
x,
pre
ssu
re
fluct
uations
i
n
the
ai
r
a
long
the
pr
op
a
gation
path o
f
the
lase
r beam
[
4].
Re
cent
stud
ie
s
there
are
m
any
AS
ER
pe
rform
ance,
ave
rage
capaci
ty
per
f
or
m
ance
for
F
SO
syst
em
s
is
recently
repor
te
d
in
[5
]
-
[14].
I
n
[
5]
De
ng
et
al.
prese
nted
analy
ti
c
ex
pressi
on
s
an
d
sta
ti
sti
cal
m
od
el
s
of
t
he
sci
ntil
la
ti
on
in
dex
an
d
a
ver
a
ge
ca
pacit
y
for
m
ulti
ple
part
ia
l
coh
ere
nt
beam
s
pr
opa
ga
ti
ng
th
rou
gh
strong
tur
bu
le
nce
MI
MO
F
SO
li
nks
.
I
n
[
6]
S
har
m
a
et
al.
e
valuat
ed
t
he
ca
pacit
y
of
MIM
O
-
OFDM/
FSO
with
inter
-
sy
m
bo
l
inter
fe
ren
ce
(
ISI)
un
der
str
ong
at
m
os
phe
ric
tu
rbu
le
nce
c
onditi
ons.
I
n
[7
]
K
ost
as
P.
Pe
pp
as
et
al
.
capaci
ty
analy
sis
of
dual
Am
plify
-
an
d
-
F
orw
ard
relay
ed
F
S
O
Syst
em
s
ov
e
r
tu
rbulence
ch
ann
el
s
with
po
inti
ng
error
s
.
I
n
[
8]
Mon
a
A
gg
a
r
w
al
.
Eval
uated
exact
capaci
ty
of
Am
plify
-
and
-
F
orward
re
la
ye
d
opti
cal
wireless
com
m
un
ic
at
ion
syst
em
s.
In
[
14
]
H
.D.
Ai
et
al
.
Ca
pacit
y
analy
sis
of
am
plify
-
and
-
f
orwa
rd
S
ISI/FS
O
s
yst
e
m
s
ov
e
r
at
m
os
ph
e
ric
tur
bule
nce
channels
.
H
ow
ever,
to
the
be
st
of
our
kn
owle
dg
e,
the
pe
rfor
m
ance
on
a
ve
rage
channel
ca
paci
ty
of
AF
-
MI
MO/FSO
syst
e
m
s
fo
r
both
we
ak
a
nd
str
ong
a
t
m
os
ph
e
ric
tu
r
bu
le
nc
e
c
ha
nnel
s
has
no
t
bee
n
cl
ari
fied.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Avera
ge
C
hannel
Ca
paci
ty
o
f
Ampli
fy
-
and
-
f
or
war
d
...
(
D
uong
H
uu Ai
)
4335
The
rem
ai
nd
er
of
t
he
pa
pe
r
is
organ
iz
e
d
as
fo
ll
ows
.
I
n
Sect
ion
2
th
e
syst
e
m
descr
ipti
ons
are
descr
i
bed
in
de
ta
il
.
In
Sect
io
n
3
at
m
os
pheri
c
tur
bule
nce
m
od
el
s
are
prese
nted.
I
n
Sec
ti
on
4
c
ha
nn
el
ca
pacit
y
of
AF
-
MIM
O/FSO
li
nk
s
is
de
rive
d
f
or
wea
k
a
nd
st
ron
g
t
urb
ulence
c
ha
nnel
s.
In
t
he
Se
ct
ion
5
the
nu
m
erical
resu
lt
s
are
pr
e
s
ented,
a
naly
zi
ng
the
in
flue
nce
of
tu
r
bu
le
nce
stren
gth
,
li
nk
di
sta
nce,
num
ber
relay
sta
ti
on
s
and
var
i
ou
s
MIMO
confi
gurati
ons
on th
e
ASE
of syst
e
m
s.
The pape
r
c
oncl
ude
s w
it
h a s
ummary
g
i
ven in t
he
end.
2.
SY
STE
M DESC
RIPTIO
NS
We
co
ns
ide
r
a
gen
e
ral
AF
–
MIM
O/FS
O
s
yst
e
m
us
ing
S
C
-
Q
AM
sign
al
s
with
M
trans
m
itti
ng
la
sers
po
i
nting
to
wa
r
d
an
N
ape
rtu
re
receive
r
as
dep
ic
te
d
in
F
igure
1.
Data
transm
issi
on
em
plo
yi
ng
the
sam
e
SC
-
Q
AM sig
na
l i
s tran
s
m
itte
d
with p
e
rf
ect
synch
ronizat
io
n
by each
of th
e
M
transm
it
te
lescopes th
r
ough
an
tur
bu
le
nce
cha
nn
el
to
wa
rd
N
phot
o
-
detect
ors
(P
D
s)
with
the
li
gh
t
beam
width
s
of
eac
h
te
le
scop
e
as
su
m
e
to
be
wide
e
nough
to
il
lum
inate
the
entire
receiver
ar
ray.
The
transm
it
t
er'
s
te
le
scop
e
arr
ay
is
assu
m
ed
to
pro
du
ce
t
he
s
a
m
e
total
op
ti
cal
power
ir
re
sp
ect
ive
of
M
to
enfo
rce
a
fair
co
m
par
is
on
with
the
s
ing
le
transm
itter cas
e.
Figure
1. The
s
ource
node
, r
el
ay
ing
node, an
d desti
natio
n n
od
e
of
AF
-
M
I
MO/FSO
syst
em
u
sing
SC
-
Q
AM
sign
al
s
over
atm
os
ph
eric t
ur
bule
nce c
ha
nnel
The
MIM
O
c
ha
nn
el
is
m
od
el
ed
an
d
ca
n
be
denoted
by
a
n
MN
m
at
rix
of
t
he
tur
bu
le
nce
cha
nn
el
,
,1
()
MN
mn
mn
Xt
X
.
The
el
ect
rical
sign
al
at
the
ou
tp
ut
of
the
PD
corres
pondin
g
to
the
n
th
receive
ape
r
tur
e
ou
t
pu
t ca
n be
e
xpresse
d
as
f
ol
lows
[
9]
21
1
1
1
0
0
11
()
(
(
)
)
,
C
M
N
C
i
e
s
i
i
mn
m
n
i
i
MN
m
n
i
mn
r
t
P
e
t
X
P
vt
(1)
(
a)
Sou
rce
node
(b)
Re
la
yi
ng nod
e
SC
-
QAM
m
od
u
-
la
ti
on
Laser
1
Laser
2
Laser
M
.
.
.
O/E
O/E
O/E
AF
AF
AF
E/O
E
/O
E
/O
Data
input
.
.
.
.
.
.
.
.
.
(
c)
relay
ing n
ode
(
d)
Desti
natio
n n
od
e
O/E
O/E
O/E
.
.
.
AF
AF
AF
E/O
E
/O
E
/O
PD
1
PD
2
PD
M
Data
ou
t
pu
t
EGC
SC
-
QAM
dem
od
ulati
on
.
.
.
.
.
.
.
.
.
.
.
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
20
88
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2
01
8
:
4334
-
4342
4336
wh
e
re
e(
t)
represents
th
e
Q
AM
sig
nal,
()
mn
Xt
den
otes
t
he
sta
ti
on
a
ry
rand
om
process
for
the
tur
bule
nc
e
channel
bet
we
en
the
m
th
la
se
r
to
the
n
th
PD,
C
is
the
num
ber
re
la
y
sta
ti
on
s
.
()
mn
t
is
the
A
WGN
with
ze
r
o
m
ean
an
d
va
ri
ance
()
0
n
N
.
U
nd
e
r
the
assum
ptio
n
of
perfect
c
hannel
est
im
a
t
ion
at
the
rec
ei
ver
si
de,
the
conditi
on
al
in
put S
NR at the
PD
ca
n be
w
ritt
en
as a
f
init
e s
um
o
f
s
ub
-
c
ha
nn
el
SN
Rs
as
2
11
0
C
MN
i
mn
mn
i
(2)
wh
e
re
mn
are
RVs
def
i
ned
as
t
he
instanta
ne
ou
s
el
ect
rical
SN
R
at
the
ou
tp
ut
of
the
n
th
PD
cause
d
by
sig
na
l
from
the
m
th
la
ser.
mn
are
g
i
ven in the
foll
owin
g
2
2
0
1
,
m
n
m
n
s
m
n
m
n
X
a
P
N
X
MN
(3)
in which
, we
de
no
te
is t
he
a
ver
a
ge SNR
of
syst
e
m
s.
2
1
0
2
21
10
11
1
1
/.
c
i
i
C
MN
i
s
i
i
mn
i
X
P
X
P
N
MN
(4)
3.
ATM
OSPHE
RIC TU
RBU
LE
NC
E
MO
D
EL
S
Ther
e
e
xist
a
few
publis
hed
pap
e
rs
co
nce
rni
ng
the
pr
ob
a
bi
li
t
y
den
sit
y
functi
on
(pdf)
of
m
ulti
-
ho
p
transm
issi
on
over
am
plify
-
an
d
-
forwar
d
rela
y
fad
ing
c
hann
el
s
[9
]
,
[10].
W
it
h
am
plify
-
and
-
f
orwa
rd
f
r
ee
-
sp
ace
op
ti
cal
syst
em
s
us
in
g
SC
-
Q
AM
m
od
ulati
on,
f
or
wea
k
a
t
m
os
ph
e
ric
tur
bule
nce
c
onditi
on
,
the
tu
r
bu
le
nce
include
d
fa
ding
is
assum
ed
to
be
a
rand
om
pr
ocess
tha
t
fo
ll
ow
s
t
hat
log
-
norm
al
distribu
ti
on
[
9],
[10],
wh
e
reas
f
or
str
ong
t
urb
ulence
cond
it
io
ns
,
a
gam
m
a
-
ga
m
m
a
distrib
ution i
s
us
e
d
[
11]
.
3
.
1.
Th
e
Log
-
No
r
mal
Tur
b
ulence
Model
of A
F
–
MI
MO
/FSO
S
ystems
In
lo
g
-
norm
al
fad
i
ng
cha
nnel
,
the
prob
a
bili
ty
den
sit
y
fu
nc
ti
on
(pd
f)
f
or
an
norm
alize
d
irra
diance
with lo
g
-
norm
al
,
0
mn
X
, is
desc
ribe
d
as
[9], [
10]
22
12
(
l
n
(
)
+
0
.
5
)
1
e
x
p
,
(
C
1
)
2
2
s
X
C
mn
a
s
s
X
fX
X
(5)
wh
e
re
2
12
e
x
p
(
)
1
s
with
1
and
2
are r
es
pecti
vely
g
ive
n by
22
22
12
7
/
6
5
/
6
2
1
2
/
5
2
1
2
/
5
22
0
.
4
9
0
.
5
1
,.
1
0
.
1
8
0
.
5
6
1
0
.
9
0
.
6
2
dd
(6)
In
e
qu
at
i
on
(6),
2
/
4
,
d
k
D
L
wh
ere
2/
k
is
the
opti
cal
wa
ve
num
ber
,
L
is
the
li
nk
dis
ta
nce
in
m
et
ers,
is
the
op
ti
cal
wav
el
e
ng
t
h,
an
d
D
is
the
receiver
a
pe
rtur
e
diam
e
te
r
of
the
PD.
Th
e
par
am
et
er
2
2
is
the Ry
tov va
ri
ance a
nd in
t
hi
s case, is
expre
ssed by [
1]
2
2
7
/
6
11/
6
2
1.23
,
n
C
k
L
(7)
wh
e
re
2
n
C
sta
nds
for
t
he
stre
ngth
of
the
at
m
os
ph
eric
tu
r
bu
le
nce,
w
hich
is
th
e
al
ti
tud
e
dep
e
ndent
and
it
giv
e
n by
2
10
2
5
2
6
(
)
0
.
0
0
5
9
4
1
0
e
x
p
(0
)
e
x
p
2
.
7
1
0
e
x
p
,
2
7
1
0
0
0
1
0
0
0
1
5
0
0
nn
v
h
h
h
C
h
h
C
(8)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Avera
ge
C
hannel
Ca
paci
ty
o
f
Ampli
fy
-
and
-
f
or
war
d
...
(
D
uong
H
uu Ai
)
4337
wh
e
re
h
is
the
al
ti
tud
e
in
m
e
ter
s,
v
is
the
wind
sp
eed
i
n
m
et
e
rs
pe
r
seco
nd
a
nd
2
(
0
)
n
C
is
the
valu
e
of
2
n
C
at
the
gro
und
in
-
3
/
2
m.
2
n
C
var
ie
s
f
r
om
1
7
-
3
/
2
1
0
m
to
1
3
-
2
/
3
1
0
m
fo
r
we
ak
up
to
st
rong
t
urbu
le
nce
cases,
resp
ect
ively
.
3
.
2
.
Th
e
G
am
ma
-
gamm
a
T
urbulence
M
odel
of
AF
–
MI
MO/FS
O
S
yst
ems
The
pdf
of
ga
m
m
a
-
ga
m
m
a
fad
in
g
cha
nnel
,
0,
mn
X
the
pd
f
for
an
norm
al
iz
ed
irrad
ia
nc
e
wi
th
gam
m
a
-
gam
ma,
0
mn
X
, is d
esc
ribe
d
as
[11
]
1
2
2
2
2,
1
ΓΓ
m
C
n
X
a
a
f
X
X
K
X
C
(9)
wh
e
re
()
is
the
Gam
m
a
fu
ncti
on
a
nd
()
K
is
the
m
od
ifie
d
Be
ssel
fu
nc
ti
on
of
t
he
seco
n
d
ki
nd
of
order
,
wh
il
e
the
pa
r
a
m
et
ers
an
d
are
directl
y
relat
ed
to
at
m
os
ph
e
ric
conditi
ons
thr
ough
the
f
ollow
i
ng
expressi
on
s:
11
12
e
x
p
(
)
1
,
e
x
p
(
)
1
.
(10)
4.
AV
E
RAGE
C
HANNEL
C
A
PACIT
Y
An
op
ti
cal
wireless
channel
is
a
ran
do
m
l
y
tim
e
-
var
ia
nt
channel
and
the
receive
d
instanta
neous
el
ect
rical
sign
a
l
-
to
-
no
ise
rati
o
(SNR)
is
a
ra
ndom
var
ia
ble.
Th
us
,
the
cha
nn
el
ca
pacit
y
m
us
t
be
co
ns
id
ered
as
a
rand
om
var
ia
ble,
an
d
it
s
av
erag
e
value
,
know
n
as
ave
ra
ge
cha
nnel
cap
aci
ty
,
C
.
T
he
A
SE
in
bits/
s/Hz
if
the freq
ue
ncy r
esp
on
se
of t
he c
hannel is
known
. T
he
a
ver
a
ge
c
hannel ca
pa
ci
ty
is g
iven
by
[
12]
.
2
B
l
o
g
1
(
)
,
C
f
d
Γ
Γ
(
bit/
s/Hz),
(11)
wh
e
re
B
is
the
channel’s
band
width
a
nd
is
th
e
total
chan
nel
SN
R
an
d
,
1
,
.
.
.
,
,
1
,
.
.
.
,
nm
n
N
m
M
is
the
m
at
rix
of the
MIM
O
at
m
os
pheric t
urbu
le
nc
e cha
nn
el
s
. T
he
joint
pdf
()
f
Γ
can
be
r
ed
uce
d
to
a
p
r
oduct
of the
first
-
order
pdf
of
eac
h
el
e
m
e
nt
nm
.
T
he
pdf
s
of
are
resp
ect
i
vely
descr
i
bed
in
log
-
norm
al
[9
]
,
[
10]
an
d
gam
m
a
-
gam
ma [11
]
distrib
ution
s
as
fo
ll
ows
22
12
(
l
n
(
)
)
1
(
)
e
x
p
,
8
2
(
C
1
)
2
mn
s
mn
mn
C
s
m
n
s
f
(12)
1
42
2
2
(
)
(
)
2
.
(
C
1
)
(
)
(
)
C
m
n
m
n
mn
mn
fK
(13)
4.1. C
apacit
y of
Log
-
Norma
l
AF
-
MI
MO/
FSO
Channel
s
Using
Eq
uatio
ns
11
an
d
12,
the
AS
E
of
a
l
og
-
norm
al
of
AF
-
M
IMO/F
S
O
cha
nn
el
cap
aci
ty
can
be
expresse
d
as
1
2
2
2
ln
l
n
1
1
e
x
p
.
8
2
(
C
1
)
2
l
n
2
C
mn
s
mn
mn
mn
s
s
mn
C
d
B
(14)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
20
88
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2
01
8
:
4334
-
4342
4338
We ca
n
le
t
the
AS
E
of a l
og
-
norm
al
o
f AF
-
MIM
O/FS
O
c
ha
nn
el
with
ou
t
re
la
y st
at
ion
(
0
)
.
C
2
2
2
0
ln
l
n
1
1
e
x
p
.
8
2
2
l
n
2
mn
s
mn
mn
mn
mn
s
s
C
C
d
B
(15)
In
Eq
uatio
n
15,
us
in
g
t
he
e
qual
it
y
1
1
l
n
(
1
)
1
/
k
k
k
x
x
k
for
0
1
,
x
an
d
the
scal
ed
c
om
ple
m
entary
error
f
unct
io
n
2
e
r
f
c
(
)
e
r
f
c
(
)
,
x
x
e
x
the
integral
of
cha
nn
el
ca
pa
ci
ty
witho
ut
r
el
ay
sta
t
ion
(
0
)
C
c
an
be
trans
form
ed
to
the
fo
ll
owin
g
su
m
m
at
ion
[
12
]
f
or
t
he
es
tim
a
ti
on
of
th
e
aver
a
ge
ca
pa
ci
ty
,
with
ha
s
the
fo
ll
owin
g form
1
0
1
0
2
2
1
4
e
r
f
c
2
e
r
f
c
2
2
2
2
2
2
e
xp
e
r
f
c
.
8
22
k
m
n
m
n
s
ss
k
ss
C
m
n
m
n
mn
s
s
C
C
k
k
Bk
(16)
In
Eq
uatio
n
17,
2
l
n
(
)
m
n
m
n
s
with
mn
is
the
instanta
neous
r
ecei
ved
SN
R
outp
ut
of
E
GC
detect
or,
a
nd
22
0
e
x
p
(
/
8
)
/
2
l
n
2
.
s
C
In
order
t
o
evaluate
the
r
e
su
lt
of
e
quat
ion
(16
)
we
obta
in
a
ve
ry
accurate
appr
ox
im
at
ion
for
the
evaluati
on
of
the
ave
ra
ge
capaci
ty
[13],
we
shou
l
d
est
i
m
at
e
the
in
finite
ly
su
m
ov
er
,
k
from
1
k
to
8,
k
with
has
t
he
f
ollo
wing for
m
1
8
0
1
0
2
2
1
4
e
r
f
c
2
e
r
f
c
2
2
2
2
2
2
e
xp
e
r
f
c
.
8
22
k
m
n
m
n
s
ss
k
ss
C
m
n
m
n
mn
s
s
C
C
k
k
Bk
(17)
Substi
tuti
ng
E
q
uatio
n
s
17
in
to
14
an
d
inte
gr
al
cal
culat
e.
The
AS
E
of
AF
–
MIM
O/F
S
O
cha
nn
el
wit
h
log
-
norm
al
d
ist
ributi
on
m
od
el
ca
n be e
xpres
sed
a
s
1
00
11
.
1
(
C
1
)
mn
CC
m
n
m
n
CC
C
C
C
C
d
B
B
C
B
(18)
4.2.
C
apacit
y of
G
amm
a
-
gamma AF
-
M
I
MO/FS
O
Cha
nnels
Substi
tuti
ng
e
quat
ion
(
13)
int
o
(
11),
t
he
ave
rag
e
ca
pacit
y
of
a
gam
m
a
-
ga
m
m
a
of
AF
-
MIM
O/FS
O
channel ca
n be
g
ive
n by
1
2
42
2
1
l
n
1
2
.
(
C
1
)
l
n
2
C
mn
m
n
m
n
m
n
m
n
m
n
C
Kd
B
(19)
Using
the
Me
ijer
G
-
functi
on,
,
pq
mn
G
to
e
xpres
s
the
lo
ga
rith
m
ic
te
r
m
of
1
,
1
1
,
2
2
,
2
1
,
0
l
n
(
1
)
x
G
x
,
an
d
,
2
2
,
0
0
,
2
,
22
1
24
x
KG
,
the
ASE
of
A
F
–
MIM
O/FS
O
c
hannel
with
gam
m
a
-
ga
m
m
a
distri
bu
ti
on
m
od
el
can
be
giv
e
n by
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Avera
ge
C
hannel
Ca
paci
ty
o
f
Ampli
fy
-
and
-
f
or
war
d
...
(
D
uong
H
uu Ai
)
4339
2
2
2
2
,1
2
44
2
6
,
1
2
,
6
2
2
2
2
2
,
,
,
,
4
4
4
4
4
1
(
)
.
2
(
C
1
)
l
n
2
1
6
CC
CC
m
n
m
n
C
G
B
(20)
5.
NUMER
IC
A
L RES
ULTS
Using
t
he
a
bove
cl
ose
d
m
ath
em
atical
fo
r
m
s
as
sh
own
in
E
quat
ion
18
and
20,
w
e
ca
n
est
im
at
e
the
aver
a
ge
ca
paci
ty
of
A
F
-
MI
MO/FSO
syst
em
ov
er
at
m
os
ph
eric
tu
r
bu
le
nc
e
cha
nn
el
.
We
us
e
(
18)
f
or
t
he
case
of
wea
k
t
urb
ulence
with
l
og
-
norm
al
distribu
ti
on
m
od
el
,
wh
il
e
(20)
is
use
d
for
st
ron
g
case
with
the
gam
m
a
-
gam
m
a
distrib
ution.
I
n
t
he
a
naly
sis
belo
w,
we
e
valuate
t
he
a
ver
a
ge
ca
pacit
y
for
th
re
e
dif
fer
e
nt
val
ues
of
tur
bu
le
nce
stre
ng
t
h
2
1
5
2
/
3
10
m
n
C
,
2
1
5
2
/
3
9
1
0
m
n
C
,
an
d
2
1
4
2
/
3
3
10
m
n
C
,
li
nk
distance
L
ha
s
bee
n
chosen
to
be
L
=
2000
m
,
L
=
40
00
m
,
diff
ere
nt
values
of
num
ber
relay
sta
ti
on
s
0,
C
1,
C
and
2
C
and
a
m
plific
at
ion
ga
in
2
d
B
.
AF
P
Assu
m
es
that,
the
relay
s
ta
ti
on
s
are
plac
ed
e
qu
i
distant,
tur
bu
le
nce
c
onditi
ons
betwee
n rela
y of sta
ti
on
s
is th
e sam
e.
Re
le
van
t pa
ram
et
ers
con
si
der
e
d
i
n o
ur analy
sis are
pro
vid
e
d
in
Ta
ble 1.
Table
1.
Rel
e
va
nt
Pa
ram
et
ers
Co
ns
ide
red i
n Our
An
al
ysi
s
Para
m
eter
Sy
m
b
o
l
Valu
e
Laser Wavelen
g
th
λ
1
5
5
0
nm
Ph
o
to
d
etector
resp
o
n
siv
ity
ℜ
1
A/W
Mod
u
latio
n
I
n
d
ex
1
Total
n
o
ise v
arianc
e
N
0
10
-
7
W
/Hz
Receiv
er
ap
er
tu
re
d
ia
m
eter
of
the PD
D
0
.08
m
In
-
p
h
ase/q
u
ad
rature
sig
n
al a
m
p
litu
d
e
s
IQ
MM
84
A
m
p
lif
icatio
n
gain
AF
P
2
dB
In
Fi
gures
2
-
3,
il
lustrate
the
AS
E
of
dif
fer
e
nt
AF
-
MIM
O/FS
O
cha
nne
ls
(i.e.,
S
ISO,
2×2
a
nd
4×
4
MIM
O/
FSO
c
hannels)
with
r
espect
to
,
for
three
values
of
the
relay
sta
ti
on
s
,
C
(
0,
C
1,
C
and
2
C
)
with
tw
o
diff
e
ren
t
li
nk
dista
nces
L
=
2000
m
and
L
=
4000
m
,
a
m
plificati
on
ga
in
2
d
B
,
AF
P
for
str
on
g
atm
os
ph
e
ric
tu
rbulence
,
2
1
4
2
/
3
3
10
m
.
n
C
It
can
be
al
so
see
n
that
the
ASE
s
tro
ng
ly
de
pe
nds
on
MIM
O
config
ur
at
io
ns,
at
achieve
the
SN
R
=
10
dB
fo
r
MIM
O
config
ur
at
io
ns
M
=
N
=
4,
C
=
0,
AS
E
=
7
b/s/H
z
with
L
=
2000
m
bu
t
L
=
4000
m
A
SE
=
6
b/s/
Hz.
Si
m
il
ar,
fo
r
M
=
N
=
2
the
co
rresp
onding
res
ul
t
is
AS
E
=
5
dB
wit
h
and
A
SE
=
4
dB
with
L
=
4
000
m
.
Fo
r
the
ca
s
e
C
=
1
a
nd
C
=
2
the
res
ults
ar
e
sim
il
ar,
AS
E
dec
reases
1
dB
.
The
AS
E
stron
gly
dep
e
nds
on
the
num
ber
relay
sta
ti
on
s,
with
L
=
2000
m
,
M
=
N
=
4
w
he
n
nu
m
ber
of
relay
sta
ti
ons
increases
f
ro
m
C
=
0
t
o
C
=
1
a
nd
f
ro
m
C
=
1
t
o
C
=
2
AS
E
of
syst
e
m
s
decr
ea
ses
3
dB
an
d
1.5
dB,
res
pecti
vely
to
achieve
t
he
S
NR
=
10
dB.
T
he
AS
E
stron
gl
y
dep
e
nds
on
the
li
nk
distance
gets
lo
nge
r,
with
C
=
0,
M
=
N
=
4,
wh
e
n
inc
reasi
ng
dista
nce
f
rom
L
=
2000
m
t
o
L
=
4000
m
AS
E
of
syst
em
s
decr
ease
s
1
dB
.
The
im
pact
of
S
NR
on
the
A
SE
of
syst
e
m
s
is
m
o
re
sig
nifica
nt
i
n
lo
w
re
gions
than
i
n
high
re
gions.
Th
e
rea
so
n
of
t
his
is
t
hat
a
s
op
ti
cal
li
nk
dis
ta
nce
gets
lo
nger,
th
e
sig
nal
pro
pa
gates
in
t
he
atm
os
pheric
with
lo
nger
dis
ta
nces.
It
has
been
that o
bs
er
ve
d
t
hat w
it
h i
nc
rea
se in t
he value
of
C,
c
apacit
y pe
rfor
m
ance of t
he
syst
em
d
et
erior
at
es
.
Figures
4
-
5,
il
lus
trat
e
the
A
SE
of
diff
e
rent
AF
-
MIM
O/F
SO
cha
nnel
s
(
i.e.
SI
S
O,
2×
2
an
d
4×
4
MIM
O/
FSO
c
hannels)
with
resp
ect
to
,
fo
r
three
values
of
the
tur
bu
le
nc
e
streng
t
h
2
n
C
,
num
ber
of
relay
sta
ti
on
s
1
C
with
t
wo
dif
fer
e
nt
li
nk
distanc
es
L
=200
0
m
and
L=4
000
m
,
a
m
plific
at
ion
gain
2
d
B
.
AF
P
I
t
can
be
al
so
se
en
that
t
he
A
SE
str
ongly
de
pends
on
the
atm
os
ph
e
ric
t
urb
ulence
st
re
ng
t
h,
at
li
nk
di
sta
nce
L=4
000
m
, M
=N=4, v
al
ue
s o
f
tu
rbulence s
tren
gth
incr
eas
es f
r
om
2
1
5
2
/
3
10
m
n
C
to
2
1
5
2
/
3
9
1
0
m
n
C
an
d
from
2
1
5
2
/
3
9
1
0
m
n
C
to
2
1
4
2
/
3
3
10
m
n
C
AS
E
of
syst
em
s
decr
eases
0.3
dB
and
0.4
dB,
res
pecti
vely
to
achieve
the
S
NR=2
0
dB
.
T
he
AS
E
str
ongl
y
dep
en
ds
on
nu
m
ber
relay
sta
ti
on
s,
an
d
as
the
li
nk
distan
ce
gets
longer
,
the
ASE
un
der
the
w
eak
t
urbu
le
nce
co
ndit
ion
s
is
higher
tha
n
i
n
the
ca
ses
of
m
od
erate
an
d
strong
tur
bu
le
nce,
e
s
pecial
ly
with
l
onge
r
li
nk
distance
L
.
T
he
r
easo
n
of
this
i
s
that
as
opti
cal
li
nk
distanc
e
gets
longer
,
the
si
gn
al
prop
a
gat
es
in
the
at
m
os
phe
ric
with
longer
distanc
es;
the
influ
e
nc
e
of
the
t
urb
ul
ence
therefo
re
be
co
m
es
stronge
r.
On
t
he
oth
e
r
ha
nd,
as
e
xpect
ed,
t
he
A
SE
c
ould
be
im
pr
ove
d
by
ap
pro
xim
at
el
y
2
(b
/s/
Hz
)
wh
e
n
the
syst
em
is
up
gra
ded
from
SI
S
O/FS
O
to
2×2
MIM
O/F
S
O
or
from
2×2
MIM
O/FS
O
t
o
4×4
MIM
O/FS
O
f
or
num
ber
of
rel
ay
sta
ti
on
s
0,
C
ap
pro
xim
a
te
ly
1
(b
/s/
Hz
)
f
or
1,
C
and
a
ppr
oxim
a
t
el
y
0.
7
(b
/s/
Hz
) for
2.
C
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
20
88
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2
01
8
:
4334
-
4342
4340
Figure
2
.
ASE
ver
s
us
t
he
a
verage ele
ct
rical
S
NR
of
var
i
ou
s
AF
-
MI
MO/FSO
ch
a
nnel
s a
nd
di
ff
e
r
ent
nu
m
ber
of
rela
y st
at
ion
f
or str
ong
at
m
os
pher
ic
tur
bu
le
nce stre
ng
t
hs
unde
r
li
nk
distance L
=
2000 m
Figure
3
.
A
SE
ver
s
us
t
he
a
verage
el
ect
rical
S
NR of
var
i
ou
s
AF
-
MI
MO/FSO
ch
a
nnel
s a
nd num
ber
r
el
ay
sta
ti
on
fo
r
str
ong at
m
os
ph
eric
turb
ulence
un
der li
nk
distance L
=4
000 m
Figure
4
.
A
SE
ver
s
us
t
he
a
verage ele
ct
rical
S
NR
of
diff
e
re
nt AF
-
MIM
O/FS
O
c
ha
nn
el
s
for wea
k
to
strong at
m
os
pheric t
urb
ulence
strength
s
unde
r
li
nk
distance L
=2
000 m
, n
um
ber
of r
el
ay
stat
ions C
=1
Figure
5
.
A
SE
ver
s
us
t
he
a
verage ele
ct
rical
S
NR of
diff
e
re
nt
A
F
-
MIM
O/FS
O
c
ha
nn
el
s
for wea
k
to
strong at
m
os
pheric t
urb
ulence
strength
s
unde
r
li
nk
distance L
=4
000 m
, n
um
ber
of r
el
ay
stat
ions C
=1
Figures 6
-
7,
il
l
us
trat
e
t
he
ASE
of d
if
fer
e
nt A
F
-
M
IMO/F
S
O
c
hannels v
e
r
su
s num
ber
of r
el
ay
sta
ti
on
s
for
three
valu
es
of
the
tu
rbulence
stre
ng
t
h
unde
r
f
ree
-
s
pace
two
diffe
ren
t
li
nk
distances
L=2
000
m
and
L=4
000
m
,
am
pl
ific
at
ion
ga
in
2
d
B
.
AF
P
It
is
cl
early
show
n
th
a
t
the
A
SE
pe
rfor
m
ance
is
im
pr
ov
e
d
sign
ific
a
ntly
with
the
incre
ase
of
num
ber
of
la
sers
an
d
receivers
a
nd
the
AS
E
pe
rfor
m
ance
is
decr
eases
sign
ific
a
ntly
w
it
h
the
inc
rease
of
num
ber
of
r
el
ay
sta
ti
on
s.
I
n
a
dd
it
io
n,
as
e
xp
ect
e
d,
AS
E
increase
s
as
nu
m
ber
of
la
sers
M
a
nd
receive
r
N
incre
ase
from
SI
S
O
to
2×
2
MIM
O
an
d
4×
4
MIM
O
.
It
can
be
al
so
see
n
that
the
AS
E
stron
gly dep
e
nds
on the
at
m
os
pheric t
urb
ulence st
rength, M
IMO
confi
gurati
ons,
a
nd as the
li
nk di
sta
nc
e
gets
lo
ng
e
r.
Increasi
ng
the
num
ber
of
rela
y
sta
ti
on
s,
ca
pa
ci
ty
per
f
or
m
a
nce
of
th
e
sys
tem
deterior
at
es
but
increases
the
ga
in of
powe
r,
t
his
prob
le
m
is v
ery im
po
rta
nt in
the
FSO
syst
e
m
.
0
10
20
30
40
50
60
0
1
2
3
4
5
6
7
8
9
10
A
v
e
r
a
g
e
e
l
e
c
t
r
i
c
a
l
S
N
R
(
d
B
)
A
v
e
r
a
g
e
s
p
e
c
t
r
a
l
e
f
f
i
c
i
e
n
c
y
(
b
/
s
/
H
z
)
S
I
S
O
M
=
N
=
2
M
=
N
=
4
C
=
2
C
=
0
C
=
1
L
=
2
0
0
0
m
,
P
A
F
=
2
,
C
n
2
=3
10
-
1
4
m
-
2
/
3
d
B
,
0
10
20
30
40
50
60
0
1
2
3
4
5
6
7
8
9
10
A
v
e
r
a
g
e
e
l
e
c
t
r
i
c
a
l
S
N
R
(
d
B
)
A
v
e
r
a
g
e
s
p
e
c
t
r
a
l
e
f
f
i
c
i
e
n
c
y
(
b
/
s
/
H
z
)
S
I
S
O
M
=
N
=
2
M
=
N
=
4
C
=
2
C
=
0
C
=
1
L
=
4
0
0
0
m
,
P
A
F
=
2
d
B
,
C
n
2
=3
10
-
1
4
m
-
2
/
3
0
10
20
30
40
50
60
0
1
2
3
4
5
6
A
v
e
r
a
g
e
e
l
e
c
t
r
i
c
a
l
S
N
R
(
d
B
)
A
v
e
r
a
g
e
s
p
e
c
t
r
a
l
e
f
f
i
c
i
e
n
c
y
(
b
/
s
/
H
z
)
C
n
2
=3
10
-
1
4
m
-
2
/
3
C
n
2
=9
10
-
1
5
m
-
2
/
3
C
n
2
=1
10
-
1
5
m
-
2
/
3
C
=
1
,
L
=
2
0
0
0
m
,
=
1
5
0
0
n
m
S
I
S
O
M
=
N
=
2
M
=
N
=
4
0
10
20
30
40
50
60
0
1
2
3
4
5
6
A
v
e
r
a
g
e
e
l
e
c
t
r
i
c
a
l
S
N
R
(
d
B
)
A
v
e
r
a
g
e
s
p
e
c
t
r
a
l
e
f
f
i
c
i
e
n
c
y
(
b
/
s
/
H
z
)
C
n
2
=3
10
-
1
4
m
-
2
/
3
C
n
2
=9
10
-
1
5
m
-
2
/
3
C
n
2
=1
10
-
1
5
m
-
2
/
3
M
=
N
=4
M
=
N
=2
S
I
S
O
C
=
1
,
L
=
4
0
0
0
m
,
=
1
5
0
0
n
m
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Avera
ge
C
hannel
Ca
paci
ty
o
f
Ampli
fy
-
and
-
f
or
war
d
...
(
D
uong
H
uu Ai
)
4341
Figure
6. A
SE
ver
s
us
t
he n
umber
of
relay
stat
ion
s
of
FSO cha
nnel
s
for weak
to st
r
ong
at
m
os
pher
ic
tur
bu
le
nce stre
ng
t
hs
,
am
plificati
on
gain
un
der
li
nk
distance L
=2
000 m
Figure
7
.
A
SE
ver
s
us
t
he n
umber
r
el
ay
stat
io
ns
of
FSO cha
nnel
s
for weak
to st
r
ong
at
m
os
pher
ic
tur
bu
le
nce stre
ng
t
hs
,
am
plificati
on
gain
2
d
B
AF
P
unde
r
li
nk
distance L=
4000
m
6.
CONCL
US
I
O
N
The
pur
po
se
of
this
pa
per
is
to
prese
nt
the
pe
rfor
m
ance
an
al
ysi
s
on
the
a
ver
a
ge
c
hannel
capaci
ty
of
AF
-
MIM
O/F
SO
syst
em
s
u
sing
SC
-
Q
AM sign
al
s ove
r
atmosphe
ric turbu
l
ence ch
a
nn
el
s
. Th
e lo
g
-
norm
a
l an
d
gam
m
a
-
gam
ma
distrib
utio
n
m
od
el
s
wer
e
us
e
d
to
descr
i
be
th
e
fluct
uation
of
t
he
op
t
ic
al
pr
opa
gatin
g
ove
r
atm
os
ph
e
ric
tu
rbulence
cha
nn
el
s.
Th
e
AS
E
i
s
cal
culat
ed
ba
sed
on
the
pr
obabili
ty
de
ns
it
y
functi
on
of
the
F
S
O
syst
e
m
co
m
bin
ing
t
he
relay
sta
ti
on
s,
A
SE
c
onside
rin
g
diff
e
ren
t
li
nk
c
ondi
ti
on
s,
num
ber
of
relay
sta
ti
o
ns
a
nd
MIM
O
c
onfig
ur
at
io
ns
.
The
nu
m
erical
resul
ts
sh
owe
d
tha
t,
with
the
sim
il
ar
li
nk
dist
ance
a
nd
t
urb
ulence
stren
gth
,
reg
a
r
dless
the
li
nk
distance
an
d
tu
rbulence
c
ondi
ti
on
,
the
AS
E
of
the
F
SO
li
nk
co
uld
be
i
m
pro
ved
by
ap
pro
xim
a
t
el
y
2
(b
/s/
Hz)
wh
e
n
the
sys
te
m
is
up
gra
ded
from
fr
om
SI
SO
/FS
O
to
2×2
MIM
O/FS
O
or
from
2×2
MIM
O/
F
S
O
to
4×
4
MIM
O/FS
O
f
or
nu
m
ber
of
r
el
ay
s
ta
ti
on
s
0,
C
appr
oxi
m
at
ely
1
(
b/s/Hz)
f
or
1,
C
and
ap
pro
xim
at
el
y
0.
7
(
b/s/Hz)
f
or
2.
C
T
he
AS
E
str
ongl
y
dep
e
nds
on
the
at
m
os
ph
e
ric
tur
bule
nce
stren
gth
,
MIM
O
co
nf
ig
urat
io
ns
,
num
ber
of
relay
sta
ti
on
s
and
as
the
li
nk
distance.
I
nc
re
asi
ng
the
num
ber
of
relay
sta
ti
on
s,
capaci
ty
per
f
or
m
ance
of
the
s
yst
e
m
deteriora
te
s
bu
t
inc
rea
ses
the
gai
n
o
f
power,
this
pr
ob
lem
is ver
y i
m
po
rta
nt in
t
he
F
SO s
yst
e
m
.
REFERE
NCE
S
[1]
A.K.
Majumdar.
Free
-
spac
e
la
ser
comm
unic
at
ion
per
form
anc
e
in
t
he
at
m
ospheric
cha
nne
l.
L.
Opt
.
Fi
ber
Comm
un.
Re
p.
2005;
2;
34
5
–
396.
[2]
S.
Arnon.
Optical
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Evaluation Warning : The document was created with Spire.PDF for Python.