
286 Optical Fiber Communication Systems with MATLAB
®
and Simulink
®
Models
The
s
ignal-dependent
n
oise
i
s
i
n
f
act
t
he
q
uantum
s
hot
n
oise
a
nd
i
s
g
iven
b
y
v q i G R A df
oSN
B
s n I
2
0
1
2 2 2
2=
∫
(7.21)
where
B
i
s
t
he
3 d
B
b
andwidth
o
f
t
he
o
verall
a
mplier
i
s
is the average photocurrent current received when a “1” was transmitted
This
c
urrent
i
s
e
stimated
a
s
f
ollows:
i
b
T
h t jT dt
s
B
p B
T
T
b
b
1
1
2
2
= ℜ −
−
−∞
∞
∫
∑
( )
/
/
(7.22)
or
i
b
T
h t dt
s
B
p
1
1
= ℜ
−∞
∞
∫
( )
(7.23)
Using
n
ormalization
w
ith
h t dt
p
( ) ,
−∞
= 1
(
7.23)
b
ecomes
i
b
T
s
B
1
1
= ℜ (7.24)
7.5.2 Probability Distribution
The optical systems under consideration are typical IM/DD systems in which the opti-
cal
energy
of