Page 365 - Fiber Optic Communications Fund

346 Fiber Optic Communications

F F
q out = u(t)e *iω c t
q in = s(t)e *iω c t u(t)
A … A BPF Homodyne
receiver

Figure 8.9 A fiber-optic transmission system with a homodyne receiver. F = fiber, A = amplifier, BPF = band-pass
filter.

AWGN
Channel
c
s(t)e *iω c t [s(t) + n (t)]e *iω c t Coherent 2RA Re[s(t) + n (t)]
c
LO
Tx ∑ Rx ∑
+ +
+ +
LO
n (t)e *iω c t A e *iω c t n d
c
LO
t = T b
LPF r(t) = u(t) + n F Threshold
H (ω) device Decision
r(T )
b
Figure 8.10 Mathematical representation of fiber-optic link with homodyne coherent receiver. LO = local oscillator,
LPF = low-pass filter.

The fiber-optic channel noise can be written as

q = n (t) exp (−i t), (8.78)
c
n
c
where n (t) is the complex field envelope of the noise field with its PSD given by Eq. (6.17),
c
ASE = n hf(G − 1). (8.79)
sp
where f is the mean frequency. The output of the fiber-optic link is the sum of the signal field and the noise
field,
q =[s(t)+ n (t)] exp (−i t). (8.80)
out c c
When the phase and frequency of the LO are aligned with those of the received signal, the current output of
the balanced homodyne receiver may be written as (see Eq. (5.112))
I (t)= 2RA Re[s(t)+ n (t)] = 2RA [s(t)+ n (t)]. (8.81)
s LO c LO cr
Here, the subscript r denotes the real part and s(t) is assumed to be real. Let n (t) be the noise introduced at
d
the detection stage. We assume that the LO power is sufficiently large so that the shot noise dominates the
thermal noise. Ignoring the thermal noise, the PSD of n (t) is given by Eq. (7.50),
d
2
= = qRA . (8.82)
n d shot,eff LO
The total current is
I tot = I (t)+ n (t)= 2RA LO [s(t)+ n(t)], (8.83)
d
s