Page 401 - Fiber Optic Communications Fund

382 Fiber Optic Communications

x (t)
i
TX RX
TF
DCF BPF

Matched filter
Figure 8.30 The filter matched to the received signal after the dispersive fiber channel. Tx = transmitter, TF =
transmission fiber, DCF = dispersion compensation fiber.

The filter matched to the received signal is
∗
∗
H()=[̃x ()− ̃x ()] exp (iT )
o,1 o,0 b
[ ]
2A 2 iT b
= exp − +
2 ∗
a 4(b ) 2
[ 2 ] [ 2 ] [ ]
2A i L iT b
2
= exp − exp − exp . (8.338)
a 4a 2 2 2
⏟⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏟⏟⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏟
band-pass filter dispersion
compensation
fiber
As shown in Fig. 8.30, the matched filter can be realized by cascading a first-order Gaussian filter with a
dispersion compensating fiber or fiber Bragg grating whose accumulated dispersion is equal in magnitude to
that of the transmission fiber, but of opposite sign. The last term in Eq. (8.338) corresponds to a delay of T ∕2,
b
which implies that the decision should be made at t = T ∕2 (instead of at t = T ).
b b

Example 8.5

Show that the PSD of noise in a balanced heterodyne receiver is
ASE shot,eff
= + . (8.339)
4 4R A
n het 2 2
LO
Solution:
Let
n = n (t)+ n (t)∕2RA , (8.340)
het ASE d LO
n = n cos ( t)+ n sin ( t). (8.341)
ASE cI IF cQ IF
The PSD of n (or n )is ∕2. Let us consider impact of multiplication by cos ( t) (or sin ( t)). Let
cI cQ ASE IF IF
n (t)= n (t) cos ( t), (8.342)
1 cI IF
̃ n ( + )+ ̃n ( − )
cI
IF
cI
IF
̃ n ()= , (8.343)
1
2