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352 Fiber Optic Communications

s(t)cos(ω IF t + ∆φ) t = T b
Decision
H s (ω)
device
r(T b ) = u(T b ) + n F (T b )
cos(ω IF t + ∆φ)

Figure 8.14 Matched filter for the baseband signal after down-conversion.

Alternatively, the photocurrent can be down-converted to the baseband by demodulating synchronously and
the result is applied to a filter H (), matched to the baseband signal s(t), as shown in Fig. 8.14. In this case,
s
we find that (see Example 8.7)
4E 1
= . (8.129)
max het
N
0
In both cases, we obtain the same and, using Eq. (8.129) in Eq. (8.39), we obtain
max
(√ )
1 het
P = erfc (8.130)
b
2 2
where
E av
het = . (8.131)
N het
0
8.4.1.1 ASE Limited Systems
2
When ASE ≫ shot ∕(4A 2 LO R ), the second term of Eq. (8.122) can be ignored. In this case,
ASE
het
N = . (8.132)
0 2
Now, Eq. (8.130) reduces to
(√ )
1 E av
het
P = erfc . (8.133)
b 2
ASE
Under the same conditions, from Eq. (8.85), we have
N homo = (8.134)
0 ASE
and
(√ )
P homo = 1 erfc E av . (8.135)
b 2
ASE
Thus, the performances of the homodyne and heterodyne receivers are the same for a PSK signal when the
ASE is dominant.

8.4.1.2 Shot Noise-Limited Systems
2
In this case, ≫ A 2 R and we ignore the first term of Eq. (8.122) and use Eq. (8.82) to obtain
shot ASE LO
shot,eff hf
N het = = (8.136)
0 2 2
2R A 2
LO