Page 358 - Fiber Optic Communications Fund
P. 358
Performance Analysis 339
where
[u (T )− u (T )] 2
b
1
b
0
= (8.28)
2
[ ∞ [ ] ] 2
∫ ̃ x ()− ̃x () H() exp (−iT ) d
1
b
0
= −∞ ∞ . (8.29)
N ∫ |H()| d
2
0 −∞
From Fig. 8.3, we see that as increases, P decreases and therefore, to minimize P , should be maximized.
b b
can be maximized by the proper choice of filter transfer function H(). If the filter is too wide (Fig. 8.4(a)),
the variance of noise given by Eq. (8.7) increases since the variance is proportional to the area under the
10 0
10 *1
P b
10 *2
10 *3
0 5 10 15 20 25 30
v
Figure 8.3 Dependence of the BER on .
∣ℱ[r(t)]∣ 2
∣H(ω)∣ 2
0 0
Frequency, ω Frequency, ω
(a) (b)
Figure 8.4 Received signal spectrum and the receiver filter transfer function: (a) wide-bandwidth filter;
(b) narrow-bandwidth filter.
