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468 Fiber Optic Communications

× 10 –3

1.5 numeric
analytic

Variance (mW) 1

0.5

0
0 20 40 60 80 100
% Pre−compensation

Figure 10.30 Variance of ‘1’ at the fiber output for an OOK direct detection system.  =100 ps/nm.
res

× 10 –3
1.2
D res = 100 ps/nm
1

0.8
Variance (mW) 0.6

0.4
D res = 200 ps/nm
0.2
D res = 150 ps/nm
0
0 20 40 60 80 100
% Pre−compensation
Figure 10.31 The variance of the signal amplitude calculated analytically for various residual accumulated dispersions
per span. The other parameters are the same as in Fig. 10.30.

and −3 dBm, respectively. The rest of the parameters are the same as in Fig. 10.29. To calculate the variance
of ‘1’, a 13-bit-long random bit sequence with the center bit being ‘1’ is transmitted over the fiber-optic link
in simulations. The bits are randomly varied, keeping the center bit fixed as ‘1’ and exhausting all possible
bit patterns. From Fig. 10.30, we see that the optimum pre-compensation ratio is about 90% when  res =
100 ps/nm. However, if the residual dispersion per span is increased, the pre-compensation ratio is lowered,
as shown in Fig. 10.31.