Page 334 - Fiber Optic Communications Fund

Transmission System Design 315

To have negligible ISI, the pulse at the receiver should remain within its bit slot. The commonly used criterion
is [4]
≤ T ∕4, (7.99)
L
B
where T is the bit interval. Using Eqs. (7.98) and (7.99), we obtain
B
[ 4 2 2 ] 1∕2
4 + L
0 2 B ≤ 1 . (7.100)
4 2 4
0
opt opt √
If we choose the optimum pulse width T , the corresponding is L∕2. Using this value of in
0 0 2 0
Eq. (7.100), we find [4]
1
1∕2
B(| |L) ≤ . (7.101)
2
4
For fixed | |, as the bit rate increases linearly, the maximum transmission distance decreases as L −1∕2 .To
2
undo the pulse broadening due to fiber dispersion, a DCF may be used (see Chapter 2) or it may be com-
pensated in the electrical domain using a DSP (see Chapter 11). In some applications such as metro/access
networks, it would be expensive to use DCF or coherent receivers. For such applications, Eq. (7.101) provides
a simple design rule relating the reach, bit rate, and dispersion.

Example 7.3
A fiber-optic system is upgraded to operate at 10 Gb/s from 2.5 Gb/s. The maximum transmission distance at
2.5 Gb/s at a BER of 10 −9 was 100 km. Find the corresponding distance at 10 Gb/s. Assume that the trans-
mission fiber is unchanged and the penalty due to fiber dispersion is the same in both systems.

Solution:
Let

B = 2.5Gb/s, B = 10 Gb/s,
1 2
L = 160 km.
1
From Eq. (7.101), we have
1∕2 1∕2
B L = B L ,
1 1 2 2
L = 10 km.
2

7.4 ASE-Induced Limitations
To transmit an optical signal over a long distance, amplifiers have to be introduced along the transmission
line. Otherwise, the received power could be too low to detect. In Section 7.2.1, we found that 9 photons/bit
−9
is required at the receiver for a PSK signal to achieve a BER of 10 . The number of photons/bit at the
receiver can be increased by introducing amplifiers. However, amplification by stimulated emission is always
accompanied by ASE, which enhances the noise in the system. In a long-haul fiber-optic system consisting
of a chain of amplifiers, ASE builds up over many amplifiers, which degrades the transmission performance.