Page 398 - Fiber Optic Communications Fund

Performance Analysis 379

fiber loss per span = 0.2dB/km × 80 km
= 16 dB. (8.315)

Amplifier gain,
G(dB)= 16 dB, (8.316)

G = 10 16∕10 = 39.81. (8.317)
PSD per amplifier,

= n hf(G − 1)
ASE,1 sp
12
= 6.626 × 10 −34 × 193.54 × 10 ×(39.81 − 1)
= 7.465 × 10 −18 J. (8.318)

Total PSD due to all amplifiers,
tot = N ASE,1 . (8.319)
ASE
From Eq. (8.307), we have
( )
1 E av
P = exp − , (8.320)
b
2 tot
ASE
E =− ln(2P ) tot , (8.321)
av
b
ASE
E av
N =−
ln(2P ) ASE,1
b
2.5 × 10 −14
=−
−5
ln(2 × 10 )× 7.465 × 10 −18
≅ 309. (8.322)
−5
Maximum achievable transmission distance so that Pb <= 10 ,
L = 309 × 80 km
max
= 24, 720 km. (8.323)

8.5.4 Comparison of Modulation Schemes with Direct Detection
Fig. 8.28 shows the performance of OOK, FSK, and DPSK in a direct detection system. The performance of
OOK and FSK is roughly similar, and DPSK has a 3-dB advantage over FSK. To compare the performance
of DPSK and PSK, let us ignore the shot noise. In this case

N homo = (8.324)
0 ASE
and
homo = DD ≡ . (8.325)