Page 343 - Fiber Optic Communications Fund

324 Fiber Optic Communications

Eq. (7.159) becomes
√
√
√ P in
Q OOK = √ eq . (7.162)
2 B
ASE e
Note that the Q-factor is independent of the responsivity R and LO power P when the shot noise and thermal
LO
noise are ignored. For PSK, I =−I and Eq. (7.159) is modified as
0 1
√
√
P in
√
Q = √ . (7.163)
PSK eq
B
ASE e
Fig. 7.17 shows the BER as a function of the number of amplifiers. Solid lines show the exact Q-factors
obtained by including shot noise and thermal noise and the × marks show the approximate Q-factors obtained
using Eqs. (7.159) and (7.163). As can be seen, PSK outperforms OOK. For a fixed BER, the transmis-
sion reach can be doubled by using PSK compared with OOK. Eq. (7.163) can be cast into another form
by setting
P T
in b
N = , (7.164)
s
hf
T
P ASE b
N = . (7.165)
n
hf
Here, N and N denote the mean number of signal photons and noise photons, respectively. Using Eqs. (7.164)
s n
and (7.165) in Eq. (7.163) and with B = 1∕(2T ), we find
b
e
2N s
Q 2 = . (7.166)
PSK
N n

10 0

OOK
10 –5

BER 10 –10 PSK

10 –15

10 –20
60 80 100 120 140 160 180
No. of amplifiers
Figure 7.17 BER as a function of the number of amplifiers for a coherent fiber-optic system. Parameters: n = 2,
sp
= 0.2 dB/km, amp. spacing = 80 km, gain G = 16 dB, R = 1000 Ω, T = 200 K, R = 1 A/W, P =−6dBm, and P =
L in LO
10 mW.