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310 Fiber Optic Communications

10 –4

10 –6
50 Ohms

BER 10 –8
100 Ohms

10 –10
200 Ohms

10 –12
5 0 5 10 15
LO power (dBm)
Figure 7.9 BER as a function of LO power. L = 230 km, other parameters are the same as those of Fig. 7.8 except for
LO power and R .
L

Next, let us consider PSK. For bit ‘1’, the mean and variances are the same as those of OOK given by Eqs.
(7.37)–(7.46). For bit ‘0’,
√
I =−2R P P , (7.60)
0
1r LO
2 2
= . (7.61)
0 1
When the P is sufficiently large, the Q-factor can be calculated as before:
LO
√
2P 1r
Q PSK =
hfB e
√
= 2 N . (7.62)
1r
For PSK, N rec = N . So, Eq. (7.62) becomes
1r
√
Q = 2 N . (7.63)
PSK rec
−9
To have a BER of 10 , the average number of signal photons per bit should be 9 assuming = 1 [1, 2].
Comparing Eqs. (7.55) and (7.63), we see that the receiver sensitivity can be improved by 3 dB using PSK
for the fixed number of mean received photons. Fig. 7.10 shows the theoretical limit on the achievable
BER for a shot noise-limited system. As can be seen, for the given mean received power, the PSK outper-
forms the OOK. In other words, to achieve a given BER, the mean received power for OOK should be 3 dB
higher than that for PSK. The reason for the superior performance of the PSK is that constellation points are
√ √
separated by 2 P for PSK, whereas the corresponding separation for OOK is 2P (P = P ∕2).
rec rec rec 1,rec
In [3], the receiver sensitivity close to the shot noise limit is experimentally demonstrated in a 10-Gb/s
PSK system.