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368 Fiber Optic Communications

stand point, FSK is preferred over OOK since the optimum threshold of FSK is fixed, whereas the optimum
threshold of OOK depends on het (see Eq. (8.217)). The performance with synchronous detection is always
better than that with asynchronous detection, but synchronous detection is more sensitive to laser phase noise.

8.5 Direct Detection
In a direct detection system, the photocurrent is directly proportional to the optical signal power. Hence, the
phase information of the optical field is lost. In other words, it is not possible to encode information on the
phase of the optical carrier (PSK) although it is possible to encode information as the phase change of a current
bit relative to the previous bit (DPSK). In this section, we analyze the performances of OOK, FSK, and DPSK.

8.5.1 OOK
Let s(t) and n (t) be the complex field envelope of the transmitted signal and channel noise, respectively (See
c
Fig. 8.20). At the receiver, the signal passes through an optical filter with transfer function H() that matches
the transmitted signal. As in the case of asynchronous detection for OOK, the matched filter need not be phase
synchronized with the received optical signal, but it can differ by an arbitrary phase factor . Using Eq. (8.40)
and taking x (t)= 0, we have
0
∗
H()= ̃x () exp (iT + i)
1 b
∗
= ̃s ( − ) exp (iT + i). (8.253)
1 c b
Here, we have replaced x(t) of Section 8.2 by s(t)e −i c t . Let the optical filter output be
r(t)=[s (t)+ n (t)]e −i c t , (8.254)
F F
with ∞
1
−i c t
s (t)e = ̃ x()H() exp (−it) d, (8.255)
F 2 ∫ −∞
∞
1
−i c t
n (t)e = 2 ∫ −∞ ̃ n ()H() exp (−it) d, (8.256)
c
F
where s (T ) and n (T ) are the base-band signal and noise field envelopes, respectively. When a bit ‘1’ is
F b F b
sent, ̃x()= ̃s ( − ) and when a bit ‘0’ is sent, ̃x()= 0. Using Eq. (8.253) in Eq. (8.255), we obtain
c
1
exp (i T + i) ∞ 2
c b
s (T )= |s ( − )| d
F b ∫ 1 c
2 −∞
= exp [i( T + )]E when ‘1’ is sent
c b 1
= 0 when ‘0’ is sent. (8.257)
x(t) =
s(t)e *iω c t [s(t) + n c (t)]e *iω c t [s F (t) + n F (t)]e *iω c t t = T b
b
Tx ∑ H(ω) PD Threshold If I(T ) > I T
+ I(t) I(T ) device select ‘1’
+ b
n c (t)e *iω c t
Figure 8.20 Direct detection receiver for OOK.