Page 253 - Fiber Optic Communications Fund

234 Fiber Optic Communications

I (t)= I (t)− I (t)=−2RA A Im{s(t) exp [−i( t +Δ)]}. (5.111)
+
d
IF
r LO
−
From Eq. (5.111), we see that the intermodulation cross-talk and DC terms are canceled because of the bal-
anced detection. For homodyne receivers, = 0. When Δ = ∕2, Eq. (5.111) becomes
IF
I (t)= 2RP Re {s(t)}. (5.112)
0
d
For binary modulation schemes, s(t) is real and in this case the current is proportional to the received signal
s(t).For M-ary signals, s(t) is complex and an IQ receiver is required, which is discussed in Sections 5.6.3
and 5.6.4. For a heterodyne receiver, the current I (t) should be multiplied by a microwave carrier, as is done
d
in Section 5.6.1.2.

Example 5.7
Repeat Example 5.6 assuming that the balanced receiver is used instead of the single-branch receiver. Com-
ment on the intermodulation cross-talk in a single-branch receiver and the balanced receiver.
Solution:
From Eq. (5.112), we have
|I (t)| = 2RP .
d
0
(a)
P LO = 10 mW,
√
P = P P = 1.259 mW,
0 r LO
|I (t)| = 2 × 0.9 × 1.259 mW = 2.2662 mW.
d
(b)
P = 0.1mW,
LO
√
P = P P = 0.1258 mW,
0
r LO
|I (t)| = 2 × 0.9 × 0.1258 mA = 0.2266 mA.
d
Since P LO < P , in the case of a single-branch receiver, the first term in Eq. (5.88) cannot be ignored. There-
r
fore, a single-branch receiver would have a significant amount of cross-talk. In contrast, for a balanced
receiver, intermodulation cross-talk is canceled out due to the balanced detection (see Eqs. (5.109)–(5.112)).

5.6.3 Single-Branch IQ Coherent Receiver
So far we have assumed that the message signal s(t) is real. Now we consider a more generalized case, in which
s(t) is complex. The examples of complex signals are multi-level PSK and QAM. To recover the real part of
s(t), the LO phase should be aligned with that of the optical carrier. Similarly, to recover the imaginary part of
s(t), the LO phase should be shifted by ∕2(exp (i∕2)= i) with respect to the optical carrier. Fig. 5.36 shows
a block diagram of the single-branch IQ coherent receiver. The received signal and LO outputs are divided