Page 369 - Fiber Optic Communications Fund

350 Fiber Optic Communications

8.4 Heterodyne Receivers
The photocurrent in a heterodyne receiver is given by Eq. (5.94),

I(t)= 2RA LO Re{[s(t)+ n (t)] exp [−i( t +Δ)]}. (8.115)
IF
c
Ignoring the thermal noise, the PSD of the noise current n (t) introduced at the detection stage is
d
= shot,eff = qRA 2 . (8.116)
n d LO
The total current is
I (t)= 2RA [s(t)+ n (t)] cos ( t +Δ)
tot LO cI IF
+2RA n (t) sin ( t +Δ)+ n (t), (8.117)
LO cQ IF d
where
n (t)= Re[n (t)], n (t)= Im[n (t)], (8.118)
c
cI
cQ
c
and s(t) is real. See Fig. 8.12. The total current may be rewritten as a summation of signal current and noise
current:
I (t)= I (t)+ n (t), (8.119)
tot s het
where
I (t)= 2RA s(t) cos ( t +Δ), (8.120)
s LO IF
{ }
d
( ) n (t)
n (t)= 2RA n cos t +Δ + n sin ( t +Δ)+ . (8.121)
het LO cI IF cQ IF
2RA
LO
Note that 2RA LO appears as a scaling factor both in the signal and noise components. As before, we drop this
scaling factor from now on. The PSD of n (t) is (see Example 8.5)
het
N het
0 ASE shot,eff
= + (8.122)
2 2
2 4 4R A
LO
ASE q
= + . (8.123)
4 4R
AWGN
channel
[s(t) + n c (t)]e *iω c t 2RA LO Re{[s(t) + n c (t)]e *i(ω IF t + Δφ) }
s(t)e *iω c t
Tx ∑ Coherent ∑
Rx
LO
n c (t)e *iω c t *i(ω LO t + φ LO ) n d (t)
A LO e

t = T b
Decision Synchronous or
device r(T b ) r(t) non-synchronous
detection

Figure 8.12 A fiber-optic link with heterodyne receiver.