Page 260 - Fiber Optic Communications Fund

Optical Receivers 241

RA A
T LO
I =− Im [M s + M s ]. (5.154)
Q,x xx x xy y
2
The complex photocurrent corresponding to x-polarization is
I = I I,x − iI Q,x (5.155)
x
RA A
T LO
= [M s + M s ]. (5.156)
xx x
xy y
2
Similarly, the y-components of the received field and LO output pass through a second balanced IQ receiver.
Its outputs are
RA A
T LO
I = Re [M s + M s ], (5.157)
Q,x yx x yy y
2
RA A
T LO
I =− Im [M s + M s ]. (5.158)
Q,y yx x yy y
2
The complex photocurrent corresponding to y-polarization is
I = I I,y − iI Q,y (5.159)
y
RA A
T LO
= [M s + M s ]. (5.160)
yy y
yx x
2
Eqs. (5.156) and (5.159) can be rewritten as
[ ][ ] [ ]
RA A xx M xy s x I x
T LO M
2 M yx M yy s y = I y . (5.161)
In the DSP unit of the coherent receiver, the matrix elements of M are adaptively estimated and its inverse is
−1
calculated (see Chapter 11). Multiplying Eq. (5.161) by M , we find
[ ] [ ]
s x = 2 M −1 I x . (5.162)
s y RA A I y
T LO
Thus, the transmitted data can be estimated using Eq. (5.162).

Example 5.9
Repeat Example 5.8 with a polarization modulated (PM) QPSK signal given by

[ ] [ ]
s x 1∠∕4
s(t)= = .
s y 1∠5∕4
Assume M to be of the form [ ]
10
M = e −L∕2 ,
01