EXFO PSO-200 Optical Modulation Analyzer - Manual (Page 254)

Coherent Detection and Sampling Methods
246 PSO-200
Signal Processing Algorithms
To reconstruct the correct time base, you must input the symbol rate to the
system. A software-based clock recovery algorithm then “time stamps”
each of the acquired optical samples. In this way, amplitude and phase eye
diagrams having very low timing jitter are measured.
Intermediate Frequency (IF) Recovery
The detected signal can conveniently be visualized in a constellation chart
via the I and Q signals. However, we only want to visualize the modulation
information (that is, data signal plus possible distortions, etc.).
In an intradyne detection scheme, the signal modulation is corrupted by
the superimposed IF, so the influence of 
IF
t must be removed. The IF is
retrieved by digital signal processing, which enables the LO laser to be
free-running in relation to the signal laser. This approach requires
high-speed sampling to accurately acquire the variations of the IF phase.
IF recovery can be performed as follows:
1. Detected I and Q signals are combined to form a complex signal, E.
2. The phase modulation of the signal is removed by raising E to the M th
power, where M is the number of phase levels of the modulation (M=4
for QPSK), in order that all modulation phases be multiples of 2.
3. The signal phase is calculated and corresponds to M
IF
(t).
4. The continuously varying phase is bandpass-filtered and divided by M.
5. The retrieved 
IF
is subtracted from the received signal phase.
The result is a signal with data modulation only, that can be visualized in
the constellation chart.
I + i Q

M 
IF (t) BPF ( . ) M arg ( . )