about π/4 DQPSK modulation (here in CIS-60 30Bd)

looking deeper at CIS-60 signal reported in the previous post, the relative constellation changes in a symbol by symbol way but always exhibiting a 4-ary constellation although absolute constellation in each-1 mode looks like a PSK-8 modulation. This condition is called "π/4 DQPSK modulation" (Pic. 1).

Pic. 1

The π/4 DQPSK modulation format uses two QPSK constellations offset by 45 degrees (π/4 radians) and transitions occur from one constellation to the other, making the illusion of a PSK-8 modulation (Pic. 2). This guarantees that there is always a change in phase at each symbol, making clock recovery easier. The data is encoded in the magnitude and direction of the phase shift, not in the absolute position on the constellation. One advantage of π/4 DQPSK is that the signal trajectory does not pass through the origin, thus simplifying transmitter design.

Pic. 2 - we see PSK-8 in absolute constellation since the π/4 DQPSK modulation format uses two QPSK constellations offset by 45 degrees and transitions occur from one constellation to the other.

I want mean  that we see two 45 deg shifted QPSK (in relative) constellations:
- the one each 1, 3, 5,... symbols
- the other each 2,4,6,.. symbols
and this also influences the pattern that we see in absolute constellation.

In order to be safe about the main modulation (4 or 8-ary) used in this waveform, I highlighted a single channel from the CIS-60 signal (Pic. 3): if it was a clean QPSK or PSK-8 modulation then we should see three harmonics  in the fourth power while there are only two and this outstands a behavior of a π/4 DQPSK modulation (and OQPSK too). 

Now, looking at the phase plane of this channel, notice that the absolute constellation (Diff-0) exhibits 8-ary, BUT, as said above, there is no transition paths through the center (as in case of a clear PSK-8!) and that the relative constellation (Diff-1) looks like QPSK but 90 degrees rotated: this suggest the π/4 DQPSK modulation.

 

Pic. 3

By the way, the π/4 DQPSK modulation format is also used in CIS-45 v2 HDR modem (Pic. 4).

Pic. 4

The channel-by-channel analysis with the SA phase-plane method should be performed on all the channels, but it requires very good signals/recordings and a lot of time; anyway all the channels have been examintaed using SA OFDM module always getting the same  constellations shown in Pic. 2.