## 31 July 2015

### calcolo delle constellazioni pi/4 DQPSK e (D)QPSK

the OFDM SA module calculates the arity (n-Ary) in automatic mode: in order to detect if the modulation in the channels is pi/4 DQPSK or QPSK/DQPSK we have to get a stable absolute constellation (with the help of shift)  and look at its arity. Carriers have pi/4 DQPSK modulation in case of the absolute constellation exhibits an 8 arity (Figure A)

 Figure A

Modulation is QPSK if the arity of the absolute constellation is 4 (Figure B)

 Figure B

Working with phase modulation, the arity must be calculated manually. In the phase module the button button Diff 0 - corresponds to an absolute mean  and Diff 1 - corresponds to the relative. In order to calculate the-arity, it is necessary to consider the harmonics at different degrees.

For example (Figure 1) QPSK carrier and side harmonics are manifested in grade 4. Accordingly, it should be seen in the phase module with the n-Ary = 4 (Figure 2).

 Figure 1
 Figure 2
Now PSK-8, carrier and the side harmonics can be seen in the eighth degree (Figure 3). Next phase module, n-Ary = 8, pay attention to the trajectory of the constellations that pass through the center ! (Figure 4).

 Figure 3
 Figure 4

Finally, pi/4 DQPSK, the carrier and the harmonics are in degree 8 (the fourth degree exhibits only 2 harmonics unlike the 3 harmonics shown in QPSK!) (Figure 5).
And now attention - look in the phase module with the n-Ary = 8 (Figure 6). Notice that there is no transition paths through the center of the constellation (as real PSK-8 does), and the constellation of a relative is ike QPSK, but rotated 90 degrees !!!

 Figure 5
 Figure 6

Below, another example of  pi/4 DQPSK measurement: