Demodulate DPSK data in a communication channel in which a phase shift is introduced.

Generate a 4-ary data vector and modulate it using DPSK.

M = 4; % Alphabet size
dataIn = randi([0 M-1],1000,1); % Random message
txSig = dpskmod(dataIn,M); % Modulate

Apply the random phase shift resulting from the transmission process.

rxSig = txSig*exp(2i*pi*rand());

Demodulate the received signal.

dataOut = dpskdemod(rxSig,M);

The modulator and demodulator have the same initial condition. However, only the received signal experiences a phase shift. As a result, the first demodulated symbol is likely to be in error. Therefore, you should always discard the first symbol when using DPSK.

Find the number of symbol errors.

errs = symerr(dataIn,dataOut)

errs =
1

One symbol is in error. Repeat the error calculation after discarding the first symbol.

Phase rotation of the DPSK modulation, specified in radians
as a real scalar. The total phase shift per symbol is the sum of phaserot and
the phase generated by the differential modulation.

If you specify phaserot as empty, then dspkdemod uses
a phase rotation of 0 degrees.

Example: pi/4

Data Types: double | single

symorder — Symbol order 'bin' (default) | 'gray'

Symbol order, specified as 'bin' or 'gray'.
This argument specifies how the function assigns binary vectors to
corresponding integers.

If symorder is 'bin',
the function uses a natural binary-coded ordering.

If symorder is 'gray',
the function uses a Gray-coded ordering.

z — DPSK-demodulated output signal vector | matrix

DPSK-demodulated output signal, returned as a vector or matrix
having the same number of columns as input signal y.

Note:
The differential algorithm used in this function compares two
successive elements of a modulated signal. To determine the first
element of vector z, or the first row of matrix z,
the function uses an initial phase rotation of 0.