Editing Phase-shift keying (section)

===Differential encoding===
{{Main article|differential coding}}

Differential phase shift keying (DPSK) is a common form of phase modulation that conveys data by changing the phase of the carrier wave. As mentioned for BPSK and QPSK there is an ambiguity of phase if the constellation is rotated by some effect in the [[communications channel]] through which the signal passes. This problem can be overcome by using the data to ''change'' rather than ''set'' the phase.

For example, in differentially-encoded BPSK a binary "1" may be transmitted by adding 180° to the current phase and a binary "0" by adding 0° to the current phase. {{anchor|SDPSK}}
Another variant of DPSK is symmetric differential phase shift keying, SDPSK, where encoding would be +90° for a "1" and −90° for a "0".

In differentially-encoded QPSK (DQPSK), the phase-shifts are 0°, 90°, 180°, −90° corresponding to data "00", "01", "11", "10". This kind of encoding may be demodulated in the same way as for non-differential PSK but the phase ambiguities can be ignored. Thus, each received symbol is demodulated to one of the <math>M</math> points in the constellation and a [[comparator]] then computes the difference in phase between this received signal and the preceding one. The difference encodes the data as described above. ''Symmetric differential quadrature phase shift keying'' (SDQPSK) is like DQPSK, but encoding is symmetric, using phase shift values of −135°, −45°, +45° and +135°.

The modulated signal is shown below for both DBPSK and DQPSK as described above. In the figure, it is assumed that the ''signal starts with zero phase'', and so there is a phase shift in both signals at <math>t = 0</math>.

[[File:DBQPSK timing diag fixed.png|center|thumb|600px|Timing diagram for DBPSK and DQPSK. The binary data stream is above the DBPSK signal. The individual bits of the DBPSK signal are grouped into pairs for the DQPSK signal, which only changes every ''T<sub>s</sub>'' = 2''T<sub>b</sub>''.]]

Analysis shows that differential encoding approximately doubles the error rate compared to ordinary <math>M</math>-PSK but this may be overcome by only a small increase in <math>E_b/N_0</math>. Furthermore, this analysis (and the graphical results below) are based on a system in which the only corruption is [[additive white Gaussian noise]] (AWGN). However, there will also be a physical channel between the transmitter and receiver in the communication system. This channel will, in general, introduce an unknown phase-shift to the PSK signal; in these cases the differential schemes can yield a ''better'' error-rate than the ordinary schemes which rely on precise phase information.

One of the most popular applications of DPSK is the [[Bluetooth#Implementation|Bluetooth standard]] where <math>\pi/4</math>-DQPSK and 8-DPSK were implemented.