The binary and multilevel (M-ary) digital bandpass modulation systems described thus far have utilized the optimum receiver implemented as a correlator. However, the correlation receiver requires a reference signal s _ref( t) that is precisely synchronized in phase and frequency with the input signal to be demodulated. Noncoherent receivers do not require a reference signal and are simpler, but are less accurate than coherent receivers.

Differential phase shift keying (DPSK) is a noncoherent binary PSK digital communication system. For a coherent binary PSK digital communication system the individual information bit b _i directly affects the phase of the transmitted carrier, as given by Equation 3.30. DPSK transmits information as the difference between the carrier phase ? _i transmitted for the current bit b _i and the carrier phase ? _{i -1} transmitted for the previous bit b _{i - 1}, as given by Equation 3.74.

(3.74)

DPSK requires a one bit initialization time at the beginning of each data transmission. The DPSK modulated sinusoidal carrier has the same analytical expression as that for the binary PSK signal in Equation 3.30. If the differentially encoded data sequence is d _i, then Table 3.14 illustrates the generation of the DPSK signal. The differential encoded data sequence d _i is the complement (NOT) of the exclusive OR (XOR) logic operation between the input binary data b _i and the delayed differential encoded data sequence d _{i -1}.