Q. Illustrate Differential phase-shift keying?

In order to eliminate the need of a local carrier, DPSK has been developed in which the receiver uses the received signal to act as its own carrier. Figure shows the functions of a DPSK system in which the leftmost product operation along with 1-bit delay is the differential encoder. The digital signal d(t) is a polar waveform of levels ±1, corresponding to binary digits 1 and 0, respectively. The output signal a(t) from the differential encoder PSK-modulates a carrier to produce the DPSK signal sDPSK(t). The product device followed by the wide-band low-pass filter acts as the coherent detector. The two inputs to the product device are obtained from the output of a filter matched to the input pulse in a single bit interval. Note that the 1-bit delayed input to the product device serves the purpose of the local oscillator for the coherent detector; that is to say, the DPSK waveform in a given bit interval serves as its own local-oscillator signal in the following bit interval.

In Figure, si(t) is the signal component of the matched filter output, and sd(t)isthe signal component of the detector output. If the phases of both si(t) and si(t - Tb) are the same, sd(t) is then a positive voltage; if their phases differ by π radians, sd(t) will then be a  negative voltage. These voltages will have maximum amplitudes at the sample time at the end of the bit interval. Because the sign of the voltage at the sampler depends upon the phase relationship between si(t) and its delayed replica, and the sign of sd(t) is of the same form as d(t), the original digital bit sequence can be determined by sampling to decide the sign of the detector output. Figure illustrates an example sequence of message binary digits, modulator wave- forms in DPSK, and phase and polarity relationships as applied to DPSK message recovery.