DPSK and its implementation

DPSK (Differential Phase Shift Keying) is a non-coherent form of PSK in which a data bit is represented by the change in carrier phase relative to the previous bit, not by an absolute phase. Typically bit 1 means no phase change and bit 0 means a $180^\circ$ change. The previous bit acts as the phase reference, so the receiver needs no coherent carrier.

Implementation: transmitter

 b_k -->[XNOR]--d_k-->[BPSK modulator]--> DPSK
          ^      |      (phase 0 / pi)
          +-[Tb delay]

1. Differential encoder: $d_k=\overline{b_k\oplus d_{k-1}}$ with an initial reference bit.
2. BPSK modulator: $d_k=1$ gives $A\cos\omega_ct$, $d_k=0$ gives $-A\cos\omega_ct$.

Example: data 1 0 1 1, reference 1 gives $d_k$ = 1 1 0 0 0, phases 0, 0, $\pi$, $\pi$, $\pi$.

Implementation: receiver

 r(t)->[BPF]-+------------>(X)->[int 0..Tb]->[sign]-> b_k
             +->[Tb delay]--^

The present bit is multiplied by the delayed previous bit and integrated; the result is proportional to $\cos(\theta_k-\theta_{k-1})$. Positive means no phase change (1), negative means a change (0). For the example, changes are no, yes, no, no, giving 1 0 1 1.

DPSK is simpler than coherent PSK and immune to phase ambiguity, with $P_e=\tfrac12e^{-E_b/N_0}$.