On Binary DPSK Detection

Optimum detection of binary DPSK yields a bit error probability, P
e
of (1/2) exp (
-E_{b}/\eta
), the classic result, but requires a reference carrier in-frequency but not necessarily in-phase with the received carrier. Any other detector will yield degraded results. Several well known textbooks give a derivation for a suboptimum detector with the above result but neglect intersymbol interference. In this paper the optimum
M
-ary DPSK receiver is shown and a derivation of P
e
for the binary case given. Two suboptimum detectors are analyzed and their performance is shown to be 1 to 2 dB worse than the optimum.