A decision directed detector for the phase incoherent Gaussian channel

A vector digital signalling scheme is proposed for simultaneous adaptive data transmission and phase estimation. The use of maximum likelihood estimation methods predicts a better performance than the phase-locked loop. The phase estimate is shown to converge to the true value, so that the adaptive nature of the detector effectively achieves phase acquisition and improvement in performance. No separate synchronization interval is required and phase fluctuations can be tracked simultaneously with the transmission of information.