Optimum detection and signal selection for partially coherent binary communication

The optimum detectors for coherent and noncoherent reception of binary signals in additive Gaussian noise and the resuiting error probabilities were obtained by Helstrom [1]. In many practical communication systems a reasonable estimate of the phase of the received signal is available as the result of an auxiliary tracking operation of the carrier signal by a coherent tracking device such as a phase-locked loop. It is shown that the optimum detector for this case, which we refer to as partially coherent reception, is a linear combination of the correlation detector and the squared envelope correlation detector, which are optimum for the coherent and noncoherent cases, respectively. The error probabilities are also obtained as a function of the energy-to-noise ratio of the channel and the variance of the error in the phase estimate, which is a function of the signal-to-noise (SNR) in the tracking loop. The signal selection problem is considered in terms of these parameters.