Phase Measurement Accuracy with Modulated Sounding Signals

In this paper the problem of measuring an unknown carrier phase shift of a transmitted sounding signal in a Gaussian noise channel is considered. Receivers which minimize the probability that phase error is larger than some value are considered. In some cases, this criterion leads to simple phase measurement techniques. When it does not, suboptimum receivers are considered. The main objective is to determine the effectiveness of the various measurement techniques by finding the cumulative probability distribution of phase error. In this way, three sounding signals are compared: an unmodulated carrier, a binary phase shift keyed (PSK) carrier, and a Gaussian pulse amplitude modulated carrier.