Phase Shift Keying with a Transmitted Reference

In this paper, an analysis is made of the performance of a communications system in which a reference tone is transmitted at a frequency adjacent to the phase keyed tone. The probability of error for a maximum likelihood receiver is obtained for an
m
-phase system of this type in the presence of additive Gaussian noise. The most advantageous division of power between the phase keyed tone and the reference tone is analyzed as a function of various system parameters. Error performance and optimum power division, when several keyed tones use a common reference tone, are also examined. The change in error performance due to differential phase delay between a data tone and the reference tone is computed. Finally, some results of an analysis of double character errors are reported.