A Class of Signals for Analog Telemetry over a Coherent Channel

This paper proposes and studies a class of signals which generalize frequency position modulation (FPM) and pulse position modulation (PPM). The generalization adds a degree of freedom analogous to a duty factor. Varying this quantity has an effect similar to that of varying the time-bandwidth occupancy in an FPM or PPM system, but it does not significantly increase the channel occupancy. The mean-square error is studied under large signal-to-noise ratio conditions and in the threshold region. We find that the additional degree of freedom allows us to trade between performance in these two ranges of signal-to-noise ratio. The nature of the signals, and their error behavior make them well suited to adaptive telemetry over a coherent channel. Small degrees of channel incoherence are considered and shown to produce only a small degradation in performance.