Error Probabilities for Telegraph Signals Transmitted on a Fading FM Carrier

Abstract

This paper presents an analysis of error probabilities for multiplexed binary telegraph signals that are used to frequencymodulate an RF carrier that is subsequently corrupted by fading and noise. Frequency-shift keying, amplitude keying, and phase-shift keying are considered. It is shown that most telegraph errors occur when the carrier fades below threshold, and the principal results of the study therefore concern the effects of the FM threshold on error rate. Various methods of diversity reception are considered. For a maximal-ratio baseband combiner and certain types of telegraph receiver, a method is given for extending the results obtained for a single receiver to nth-order diversity. This makes it possible to use experimental data to describe either the threshold or the fading of the carrier. Study of threshold models indicates a serious conflict between the requirements of telephone channels and those of telegraph channels. Furthermore, good telegraph performance demands great care in the design of diversity combiners to work below threshold. The analysis pertains most directly to troposcatter systems, but the general conclusions regarding the effect of FM threshold should be relevant also for fading transmission paths such as those met in line-of-sight and telemetry.