Theory of Error Rates for Digital FM

Theoretical investigations of FM receivers with analog input signals date back to J. R. Carson and T. C. Fry, 1 and to M. G. Crosby. 2 These investigators and others that followed them 3,4 ' 5 were primarily concerned with the signal-to-noise (S/N) transfer attainable in FM receivers and the determination of threshold effects. Recently S. (). Rice,6 and previously J. Cohn, 7 attacked the threshold problem in FM receivers from a fresh point of view by using the notion of "clicks." It has been observed that when the noise at the input of an FM receiver is increased beyond some value, the receiver "breaks," that is, for a given (S/N) at the input, a much poorer (S/N) at the output is measured than would be predicted from a linearized analysis of the receiver. Before the breaking point, clicks are heard in the output of an audio receiver. As the input 1511 1512 T H E B E L L SYSTEM T E C H N I C A L J O U R N A L , N O V E M B E R 1966 noise is further increased, the clicks merge into a sputtering sound. Rice's approach is to relate this breaking point with the expected number of clicks per second at the output due to the added noise at the input. While in analog application the criterion of (S/N) transfer is satisfactory, in digital data transmission it does not by itself furnish an adequate performance criterion. Usually performance is judged in terms of error rates which cannot be predicted from the (S/N) transfer for nonlinear receivers. The error rate clearly depends on the statistical distribution of the output noise.