Theory of Error Rates for Digital FM

Abstract

A general theory is presented for evaluating the error performance of a digital FM system in the presence of additive noise. The digital system considered is a conventional one employing a voltage-controlled oscillator as the modulator and a limiter-discriminator followed by a low-pass filter as the demodulator. Because of the nonlinear nature of the demodulation process, no adequate analytical techniques have been available to provide a satisfactory treatment. Adopting the notion of “clicks” used by S. O. Rice to study threshold effects in analog FM systems, we have succeeded in evolving a theory capable of predicting performance for a wide range of applications. While our theory reinforces some previously derived results for binary and for narrow-band systems, the results obtained here are not confined to these situations. In particular, the inefficiency of the FM discriminator as a detector for a large number of orthogonal signals is quantitatively evaluated, as well as the role of the post-detection filter. Some qualitative aspects of the error-causing mechanisms discussed in the paper are general, but quantitative results are confined to additive Gaussian noise and large signal-to-noise ratios.