On the Theory of Error Rates for Narrow-Band Digital FM

The theory of error rates for narrow-band digital FM with limiter-discriminator detection and integrate and dump postdetection filtering is considered. The goal is that of simplifying the existing theory, which has evolved primarily in the frequency domain, and requires numerical integration and differentiation of Fourier series expansions, numerical convolution, and multibit pattern averaging. A fresh approach in the time domain, within certain ranges of frequency deviation ratio, and time-bandwidth product, leads to a theory which 1) gives Simple closed form solutions for the relevant system parameters, 2) allows for arbitrary IF filtering, 3) does not require numerical integration nor differentiation of Fourier series or computer convolutions, and 4) provides greater insight into the underlying error mechanisms. The subsequent, less involved BER calculations using the new approach compare favorably with previously published results. An unexpected bonus, resulting from the analysis, is that nonlinear IF filter phase characteristics can, in many cases, be shown to be unimportant in affecting the bit error rate.