Carrier Transmission of Binary Data in a Restricted Band

The spectra of digital frequency modulation (FM) signals have been observed to be narrow compared with the spectra of digital baseband signals or the corresponding amplitude modulation (AM) and phase modulation (PM) signals. This suggests a high efficiency of transmission in terms of occupied bandwidth for binary FM. Here the desirability of digital FM systems is investigated further with an examination of the probability of bit error. The FM receiver considered consists of a predetection filter, a limiter-discriminator, and a postdetection filter. New results are presented on the effect of predetection bandwidth restriction on the error performance of binary FM systems for various frequency deviations. Theoretical results have been obtained by a Fourier analysis of the distorted FM signals and by Rice's click analysis of FM noise. The data presented permits an optimum selection of system parameters such as frequency deviation ratio and predetection filter bandwidth. It is found that in narrow-band operation a peak-to-peak frequency deviation of about 0.7 times the bit rate and a bandpass filter bandwidth of about 1.0 times the bit rate yield a minimum probability of error. Experimental measurements have been made and there is, in general, good agreement with the theory. A comparison of the error performance of noncoherent binary FM, coherent AM, and coherent PM in a restricted band is made. Narrow-band noncoherent FM proves superior to AM in any bandwidth. In narrow-band operation, the noncoherent FM gives a somewhat better error performance than the coherent PM. For example, for an error rate of 10
^-4
and a bandpass filter bandwidth of one times the bit rate, the performance of a noncoherent FM system is 0.7 dB better than that of a coherent PM system.