Error rate in a multiple-frequency-shift system

Based on the assumption of a fading-free signal and an additive white Gaussian noise, the element and symbol error rates in a multiple-frequency-shift (m.f.s.) system and the output signal/noise ratio in a frequency-modulation (f.m.) and a pulse-code-modulation/frequency-shift (p.c.m.f.s.) system are evaluated for wide ranges of system parameters. It is shown that the required intrinsic signal/noise ratio for a given symbol error rate in an m.f.s. system can be reduced by increasing the number of frequencies in the keying. The possibility of improving the threshold of an f.m. system beyond that of a conventional one, by frequency-modulating the carrier with sampled values and demodulating the modulated wave with a band-dividing demodulator, is shown. A brief discussion on the threshold effects in the frequency-lock and phase-lock f.m. demodulators suggests that the threshold of these feedback demodulators cannot be improved beyond that of a band-dividing one. It is shown that the threshold in a p.c.m.f.s. system can be reduced by increasing the base in the coding. The comparison of a p.c.m.f.s. system with a band-dividing f.m. system shows the inferiority of the former to the latter, in so far as the minimum-power criterion of system comparison is concerned.