Theoretical Diversity Improvement in Multiple Frequency Shift Keying

Multiple frequency shift keying (MFSK) is a modulation suitable for transmitting digital data under fading conditions. A quantitative analysis of MFSK-with-diversity is presented. The MFSK signals on the several diversity channels are presumed to be perturbed independently by Rayleigh fading and additive white Gaussian noise. Also, it is assumed that fading is slow and that envelope, cross-correlation (matched filter) detection is used. The diversity combining method is chosen so that the receiver performs a likelihood-ratio test in deciding which one of frequencies was transmitted. This optimum comibining method is to square and add the detected outputs of corresponding filters from each diversity channel. Theoretical error probability as a function of signal-energy-per-bit received is derived, and curves are plotted for two-, four-, and eight-frequency MFSK-with-diversity. Bandwidth requirements, as a function of type and order of diversity, are determined. Eight-frequency MFSK with triple diversity has a 21.8-db advantage over simple FSK for transmitting 6-bit characters with a 0.001 error probability.