Differential modulation and demodulation of multi-frequency digital communications signals

Multiple-frequency modulation (MFM) is a bandwidth-efficient digital communication signaling technique that may be used effectively in mobile satellite communications links. Algorithms for generating and demodulating differentially encoded multifrequency quadrature phase shift keyed (MFQPSK) signals using discrete Fourier transform (DFT) techniques are discussed. The theory and a prototype system for differentially encoding and decoding MFQPSK in the frequency domain are developed. By using long baud intervals and corresponding small spacing of the carrier tones, problems associated with channel fading are greatly relieved with respect to the previous method of differentially encoding the multiple carrier tones from baud to baud. An MFM system has been configured to transmit MFQPSK over a 4-kHz bandpass channel. Tone spacings, or baud rates, of 15, 30, 60, 120, and 240 Hz were tested. Output signal-to-noise ratios were estimated by computing sample means and variances of the real and imaginary parts of X_a. Experimental results are presented showing good agreement with the theory