On the modulation levels in a frequency multiplexed communication system by statistical methods

This paper presents a mathematical analysis with experimental verification of the distribution of the instantaneous voltage of a complex signal resulting from the combination at random of a small number
n
of sinusoidal oscillations. The resulting calculated distributions are plotted in the form of a set of probability curves for comparison with curves obtained by experiment. Further laboratory measurements in which the individual sinusoidal oscillators are frequency-modulated in a manner suitable for communicating information in a binary form, yield substantially no change in the amplitude distribution as determined for the modulated oscillators. Consequently, the results of the mathematical analysis may be applied in the determination of
M
, the degree to which each subcarrier may amplitude modulate a final carrier in a FM-AM frequency multiplexed system.
M
may be determined for any desired degree of overmodulation in excess of one per cent and for as many subcarriers as are required in the system. Modulation levels determined according to approximate methods and the method described here are tabulated and compared.