Interchannel Interference in FM and PM Systems Under Noise Loading Conditions

The systems Ave shall consider are of the F D M - F M and F D M - P M types; that is, systems in which the composite signal wave (the "baseband signal") from a group of carrier telephone channels in frequency division multiplex ( F D M ) is transmitted by frequency modulation (FM) or phase modulation (PM). Such methods are currently being used in 601 624 TIIE BELL SYSTEM TECHNICAL JOURNAL, MAY 1 9 5 5 the Bell System to send large groups of telephone channels by microwave radio. If the FM signal is accompanied by echoes, which may be due to reflections in the equipment or in the transmission medium, the wave of instantaneous frequency versus time is distorted in a nonlinear manner and interchannel interference occurs. Here we shall be concerned with this interference. The distortion has been analyzed in a number of previous publications1"4 for the case in which the base-band signal may be represented by one or more sine waves. However, when the number of telephone channels is not small, the sine wave representation becomes unwieldy because a large number of both low and high order modulation products must be considered. Here we avoid this difficulty, at the cost of somewhat more complex analysis, by using a band of random noise to represent the multiplex signal. It has been found in practice that such a random noise signal of appropriate bandwidth and power adequately simulates a composite speech signal. For studies involving interchannel interference the energy corresponding to some particular telephone channel is removed.