Signal-to-Crosstalk Power Radio in Smoothly Limited Multichannel FDM Signals

The passage of multichannel frequency division multiplexed (FDM) signals through an amplitude limiting nonlinear device produces crosstalk in each channel output due to intermodulations among signals in all channels. The signal power S
0
to crosstalk power N
c
ratio in any particular channel determines signal degradation. This paper considers multichannel FDM signals passing through a saturated bandpass amplifier with transfer characteristic of smoothly limiting error function curve, and determines a lower bound of
S_{0}/N_{c}
as a function of
q
, which is related to the limiting level. By invoking the central limit theorem, the FDM signals are represented by a Gaussian noise, excepting the signal in the channel where
S_{0}/N_{c}
is to be determined. The signal in the channel under consideration is represented by a constant amplitude sine wave. When an assumption that the input noise power spectral density is symmetric about the center band is made, such as a Gaussian power spectrum considered in the analysis, the computation of a lower bound for
S_{0}/N_{c}
was equivalent to the consideration of the center channel, where the crosstalk power is maximum. The problem is an extension of an earlier work by Cahn, who considered an idealized saturation amplifier. The result is presented in a graph where it is seen that an infinite clipping case of the present analysis agrees with that of Cahn.