Frequency or phase modulation with a noise carrier

The behavior of an ideal angle-modulation system in which the usual sinusoidal carrier has been replaced by a narrow-band Gaussian random noise or by an amplitude-limited narrow-band Gaussian random noise is studied. The use of a noise carrier results in an additive output noise (in addition to the usual output noise due to the noise in the channel, which is neglected here). It is assumed that the system is to be used to transmit a single-sideband multiplex signal consisting of many adjacent, narrow-band channels, and that the same output signal-to-noise ratio is desired in each of these channels. Subject to these assumptions, it turns out that the phase modulator need have a peak phase index of only about 1 radian. Further, this phase modulator should be driven by a band-pass modulating signal with an appropriately shaped spectrum, rather than by a base-band signal. Based on results of S. O. Rice, curves are presented relating the output signal-to-noise ratio, the required channel bandwidth, the bandwidth of the intelligence transmitted over the system, the required frequency translation of a baseband multiplex signal before modulation, and the peak phase index required of the modulator; all three bandwidths are normalized to the half-bandwidth of the noise carrier.