Amplitude modulation with a noise carrier

Consider an ideal amplitude modulation system in which the usual sinusoidal carrier is replaced by a narrow band of random noise, of midband frequency f
0
and half-bandwidth B; the spectral density and the total power of the output noise of this system are determined. An optical system of this type would use an incoherent spectral line as a carrier, rather than the coherent output of an optical maser. Considerable improvement is obtained by shifting a baseband modulating signal to a frequency band much lower in frequency than f
0
but much higher than B, before modulating the noise carrier. In an optical system this translated modulating signal might lie in the microwave region. Even so W, the bandwidth of the modulation, must be very small compared to B to attain a high output signal-to-noise ratio.