If you replace the carrier signal in a phase modulated circuit with noise then presumably the noise will be modulated. What must be considered if we wish to detect this noise modulation? I’ve attempted to phase-modulate various types of noise in Matlab (pmmod), and in the FFT spectra I was expecting to see some sidebanding of the more discrete higher-amplitude components (in some frequency ranges) but none are visible. I assume it depends strongly on noise type.
The classic analog spectrum analyzer cannot detect phase variations of the carrier, unless sidebands are created.
Given the modulation Factor is deltaFreq/Fmodulation, and the modulation factor is expressed in radians, wee can see the simply fact of "some phase modulation" might not cause sidebands to exist.
By the way, on a spectrum-analyzer you cannot tell the difference between PM sidebands and AM sidebands. You need to examine the sidebands as PHASORS; PM have oppositely rotating phases, so the carrier energy remains constant; AM phasors rotate in the same direction and cause variation in the carrier energy.