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What is the mathematical relationship between phase modulated (PM) signal and the complex phase/magnitude of the frequency component at the carrier frequency used?

This is partially related to the question that I asked on phase noise, but it seems that the complex magnitude of this component is the same for all PM signals using that carrier, just that the phase is rotated. Is it something like the average instantaneous phase difference?

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What is the mathematical relationship between phase modulated (PM) signal and the complex phase/magnitude of the frequency component at the carrier frequency used?

The phase of the carrier wave is your data-carrying signal. It also is the phase in complex equivalent baseband.

So, that's the mathematical relationship: equality.

Magnitude doesn't matter to PM. It might be the same for all signals you consider, but it doesn't have to be; it's simply irrelevant to the information signal.

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  • $\begingroup$ This is where my understanding is going wrong: When the flicker noise of the oscillator becomes phase modulated with the carrier then how does this noise result in a fixed phase rotation value for all subcarriers in an OFDM symbol? Like what actually is that phase $e^{j\theta}$ that gets multiplied with the signal (which causes the peak of the phase noise in the frequency domain to rotate, which then gets convolved with each subcarrier). It seems to be some kind of average, unless this is a phase mismatch that is separate to the phase noise i.e. a uniform mismatch of phase with the rx osc. $\endgroup$
    – Lewis Kelsey
    Commented Nov 7, 2020 at 22:22
  • $\begingroup$ Ok, that is a different question and should probably be answered separately, but. If your local oscillator makes a phase jump, then that has nothing to do with the OFDM you transport; your equivalent baseband gets multiplied with a factor; that's not something that's only applicable to a single subcarrier. $\endgroup$
    – Marcus Müller
    Commented Nov 7, 2020 at 22:42

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