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I have a oscillator with a phase noise mask that was represented in dBc at specific offsets from a carrier.

Two options for a multicarrier signal going into a converter, apply the phase noise mask (dBc/Hz) on the total signal power of a multichannel signal (multi-carrier or multiple subcarriers - however you call it) or the dBc is applied on each individual power of the channels. dBc/Hz is a meaningless value until its changed into dBW/Hz. My question is whether in a mixer with a multi-channel signal, to apply phase noise is it applied against total signal power or each individual channel/subcarrier/carrier power...

Representing the oscillator with phase noise spectrum as one number, but noting that in reality it covers a bandwidth.

$$Oscillator=Ae^{i \theta } $$

Representing the signal with 3 channels or 3 carriers as below, but noting that in reality each channel covers a bandwidth

$$Signal=e^{i x } + e^{i x }+e^{i x }$$

Then the conversion process is just a multiplication (but is it really this simple multiplication for multicarrier?).

$${Signal} \times {Oscillator} =Ae^{i \theta } (e^{i x } + e^{i x }+e^{i x })=Ae^{i (x+ \theta ) } + Ae^{i (x+ \theta )}+Ae^{i (x+ \theta )}$$

This means the same phase noise mask is applied onto each channel or carrier and in this case the phase noise contribution is based on total signal power going into the converter.

It cannot be this simple multiplication because applying the same phase noise mask where it is based on a dBc of total carrier power dramatically increases the EVM from the phase noise in multicarrier situation. Basically 2 carriers gives a 3 dB worse EVM, 4 carriers is 6 dB worse EVM and 8 carriers is 9 dB worse EVM.

But if the phase noise dBc is applied on each individual channel or carrier power then how is that working in real physical world, a signal is multiplied by an LO and that LO has the phase noise thats being imparted onto the signal where that signal is composed of many channels or carriers.

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The Local Oscillator is multiplied in the time domain with the received (or transmitted) signal and therefore the spectrums (phase noise spectrum and signal spectrum) will convolve in frequency.

A significant driver of the phase noise mask in the receiver is blocking (jamming) resistance and ability to demodulate two closely spaced channels that have a large power difference. In these cases you can see how the stronger signal will convolve with the phase noise spectrum dumping a lot of noise right over the lower power signal of interest unless the phase noise is low enough.

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  • $\begingroup$ but if you have a phase noise mask given in dBc and a multicarrier signal, is this dBc applied on the total signal power or each individual channel power? $\endgroup$
    – Villere_DSP
    Commented Aug 28, 2021 at 9:37
  • $\begingroup$ @Villere_DSP the “phase noise mask” is a requirement on your local oscillator. With that you will have an actual local oscillator with a phase noise power spectral density given in dBc/Hz at each offset from the oscillator center frequency. What exactly are you trying to determine? If you want to know the impact of that phase noise on the receiver, the phase noise from the LO convolves with the entire spectrum presented to the mixer RF input. $\endgroup$
    – Dan Boschen
    Commented Aug 28, 2021 at 11:07
  • $\begingroup$ Convolves in frequency, not multiplies. If all channels had the same power level, the phase noise would then effect each channel equally. EVM is typically not the driver setting phase noise mask requirements but blocking immunity (anti-jam) for the likely cases of a stronger signal being received together with a weaker signal. $\endgroup$
    – Dan Boschen
    Commented Aug 28, 2021 at 11:11
  • $\begingroup$ I am looking at the impact of multiple channels with an oscillator at the same time. I have an oscillator phase noise response that I have converted into time. This multiplies the incoming time domain signal which contains all the channels. So phase noise is imparted onto each channel. But the conversion of phase noise in frequency to time is the issue, it's dBc/Hz at offsets from carrier but is that dBc/Hz on the total signal power (that includes all channels ) or each individual channel, if it's the latter then it's not a straight multiplication of oscillator x Signal ? $\endgroup$
    – Villere_DSP
    Commented Aug 31, 2021 at 10:36
  • $\begingroup$ @Villere_DSP As I said, this multiplication in time is convolution in frequency. The phase noise given in terms of dBc/Hz is already in the frequency domain, not the time domain, so much easier to stay in that domain. To see the effect on each channel consider how that effects the frequency domain spectrum. If you are less familiar with convolution, review what that does (even the simple graphical explanation) and then reread my answer to understand the dominant effect. $\endgroup$
    – Dan Boschen
    Commented Aug 31, 2021 at 23:07

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