# Can phase noise be averaged out?

I have an ADC sampling a downconverted RF signal at fs. I obtain N=2^15 samples of the RF input signal "fcarrier + fs/10".

The more I average, the more the entire noise floor shifts down (as expected, 10dB/dec) but also the phase noise skirt. I can average down to 100dB SNR (I didn't wait longer). For 1000 averages, the (zoomed) spectrum looks like this: The phase noise skirt just moved down by 30dB as compared to the non-averaged version. This suggests I can average the phase noise out. But I would not expect it to be averaged out. According to http://www.bitsofbits.com/2015/07/07/signal-jitter-and-averaging/, the signal should be a cosine convolved with an exponential ("signal-leakage like") after infinite averages.

• Can phase noise be reduced?
• If yes, does can it be averaged out same as white noise? (This is what I observe above).
• How does this fit into the link posted above?
• Does it depend on the input signal? (sinusoid vs wideband)?
• What sort of equipment gives enough resolution to read 4.761904761904762 MHz with that level of precision? – Transistor Jul 10 '18 at 22:32
• As an engineer, numbers like 4.761904761904762 make me chuckle. – evildemonic Jul 10 '18 at 22:34
• It just does not matter. Then no numbers. Numbers removed. – divB Jul 10 '18 at 22:37
• @Transistor Answer: An extremely picky filter with the highest frigging Q-factor you've ever seen. Float value needs to be more specific. – KingDuken Jul 10 '18 at 23:08
• If you have random noise, doesn’t an average of 2 = -3dB and 1000= -30dB in noise? – Tony Stewart Sunnyskyguy EE75 Jul 11 '18 at 0:30

Let us model additive noise, atop a sinusoidal carrier, as 2 small noise sources in quadrature.

We have this vector diagram simulate this circuit – Schematic created using CircuitLab

The inphase noise is AM: amplitude modulation noise.

The quadrature noise is PM: phase modulation, or phase noise or jitter.

Is there any specific reason why more samples, averaged together, would not produce a lower standard deviation?

By the way, what is the ADC/sampling_clock phase noise spectrum?

• This answer does not really help me yet and does not answer the question (IMO) but maybe I don't understand it yet. There is oscillator noise (consisting on amp.&phase noise) but phase noise is by definition phase only (and let's not assume I/Q for simplicity but only consider one channel). As I hinted in my question, PN is not additive but multiplicative, hence I don't expect averaging to work. Furthermore, does it make a difference if the signal is purely sinusoidal or a complex modulated signal? – divB Aug 7 '18 at 7:53
• If you show the noise as a centroid around the tip this would be clearer. – Scott Seidman Jun 22 at 16:34