# PLL in noise-free and noisy channels

I'm trying to evaluate the performance of PLL in compensating the phase noise in the absence and presence of AWGN noise, and the counterintuitive result I consistently get is that PLL performs better in noisy channels. Is this expected? and Why?

The code with which I get this result is a little bit complicated because it's part of a larger project, but what I do basically:

I generate the phase noise, which is symbol-by-symbol. I have the symbols in blocks of length K. So, what I do, I first find the the mean of the magnitude squares of the generated noise, and I find the mean of the magnitude squares of the residual error at the output of the PLL between the estimated phase noise, and the actual phase noise. The latter is larger the former in case of noise-free AWGN channel, but smaller in case of noisy channels.

• "I get the result", " why?" Please show how you get that result. The answer to "why" is exactly there! Instead of letting us get out a textbook and copy something you've probably read elsewhere already, show us how you get that result and we can discuss it exactly at your level of understanding. Sep 14 at 11:49
• OK, the code is a little bit complicated because it's part of a larger project, but what I do basically, I generate the phase noise, which is symbol-by-symbol. I have the symbols in blocks of length $K$. So, what I do, I first find the the mean of the magnitude squares of the generated noise per block, and I find the mean of the magnitude squares of the residual error at the output of the PLL between the estimated phase noise, and the actual phase noise for the same block. The latter is larger the former in case of noise-free AWGN channel, but smaller in case of noisy channels. Sep 14 at 12:02
• I added that information – it's highly relevant – to your question's body. Sep 14 at 12:58
• Shouldn't the error in the PLL be between the output phase and zero phase errror, not "estimated phase noise"? The PLL removes phase noise at the oscillator output, within it's loop bandwidth. Sep 14 at 13:04
• @DanBoschen Thank you for pointing this out. You're right. I was evaluating the performance wrongly. Now I get better performance after PLL in both cases, noisy and noise-free channels. Thanks again! Sep 15 at 11:34