Interesting question. The PSD is a *power* spectral densitty. While it would be possible to calculate the PSD of the phase (if you really desire so), what would be its meaning? For the case of a filter, i can imagine that fast and irregular changes in the phase (i.e.a  PSD of the phase with strong components at high frequencies) are indicative of an increased variation in the group delay of received signals. However, for general signals, it seems like a bizarre transformation.

What would be the motivation to calculate the PSD of the phase?

Answering your question, it could make sense to use the same classic windowing functions as for any other PSD calculation.

Dr Cuypers

Thanks for your time.

I work with GPS signals. I am interested in the L1C frequency ( http://www.navipedia.net/index.php/GPS_Signal_Plan ). Here the signal has to travel through the ionosphere, which may disturb the signal. The phase of the signal is of interest as it will have the signature of the ionosphere.

If you had a frequency of 1575.42 MHz, how would you window it to calculate the PSD of it's amplitude and the PSD of it's phase, from an engineering point of view?

There may be a few problems with this plan.

A first problem is that the GPS signals are 20 dB -give or take a few dBs- below the thermal noise floor. In other words: whatever window and whatever bandwidth you use, you would get a spectrum of white thermal noise (and other interference).

A second problem is that there are typically around 12 GPS-satellites in view. Even if the thermal noise would not be present, it would be impossible to distinguish between these satellites. Even worse: they are not only sending the C/A code but also the P-code. And Galileo and Beidou satellites transmit there as well.

So you cannot just capture a signal, calculate the PSD and phase and be done. I have linked a plot with a typical spectrum, the red arrow points at 1575.42 showing the composite power of all GNSS satellites. It also shows interference here and there.

A solution to both of these problems is the use of a highly directional antenna and tracker system to isolate and amplify the signal of only one satellite. That is not impossible, but not easy either, because it requires a large dish antenna.

On a related note,  it *is* possible to get *some* phase information at the carrier frequency by decorrelating with the C/A code. By doing the same on L2 and comparing the differences in phase delay and group delay, it is possible to make a statement about the ionosphere (as you probably knew already).

Maybe you can find a way around these problems. I wish you good luck.

Thank you very much, Dr Cuypers.

I worked with multiple brands of GNSS receivers which would log the amplitude and phase data along with other parameters. These receivers simultaneously isolate, track and amplify signals from multiple satellites (they can have 12 dedicated channels,so signals from 12 different satellites perhaps). 

So, I have the data, and I think the amplitude data of the signal could be Hann'd. But I definitely need help choosing the window function for the Phase data. The phase may reach a large value for GPS L1C (~108 cycles). It perhaps varies by different amounts due to the various contributing factors. Will the Rectangle be a bad function to use?

Decorrelating the phase information with the C/A code both at L1 and L2 and comparing the results: I will work on that.

Okay, I have apparently misunderstood your question. These receivers log the amplitude and phase data of the *decorrelated* signal, you want to calculate the PSD of the evolution of the phase and amplitude of this decorrelated signal over time. And when you unwrap the phase this will obviously lead to very large values if you have a large number of samples. This will have a large DC component and a large component due to the strong linear contribution of the evolving phase. (It may be more logical to study the shift of the code timing versus the carrier phase. I expect that these should not run away so much, but I am no expert in this field.)

Anyway: the window you use is a trade-off between the selectivity and the side lobes you want. If you don't know which one of these is the most important, the rectangular window is probably a good choice. Good luck!

Thank you.