Relative phase measurements

[Paul Colby]

I'm trying to measure correlation between two RF noise sources and as usual trying to do it on the cheep. I've purchased 2 SDRPlay RSP2pro radios. These operate from 500kHz or so to 2 GHz with sampling rates from 2 to 10 MHz. Not bad for $200 and they work well as radios. The RSP2s have in and out clock ports allowing the user to operate them off a common clock which is a 1.5Vpp signal at 24MHz. For my application I need the relative phase reference to be good to some tolerance (say $\pm 5^\circ$ I'm guessing). As an initial test I've driven the radios off of a common external 24MHz signal. The center frequency is set to 15MHz. A second signal generator is set to 15.1 MHz at 10mV and passed through ~80dB attenuator and teed into the input port of each. I collect IQ data from each radio. A 2048 sample wide window in FFT'd leading to a peak at 15.1MHz where I extract the amplitude and phase off each radio. With this data I can compute the relative phase between the two identical signals. What I get is a meandering relative phase between the two signals which has a rather wide swing.

My operating theory is this meandering phase is due to the Phase Lock Loop internal to each radio caring more for frequency than phase. I'd love to post the plot but it's not clear how to do this (I seem to be homepageless).

Ah, just tried the same experiment with the radios running internal clocks and the results are quite comparable.

So, I guess my basic problem is I'll need to measure the relative phase by injecting a synchronization signal, remove the synchronization signal from the data, correct the data and then do my correlation?

 

[anorlunda]

I'd love to post the plot but it's not clear how to do this

There is an UPLOAD button to the right of the POST button that allows you to upload pictures to your post.

 

[tech99]

I'm trying to measure correlation between two RF noise sources and as usual trying to do it on the cheep. I've purchased 2 SDRPlay RSP2pro radios. These operate from 500kHz or so to 2 GHz with sampling rates from 2 to 10 MHz. Not bad for $200 and they work well as radios. The RSP2s have in and out clock ports allowing the user to operate them off a common clock which is a 1.5Vpp signal at 24MHz. For my application I need the relative phase reference to be good to some tolerance (say $\pm 5^\circ$ I'm guessing). As an initial test I've driven the radios off of a common external 24MHz signal. The center frequency is set to 15MHz. A second signal generator is set to 15.1 MHz at 10mV and passed through ~80dB attenuator and teed into the input port of each. I collect IQ data from each radio. A 2048 sample wide window in FFT'd leading to a peak at 15.1MHz where I extract the amplitude and phase off each radio. With this data I can compute the relative phase between the two identical signals. What I get is a meandering relative phase between the two signals which has a rather wide swing.

My operating theory is this meandering phase is due to the Phase Lock Loop internal to each radio caring more for frequency than phase. I'd love to post the plot but it's not clear how to do this (I seem to be homepageless).

Ah, just tried the same experiment with the radios running internal clocks and the results are quite comparable.

So, I guess my basic problem is I'll need to measure the relative phase by injecting a synchronization signal, remove the synchronization signal from the data, correct the data and then do my correlation?

I presume the radio is providing SSB demodulation. This makes it sensitive to LO phase. If you use envelope detection it will not be sensitive to LO phase. But you will need to use a modulated source or a noise source.

 

[Paul Colby]

Okay, that works. We have two radios being fed a common 15.1MHz sine wave. Both radios tuned to a 15MHz center frequency. The x-axis in the plot is IQ sample number while the y-axis is the relative phase of the two 15.1MHz peaks as seen by each radio. The way I interpret this is as the relative phase between the two separate LOs on a sample by sample basis. The rate at which this overall phase drifts is slow in relative terms so it's not clear this would be a great effect on SSB demodulation (not that I understand SSB demodulation very well).

Now my complaint is that the difference between using a common 24MHz clock for the radios doesn't improve the above the way I would expect. The ideal situation would be for the above plot to be a flatish line about 0 degrees because, after all, both radio LOs are phase locked to a common 24MHz signal and the received signals have identical phases and amplitudes. The reason to want this is long term averaging of correlated signals isn't going to end well with the relative phase drifting about.

 

[Tom.G]

Looks like 3 or 4 major confounding anomolies, the predominant with a characteristic period around 10 000 samples, and a mix of 'others' down to maybe 1 000 samples. If you want to try tracking them down, do an FFT on that graphed data; it could be external interference.

The predominant cause could also be slightly different gains in the PLLs or slightly different free-running frequencies of the local oscillators. Either could cause that ~10 000 sample period, especially if it is stable. At least for testing, try using a single oscillator in place of the two LOs. To avoid interference and beat frequencies, you will probably have to disable the onboard LOs to do this.

You could also get that effect If the LO frequency is not an integer multiple or sub-multiple of the 24MHz clock. Without an integer ratio, the receivers probably vary the divider ratios to get an average frequency that centers on the desired one... and those dividers will not necessarily be coherent between the receivers.

If the receivers will be widely separated in deployment, you can implement LO phase locking by locking them to GPS signals, or even to a local TV or radio station (AM or FM). (Watch out for multipath distortions when using a TV or FM station.)

Sounds like an interesting problem. Please keep us updated.

Tom

 

[Averagesupernova]

What kind of test equipment do you have at your disposal? I'd there a way you can tune into the local oscillators of each receiver? A good SSB receiver will show up phase noise with ease. If you have a scanner that is able to tune the local oscillator you might be able to hear the suspected phase noise in the FM detector. A spectrum analyzer could tell you plenty.

 

[Paul Colby]

The predominant cause could also be slightly different gains in the PLLs or slightly different free-running frequencies of the local oscillators. Either could cause that ~10 000 sample period, especially if it is stable. At least for testing, try using a single oscillator in place of the two LOs. To avoid interference and beat frequencies, you will probably have to disable the onboard LOs to do this.

Thanks for the reply. Without prying the case open I don't have access to the LO. The radios are based on the MSI001 tuner chip and a MSI2500 DSP. Not much info on these that I could find although I do have pin assignments. To make matters worse the software API is not what I consider well documented and the source is unavailable (why do this? ever?). Turning off the DC correction and the IQ correction reduces the wild phase excursions, however, the average relative phase between two identical sine waves (same oscillator split with a T) is a random number run to run. It's like the PLL inside the radio doesn't care about the P part of PLL at all. I have this (possibly wrong) feeling that two oscillators phase locked to the same reference should have identical phases and zeroish phase difference between them. OTOH if the Is and Qs are computed digitally, well the phase reference could well be meaningless. If this is the case I see no point to providing an external clock as you will never be able to make a phased array of any shape or form.

If the receivers will be widely separated in deployment, you can implement LO phase locking by locking them to GPS signals, or even to a local TV or radio station (AM or FM). (Watch out for multipath distortions when using a TV or FM station.)

For now the receivers are collocated. However, if I see anything that looks like a positive result, separating the receivers is essential. What your suggesting here sounds like using a reference provided on the radio input, much like the test signal I'm currently showing data for. The more I consider it the more plausible using a known phase reference on the radio input as a way of providing long term phase stability. Actually for my intended purpose the phase may drift from here and yon provided both radios drift identically. This is what I was trying to get with common clock signals.

 

[Paul Colby]

What kind of test equipment do you have at your disposal? I'd there a way you can tune into the local oscillators of each receiver? A good SSB receiver will show up phase noise with ease. If you have a scanner that is able to tune the local oscillator you might be able to hear the suspected phase noise in the FM detector. A spectrum analyzer could tell you plenty.

I do have an Hp spectrum analyzer though I'm not certain how it would be useful. It's important to consider that the measurement I'm doing the phase noise of the input reference signal should cancel. The only way I can see getting the above result is if the relative phase of the radio LOs are drifting independently.

I can see how a good SSB receiver would detect very low levels of phase noise however, how does this help?

 

[Averagesupernova]

I guess I'm not sure what you are after here. If there is phase discrepancy between the output of two identical receivers fed with the same signal it stands to reason the phase discrepancy is generated within one or both receivers. The local oscillator is the place to start. If you can view the LO on the spectrum analyzer you may be able to see it.
-
PLL implies perfect phase but that is far from reality. PLL does exactly what we suspect your local oscillators are doing. It maintains an average frequency. It does so by measuring phase. Sometimes the phase is off one way and sometimes it is off the other way. But the end result is an average that is on frequency with quite possibly loads of phase noise.

 

[Paul Colby]

I guess I'm not sure what you are after here. If there is phase discrepancy between the output of two identical receivers fed with the same signal it stands to reason the phase discrepancy is generated within one or both receivers. The local oscillator is the place to start. If you can view the LO on the spectrum analyzer you may be able to see it.

Thanks, it's good to hear the LOs are the likely culprit. I haven't figured out how to pry into the case yet.

PLL implies perfect phase but that is far from reality. PLL does exactly what we suspect your local oscillators are doing. It maintains an average frequency. It does so by measuring phase. Sometimes the phase is off one way and sometimes it is off the other way. But the end result is an average that is on frequency with quite possibly loads of phase noise.

One possibility is my clock signal has enough phase noise to keep the PLL agitated but I don't think this is the case. If I just run the radios with their own internal clock I get very similar short term fluctuations with but stronger long term drift. This could just be the performance limit of these radios though I'm at somewhat of a loss what the external clock inputs intended use is. In the 12-15 MHz range the frequency of a free running radios looks spectacular. My reference signal overlays between the two so why bother with a common clock?

 

[Averagesupernova]

You should be able to pick up the LO without opening the case unless the unit has excellent shielding.

 

[Tom.G]

Here is a link to the 25 page datasheet for the MSi001: http://www.cqham.ru/forum/attachment.php?attachmentid=199248&d=1428341442

It seems the on-chip synthesizer is a Frequency Lock Loop, not a Phase Lock Loop. This is indicated by it being called a Fractional-N synthesizer and also by its general description. See page 16 of the datasheet. That being the case, you will never get phase lock to any external reference, only an average frequency lock.

There are two possible solutions I see:
1.) scrap it and start over with a different chip set.
2.) It might be possible LO synthesizer Frac and Threshold (registers 2 & 5) to zero and Threshold (reg 5) to 0xFFF, or disable them. Then select your reference frequency and LO Integer field for the desired LO. You could then build your own PLL, digitize its output, and send it to the AFC field in register 3.

In the end, this chip was never designed to do what you need it to do. I think you would be best served to start over with a different chipset, if available... or if you are up to it, design your own PLL for this chipset with building-block ICs (Oscillator, PLL, etc.), but keeping low jitter in a PLL can be a challenge.

Good Luck! (and keep us posted)
Tom

 

[Paul Colby]

Thanks Tom, this is very helpful.

 

[Tom.G]

You're welcome.
See edited post #12 for correction on register setting.

(I'm off to cataract surgery in an hour so may not be online for a day or three.)

 

[Paul Colby]

Hey, best of luck with the procedure. Thanks again for the FLL versus PLL distinction. This is quite critical for what I intend and really fits with what I'm seeing. The software API provided is pretty much a black box and complex so setting individual registers isn't something provided for. This is why I dislike APIs without the source code. Strange when releasing their code would likely increase sales rather than decrease them but they are likely bound by agreements with chip vendors etc. I'm unconvinced that protecting this type of info does squat for people with this class of product.

I think what I'm going to attempt is injecting a common signal to be used as a phase reference to extract/correct the relative LO phase between radios. This clearly will add common noise to the input of both radios but if this common noise is in a narrow enough band it can be filtered out. If this doesn't work it might be time to build my own special purpose synchronous radio. Seams like a pair of good mixers and a stereo sound card might get me closer to what's needed.

 

[Paul Colby]

Thanks to the explanation from Tom progress has been made. The RSP2 are direct conversion radios. They use ADCs to sample the radio input and down convert the resulting data stream to base band. The result is a series of I and Q values which are delivered to the user via USB at a rate of 2 to 10 MHz. Actually, in practice the IQ values are delivered in chunks (I call them frames) of some length (strange numbers like 1344 at a time) the exact number determined in the API from the setup of the radio. All corrections like DC offset and IQ circularity are performed on a frame by frame basis. I surmised that the frequency loop in the synthesizer might also be synchronized to performed it's corrections on a frame by frame basis. With this assumption I fed both radios the same 12.1MHz sine wave @10mV through 76dB attenuation. The resulting spectra look like,

Okay, the peaks just right of the center is the 12.1 MHz sine wave as seen by each radio. Next, each data frame is FFTed and the complex coefficient at the peaks are used to extract the the phase of the peak as seen by each radio. The plot of the resulting phases for each radio as a function of frame (I took 100 frames of data) look like thus,

which is understood as the frequency correction of each radio being applied separately for each frame.

Since the only thing I think I care about is a common phase reference for each frame, I can use these phases to correct each radio. Time to do a happy dance.

 

[Tom.G]

RSP2 are direct conversion radios. They use ADCs to sample the radio input and down convert the resulting data stream to base band.

The datasheet for RSP2 from "SDRPLAY" says "Compatible with Mirics radio & TV software" and also states "Sample frequency 2MSPS - 10.66MSPS"
That means the highest RF frequency they can directly sample is <5.33Mhz. Anything higher is subsampled and interpolated. This is not to say it won't work for you, it may well be 'good enough.' I will even stick my neck out to say your approach of including a phase standard in the signal, to be later de-convolved, has a high probability of solving the problem. It comes down to how accurately you can measure/detect the phase standard (assuming no receiver 'correction' happens within a frame.)

The cataract procedure went well. Screen time will be limited for a few days yet. The general anesthetic is still wearing off though. (I hope the above msg isn't too garbled/unreasonable!)

If you aren't giving anything away, what is this project?

 

[Paul Colby]

The datasheet for RSP2 from "SDRPLAY" says "Compatible with Mirics radio & TV software" and also states "Sample frequency 2MSPS - 10.66MSPS"

The center frequency maxes out at 2GHz. The tuner chip mixes the radio input down an the ADC's then sample and decimate. The conversion is done in one frequency translation step. Maybe direct conversion is the wrong term for this? The end result is one has a frequency band which is translated down to "base band".

If you aren't giving anything away, what is this project?

Well, since you asked,

I've had a long term project centered on the detection of radio frequency gravitational waves. It's an interesting question how would one go about detecting GW in the AM band and above. I've looked at quite a few schemes in the past 5 years. By far the most sensitive one uses bulk piezoelectric materials. When illuminated by GW at these frequencies the material of the detector is strained by the wave over timescales too short to compensate for. For example a 4MHz quartz resonator is 0.4mm thick so the wavelength of a shear wave in quartz has a wavelength on the order of 0.8mm. A 2cm thick crystal illuminated by a 4MHz GW will develop an induces D-field over most of its volume. This D-field will appear as an RF excitation. So, this is an attempt to see how sensitive of a detector I could make from garden variety components.

There is also a separate discussion on the measurement of evanescent gravitational waves. As you may know the field in the neighborhood of an electric dipole antenna increase much faster than $1/r$ due to evanescent waves. With GW these near fields grow much more rapidly than with EM more like $1/(kr)^5$. These near fields can become exceedingly large when compared to the static time independent terms. It's fair to ask if these can be measured. There was a thread I started on the relativity forum if you're interested. Search for Are Evanescent Gravitational Wave Measurable or such.

 

[Paul Colby]

I'm using two 15dB directional couplers and some attenuators to inject a common 12.8MHz signal into two radios, A and B. The setup shown here.

where the attenuators connected to the coupling ports are 10bB. The attenuator on the center line of the T is 20dB. Ideally I would like more like 30 or 40 dB for the attenuators on the coupling ports because this will reduce unwanted cross talk but for this proof of concept 10 dB is just fine. The RG-316 coaxed snaking off to the right and and top of the image are headed toward radio B and A, respectively. The adjustable attenuator is connected to another signal generator into radio A. Averaging 1000 phase corrected data frames I get,

The x-axis is frequency and the y is proportional to power. The green curve labeled 'fftAB.dat' is the real part of the product of A's IQ's times the conjugate of B's IQ's at each frequency. The missing data on the green curve is where gnuplot kindly drops negative values when using a log scale.
It's interesting that the signal on A doesn't appear on B or AB at noticeable levels (yet).
Also, we see that this scheme is successfully removing the noise intrinsic to each radio. Cool.

 

[Paul Colby]

Okay, the calibration signal above is from one of my two Hp signal generators. Clearly it's the one with atrocious phase noise. Substituting the better of the two gives,

Actually, the smallish peaks appearing on radio A are due to stray RF pickup through a 30 dB attenuation from my broken signal generator which is off. The calibration signal is 1mVpp at 12.8MHz through ~45dB of attenuation. This is the result of 10000 data frames.

 

[Tom.G]

Unfortunately the image resolution doesn't allow reading the legends or discerning the overlayed traces. Part of the axis labeling is decipherable, and it looks like the Y axes are scaled differently. I take it the 12MHz signal is the from the second signal generator feeding receiver A. I see a (extraneous?) beat in the second plot repeating around 800KHZ from one of the radios, can't tell which one from the plots but probably the A. Probably due to the wide bandwidth down-conversion.

BTW, what is the frequency of the expected phase shift signal?

 

[Paul Colby]

Sorry for being unclear. I hope you are feeling well.

All curves appearing in post #20 are on the same logarithmic scale. Each radio is producing $I$ and $Q$ data frames consisting of 1344 pairs. The data are short integer values. Each of frame is FFTed to yield $I$ and $Q$ values in the frequency domain. The radio traces are,

$P_A = \langle I_A^2\rangle+\langle Q_A^2\rangle$
$P_B =\langle I_A^2\rangle+\langle Q_A^2\rangle$
$P_{AB} =\left| \langle I_A I_B\rangle + \langle Q_A Q_B\rangle\right|$

The absolute value in the definition of $P_{AB}$ is the complex number magnitude not the real number absolute value (sorry for the lousy notation). If $k$ is the frame index and $N$ the number of frames, the average of $X$ is defined

$\langle X\rangle = \frac{1}{N} \Sigma_{k=1}^N X_k$

where $X$ is any of the expressions appearing between the brackets.

The y-axis numbers are $1\times 10^{10}, 1\times 10^8, 1\times 10^6, 10000, 100, 1, 0.01$ from top to bottom. The horizontal grid line grid spacing is 20dB.

There is considerable amount of noise in the $P_A$ plot because as shown in the photo of the couplers radio A is connected through the adjustable attenuator to a non-powered hp signal generator through a 6' length of RG-58 coax. The noise on A however is fairly uncorrelated with the noise on radio B which is why it doesn't appear in $P_{AB}$. This is a good thing and the whole point of the effort. Adding up the nominal attenuations, the input calibration signal at 12.8MHz in the plot is about 5 micro volts. which puts the $P_{AB}$ curve noise floor at about 5 to 6 nano volts. The annoying peak at 12.00MHz is what remains of the usual spurious DC peak after the correction applied by each radio. It's common to both radios so the error in the correction appears in $P_{AB}$.

The signal I'm ultimately looking for is very likely well beyond my capabilities so finding it's phase angle isn't yet the dominate concern. $P_{AB}$ of course is independent of the phase, however, I retain the real and imaginary components so I have the phase info when required. I'll be testing this as soon as I get enough attenuators .

 

[Paul Colby]

Okay, looking at the equations I wrote I think I should be more careful. Let's define the complex signal as,

$Z = I + i Q$

with the complex conjugate

$Z^\ast = I - i Q$

Then

$P_A = \langle Z_A Z_A^\ast\rangle$ The red curve in #20
$P_B = \langle Z_B Z_B^\ast\rangle$ The blue curve in #20
$P_{AB} = \left|\langle Z_A Z_B^\ast\rangle\right|$ The green curve in #20.

I will make an effort to improve the graphing text.

 

[Paul Colby]

Something is definitely off in what I'm doing. I think it may have to do with normalizations and such. More later.

 

[Paul Colby]

Okay, when in doubt, write it out. suppose we have a sine wave signal input to a pair of SDRs. This signal is

$v_k(t) = A_k \cos(\omega t + \phi)$

where $k = 1, 2$. What each radio will do is multiply by, $e^{-i(\omega_k t + \Phi_k)}$ where $\omega_k$ is the center frequency for the $k$th radio and $\Phi_k$ is whatever phase the radio is at. What the radios do with this is filter out the resulting sum frequency leaving a time sampled complex signal,

$Z_k(t_n) = \frac{A_k}{2}e^{(\omega - \omega_k)t_n+\phi+\Phi_k}$

One of the things the radio software API does do well is make the time samples, $t_n$, the same for both.

We take a series of data frames. DFT each frame and extract $Z_k(\omega-\omega_k)$. For each frame length, $N$, we compute,

$\Delta\Phi_K = \arg(Z_1(\omega-\omega_1)/Z_2(\omega-\omega_2)) = (\omega_2-\omega_1)t_K+(\Phi_2-\Phi_1)$

the $t_K$ is the center time of the $K$-th data frame. The radios are phase locked if $\Delta\Phi_K = 0$ or close to it.

Plots of $\Delta\Phi$ show that the radios are quite close in frequency but differ enough for them to wander linearly. $\Delta\Phi_K$ is essentially a linear ramp in angle. The API provide a parts per million frequency adjustment. By hand I was able to get the phase nearly constant with a ppm=-0.35 applied to radio 1. It looks quite feasible to make a phase lock loop in software which adjusts the ppm of radio 1 to match radio 2. This will take some time since my program would have to be running as a server to allow the software PLL to lock.

On another front, these pigs leak RF like sieves. I paid extra for the metal case A) because I like the look and feel and B) because of some misguided belief that more would be done for RFI than the plastic case. Did some RF sniffing by waving a small antenna fed with a signal generator. The spurious signal doesn't appear to enter either by the radio inputs or the USB connector. Seems to blow right through the clamshell case. Fortunately I have a small commercially made Faraday cage. With some work this may address this problem. A more serious problem are the spurious broad peaks at ~4.6MHz and other places. A) these peaks are at significantly different frequencies for each radio and B) are unchanged by USB cables of moving the radios about. These peaks seem to be generated within the radio.

 

[Tom.G]

A more serious problem are the spurious broad peaks at ~4.6MHz and other places. A) these peaks are at significantly different frequencies for each radio and B) are unchanged by USB cables of moving the radios about. These peaks seem to be generated within the radio.

Perhaps caused by (a 3rd harmonic of?) this? See datasheet pg.17, section 5.6 Programming the Ancillary Voltage Generator.

My browser has the same problem some others have reported, all the equations are shown as their source code.
[$\Delta\Phi_K = \arg(Z_1(\omega-\omega_1)/Z_2(\omega-\omega_2)) = (\omega_2-\omega_1)t_K+(\Phi_2-\Phi_1)$]
Consequently I have yet to decipher them.

 

[Paul Colby]

Okay, I've rewritten the data collection software to allow the goofy song and dance one must do to slave one of the radios to the clock of the other. This went well. I've set the center frequency of each radio to 4.5MHz and found some stray peaks I believe are internally generated. These are cheap radios so some blemishes are expected. I'm using the coupling network shown in #18 to inject a 1mV signal at 5.2MHz to act as a phase measurement between the radios. I get this result for 10000 1344 long data frames.

what is plotted is (proportional to) power along y and frequency in MHz along x. The 5.2MHz calibration peak is at -77dBm - 45 = -122dBm, the 45 dB is the sum of the attenuation in the feed network. The cross coupling of the spurious peaks at ~4.3-4.4 in the B radio and ~4.7-4.8ish do bleed through into the correlation spectrum which is at -177dBm if I counted my dB's correctly.

The calibration peak allow me to extract the relative phase of the radios to obtain,

which certainly meets my needs for long term averaging. So far I consider this quite successful.