SDR Interferometer

[Roland Pouliot]

I've spent the past couple weeks experimenting with gnuradio and how to model a source and a cross correlation interferometer. My goal is to see if is possible to build an interferometer in the gnuradio environment where in theory it should be easier to do things like delay, tracking etc. Obviously, doing the simulations up front before spending any money is far more efficient.

It is apparently not an easy subject to search for either. I found the allbins project, but that seems to be stale.

One of the things I am confused about is the delay function in gnuradio. The block text says that it is a delay based on the sample rate. For the standard interferometer diagram, the delay value is t = B sin (Theta) /c where B is the baseline and theta is the angle between the receiver and the normal line. For something like a nominal baseline of 100m and a 30 degree angle, this comes out to be 167 nS. To create a "delay" of 167 nS would theoretically require a sample rate of at least 6 million.

I put together a simulation anyway, using a gaussian distribution as a proxy for the bessel function for the beamwidth of a dish. I used a slow moving sawtooth wave as my "for" loop, for doing both the gaussian as well as the simulated delay for the dishes. It did end up producing the typical sinc curve. But I'm struggling with the units, since it doesn't seem to add up. There's some part of the flow graph, maybe it's the units, maybe some ratio of frequency to sample rate that I just don't quite get yet. 

I'm also hoping that maybe someone else has already done this and has some tips or pointers. I've attached the flowgraph and a screen shot of the output. The chart recorder colors are red is the "for" loop, green is the gaussian, and blue is the mixer output. I threw some noise in there for good measure, but it doesn't seem to make too much of a difference. Obviously, the model doesn't include the locked LOs for the LNBs or LNAs, but the general idea here is that the input would be from something like two BladeRF devices connected to the LNA/LNBs.

[Marcus Leech]

I don't have time to fully internalize your flow-graph, but you're on the right track.

It helps to think of the geo-delay in terms of phase-difference, and that phase-difference carries-through into downconversion stages.  So a 30deg phase-difference

  in the "sky" will show up as a 30deg phase difference in your IF (or baseband, in this case).   A single-sample delay amounts to a 180deg phase slip, assuming your

  data are strictly-nyquist sampled.  The interferometer code in simple_ra carries the complex signal stream all the way through from the dual sources, and does

  a complex-conjugate multiply prior to integration.  Also, there are delay blocks, and a phase-rotator block (which is just a complex multiply-- complex(cos(ang),sin(ang)),
  with the angle converted into radians.  The phase-rotator in simple_ra can be updated dynamically for fringe-stopping, if so desired.

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[Roland Pouliot]

Thanks. That was very helpful. The output of the multiply conjugate would then have the real component as the cosine correlator and the imaginary as the sine component.

Using a phase shift instead of a delay would then mean that the corresponding phase angle would be something like this:

Phase_shift = (2*pi* B/ lambda) * sin (theta)

Which would mean that there would now be a frequency dependence on phase shift. That means either  limiting the bandwidth so it doesn't matter or splitting up the bandwidth into smaller pieces and doing the correlation per smaller bandwidth.

I remember reading about adding a phase change in the LO for an LNB setup to compensate for adding a time delay. But if a phase shift is being used instead of a time delay, would that LO phase shift no longer be necessary? 

[Marcus D. Leech]

Over the bandwidths we use in amateur radio astronomy, you don't need to
split up the band.




--
Marcus Leech
Principal Investigator
Shirleys Bay Radio Astronomy Consortium
http://www.sbrac.org