[widar-wg] Simulation tests, re: Zeeman signature investigation

[Brent Carlson]

I forgot to mention that in the test below, *exactly* the same signal 
vectors (i.e. samples) were fed into both types of correlators.  So, the 
noise difference you see is differential and purely from the noise 
effects of the 3-level phase rotator.  The absolute noise level, which 
is too small to see in the linear plot of the line has an RMS ~0.1, and 
peaks up to ~0.27.  So, the artifacts are not greater than the absolute 
noise levels, but definitely greater than the differential noise levels 
outside the region of the line.

--Brent

On 30/06/2011 4:36 PM, Brent Carlson wrote:
> Using the 'C' code I originally developed over 10 years ago, I ran 
> some software correlator simulation tests to determine the distortion 
> of a spectral line, with some width (created by shoving a broad-band 
> noise source thru a narrow passband FIR filter).  I didn't generate 
> two lines at slightly different frequencies, rather I correlated the 
> same data with a 3-level phase rotator, and a floating-point phase 
> rotator, both 4-bit quantization, for the purposes of comparing them.
>
> The frequency shift difference was ~8.7 spectral channels (X=15.6 
> channels, Y=6.9 channels) in the plots, or, if the sub-band width were 
> 128 MHz, equivalent to ~270 kHz, and with the line width ~1 MHz.  
> There was no continuum correlation component.
>
> I ran a simulation with 10e6 samples, and see "spiky" artifacts at 
> about the 10e-3 level, and about 4X the noise level, spread ~20X the 
> fshift frequency around the line.
>
> Here are the plots:
>
>
>
> What I believe is going on is that the harmonics of the 3-level phase 
> rotator are multiplying the strong line, and producing copies of 
> themselves imprinted in the noise (i.e. since there is only one 
> 3-level mixer the harmonics don't correlate, but ghosts of them haunt 
> the data as higher noise), but only in the region of the strong line, 
> and only with a spread about the line of, say ~20 or so times the 
> phase rotator fundamental.
>
> I think this is likely the cause of the Zeeman problems seen on the 
> sky in recent testing.
>
> In looking back at my original simulations in NRC-EVLA memo#001 (e.g. 
> page 95, 96), I compare a strong line with the same two correlators, 
> and show the amplitude difference in percentage terms, but with a 
> fairly strong continuum signature as well, and such a difference 
> didn't particularly show up, although there was likely not enough 
> spectral resolution to see.  In the case where there was a strong line 
> with no continuum source (pages 106 and 107), it doesn't appear I did 
> this kind of comparison, as I was primarily looking for the effect on 
> quantizer-generated harmonics from a strong line.
>
> I believe the spiky noise signature is not a correlation, but rather 
> is imprinted in the noise and integrates down with time, but is still 
> larger than the noise.  Of course, as the fshift frequencies drop, the 
> spread of the spiky stuff decreases, and at some point it could be 
> less than a spectral channel.
>
> This weekend I'm running a 10e7 sample comparative correlation to see 
> if this is the case (i.e. integrates down with time), and will 
> hopefully report on it early next week.
>
> The workaround for these kinds of line observations, is to use the SSB 
> mixer in stage 2 of the Filter FPGA.  It has 10 bits of phase 
> resolution, and so harmonics of the mixer will be at ~-60 dB, and will 
> correlate at that level.  In talking to Dave, it is all ready to go, 
> can run at all required sub-band bandwidths including 128 MHz.  What 
> needs to happen is the 32-bit phase models going to the Baseline 
> Boards need to be set to 0 (for the sub-bands that want to do this), 
> and instead the coefficients go into the SSB mixer phase synthesizers, 
> and some bit gets set in the filter fpga to direct PHASERR to the SSB 
> mixer to set it to zero going to the Baseline Boards (you could set 
> the corr chip phase enable to off, but the RXP phasing logic is still 
> using the models verbatim, so best to generate them with 0-valued 
> coefficients).
>
> As a fallback to the above, I've checked the resources in the Recirc 
> FPGA, and 8 SSB mixers should fit, but with 8-bit arithmetic, and 
> 32-tap Hilbert FIRs, good for -50 dB mixer harmonics, and losing 
> ~1/16th of the sub-band at either end.  The SSB mixer in the filter 
> fpga is definitely the better performing solution.
>
> In both SSB mixer cases, if there is no artificial fshift, and it is 
> just earth-rotation phase that is removed, the harmonics of the mixer 
> will likely be << channel width, and no artifacts at any level should 
> be seen.
>
> In either case, if the SSB mixer is used instead of the 3-level phase 
> rotator, phase is undefined near the sub-band edges, so seamless 
> stitching of sub-bands is not possible.  Presumably for targetted 
> spectral-line observations, this would not have to be done.
>
> Apologies for yet another correlator signal processing skeleton.  Sigh.
>
> --Brent
> -- 
> Brent R. Carlson
> Brent.Carlson at nrc-cnrc.gc.ca
> Tel: 250-497-2346                  |  Fax: (250) 497-2355
> Design Engineer                    |  Ingenieur Concepteur
> National Research Council Canada   |  Conseil national de recherches Canada
> Dominion Radio Astrophysical Obs.  |  Observatoire federal de radioastrophysique
> P.O. Box 248, 717 White Lake Rd    |  C.P. 248, 717 Rue White Lake
> Penticton, BC, Canada V2A 6K3      |  Penticton, (C.-B.), Canada V2A 6K3
> Government of Canada               |  Gouvernement du Canada
>
> "When and where humans are involved, mistakes inevitably happen"
>
>
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-- 
Brent R. Carlson
Brent.Carlson at nrc-cnrc.gc.ca
Tel: 250-497-2346                  |  Fax: (250) 497-2355
Design Engineer                    |  Ingenieur Concepteur
National Research Council Canada   |  Conseil national de recherches Canada
Dominion Radio Astrophysical Obs.  |  Observatoire federal de radioastrophysique
P.O. Box 248, 717 White Lake Rd    |  C.P. 248, 717 Rue White Lake
Penticton, BC, Canada V2A 6K3      |  Penticton, (C.-B.), Canada V2A 6K3
Government of Canada               |  Gouvernement du Canada

"When and where humans are involved, mistakes inevitably happen"

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