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

[Brent Carlson]

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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