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Ka Receiver Performance Characterization, Fall 2005

Brian Mason, Larry Morgan

Since spring a new LO system has been installed, providing all four Beam/Polarization's, and new mmconverter cables have been installed to mitigate previously seen spectral baselines.

Datasets

• TKA_06
  • total power is nice and stable over this whole run.
  • 90 sec each scan (3 min per nods plus overheads)
  • s.77 - 137 -- blank sky NODs, 31.4 GHz. this is the data where the overall baselines look reasonable to me. The actual data goes to scan 237.
  • s.73/74, 75/76 -- NODs on 3c147=1.4 Jy x 1.5 K/Jy = 2.1 K. Same tuning (31.4 GHz...) as s.77 - 137.
  • we balanced at the beginning of the run, but not after. A low-order baseline ripple develops over the course of the night; my first thought was that perhaps this was due to spectrometer samplers saturating as the source tracked lower in the sky. In retrospect, however, the total elevation change over the whole night is only about 20 degrees (72 down to 52 deg) and the total power level won't have changed all that much... so I don't know what's going on there.
• TKA_07
  • balancing fairly regularly
  • 120 sec each scan (4 min per nod)
  • s.35-172 -- blank sky nods, same tuning as TKA_06 (31.14 GHz). range of elevations is about 80 deg at start to about 45 deg at end.
  • s.155 - 172 -- cold load. not sure if this was done with astrid (i think it was) as opposed to scan coordinator. I vaguely recall it was astrid but SDFITS for some reason still didn't like the data so may need to be reduced with GLISH.
• TKA_01
  • 32 GHz data on blank sky, s.66-147
  • 60 sec nods
• TKA_02
  • 28 GHz data on blank sky, 2.26-166
  • 60 sec nods
• TKA_03
  • 38 GHz data on blank sky, s.21 - 140 (perhaps all the way up to 183 but for some reason I was omitting the last 43)
  • 60 sec nods

Data Processing

(BSM)

Data were collected in a beamswithed NOD and combined, for a single spectrometer port, as:

    1   (SA-RA)-(SB-RB)
F= ---  --------------------
    2   (SA-RA)_on - (SA-RA)

In principle, you should be able to also include the Cal On phases in the numerator of the above expression. When we do this the spectral noise level hardly goes down at all, and this is a big worry (possibly a clue). Roger suggests 10 Hz 4-phase switching is faster than typical for spectrometer and we might want to try slower switching Rich thinks the spectrometer should not have a problem with this switch rate. The autocorrelator chips dump data every 1.3mSec regardless. - RDN.

All our data was collected in the 800 MHz mode of the spectrometer. The theoretical noise level for a single phase of a single scan is as follows:

               K1 Tsys
sigma = ------------------
         sqrt(K2 t dNu/Nchan)

For our analysis we also bin the data down by a factor of 16 for a low-resolution (16x390 kHz=6.24 MHz) spectrum appropriate for broad-line measurements. In this case the noise is expected to be sqrt(8) lower, accounting for the fact that in effect the resolution of the Hanning-smoothed spectrum is about two 390-kHz bins. This gives 3.1 mK or 2.1 mJy for a single NOD with 60 seconds spent on each scan. The recommended procedure will always be to use BOTH polarizations of a given feed and spectral window and average them after calibration; this procedure should yield, in one 2-minute NOD, a 6.24-MH-resolution RMS of 1.48 mJy.

One of the main findings is that the RMS noise level per scan (ie the RMS across the spectrum) is dramatically variable from scan to scan. The origin of this variation is unknown. In adding scans together, therefore, each scan was weighted by 1/(its RMS)^2. The cumulative spectrum RMS therefore doesn't go down strictly as sqrt(Nscans) but how it should go, given the weights used, is easily computed.

Caution: The Tsys is substantially higher at the lower portion of the Ka band.

Results

Periodograms

Baseline ripple with a period of 10 to 30 MHz, and an amplitude up to roughly 0.5% of Tsys, is sporadically seen in the data.The power spectrum of the frequency spectrum was computed for several tunings and is shown below. These data are double-beamswitched NODs. Note that the y-axis is a variance in units of cals^2 and the cal is quite different from band to band (in particular it is very weak at the top of the receiver band hence the high variance in the 38 GHz plot). Also note, I think the individual spectra were not weighted by spectrum RMS when the total is accumulated, in this analysis (unlike others on this page).

• 27 GHz periodogram (KA_02 s.26-166):
  

• 32 GHz periodogram (KA_01 s.66-147:
  

• 38 GHz periodogram (KA_03 s.1-140 i think):
  

Generally structure is seen in the range 12.5 to 50 MHz. At 32 GHz the 25 MHz structure dominates, though at 27 GHz for example there is comparable power in a wide range of harmonics. The amplitude of the observed ripple is on the order of 1/1000th of a cal diode generally speaking.

Variation of the Scan RMS

The amount of baseline ripple is seen to vary dramatically from scan to scan. Here is a "waterfall plot" showing a series of individual NOD observations:

• 27 GHz waterfall. Vertical offset is arbitrary, but individual nods are in units of the Cal diode:
  

• 32 GHz waterfall:
  

• 38 ghz waterfall (note- the cal is very weak at the top of the receiver band so I don't know how much to read into the increasing ripple on the right of these plots):
  

Here are plots showing, for TKA_06 and TKA_07 data, how the cumulative RMS averages down as scans are added. The upper left panel is the cumulative RMS; the upper right is the expected cumulative RMS given the individual scan weights; the lower left is the ratio of these; and the lower right is the individual scan RMS. (NB, these are all in mJy for the 31.4 GHz data, and the data are not binned down by 16x). The white line is the raw channel RMS and the purple line is after binning down 16x for 6.24 MHz channels. Again, note that the expected RMS is NOT the theoretically expected RMS, but the RMS that's expected in the cumulative spectrum given the RMS's in the individual spectral comprising it, and the fact that they go in with weights of 1/RMS^2.

• RMS vs scan for tka06:
  

• tka07:
  

The variations in scan RMS do not correlate well with total power variations. For TKA07, the end of the night does appear to have clouded up, and increase in Tsys and the baseline ripple are both seen; however the Tsys only increases by a few Kelvin, and there are instances in TKA06 where the RMS is much greater than other scans even though Tsys was very stable over the whole run. Weather may contribute but is not the sole cause of what we see.

• scan rms (mJy) vs tsys (~K) for TKA06:
  

• scan rms vs tsys, tka07:
  

Blank-Sky RMS at 31.4 GHz

In 7 hours wall-clock time, integrating on blank sky at a single tuning (TKA_06 and TKA_07) we obtain an RMS across the spectrum of 0.45 mJy in 6.24 MHz bins, using only data from a single spectrometer port. Combining both polarizations for that feed and spectral window will yield about 0.32 mJy RMS -- our reference point for comparison. Data were calibrated by an approximate Scal derived with reference to 3C147. No correction for tau_atm or telescope gain curves has been made but this should be less than a 10% effect over the given range of elevations.

Combining data from the four ports (L1, L2, R1, R2) at that spectral window, we obtain an RMS of 0.25 mJy.

• L poln, Feed 1, only -- TKA06 + TKA07 added together(7h total wall clock). X is GHz and Y is mJy. White is the raw (well, calibrated, but not binned in freq) 2048-channel spectrum; red is binned 16x for 6.24 MHz resolution:
  

• all feeds + polns, TKA06 +07 (7h total wall clock). X=GHz, y=mJy:
  

This can be compared to the theoretical, thermal-noise-limited performance, as follows. For a single 2-minute NOD, combining both polarizations from a single feed in a single spectral window, the 6.24-MHz RMS is expected to be 1.48 mJy as described above. To achieve 0.32 mJy RMS then requires about 22 2-minute NODs, or an hour of wall-clock time including slewing and calibration overheads. Therefore, at what is probably the best portion of the receiver band, a given experiment requires 7x longer than the radiometer equation would predict (ie we are on average 2.65 x above the theoretical noise level). Since the unpredictable variation in noise level is a dominant effect in the data, however, sometimes you might do better than this, and sometimes you might do much worse. The earlier conclusion that the observed baseline ripple continues to diminish with integration time is supported. This is puzzling in light of the fact that Spring 2005 data failed to do so beyond an hour; this could be because the new IF cables mitigated the problem somewhat, or because our new 7 hour dataset was fortuitously benign.

Data Correlations

In addition I used the TKA_06 (calibrated, 16x rebinned) data to search for noise correlations between the 4 spectrometer input ports. If everything is working properly these will be statistically independent spectra: that's the reason we bother to collect data from multiple feeds and polarizations. A significant correlation is found between L1 and R2, and L2 and R1. No significant correlation is found between other channels. This is also how inputs to the differencing assemblies (aka "Radiometers" ... the paired hybrids in series) are paired, and could be a clue that the origin of the baseline ripple comes from this part of the receiver (such as the phase/beam switches). Or it could be that these channels have low-level correlated gain fluctuations (or something else) which is introduced, and interact with something downstream to cause the ripple.

Here are the correlations (I have plotted the individual 6 MHz-width spectrum values for L0 vs those for R1, etc):

• spectrum correlations, TKA06:
  

Note that the "correlations" are correlations between calibrated spectra. Consider L1 and R2. Because the data are differentially calibrated, and we are firing the "L" cal only, and the beamswitch operates between opposite polarizations, the calibrated L1 spectrum is (L1-R2)/LCAL. R2 is (R2-L1)/(-LCAL) because the L cal is only seen in the REF phase. The raw differenced spectra (L1-R2 and R2-L1) in counts therefore are anticorrelated . Due to the receiver architecture a number of sources of such correlations can be imagined. But the sign of this particular correlation suggests something coming from before the first hybrid (such as standing waves between feed1 and feed2 bouncing off the subreflector). If this analysis is correct, the effect we see could be a problem for ZSPEC ... correlation may not "make it go away". It is also possible that a nonlinearity downstream of the second hybrid could cause what we see-- perhaps a slight gain expansion in one OD, and a slight gain compression in the other, modulating a low-level ripple in the total power band or something?

I double-checked the above convoluted reasoning by cross-correlating the raw spectra from L1 and R2 for scans 37/38 of TKA_07. Here I just formed (sa-ra)-(sb-rb) -- no cal normalization -- for each sampler and cross correlated them. The raw counts so formed indeed are anti-correlated, and at higher significance than the accumulated rebinned spectrum (15 sigma). The linear correlation coefficient is r= -0.33 +/- 0.02.

In practice observers wanting lots of bandwidth should probably would route only one Beam (B1 in cfg tool)... both pols will get routed, and this avoids the correlated combinations thus maximizing the useful data the observer gets. However this effect really needs to be understood, for presently accepted proposals and the near-future wideband spectrometer.

LO Harmonics and RFI(???)

An LO1A x 2 Harmonic at (14 + 2/3) x 2 = 29 + 1/3 GHz persists in the data. It is very narrow but quite strong. (Plot attached below)

There is also a very strong signal at 27.3163 GHz or so. I don't recall seeing this before and it is really strong. We need to check again a few times and see if this might be RFI, it seems unrelated to our LO frequencies. (Plot attached below)

Is it coincidental that the baselines appear to be worst and most variable in the low sky frequency band, where both of these signals are? One experiment worth doing would be to set up one spectral window on each of these, and one spectral window on a blank region of the spectrum and see if variations correlate over time. With sleight of hand you can even manually defeat the config tool, and set one of the MMCONVERTERs to its straight through path and be looking at one chunk of spectrum centered on 38 GHz (sky). An argument against this being the problem is the L1/R2, L2/R1 correlation.

Another experiment we might do: do nods with the LO1 kept fixed. Note: LO1A fits files in both TKA_06 and TKA_07 indicate the LO1 was in topocentric mode, and the synthesizer frequency was constant throughout the observations. - RDN

Larry: did you say these spikes once saturated the lower band or did we figure that was another problem? Also what are the units in the plot?

• 04_11_05_27GHz_spike.ps: 27 ghz spike

• 04_11_05_29GHz_spike.ps: 29 ghz spike (LO1A x 2)

-- BrianMason - 14 Nov 2005

Attachment:	Action:	Size:	Date:	Who:	Comment:
ka27allnodLLpspec.png	action	13695	14 Nov 2005 - 20:19	BrianMason	27 GHz periodogram
ka32allNodLLpspec.png	action	14515	14 Nov 2005 - 20:19	BrianMason	32 GHz periodogram
ka38allnodLLpspec.png	action	13493	14 Nov 2005 - 20:20	BrianMason	38 GHz periodogram
tka02-27ghz-waterfall.png	action	36269	14 Nov 2005 - 20:55	BrianMason	27 GHz waterfall plot
tka01-32ghz-waterfall.png	action	24333	14 Nov 2005 - 20:56	BrianMason	32 GHz waterfall
tka03-38ghz-waterfall.png	action	29488	14 Nov 2005 - 20:57	BrianMason	38 ghz waterfall
TKA_06LL-fd0-IF0-s77-s137-Rmss.png	action	9692	14 Nov 2005 - 20:57	BrianMason	RMS vs scan for tka06
TKA_07LL-fd0-IF0-s35-s152-Rmss.png	action	10533	14 Nov 2005 - 20:58	BrianMason	tka07
TKA_06LL-fd0-IF0-s77-s137-TpRms.png	action	4056	14 Nov 2005 - 20:59	BrianMason	scan rms (mJy) vs tsys (~K) for TKA06
TKA_07LL-fd0-IF0-s35-s152-TpRms.png	action	4651	14 Nov 2005 - 21:00	BrianMason	scan rms vs tsys, tka07
TKA_06LLRR-fd99-IF0-s77-s137-CrossCorrel.png	action	14986	14 Nov 2005 - 21:02	BrianMason	spectrum correlations, TKA06
fastCalibOne.pro	action	4931	14 Nov 2005 - 21:24	BrianMason	GBTIDL calibration routine
TKA06TKA07LL-fd99-IF0-s35-s152-smoSpec.png	action	8385	14 Nov 2005 - 22:44	BrianMason	L poln, feed 1 only -- TKA06 + TKA07 data combined
TKA06TKA07LLRR-fd99-IF0-s35-s152-smoSpec.png	action	8071	14 Nov 2005 - 22:44	BrianMason	all feeds + polns, TKA06 +07 (7h total wall clock)
04_11_05_27GHz_spike.ps	action	38605	15 Nov 2005 - 04:42	BrianMason	27 ghz spike
04_11_05_29GHz_spike.ps	action	39135	15 Nov 2005 - 04:43	BrianMason	29 ghz spike (LO1A x 2)