Preliminary summary of ACA Testing Campaign(2014 September)
ALMA Technical Note Number: 14
Status: DRAFT
Prepared by:

Organization:

Seiji Kameno

JAO/NAOJ

Takeshi Kamazaki

JAO/NAOJ

Date:
17 October 2014

Preliminary summary of ACA Testing Campaign (2014 September)
Kamazaki, T. and Kameno, S.
(2014/10/17)

1.

Overview

ACA Testing Campaign was done between September 23th and 30th for the verification of ACA
Correlator software functions. Its main item was to verify on-line 4-bit linearity correction, which
was improved on ALMA 2014.02. Another item was preliminary study for coming 3-bit linearity
correction. This focused on the relation between input-power level to 3-bit digitizer and digitizer
level histogram. Our data analysis is still on-going, but in our preliminary results, the revised 4-bit
linearity correction works as designed. In the study of 3-bit digitizer, we have found that the relation
looks to vary according to input-power level.

2.

On-line 4-bit linearity correction (CSV-3133)

On-line 4-bit linearity correction is revised on ALMA 2014.02 so that the update interval of its
correction factors is now integration/channel-average duration for full-resolution/channel-averagedata. This change is realized by software update and nothing is changed in correlator hardware. In
the previous version, the interval was correlator calibration, and there could remain non-linearity due
to the 4-bit re-quantizer if signal-level varied between the calibrations (e.g. PRTSIR-656).
We verified the revised correction according to the following steps:
Step1. Algorithm verification using ACA Correlator simulator (CSV-3134)
We verified the algorithm of the 4-bit linearity correction using computational simulation.
Step2. On-line correction verification (CSV-3135 and CSV-3136)
On-line 4-bit linearity correction was tested by comparing its products with its off-line correction
products, whose correction algorithm was verified in Step 1.
Step3. Linearity check between input and output power of 4-bit re-quantization (CSV-3138)
We also tested the linearity between input and output power of 4-bit re-quantization under theon-line 4-bit linearity correction.
2.1.

Algorithm verification using ACA Correlator simulator (CSV-3134)

First, we verified the correction algorithm beforehand using ACA Correlator simulator, which could
calculate bit-accurate results of ACA Correlator processing. Known 3-bit data were input to thesimulator and re-quantized by 4-bit with two different input-levels employing an optimized
scaling-factor every channel and a constant scaling-factor over channels. Then, 4-bit linearity
correction was applied to output spectra and compared with original inputs. Figure 1 shows thecomparison results where original and 4-bit quantized spectra agree well with each other after the
4-bit linearity correction.

1

Figgure 1 Compputational sim
mulation of thet 4-bit lineearity correcttion(Uppeer) auto-correelation spectraa with 4-bit re-quantizatioon (red and greenglines) aand original spectras(blackk line). Red annd green liness correspond tot 4-bit re-quaantization withh optimized sscaling-factorss and aconstaant scaling facctor, respectivvely. Their ratiios to originall spectra are shownsby pinkk (= red / blacck) lineand light green (== green / blaack) line. (Loower) auto-coorrelation spectra correctedd by 4-bit linnearity
correcction (red andd green lines) anda original spectras(black line). These threet
spectra aare well overlapped,
indicaating that theyy are well consistent. This canc be also confirmed by thheir ratios, whhich are pink (= red /black)) line and lighht green (= greeen / black) linne.
2.2.

On-line corrrection veriification (CSSV-3135 and CSV-3136)

oand off-line corrrection
Next,, we tested on-line 4-bitt linearity coorrection by comparing on-line
produucts, because the off-line correction was
w already coonfirmed in StepS
1. In thee verificationn tests,
internnal signal-level was optim
mized at 0 dB correspondin
ng to +2.4 dBm in an absolute value annd then,the leevel was increeased from -77 dB to +3 dB
B by changing
g attenuator settingswithinn a subscan. DuringDit, autto-correlationn spectra tow
ward the southh pole were continuouslyy taken with/w
without the on-lineocorrecction. Then, wew applied thhe off-line corrrection to thhe spectra witthout the on-lline correction
n. Thecompparison resultts between onn-line and offf-line correcctions are shoown in Figurre 2 and Fig
gure 3.
Goodd agreement betweenbthemm can be seen in these plotss.

2

Figure 2 Channel-averCrage amplitu
ude ratios of on-line to offf-line correccted spectra
Each symbol indiccate channel--average ampplitude ratios of on-line annd off-line ccorrected specctra ofBB1-X
XX of each antenna.
aCorrrelator calibraation was carrried out at 0 dB,d corresponnding to +2.4
4 dBm.
Their differences between on-linne and off-linee corrected speectra are less thant±1%.

FFigure3 On-line and off--line correcteed spectra annd their ratioos(Uppeer) Auto-correelation spectrra with on-linne correction at CM01-BB
B1-XX. Differrent colors inndicatedifferent input signnal-levels (-7 dB
d to +3 dB by 1 dB step). (Middle) Autoo-correlation spectra with off-line
ocorrecction. The coolors are same as those off the upper plot.
p(Lower) The ratio off on-line to off-line
ocorrecction spectra. They are close to 1.0 and thhe differencess are roughly within
w±1%.
2.3.

Linearity checkc
betweeen input andd output pow
wer of 4-bit ree-quantizatioon (CSV-3138)

3
digitizerr level histo
ogram was comparedcwitth auto-correelation
Finallly, simple variance of 3-bit
ampliitude, to whicch no 3-bit liinearity correection was appplied. They correspond tto input and output
opoweer of the 4-bit re-quantizatiion, respectivvely. Figure 4 shows good linearity betw
ween them.
3Figuure 4 Auto-ccorrelation am
mplitude vs.. 3-bit digitizzer output poower
Auto--correlation am
mplitudes of channelcaverage data withoout 3-bit linearrity correctionn are plotted against
a3-bit digitizer
doutpuut power-levels, which are simple variance of digitizerr level histogrrams.

3.

I
Input-poweer level estiimated fromm digitizerr level histoogram (CSVV-2311)

We allso studied thhe relation bettween input-ppower level too 3-bit digitizzer and digitizzer level histogramof 3-bbit digitized signals.
sACA
A Correlator compensates
cfor the non-llinearity of 33-bit digitizerr using
the relation,
rwhiich is derivved assumingg ideal 3-biit digitizer. However, rrecent issuess (e.g.
PRTS
SIR-656 and Tsys differeences between BLC-TDM
M and ACA by several ppercent reporrted in
TP/A
ACA non-lineaarity Tiger Teeam meeting)) suggest that there seem too be non-negligible errors in theassum
mption of the correction. For
F its investiggation, we measured
mdigittizer level hisstograms withh ACA
Correelator and basseband poweer levels withh baseband poower detectorrs by varyingg input-powerr levelto 3-bbit digitizer inn the range ofo -7 dB to +3+ dB by 1 dB
B step. Fromm our quick annalysis of ob
btaineddata, we got the foollowing preliiminary resullts.
1. Linnear relation can be rouughly seen between
bthe level histogrram and thee baseband power.
pH
However,takking a close looklat them,, there looks to be departuures from thee linear regreession.
O possiblee explanation is that thresshold voltagees of the 3-biit digitizers wOnewere not unifformlysspaced
or varriable as a fuunction of inpput power levvel. Or the proobability dennsity distributtion oft input anallog signal didd not follow thethet normal distribution.

4

Figure 2 of "ADCLevel20140927.pdf" in CSV-2311
Comparison of the total power measurements with baseband detector (horizontal axis) and digitizer level
histogram (vertical axis). Linear regression was applied except the highest power point to determine theslope and the intercept.

Figure 5 of "ADCLevel20140927.pdf" in CSV-2311
Estimated threshold voltages of 3-bit quantization in the digitizer as a function of input power level. If thethresholds were constant, uniformly spaced, and the probability density distribution of the input voltage
followed the normal distribution (ideal case), the estimated thresholds would lie on the integer values
regardless the power level. Departures from the ideal case are shown in percentile.
52. The accuracy of the threshold voltages is good for 2-bit (4-level) but insufficient for 3-bit (8-level)
quantization.

Figure 7 of "ADCLevel20140927.pdf" in CSV-2311
Estimated threshold voltages for 2-bit quantization. The same level-histogram data with Figure 5 wereused to produce 2-bit quantized samples by combining pairs of adjacent levels. Since current BLC-TDM
employs 2-bit quantization, its linearity will be less affected.
3. The error in threshold voltages can cause significant non-linearity of power measurements with
the ACA Correlator which uses 3-bit quantized signals.

Figure 2 of "ADCLevel20140928.pdf" in CSV-2311
Systematic errors of digital power measurements as a function of input analog power level. The optimal
input level stands for 0 dB. Each estimated threshold voltage is used to evaluate the systematic errors.
6

We need to investigate stability of the threshold-voltage behavior and consider its correction way forthe further improvement of 3-bit quantization correction.

4.

Summary and additional work plans

4.1.

On-line 4-bit linearity correction and additional tests for it

From our quick analysis so far, output spectra with the revised on-line 4-bit linearity correction are
consistent with those from the off-line correction, which is already verified using computational
simulation. This consistency is confirmed in varying signal-level within a subscan. Thus, we thinkthat the revised on-line 4-bit linearity correction works as designed, although they are still
preliminary results from a part of obtained data. We are now looking at remaining data in order tomake sure that the 4-bit correction widely works. For the purpose, enough data were already taken,
and further data are not required.
4.2.

3-bit digitizer issue

About the issue of variable threshold voltages of 3-bit digitizer, it is necessary to repeat themeasurement done in CSV-2311 in order to pursue its behaviors and establish its correction method.
In addition, it may be better to measure in other receiver bands than band 3, although we think theissue is specific to each digitizer. We plan to do these additional measurements in Kameno-san's
regular OSF shift. We are also considering similar measurements using noise source and power
meter, which are calibrated well.

Related tickets- CSV-3133 ACACORR: On-line 4-bit linearity correction of ACA Correlator- CSV-3134 ACACORR: Simulation of the 4-bit linearity correction- CSV-3135 ACACORR: Comparison with/without the new 4-bit linearity correction- CSV-3136 ACACORR: Variable signal-levels in a subscan- CSV-3138 ACACORR: Linearity measurement between digitizer level histogram andauto-correlation amplitude 3-bit correction task
- CSV-2311 Measure non-linearity between signal levels input to 3-bit digitizer and digitizer level
histogram taken with the ACA Correlator

References- Kameno, S., Kamazaki, T., "Stability and Uniformity of the Digitizer Threshold Voltages(CSV-2311)”, “ADCLevel20140927.pdf” in CSV-2311- Kameno, S., Kamazaki, T., “Non-uniformity of the Digitizer Threshold Voltages and Impact toAmplitude Linearity (CSV-2311)”, “ADCLevel20140928.pdf” in CSV-2311- Kameno, S., Kamazaki, T., “Daily Stability of the Threshold Voltages of the Digitizers

7

(CSV-2311), “ADCLevel20141002.pdf” in CSV-2311- Kameno, S., Kamazaki, T., “Linearity of power measurements in the ACA correlator (CSV-3638),“ADCLevel20141016.pdf” in CSV-3638

8