Phased-Array Feed Instrumentation and Processing for Astronomical Detection, Interference

200 Pages·2017·5.3 MB·English

Brigham Young University
BYU ScholarsArchive
All Theses and Dissertations
2017-12-01
Phased-Array Feed Instrumentation and Processing
for Astronomical Detection, Interference
Mitigation, and Transient Parameter Estimation
Richard Allen Black
Brigham Young University
Follow this and additional works at:https://scholarsarchive.byu.edu/etd
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BYU ScholarsArchive Citation
Black, Richard Allen, "Phased-Array Feed Instrumentation and Processing for Astronomical Detection, Interference Mitigation, and
Transient Parameter Estimation" (2017).All Theses and Dissertations. 6627.
https://scholarsarchive.byu.edu/etd/6627
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PhasedArrayFeedInstrumentationandProcessingforAstronomicalDetection,
InterferenceMitigation,andTransientParameterEstimation
RichardAllenBlack
Adissertationsubmittedtothefacultyof
BrighamYoungUniversity
inpartialfulfillmentoftherequirementsforthedegreeof
DoctorofPhilosophy
BrianD.Jeffs,Chair
KarlF.Warnick
NealK.Bangerter
MichaelRice
DavidG.Long
DepartmentofElectricalandComputerEngineering
BrighamYoungUniversity
Copyright(cid:13)c 2017RichardAllenBlack
AllRightsReserved
ABSTRACT
PhasedArrayFeedInstrumentationandProcessingforAstronomicalDetection,
InterferenceMitigation,andTransientParameterEstimation
RichardAllenBlack
DepartmentofElectricalandComputerEngineering,BYU
DoctorofPhilosophy
Radio astronomy, the survey and study of naturally occurring astronomical radio signals,
is a challenging field in terms of engineering requirements. The typical astronomical signal of in-
terestisincrediblyfaint,resultinginverylowsignal-to-noiseratios(SNRs)ontheorderof-30dB
or lower. To detect such signals, one must have an uncommonly low and stable receiver noise
temperature, high gain through large aperture reflectors, and state-of-the-art signal processing al-
gorithms. One must also be able to mitigate the effects of interference, the presence of which,
even if extremely weak, can completely mask the faint astronomical signals of interest. To this
end, this work presents the development of and results from a new broadband phased array feed
(PAF) named the Focal L-Band Array for the Green Bank Telescope (FLAG). This instrument is
able to form multiple simultaneous beams to survey a large patch of sky instantaneously, and has
a minimum system noise temperature (T ) of 16.83 K. This PAF also has the potential to use
sys
spatial filtering techniques to place pattern nulls in the direction of interfering signals through the
use of an orthogonal projection. This work will also present an improved method for computing
an orthogonal projection operator, which is able to place a spatially broad null in the direction of
a moving RFI source. A formal derivation of some detection and estimation theory properties for
astronomical radio transients is also presented, which formalization is lacking within the astro-
nomical community. This includes maximum-likelihood detectors and estimators and a Crame´r
Raobound(CRB)analysisofastronomicaltransientparameters.
Keywords: arraysystems,radioastronomy,radiofrequencyinterference,pulsars,fastradiobursts,
phasedarrayfeed
ACKNOWLEDGMENTS
A work of this magnitude does not come about without the contributions and support of
several people. In this case, this dissertation represents the culmination of nearly 30 years of
concerted effort by loving parents, dedicated teachers, encouraging colleagues, and a supportive
spouse. Withouttheirsacrificesonmybehalf,thisworkwouldnotexist.
I would first like to acknowledge my graduate advisor Dr. Brian Jeffs, who challenged me
to stretch beyond my perceived limits and taught me how to critically analyze my own work. He
was a consistent champion for my ideas and research, even when receiving disappointing news
about multiple rejected manuscripts. His interest in my life beyond graduate school helped me
feellikeafellowcolleague,whichgavemetheconfidencetoproposenewandcrazyideaswithout
fear of rebuke. The same holds true for the other faculty members on my committee, namely Karl
Warnick,NealBangerter,MichaelRice,andDavidLong.
My parents Guy and Maria deserve more recognition than they currently receive for their
many sacrifices in making me who I am today. Once in elementary school, my teacher informed
them that I “would never pull [my] weight in math.” In response, my parents challenged me every
night, drilling me until the math became second-nature. Without their diligence, I would not have
pursued engineering as my career path or even considered a doctorate degree. Furthermore, their
frequentwillingnesstobabysitmychildrengavemewithprecioustimetowrite.
Lastly,wordscannotbegintodescribehowmuchmywonderfulwifeKarencontributedto
the completion of this work. For the last five years, she has supported me emotionally, intellectu-
ally,andfinanciallysimplybecauseshelovedmeandwantedtosupportme. Duringthistime,she
gavebirthtoourtwochildrenChloeandSamandstayedhomewiththemwhileremotelyworking
a full-time job. At times, I felt like I was putting an undue burden on her, a feeling which she
quicklydispelledwithoutcomplaint. Mylifehasbeeninfinitelybettersinceshecameintomylife.
I love her, and I look forward to the day in which I can, in some small way, repay her for all that
shehasdoneforme.
TABLEOFCONTENTS
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Chapter1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 ProblemStatements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 RelatedWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 PhasedArrayFeeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 TransientDetectionandEstimation . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 InterferenceMitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 DissertationContributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 FocalL-BandArrayfortheGreenBankTelescopeDevelopment . . . . . . 7
1.3.2 AstronomicalTransientDetectionandEstimationTheory . . . . . . . . . . 8
1.3.3 RadioFrequencyMitigationAlgorithms . . . . . . . . . . . . . . . . . . . 9
1.4 DissertationOutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Chapter2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 PhasedArrayFeedSignalModel . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 BeamformerWeights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 MaximumGainBeamformer . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 MaximumSNRBeamformer . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.3 LinearConstraintMinimumVarianceBeamformer . . . . . . . . . . . . . 16
2.4 ArrayFeedCalibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 FundamentalsofAstronomicalTransients . . . . . . . . . . . . . . . . . . . . . . 19
2.6 DetectionofAstronomicalTransients . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 EstimationofAstronomicalTransientParameters . . . . . . . . . . . . . . . . . . 22
2.8 Radio-FrequencyInterferenceMitigationMethods . . . . . . . . . . . . . . . . . . 22
2.8.1 OrthogonalProjections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter3 MaximumLikelihoodDetectionandEstimationforPhasedArrayFeeds . 25
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 MaximumLikelihoodFramework . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.1 UsefulTheorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 ArraySteeringVectorEstimator . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 TransientDetectioninElementSpace . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4.1 SpatiallyWhiteNoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.2 CalibratedArray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.3 UncalibratedArray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 TransientDetectioninBeamSpace . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5.1 SpatiallyWhiteNoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.2 CalibratedArray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
iv
3.5.3 UncalibratedArray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Chapter4 Crame´rRaoBoundforAstronomicalTransientParameters . . . . . . . . 39
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 SignalModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2.1 Single-PixelModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.2 ArrayAntennaModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.3 PulseShapeModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3 FrameworkforCrame´rRaoBound . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3.1 Single-PixelAntenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3.2 ArrayAntenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.5.1 WindowSize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.5.2 PulseStartTime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.5.3 DispersionMeasure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.5.4 Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.5.5 ContiguousBandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.5.6 FractionalNon-ContiguousBandwidth . . . . . . . . . . . . . . . . . . . . 53
4.5.7 FrequencyResolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5.8 PulseWidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5.9 TemporalResolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.5.10 Signal-to-NoiseRatio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5.11 AngleofArrival . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Chapter5 FocalL-BandArrayfortheGreenBankTelescopeBackEnd . . . . . . . 66
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2 OperationalModes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2.1 Coarse-ChannelMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2.2 Fine-ChannelMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3 HPCSpecifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3.1 GraphicsCards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3.2 NetworkCards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.4 HASHPIPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.5 GPULibraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.5.1 xGPU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.6 July2016CommissioningResults . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.7 May2017CommissioningResults . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.7.1 OutdoorTestFacilityExperiments . . . . . . . . . . . . . . . . . . . . . . 81
5.7.2 On-Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.8 August2017CommissioningResults . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.9 ConclusionsandFutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
v
Chapter6 Deep Broad Null Formation via Orthogonal Projection and Subspace
Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 SignalModelandAlgorithmDevelopment . . . . . . . . . . . . . . . . . . . . . . 106
6.3 Projection-BasedRFIMitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.3.2 AFrameworkforExistingRFIProjectionAlgorithms . . . . . . . . . . . . 110
6.3.3 ProposedAlgorithmforBroadNullFormation . . . . . . . . . . . . . . . 114
6.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.1 SimulationDetails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.2 PerformanceMetrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4.4 CancelingMultipleRFI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4.5 STILengthConsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4.6 LTILengthConsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Chapter7 ConclusionsandFutureWork . . . . . . . . . . . . . . . . . . . . . . . . . 133
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
AppendixA DerivationsofJacobians . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
A.1 JacobianforSingleAntennaModel . . . . . . . . . . . . . . . . . . . . . . . . . . 146
A.2 JacobianforArrayAntennaModel . . . . . . . . . . . . . . . . . . . . . . . . . . 147
AppendixB FLAGDevelopmentDetails . . . . . . . . . . . . . . . . . . . . . . . . . . 151
B.1 xGPUDetails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
B.2 HASHPIPEPlugins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
B.3 HASHPIPEThreads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
B.3.1 flag net thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
B.3.2 flag transpose thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
B.3.3 flag pfb transpose thread . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
B.3.4 flag frb transpose thread . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
B.3.5 flag bx transpose thread . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
B.3.6 flag pfb thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
B.3.7 flag correlator thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
B.3.8 flag frb correlator thread . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
B.3.9 flag pfb correlator thread . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
B.3.10 flag beamform thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
B.3.11 flag bx thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
B.3.12 flag bfx thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
B.3.13 flag corsave thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
B.3.14 flag frb corsave thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
B.3.15 flag pfbsave thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
vi
B.3.16 flag pfb corsave thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
B.3.17 flag beamsave thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
B.3.18 flag bx save thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
B.3.19 flag bfx save thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
B.4 Dealer/PlayerImplementationDetails . . . . . . . . . . . . . . . . . . . . . . . . 162
B.5 ScanOverlord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
B.6 MATLABPost-ProcessingCodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
B.6.1 kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
B.6.2 sensitivity maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
B.6.3 patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
B.6.4 tsys plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
B.6.5 word lock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
B.6.6 misc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
AppendixC HASHPIPEHelloWorld . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
C.1 hw databuf.h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
C.2 hw databuf.c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
C.3 hw thread1.c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
C.4 hw thread2.c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
C.5 Makefile.am . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
C.6 configure.ac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
C.7 hashpipe.m4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
vii
LISTOFTABLES
4.1 MajorEffectsofParametersonCRBforDM . . . . . . . . . . . . . . . . . . . . . . 64
5.1 HPCSpecifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 PCI-ESlotPopulation(out-of-date) . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3 GeForceGTX780TiSpecifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.4 GeForceGTX980TiSpecifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.1 PerformanceonGBTwithoutAuxiliary . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.2 PerformanceonGBTwithAuxiliary . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.3 DataRatesforVariousApproaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
B.1 Real-TimeBeamformerMetadata . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
B.2 FLAGBackEndOperationalModeTable . . . . . . . . . . . . . . . . . . . . . . . . 164
viii
LISTOFFIGURES
1.1 Artisticrenditionofapulsar,depictingmagneticfieldlinesandradiationpattern. . . . 2
2.1 PAFsarecalibratedbysteeringthedishacrossastrongpointsourceandestimatingthe
correspondingsteeringvectorvectorsforeachpointing. Thereddotsindicatean“on”
pointing,andthebluedotsindicatean“off”pointing. . . . . . . . . . . . . . . . . . . 18
4.1 Effect of total window size on CRB. The vertical line indicates when the pulse was
containedinthewindow(i.e.,t +T). . . . . . . . . . . . . . . . . . . . . . . . . . . 50
0
4.2 Effect of pulse start time t on CRB. The region within the vertical lines is where the
0
processingwindowcontainsatleast90%ofthepulsepower. . . . . . . . . . . . . . . 51
4.3 EffectofDispersionMeasureonCRB. . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 EffectofobservationfrequencyonCRB. . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.5 EffectoftotalbandwidthonCRB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.6 Testedfrequencychannelsubsets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.7 CRBforthetestedfrequencychannelsubsets. . . . . . . . . . . . . . . . . . . . . . . 56
4.8 EffectofobservationfrequencyresolutiononCRB. . . . . . . . . . . . . . . . . . . . 57
4.9 EffectofpulsewidthonCRB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.10 EffectoftemporalresolutiononCRB. . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.11 EffectofpulsewidthonCRBforvarioustemporalresolutions. . . . . . . . . . . . . . 60
4.12 ThetemporalresolutionthatminimizestheCRBforagivenpulsewidth. . . . . . . . . 61
4.13 EffectofarrivalangleonCRBwithlowerS/N. . . . . . . . . . . . . . . . . . . . . . 62
4.14 EffectofarrivalangleonCRB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.15 EffectofarrivalangleonCRBwithlowerS/N. . . . . . . . . . . . . . . . . . . . . . 64
5.1 High-levelanalogreceiveranddigitalprocessorblockdiagram. . . . . . . . . . . . . . 67
5.2 AsingleGBT-2dipole. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.3 Blockdiagramdescribingthevariousoperationalmodes. . . . . . . . . . . . . . . . . 69
5.4 AphotoofoneofthefiveHPCs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.5 AgenericHASHPIPEprogramblockdiagram. . . . . . . . . . . . . . . . . . . . . . 73
5.6 Thecorrelatoroutputforasinglefrequencychannel. . . . . . . . . . . . . . . . . . . 74
5.7 Apictureofthearrayfeedintheoutdoortestfacilitypriortoinstallationonthedish. . 75
5.8 Thesensitivitymapforacalibrationgridon3C295. . . . . . . . . . . . . . . . . . . . 77
5.9 Thearrayelementlayoutasseenfromtherear. . . . . . . . . . . . . . . . . . . . . . 78
5.10 Elementpatternmapsfromacalibrationgridon3C295. . . . . . . . . . . . . . . . . . 79
5.11 Theformedbeamlayoutonthesky. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.12 Formedbeampatternmapsfromacalibrationgridon3C295. . . . . . . . . . . . . . . 80
5.13 MeasuredT withbitunderflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
sys
5.14 MeasuredT withimprovedre-quantization. . . . . . . . . . . . . . . . . . . . . . . 83
sys
5.15 TheX-polarizationsensitivitymapforacalibrationgridon3C295. . . . . . . . . . . . 85
5.16 TheY-polarizationsensitivitymapforacalibrationgridon3C295. . . . . . . . . . . . 85
5.17 X-polarizationT /η spectrumon3C295. . . . . . . . . . . . . . . . . . . . . . . . . 86
sys
5.18 Y-polarizationT /η spectrumon3C295. . . . . . . . . . . . . . . . . . . . . . . . . 86
sys
5.19 X-polarizationelementpatternmapsfromacalibrationgridon3C295. . . . . . . . . . 87
ix