Table Of ContentAntenna Array Characterization via Radio
Interferometry Observation of Astronomical Sources
T. M. Colegate∗†, A. T. Sutinjo†, P. J. Hall†, S. K. Padhi†, R. B. Wayth†,
J. G. Bij de Vaate‡, B. Crosse†, D. Emrich†, A. J. Faulkner§, N. Hurley-Walker†,
E. de Lera Acedo§, B. Juswardy†, N. Razavi-Ghods§, S. J. Tingay†, A. Williams†
†International Centre for Radio Astronomy Research (ICRAR), Curtin University,
GPO Box U1987, Perth, WA 6845, Australia
E-mail: t.colegate@curtin.edu.au
5
‡ASTRON, Netherlands Institute for Radio Astronomy, 7990 AA, Dwingeloo, The Netherlands
1
0 § Cavendish Laboratory, University of Cambridge, JJ Thompson Avenue, Cambridge, CB3 0HE UK
2
n
Abstract—We present an in-situ antenna characterization Observatory (MRO) in the Mid West region of Western Aus-
a
J method and results for a “low-frequency” radio astronomy tralia[4].Unlikemeasurementsinananechoicchamberwhere
0 engineeringprototypearray,characterizedoverthe75–300MHz the operator has full control of the RF sources, astronomical
frequency range. The presence of multiple cosmic radio sources,
2 sources are beyond our control. This is especially true in
particularly the dominant Galactic noise, makes in-situ char-
acterization at these frequencies challenging; however, it will low-frequency radio astronomy, where the spatially extended
]
M be shown that high quality measurement is possible via radio component of the emission from the plane of the Milky
interferometry techniques. This method is well-known in the Way Galaxy is the dominant source of noise [5]. Meaning-
I radio astronomy community but seems less so in antenna mea-
ful LFAA measurement, therefore, requires exclusion of the
.
h surement and wireless communications communities, although
diffuse Galactic emission while maintaining responsiveness to
p themeasurementchallengesinvolvingmultipleundesiredsources
- intheantennafield-of-viewbearsomesimilarities.Wediscussthis previouslywell-characterized,point-likeextragalacticsources;
o approachandourresultswiththeexpectationthatthisprinciple this may be accomplished by cross-correlating the output
r may find greater application in related fields. voltages of pairs of AUTs which are spaced with sufficient
t
s distance such that the Galactic noise is uncorrelated. This
a
[ I. INTRODUCTION concept will be discussed in Sec. II. Measurement results are
andconclusionsarepresentedinSecs.IIIandIVrespectively.
1 Aswithanyantennaengineeringproject,characterizationof
v low-frequencyradioastronomyarrays(referredtoas“aperture
7 arrays” to distinguish them from dish antennas) is required to
1
validate that the design meets requirements and that modeling
0
tools involved in the process are reliable. Low-frequency
5
0 aperturearrays(LFAA)areparticularlychallengingtomeasure
. for a combination of reasons: they are difficult to point
1
0 mechanically, are more closely coupled to the environment
5 (see array placement in Fig. 1) and their physical area is
1 large for a given directivity (scales by λ2). As a consequence
:
v of the latter, larger distances (scales by the square of the
i array diameter) are required to satisfy the far-field condition.
X
Without specialized facilities, measurements of LFAAs in an
r anechoic chamber or outdoor range are not practical.1 The
a
capability of testing larger-diameter LFAAs will be important
in the pre-construction work of the Square Kilometre Array
(SKA) radio telescope [2].
In-situ LFAA measurements offers a number of obvious
Fig. 1. An LFAA prototype array of 16 SKALA antennas. This system is
advantages: no bespoke facility is required and the array is
referredtoasApertureArrayVerificationSystem0.5(AAVS0.5),andisan
situated in the intended environment. Fig. 1 illustrates the initiativeoftheSKAArrayDesignandConstructionConsortium(AADCC).
AUT: an array of 16 dual-polarized log-periodic “SKALA” ItwasconstructedbytheInternationalCentreforRadioAstronomyResearch
(ICRAR), University of Cambridge and the Netherlands Institute for Radio
antennas [3] deployed at the Murchison Radio-astronomy
Astronomy(ASTRON).TheSKALAsareplacedinapseudo-randomconfig-
urationwithinanarea8mindiameter.
1Unmannedaerialvehiclesenableoutdoormeasurements[1],howeverthe
airborneheightrequiredtomeetthefar-fieldconditionlimitsthesizeofthe
antennaorarrayundertest(AUT).
II. BACKGROUNDTHEORY 7048
A. Measurand
Thesensitivityofaradiotelescopeisquantifiedbytheratio km)7047
of its effective aperture area (A in m2) to the system noise ng (
hi
temperature (Tsys in K): Nort7046
A
A/T = e . (1) MWA Tiles
Tsys 7045 466 467 468 AA4V6S9 0.5
This figure-of-merit is a key term in the expression for the Easting (km)
telescope output signal-to-noise (S/N) ratio; many readers
Fig. 2. A map showing the AAVS0.5 location (blue circle) and MWA
will recognize that it is similar and is convertible to G/T
telescopetiles(blackcross)inEasting/NorthingforMapGridAustraliaUTM
which is common in telecommunications. The antenna beam zone50.
patternmaybeobtainedbymeasuringA/T alongtheapparent
trajectoryofasuitableastronomicalsource.Thisassumesthat
the sky noise does not change T appreciably during the where V is the complex visibility on the baseline between
sys 12
observation; in practice, this is a reasonable approximation. antennas1and2,I(l,m)istheskybrightnessdistribution,u,v
are the baseline vector components normalized to wavelength
B. Measurement Method
andl,marethedirectioncosineswithrespecttouˆ,vˆofaunit
√
ThissubsectionpresentsasimplifiedversionofhowA/T is vectorsˆ=luˆ+mvˆ+ 1−l2−m2wˆ wherewˆ isaunitvector
obtainedinradiointerferometry.Interestedreadersarereferred normal to the uv plane (i.e., points to the “phase center”).
to standard textbooks such as [6] and [7] for more complete Simplifying further to the 1-D case, (3) becomes
discussions. Let us assume an interferometer involving 3 (cid:90)
single-polarized antennas (or antenna arrays as the case may V = I(l)e−j2π(u12l)dl, (4)
12
be) observing a point source with flux S (in W/m2/Hz or
Jy) in its phase center (in this context “phase center” refers where l = sinθ(cid:48) and θ(cid:48) is the angle between wˆ and sˆ. We
to that position in the sky for which the interferometer is recognize V12 and I(l) as a Fourier transform pair. Hence,
intended to point to by applying relative phase shifts between structures with large l extent are mostly visible for small u12.
its elements). The measured cross-correlation products are: From MWA observing experience, with its small-diameter
(3.3m) tiles, correlated Galactic noise is measurable on base-
V12 =a˜1a˜∗2S lines of length <30λ and should therefore be excluded.2
V =a˜ a˜∗S It can be shown (see Ch. 9 of [6]) that after calibration of
13 1 3
V =a˜ a˜∗S, (2) themeasuredcross-correlationproducts,thestandarddeviation
23 2 3
in flux density for each baseline is inversely proportional to
where a˜ is referred to as complex “gain” (voltage quantity) the square root of the products of the A/T for the AUTs in
containing a combination of both antenna and receiver elec- question:
tronic gains. Assuming S is known, the complex “gains” may (cid:115)
be solved from these 3 equations. This is typically done by 2
∆S ≈ , (5)
solving the amplitudes and phases separately [6]. ij k2(A/T)i(A/T)jBtacc
To obtain antenna gains, amplitude-only solutions are suf-
where k is Boltzmann’s constant, B is the bandwidth and
ficient. Note that this method is analogous to the well-
t is the accumulation time. Thus, by measuring ∆S for all
known “three-antenna” measurement technique [8]. With N acc
baselines for which the Galactic noise is uncorrelated, A/T
elements, N(N −1)/2 pair-wise combinations (“baselines”)
for each AUT may be solved.
are available, leading to an overdetermined system solvable
withaleast-squaresmethod.AsshowninFig.2,theAAVS0.5 III. CHARACTERIZATIONRESULTS
is co-located with the Murchison Widefield Array (MWA) To measure A/T through cross-correlation, we point the
radio telescope [9], [10] to take advantage of this multi- interferometer towards Hydra A, a compact calibrator source
baseline arrangement (with N =128) to minimize calibration that is sufficiently bright for a good S/N calibration solution
uncertainties. Each of the MWA’s 128 “tiles” is a 16-antenna to be obtained from a 2 minute snapshot observation (Fig. 3).
array of bow-tie dipoles. The AAVS0.5 and MWA tile pointing is achieved with 5-bit,
By selecting interferometry baselines larger than a certain time-delay analog RF beamformers. The data is channelised
minimum, the dominant spatially-extended Galactic noise is prior to correlation into channels of width B=40kHz, and
no longer correlated and “bright” point-like sources are de- averaged post-correlation to t =4s. For each channel, ∆S
acc ij
tectable. This may be illustrated by examining the spatial is calculated for all samples in the snapshot period.
coherence function due to a distributed source (Ch. 1 in [6]):
(cid:90) (cid:90) 2Some readers will recognize a similar situation in a highly multipath
V = I(l,m)e−j2π(u12l+v12m)dldm, (3) environment: the signal envelope is uncorrelated at locations separated in
12 distanceby>∼1λ[11].
22 May 2014: sensitivity (A/T) for tile pointing Az=0, El=75.4, calibrator=Hydra A
0.08
T. Colegate, ICRAR−Curtin, June 2014
0.07
0.06
K)
2m/0.05
T (
A/
nt 0.04
e
m
ele0.03
−
6
1
0.02
Fig.3. X-polarizationcross-correlationimageofHydraAat119MHz,using
only baselines between MWA tiles and the AAVS0.5 array. The red ellipse 0.01
(bottom-leftcorner)showsthesizeofthecross-correlationbeam.
0
50 100 150 200 250 300 350
Frequency (MHz)
Measured AAVS 0.5 X−pol (cyan)
A. Sensitivity
Simulated AAVS 0.5, 2% soil moisture
Fig.4showsanA/T measurementforasnapshot,madeon 22 May 2014: sensitivitSy i(mAu/Tla) tfeodr AtilAe VpSo in0t.i5n,g 1 A0%z= 0s,o Eil lm=7o5is.t4u,r cealibrator=Hydra A
0.08
T. Colegate, ICRAR−Curtin, June 2014
22 May 2014, where the channels comprising the 30.72MHz
bandwidth have been grouped at 6 points across the available 0.07
75–300MHzfrequencyrange.ThetoppanelshowstheX(E– 0.06
K)
W) antenna polarization in cyan dots, the lower panel shows 2m/0.05
the Y (N–S) polarization in blue dots. In this observation, T (
A/
both the AAVS0.5 array and the MWA tiles were pointed at nt 0.04
e
HydraA,atazimuth(clockwisefromNorth)Az=0◦,elevation m
El=75.4◦.Thescatteringofdatapointsat∼270MHzisdueto −ele0.03
6
1
the persistent satellite-based RFI corrupting the measurement 0.02
in these channels. 0.01
Fig. 4 also shows simulated results of this measurement as
0
dashedcurves;thesefollow(1)andincludemeasuredreceiver 50 100 150 200 250 300 350
Frequency (MHz)
temperature, and the sky model [12] and array gain pattern
Measured AAVS 0.5 Y−pol (blue)
at the time of observation. We used full-wave electromagnetic
Simulated AAVS 0.5, 2% soil moisture
(FEKO4) simulation to determine the array gain pattern for Simulated AAVS 0.5, 10% soil moisture
each polarization, and with a ground of either 2% or 10%
Fig. 4. Measured A/T for a 2 minute observation of Hydra A starting at
moisture to represent a reasonable range of the likely soil
22-May-201417:30:32attheMRO,X-polarization(East–Westarm)top,Y-
moisture level experienced at the MRO [13]. polarization(North–Southarm)bottom.Eachdatapointisa40kHzchannel
The measured and simulated results show good agreement measurement.TheAAVS0.5arraypointingisAz=0◦,El=75.4◦.
at all frequency points. With the exception of the corrupted
data at ∼270MHz, the tight clustering of the results at
each frequency point gives us confidence in the measurement results in Fig. 5 are for the same trajectory. The solid orange
process. curve simulates the real-world scenario where the sky “seen”
B. Beam pattern by the AAVS0.5 beam varies as a function of time, inducing
changes in T . The dashed curve is simply the beam pattern
Sensitivity can also be measured at Az, El angles away sys
(i.e. no sky is present).
from the beam pointing direction enabling investigation of
Towards the end of the observation (∼23:10), the sidelobe
beampattern.ThisisachievedbykeepingtheAAVS0.5beam
level from the model sky curve is decreasing relative to the
pointedinafixeddirectionwhiletrackingthecalibratorsource
“no sky” curve; this is caused by a reduction in A/T due to
with the MWA. Fig. 5 shows the X-polarization beam for
increasing sky noise. However, the small difference between
such a measurement, where the MWA tracks Hydra A over
the two beam simulations is encouraging, indicating that the
a 4 hour period and the AAVS0.5 beam remains pointed at
measured beam pattern (which intrinsically varies with time)
Az=0◦, El=75.4◦. For each snapshot and channel, calibration
is representative of the actual beam pattern, at least for the
isperformedandA/T iscalculatedfortheAAVS0.5beamat
sky near Hydra A.
the direction of Hydra A. The data is normalized to the beam
We also estimate errors in the beam pattern introduced due
maximum. For clarity, only the 2% moisture case is shown,
to the analog RF beamforming system. Our estimate of the
as the difference with the 10% case is not significant.
errors is calculated from measured phase (σ = 0.069) and
Fig. 5 is a slice through the AAVS0.5 beam pattern corre- φ
amplitude(σ =0.10)errors.Thecalculationfortheensemble
sponding to the Az, El trajectory of Hydra A; the simulated a
mean beam pattern (sidelobe level) that incorporates these
4http://www.feko.info/ errors is well-known [14]–[16]; for our results there is no
0 T. Colegate, ICRAR−Curtin, June 2014 REFERENCES
B)
um (d −5 [1] GF..PaVoinroenssea,,OA..PLevinegriunai,,GM..AdPdiarams,o,Aan.dCRi.nTa,ascFo.nPe,er“iAnni,tenJ.naMpoatntaerrin,
xim verificationsystembasedonamicrounmannedaerialvehicle(UAV),”
ma−10 AntennasandWirelessPropagationLetters,IEEE,vol.13,pp.169–172,
m 2014.
a
e [2] J.G.BijdeVaate,E.deLeraAcedo,G.Virone,A.Jiwani,N.Razavi,
b−15
ve to Kte.buZganrboliA,dAa.mGi,uJn.sMt,oPn.aHria,lSl,.AP.adFhaiu,lGkn.eAr,dadnadmoA,.Ov.anPeAverrdienni,nSe,.“MLoonw-
elati−20 frequencyaperturearraydevelopmentsforphase1SKA,”inProceedings
R oftheXXXthGeneralAssemblyofInternationalUnionofRadioScience
−25 (URSI). Istanbul,Aug.2011.
19:40 20:09 20:38 21:07 21:36 22:04 22:33 23:02 23:31 [3] E. de Lera Acedo, “SKALA: A log-periodic antenna for the SKA,” in
Local time (HH:MM)
ElectromagneticsinAdvancedApplications(ICEAA),2012International
Measured AAVS 0.5, X−pol (cyan) Conferenceon,sept.2012,pp.353–356.
Frequency−averaged measurements [4] P. Hall, A. Sutinjo, E. de Lera Acedo, R. Wayth, N. Razavi-Ghods,
Simulated beam pattern in model sky T.Colegate,A.Faulkner,B.Juswardy,B.Fiorelli,T.Booler,J.deVaate,
Simulated beam pattern, no sky
M.Waterson,andS.Tingay,“FirstresultsfromAAVS0.5:Aprototype
2σ error on the mean power pattern
array for next-generation radio astronomy,” in Electromagnetics in
Advanced Applications (ICEAA), 2013 International Conference on,
Fig.5. TheAAVS0.5X-polarizationbeampatternat220MHzforAz=0◦, 2013,pp.340–343.
El=75.4◦pointing.HydraAwascontinuouslyobservedon21-Mar-2014with [5] J.Kraus,RadioAstronomy,3rded. Cygnus-QuasarBooks,1986,ch.8.
2 minute snapshots and 5.12MHz bandwidth. Each data point is a 40kHz [6] G.B.Taylor,C.L.Carilli,andR.A.Perley,“Synthesisimaginginradio
channelmeasurement.Theblackcurveisthesamedata,frequency-averaged astronomyII,”vol.180,1999.
for each snapshot. The oranges curves are simulated (“error-free”) beam [7] A.R.Thompson,J.M.Moran,andG.W.Swenson,Interferometryand
patterns for 2% moisture in the presence of model sky (solid) or no sky SynthesisinRadioAstronomy,2nded. NewYork:Wiley-VCH,2001.
(dashed).Thepurplecurveisthe2σ uncertaintyonthebeampattern. [8] W. H. Kummer and E. S. Gillespie, “Antenna measurements-1978,”
ProceedingsoftheIEEE,vol.66,no.4,pp.483–507,April1978.
[9] S. J. Tingay, R. Goeke, J. D. Bowman, D. Emrich, S. M. Ord,
D. A. Mitchell, M. F. Morales, T. Booler, B. Crosse, R. B. Wayth,
C. J. Lonsdale, S. Tremblay, D. Pallot, T. Colegate, A. Wicenec,
significantdifferencetotheerror-freebeampattern.Weplotin
N.Kudryavtseva,W.Arcus,D.Barnes,G.Bernardi,F.Briggs,S.Burns,
purple the estimated ±2σ error on the mean pattern, where σ J.D.Bunton,R.J.Cappallo,B.E.Corey,A.Deshpande,L.Desouza,
is approximated using the formula in [17] for large N. These B. M. Gaensler, L. J. Greenhill, P. J. Hall, B. J. Hazelton, D. Herne,
J. N. Hewitt, M. Johnston-Hollitt, D. L. Kaplan, J. C. Kasper, B. B.
curves show that main beam and most of the sidelobes are
Kincaid, R. Koenig, E. Kratzenberg, M. J. Lynch, B. Mckinley, S. R.
within 2σ of the mean beam pattern; the exception being the Mcwhirter, E. Morgan, D. Oberoi, J. Pathikulangara, T. Prabu, R. A.
first sidelobe at 20:38, which is ∼ 4σ from the mean beam Remillard,A.E.E.Rogers,A.Roshi,J.E.Salah,R.J.Sault,N.Udaya-
Shankar,F.Schlagenhaufer,K.S.Srivani,J.Stevens,R.Subrahmanyan,
pattern.
M.Waterson,R.L.Webster,A.R.Whitney,A.Williams,C.L.Williams,
and J. S. B. Wyithe, “The Murchison Widefield Array: The Square
KilometreArrayPrecursoratLowRadioFrequencies,”Publicationsof
IV. CONCLUSION theAstron.Soc.ofAustralia,vol.30,p.7,Jan.2013.
[10] C. Lonsdale, R. Cappallo, M. Morales, F. Briggs, L. Benkevitch,
This work demonstrates far-field sensitivity and beam pat- J. Bowman, J. Bunton, S. Burns, B. Corey, L. deSouza, S. Doeleman,
M.Derome,A.Deshpande,M.Gopala,L.Greenhill,D.Herne,J.He-
tern characterization of a low-frequency aperture array. The
witt,P.Kamini,J.Kasper,B.Kincaid,J.Kocz,E.Kowald,E.Kratzen-
measurements are in-situ, both in terms of physical location berg, D. Kumar, M. Lynch, S. Madhavi, M. Matejek, D. Mitchell,
and intended astronomical use. The interferometric observa- E.Morgan,D.Oberoi,S.Ord,J.Pathikulangara,T.Prabu,A.Rogers,
A.Roshi,J.Salah,R.Sault,N.Shankar,K.Srivani,J.Stevens,S.Tin-
tion of astronomical sources using the MWA radio telescope
gay, A. Vaccarella, M. Waterson, R. Wayth, R. Webster, A. Whitney,
andtheAAVS0.5arrayundertestresultsinmeasurementscal- A.Williams,andC.Williams,“TheMurchisonWidefieldArray:Design
ibratedtoanabsolutescale.Thesensitivitymeasurementsand overview,”ProceedingsoftheIEEE,vol.97,no.8,pp.1497–1506,aug.
2009.
theirfrequency-dependenttrendsareconsistentwithsimulated
[11] T. Rappaport, Wireless Communications: Principles and Practice,
results. The measured and simulated beam patterns generally 2nded. UpperSaddleRiver,NJ,USA:PrenticeHallPTR,2001.
show good agreement as to the location and height of the [12] A. de Oliveira-Costa, M. Tegmark, B. M. Gaensler, J. Jonas, T. L.
Landecker, and P. Reich, “A model of diffuse Galactic radio emission
sidelobes within the error. This type of characterization will
from10MHzto100GHz,”MonthlyNoticesoftheRoyalAstronomical
be essential for verifying the performance of future prototype Society,vol.388,pp.247–260,Jul.2008.
low-frequency aperture arrays deployed at the MRO. [13] A.T.Sutinjoetal.,“ApertureArrayVerificationSystem0.5:aprototype
array for next-generation low-frequency radio astronomy,” in unpub-
lished.
[14] R.E.CollinandF.J.Zucker,Eds.,AntennaTheory,Part.2. McGraw-
ACKNOWLEDGEMENT
Hill,1969,ch.21.
[15] R. J. Mailloux, Phased Array Antenna Handbook, 3rd ed. Artech
We acknowledge the Wajarri Yamatji people as the tradi- House,2005.
tionalownersoftheMurchisonRadioAstronomyObservatory [16] R.C.Hansen,PhasedArrayAntennas. Wiley-Interscience,1998.
[17] Y.Lo,“Amathematicaltheoryofantennaarrayswithrandomlyspaced
site. The MRO is operated by CSIRO, whose assistance we
elements,” Antennas and Propagation, IEEE Transactions on, vol. 12,
acknowledge. The AAVS0.5 operates as an external instru- no.3,pp.257–268,may1964.
ment of the MWA telescope and we thank the MWA project
and personnel for their support.
