accurate beam prediction through characteristic basis function patterns for the meerkat/ska radio...

2466 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 5, MAY 2013

Accurate Beam Prediction Through CharacteristicBasis Function Patterns for the MeerKAT/SKA

Radio Telescope AntennaAndré Young, Rob Maaskant, Member, IEEE, Marianna V. Ivashina, Member, IEEE,

Dirk I. L. de Villiers, Member, IEEE, and David Bruce Davidson, Fellow, IEEE

Abstract—A novel beam expansion method is presented thatrequires employing only a few Characteristic Basis FunctionPatterns (CBFPs) for the accurate prediction of antenna beampatterns. The method is applied to a proposed design of theMeerKAT/SKA radio telescope, whose antenna geometry is sub-ject to small deformations caused by mechanical or gravitationalforces. The resulting deformed pattern, which is affected in anonlinear fashion by these deformations is then sampled in a fewdirections only after which the interpolatory CBFPs accuratelypredict the entire beam shape (beam calibration). The procedurefor generating a set of CBFPs—and determining their expansioncoefficients using a few reference point sources in the sky—isexplained, and the error of the final predicted pattern relativeto the actual pattern is examined. The proposed method showsexcellent beam prediction capabilities, which is an important stepforward towards the development of efficient beam calibrationmethods for future imaging antenna systems.

Index Terms—Beam modeling, calibration, characteristic basisfunction patterns, radio telescopes, reflector antennas.

I. INTRODUCTION

C ALIBRATION measurements on cosmic radio sources orgeostationary satellites are often used to predict the far-

field patterns of directive antennas, such as antennas for ground-based radio and (sub-) millimeter space telescopes. For theseapplications, it is very important to determine the antenna pat-tern down to the noise floor level in the measurements [1]–[3].In practice, however, it is difficult to achieve this high accu-racy due to atmospheric propagation (i.e. emission, absorption)

Manuscript received August 01, 2012; revised November 20, 2012; acceptedDecember 26, 2012. Date of publication January 14, 2013; date of current ver-sion May 01, 2013. This work was supported in part by the South African Re-search Chairs Initiative of the Department of Science and Technology (DST);in part by the National Research Foundation (NRF); in part by the NetherlandsOrganisation for Scientific Research (NWO); in part by the Swedish Agency forInnovation Systems VINNOVA; and in part by the Swedish Research CouncilVR. Any opinion, findings, and conclusions or recommendations expressed inthis material are those of the authors and therefore the NRF and DST do notaccept any liability with regard thereto.A. Young, D. I. L. de Villiers, and D. B. Davidson are with the Department of

Electrical and Electronic Engineering, University of Stellenbosch, Stellenbosch,South Africa (e-mail: [email protected]; [email protected]; [email protected]).R. Maaskant and M. V. Ivashina are with the Signals and Systems Depart-

ment of Chalmers University of Technology, Gothenburg, Sweden (e-mail: [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TAP.2013.2239954

and instrumental effects. The most important instrumental ef-fects are: (i) the direction dependent signal-to-noise-ratio (SNR)for observing the reference source over the desired region of themeasured beam, and; (ii) the system instability due to e.g. me-chanical deformations of the antenna structure and/or variationof the receiver gain.Conventionally used pattern calibration models used in radio

astronomy applications are only accurate down to a few per-cent relative to the beam maximum [3]–[6], and reaching the re-quired levels of accuracy presents a great challenge, especiallygiven that the pattern models may need to be estimated repeat-edly during the course of an observation in order to calibratefor the time-varying radiation characteristics of the antenna [7].This limits the time practically available for performing the cal-ibration measurements necessary for beam model estimation,thus precluding measurement on a direction-by-direction basis.Recently, a different class of pattern measurement techniques

has been proposed that incorporates a priori information aboutthe antenna structure through employing physics-based beamprediction models, thereby reducing the degrees of freedom formodeling the pattern significantly [8], [9]. Among these, a novelmethod has been proposed which requires employing only a fewCharacteristic Basis Function Patterns (CBFPs) for the accurateexpansion of the antenna beam pattern [10]. The expansion co-efficients were found by measuring the antenna array responseon a few calibration sources only. In that specific case, it wasshown that the perturbed array embedded element pattern due toimpedance matching errors could be accurately predicted. Thisis an important step forward towards the development of effi-cient beam calibration methods for future imaging antenna sys-tems, such as for the Square Kilometre Array, where fast andaccurate calibration and imaging techniques are considered tobe major research topics [11].In this paper we propose to employ CBFPs for the first time

for single-beam antenna systems. The objective is to accuratelypredict the beam pattern of a proposed design of the offsetGregorian MeerKAT/SKA Radio Telescope Antenna whenthis system is subject to geometrical deformations [12]. InSection II the method of employing CBFPs is described in ageneral manner, thereby demonstrating the close resemblancewith the method of weighted residuals. The procedure forgenerating the CBFPs that can compensate for pattern errorscaused by geometrical deformations is discussed in Section III.Finally, in Section IV, numerical results on the accuracy of themethod are described.

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YOUNG et al.: ACCURATE BEAM PREDICTION THROUGH CHARACTERISTIC BASIS FUNCTION PATTERNS 2467

II. CHARACTERISTIC BASIS FUNCTION PATTERNS

Following the CBFP-method as presented in [13], but hereinapplied to a single beam antenna system, we aim to predict theactual reference beam pattern —which may differ fromthe ideally expected pattern due to various errors in thesystem—through the model . To this end, the com-plex-valued vector function is expanded into a relativelysmall set of CBFPs , i.e.,

(1)

where is the set of unknown CBFP expansion coeffi-cients. Next, and analogously to the method of weighted resid-uals, the expansion coefficient vector ,where denotes transpose, is chosen such as to minimize thebeam error function over a desiredangular region. This can be done by weighting to zero throughthe—yet to be chosen— testing functions ,where . Hence

(2)

where the symmetric product is used for testing. Substitution of(1) in (2) leads to the matrix equation

(3)

for . Henceforth, we will assume that thebeam pattern is tested at discrete directions, i.e., is mea-sured successively using known reference point sources inthe sky, so that , where is the-field polarization vector radiated by the th reference far-

field source in the direction of the receiving antenna. The selec-tion of Dirac distribution functions for testing the pattern (collo-cation method) is a logical choice since several relatively strongfar-field point sources1 are readily available as natural calibratorsources [14]. Accordingly, (3) reduces to the matrix equation

(4)

where

(5)

One can solve for through the Moore-Penrose pseudoinverse,, where the superscript denotes the con-

jugate transpose. Note that the choice of testing through a sym-metric product in (2) is in correspondence with the reaction con-cept in electromagnetics, so that the element in (5) is pro-portional to the measured antenna output voltage for the thsource.

A. Incoherent Power Point Sources

In most practical cases the reference sources in the skyare natural incoherent power point sources. In that case, one

1Note that (3) allows us to measure (or test) on sky reference sources that arespatially distributed as well.

Fig. 1. Rotatable test antenna measuring a reference power point source in thedifferent directions . The complex-valued receive voltages are

obtained by correlating the respective output powers with a reference antennapointing at the same source. Afterwards, the CBFP expansion coefficientsare determined for modeling the unknown beam pattern of the antenna undertest.

instead will measure the real-valued time-averaged antennaoutput powers , for . Accord-ingly, from (4)

(6)

where takes the diagonal of the square matrix andplaces these elements in a column vector. To the authors’ bestknowledge, a closed-form solution to in [10], given , doesnot exist, so that one has to resort to nonlinear equation solvers[10]. Furthermore, since , where is a uni-tary matrix (for example a diagonal matrix with arbitrary phasefactors on its diagonal), the solution to suffers from a unitarymatrix (or phase) ambiguity and is therefore not unique. Sim-ilarly, if in addition the reference sources are unpolarized, onealso has to deal with a polarization ambiguity in the modeledpattern.Alternatively, and rather than using a single antenna, one can

directly measure the complex-valued receive voltage vectorin (4) by correlating the measured antenna output power withthat of a reference antenna as shown in Fig. 1 (cf. also [14] and[15]).After correlating the output signals, the measured 2 2

rank-one covariance matrix is obtained as

(7)

whose dominant eigenvector is composed of the complexvoltage phasors , and has the eigenvalue

. Hence, the element in (5) canbe computed as , where we normalized toin order to compensate for possible phase and amplitude

variations of the reference source signal.

III. CBFP-METHOD APPLIED TO MEERKAT

A. CBFP Generation

The next step is to select a representative set of CBFPs, whosepowerful property is that relatively few of them are required for


the accurate modeling of the beams. We distinguish betweenprimary and secondary CBFPs: (i) the primary CBFP, , is asimulated or measured pattern corresponding to the ideally ex-pected beam pattern, , in the absence of system errors.This physics-based pattern alone is assumed to be already veryclose to the actual (slightly perturbed) reference pattern ;(ii) the secondary higher-order CBFPs, , need to beable to compensate for expected beam errors to be able to ac-curately predict . The secondary CBFPs should thereforespan the space of beam patterns that are to be expected whenthe antenna system is subject to certain types of errors. That is,the set of secondary CBFPs correspond to the radiation patternsof a set of possible systems that are representative of the var-ious expected errors. This set of pattern basis functions may bedetermined through simulation (depending on how accuratelythe actual system—with or without errors—can be modeled), ormeasurement (depending on how well representative error con-ditions can be enforced on the actual system), or a combinationof both.As an example, the set of CBFPs used to model antenna

beams for a reflector system under varying thermal loading con-ditions may consist of a simulated pattern of the ideal antennageometry (primary CBFP), and a number of measured patternsobtained at different times of the day (secondary CBFPs) [5, cf.Fig. 19]. If other types of geometrical errors are to be modeledas well (e.g. positioning error of the feed and/or subreflector,ground roughness, etc.), the set of secondary CBFPs needs tobe augmented with basis function patterns obtained for the cor-responding erroneous systems. Since the relation between ge-ometrical deformations and radiation pattern shape is gener-ally nonlinear, CBFPs obtained from system configurations con-taining multiple anticipated errors may also be required. How-ever, depending on the magnitude of the expected errors (whichare generally relatively small) the addition of more basis func-tions may result in a certain degree of redundancy, and an ac-curate pattern model may be achieved without using all thegenerated CBFPs. At any rate, a larger number of CBFPs maytherefore be required to address the problem of modeling non-linear beam pattern variations for the geometrical errors dis-cussed here, as opposed to e.g. beamformer weight errors whichconstitute a linear problem [10]. As an illustrative example ofthe proposed method, herein we will consider the case where thebeam errors are a result of geometrical deformations resultingin displacement of the feed and subreflector only.Consider the offset Gregorian candidate design for the

MeerKAT antenna in Fig. 2 [16]. The estimated toleranceson the subreflector position are presented in Table I (for twodifferent frequencies of operation) and are defined in the co-ordinates shown at the base of the support armon which the feed and subreflector are mounted. The gainpattern variations caused by these geometrical variations havebeen examined in [12]. The geometrical position error of thefeed and subreflector are proportionally affected since thesecomponents are supported by the same structure. Hence, wewill define the subreflector position error as ,from which the feed position error is determined as the ratioof the position of the feed along the support arm to that ofthe subreflector. Accordingly, the 3-D Euclidean space of

Fig. 2. Geometry of the proposed offset Gregorian MeerKAT system with thedomain space of subreflector position errors shown on an exaggerated scalefor clarity. The vector extends from the center of which is located at thebase of the subreflector (ideal position). The indicated positions wereused to construct the secondary CBFPs for set . The position error of the feed(relative to the ideal location ) is proportional to that of the subreflector.indicates the primary focus point.

TABLE IESTIMATED TOLERANCES ON SUBREFLECTOR POSITION

IN UNIT WAVELENGTHS [12]

position errors is defined, whose domain is bounded by thevalues listed in Table I. Upon taking samples within , theset of geometrical error vectors is obtained.2 With thefinite set of error vectors thus defined, the generation of thecorresponding set of CBFPs can proceed.The primary CBFP is chosen as the simulated far field pattern

of the error-free antenna geometry, i.e. .Similarly the set of secondary CBFPs is obtained through simu-lation and by setting for . Usingthe so-generated initial set of CBFPs (primaries secon-daries), each of which is simulated at a total of far fielddirections, a matrix can be formed (2 far fieldcomponents)

.... . .

... (8)

where denotes a sampled (simulated) far-field direction. Alinear dependency between the angular sampled version of theCBFPs (i.e. columns of ) may exist, which renders the matrixrank-deficient. The CBFPs can be orthonormalized and re-

dundant ones be eliminated through the application of the Sin-gular Value Decomposition (SVD), as is done in the Character-istic Basis Function Method (CBFM) [17]. In the present con-text, we then retain only the first left-singular vectors of as

2The probability density function of the displacement error can be used toobtain a nonuniform sampling grid.


the reduced set of CBFPs, which are the ones corresponding tosingular values whose magnitudes are above a certain specifiedthreshold relative to the largest singular value. Furthermore, itis pointed out that several rows of can be discarded duringthe SVD process if the objective of the CBFPs is to model thebeam pattern only over a limited angular region. Generally, thesmaller the angular region, the lesser the number of retainedCBFPs. Afterwards, and if desired, the corresponding CBFPbeam functions outside the limited angular support can be re-covered through using the first right-singular vectors as ex-pansion coefficient vectors for the initial set of CBFPs. This per-mits modeling the beam over the entire angular support, whilethe accuracy is highest within the limited angular region.When measured (as opposed to simulated) CBFPs are em-

ployed, e.g. by manually introducing displacement errors andmeasuring the corresponding pattern functions, it becomes prac-tically intractable to generate a large initial set of CBFPs. There-fore, we also consider the case of generating only initialsimulated CBFPs, that is, at the center (primary CBFP) and cor-ners (secondary CBFPs) of the cuboidal-shaped subdomain(cf. Fig. 2).Hence, the following sets of CBFPs will be considered: (i) set, composed of CBFPs (no SVD); (ii) set , composed

of CBFPs (after SVD on ); (iii) set , composedof CBFPs (after SVD), which is obtained throughregularly sampling the error subdomain . The SVD will onlybe used to orthonormalize the CBFPs, i.e. no threshold on thesingular values is applied to reduce each set of CBFPs, so that

; instead, the model accuracy is examined as a func-tion of the number of admitted CBFPs in decreasing order ofimportance (for and this is based on the magnitude ofthe singular values, while for the ordering is as indicated inFig. 2).

B. Selection of Testing Points

The numerical solution accuracy of the expansion coefficientvector in (1), and therefore , depends on the matrix con-dition number of in (4). In turn, depends on the totalnumber and positions of the testing points. In the following, wewill choose the total number of testing points equal to thetotal number of employed CBFPs , and let the first testingpoint correspond to the on-axis direction . For eachadditional CBFP included in the model, the correspondingto be selected next is chosen such as to increase by theleast amount. Furthermore, the points are limited to a region

around the expected beam maximum where the an-tenna sensitivity is expected to attain high values as well. Notethat the procedure for generating the sets and needsto be performed only once for the construction of in (4),whereas the forcing vector needs to be updated at regular timeintervals to calibrate the beam during operation.Fig. 3 shows the resulting testing points for and at

580 MHz, where the value of was selected so thatall testing points are approximately within the 5 dB beam ofthe ideally expected pattern. As can be seen, most of the testingpoints were found to reside close to or on the boundary

Fig. 3. Testing points for (‘ ’) and (‘ ’) shown on the ideally expectednormalized gain pattern at 580 MHz. The contour is indicated as asolid black line.

. At 1.75 GHz a value of was chosen (contourplot not shown).

IV. NUMERICAL RESULTS

Fifty simulated reference patterns were analyzed by ran-domly3 selecting position errors of the subreflector (andcorrespondingly of the feed) within . Accordingly, the threference pattern, , for , is predictedthrough the modeled pattern by employing CBFPs,where , and for the CBFP sets , where

. As a result, each of the 50 reference patterns wasmodeled in 27 different ways, which enabled us to performa detailed comparative analysis. Afterwards, the pertainingpattern error function was calculated for each of the casesand then normalized to the maximum of the correspondingreference pattern. Two error metrics were considered: the firsterror metric was chosen as the average of over the

angular region where the normalized is above the 10-dBlevel, and averaged over all ; the second error metricwas chosen as the maximum of over the angular regionwhere the normalized is above the 30 dB level, and theworst case selected from all . The generation of the CBFPs aswell as the error calculations were performed separately at thetwo frequency points 580 MHz and 1.75 GHz.Fig. 4(a) shows the average error metric as a function offor the various sets of CBFPs at 580 MHz. The average error

between the actual reference patterns and the corresponding ide-ally expected patterns (when ) is also shown in the figureby the black dashed line. Not surprisingly, a single CBFP fromresults in an error ( 1%)which is exactly equal to that for the

ideal pattern since the primary CBFP was chosen to be equal to. Similarly, the primary CBFPs for the sets and

(obtained after the SVD) closely resemble and, conse-quently, the error for a single CBFP from these sets is at the samelevel as for and . Upon increasing , the error in themodeled pattern decreases relatively slowly when employingCBFPs from , as opposed to the CBFPs from , whose errorreduces much more rapidly (even for small ) owing to theorthonormalization of the CBFPs over the angular region near

3A uniform probability distribution was assumed for within , which repre-sents a worst-case scenario for the actual performance of the antenna in practice.


Fig. 4. Average error in the model pattern using different numbers of employed CBFPs . The average error for all geometrical deformations is used anda comparison is shown between CBFPs from (without SVD), ( after SVD), and (after SVD). (a) 580 MHz; (b) 1.75 GHz.

Fig. 5. Worst case maximum error in the model pattern obtained using different numbers of employed CBFPs . Comparison is shown between CBFPsfrom (without SVD), ( after SVD), and (after SVD). (a) 580 MHz; (b) 1.75 GHz.

the beam maximum. Ultimately, for , the beam approx-imation errors for the sets and are the same, since bothsets span the same space of beam patterns. However, employingCBFPs from set , and for the error can be reducedfurther by about an order of magnitude. The method is shownto model the variation in the beam patterns with high accuracy,i.e., even with CBFPs from alone, the average error can bereduced to a level of about ( 100 dB).The average error computed at 1.75 GHz is shown in Fig. 4(b)

and the results are similar to that for the lower frequency. How-ever, due to the larger electrical distance of the mechanical dis-placements at the higher frequency, the shape of the referencepatterns deteriorate, generally resulting in a larger error betweenthe reference and the modeled patterns (as well as between thereference and the ideally expected patterns). Also, the conditionnumber is smaller at the higher frequency for the same setof CBFPs, which is a direct consequence of the increased ef-fect of the geometrical errors on the beam patterns at the higherfrequency. However, although the matrix condition number im-proved, more CBFPs may need to be employed to achieve thesame accuracy at higher frequencies. Upon employing all nineCBFPs from either or , the error can be reduced to as little

as , and even further by a factor four when employingthe same number of CBFPs from .The maximum error is shown in Fig. 5(a) and (b), at the

lower and higher frequencies, respectively, and as a functionof for the different sets of CBFPs. The worst case error be-tween the ideally expected and actual reference pattern is shownto range from about 5% at 580 MHz up to 20% at 1.75 GHz.The importance of improving the conditioning of (4) throughthe application of the SVD is emphasized by the difference inthe results for and .Whereas the worst case error decreasesnearly monotonically for with every additionally employedCBFP, the reduction in error for using CBFPs from is sig-nificantly slower. Moreover, the results at 1.75 GHz show thatthe error in the model pattern may even be larger than theerror in the expected (uncalibrated) pattern as is evidenced bythe error for . As before, the use of basis functions fromis seen to improve the error in the model pattern by approx-

imately a factor five at the lower and a factor two at the higherfrequency, respectively, for .Fig. 6(a) and (b) shows the reference and CBFP-modeled pat-

terns for the geometrical error resulting in the largest maximumerror in the ideally expected pattern at each of the two frequen-


Fig. 6. Normalized gain patterns at (a) 580 MHz and (b) 1.75 GHz comparing the reference pattern , modeled pattern , and the expected patternfor the worst case subreflector displacement . Normalized error patterns for the modeled and expected patterns for the same subreflectordisplacement are also shown in (c) 580 MHz and (d) 1.75 GHz. All patterns are shown in the plane of the reference pattern maximum. (a) Beam pattern @580 MHz

; (b) Beam pattern @1.75 GHz ; (c) Error function @580 MHz ; (d) Error function @1.75 GHz .

cies. The modeled patterns are produced using CBFPs from set, with at the lower, and at the upper frequency.

For comparison, the ideally expected patterns (no displacementerror) at each of the frequencies are also shown, and the actualreference beam pattern at the lower frequency is seen to suffermainly from a small pointing error, whereas at the higher fre-quency this error is substantially larger and the sidelobes arealso affected significantly. By employing seven CBFPs from, the lower frequency modeled pattern is visually indistin-

guishable from the reference pattern, and at the higher frequencythe difference between these two patterns is only visible fromaround the 30 dB level. The beam error functions (normal-ized to the maximum of ) corresponding to these modeledpatterns are shown in Fig. 6(c) and (d), along with the beamerror functions (also normalized) for the ideally expected pat-terns. These error patterns show that the model error is reducedto an extremely low level in the main beam area (over the an-gular region ), and even over the sidelobe region theerror in the model pattern is still well below 40 dB (1%).Finally, the effect of on the error in was examined

for the worst case geometrical error at 1.75 GHz by increasingthe angular region over which the CBFPs are orthonormalizedfrom ( 5 dB level of ) to

Fig. 7. Normalized error patterns for worst case geometrical error at 1.75 GHzshown over an angular region . Comparison between (left)and (right) .

( 20 dB level of ). The normalized error patterns resultingfor these two cases are shown in Fig. 7, where increasing the an-gular region is seen to reduce the error in an average sense overa similarly larger region at the price of an increase in error insidethe region . The testing points for best conditioning of(4) in either case were mostly arranged on or near ,


as can be seen from the deep nulls in the error function wherepoint matching is performed.

V. CONCLUSIONS AND RECOMMENDATIONS

The extent to which the sensitivity offered by future radiotelescopes can be utilized is dependent on the accuracy withwhich the antenna beam pattern can be estimated using theleast number of calibration measurements. In this contribu-tion a beam estimation procedure based on the CharacteristicBasis Function Pattern method [10] is proposed to addressthis requirement for single beam antennas, and provides aradiation pattern model that can be used to accurately accountfor instrumental direction-dependent effects during calibrationand imaging [6]. Specifically, the method is demonstrated tocompensate for certain mechanical deformations that are tobe expected in an offset Gregorian antenna, in which casepresented simulation results show a reduction in the maximumbeam model error of a noncalibrated system from 15% downto a value less than 0.2%. This level of accuracy is achievedby employing only nine CBFPs to model the actual perturbedbeam pattern, and therefore requires as little as nine calibrationmeasurements, indicating that the estimation method is alsotime-efficient.The application of the CBFP method to compensate for var-

ious other types of system errors, the polarization ambiguitythat arises when calibrating on unpolarized sources, and exper-imental demonstration on an actual antenna system using mea-sured CBFPs, are subjects of ongoing research.

ACKNOWLEDGMENT

The authors would like to thank O. Iupikov for the develop-ment of the GRASP toolbox used in this work.

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[14] P. G. Smith, “Measurement of the complete far-field pattern of largeantennas by radio-star sources,” IEEE Trans. Antennas Propag., vol.14, no. 1, pp. 6–16, Jan. 1966.

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André Young was born in the Free State, SouthAfrica, on April 6, 1983. He received the B.Eng.degree in electrical and electronic engineering withcomputer science (cum laude) and the M.Sc.Eng.degree in electronic engineering (cum laude) in2005 and 2007, respectively, from the Universityof Stellenbosch, Stellenbosch, South Africa. HisM.S. thesis was on mesh termination schemes forthe finite element method in electromagnetics. Heis currently pursuing the Ph.D. degree in electronicengineering at the University of Stellenbosch.

He has worked on various engineering projects for Azoteq (Paarl, SouthAfrica) and Entersekt (Stellenbosch), and was appointed as a Junior Lecturerin 2009 and 2011 at the University of Stellenbosch. Since 2011, he has spentseveral months as a visiting researcher with the Antenna Group at the ChalmersUniversity of Technology, Gothenburg, Sweden. His main research interestsinclude computational electromagnetics and antennas.

Rob Maaskant (M’11) was born in The Nether-lands on April, 14th, 1978. He received the M.Sc.degree (cum laude) in 2003 and the Ph.D. degree(cum laude) in 2010, both in electrical engineeringfrom the Eindhoven University of Technology,Eindhoven, The Netherlands.From 2003–2010, he was an antenna research

scientist at the Netherlands Institute for RadioAstronomy (ASTRON), Dwingeloo, and from2010–2012, he was a postdoctoral researcher inthe Antenna Group of the Signals and Systems

Department at the Chalmers University of Technology, Sweden, for which hewon a Rubicon postdoctoral fellowship from the Netherlands Organization forScientific Research (NWO), 2010. He is currently an Assistant Professor in thesame Antenna Group. He is the primary author of the CAESAR software—anadvanced integral-equation-based solver for the analysis of large antenna arraysystems. His current research interests are in the field of receiving antennas forlow-noise applications, meta-material-based waveguides, and computationalelectromagnetics to solve these types of problems.Dr. Maaskant’s Ph.D. dissertation was awarded “the best dissertation of the

Electrical Engineering Department, 2010.” He received the 2nd best paper prize(“Best Team Contribution”) at the 2008 ESA/ESTEC workshop, Noordwijk,and was awarded a Young Researcher grant from the Swedish Research Council(VR), in 2011.


Marianna V. Ivashina (M’11) received the Ph.D.degree in electrical engineering from the SevastopolNational Technical University (SNTU), Ukraine, in2001.From 2001 to 2004, she was a Postdoctoral

Researcher and from 2004 until 2010, an AntennaSystem Scientist at The Netherlands Institute forRadio Astronomy (ASTRON). During this period,she carried out research on an innovative PhasedArray Feed (PAF) technology for a new-generationradio telescope, known as the Square Kilometer

Array (SKA). The results of these early projects have led to the definition ofAPERTIF—a PAF system that is being developed at ASTRON to replace thecurrent horn feeds in the Westerbork Synthesis Radio Telescope (WSRT). Shewas involved in the development of APERTIF during 2008–2010 and acted asan external reviewer at the Preliminary Design Review of the Australian SKAPathfinder (ASKAP) in 2009. Since 2011, she has assisted the SKA office inthe development of the statement of work of the next phase of the SKA project.She is currently an Associate Professor at the Antenna Group of the Signalsand Systems Department (Chalmers University of Technology, Sweden). Herinterests are phased arrays and reflector antennas, antenna system modelingtechniques, array signal processing, and radio astronomy.Dr. Ivashina was a Guest Editor of the IEEE TRANSACTIONS ON ANTENNAS

AND PROPAGATION ONANTENNAS Special Issue on Next Generation Radio Tele-scopes (June, 2011). She has received several scientific distinctions, includingthe 2nd Best Paper Award (“Best Team Contribution”) at the ESA AntennaWorkshop (2008) and the International Qualification Fellowship of the VIN-NOVA—Marie Curie Actions Program (2009).

Dirk I. L. de Villiers (S’05–M’08) was born inLangebaan, South Africa, on October 13, 1982. Hereceived the B.Eng. and Ph.D. degrees in electricaland electronic engineering from the University ofStellenbosch, Stellenbosch, South Africa, in 2004and 2007, respectively.During 2005 to 2007, he spent several months

as visiting researcher with the Computational Mod-eling and Programming Group at the University ofAntwerp, Antwerp, Belgium. From 2008 to 2009,he was a postdoctoral fellow at the University of

Stellenbosch working on antenna feeds for the South African SKA program.During this time, he was also a part-time lecturer at the Cape PeninsulaUniversity of Technology. He is currently a Senior Lecturer at the Universityof Stellenbosch and his main research interests include reflector antennas, aswell as the design of wideband microwave components, such as combiners,filters, and antennas.

David Bruce Davidson (M’85–SM’07–F’12) wasborn in London, U.K., in 1961. He was raised and ed-ucated in South Africa, receiving the B.Eng, B.Eng(Hons), and M.Eng. degrees (all cum laude) from theUniversity of Pretoria, South Africa, in 1982, 1983,and 1986, respectively, and the Ph.D. degree fromthe University of Stellenbosch, Stellenbosch, SouthAfrica, in 1991.Following national service (1984–1985) in the

then South African Defence Force, he was withthe Council for Scientific and Industrial Research,

Pretoria, prior to joining the University of Stellenbosch in 1988. As of 2011,he holds the South African Research Chair in Electromagnetic Systems andEMI Mitigation for SKA there. He was a Visiting Scholar at the University ofArizona in 1993; a Visiting Fellow Commoner at Trinity College, CambridgeUniversity, U.K., in 1997; a Guest Professor at the IRCTR, Delft Universityof Technology, The Netherlands, in 2003; and an Honorary Visitor, Universityof Manchester, U.K., in 2009. His main research interest through most of hiscareer has been computational electromagnetics (CEM), and he has publishedextensively on this topic. He is the author of the recently revised text Com-putational Electromagnetics for RF and Microwave Engineering (CambridgeUniversity Press, 1st Ed., 2005; 2nd Ed., 2011). Recently, his interests haveexpanded to include engineering electromagnetics for radio astronomy.Prof. Davidson is a member of the South African Institute of Electrical Engi-

neers and the Applied Computational Electromagnetic Society. He is a recipientof the South African FRD (now NRF) President’s Award; presently, he has a B2research rating from the NRF. He received the Rector’s Award for ExcellentResearch from the University of Stellenbosch in 2005. He is a Past Chairman ofthe IEEE AP/MTT Chapter of South Africa and served as an Associate Editorof the IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS (2006–2008).Currently, he is the Editor of the “EM Programmer’s Notebook” column of theIEEE Antennas And Propagation Magazine and serves on the IEEE Antennasand Propagation AdCom (2011–2013). He served as General Chair of the 8thInternational Workshop on Finite Elements for Microwave Engineering, heldin Stellenbosch, May 2006. He was Chair of the local organizing committee ofICEAA-IEEE APWC-EEIS’12, held in Cape Town, South Africa, in September2012.

accurate beam prediction through characteristic basis function patterns for the meerkat/ska radio...

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