A Wideband, Four-Element, All-DigitalBeamforming System for Dense Aperture Arrays in

Radio AstronomyRichard P. Armstrong∗‡, Kristian Zarb Adami∗ and Mike E. Jones∗

∗University of Oxford Astrophysics, Department of Physics, Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH‡corresponding author: richard.armstrong@physics.ox.ac.uk

Abstract—Densely-packed, all-digital aperture arrays form akey area of technology development required for the SquareKilometre Array (SKA) radio telescope. The design of real-timesignal processing systems for digital aperture arrays is currentlya central challenge in pathfinder projects worldwide. We describean hierarchical, frequency-domain beamforming architecture forsynthesising a sky beam from the wideband antenna feeds ofdigital aperture arrays.

I. INTRODUCTION

Densely-packed, all-digital aperture arrays form a key areaof technology development required for the Square KilometreArray (SKA) radio telescope. The design of real-time signalprocessing systems for aperture arrays is certainly one ofthe most challenging tasks in the design of next-generationinstruments. In this paper, we describe the design andimplementation of an hierarchical beamforming architecturefor wideband radio telescopes.

This document is organised as follows. Chapter I is anintroduction to the problem domain. Chapter II describesthe theory and process of ‘beamforming’ for aperture arraysused in radio astronomy. Chapter III describes the design andimplementation of a frequency-domain beamformer. ChapterIV describes calibration procedures for the array, and isfollowed by results and conclusions.

A. Aperture Phased Arrays

An aperture phased array is a collection of fixed, non-directional antennas whose outputs are combined to synthesisean effective directional antenna. This synthesised antenna ispointed electronically; significantly the physical componentantennas do not ever move. The electronic combination ofsignals with beamforming techniques performs the samespatial filtering task as a parabolic dish would in a traditionalradio telescope dish. Figure 1 illustrates the basic principleof this operation.

The flexibility, survey speed, system-level autonomy andscalability provided by antenna arrays make them extremelyattractive for next-generation radio instruments, for use, inour application, in radio astronomy, but also applicable toother wideband detection and communication instruments.

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Fig. 1. An illustration of the electronic processing of signals received from anarray of antennas for concentrating the signal from a certain direction. This isthe basic principle of the phased aperture array: different delay configurationsallow beams to be formed in different directions of θ

Future radio instruments will certainly be dependent on theavailability of high-performance signal processing systemssuch as these. Since aperture arrays are seen as a criticalantenna technology to achieve the required sky survey speedin future radio telescopes (see, for example, [1] and [2]),the development of a scalable signal processing system is ofgreat importance.

II. BEAMFORMING

A. Digital, Frequency-Domain Beamforming

The process of beam forming, shaping and summingof tile elements may be performed in either the digital oranalogue domains. Digital beamformers are distinguishedfrom analogue and partially analogue beamformers by signaldigitisation directly after initial RF amplification, followedby processing entirely in the digital domain. The all-digitalapproach offers maximum flexibility in manipulation ofincoming signals both in beamforming and in calibration ofthe wideband signals. However, there are many tradeoffs inthis space, and different applications will dictate eventualimplementation.

Beamforming techniques may be generally categorised

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as time-domain or frequency domain. For broadbandapplications, sub-banded frequency-domain techniques maybe seen as superior due to their computational advantageif fine sample interpolation operation is implemented (see,for example, [3]) and the ability to calibrate band-passcharacteristics of the analogue system (see [4]) by applyinga phase shift to each sub-band in the transform domain. Forthese reasons, we choose to perform the beamfoming inFourier space.

B. Signal Processing and Dataflow Requirements for Wide-band Phased Aperture Arrays

In this section we describe the signal processing anddataflow requirements of the narrowband phase shiftbeamforming architecture.

The sampled broadband signal from each antenna isbroken up into many narrow frequency bands. Each bandis independently processed (delayed and combined with thesignals from other antennas) with a narrowband phase-shiftbeamformer. The results of these narrowband beamformersare combined to form a broadband beam in the requiredspatial direction. This operation is repeated for each beamthat is formed. Channelisation or ‘frequency binning’ oflarge-bandwidth input signals for beamforming can beperformed with various techniques.

Figure 2 shows the signal processing flow for the phase-shift beamforming architecture. N single-polarisation antennasignals are digitised then combined with phase correctionfactors to form B beams in the beamformer processor. Thesebeams are combined in a beam-combiner processor1. Theresultant ‘station beams’ (which are wideband spectra) arethen sent to a central correlator for interferometric processing.

We now analyse the dataflow requirements: the analogueinput signal ranges from 0.5GHz to 0.7GHz (a bandwidthof 0.2GHz), and is sampled with q bits of precision, whichresults in a digital input bandwidth from each antenna

1The beam-combiner processor may be a further hierarchy of processors

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polarisation of q *0.4Gbps. This means that the first-stagebeamformer processor will have a raw input data-rate ofNq ∗ 0.4 Gbps and an output data rate of Bqs*0.4 Gbps,where s is the bitwidth scaling factor of the beamformer.

Note that there is a strong distinction between high-performance, real-time processing which must be performedat the input data-rate and more computationally complexco-efficient calculation which may be performed at a muchreduced rate. In this paper, we concentrate on the former;this is an implementation of the high-performance processingsystem. We allow the steering and correction coefficients tobe updated at a lower rate, dictated by the speed with whichthe array must be able to scan the sky.

III. AN HIERARCHICAL, FREQUENCY-DOMAINBEAMFORMING ARCHITECTURE

In this section, we describe the design and implementationof an FPGA-based digital system for the frequency sub-bandphase-shift beamforming architecture.

Figure 3 is an architectural schematic of the 4-elementbeamformer digital system. The Analogue to Digital Converter(ADC) samples the incoming antenna signal at 800MSa/swith 8 bits of precision. This 400MHz bandwidth signal isimmediately Digitally Down-Converted (DDC) by mixingwith an complex sinusoid at 3/4 of the ADC clock rateto yield a base-banded 500MHz to 700MHz input signal.Channelisation is the next step in the processing pipeline:an efficient technique is the Polyphase FFT2 Filter Bank(PFFB) channeliser, which improves frequency isolation ofthe FFT operation (see for example [5]) and has shown to beefficient for large numbers of equally spaced channels [6].

2Fast Fourier Transform (FFT)

The beamformer applies steering and correction coefficientsto each signal stream and then performs beam summation.We then accumulate the power sum of the raw voltage beamsignal for a run-time configurable length of time.

We have implemented this design with signal processinglibraries and hardware designed by the Collaboration forAstronomy Signal Processing Research (CASPER). We areindebted to all collaborators of this group for the support theyhave provided with hardware and libraries.

The FPGA-based design uses embedded multipliers in aXilinx Virtex II Pro device. Since these fixed hardware blocksare natively 18-bit, we preferentially use 18-bit multiplicationsand datapaths throughout the design.

IV. CALIBRATION AT APERTURE ARRAY TILE LEVEL

Calibration of individual elements of a dense aperture arrayat the tile level is fundamentally different from traditionalradio telescope calibration for two reasons. Firstly, individualantennas ‘see’ the entire observable sky; the dish-centricconcept of Field of View (FoV) at the antenna level is notvalid. Secondly, each individual element does not have thesensitivity to detect astronomical sources.

Thus we must approach the calibration in other ways.Perhaps the obvious first suggestion would be to fullyconstrain the analogue system. Certainly, this is done to thefirst degree. We refer the reader to [4] for discussions aboutanalogue signal chains, including S-parameter propagation,variation due to temperature, component anisotropy andradio-frequency interference (RFI) effects. That is, a typicalanalogue system is frequency, temperature, signal chain,component, RFI-environment and pointing angle dependent,and needs to be continuously calibrated on timescales fasterthan the fastest varying of the set of all these.

A first approach to this calibration problem would be thecorrelation approach. At a minimum, a correlation-basedtechnique must perform an Nx1 correlation. A full correlationof all baselines would allow a over-constrained set of linearequations to be formed, providing a robust solution for gainand phase of each element. In this case, full broadband signalpath calibration is possible with any signal, including noise.However, a real-time correlator may require an even largerdigital system than the entire beamformer. Thus, correlationapproaches may be required to be time multiplexed.

Another possible solution is to use the existing beamformerarchitecture to calibrate off a strong signal. This signal maybe externally injected into the analogue system either directlywith a noise diode power-combiner scheme or with a knownstrong signal beamed at the entire array. We chose the latterfor our calibration and beam a CW source at the antenna arrayfrom the far field.

Fig. 4. An image showing the four-element antenna array in the anechoicchamber.

A. Calibration Procedure

The calibration procedure for the array for each frequencybin in the band proceeds as follows:

1) Fix the correction co-efficient for a reference element2) Sweep the phase of a second element, and record the

power output of the beamformer for 2π of phase3) Record the coefficient that results in the largest power

output of the beamformer, as well as the output power4) Repeat for all elements5) For each element, upload a coefficient eiφ such as to

compensate for the phase error of each element

V. RESULTS AND DISCUSSION

A. Anechoic Chamber Testing

We have tested the 4-element beamformer using thiscalibration procedure in a radio-frequency anechoic chamberat the Department of Engineering at Oxford University.Significantly, the beamformer is tested without the analoguechain that is required in the eventual radio instrument in thefield. Figure 4 shows the linear, four-element antenna array inthe chamber. The transmit antenna is located in the far-fieldof the receive array so we neglect the transmit apertureillumination function.

Figure 5 shows the beamformer response to a source at 45degrees from broadside when a digital beam is swept acrossthe aperture.

B. Field Deployment

This calibration process has also been trialled in the field.A transmitter is positioned atop a mast (again, in the far-fieldof the receive array) and pointed at the array. However, inthis case, we included the analogue chain to the antennasbefore digitisation. The calibration procedure was performedin the same way as before. Figure 6 shows a 700MHz beam

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Fig. 5. Beamformer response in the anechoic chamber for a transmitterlocated at 45 degrees from broadside. The array has been calibrated for thetransmitter and a digital beam is swept across the array. The abscissa is thescan angle in degrees from broadside and the ordinate is an arbitrary powerscale relative to maximum signal power.

Fig. 6. A plot of the beam pattern of the array at 700MHz in both an ideal RFIenvironment (anechoic chamber) and in the field. Each of the plots is takenafter performing the calibration procedure described earlier. The abscissa isthe scan angle in degrees from broadside and the ordinate is an arbitrary powerscale relative to maximum signal power at the calibrated 0 degree pointing.

at 0 degrees obtained in the anechoic chamber overlaid witha beam at the same frequency obtained in the field.

We expect that the ‘field’ beam will be corrupted byeffects like structure scattering3 and the various analoguesystem effects. Figure 6 clearly shows that field calibrationand measurement results in a beam with significant errorcompared to the beam obtained in the anechoic chamber.

3where structure scattering is taken to mean signal reflection off arraystructures, ground planes and surrounding vegetation

C. Future Work

The extension to more elements and larger bandwidth is thenatural progression for this work. We are currently workingon the design of a 16 element, dual polarisation beamformer.

The full digital calibration of close-packed, strongly elec-tromagnetically coupled antenna arrays has been shown to bea challenging problem. We intend to develop a more robustcalibration scheme in order to achieve the high dynamicrange required of digital aperture arrays. Currently, we areinvestigating full-NxN correlation-based calibration for thistask.

VI. CONCLUSION

In this paper we propose that digital aperture arrays area fast, useful and elegant collector technology for GHzradio astronomy, that the development of high-performancesignal processing systems is critical to the success of next-generation radio instruments, and have described the designof a 4-element frequency-domain aperture array beamformer.

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