Some Design and Calibration Considerations for Dense Aperture Arrays

Some Design and Calibration Considerations for Dense Aperture Arrays

Richard ArmstrongCASPER WORKSHOP 2009

Cape Town

ska.physics.ox.ac.uk

Introduction

Beamforming Architectures

Richard Armstrong – [email protected]

Heirarchical Beamformer Design

Tile-level Calibration


Radio Receiver Evolution

Large Dishes


Arrays of Small Telescopes

Aperture Arrays

Increasing order of complexity of

electronics


Dense Aperture Arrays

Spatial Nyquist sampling of the incident wavefront over the entire aperture.

Element spacing < λ/ 2 distinguishes dense AA from their sparse cousins.

Full wavefront sampling but less Aeff per receiver chain



Digital Beamforming Architectures

Time Delay Sub-sample delays (sample interpolation) Time delays are frequency independent Wide bandwidths => large analogue

variation

Spatial DFT 2-dimensional spatial transform on signal

subspace Computational advantage by using the FFT Usually most efficient for a multiplicity of

beams (exact number depending on FFT implementation)

Beam interpolation to obtain non-integral beams



Digital Beamforming Architectures

Narrowband Phase-shift Matrix-vector multiplication Set of complex steering and correction co-

efficients multiplied with incoming channelised signal

Implementation in dual-polarisation 16-el digital beamformer

Time-Space-Frequency Beamforming Interleaved frequency decomposition with beam

summing + steering. Each stage involves a frequency decomposition

and a space summation reduced quantisation errors within the time-

space-frequency processing engine See “Techniques of All-Digital Wideband

Beamforming,” Khlebnikov et al. 2009) Richard Armstrong – [email protected]


2

Synchronous, Heirarchical Beamformer

Design



Hierarchical Beamformer Design



XAUI Synchronisation

Perhaps the longest time spent on this! Specifically, determination of the error

model of XAUI links Synchronous clocking NRAO’s GUPPi digital engineers (Jason

Ray and John Ford) and others faced similar problems

Many within CASPER might be very strong advocates of (globally) asynchronous, loosely coupled systems for this reason

Decided on synchronous beamforming system




Solution: Synchronously clocked hardware:

All iBOBs clocked off same source Synchronised with known periodic pulse

(1PPS) iBOB to BEE2 clock conversion

Model of XAUI links: Maximum delay between separate links

composed of: A +-156.25MHz local clock, specific to

each Xilinx RocketIO transceiver. Transmit clock recovered at receive core 8b10b codec requires elastic buffers,

can result in +-3/4 clock misalignment (reported by NRAO)




Design model Either send in-stream sync pulse or

alignment tag Digital test bench for error model

design, check on actual hardware. Decided to use sync-pulse recovery

based model NRAO uses tag-based alignment and

reference stream

Tutorial X



3

Antenna Calibration at the Tile Level



Calibration at the Tile level

Why Calibrate? Sources of Error

Co-channel gain and phase deviation Mutual coupling effects Structure scattering Element location uncertainty Environmental effects





Radiation Power PatternAperture Arrayhttp://wiki.oerc.ox.ac.uk/oskar




Angle (taking as reference)

W/b

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Scan angle in degrees from broadside

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Full Analogue Characterisation1

Not always possible for all environmental variations

Correlator Full NxN or Nx1?

Signal Injection Loud, far-field source Companion-transmit scheme

Subspace-based Eigenstructure Methods


1. for more information, see Price and Schediwy (2009)


Analogue Characterisation

Fully characterise each RF component Each component characterised with vector

analyser Database of gain + phase for each

component, described by a scattering parameter matrix

S-parameter cascade to calculate full chain gain + phase modification

Good for a replaceable database model, initial calibration estimate

Fully characterise each chain May need to be completely re-done when

components are replaced or re-assembled

Issues: Environmental effects (temp, humidity, etc)

cause different analogue response.



Correlator Calibration

Nx1 correlator: calculate amplitude and phase of each

signal chain relative to a single chain Sensitive to individual ‘baseline’ or

antenna pair errors

NxN correlator? Overconstrained set of linear equations Robust solution set

But: Hardware Inefficiency (correlators are, if

anything, more complex than beamformers)

Signal duplication requiredRichard Armstrong – [email protected]


Subspace-based Calibration

Basic Idea: Iteratively estimate the array manifold

subspace Use this estimate to predict the array

manifold for all AoA

Requirements: At least 3 signal sources OR 1 moving signal source

As good as Correlator? Needs external signal, bright enough to

be seen above noise External processor needs access to raw

signals Less hardware Approximation to the true delay matrix



4-element Calibration Scheme


Signal injection calibration Fix reference channel Output power measured as

beamforming coefficients are swept for other channels

Create correction matrix (phase and amplitude) for each channel

Anechoic chamber vs. Field Structure scattering effects RFI Analogue chain not

predictable/stable


4-element Calibration


Scan angle in degrees from broadside

Pow

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Comparison of Anechoic Beam with Field Beam 700MHz


Ultimate Beamforming Architecture


What’s the best phased array beamforming architecture to build? Must include possibility of

calibration at the tile level An entire NxN correlator for an

N-element beamformer?!!

Thesis: one is better off calibrating

less often, but more accurately

Shoot down (if untrue)




















Flexibility

Astronomy Signal Processors Thesis:

discrete flexibility is the gold standard



Thanks

Questions?


Some Design and Calibration Considerations for Dense Aperture Arrays

Documents

electronicsrichard armstrong

architecturesrichard

cape townrichard armstrong

frequency processing

digital beamformertimespace

entire aperture

wavefront sampling

space summation