1. Some Design and Calibration Considerations for Dense Aperture Arrays
Richard Armstrong
CASPER WORKSHOP 2009
Cape Town

2. Introduction Beamforming Architectures Heirarchical Beamformer Design
Tile-level Calibration
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3. Radio Receiver Evolution
Arrays of Small Telescopes
Large Dishes
Aperture Arrays
Increasing order of complexity of electronics
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4. 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
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5. 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
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6. 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)
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7. Synchronous, Heirarchical Beamformer Design2
Synchronous, Heirarchical Beamformer Design
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8. Hierarchical Beamformer Design
Compute to I/O ratio is low
Beamformer resembles Network Switch
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9. 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
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10. XAUI Synchronisation 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 MHz 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)
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11. XAUI Synchronisation Design model Tutorial X
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
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12. Antenna Calibration at the Tile Level3
Antenna Calibration at the Tile Level
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13. 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
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14. Calibration at the Tile level
Aperture Array
Radiation Power Pattern
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15. Calibration at the Tile level
Scan angle in degrees from broadside
Power magnitude relative to maximum
W/bin (arbitrary power scale)
Angle (taking as reference)
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16. Calibration at the Tile level
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)
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17. 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.
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18. 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 required
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19. 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
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20. 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
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21. 4-element Calibration Comparison of Anechoic Beam with Field Beam
700MHz
Scan angle in degrees from broadside
Power magnitude relative to maximum
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22. 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)
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23. 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)
Richard Armstrong –

24. 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)
Richard Armstrong –

25. Flexibility Astronomy Signal Processors Thesis:
discrete flexibility is the gold standard
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26. Thanks
Questions?
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