Some Design and Calibration Considerations for Dense Aperture Arrays

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 Richard Armstrong – richard.armstrong@astro.ox.ac.uk

3. Radio Receiver Evolution Large Dishes Arrays of Small Telescopes Aperture Arrays Increasing order of complexity of electronics Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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 Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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 Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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) Richard Armstrong – richard.armstrong@astro.ox.ac.uk

7. 2 Synchronous, Heirarchical Beamformer Design Richard Armstrong – richard.armstrong@astro.ox.ac.uk

8. Hierarchical Beamformer Design Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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 Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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 +-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) Richard Armstrong – richard.armstrong@astro.ox.ac.uk

11. XAUI Synchronisation • 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 Richard Armstrong – richard.armstrong@astro.ox.ac.uk

12. 3 Antenna Calibration at the Tile Level Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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 Richard Armstrong – richard.armstrong@astro.ox.ac.uk

14. Calibration at the Tile level Aperture Array Radiation Power Pattern http://wiki.oerc.ox.ac.uk/oskar Richard Armstrong – richard.armstrong@astro.ox.ac.uk

15. Calibration at the Tile level W/bin (arbitrary power scale) Power magnitude relative to maximum Angle (taking as reference) Scan angle in degrees from broadside Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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) Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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. Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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 Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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 Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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 Richard Armstrong – richard.armstrong@astro.ox.ac.uk

21. 4-element Calibration • Comparison of Anechoic Beam with Field Beam • 700MHz Power magnitude relative to maximum Scan angle in degrees from broadside Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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) Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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 – richard.armstrong@astro.ox.ac.uk

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 – richard.armstrong@astro.ox.ac.uk

25. Flexibility • Astronomy Signal Processors • Thesis: • discrete flexibility is the gold standard Richard Armstrong – richard.armstrong@astro.ox.ac.uk

26. Thanks • Questions? Richard Armstrong – richard.armstrong@astro.ox.ac.uk