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

Introduction Beamforming Architectures Heirarchical Beamformer Design Tile-level Calibration Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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

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

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

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

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

Hierarchical Beamformer Design Compute to I/O ratio is low Beamformer resembles Network Switch Richard Armstrong – richard.armstrong@astro.ox.ac.uk

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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