1 / 27

Beamforming and Calibration with CASPER

Beamforming and Calibration with CASPER. Jack Hickish, University of Oxford CASPER Workshop 2009, Cape Town SA. Beamforming & Gateware Calibration. Introduction. CASPER for Students. CASPER for Students. CASPER for Students. Beamforming & Gateware Calibration. Jack Hickish.

loren
Télécharger la présentation

Beamforming and Calibration with CASPER

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Beamforming and Calibration with CASPER Jack Hickish, University of Oxford CASPER Workshop 2009, Cape Town SA

  2. Beamforming & Gateware Calibration Introduction CASPER for Students Jack Hickish

  3. CASPER for Students CASPER for Students Beamforming & Gateware Calibration Jack Hickish

  4. CASPER for Students CASPER as an educational tool. • CASPER is not just beamformers & correlators! Communications Radio / TV Jack Hickish

  5. Beamforming & Calibration CASPER for Students Beamforming & Gateware Calibration Jack Hickish

  6. Beamforming & Calibration DIGITAL BEAM Jack Hickish

  7. Beamforming & Calibration N-element Beamforming N-element Diffraction Jack Hickish

  8. Beamforming & Calibration I(θ) sin θ Jack Hickish

  9. Time Domain Beamforming Delay by integer FPGA clock periods Delay by integer ADC clock periods Interpolation between samples > > • Delay and Sum – simple, right? • Delay precision << 1/Bandwidth Jack Hickish

  10. Time Domain Beamforming • Integer FPGA periods • FIFO / Programmable Delay • Integer ADC periods • Reordering of demuxed ADC output • Interpolation • N tap FIR filter • Implementation on CASPER hardware (Nagpal, 2006) Jack Hickish

  11. Time Domain Beamforming • Calibration • Unwanted, uncontrollable “delays” introduced into the signal chains before digitisation Jack Hickish

  12. Time Domain Beamforming • 2PAD: delays between 4 analogue channels (D. Price & S. Schediwy, 2009) Jack Hickish

  13. Time Domain Beamforming Effect of calibration errors on station beam patterns (at 1GHz) (Price, Schediwy, 2009), as simulated in OSKAR (wiki.oerc.ox.ac.uk/OSKAR) 4x4 array (≈ 2PAD) 300x300 array (≈ SKA) Jack Hickish

  14. Time Domain Beamforming For a 4x4 array, with <5° pointing error, time delays calibration error <0.03ns (11°) at 1GHz Relative delays across band for 4 2PAD channels (Price & Schediwy, 2009) Jack Hickish

  15. Frequency Domain Beamforming • Before summing analogue inputs, channelise using FFT/PFB • Multiply data streams by complex phase and sum Jack Hickish

  16. Frequency Domain Beamforming Basic frequency domain beamforming algorithm… ADC FFT 10GbE ∫ X Beam Coefficients ADC FFT iBOB: 4 x 200MHz BW X Roach: 4 x 400MHz BW Jack Hickish

  17. Frequency Domain Beamforming Time delay errors (and other phase distortions) manifest themselves as relative phases between inputs. ADC FFT Conjugate BRAM ∫ Multiply Vector Accumulator ADC FFT Calibration for frequency dependent errors Jack Hickish

  18. Frequency Domain Beamforming • Beamforming coefficients are different for each spectral channel • - Can calibrate for dispersion/non-uniform delay errors across band Software Calibration Algortihm Implemented in Software Jack Hickish

  19. Frequency Domain Beamforming • A simple calibration algorithm… • Designate one signal the “reference”. • Compare phases of other channels to the “reference” – FX correlate • Use PC software to grab correlation result. • Calculate phase of result (which is “CASPER format” complex number) (arctan operation) • Generate pure phase “CASPER format” complex coefficients (sin/cos operation) • Upload coefficients to FPGA accessible memory. Jack Hickish

  20. Frequency Domain Beamforming Jack Hickish

  21. CORDIC Operations CO-ordinate Rotation DIgital Computer Efficient calculation of (amongst others) sine/cosine/arctan Eg. Sin/Cos Rotate initial vector (1,0) using rotation matrix Express sin θ, cos θ in terms of tan θ. Choose rotation angles, ß, such that tan(ß) = ±2-n Jack Hickish

  22. Frequency Domain Beamforming Calibration in gateware Jack Hickish

  23. Frequency Domain Beamforming Gateware calibration engine: Resource use, approx 5-10% of VirtexIIP Jack Hickish

  24. Frequency Domain Beamforming • Why calibrate in gateware? • Faster, and more reliable than uploading coefficients over ethernet • Elements (eg CORDIC sin/cos) of calibration engine can likely be used for rapid calculation and application of beamforming coefficients. • Less shared BRAM – less resource waste Jack Hickish

  25. Frequency Domain Beamforming Mean Error: 0.5 degrees Jack Hickish

  26. Gateware Beamforming How easy is CASPER, really? 4 input internally calibrated F-domain beamformer - Development time << 8 weeks Jack Hickish

  27. Gateware Beamforming “ one would assume that an FFT block has a base minimum sync pulse period equal to the FFT length… How easy is CASPER, really? 4 input internally calibrated F-domain beamformer - Development time << 8 weeks ” Jack Hickish

More Related