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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. - PowerPoint PPT Presentation
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Jack Hickish, University of OxfordCASPER Workshop 2009, Cape Town SA
Beamforming and Calibration with CASPER
CASPER for Students
Jack Hickish
Beamforming & Gateware Calibration
CASPER for Students
CASPER for Students
Jack Hickish
• CASPER is not just beamformers & correlators!
Communications
Radio / TV
CASPER as an educational tool.
Beamforming & Calibration
Jack Hickish
Beamforming & Gateware Calibration
CASPER for Students
Beamforming & Calibration
Jack Hickish
N-element Beamforming
N-element Diffraction
Time Domain Beamforming
Jack Hickish
• Delay and Sum – simple, right?
• Delay precision << 1/Bandwidth
Delay by integerFPGA clock periods
Delay by integerADC clock periods
Interpolationbetweensamples
> >
Time Domain Beamforming
Jack Hickish
• 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)
Time Domain Beamforming
Jack Hickish
Calibration
• Unwanted, uncontrollable “delays” introduced into the signal chains before digitisation
Time Domain Beamforming
Jack Hickish
2PAD: delays between 4 analogue channels (D.
Price & S. Schediwy, 2009)
Time Domain Beamforming
Jack Hickish
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)
Time Domain Beamforming
Jack Hickish
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)
Frequency Domain Beamforming
Jack Hickish
• Before summing analogue inputs, channelise using FFT/PFB
• Multiply data streams by complex phase and sum
Frequency Domain Beamforming
Jack Hickish
Basic frequency domain beamforming algorithm…
ADC X
Beam Coefficients
∫ 10GbEFFT
ADC XFFTiBOB: 4 x 200MHz BW
Roach: 4 x 400MHz BW
Frequency Domain Beamforming
Jack Hickish
Time delay errors (and other phase distortions) manifest themselves as relative phases between inputs.
ADC FFT
ADC FFT
Conjugate
Multiply ∫ BRAM
Vector Accumulator
Calibration for frequency dependent errors
Frequency Domain Beamforming
Jack Hickish
• Beamforming coefficients are different for each spectral channel- Can calibrate for dispersion/non-uniform delay errors across band
Implemented in SoftwareSoftware CalibrationAlgortihm
Frequency Domain Beamforming
Jack Hickish
A simple calibration algorithm…
1. Designate one signal the “reference”.
2. Compare phases of other channels to the “reference” – FX correlate
3. Use PC software to grab correlation result.
4. Calculate phase of result (which is “CASPER format” complex number) (arctan operation)
5. Generate pure phase “CASPER format” complex coefficients (sin/cos operation)
6. Upload coefficients to FPGA accessible memory.
CORDIC Operations
Jack Hickish
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
Frequency Domain Beamforming
Jack Hickish
Gateware calibration engine: Resource use, approx 5-10% of VirtexIIP
Frequency Domain Beamforming
Jack Hickish
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
Gateware Beamforming
Jack Hickish
How easy is CASPER, really?
4 input internally calibrated F-domain beamformer - Development time << 8 weeks
Gateware Beamforming
Jack Hickish
How easy is CASPER, really?
4 input internally calibrated F-domain beamformer - Development time << 8 weeks
one would assume that an FFT block has a base minimumsync pulse period equal to the FFT length…“
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