FPGA-based Dedispersion for Fast Transient Search

1. FPGA-based Dedispersionfor Fast Transient Search John Dickey 23 Nov 2005 Orange, NSW

2. ALTIUM, Ltd. corporate donation: FPGA application development software, nanoboard platform, design tools, and training, retail purchase price of everything ~$150,000. Partial funding by an ARC Discovery grant. UTas Staff: JD, Simon Ellingsen (senior lecturer) Eric Baynes (sr. electronics tech) Aidan Hotan (postdoc) Jamie Stevens (postdoc) three grad students (associated) David Warren (Altium and UTas) Brett Muir (design engineer) John Russell (digital engineer)

3. FPGA applications in Radio Astronomy • Pulsar and transient searches (dedispersion) • Autocorrelators (spectrometers) • Cross-correlators (interferometry, VLBI) • Data editing, calibration, mapping • Real-time adjustment of receivers, delays… • Multi-beaming, focal plane array processing • Studying the e-field at the Nyquist rate

4. UTas - Altium Board • design nearly finished (Brett Muir, John Russell) chips purchased, board fabrication in ~1.5 month • Xilinx virtex 4 - SX55 workhorse FPGA • Xilinx spartan 3 (for jtag chain) and virtex 2-pro (for control) • memory, ethernet, config devices • high speed scsi-2 input plus up/down links The goal: a general purpose board to replace all observatory backends!

5. 512 times: 55,296 times: Xilinx Virtex-4 SX55

6. August 2005 -- Aidan Hotan: Correlator Implementation Using Altium Virtex 4 SX35 daughterboard with nanoboard Device performs autocorrelation and cross correlation of RF input signals plus noise at speeds up to 80 M s/s. FPGA substrate provides latch in, shift register, multiply and accumulate, readout, and VGA graphics display. Embedded (simulated) processors provide program control.

7. S S S S S x x x x x x x x x S S x S S S S x x S digitised signal in multiply and accumulate autocorrelation function present data Fourier Transform using synthesized TSK3000 processor on-board FPGA Correlator Architecture shift with adjustable time step

8. February? 2006: Example of SX55 application: Fourier Transform Dedispersion digitised signal in FFT, bit-reverse, magnitude Dynamic Spectra Floating- point Processors latch shift at adjustable time step

9. Dedispersion from Dynamic Spectra time • Sum along dispersion lines • fast algorithm • addition (can use gates only) frequency timeseries

10. The Observing Frequency and the DM Determine the Storage and Computation Load t n Dn= N dn dt dn Nyquist Cells: dndt = 1/2

11. The Observing Frequency and the DM Determine the Storage and Computation Load t example: observing at 1.4 GHz Dt n Dn= N dn for DM=100, Dn = 100 MHz Dt = 30ms = 6000 dt where dt dn for N=1000 frequency channels, dt = 5 ms

12. Xilinx Virtex 4 SX55 This FPGA chip is effectively a 512 processor supercomputer,with a substrate of 55,296 logic cells

13. Speed is No Problem… For a 64 channel spectrum, the SX55 could use a DSP for every block. Thus it can compute a new spectrum every 4 clock cycles = 10 ns, for a sample rate of 0.16 ns, bandwidth of 3.2 GHz. For a 512 channel spectrum, the SX55 could use a DSP for every row. Thus it can compute a new spectrum every 36 clock cycles = 90 ns, for a sample rate of 0.18 ns, bandwidth of 2.8 GHz.

14. … so the DSP’s can do several jobs. time series thresholding, RFI suppression… For a 100 MHz bandwidth, the FPGA could take the Fourier transform 30 times in the N dt time it takes to collect the data.

15. Want Correlators? The EVLA correlator will handle 40 antennas (780 baselines) with 8 bands of 2 GHz each. This would require about 400 FPGA’s similar to the SX55, cost ~$500K (vs. $12M budget). The LN-SD SKA (~4000 antennas ?), say 107 baselines, BW ~ 1GHz(?) could be done with a few 104 Virtex 4’s. Today’s cost, a few 107 $. In 2015, by Moore’s Law, ~105 $. (This is without any grouping of the antennas into “stations”, and assuming direct FT rather than cross correlation.)

16. Conclusions • FPGA technology offers the advantages of the “software correlator”, i.e. to upgrade to new platforms without reworking the design. • Altium design tools make programming the FPGA as easy as … (as programming a computer?). • We can finally do our signal processing at the Nyquist rate, in real time!!