1. Adaptive Filters for RFI Mitigation in Radioastronomy
M. Kesteven
Australia Telescope National Facility
IVS Symposium In Korea
New Technologies in VLBI
Nov, 2002

2. Outline What is an adaptive filter? How can it help radioastronomy?
Some implementations
Application to VLBI

3. Adaptive Filter (schematic)

4. Single Dish - Autocorrelation
Reference antenna
Parkes 64m

5. Synthesis Array Filtering

6. Critical Parameters
INR : the ratio of Interference power to System noise, in the reference channel.
tc : the time scale of the stability of the coupling: relative delay; multi-pathing; changing sidelobes.
A2I : the ratio of interference power in the astronomy channel to the interference in the reference channel.

7. Adaptive Filter – hardware version

8. Adaptive Filter - theory
Balance Increasing filter gain to improve RFI cancellation
Against Decreasing filter gain to reduce added noise from reference channel receiver.
Optimum leads to residual power with the RFI signature :

9. Adaptive Filter - features
Robust, automatic tracking of changing propagation characteristics
No added noise when RFI disappears
Multi-pathing handled correctly
Can treat multiple sources of RFI provided there is no frequency overlap.
Cancellation starts to fail when INR ~ 1

10. Post-Correlation filter

11. Post-Correlation filter
The interference in each channel can be written:
The coupling terms c(t), vary slowly, so can be extracted from each cross-product:

12. Post-Correlation filter
We combine three cross-products to get a good estimate of the interference in the Astronomical channel.
No total power products in the cross-products, thus no bias.
Noise*RFI products are also removed.
The signal/noise is set by the ratio of Correlated RFI to noise products -

13. A2I = 1.
(A2I*Tsys)

15. Post-Correlation Filter
Cancellation is exact (but noisy)
Cancellation starts to fail when

16. A2I = 1.

17. Post-Correlation Filter in an ARRAY

18. Connected-element Arrays
Correlator requirements: the reference antenna amounts to one additional station in the array.
The cancellation is enhanced by the phase tracking machinery.
The RFI mitigation is most important on the short calibration observations.

19. ATCA MHz; 4 MHz BW

20. Before and after images

21. RFI and VLBI
RFI generally does not correlate over VLBI baselines, so is less of a problem.
It will appear as increased noise, and so degrade the SNR.
An adaptive filter, by removing the RFI, will improve the SNR

22. Application to VLBI
RFI is only a problem when strong –> adaptive filter quite suitable

23. The planned wide bandwidths (eg, 1 GHz) will be a serious challenge to a simple adaptive filter.
At the observatory : Filter just the affected sub-bands.
Transport the reference IF to the correlator: only two additional cross-spectra required for each RFI source. Remove (Noise*RFI) products from the visibilities.

24. Conclusions Adaptive filters work well in radioastronomy
Post-correlation filters are preferred for
Single dish spectroscopy
Imaging arrays (connected element)
Hardware adaptive filters suitable for VLBI