1. Examples of cyclostationary approaches for phased array radio telescopes R. Weber (Station de radioastronomie de Nançay / Université d’Orléans) R. Feliachi (Université d’Orléans) A.J. Boonstra (Astron) 1 Project PrepSKA (contract no 212243), ANR (contract ANR-09-BLAN-0225-04)

2. Outline Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 2 The context The cyclostationarity concept First example : Cyclic detectors Second example : Estimation and subtraction Third example : cyclic spatial filtering Conclusions and perspectives

3. Classic approach Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 3 Hypothesis : M-K 1 last eigenvectors dominant eigenvectors Signal subspace depending on RFI Noise subspace EVD Spatial filtering RFI detection (see papers from A. Leshem, A.J. Boonstra, A.J van der Veen) Illustration: Initial sky map filtered sky map M antennas K 1 RFI

4. General case issue Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 4 EVD dominant eigenvectors M-K 1 -K 2 last eigenvectors Signal subspace depending on cosmic sources +RFI (+ noise) Noise subspace Illustration with : Initial sky map filtered sky map

5. Outline Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 5 The context The cyclostationarity concept First example : Cyclic detectors Second example : Estimation and subtraction Third example : cyclic spatial filtering Conclusions and perspectives

6. Cyclostationarity concept Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 6 Stationary process Cyclostationary process  statistics are periodic  statistics time-independent T = hidden periodicity s(t) or n(t) r(t) Example : second order statistics   0 0 Cyclic correlation Cyclic signature Cyclic frequency Cyclic frequency In practice : Gardner and Giannakis

7. The multidimensional case Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 7 SVD dominant eigenvectors M-K 1 last eigenvectors Signal subspace depending on RFI Noise subspace Spatial filtering RFI detection Estimation & subtraction Cyclic correlation matrix

8. Outline Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 8 The context The cyclostationarity concept First example : Cyclic detectors Second example : Estimation and subtraction Third example : cyclic spatial filtering Conclusions and perspectives

9. Cyclic detectors Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 9 FFT 0 Several implementations: - Blind detector - Example at Westerbork telescope with GPS data

10. Cyclic detector performance Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 10 AM RFI, no cosmic sources Power fluctuations between antennas = 20%

11. Outline Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 11 The context The cyclostationarity concept First example : Cyclic detectors Second example : Estimation and subtraction Third example : cyclic spatial filtering Conclusions and perspectives

12. Estimation & subtraction (1) Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 12 Consider 1 BPSK RFI : 2) SVD 1) 3) OK for AM, BPSK + QAM if h(t) known 4) 5)

13. Estimation & subtraction (2) Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 13 Example of an AM RFI in the LOFAR band Simulation with a BPSK RFI AM Fake RFI

14. Outline Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 14 The context The cyclostationarity concept First example : Cyclic detectors Second example : Estimation and subtraction Third example : cyclic spatial filtering Conclusions and perspectives

15. Cyclic Spatial Filtering (1) Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 15 Spatial filtering: 1) projector cleaning:2) 1)SVD : 2)Extract the RFI subspace : 3)Since, Projector Estimation of : 1…KrKr 45 p eigenvalues eigenvectors Initial sky map filtered sky maps classic cyclic Simulations with 3 BPSK

16. Cyclic Spatial Filtering (2) Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 16 RFI : pager Example with real data from LOFAR

17. Conclusions & Perspectives Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL 17 - Robustness of the cyclic approach - Just replace R by R  in the classical algorithms - For some modulations, it is possible to estimate R rfi  performance analysis, impact on sky map  exhaustive tests on real data (LOFAR,…)  broadband issue.  “virtual reference antenna” approach Automatic cyclic beamformer array Clean signal + -