Examples of cyclostationary approaches for phased array radio telescopes

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) Project PrepSKA (contract no 212243), ANR (contract ANR-09-BLAN-0225-04)

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

3. Classic approach Hypothesis : M antennas K1 RFI dominant eigenvectors Signal subspace depending on RFI EVD M-K1 last eigenvectors Noise subspace Illustration: RFI detection Spatial filtering (see papers from A. Leshem, A.J. Boonstra, A.J van der Veen) filtered sky map Initial sky map Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL

4. General case issue dominant eigenvectors Signal subspace depending on cosmic sources +RFI (+ noise) EVD M-K1-K2 last eigenvectors Noise subspace Illustration with : Initial sky map filtered sky map Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL

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

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

7. The multidimensional case Cyclic correlation matrix dominant eigenvectors Signal subspace depending on RFI SVD M-K1 last eigenvectors Noise subspace Estimation & subtraction Spatial filtering RFI detection Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL

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

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

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

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

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

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

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

15. Cyclic Spatial Filtering (1) Spatial filtering: 1) projector 2) cleaning: eigenvalues Estimation of : • SVD : • Extract the RFI subspace : • Since , • Projector 1 … Kr 4 5 p eigenvectors Initial sky map filtered sky maps Simulations with 3 BPSK classic cyclic Examples of cyclostationary approaches for phased array radio telescopes, R.Weber et al., RFI 2010, Groningen, NL

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

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