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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 ), ANR (contract ANR-09-BLAN )

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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

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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

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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

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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

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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

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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

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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

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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

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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%

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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

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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)

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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

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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

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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

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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

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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 + -

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