Examples of cyclostationary approaches for phased array radio

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 Prep. SKA (contract no 212243), ANR (contract ANR-09 -BLAN-0225 -04)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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