Adaptive Selective Sidelobe Canceller Beamformer

Transcription

1 Adaptive Selective Sidelobe Canceller Beamformer Radio Imaging With Strong Interfering Sources Ronny Levanda Supervisor: Prof. Amir Leshem Bar-Ilan Univ. Israel CALIM Aug 25, 2010 Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

2 Adaptive Selective Sidelobe Canceller Beamformer 1 Introduction 2 ASSC Rational 3 The ASSC Algorithm 4 Simulated Examples In FOV Interference Out-of-FOV strong interference 5 Preliminary Results of Radio Astronomical Measurements Abell 2256 Cassiopeia A 6 Summary Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

3 Introduction Visibility and the dirty image Radio telescope measures the correlation/visibility between antenna pairs. The classic dirty image is given by Î (l, m) = 1 M M q=1 V (u q, v q )e 2πj λ (uql+uqm) * l n m (u q, v q ) are the baselines at time t q. M is the number of measurements. V (u q, v q ) is the measured correlation (visibility) of the antenna pair. λ is the wavelength. (l, m) are the direction cosines. τ j τ j+1 Corr V(u,v) u w v Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

4 Matrix Based Approach Introduction Define R k (P P) the measured correlation matrix at epoch k R k (i, j) V (u k (i, j), v k (i, j)) a k (l, m) the array steering vector at epoch k where a k (l, m) e 2πj λ (uk 1,0 l+v k 1,0 m). e 2πj λ (uk P,0 l+v k P,0 m) P - the number of antennas in the array. (ui,0 k, v i,0 k ) - the location of antenna i at the k Th epoch, relative to some convenient point (u 0, v 0 ) Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

5 Introduction Matrix Based Approach Cont. The classic dirty image Î (l, m) = 1 M M q=1 V (u q, v q )e 2πj λ (uql+uqm) is mathematically equivalent to the classic (Bartlett) beamformer Î (l, m) = 1 K K wk H (l, m)r kw k (l, m) = 1 K k=1 K Î k (l, m) k=1 w k (l, m) = 1 P a k(l, m) MVDR (Minimum Variance Distortionless Response) adaptive beamformer w MVDR = arg min w wh Rw wmvdra H = 1 Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

6 Introduction Imaging Measured Visibility R 1, R 2,, R k Deconvolution Dirty Image Calculation The spatial resolution and accuracy of the dirty image is a limiting factor in the deconvolution process. Producing a better dirty image will result in a more accurate reconstructed image. Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

7 ASSC Rational ASSC Rational Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

8 ASSC Rational What Happens When the Array is Rotating R 1 R 2 t K t 2 t 1 v ii v ij v in v iq v * ij v jj v ii v jn v ij v jq v in v iq v * in v * jn v * ij v nn v jj v nq v jn v jq v * iq v * jq v * v * in nq v * jn v qq v nn v nq v iq * v jq * v nq * v qq i R K q j v ii v ij v in v iq n v ij * v jj v jn v jq v in * v jn * v nn v nq v iq * v jq * v nq * v qq Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

9 ASSC Rational What Happens When the Array is Rotating Cont. Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

10 ASSC Rational Illustrative Example Original image Classic dirty image East-West array with 20 antennas λ/2 spaced. Observation was done every 6 minutes for a 12-hour period. Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

11 ASSC Rational i j v ii v ij v in v iq v * in v * jn v * ij v nn v jj v nq v jn v jq v * iq v * jq v * v * in nq v * jn v qq v nn v nq v iq * v jq * v nq * v qq v ij * v jj v jn v jq v in * v jn * v nn v nq v iq * v jq * v nq * v qq Illustrative Example Cont. R 1 R 2 t K t 2 t 1 v * ij v jj v ii v jn v ij v jq v in v iq R K q v ii v ij v in v iq n Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

12 ASSC Rational Illustrative Example Cont. Number of pixels, a specific time epoch estimated the minimal power Classic beamformer MVDR beamformer Image contains pixels For the classic beamformer Most epochs (more than 90%) suffered from minimal interference for at least 661 pixels. Over 65% of epochs suffered from minimal interference for 90% of the pixels. For the MVDR beamformer Most epochs (more than 90%) suffered from minimal interference for at least 507 pixels. Over 45% of epochs suffered from minimal interference for 90% of the pixels. Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

13 ASSC Rational The Main Idea behind the ASSC For a specific direction (l, m) The dirty image intensity measured by most time ticks, is significantly higher due to interfering sources. Only the few time ticks that benefit from minimal interference, yield an unbiased intensity estimation. For each observation direction Choosing the time epoch with the minimal power, we choose the correlation matrix with the smallest interfering power, that happens to best suppress the interference. Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

14 The ASSC Algorithm The ASSC Algorithm Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

15 ASSC Algorithm Flow The ASSC Algorithm Measured Visibility R 1 Dirty Image #1 Measured Visibility R R 2 Dirty Image #2 For each pixel: Adaptive selection ASSC Dirty Image Measured Visibility R K Dirty Image #K Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

16 The ASSC Algorithm Calculate the dirty image for each time tick separately Measured Visibility R 1 Dirty Image #1 Î k (l, m) = w H k (l, m)r kw k (l, m). Measured Visibility R 2 Dirty Image #2 For each pixel: Adaptive selection ASSC Dirty Image Measured Visibility R K Dirty Image #K For the classic beamformer w k (l, m) = 1 P a k(l, m) For the MVDR beamformer w H MVDR(l, m) = a H k a H k (l, m)r 1 k (l, m)r 1 k a k(l, m). Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

17 The ASSC Algorithm Adaptive selection per pixel ASSC parameters k - the number of epochs to consider. µ k - their weight. Measured Visibility R 1 Measured Visibility R 2 Measured Visibility R K Dirty Image #1 Dirty Image #2 Dirty Image #K For each pixel: Adaptive selection ASSC Dirty Image Find the k minimal values among [Î1 (l, m),..., Î K (l, m)] [Î(1) (l, m),..., Î ( k) (l, m) ] The ASSC dirty image is Î ASSC (l, m) = k k=1 µ k Î (k) (l, m) Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

18 ASSC Parameters The ASSC Algorithm Classic beamformer for S 1 Classic beamformer for S 2 Original image - zoom in view MVDR beamformer for S 1 MVDR beamformer for S 2 k - number of epochs to consider Typically, k < 5%. The stronger the interference, the smaller the k µ k - epochs weight µ k+1 µ k k k=1 µ k = 1 Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

19 Simulated Examples Simulated Examples Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

20 Simulated Examples In FOV Interference In FOV Interference - 1D example Array with 20 antennas λ/2 spaced. Array rotation angle 0 o 90 o Measurement was done every 10 o k = 1, µ = 1. Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

21 Simulated Examples In FOV Interference In FOV Interference Classic dirty image ASSC classic dirty image Original image MVDR dirty image ASSC MVDR dirty image East-West array with 20 antennas λ/2 spaced. Measurement was done every 6 minutes for a 12-hour period. k = 3, µ k = 1 3. Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

22 Simulated Examples In FOV Interference In FOV Interference - Zoom In View Classic dirty image ASSC classic dirty image Original image MVDR dirty image ASSC MVDR dirty image Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

23 Simulated Examples Out-of-FOV strong interference Out-of-FOV Interference Interference stronger by 10, 000 than sources in the FOV Original image Classic dirty image ASSC classic dirty image East-West array with 20 antennas λ/2 spaced. Measurement was done every 6 minutes for a 12-hour period. Interference is stronger by 10, 000 than sources in FOV. k = 3, µ k = 1 3. MVDR dirty image ASSC MVDR dirty image Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

24 Simulated Examples Out-of-FOV strong interference Out-of-FOV Interference Interference stronger by 10 6 than sources in the FOV Original image Classic dirty image East-West array with 20 antennas logarithmically spaced 0 200λ. Measurement was done every minute for a 12-hour period. Interference is stronger by 10 6 than sources in FOV. k = 5, µ k = 1 k. MVDR dirty image ASSC MVDR dirty image Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

25 Preliminary Results of Radio Astronomical Measurements Preliminary Results of Radio Astronomical Measurements Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

26 Preliminary Results of Radio Astronomical Measurements Abell 2256 Abell 2256 Cleaned Images CLEAN using ASSC classic dirty image CLEAN using classic dirty image CLEAN using ASSC MVDR dirty image Observed by the VLA Single frequency bin around 1369 MHz T. Clarke and T. Ensslin, Deep 1.4 GHz very large array observations of the radio halo and relic in Abell Data was calibrated and provided by Prof. Huub Rottgering and Huib Intema Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

27 Preliminary Results of Radio Astronomical Measurements Cassiopeia A Cassiopeia A Cleaned Images CLEAN using classic dirty image CLEAN using ASSC classic dirty image Observed by the Allen Telescope Array Single frequency bin around 4.2 GHz. Data was calibrated and provided by Gerald Harp Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

28 Summary Summary We propose the Adaptive Selective Sidelobe Canceller beamformer - a novel method to produce a dirty image to be further processed by CLEAN or MEM. For interference dominant cases,the ASSC algorithm obtains images with higher spatial resolution and interference cancellation than either the classic and MVDR beamformers. The ASSC performance were demonstrated over simulated and radio astronomical data. Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29

29 Summary Thank you Ronny Levanda (BIU) ASSC beamformer CALIM Aug 25, / 29