1. 1 Oguz Kazanci and Jeffrey Krolik Duke University Department of Electrical and Computer Engineering Durham, NC 27708 Supported by the CNTPO R&D Program Beam-Space Adaptive Compensation of Faulty Sensors in OTH Radar US-Australia MOA Meeting October 2005

2. 2 Array Beam Pattern with Missing Sensors Faulty receive elements can degrade the beam pattern significantly depending on their locations in the array. Beam pattern with 8 missing sensors exhibits 7 dB higher peak sidelobes and up to 20 dB higher off-angle sidelobes compared to a full array. Compensation of missing sensors intended to reduce leakage of interferences and azimuthally-dependent Doppler-shifted clutter into target directed beam.

3. 3 Element-Space Adaptive Channel Compensation (ACC) Using good sensors to MMSE interpolate missing elements does not explicitly minimize sidelobe leakage and thus only indirectly mitigates bad channels. Idea: Adaptively reconstruct full-array snapshot such that interference leakage into nominally quiet directions is minimized. Adaptive channel compensation (ACC) minimizes interference leakage into quiet plane-wave directions subject to the constraint that the data distortion at the good elements is within some tolerance. Effect of ACC is to make interferers look more like plane-waves across the full-array which can then be effectively nulled by conventional beamformer shading. Doppler Processing Compute Covariance Matrix Eigenvectors Detection Conventional Beamforming Missing Sensors Interpolation PBIQ data Output

4. 4 Doppler-Azimuth Spectrum Element-Apace ACC The Doppler-Azimuth plots for Conventional (left) and Elementspace ACC from 12 Dec, 2001. Dwell: 17:11:42 Note the sidelobes of the strong interference in the transmitter mainlobe leaking into other directions. With element-space ACC, sidelobe reduction greatest in transmitter sidelobe versus mainlobe region. Element-space ACC computation time prohibitive. E.g. 2 s to process 372 element array (1x372 data) for 124 Dwells, 128 Doppler bins; t = 124x128x2 sec = 8.8 hours!

5. 5 Beamspace Adaptive Channel Compensation Motivated by the need to constrain ACC to minimize leakage of interference into receive directions covered by the transmit mainlobe where target detection is performed. Beamspace ACC adaptively reconstructs the receive beams of the full array in the transmit mainlobe region so that strong directional components have minimal leakage into adjacent beams, subject to the constraint that data distortion at the good elements is within some tolerance. Beam-space ACC facilitates suppression of interferences which are present or have leaked into conventional receive beams. Because matrices to invert and decompose are of dimension equal to the number of beams (e.g. 18) vs. the number of elements (e.g. 372), beamspace ACC is much faster for large receive arrays. For ROTHR data, beamspace ACC is ~ 40 times faster than element-space ACC (e.g. what took 4 hours now takes 6 minutes) and 5 times faster than MMSE. Time per range/Doppler cell is 45 ms. Choice of tolerance parameter determines the trade-off between leakage of mainlobe clutter into adjacent beams and signal wavefront distortion.

6. 6 03 August 2004 PBIQ data 06:15:55 to 06:28:59 collected using ROTHR Virginia to illuminate the Kennedy space center. One of the receive shelters was offline, so 32 receivers near the middle of the array have gone bad. The geo-display on the left shows the location of the rocket at 06:18:59. 03 Aug 2004 Rocket Data Analysis Using BACC

7. 7 Identifying the Faulty Sensors Covariance matrix (averaged over all Doppler and range bins), indicates there are faulty sensors undetected by system. BACC software treats all sensors with normalized power above or below 3 dB deviation as faulty.

8. 8 Doppler vs. Dwell Displays for Rocket Launch Scroll Displays (Doppler vs. Time) at target range and azimuth showing the rocket movement from 06:15:55 to 06:19:15. Conventional (left) and BACC (right) Note that BACC shows a clean track of the rocket with reduced noise.

9. 9 Scroll Display for Conventional Processing Conventional Scroll Display Note the sidelobe levels especially at Dwells: 6, 8, 12, 21, 25, 29, 34 are reduced considerably using BACC. 34 29 25 21 12 8 6

10. 10 Scroll Display for Beamspace ACC Processing BACC Scroll Display Note the sidelobe levels especially at Dwells: 6, 8, 12, 21, 25, 29, 34 are reduced considerably using BACC. 34 29 25 21 12 8 6

11. 11 Conventional vs. BACC Range-Doppler Surface for Dwell 8 The Range-Doppler plots for Dwell 8 at 06:16:38 Conventional (left) BACC (right) The location of the rocket is shown with a circle. The rocket cannot be seen clearly using conventional procedure.

12. 12 Power vs. Range and Doppler Plots for Dwell 8 Range and Doppler cuts at target Doppler, Range for Dwell 8 at 06:16:38 The rocket is shown with the arrows. Range cut (left) for conventional (red) and BACC (blue) at Doppler: -10.78 Hz Doppler cut (right) for conventional (red) and BACC (blue) at Range bin: 41 Note the 10-15 dB reduction in the sidelobes with BACC.

13. 13 Conventional vs. BACC Range-Doppler Surface for Dwell 21 The Range-Doppler plots for Dwell 21 at 06:17:56 Conventional (left) BACC (right) The location of the rocket is shown with a circle. The rocket cannot be seen clearly using conventional procedure.

14. 14 Power vs. Range and Doppler Plots for Dwell 21 Range and Doppler cuts at target Doppler, Range for Dwell 21 at 06:17:56 Range cut (left) for conventional (red) and BACC (blue) at Doppler: -8.95 Hz Doppler cut (right) for conventional (red) and BACC (blue) at Range bin: 42 Note the reduced sidelobes and sharper peaks with BACC.

15. 15 Conventional vs. BACC Range-Doppler Surface for Dwell 29 The Range-Doppler plots for Dwell 29 at 06:18:45 Conventional (left) BACC (right) The rocket cannot be seen at all using conventional procedure. The sidelobes are reduced more than 10 dB and as a result the rocket can be seen with BACC.

16. 16 Power vs. Range and Doppler Plots for Dwell 29 Range and Doppler cuts at target Doppler, Range for Dwell 29 at 06:18:45 Range cut (left) for conventional (red) and BACC (blue) at Doppler: -10.58 Hz Doppler cut (right) for conventional (red) and BACC (blue) at Range bin: 42 Note that the target can be seen clearly with BACC.

17. 17 Conventional vs. BACC Range-Doppler Surface for Dwell 34 The Range-Doppler plots for Dwell 34 at 06:19:15 Conventional (left) BACC (right) The location of the rocket is shown with a circle. The rocket can be seen clearly using BACC.

18. 18 Power vs. Range and Doppler Plots for Dwell 34 Range and Doppler cuts at target Doppler, Range for Dwell 34 at 06:19:15 The rocket is shown with the arrows. Range cut (left) for conventional (red) and BACC (blue) at Doppler: -10.78 Hz Doppler cut (right) for conventional (red) and BACC (blue) at Range bin: 41 Note that the sidelobes are decreased significantly with BACC.

19. 19 Conventional vs. BACC Doppler-Azimuth Surface for Dwell 29 Doppler-Azimuth plots for the transmitter mainlobe region for Dwell 29 Conventional (left) and BACC (right) Rocket is shown with a circle. The sidelobe leakage from the directional interference into the other beams is reduced using ACC, as a result the target can be seen clearly.

20. 20 Conventional vs. BACC Doppler-Azimuth Surfaces for Dwell 23 Doppler-Azimuth plots for the transmitter mainlobe region for Dwell 23 Conventional (left) and BACC (right) The leakage of the sidelobes from the interference is reduced considerably

21. 21 Summary and Conclusion Adaptive channel compensation (ACC) of faulty sensors important when directional clutter and/or interference present. ACC performed on a single snapshot of post-Doppler processed data which avoids the training snapshot requirements of adaptive beamforming solutions. ACC proposed as a means of compensating the entire array so that strong interferers made to look more like uncorrelated plane-waves which can then be suppressed by conventional beamformer shading. Unlike element-space ACC, which suppresses the sidelobe leakage from all directions, Beam-space ACC is focused on the transmitter mainlobe where the detection is performed. The analysis of 03 Aug 2004 rocket launch data shows that BACC suppresses sidelobes as much as 10-15 dB in some dwells, and improves detection of the target significantly. Mathematical formulation of BACC can be applied to sparse array beamforming with potential application to 2-D receive arrays.