1. www.thalesgroup.com OPEN THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 © THALES UK LTD AND/OR ITS SUPPLIERS. THIS INFORMATION CARRIER CONTAINS PROPRIETARY INFORMATION WHICH SHALL NOT BE USED, REPRODUCED OR DISCLOSED TO THIRD PARTIES WITHOUT PRIOR WRITTEN AUTHORIZATION BY THALES UK LTD AND/OR ITS SUPPLIERS, AS APPLICABLE. Degradation of Covariance Reconstruction- Based Robust Adaptive Beamformers SSPD 2014 Samuel D. Somasundaram Maritime Mission Systems, Thales UK Andreas Jakobsson Department of Mathematical Statistics, Lund University, Sweden

2. 2 /2 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Overview of Presentation  Adaptive beamforming background  Covariance matrix reconstruction  Results  Conclusions

3. 3 /3 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Background  Beamformer (spatial filter)– combines sensor outputs to steer a receive beam in a specified direction  Array measurement model  MVDR  MPDR or Capon beamformer - does not require signal-free snapshots  Idea is to recover signal waveform

4. 4 /4 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Background  MPDR sensitive to errors in steering vector model and R estimate  Pointing errors, calibration errors, multipath propagation  More recently, covariance matrix reconstruction based approaches have been proposed  Reconstruct, IAA  Reconstruct  Reconstructs Q and inserts into MVDR equation  Rationale is that MVDR is less sensitive to SOI steering vector errors  IAA  Can be interpreted as reconstructing R and inserting into MPDR equation  Motivated diagonally loaded beamformers  Include worst-case optimisation, robust Capon beamformer

5. 5 /5 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Covariance matrix reconstruction 0180 0   Integrate spatial response over some angular region SOI Region Noise-plus-interference region  Reconstruct forms NPI covariance using Capon estimator Vector of angles sampling SOI region Vector of angles sampling NPI region  IAA can be viewed as reconstructing data covariance

6. 6 /6 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Algorithms Evaluated  Reconstruct Q using Capon estimator and insert into MVDR equation-> MVDR-Q-Capon  Reconstruct R using IAA estimator and insert into MPDR equation -> MPDR-R-IAA, IAA  Sample covariance based estimators MPDR-SCM and RCB-SCM  Recon-Est - MVDR-Q-Capon with additional robustness to SOI steering vector error  Reconstruct Q using IAA estimator and insert into MVDR equation- > MVDR-Q-IAA  Reconstruct R using Capon estimator and insert into MPDR equation -> MPDR-R-Capon

7. 7 /7 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Results – No steering vector errors 20 element ULA, K = 60 snapshots, 4 sources embedded in white Gaussian noise SOI is source nominally at 90 0 Covariance matrix reconstruction works well when there are no steering vector errors

8. 8 /8 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Results – AOA Error Only SOI now at 90-1.22 0 Reconstruction based on Capon estimator degrades significantly Reconstruction based on IAA estimator better Intf AOA Error Only SOI + Intf AOA Errors

9. 9 /9 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Results – Arbitrary Errors Intf Arbitrary Error Only All covariance matrix reconstruction highly sensitive to arbitrary steering vector errors

10. 10 /10 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Conclusions  Covariance matrix reconstruction based approaches highly sensitive to the structure of the noise-plus-interference  Previous results had not shown this sensitivity  SCM-based approaches insensitive to noise and interference structure  MPDR sensitive to SOI steering vector errors  Diagonal loading (e.g, in RCB) fixes the sensitivity to SOI steering vector errors  Noise plus-interference can take many forms and we often don’t really know its structure  Interference not necessarily point sources, could be near-field, platform etc.  In many realistic scenarios, diagonally loaded SCM based adaptive beamforming preferable to covariance matrix reconstruction

11. 11 /11 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Thank you for your time Any questions?

12. 12 /12 /11 THALES UK Ltd. SSPD 2014, Edinburgh, Sep. 2014 OPEN © THALES UK LTD. AND/OR ITS SUPPLIERS Subject to restrictive legend on title page Adaptive beamforming Theory – Frequency Domain Signal of interest can be written as Frequency-domain measurement can be written as