Degradation of Covariance Reconstruction-Based Robust Adaptive Beamformers SSPD 2014

1. Degradation of Covariance Reconstruction-Based Robust Adaptive BeamformersSSPD 2014 Samuel D. Somasundaram Maritime Mission Systems, Thales UK Andreas Jakobsson Department of Mathematical Statistics, Lund University, Sweden

2. Overview of Presentation • Adaptive beamforming background • Covariance matrix reconstruction • Results • Conclusions

3. Background • Array measurement model • Idea is to recover signal waveform • Beamformer (spatial filter)– combines sensor outputs to steer a receive beam in a specified direction • MVDR • MPDR or Capon beamformer - does not require signal-free snapshots

4. Background MPDR sensitive to errors in steering vector model and R estimate Pointing errors, calibration errors, multipath propagation • Motivated diagonally loaded beamformers • Include worst-case optimisation, robust Capon beamformer • 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

5. Covariance matrix reconstruction Integrate spatial response over some angular region Vector of angles sampling SOI region  SOI Region 0 1800 Noise-plus-interference region Vector of angles sampling NPI region • Reconstruct forms NPI covariance using Capon estimator • IAA can be viewed as reconstructing data covariance

6. 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 • 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 • Recon-Est - MVDR-Q-Capon with additional robustness to SOI steering vector error • Sample covariance based estimators MPDR-SCM and RCB-SCM

7. Results – No steering vector errors 20 element ULA, K = 60 snapshots, 4 sources embedded in white Gaussian noise SOI is source nominally at 900 Covariance matrix reconstruction works well when there are no steering vector errors

8. Results – AOA Error Only Intf AOA Error Only SOI now at 90-1.220 SOI + Intf AOA Errors Reconstruction based on Capon estimator degrades significantly Reconstruction based on IAA estimator better

9. Results – Arbitrary Errors Intf Arbitrary Error Only All covariance matrix reconstruction highly sensitive to arbitrary steering vector errors

10. Conclusions Covariance matrix reconstruction based approaches highly sensitive to the structure of the noise-plus-interference Previous results had not shown this sensitivity • 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. • 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 • In many realistic scenarios, diagonally loaded SCM based adaptive beamforming preferable to covariance matrix reconstruction

11. Thank you for your time Any questions?

12. Adaptive beamforming Theory – Frequency Domain Signal of interest can be written as Frequency-domain measurement can be written as