Unit circle rectification of the MVDR beamformer
For signal processing applications using uniform linear arrays, this method offers a practical improvement in beamforming performance under limited snapshots.
The paper proposes a unit circle rectification technique for the MVDR beamformer that constrains the zeros of the weight array polynomial to lie on the unit circle, improving suppression of discrete interferers and white noise compared to the classic SMI beamformer and outperforming diagonally loaded MVDR in discrete interferer suppression.
The sample matrix inversion (SMI) beamformer implements Capon's minimum variance distortionless (MVDR) beamforming using the sample covariance matrix (SCM). In a snapshot limited environment, the SCM is poorly conditioned resulting in a suboptimal performance from the SMI beamformer. Imposing structural constraints on the SCM estimate to satisfy known theoretical properties of the ensemble MVDR beamformer mitigates the impact of limited snapshots on the SMI beamformer performance. Toeplitz rectification and bounding the norm of weight vector are common approaches for such constrains. This paper proposes the unit circle rectification technique which constraints the SMI beamformer to satisfy a property of the ensemble MVDR beamformer: for narrowband planewave beamforming on a uniform linear array, the zeros of the MVDR weight array polynomial must fall on the unit circle. Numerical simulations show that the resulting unit circle MVDR (UC MVDR) beamformer frequently improves the suppression of both discrete interferers and white background noise compared to the classic SMI beamformer. Moreover, the UC MVDR beamformer is shown to suppress discrete interferers better than the MVDR beamformer diagonally loaded to maximize the SINR.