Title: Unit circle rectification of the MVDR beamformer,
Abstract: 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.