Insertion of diagonal loading into the multistage Wiener filter

Diagonal loading is a well-known technique for adding robustness to beamformer solutions. Diagonal loading will add robustness to steering vector direction-of-arrival mismatch; element position, gain, and/or phase perturbations; "statistical" mismatch due to finite sample support; etc. In a traditional sample matrix inversion implementation of the minimum variance distortionless response beamformer diagonal loading can be inserted by adding a scaled version of the identity matrix to the sample covariance matrix. Other adaptive beamformers (e.g. LMS) have their own approaches for adding diagonal loading. In this paper we describe how diagonal loading can be added to the multistage Wiener filter (MWF). Previous published results have developed one form of loading for the MWF called "error loading". In this paper we introduce two new forms of loading and show that each of these is equivalent to diagonal loading, whereas, error loading is distinct.