Adaptive beamforming using the multistage Wiener filter with a soft stop

To use adaptive beamforming in underwater acoustics, this paper considers processing data in short rank-deficient blocks so the moving interferers will not move as far per block. As a baseline algorithm, we consider the traditional minimum variance distortionless response (MVDR) formula using a data sample covariance matrix inversion (SMI) with diagonal loading added to limit the downward bias and signal cancellation associated with rank deficiency. As a new algorithm, we use the multistage Wiener filter (MWF) terminated with a "soft stop" to limit the downward bias and signal cancellation. The soft stop approach also applies to other adaptive filtering problems where the target signals are present in the training data.