An adaptive beamformer algorithm using a quadratic norm of the Poynting vector for vector sensor arrays

Abstract

An adaptive beamformer for vector sensor arrays (VSA's), which uses a quadratic norm of the acoustic Poynting vector (PV) and linear constraint on the PV itself, is introduced. The paradigm follows minimum variance distortionless response (MVDR) but now the metric to be minimized is a quartic function of the filter weights and the constraint is quadratic. This leads to numerical approaches for the optimization instead of a matrix inversion for MVDR. This exploration is motivated by the observation that many nonlinear processing methods lead to “better” performance when a signal is above some threshold SNR. Examples of these include split beam arrays, DIFAR's and monopulse systems. This presentation discusses the optimization method and compares the results for ABF with linear processing for VSA's. The use of linear and quadratic refer to the clairvoyant processing where the ABF uses ensemble covariances and leaves open the problem of sample covariance estimation. [Work supported by ONR Code 321, Undersea Signal Processing.]