Rapid Convergence Rate in Adaptive Arrays

TLDR

Adaptive arrays are limited by convergence rate, which must keep pace with external noise changes and worsens with many adaptive degrees and widely varying noise covariance eigenvalues. A theory based on Goodman’s work predicts the achievable convergence rate of the technique and has been verified by simulation. The direct method using a sample covariance matrix yields very rapid convergence regardless of eigenvalue distribution, and a theory based on Goodman’s work predicts this rate and has been verified by simulation.

Abstract

In many applications, the practical usefulness of adaptive arrays is limited by their convergence rate. The adaptively controlled weights in these systems must change at a rate equal to or greater than the rate of change of the external noise field (e.g., due to scanning in a radar if step scan is not used). This convergence rate problem is most severe in adaptive systems with a large number of degrees of adaptivity and in situations where the eigenvalues of the noise covariance matrix are widely different. A direct method of adaptive weight computation, based on a sample covariance matrix of the noise field, has been found to provide very rapid convergence in all cases, i.e., independent of the eigenvalue distribution. A theory has been developed, based on earlier work by Goodman, which predicts the achievable convergence rate with this technique, and has been verified by simulation.