Frequency-domain implementation of Griffiths–Jim adaptive beamformer

Abstract

It is well known that the drawback of the time-domain least-mean-square (LMS) algorithm proposed by Widrow [Proc. IEEE 63, 719–720 (1975)] in adaptive filter applications is that its convergence speed decreases as the eigenvalue spread of the input autocorrelation matrix increases. However, this problem can be overcome by employing the transform-domain LMS method [Narayan et al., IEEE Trans. ASSP 31, 609–615 (1983)] which first transforms input time-domain signals into another transform-domain signals through DFT or some orthogonal transforms and then uses the self-orthogonalizing algorithm [Gitlin and Magee, IEEE Trans. Commun. 25, 666–672 (1977)] to optimize the variable weights of an adaptive filter. This method has been shown to offer great improvement in convergence rate over the time-domain LMS method. The objective of this paper is to apply the frequency-domain LMS algorithm with the self-orthogonalizing technique, called FLMS, to the Griffiths–Jim adaptive beamformer to accelerate the convergence rate for real-time processing of adaptive array signals. It is shown that the two minimum mean-square errors of the beamformer implemented in the time and frequency domains are identical. Computer simulations show that the adaptive beamformer using the FLMS exhibits faster convergence behavior and better performance of nulling jammers than that using the LMS, especially for the larger eigenvalue spread.