Tracking of coherent broadband sources using adaptive directional filter with maximally flat responses at null directions

Abstract

A new algorithm for tracking coherent broadband sources in linear arrays employing tapped delay line processing is presented and investigated. To resolve M-directional broadband sources with a maximum coherent group size of M a , the original ( M + l)-element power inversion array is augmented by M a − 1 elements to result in a total of M a identical but spatially shifted ( M + l)-element subarrays. Using this technique, each broadband source is individually tracked in a cyclical time multiplexed manner, by steering a broadband null in each subarray formed from the use of a tapped delay line filter with weights constrained to have maximally flat frequency response at the nulling direction, to minimise the spatially averaged power output. Since the new algorithm updates only one tapped delay line filter at any instant, the overall implementation complexity of the proposed algorithm is comparable to that of using the LMS algorithm directly on a broadband array. However, unlike the latter algorithm, the new algorithm possesses a convergence behaviour that is significantly faster and almost independent of the external noise environment and provides the sources' directions directly without employing a root-finding routine.