Resolution of coherent sources in power inversion arrays with a fast zero tracking algorithm

A fast zero tracking algorithm for resolving coherent sources in power inversion adaptive arrays is investigated. To resolve M directional sources with a maximum coherent group size of M _a, the original M+1 element power inversion array is augmented by M _a-1 elements to result in a total of M _a identical but spatially shifted M+1 element arrays. After performing some simple preprocessing, the M controlling zeros in these M _a arrays are adaptively updated in a time-multiplexed manner by using the LMS algorithm to minimise the spatially averaged output power to track the external environment. Since only one zero is adjusted at any instant, the new algorithm has almost the same implementation complexity as when the LMS algorithm is used directly. However, rather than having to use a foot-finding routine, the directions of the sources can be obtained directly from the zeros being updated in the new algorithm. Also, with the same asymptotic time constant for all the zeros, the new algorithm can be much faster than the conventional LMS algorithm, especially under situations where the eigenvalue spread of the element covariance matrix is large.<>