A compensating beamformer which requires orders of magnitude fewer calculations that prior art methods. A compensating beamformer is provided which comprises a plurality of sensing elements and a plurality of analog-to-digital converters, for converting incoming analog signals to digital form. Digital signals from at least four such elements are used to compute phase angle information which is combined to form a matrix of input data in the frequency domain. An unweighted steering vector is determined to sample data from the target direction. A corrector matrix is calculated based on input data from sensing elements. That corrector matrix along with its inverse, which is determined recursively, is used in combination with the unweighted steering vector to determine an optimal steering vector. The input data in the frequency domain are then multiplied by the optimal steering vector to obtain signals in the directions of interest. In preferred embodiments of this invention these calculations are repeated systolically to provide optimal steering vector updates on an essentially real-time basis.