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Most high-resolution algorithms for sensor array processing require an eigendecomposition, which is a computation that is difficult to implement in parallel and requires O(M3) multiplications for an M×M matrix, corresponding to M sensors. Beamspace transformation is one way of reducing computation and sometimes improving the estimation accuracy. As a consequence of the beamspace transformation performed, however, arrays such as uniform linear arrays commonly used in direction finding lose their displacement invariance structure. As a result, computational complexity may actually increase since the computationally efficient ESPRIT algorithm cannot be applied directly. In this paper, a method for restoring the invariance structure resulting in a beamspace ESPRIT algorithm is described. Asymptotic performance analysis of beamspace ESPRIT and simulation results are presented as well