A sparse approach in partially adaptive linearly constrained arrays

In conventional partially adaptive linearly constrained minimum variance (LCMV) beamformer design the approach has been to represent the noise subspace with some reduced set of vectors, typically the eigenvectors associated with the largest eigenvalues of the noise covariance matrix. This, whilst yielding good performance, will not give the optimum performance for a given partially adaptive dimension. The paper presents an alternative method for selecting the “best” degrees of freedom to be retained in a partially adaptive design. The iterative algorithm described selects those degrees of freedom which minimize the beamformer output mean square error. This approach leads to a sparse structure for the transformation matrix, which when implemented in a generalize sidelobe canceller (GSC) structure will reduce the computational load. This approach also allows a reduction in adaptive dimension as compared to the eigenvector based approach. An illustrative example demonstrates the effectiveness of this method