Spatial/Spectral filtering with linearly constrained minimum variance beamformers

In this paper, orthogonal low-dimension models for broad-band sources, as observed by an array/delay-line structure, are developed. The models are termed broad-band source representation spaces, and are subspaces of the observation space. They are generated from eigenstructures of source sample covariance matrices and represent sources efficiently in the 2nd-order statistical sense. For a single broad-band source, propagating in a pure delay environment and observed with an isotropic array, an accurate indication of the model dimension is derived which is independent on the array configuration, being a function of the observed source time-bandwidth product only. Using these representations, procedures are described for controlling the spatial and spectral response of linearly constrained minimum variance broad-band array/beamformers. The procedures employ linear constraints to control complex gain characteristics, over selected bands of frequency, for multiple points of 3-D regions of source locations and do not require the use of steering delays. The constraints are derived from source representation spaces and are termed eigenvector constraints. Simulations are presented which illustrate the effectiveness of the new linear constraints.