On the efficient implementation and time-updating of the linearly constrained minimum variance beamformer

The linearly constrained minimum variance (LCMV) method is an extension of the classical minimum variance distortionless response (MVDR) filter, allowing for multiple linear constraints. Depending on the spatial filter length and the desired frequency grid, a direct computation of the resulting spatial beampattern may be prohibitive. In this paper, we exploit the rich structure of the LCMV expression to find a non-recursive computationally efficient implementation of the LCMV beamformer with fixed constraints. We then extend this implementation by means of its time-varying displacement structure to derive an efficient time-updating algorithm of the spatial spectral estimate. Numerical simulations indicate a dramatic computational gain, especially for large arrays and fine frequency grids.