On the Numerical Instability of an LCMV Beamformer for a Uniform Linear Array

We analyze the conditions for numerical instability in the solution of a linearly constrained minimum variance (LCMV) beamformer with multiple directional constraints for a uniform linear array. An analytic expression is presented to determine the frequencies (for broadband signals such as speech) where the inverse term in the solution of the LCMV beamformer does not exist. Simulation results and power patterns are provided to further illustrate the problem. In addition, we investigate and discuss possible solutions to the problem.