Finite-time performance of a quadratically constrained MVDR beamformer

The finite-time behavior of a quadratically constrained version of the minimum-variance, distortionless-response line-array beamformer is examined. An entity known as the weight ratio is defined and it is demonstrated that there are simple expressions that relate the weight ratio to the field scenario which explicitly take into account the finite-time misadjustment phenomenon. It is further demonstrated that holding the weight ratio to a value of about 0.5 produces an adaptive beamformer with a beneficial combination of robustness to nonideal situations (e.g., sensor misalignment, pointing errors, correlated interferers, misadjustment effects, etc.) while retaining the ability to adapt quickly in highly dynamic fields.