Optimal beamforming techniques for imperfectly calibrated arrays

Sonar image quality is typically limited by two factors: noise received at the array, or reverberation from directions outside each received beam. Optimal receive beamforming techniques have been developed for each of these two cases. Typically, the goal has been to optimize receive beam patterns rather than optimize composite beam patterns-formed from the product of the transmit beam and receive beam. The authors examine a typical insonification pattern, noise field, and reverberation field to derive optimization goal for the composite beam pattern. They show a closed-form solution for minimizing the signal energy received in each composite beam subject to the constraint that each beam must have a unit response in the desired direction. Next, they present an analysis to determine the sensitivity of the various optimal beamforming techniques to residual calibration errors