Robust beamforming using sensors with nonidentical directivity patterns

The optimal weights for a beamformer that provide maximum directivity, are often found to be severely lacking in terms of robustness. Although an ideal implementation of the beamformer with these weights provides high directivity, minor perturbations of the weights or of sensor placement cause severe degradation. Therefore, a robustness constraint is often imposed during the beamformer´s design stage. The classical method of diagonal loading is commonly used for this purpose. There are known results in this field which pertain to an array consisting of sensors with identical directivity-patterns and orientations. We extend these results to account for sensors with nonidentical directivity patterns, and sensors which share placement errors. We show that in such cases, modification of the classical loading scheme to incorporate nonidentical diagonal elements and off-diagonal elements is beneficial.