Design of robust superdirective beamformer for circular sensor arrays

Two approaches to design robust superdirective beamformer for circular sensor arrays are presented in this paper. The first one is directly based on the eigen-decomposition of the circulant noise covariance matrix. Since the optimal solution can be accurately decomposed into sub-solutions denoted as eigenbeams and their robustness decreases with increasing of order number, a reduced-rank technique can be applied to obtain robust superdirectivity by truncating some error-intolerable high order eigenbeams. The results are all expressed in closed-form. The second approach is to formulate the beamformer as an optimization problem which can give an appropriate trade-off among directivity factor, sidelobe level and robustness. The robustness constraint parameter can be estimated from the performance of eigenbeams. Although it needs to be computed numerically, the computation efficiency can be improved using the properties of circular arrays. Experimental results show these two beamformers will provide good convenience to the practical implementation of robust high-order superdirectivity.