An online calibration method for superdirective arrays with unknown gain-phase errors

Superdirectivity is a very attractive option in array aperture constrained applications due to its high directivity and good angular discrimination. However, it is hardly applied in practice because of its extreme sensitivity to small random array errors. In this paper, we propose an online calibration method for superdirective arrays with gain-phase errors. Unlike the currently well-known robust superdirective solutions, which attempt to achieve a trade-off between the directivity factor and the sensitivity function, the proposed method could almost reach the theoretical superdirectivity after calibration. Our calibration method is based on orthogonal subspace theory and does not need any calibration sources. To assure the stability and accuracy of this method, an iterative process is applied. In addition, it can be applied to arbitrary geometric superdirective arrays with known sensor locations. At last, a widely used circular array is taken as an example to show the good performance and effectiveness of this method by numerical simulations.