Tikhonov Source current reconstruction for NF/FF Transformation

What is it about?

Source current Reconstruction Method (SRM) is a field transformation technique in which the equivalent currents at the antenna aperture are reconstructed from the known radiated fields. In order to stabilize SRM equations and reduce the effect of measurement errors and noise, the Tikhonov SRM has been frequently used. However, finding the regularization parameter and solving the Tikhonov SRM equation has a high computational cost especially for large-scale problems or in the presence of both electric and magnetic currents. Here, a hybrid regularized least square minimum residual (LSMR) technique is proposed to implement the Tikhonov SRM equation. In this method, the Tikhonov SRM is applied on the Krylov subspace that is created by the LSMR iterative solver. The regularization parameter of the hybrid Tikhonov equation is determined at each iteration of the projected problem with the generalized cross-validation (GCV) method.

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Why is it important?

In this paper, a hybrid Tikhonov SRM for large-scale problem is proposed. This method is based on implementing the Tikhonov SRM equation on the Krylov subspace, which is created by the least square minimum residual (LSMR) iterative solver. The regularization parameters of the Tikhonov SRM are calculated by the standard GCV method at each iteration in the projected problem. Results of current reconstruction and NF/FF transformation with the proposed hybrid Tikhonov SRM are reported in the paper and compared with the standard Tikhonov SRM equation. It is shown in both simulation and measurement examples that a significant reduction in time consumption and computational cost is realized with the proposed hybrid method while all of the benefits of the standard Tikhonov SRM equation are preserved.

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