Hybrid Tikhonov source current reconstruction method for large‐scale problems

Abstract

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. To stabilise SRM equations and reduce the effect of measurement errors and noise, the Tikhonov SRM has been frequently used. However, finding the regularisation parameter and solving the Tikhonov SRM equation have a high computational cost especially for large‐scale problems or in the presence of both electric and magnetic currents. Here, a hybrid regularised 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 regularisation parameter of the hybrid Tikhonov equation is determined at each iteration of the projected problem with the generalised cross‐validation method. Results of current reconstruction and near‐field/far‐field transformation with the proposed hybrid Tikhonov SRM are reported in this study and compared with the standard Tikhonov SRM. It is shown in both simulation and measurement examples that a significant improvement in the computational cost is realised with the proposed hybrid method while all of the benefits of the traditional method are preserved.

Phaseless near‐field to far‐field transformation based on source current reconstruction and signal subspace optimization

“…Recently a very fast and adaptive scheme for implementing the regularized SRM is proposed by the authors of this article. 12 In this technique, Tikhonov equation is applied to the Krylov subspace, which an iterative solver creates. The method is called a hybrid Tikhonov SRM and significantly reduces the computational cost of the conventional Tikhonov SRM.…”

“…After finding the deterministic currents from Equation (5), the ambiguous portion is calculated from several iterative forward and backward propagations with hybrid Tikhonov SRM. 12 The deterministic current found in the SOM procedure is used as a judicious initial guess of the iterative method. The detailed steps of the proposed phaseless SRM are shown in Figure 1.…”

“…To quantitatively compare the proposed method with the conventional methods, a far-field transformation error ε FF ð Þ is defined as follows 12 :…”

“…[1][2][3][4] The newest method which has more flexibility to select the acquisition and reconstruction domain is called the source current reconstruction method (SRM). [5][6][7][8][9][10][11][12][13] SRM is based on the reconstruction of the equivalent currents at the AUT aperture from the fullwave radiation integral equation. Regarding the flexibility of the SRM, this method is selected for the field transformation in this article.…”

“…Another problem with the phaseless NF to FF transformation is the ill-conditioning of the problem. [10][11][12][13] It means that the solutions of the problem are sensitive to measurement errors and noise. Therefore, a regularization technique should also be applied in the phaseless NF to FF transformation algorithms.…”