Projection Method for Inverse Problem in Antenna Measurement

In the article, the problems of determining the main characteristics of antennas are considered in the form of an inverse problem described by linear operator equations of the first kind. The solution of the inverse problem is realized within the framework of the numerical approach by reducing the operator equation to a matrix representation and searching for a solution using the least squares method. This is achieved by projecting the original function spaces onto the finite-dimensional subspaces formed by the linear span of the truncated Schauder basis. To obtain a solution using the least squares method, an iterative method is proposed, which is based on the procedure of projecting an element of a finite-dimensional space onto a hyperplane. The efficiency of the method is demonstrated by the example of solving the problem of restoring the far-field radiation pattern of a waveguide slotted antenna array and a horn antenna from near-field data calculated from electrodynamic antenna models in ANSYS HFSS. A quantitative assessment of the errors in the reconstruction of the far-field radiation patterns of various angular sectors has been carried out.