Reproducing Kernel Approximation for Electromagnetic Far Field Representation Without Prior Knowledge of the Radiation Source

An elementary method, which amalgamates Electromagnetic Theory and Complex Analysis, is proposed to obtain orthonormal basis in the total field strength (FS) space. The FS reconstruction problem could be defined as a nonlinear analogue of a functional decomposition into formal series. The FS function space could be represented as sum of a set of basis functions (known as electromagnetic features) computed from the formal series. Consequently, the total FS function can be decomposed in the span of repeating parameterized Szegö kernels, which are in the reproducing kernel Hilbert space. The quality of the proposed method is confirmed with different EM sources and sampling steps.