N. G. Parhomenko

A regularization method is considered in the paper to solve the spatial localization problem for polarized electromagnetic field sources with the resolution higher than Rayleigh diffraction limit. A two-component vector of spatial distribution for source complex amplitudes is introduced, the vector components correspond to two independent field polarization. Bearing relief vector is introduced as the distribution of sources energy over the space. Regularizing functional is set up as a weighted sum of residual vector Euclidean norm for equation system for sources complex amplitude vector and stabilizing functional dependent to spatial energy distribution of the field sources. Condition for regularizing functional minimum leads to nonlinear equation system in source complex amplitudes, that can be deduced to equation system in source energy distribution. To solve the equation system the iterative method is used. A special case of quadratic regularization where the resolution is lower than the Rayleigh diffraction limit is considered. High resolution of the considered method is provided by stabilizing functional selection as an analogue of Holder norm for bearing relief. It provides the resolution higher than the Rayleigh diffraction limit without assumption about signal incoherence. A special case of regularization ignoring polarization that can be deduced to the well-known one is considered. Numerical simulation results for antenna array with the polarization-sensitive elements are given. It is shown that the proposed method that considers electromagnetic field vector character distinguishes the sources at low angular distance. The simulation results ignoring the polarization are also given, turning out to be unsatisfactory. Thus, the given method provides the source localization of polarized electromagnetic field with the resolution higher than Rayleigh diffraction limit, including the coherent signal sources.