The model-based parameter estimation of antenna radiation patterns using windowed interpolation and spherical harmonics

Techniques previously reported for interpolating antenna radiation patterns simultaneously in both the spatial and frequency domains are reexamined here in order to develop new algorithms with improved efficiency and speed while maintaining comparable accuracy. To this end, interpolation in the frequency domain is constrained to a windowed scheme whereby a series of reduced-order Pade´ rational function fitting models of only three or four sampling frequencies are used to interpolate over a relatively large bandwidth. The use of this piece-wise technique is shown to reduce the complexity of determining the unknown coefficients without any significant loss in the resulting interpolation accuracy or increase in the required number of sampling frequencies. In this paper, exact analytical expressions are found for the unknown coefficients that allow the spatial domain interpolation to be performed entirely separate from the frequency domain interpolation. The technique is applied to the case of a 0.5 meter dipole modeled from 150 to 950 MHz, and for θ from 0° to 90°, using fitting windows with three and four sampling frequencies. The results are compared to those obtained using a previously developed generalized simultaneous interpolation procedure. In the spatial domain, spherical harmonics are introduced as model-based fitting functions for antenna radiation patterns. Specifically, interpolation procedures are developed using zonal harmonics and tesseral harmonics to model one- and two-dimensional far-field radiation patterns, respectively. The case of a z-oriented 0.5 meter dipole is considered to demonstrate the efficiency and accuracy obtained by applying these physically-based fitting models in the spatial domain. Zonal harmonics are used to interpolate far-field radiation patterns of this antenna for θ from 0° to 180° for several different frequencies over the range from 150 to 950 MHz. This example demonstrates the attractiveness of using spherical harmonics functions to accurately and efficiently interpolate radiation patterns in the spatial domain.