Modelling and manipulation of Polarimetric antenna beam patterns via spherical harmonics

Measured antenna responses, namely their beam patterns with respect to the vertical and horizontal polarizations, play a major role in realistic wireless channel modelling as well as in parameter estimation techniques. The representations commonly used suffer from drawbacks introduced by the spherical coordinate system which is affected by two knots at the poles. In general, all methods which describe the beam pattern with a matrix fail in correctly reproducing its inherent spherical symmetry. In this contribution we propose the use of the Spherical Fourier Transformation (SFT) which allows the description of the beam pattern via spherical harmonics. This mathematical tool, well known in other fields of science, is rather new to wireless communications. In this context, the main applications of the SFT include the efficient description of a beam pattern, noise filtering, the precise interpolation in the spherical Fourier domain, and the possibility to obtain an equivalent description of the beam pattern for an arbitrary coordinate system. The latter allows us to improve an existing 2-D FFT based technique: the Effective Aperture Distribution Function (EADF).