Modelling of radiation patterns using scalar spherical harmonics with vector coefficients

Antenna radiation patterns can be compactly represented using an expansion in spherical harmonic functions. In contrast to widely used expansions in vector spherical wave functions, we use an expansion in scalar spherical harmonics with vector coefficients to represent the vector-valued transverse electric far field (including arbitrary polarization state). The vector coefficients can be obtained using numerical integration or by a least-squares solution, the latter being also applicable to measurement data with incomplete angular coverage. Using the spherical harmonic representation, the rotation and interpolation of radiation patterns becomes very straightforward. The representation can also be used in signal processing algorithms.