On the influence of incomplete radiation pattern data on the accuracy of a spherical wave expansion

The accuracy of a spherical wave expansion is examined when the expansion is calculated from incomplete data of the radiation pattern, i.e., when field data on a part of the far-field sphere is missing. The effect of antenna size and truncation index on the interpolation capacity of a SWE is examined by using an analytical expression for the radiation pattern of wire antennas of different lengths. The error of the SWE is seen to increase drastically when the smallest diameter of the dead zone surpasses the length of a period of the highest included wave function. The influence of the size and shape of the dead zone is studied by the aid of a measured pattern, of which a part of the field data is ignored. Two different ways are proposed for estimating the accuracy of the obtained SWE in a practical instance, when the field in the dead zone is unknown.