Computing RMS and Integrated Array Sidelobes

This paper recommends a consistent and efficient approach to computing the integrated sidelobe ratio (ISLR) and the rms or mean sidelobe level of an antenna. In the proposed method, radiated power (electric field amplitude squared) is integrated on the surface of a hemisphere using spherical polar coordinates. The fields are measured at positions, however, that lie on a square grid in the u-v plane. The former ensures proper integration in physical beam space, while the latter provides uniform sampling of the main lobe and all sidelobes, since these all have the same size in the u-v plane. Compared to uniform sampling in spherical coordinates, u-v plane sampling requires fewer measurements for the same accuracy and has integration boundaries that do not change shape or size with scan. Expressions are presented in both one- and two-dimensional versions, together with an example of their use.