The statistics of antenna sidelobe distributions

This short note is intended to simplify and clarify the calculation of antenna sidelobe levels when random phase and amplitude errors are present. Curves are presented showing the distribution of sidelobes exceeding the ideal sidelobe level by a given margin. The note supplements, rather than supersedes, the work presented by Carlier (1979). To corroborate the statistical approach summarized by these distributions, examples are given of the effect of a range of random errors on the radiation pattern of an antenna array designed for 40 dB equal amplitude sidelobes.