Random phase errors in arrays of line-source antennas

An analysis of phase errors in arrays of line-source antennas containing random dissimilarities in wave-guide cross section is presented. The expectation of the Fraunhofer power response is derived. A transformation is found which, through use of the central limit theorem, allows derivation of the complete probability distribution of the electric field in the side-lobe region. For errors small enough, the field is given very nearly by the Rice distribution. The results are used to relate manufacturing tolerance to side-lobe deterioration.