Effects of random errors on the performance of a linear butler array

A statistical analysis is presented which, assuming the errors in the beam forming matrix of a linear Butler array to be small independent Rayleigh-distributed random errors, indicates that the resultant power pattern has a modified Rayleigh distribution. The results of the analysis were then applied to determine the effects upon sidelobes and beam pointing yielding the following results. The allowable limits of phase and amplitude errors for a specified sidelobe deterioration are greatly reduced in comparison to the limits for an array whose elements are independently excited; furthermore, the limits are to a great extent independent of the number of elements in the array. The beam-pointing error is not severely affected and is inversely proportional to the number of elements. The nature of the results confirm what was to be expected from the periodic fashion in which errors within the matrix are distributed across the array.