Normalized relationship among errors and sidelobe levels

This paper examines the effect of errors on the peak sidelobe level of a phased array. The sidelobe level distribution of the radiation pattern for both linear and planar arrays is seen to be Rician. A set of constant probability curves is presented which relates the allowable phase and amplitude errors with the allowable sidelobe level deterioration. Examples are presented to demonstrate how these curves can be used to design a low sidelobe array with a better tolerance of error. These curves, or extensions of them, provide a useful tool for the engineer designing an array antenna. For a planar array with correlated errors the total variance σ is the root-sum-square of the error in each element σ_μ (including both correlated and uncorrelated errors) and the contribution of correlated error in a subarray σ_c. Both σ_μ and σ_c are functions of the errors and the illuminations, but σ_c is also a function of the pattern of the subarray in which the errors are correlated.