Impact of Deformations on Beamforming Performance of Uniform Rectangular Arrays

Phased arrays often use a uniform rectangular array (URA) with phasing of the elements. In large phased arrays, deformations may occur due to fabrication tolerances and other influences, which will cause errors in the position of the antenna elements. The impact of such errors on the antenna pattern can be analyzed by sampling the distribution of the deformations and computing the mean radiation pattern (MRP). However, this will be time-consuming when the number of elements is large and it will not give much insight into the impact of the deformations. Here, an analytical expression is presented for the MRP of a deformed URA considering different distributions of the deformation in x, y, and z, including uniform distribution, normal distribution, and triangular distribution. As an example, the analytical expression is compared to Monte Carlo simulations for a 4 × 4 array and good agreement is observed. The analytical expression is further used to investigate the impact of the deformation on the pattern and the gain of a 4×4 and a 16× 16 array with isotropic elements under different distributions.