Effects of failed elements on sidelobes of array beampatterns.

Abstract

It is common for arrays to degrade as elements fail, resulting in high sidelobes. The sensitivity of sidelobe levels to element failures is examined for an arbitrarily shaded array. Using the difference of complex beampatterns, it is found that the beampattern, which can be associated with just the failed elements, controls the degraded array response in the deep sidelobe region. Using results for addition of weighted random phasers, expressions are presented for an upper bound, the mean and standard deviation of the power sidelobes of the degraded array in terms of the number and shading weights of the failed elements. The upper bound depends on the percent of elements that fail and is independent of array size. The average sidelobe level depends on both the failed-to-good ratio and the number of remaining good elements, making large arrays more robust for the same percentage of failed elements. The standard deviation of sidelobe levels is approximately equal to the mean. The ratio of failed to remaining good elements is analogous to the combined amplitude and phase variance for uncorrelated tolerance errors. Combined effects of element failures and random amplitude and phase errors are then presented.