Tolerances in self-cohering antenna arrays of arbitrary geometry

In a conventional array, the location of each element must be known to an accuracy of about for phasing and scanning purposes. A larger tolerance on the element location results in the loss of gain and deterioration of the radiation pattern. In a self-cohering phased array, the phasing of the array elements is accomplished closed-loop and adaptively; therefore, no information on the element location is necessary. On the other hand, to scan the adaptively formed beam about the direction of the received wave, which has to be performed open-loop, one requires information on the element locations. In this paper, basic relations pertaining to the open-loop scanning of adaptive antenna arrays of arbitrary geometry are derived for both far-field and near-field scanning problems, and the transition between the two cases and the required accuracy in the knowledge of the same distance are explored. It is shown that the tolerance requirement on the element locations is the conventional tolerance divided by the maximum scan angle. In large systems designed for target imaging, it is shown that the tolerance on element location can be two or more orders of magnitude larger than that in a conventional array.