Fresnel-Zone Focused Antenna Arrays: Tolerance Analysis for Biomedical Applications

A detailed tolerance analysis for antenna arrays focused on the Fresnel zone is presented in this work, with the aim to derive the field distribution guaranteeing health safety issues. In particular, random errors related to the amplitudes and phases of the radiators, and random element failures, are considered. As such, the presented tolerance analysis falls within the more prominent theory of random arrays. A particular stochastic function related to the electric field distribution is analyzed and partially characterized by first- and second-order statistics. Subsequently, a discussion is carried out on the estimation of the cumulative distribution function (cdf) for the squared magnitude of the aforementioned random function. This leads to determine (confidence) level curves inherent to the squared magnitude of the electric field, representing a crucial aspect, in particular for safety issues in biomedical applications. The achieved results confirm the validity of the proposed approach, by extending also the literature for far-field focused arrays.