Non-uniform Antenna Loading Effect on Embedded Element Patterns and Application to Fault Detection

An iterative technique is presented to calculate the Embedded Element Pattern (EEP) transformation from a set of patterns computed for a uniform antenna port loading (scaled identity matrix) to a set of those computed for a non-uniform one (arbitrary diagonal matrix). Inverting this transformation to derive the non-uniform impedances of the arbitrary load leads to a new, efficient algorithm which disposes of the redundancy of the trivial use of all \( N \) EEPs at the faulty array condition, requiring only one such EEP for numerically stable impedance fault calculation. As the EEPs are envisioned to be obtained primarily through measurement, our method is also tested with the inclusion of various noise components and its convergence is evaluated, leading to suggested measurement apparatus SNR and fading levels, as well as the optimal choice of reference antenna to minimize the estimation error.