Deriving Mutual Impedance Matrix of a Large Antenna Array From Embedded Element Patterns With Measurement Noise

Measuring the in situ mutual impedance matrix (MIM) of a large phased array with a quasi-random element layout is a very challenging operation. A recently developed method for extracting the impedance matrix of a phased array of antennas from its embedded element patterns (EEPs) is implemented and tested with a cluster of 16 log-periodic antennas that served as a square kilometer array (SKA) prototype. The extraction algorithm is improved in its convergence with physics-based bounds based on the diagonally dominant structure of the impedance matrix. EEPs corrupted by noise arising both by random as well as propagation-related phenomena in a receiving system are then used to test the robustness of the method; such EEPs are artificially created, but the noise estimates from real on-site measurements are also used for comparison. The mutual impedance matrices extracted from the "noisy" radiation patterns at 110 and 320 MHz are accurate to within 2%-3%. This work has direct application to the SKA-Low telescope (SKA-Low).