Identifying narrow-band mutual coupling resonances in SKA-low stations using frequency-independent current basis functions

Mutual coupling between closely spaced elements in aperture arrays introduces narrow-band spectral features in the Embedded Element Patterns (EEPs), threatening measurements of the 21-cm power spectrum with instruments such as SKA-low. We detail a method to identify such features through the construction of frequency-independent current basis functions, utilising a singular value decomposition of frequency-dependent basis functions. We demonstrate the method on a three-element linear array and full pseudo-random station of SKA log-periodic antennas and examine the current power induced by mutual coupling. For the pseudo-random layout station we note many narrow-band resonance features, including strong resonances at 50.8~MHz and 83.6~MHz, where the coupled power on the passive antennas can approach or exceed that of the excited antenna. Simulated delay power spectra for the SKA-low core show that observing in frequency bands including resonance features causes large foreground leakage within the delay power spectra, obscuring the EoR window. For the pseudo-random layout station with SKALA4.0 we identify two significant frequency bands from 59.2--76.2~MHz and 84.2--103.3~MHz which are free of contamination from current resonances, preserving the EoR window in these frequency ranges.