Factorised Machine-Learning Inversion of 5G Coexistence Masks on Compact MIMO Apertures with Electrically Orthogonal Metamaterial Operators

Compact ultra-wideband (UWB) multiple-input multiple-output (MIMO) front-ends must stay matched over a wide continuum, reject licensed 5G interferers and remain uncorrelated at sub-wavelength spacing. This paper formulates coexistence as the inversion of a mask M = (N(f), I(f), rho-max, eta-min) and treats complementary split-ring resonators (CSRRs) and a split-ring resonator (SRR) fence as operators acting on electrically distinct regions. Sufficient conditions for a conditionally factorised inverse are derived (bounded interaction on the support of N(f), bounded cross-sensitivity and a well-conditioned rejection Jacobian), together with a first-order bound on the inversion error. The rejection factor is implemented by inverse regressors with a forward-consistency check and an out-of-domain detector (random forest and k-nearest neighbours, R-squared = 0.9825 and 0.9921 on unit-cell data); non-uniqueness is handled by selecting, among forward-consistent candidates, the geometry with the largest fabrication margin. While ten target specifications are queried across the C-band and WLAN windows, only the two fabricated unit cells have undergone dedicated full-wave and experimental validation, whereas the remaining eight are compared against their nearest training-set neighbours, leaving multi-target generalisation across the specification space only partially validated. A two-element FR4 prototype designed as an experimental testbed for the union of a C-band and a WLAN mask, with 10mm edge-to-edge spacing (0.07 wavelength at 2.1GHz and 0.097 at the 2.9GHz lower matched edge in full wave), is measured and scored against the mask. In measurement, frequency-domain coupling stays below −20 from 2.1 to about 14.8GHz (full wave: 67 % of the band). Rejection is the weak coordinate: the measured reflection of the two-port board peaks at about −9.5 in both stop-bands, against −2.9 and −2.0 in full wave, so the −10 criterion is met over about 44 % of the combined mask, and the C-band mask is covered only from about 3.9GHz. This partial compliance exposes the effects of uncompensated unit-cell-to-aperture transfer offsets, stop-band bandwidth mismatch and FR4 Q-factor damping, showing that the prototype demonstrates the diagnostic scoring pipeline rather than a fully compliant hardware realisation of coexistence-mask inversion. The four-configuration test, carried out in full wave at the fabricated design, shows an interaction residual (0.61 in magnitude norm) far above the rejection-margin threshold (0.019), so condition (C1) is not met and factorised inversion remains a strictly conditional formulation that is not experimentally validated by the current prototype. Moreover, because pattern-based correlation is evaluated only from simulated patterns at six spot frequencies (ECC at most 0.015) without measured pattern validation, and because group delay and fidelity factor have not been assessed, wideband performance claims are restricted to continuous-wave frequency-domain matching and isolation. The changes needed to close this gap, the tolerance budget of both cells and the validation that remains open are stated explicitly, and modelled results are separated from measured ones.