Virtual VNA 2.0: Ambiguity-Free Scattering Matrix Estimation by Terminating Inaccessible Ports With Tunable and Coupled Loads

We recently introduced the "Virtual VNA" concept which estimates the $N \times N$ scattering matrix characterizing an arbitrarily complex linear system with $N$ monomodal ports by inputting and outputting waves only via $N_\mathrm{A}<N$ ports while terminating the $N_\mathrm{S}=N-N_\mathrm{A}$ remaining ports with known tunable individual loads. However, vexing ambiguities about the signs of the off-diagonal scattering coefficients involving the $N_\mathrm{S}$ not-directly-accessible (NDA) ports remained. If only phase-insensitive measurements were used, an additional blockwise phase ambiguity ensued. Here, inspired by the emergence of "beyond-diagonal reconfigurable intelligent surfaces" in wireless communications, we lift all ambiguities with at most $N_\mathrm{S}$ additional measurements involving a known multi-port load network. We experimentally validate our approach based on an 8-port chaotic cavity, using a simple coaxial cable as two-port load network. Endowed with the multi-port load network, the "Virtual VNA 2.0" is now able to estimate the entire scattering matrix without any ambiguity, even without ever measuring phase information explicitly. Potential applications include the characterization of antenna arrays.