Virtual VNA 2.0: Ambiguity-Free Scattering Matrix Estimation by Terminating Not-Directly-Accessible Ports With Tunable and Coupled Loads

We recently introduced the “virtual vector network analyzer (VNA)” concept, which estimates the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N \times N$ </tex-math></inline-formula> scattering matrix characterizing an arbitrarily complex linear reciprocal system with N monomodal lumped ports by inputting and outputting waves only via <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{\mathrm {A}}\lt N$ </tex-math></inline-formula> ports while terminating the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{\mathrm {S}}=N-N_{\mathrm {A}}$ </tex-math></inline-formula> remaining ports with known tunable individual loads. However, vexing ambiguities about the signs of the off-diagonal scattering coefficients involving the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{\mathrm {S}}$ </tex-math></inline-formula> 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 (BD-RISs)” in wireless communications, we lift all ambiguities with at most <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{\mathrm {S}}$ </tex-math></inline-formula> additional measurements involving a known multiport load network (MPLN). We experimentally validate our approach based on an eight-port chaotic cavity, using a simple coaxial cable as a two-port load network (2PLN). Endowed with the MPLN, the “Virtual VNA 2.0” now can estimate the entire scattering matrix without any ambiguity, even without ever measuring phase information explicitly. Potential applications include the challenging characterization of large and/or embedded antenna arrays.