Scalable Multiport Antenna Array Characterization with PCB-Realized Tunable Load Network Providing Additional "Virtual" VNA Ports

We prototype a PCB-realized tunable load network whose ports serve as additional "virtual" VNA ports in a "Virtual VNA" measurement setup. The latter enables the estimation of a many-port antenna array's scattering matrix with a few-port VNA, without any reconnections. We experimentally validate the approach for various eight-element antenna arrays in an anechoic chamber in the 700-900 MHz regime. We also improve the noise robustness of a step of the "Virtual VNA" post-processing algorithms by leveraging spectral correlations. Altogether, our PCB-realized VNA Extension Kit offers a scalable solution to characterize very large antenna arrays because of its low cost, small footprint, fully automated operation, and modular nature.

Virtual VNA 3.0: Unambiguous Scattering Matrix Estimation for Non-Reciprocal Systems by Leveraging Tunable and Coupled Loads

We present the "Virtual VNA 3.0" technique for estimating the scattering matrix of a \textit{non-reciprocal}, linear, passive, time-invariant device under test (DUT) with $N$ monomodal ports using a single measurement setup involving a vector network analyzer (VNA) with only $N_\mathrm{A}<N$ ports -- thus eliminating the need for any reconnections. We partition the DUT ports into $N_\mathrm{A}$ "accessible" and $N_\mathrm{S}$ "not-directly-accessible" (NDA) ports. We connect the accessible ports to the VNA and the NDA ports to the "virtual VNA ports" of a VNA Extension Kit. This kit enables each NDA port to be terminated with three distinct individual loads or connected to neighboring DUT ports via coupled loads. We derive both a closed-form and a gradient-descent method to estimate the complete scattering matrix of the non-reciprocal DUT from measurements conducted with the $N_\mathrm{A}$-port VNA under various NDA-port terminations. We validate both methods experimentally for $N_\mathrm{A}=N_\mathrm{S}=4$, where our DUT is a complex eight-port transmission-line network comprising circulators. Altogether, the presented "Virtual VNA 3.0" technique constitutes a scalable approach to unambiguously characterize a many-port \textit{non-reciprocal} DUT with a few-port VNA (only $N_\mathrm{A}>1$ is required) -- without any tedious and error-prone manual reconnections susceptible to inaccuracies. The VNA Extension Kit requirements match those for the "Virtual VNA 2.0" technique that was limited to reciprocal DUTs.

Benefits of Mutual Coupling in Dynamic Metasurface Antennas for Optimizing Wireless Communications -- Theory and Experimental Validation

Dynamic metasurface antennas (DMAs) are a promising embodiment of next-generation reconfigurable antenna technology to realize base stations and access points with reduced cost and power consumption. A DMA is a thin structure patterned on its front with reconfigurable radiating metamaterial elements (meta-atoms) that are excited by waveguides or cavities. Mutual coupling between the meta-atoms can result in a strongly non-linear dependence of the DMA's radiation pattern on the configuration of its meta-atoms. However, besides the obvious algorithmic challenges of working with physics-compliant DMA models, it remains unclear how mutual coupling in DMAs influences the ability to achieve a desired wireless functionality. In this paper, we provide theoretical, numerical and experimental evidence that strong mutual coupling in DMAs increases the radiation pattern sensitivity to the DMA configuration and thereby boosts the available control over the radiation pattern, improving the ability to tailor the radiation pattern to the requirements of a desired wireless functionality. Counterintuitively, we hence encourage next-generation DMA implementations to enhance (rather than suppress) mutual coupling, in combination with suitable physics-compliant modeling and optimization. We expect the unveiled mechanism by which mutual coupling boosts the radiation pattern control to also apply to other reconfigurable antenna systems based on tunable lumped elements.

Updatable Closed-Form Evaluation of Arbitrarily Complex Multi-Port Network Connections

The design of large complex wave systems (filters, networks, vacuum-electronic devices, metamaterials, smart radio environments, etc.) requires repeated evaluations of the scattering parameters resulting from complex connections between constituent subsystems. Instead of starting each new evaluation from scratch, we propose a computationally efficient method that updates the outcomes of previous evaluations using the Woodbury matrix identity. To enable this method, we begin by identifying a closed-form approach capable of evaluating arbitrarily complex connection schemes of multi-port networks. We pedagogically present unified equivalence principles for interpretations of system connections, as well as techniques to reduce the computational burden of the closed-form approach using these equivalence principles. Along the way, we also achieve the closed-form retrieval of the power waves traveling through connected ports. We illustrate our techniques considering a complex meta-network involving serial, parallel and cyclic connections between multi-port subsystems. We further validate all results with physics-compliant calculations considering graph-based subsystems, and we conduct exhaustive statistical analyses of computational benefits originating from the reducibility and updatability enabled by our approach. Finally, we find that working with scattering parameters (as opposed to impedance or admittance parameters) presents a fundamental advantage regarding an important class of connection schemes whose closed-form analysis requires the treatment of some connections as delayless, lossless, reflectionless and reciprocal two-port scattering systems. We expect our results to benefit the design (and characterization) of large composite (reconfigurable) wave systems.

Mutual Coupling in Dynamic Metasurface Antennas: Foe, but also Friend

Dynamic metasurface antennas (DMAs), surfaces patterned with reconfigurable metamaterial elements (meta-atoms) that couple waves from waveguides or cavities to free space, are a promising technology to realize 6G wireless base stations and access points with low cost and power consumption. Mutual coupling between the DMA's meta-atoms results in a non-linear dependence of the radiation pattern on the DMA configuration, significantly complicating modeling and optimization. Therefore, mutual coupling has to date been considered a vexing nuance that is frequently neglected in theoretical studies and deliberately mitigated in experimental prototypes. Here, we demonstrate the overlooked property of mutual coupling to boost the control over the DMA's radiation pattern. Based on a physics-compliant DMA model, we demonstrate that the radiation pattern's sensitivity to the DMA configuration significantly depends on the mutual coupling strength. We further evidence how the enhanced sensitivity under strong mutual coupling translates into a higher fidelity in radiation pattern synthesis, benefiting applications ranging from dynamic beamforming to end-to-end optimized sensing and imaging. Our insights suggest that DMA design should be fundamentally rethought to embrace the benefits of mutual coupling. We also discuss ensuing future research directions related to the frugal characterization of DMAs based on compact physics-compliant models.

Multiport Network Theory for Modeling and Optimizing Reconfigurable Metasurfaces

Multiport network theory (MNT) is a powerful analytical tool for modeling and optimizing complex systems based on circuit models. We present an overview of current research on the application of MNT to the development of electromagnetically consistent models for programmable metasurfaces, with focus on reconfigurable intelligent surfaces for wireless communications.

A physics-compliant diagonal representation for wireless channels parametrized by beyond-diagonal reconfigurable intelligent surfaces

The parametrization of wireless channels by so-called "beyond-diagonal reconfigurable intelligent surfaces" (BD-RIS) is mathematically characterized by a matrix whose off-diagonal entries are partially or fully populated. Physically, this corresponds to tunable coupling mechanisms between the RIS elements that originate from the RIS control circuit. Here, we derive a physics-compliant diagonal representation for BD-RIS-parametrized channels. Recognizing that the RIS control circuit, irrespective of its detailed architecture, can always be represented as a multi-port network with auxiliary ports terminated by tunable individual loads, we physics-compliantly express the BD-RIS-parametrized channel as a multi-port chain cascade of i) radio environment, ii) static parts of the control circuit, and iii) individually tunable loads. Thus, the cascade of the former two systems is terminated by a system that is mathematically always characterized by a diagonal matrix. This physics-compliant diagonal representation implies that existing algorithms for channel estimation and optimization for conventional ("diagonal") RIS can be readily applied to BD-RIS scenarios. We demonstrate this in an experimentally grounded case study. Importantly, we highlight that, operationally, an ambiguous characterization of the cascade of radio environment and the static parts of the control circuit is required, but not the breakdown into the characteristics of its two constituent systems nor the lifting of the ambiguities. Nonetheless, we demonstrate how to derive or estimate the characteristics of the static parts of the control circuit for pedagogical purposes. The diagonal representation of BD-RIS-parametrized channels also enables their treatment with coupled-dipole-based models. We furthermore derive the assumptions under which the physics-compliant BD-RIS model simplifies to the widespread linear cascaded model.

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.

Training of Physical Neural Networks

Physical neural networks (PNNs) are a class of neural-like networks that leverage the properties of physical systems to perform computation. While PNNs are so far a niche research area with small-scale laboratory demonstrations, they are arguably one of the most underappreciated important opportunities in modern AI. Could we train AI models 1000x larger than current ones? Could we do this and also have them perform inference locally and privately on edge devices, such as smartphones or sensors? Research over the past few years has shown that the answer to all these questions is likely "yes, with enough research": PNNs could one day radically change what is possible and practical for AI systems. To do this will however require rethinking both how AI models work, and how they are trained - primarily by considering the problems through the constraints of the underlying hardware physics. To train PNNs at large scale, many methods including backpropagation-based and backpropagation-free approaches are now being explored. These methods have various trade-offs, and so far no method has been shown to scale to the same scale and performance as the backpropagation algorithm widely used in deep learning today. However, this is rapidly changing, and a diverse ecosystem of training techniques provides clues for how PNNs may one day be utilized to create both more efficient realizations of current-scale AI models, and to enable unprecedented-scale models.

Physics-compliant diagonal representation of beyond-diagonal RIS

Physics-compliant models of RIS-parametrized channels assign a load-terminated port to each RIS element. For conventional diagonal RIS (D-RIS), each auxiliary port is terminated by its own independent and individually tunable load (i.e., independent of the other auxiliary ports). For beyond-diagonal RIS (BD-RIS), the auxiliary ports are terminated by a tunable load circuit which couples the auxiliary ports to each other. Here, we point out that a physics-compliant model of the load circuit of a BD-RIS takes the same form as a physics-compliant model of a D-RIS-parametrized radio environment: a multi-port network with a subset of ports terminated by individually tunable loads (independent of each other). Consequently, we recognize that a BD-RIS-parametrized radio environment can be understood as a multi-port cascade network (i.e., the cascade of radio environment with load circuit) terminated by individually tunable loads (independent of each other). Hence, the BD-RIS problem can be mapped into the original D-RIS problem by replacing the radio environment with the cascade of radio environment and load circuit. The insight that BD-RIS can be physics-compliantly analyzed with the conventional D-RIS formalism implies that (i) the same optimization protocols as for D-RIS can be used for the BD-RIS case, and (ii) it is unclear if existing comparisons between BD-RIS and D-RIS are fair because for a fixed number of RIS elements, a BD-RIS has usually more tunable lumped elements.