Beyond-Diagonal Dynamic Metasurface Antenna

Dynamic metasurface antennas (DMAs) are an emerging technology for next-generation wireless base stations, distinguished by hybrid analog/digital beamforming capabilities with low hardware complexity. However, the coupling between meta-atoms is fixed in existing DMAs, which fundamentally constrains the achievable performance. Here, we introduce reconfigurable coupling mechanisms between meta-atoms, yielding finer control over the DMA's analog signal processing capabilities. This novel hardware is coined "beyond-diagonal DMA" (BD-DMA), in line with established BD-RIS terminology. We derive a physics-consistent system model revealing (correlated) "beyond-diagonal" programmability in a reduced basis. We also present an equivalent formulation in a non-reduced basis with (uncorrelated) "diagonal" programmability. Based on the diagonal representation, we propose a general and efficient mutual-coupling-aware optimization algorithm. Physics-consistent simulations validate the performance enhancement enabled by reconfigurable coupling mechanisms in BD-DMAs. The BD-DMA benefits grow with the mutual coupling strength.

Virtual VNA 3.1: Non-Coherent-Detection-Based Non-Reciprocal Scattering Matrix Estimation Leveraging a Tunable Load Network

We refine the recently introduced "Virtual VNA 3.0" technique to remove the need for coherent detection. The resulting "Virtual VNA 3.1" technique can unambiguously estimate the full scattering matrix of a non-reciprocal, linear, passive, time-invariant device under test (DUT) with $N$ monomodal ports using an $N_\mathrm{A}$-channel coherent wavefront generator and an $N_\mathrm{A}$-channel non-coherent detector, where $N_\mathrm{A}<N$. Waves are injected and received only via a fixed set of $N_\mathrm{A}$ "accessible" DUT ports while the remaining $N_\mathrm{S}$ "not-directly-accessible" DUT ports are terminated by a specific tunable load network. To resolve all ambiguities, an additional modified setup is required in which waves are injected and received via a known $2N_\mathrm{A}$-port system connected to the DUT's accessible ports. We experimentally validate our method for $N_\mathrm{A}=N_\mathrm{S}=4$ considering a non-reciprocal eight-port circuit as DUT. By eliminating the need for coherent detection, our work reduces the hardware complexity which may facilitate applications to large-scale or higher-frequency systems. Additionally, our work provides fundamental insights into the minimal requirements to fully and unambiguously characterize a non-reciprocal DUT.

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.