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.

Minimal-Ambiguity Scattering Matrix Estimation with Load-Tunable Ports

We address the following generic wave problem: is the estimation of an arbitrarily complex linear $N$-port system's scattering matrix possible if waves can be input and output only via $N_\mathrm{A}<N$ ports while the remaining $N_\mathrm{S}=N-N_\mathrm{A}$ ports are terminated with tunable loads? Fundamentally, this problem is intriguing because it ultimately probes to what extent inherent structure in Maxwell's equations constrains the scattering coefficients. Various limited versions of the problem are of temporary scientific and technological interest, ranging from optimal non-invasive focusing on perturbation-inducing targets in complex media, via the characterization of miniaturized, embedded, receive-only and/or multi-element antenna systems to physics-compliant end-to-end channel models for complex metasurface-programmable "smart radio environments". More generally, solutions to the problem may yield promising measurement techniques to characterize an arbitrary linear $N$-port system with an $N_\mathrm{A}$-port measurement device, where $N_\mathrm{A} \ll N$. We show theoretically that if $N_\mathrm{A}\geq 2$ and at least three distinct tunable loads are available, the problem can be solved except for sign ambiguities on the off-diagonal scattering coefficients involving the $N_\mathrm{S}$ not-directly-accessible (NDA) ports. If the transmission from at least one accessible port to the NDA ports can be measured, the sign ambiguity can be lifted. We corroborate our results with microwave experiments on an 8-port chaotic cavity with $N_\mathrm{A}=N_\mathrm{S}=4$. Moreover, we reveal additional constraining structure in Maxwell's equations by showing that a limitation to phase-insensitive measurements only results in a mild additional blockwise phase ambiguity that can be lifted simultaneously with the sign ambiguity.

Optimal blind focusing on perturbation-inducing targets in sub-unitary complex media

The scattering of waves in a complex medium is perturbed by polarizability changes or motion of embedded targets. These perturbations could serve as perfectly non-invasive guidestars for focusing on the targets. In this Letter, we theoretically derive a fundamental difference between these two perturbation types (the change of the scattering matrix is of rank one [two] for target polarizability changes [motion]) and identify accordingly optimal strategies to perfectly focus on the target in both cases. For target motion, at least two displacements are necessary. Furthermore, for the case of dynamic complex media additionally featuring parasitic perturbers, we establish a non-invasive scheme to achieve optimal time-averaged power delivery to a perturbation-inducing target. In all cases, no assumptions about the unitarity of the system's scattering matrix or the size of the perturbation are necessary. We experimentally demonstrate all results in the microwave regime using a strongly sub-unitary lossy chaotic cavity as complex medium. Our experiments highlight that the target's "structural scattering" is irrelevant [must be negligible] in the case of target polarizability changes [motion]. We expect our results to find applications in communications, cybersecurity, bioelectronics, flow-cytometry and self-propelled nano-swimmers.

Over-the-Air Emulation of Electronically Adjustable Rician MIMO Channels in a Programmable-Metasurface-Stirred Reverberation Chamber

We experimentally investigate the feasibility of evaluating multiple-input multiple-output (MIMO) radio equipment under adjustable Rician fading channel conditions in a programmable-metasurface-stirred (PM-stirred) reverberation chamber (RC). Whereas within the "smart radio environment" paradigm PMs offer partial control over the channels to the wireless system, in our use case the PM emulates the uncontrollable fading. We implement a desired Rician K-factor by sweeping a suitably sized subset of all meta-atoms through random configurations. We discover in our setup an upper bound on the accessible K-factors for which the statistics of the channel coefficient distributions closely follow the sought-after Rician distribution. We also discover a lower bound on the accessible K-factors in our setup: there are unstirred paths that never encounter the PM, and paths that encounter the PM are not fully stirred because the average of the meta-atoms' accessible polarizability values is not zero (i.e., the meta-atoms have a non-zero "structural" cross-section). We corroborate these findings with experiments in an anechoic chamber, physics-compliant PhysFad simulations with Lorentzian vs "ideal" meta-atoms, and theoretical analysis. Our work clarifies the scope of applicability of PM-stirred RCs for MIMO Rician channel emulation, as well as electromagnetic compatibility test.

RIS-Parametrized Rich-Scattering Environments: Physics-Compliant Models, Channel Estimation, and Optimization

The tunability of radio environments with reconfigurable intelligent surfaces (RISs) enables the paradigm of smart radio environments in which wireless system engineers are no longer limited to only controlling the radiated signals but can in addition also optimize the wireless channels. Many practical radio environments include complex scattering objects, especially indoor and factory settings. Multipath propagation therein creates seemingly intractable coupling effects between RIS elements, leading to the following questions: How can a RIS-parametrized rich-scattering environment be modelled in a physics-compliant manner? Can the parameters of such a model be estimated for a specific but unknown experimental environment? And how can the RIS configuration be optimized given a calibrated physics-compliant model? This chapter summarizes the current state of the art in this field, highlighting the recently unlocked potential of frugal physical-model-based open-loop control of RIS-parametrized rich-scattering radio environments.

Systematic Physics-Compliant Analysis of Over-the-Air Channel Equalization in RIS-Parametrized Wireless Networks-on-Chip

Wireless networks-on-chip (WNoCs) are an enticing complementary interconnect technology for multi-core chips but face severe resource constraints. Being limited to simple on-off-keying modulation, the reverberant nature of the chip enclosure imposes limits on allowed modulation speeds in sight of inter-symbol interference, casting doubts on the competitiveness of WNoCs as interconnect technology. Fortunately, this vexing problem was recently overcome by parametrizing the on-chip radio environment with a reconfigurable intelligent surface (RIS). By suitably configuring the RIS, selected channel impulse responses (CIRs) can be tuned to be (almost) pulse-like despite rich scattering thanks to judiciously tailored multi-bounce path interferences. However, the exploration of this "over-the-air" (OTA) equalization is thwarted by (i) the overwhelming complexity of the propagation environment, and (ii) the non-linear dependence of the CIR on the RIS configuration, requiring a costly and lengthy full-wave simulation for every optimization step. Here, we show that a reduced-basis physics-compliant model for RIS-parametrized WNoCs can be calibrated with a single full-wave simulation. Thereby, we unlock the possibility of predicting the CIR for any RIS configuration almost instantaneously without any additional full-wave simulation. We leverage this new tool to systematically explore OTA equalization in RIS-parametrized WNoCs regarding the optimal choice of delay time for the RIS-shaped CIR's peak. We also study the simultaneous optimization of multiple on-chip wireless links for broadcasting. Looking forward, the introduced tools will enable the efficient exploration of various types of OTA analog computing in RIS-parametrized WNoCs.

Experimentally realized physical-model-based wave control in metasurface-programmable complex media

The reconfigurability of radio environments with programmable metasurfaces is considered a key feature of next-generation wireless networks. Identifying suitable metasurface configurations for desired wireless functionalities requires a precise setting-specific understanding of the intricate impact of the metasurface configuration on the wireless channels. Yet, to date, the relevant short and long-range correlations between the meta-atoms due to proximity and reverberation are largely ignored rather than precisely captured. Here, we experimentally demonstrate that a compact model derived from first physical principles can precisely predict how wireless channels in complex scattering environments depend on the programmable-metasurface configuration. The model is calibrated using a very small random subset of all possible metasurface configurations and without knowing the setup's geometry. Our approach achieves two orders of magnitude higher precision than a deep learning-based digital-twin benchmark while involving hundred times fewer parameters. Strikingly, when only phaseless calibration data is available, our model can nonetheless retrieve the precise phase relations of the scattering matrix as well as their dependencies on the metasurface configuration. Thereby, we achieve coherent wave control (focusing or enhancing absorption) and phase-shift-keying backscatter communications without ever having measured phase information. Finally, our model is also capable of retrieving the essential properties of scattering coefficients for which no calibration data was ever provided. These unique generalization capabilities of our pure-physics model significantly alleviate the measurement complexity. Our approach is also directly relevant to dynamic metasurface antennas, microwave-based signal processors as well as emerging in situ reconfigurable nanophotonic, optical and room-acoustical systems.