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Optimizing a real-life RIS-parametrized wireless channel with a physics-consistent multiport-network model necessitates prior remote estimation of the mutual coupling (MC) between RIS elements. The number of MC parameters grows quadratically with the number of RIS elements, posing scalability challenges. Because of inevitable ambiguities, independently estimated segments of the MC matrix cannot be easily stitched together. Here, by carefully handling the ambiguities, we achieve a separation of the full estimation problem into three sequentially treated sets of smaller problems. We partition the RIS elements into groups.First, we estimate the MC for one group as well as the characteristics of the available loads.Second, we separately estimate the MC for each of the remaining groups, in each case with partial overlap with an already characterized group.Third, we separately estimate the MC between each distinct pair of groups. Full parallelization is feasible within the second and third sets of problems, and the third set of problems can furthermore benefit from efficient initialization. We experimentally validate our algorithm for a 4 × 4 MIMO channel parametrized by a 100-element RIS inside a rich-scattering environment. Our experimentally calibrated 5867-parameter multiport-network model achieves an accuracy of 40.5 dB, whereas benchmark models with limited or no MC awareness only reach 16.9 dB and 13.8 dB, respectively. Based on the experimentally calibrated models, we optimize the RIS for five wireless performance indicators. Experimental measurements with the optimized RIS configurations demonstrate only moderate benefits of MC awareness in RIS optimization in terms of the achieved performance. However, we observe that limited or no MC awareness markedly erodes the reliability of model-based predictions of the expected performance.

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-compliantdiagonalrepresentation for BD-RIS-parametrized channels. We recognize that any RIS control circuit can always be separated into its static parts (SLC) and a set of tunable individual loads (IL). Therefore, a BD-RIS-parametrized channel results from the chain cascade of three systems:i)radio environment (RE),ii)SLC, andiii)IL. RE and SLC are static non-diagonal systems whose cascade K is terminated by the tunable diagonal system IL. This physics-compliant representation in terms of K and IL is directly analogous to that for conventional (“diagonal”) RIS (D-RIS). Therefore, scenarios with BD-RIS can also readily be captured by the physics-compliant coupled-dipole model PhysFad, as we show. In addition, physics-compliant algorithms for system-level optimization with D-RIS can be directly applied to scenarios with BD-RIS. We demonstrate this important implication of our conceptual finding in a case study on end-to-end channel estimation and optimization in a BD-RIS-parametrized rich-scattering environment. Our case study is the first experimentally grounded system-level optimization for BD-RIS: We obtain the characteristics of RE and IL from experimental measurements and a commercial PIN diode, respectively. Altogether, our physics-compliant diagonal representation for BD-RIS enables a paradigm shift in how practitioners in wireless communications and signal processing implement system-level optimizations for BD-RIS because it enables them to directly apply existing physics-compliant D-RIS algorithms.

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 and conduct a performance evaluation in terms of the bit error rate. Looking forward, the introduced tools will enable the efficient exploration of various types of OTA analog computing in RIS-parametrized WNoCs.

The wireless channel is a linear input-output relation that depends non-linearly on the RIS configuration: physics-compliant models involve the inversion of an “interaction” matrix. We identify two independent origins of this structural non-linearity:i) proximity-induced mutual coupling between close-by RIS elements;ii) reverberation-induced long-range coupling between all RIS elements arising from multi-path propagation in complex radio environments. Mathematically, we cast the “interaction” matrix inversion as the sum of an infinite Born series [fori)] or Born-like series [forii)] whoseKth term physically represents paths involvingKbounces between the RIS elements [fori)] or wireless entities [forii)]. We identify the key physical parameters that determine whether these series can be truncated after the first and second term, respectively, as tacitly done in common cascaded models of RIS-parametrized wireless channels. We also quantify the non-linearity of a channel’s RIS parametrization in diverse numerical and experimental radio environments ranging from an anechoic (echo-free) chamber to rich-scattering reverberation chambers to corroborate our analysis. Our findings raise doubts about the reliability of existing performance analyses and channel-estimation protocols for cases in which cascaded models poorly describe the physical reality.

Programmable radio environments parametrized by reconfigurable intelligent surfaces (RISs) are emerging as a new wireless communications paradigm, but currently used channel models for the design and analysis of signal-processing algorithms cannot include fading in a manner that is faithful to the underlying wave physics. To overcome this roadblock, we introduce a physics-based end-to-end model of RIS-parametrized wireless channels with adjustable fading (coined PhysFad) which is based on a first-principles coupled-dipole formalism. PhysFad naturally incorporates the notions of space and causality, dispersion (i.e., frequency selectivity) and the intertwinement of each RIS element’s phase and amplitude response, as well as any arising mutual coupling effects including long-range mesoscopic correlations. The latter are induced by reverberation and yield a highly nonlinear parametrization of wireless channels through RISs, a pivotal property which is to date completely overlooked. PhysFad offers the to-date missing tuning knob for physics-compliant adjustable fading. We thoroughly characterize PhysFad and demonstrate its capabilities for a prototypical problem of RIS-enabled over-the-air channel equalization in rich-scattering wireless communications. We also share a user-friendly version of our code to help the community transition towards physics-based models with adjustable fading.

The integration of Reconfigurable Intelligent Surfaces (RISs) into wireless environments endows channels with programmability, and is expected to play a key role in future communication standards. To date, most RIS-related efforts focus on quasi-free-space, where wireless channels are typically modeled analytically. Many realistic communication scenarios occur, however, in rich-scattering environments which, moreover, evolve dynamically. These conditions present a tremendous challenge in identifying an RIS configuration that optimizes the achievable communication rate. In this paper, we make a first step toward tackling this challenge. Based on a simulator that is faithful to the underlying wave physics, we train a deep neural network as surrogate forward model to capture the stochastic dependence of wireless channels on the RIS configuration under dynamic rich-scattering conditions. Subsequently, we use this model in combination with a genetic algorithm to identify RIS configurations optimizing the communication rate. We numerically demonstrate the ability of the proposed approach to tune RISs to improve the achievable rate in rich-scattering setups.

We present a framework for operating a self-adaptive RIS inside a fading rich-scattering wireless environment. We model the rich-scattering wireless channel as being double-parametrized by (i) the RIS, and (ii) dynamic perturbers (moving objects, etc.). Within each coherence time, first, the self-adaptive RIS estimates the status of the dynamic perturbers (e.g., the perturbers’ orientations and locations) based on measurements with an auxiliary wireless channel. Then, second, using a learned surrogate forward model of the mapping from RIS configuration and perturber status to wireless channel, an optimized RIS configuration to achieve a desired functionality is obtained. We demonstrate our technique using a physics-based end-to-end model of RIS-parametrized communication with adjustable fading (PhysFad) for the example objective of maximizing the received signal strength indicator. Our results present a route toward convergence of RIS-empowered localization and sensing with RIS-empowered channel shaping beyond the simple case of operation in free space without fading.

We recently introduced the concept of reconfigurable Wireless Networks on Chips (r-WNoCs) for which an on-chip reconfigurable intelligent surface (RIS) endows the wireless on-chip propagation environment with programmability. In this work-in-progress report, we apply this idea to a single-input multiple-output (SIMO) context. Specifically, we demonstrate that using an on-chip RIS we can simultaneously shape multiple channel impulse responses (CIRs) such that they become essentially pulse-like despite rich scattering inside the chip enclosure. Pulse-like CIRs are essential to enable high-speed information exchange between different processors on the same chip with the simple on-off-keying modulation schemes envisaged for WNoCs.