Mutual-Coupling-Aware Optimization of a Time-Floquet RIS for Harmonic Backscatter Communications

This Letter studies the optimization of a wireless communications system empowered by a periodically time-modulated reconfigurable intelligent surface, coined time-Floquet RIS (TF-RIS), in the presence of mutual coupling (MC) among the RIS elements. In contrast to a conventional RIS whose elements may be reconfigured between signaling intervals, a TF-RIS periodically modulates its elements within a signaling interval, thereby inducing frequency conversion. Periodic time modulation is particularly attractive for harmonic backscatter communications to avoid self-jamming. Based on time-Floquet multiport network theory, we formulate an MC-aware optimization problem for binary-amplitude-shift-keying (BASK) harmonic backscatter communications with practical 1-bit-programmable TF-RIS elements. We propose a general discrete-optimization algorithm and evaluate its performance based on realistic model parameters. We systematically examine the performance dependence on the time resolution of the periodic modulation and the number of retained harmonics. Benchmarking against an MC-unaware approach reveals the importance of MC awareness for the more challenging optimization problem of simultaneous desired-harmonic-channel-gain maximization and undesired-harmonic-channel-gain minimization.

Channel Estimation via Tensor Decomposition for Dynamic Metasurface Antennas with Known Mutual Coupling: Algorithms and Experiments

Dynamic metasurface antennas (DMAs) are an emerging hybrid-MIMO technology distinguished by an ultrathin form factor, low cost, and low power consumption. In real-world DMA prototypes, mutual coupling (MC) between meta-elements is generally non-negligible; some architectures even deliberately exploit strong MC to enhance wave-domain flexibility. In this paper, we address channel estimation (CE) for DMAs with known MC by formulating it as a tensor-decomposition problem. We develop a generalized block Tucker alternating least squares (BTALS) algorithm, together with specialized variants for cases with known direct and/or feed channel. We also develop a reciprocity-aware bilinear factorization method for the case with known direct channel. We experimentally validate our algorithms using an 18 GHz DMA prototype whose 7 feeds and 96 meta-elements are strongly coupled via a chaotic cavity. Our general BTALS algorithm reaches an accuracy of 43.1 dB, only 0.3 dB below the upper bound imposed by experimental noise. All proposed algorithms generally outperform the prior-art reference scheme thanks to the superior noise rejection enabled by the tensor-based framework. We further study the minimum number of required measurements as a function of the number of feeds and demonstrate the importance of MC awareness by comparison with an MC-unaware benchmark. Finally, we apply BTALS to a second setup enabling the prediction of the DMA's full dual-polarization 3D radiation diagram. We also measure the latter for DMA configurations optimized for channel-gain enhancement based on the estimated channels. Altogether, our work establishes the practical relevance of MC-aware tensor methods; beyond DMAs, it applies to all wireless systems with wave-domain programmability enabled by tunable lumped elements.

Expressivity of Programmable-Metasurface-Based Physical Neural Networks: Encoding Non-Linearity, Structural Non-Linearity, and Depth

Wave-based signal processing conventionally encodes input data into the input wavefront, making it challenging to implement non-linear operations. Programmable wave systems enable an alternative approach: encoding the input data into the scattering properties of tunable components. With such structural input encoding, two potentially non-linear mappings are involved: first, from the input data to the tunable components' scattering characteristics, and, second, from these scattering characteristics to the output wavefront. In this paper, we systematically examine the expressivity of a wave-based physical neural network (WPNN) with structural input encoding. Our analysis is based on a physics-consistent multiport-network model of a compact D-band rich-scattering cavity parametrized by a 100-element programmable metasurface. We separately control encoding non-linearity, structural non-linearity, and network depth in order to examine their interplay, considering a controlled scalar regression task. With phase encoding and strong inter-element mutual coupling (MC), both aforementioned mappings are strongly non-linear and the WPNN performs very well even with a single layer. We further observe that additional layers can partially compensate for weak inter-element MC. In addition, we demonstrate that WPNN depth can improve expressivity even when it is not associated with an increase in trainable weights. Altogether, our results provide a physics-consistent picture of how encoding choice, MC strength, and depth jointly govern the expressive power of PM-based WPNNs, informing design choices for future experimental implementations of WPNNs.

Electromagnetic Bounds on Realizing Targeted MIMO Transfer Functions in Real-World Systems with Wave-Domain Programmability

A key question for most applications involving reconfigurable linear wave systems is how accurately a desired linear operator can be realized by configuring the system's tunable elements. The relevance of this question spans from hybrid-MIMO analog combiners via computational meta-imagers to programmable wave-domain signal processing. Yet, no electromagnetically consistent bounds have been derived for the fidelity with which a desired operator can be realized in a real-world reconfigurable wave system. Here, we derive such bounds based on an electromagnetically consistent multiport-network model (capturing mutual coupling between tunable elements) and accounting for real-world hardware constraints (lossy, 1-bit-programmable elements). Specifically, we formulate the operator-synthesis task as a quadratically constrained fractional-quadratic problem and compute rigorous fidelity upper bounds based on semidefinite relaxation. We apply our technique to three distinct experimental setups. The first two setups are, respectively, a free-space and a rich-scattering $4\times 4$ MIMO channel at 2.45 GHz parameterized by a reconfigurable intelligent surface (RIS) comprising 100 1-bit-programmable elements. The third setup is a $4\times 4$ MIMO channel at 19 GHz from four feeds of a dynamic metasurface antenna (DMA) to four users. We systematically study how the achievable fidelity scales with the number of tunable elements, and we probe the tightness of our bounds by trying to find optimized configurations approaching the bounds with standard discrete-optimization techniques. We observe a strong influence of the coupling strength between tunable elements on our fidelity bound. For the two RIS-based setups, our bound attests to insufficient wave-domain flexibility for the considered operator synthesis.

Electromagnetically Consistent Bounds on Information Transfer in Real-World RIS-Parametrized Wireless Channels

A reconfigurable intelligent surface (RIS) endows a wireless channel with programmability that can be leveraged to optimize wireless information transfer. While many works study algorithms for optimizing such a programmable channel, relatively little is known about fundamental bounds on the achievable information transfer. In particular, non-trivial bounds that are both electromagnetically consistent (e.g., aware of mutual coupling) and in line with realistic hardware constraints (e.g., few-bit-programmable, potentially lossy loads) are missing. Here, based on a rigorous multiport network model of a single-input single-output (SISO) channel parametrized by 1-bit-programmable RIS elements, we apply a semidefinite relaxation (SDR) to derive a fundamental bound on the achievable SISO channel gain enhancement. A bound on the maximum achievable rate of information transfer at a given noise level follows directly from Shannon's theorem. We apply our bound to several numerical and experimental examples of different RIS-parametrized radio environments. Compared to electromagnetically consistent benchmark bounding strategies (a norm-inequality bound and, where applicable, a relaxation to an idealized beyond-diagonal load network for which a global solution exists), we consistently observe that our SDR-based bound is notably tighter. We reach at least 64 % (but often 100 %) of our SDR-based bound with standard discrete optimization techniques. The applicability of our bound to concrete experimental systems makes it valuable to inform wireless practitioners, e.g., to evaluate RIS hardware design choices and algorithms to optimize the RIS configuration. Our work contributes to the development of an electromagnetic information theory for RIS-parametrized channels as well as other programmable wave systems such as dynamic metasurface antennas or real-life beyond-diagonal RISs.

AI-Aided Annealed Langevin Dynamics for Rapid Optimization of Programmable Channels

Emerging technologies such as Reconfigurable Intelligent Surfaces (RIS) make it possible to optimize some parameters of wireless channels. Conventional approaches require relating the channel and its programmable parameters via a simple model that supports rapid optimization, e.g., re-tuning the parameters each time the users move. However, in practice such models are often crude approximations of the channel, and a more faithful description can be obtained via complex simulators, or only by measurements. In this work, we introduce a novel approach for rapid optimization of programmable channels based on AI-aided Annealed Langevin Dynamics (ALD), which bypasses the need for explicit channel modeling. By framing the ALD algorithm using the MAP estimate, we design a deep unfolded ALD algorithm that leverages a Deep Neural Network (DNN) to estimate score gradients for optimizing channel parameters. We introduce a training method that overcomes the need for channel modeling using zero-order gradients, combined with active learning to enhance generalization, enabling optimization in complex and dynamically changing environments. We evaluate the proposed method in RIS-aided scenarios subject to rich-scattering effects. Our results demonstrate that our AI-aided ALD method enables rapid and reliable channel parameter tuning with limited latency.

Frozen differential scattering in reconfigurable complex media

The sensitivity of transmission to the input wavefront is a hallmark feature of complex media and the basis for wavefront shaping techniques. Yet, intriguing special cases exist in which the output wavefront is "frozen" (agnostic to the input wavefront). This happens when special structure in the complex medium collapses the rank of its transmission matrix to unity. Here, we unveil that an analogous phenomenon exists more universally for differential scattering (including reflection) in reconfigurable complex media. Specifically, for a localized perturbation, the differential scattering matrix of any complex medium has rank one. One consequence is that the differential output signal is perfectly coherent irrespective of the input wavefront's coherence. Moreover, the thermal noise emitted into the frozen differential output mode has a particular structure that can be exploited for thermal noise management. We experimentally evidence frozen differential scattering in a rich-scattering wireless link parametrized by a programmable meta-atom. Then, we demonstrate "customized freezing" by optimizing the configuration of additional programmable meta-atoms that parametrize the wireless link, as envisioned for 6G networks. We impose particular shapes of the frozen differential output mode, and maximize its signal-to-thermal-noise ratio. Potential applications include filtering and stabilization of differential wavefronts, as well as imaging, sensing, and communication in complex media.

Ambiguity-Aware Segmented Estimation of Mutual Coupling in Large RIS: Algorithm and Experimental Validation

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 4x4 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 17.0 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.

Experimental Multiport-Network Parameter Estimation and Optimization for Multi-Bit RIS

Physics-consistent theoretical studies on RIS-parametrized wireless channels use models from multiport-network theory (MNT) to capture mutual-coupling (MC) effects. However, in practice, RIS design and radio environment are partially or completely unknown. We fill a research gap on how to estimate the MNT model parameters in such experimentally relevant scenarios. Our technique efficiently combines closed-form and gradient-descent steps, and it can be applied to multi-bit-programmable RIS elements. We discuss inevitable (but operationally irrelevant) parameter ambiguities. We experimentally validate our technique in an unknown rich-scattering environment parametrized by eight 8-bit-programmable RIS elements of unknown design. We experimentally evaluate the performance of RIS configurations optimized with the estimated MNT model and an MC-unaware cascaded model. While the models differ in accuracy by up to 17 dB, the end-to-end performance differences are small.

End-to-End Dynamic Metasurface Antenna Wireless System: Prototype, Opportunities, and Challenges

Dynamic metasurface antennas (DMAs) are a promising hybrid analog/digital beamforming technology to realize next-generation wireless systems with low cost, footprint, and power consumption. The research on DMA-empowered wireless systems is still at an early stage, mostly limited to theoretical studies under simplifying assumptions on the one hand and a few antenna-level experiments on the other hand. Substantial knowledge gaps arise from the lack of complete end-to-end DMA-empowered wireless system prototypes. In addition, recently unveiled benefits of strong inter-element mutual coupling (MC) in DMAs remain untapped. Here, we demonstrate a K-band prototype of an end-to-end wireless system based on a DMA with strong inter-element MC. To showcase the flexible control over the DMA's radiation pattern, we present an experimental case study of simultaneously steering a beam to a desired transmitter and a null to an undesired jammer, achieving up to 43~dB discrimination. Using software-defined radios, we transmit and receive QPSK OFDM waveforms to evaluate the bit error rate. We also discuss algorithmic and technological challenges associated with envisioned future evolutions of our end-to-end testbed and real-life DMA-based wireless systems.