Bruno Clerckx

Binggui Zhou, Bruno Clerckx

Microwave linear analog computers (MiLACs) offer a transformative paradigm for future multiple-input multiple-output (MIMO) systems by shifting complex signal processing into the analog domain, thereby significantly reducing computational complexity, radio-frequency chains, and analog-digital converters, while speeding up computation. However, the practical deployment of MiLACs is severely constrained by the inherent hardware losses of the tunable admittance components (TACs) interconnecting MiLAC ports, which introduce severe inter-stream interference and fundamentally limit the spectral efficiency (SE) of the system. In addition, while denser architectures offer greater spatial degrees of freedom to mitigate inter-stream interference, the cumulative hardware losses and power consumption of massive TACs severely degrade the system's energy efficiency (EE). Consequently, designing architectures for lossy MiLACs emerges as a critical yet unresolved challenge, as it necessitates striking a delicate tradeoff between interference suppression and cumulative hardware losses/power consumption. To address this challenge, this paper investigates the joint MiLAC architecture design and performance (SE/EE) maximization in lossy MiLAC-aided MIMO systems. We propose a novel learning-based joint architecture and performance optimization framework (LJAPOF) that unifies the design of MiLAC architectures and analog beamforming configurations for lossy MiLACs under both SE- and EE-oriented objectives. Numerical results demonstrate that by intelligently navigating the fundamental tradeoff between interference suppression and hardware/power consumption, the proposed LJAPOF can design optimal MiLAC architectures that consistently outperform stem-connected and fully-connected MiLACs in maximizing the system's SE and EE.

Rafael Cerna Loli, Onur Dizdar, Bruno Clerckx et al.

Effective and adaptive interference management is required in next generation wireless communication systems. To address this challenge, Rate-Splitting Multiple Access (RSMA), relying on multi-antenna rate-splitting (RS) at the transmitter and successive interference cancellation (SIC) at the receivers, has been intensively studied in recent years, albeit mostly under the assumption of perfect Channel State Information at the Receiver (CSIR) and ideal capacity-achieving modulation and coding schemes. To assess its practical performance, benefits, and limits under more realistic conditions, this work proposes a novel design for a practical RSMA receiver based on model-based deep learning (MBDL) methods, which aims to unite the simple structure of the conventional SIC receiver and the robustness and model agnosticism of deep learning techniques. The MBDL receiver is evaluated in terms of uncoded Symbol Error Rate (SER), throughput performance through Link-Level Simulations (LLS), and average training overhead. Also, a comparison with the SIC receiver, with perfect and imperfect CSIR, is given. Results reveal that the MBDL receiver outperforms by a significant margin the SIC receiver with imperfect CSIR, due to its ability to generate on demand non-linear symbol detection boundaries in a pure data-driven manner.

Rafael Cerna Loli, Bruno Clerckx

Optimization algorithms for wireless systems play a fundamental role in improving their performance and efficiency. However, it is known that the complexity of conventional optimization algorithms in the literature often exponentially increases with the number of transmit antennas and communication users in the wireless system. Therefore, in the large scale regime, the astronomically large complexity of these optimization algorithms prohibits their use and prevents assessing large scale wireless systems performance under optimized conditions. To overcome this limitation, this work proposes instead the use of an unsupervised meta-learning based approach to directly perform non-convex optimization at significantly reduced complexity. To demonstrate the effectiveness of the proposed meta-learning based solution, the sum-rate (SR) maximization problem for the following three emerging 6G technologies is contemplated: hierarchical rate-splitting multiple access (H-RSMA), integrated sensing and communication (ISAC), and beyond-diagonal reconfigurable intelligent surfaces (BD-RIS). Through numerical results, it is demonstrated that the proposed meta-learning based optimization framework is able to successfully optimize the performance and also reveal unknown aspects of the operation in the large scale regime for the considered three 6G technologies.

Rafael Cerna Loli, Bruno Clerckx

In this letter, we propose the use of a meta-learning based precoder optimization framework to directly optimize the Rate-Splitting Multiple Access (RSMA) precoders with partial Channel State Information at the Transmitter (CSIT). By exploiting the overfitting of the compact neural network to maximize the explicit Average Sum-Rate (ASR) expression, we effectively bypass the need for any other training data while minimizing the total running time. Numerical results reveal that the meta-learning based solution achieves similar ASR performance to conventional precoder optimization in medium-scale scenarios, and significantly outperforms sub-optimal low complexity precoder algorithms in the large-scale regime.

Matteo Nerini, Bruno Clerckx

In this letter, we address blockage detection and precoder design for multiple-input multiple-output (MIMO) links, without communication overhead required. Blockage detection is achieved by classifying light detection and ranging (LIDAR) data through a physics-based graph neural network (GNN). For precoder design, a preliminary channel estimate is obtained by running ray tracing on a 3D surface obtained from LIDAR data. This estimate is successively refined and the precoder is designed accordingly. Numerical simulations show that blockage detection is successful with 95% accuracy. Our digital precoding achieves 90% of the capacity and analog precoding outperforms previous works exploiting LIDAR for precoder design.

Matteo Nerini, Bruno Clerckx

Microwave linear analog computers (MiLACs) have recently emerged to enable high-performance and efficient beamforming in the analog domain. In this paper, we introduce a dual-functionality framework for MiLAC-aided transceivers. Beyond analog-domain precoding/combining (active beamforming), a MiLAC and its antenna array can simultaneously act as a reconfigurable intelligent surface (RIS) (passive beamforming). This allows the MiLAC to execute beamforming for transmission/reception while reflecting external incident signals. We provide an optimal reconfiguration strategy for this dual-functional MiLAC, and characterize the fundamental limits on the trade-off between active and passive rate, namely the capacity region bounds and the sum-rate capacity.

Matteo Nerini, Bruno Clerckx

To meet the demands of future wireless networks, antenna arrays must scale from massive multiple-input multiple-output (MIMO) to gigantic MIMO, involving even larger numbers of antennas. To address the hardware and computational cost of gigantic MIMO, several strategies are available that shift processing from the digital to the analog domain. Among them, microwave linear analog computers (MiLACs) offer a compelling solution by enabling fully analog beamforming through reconfigurable microwave networks. Prior work has focused on fully-connected MiLACs, whose ports are all interconnected to each other via tunable impedance components. Although such MiLACs are capacity-achieving, their circuit complexity, given by the number of required impedance components, scales quadratically with the number of antennas, limiting their practicality. To solve this issue, in this paper, we propose a graph theoretical model of MiLAC facilitating the systematic design of lower-complexity MiLAC architectures. Leveraging this model, we propose stem-connected MiLACs as a family of MiLAC architectures maintaining capacity-achieving performance while drastically reducing the circuit complexity. Besides, we optimize stem-connected MiLACs with a closed-form capacity-achieving solution. Our theoretical analysis, confirmed by numerical simulations, shows that stem-connected MiLACs are capacity-achieving, but with circuit complexity that scales linearly with the number of antennas, enabling high-performance, scalable, gigantic MIMO.

Matteo Nerini, Bruno Clerckx

Smart radio environments (SREs) enhance wireless communications by allowing control over the channel. They have been enabled through surfaces with reconfigurable electromagnetic (EM) properties, known as reconfigurable intelligent surfaces (RISs), and through flexible antennas, which can be viewed as realizations of SREs in the EM domain and space domain, respectively. However, these technologies rely on electronically reconfigurable or movable components, introducing implementation challenges that could hinder commercialization. To overcome these challenges, we propose a new domain to enable SREs, the frequency domain, through the concept of movable signals, where the signal spectrum can be dynamically moved along the frequency axis. We first analyze movable signals in multiple-input single-output (MISO) systems under line-of-sight (LoS) conditions, showing that they can achieve higher average received power than quantized equal gain transmission (EGT). We then study movable signals under non-line-of-sight (NLoS) conditions, showing that they remain effective by leveraging reflections from surfaces made of uniformly spaced elements with fixed EM properties, denoted as fixed intelligent surfaces (FISs). Analytical results reveal that a FIS-aided system using movable signals can achieve up to four times the received power of a RIS-aided system using fixed-frequency signals.

Valentina Rizzello, Matteo Nerini, Michael Joham et al.

In this work, we propose an efficient method for channel state information (CSI) adaptive quantization and feedback in frequency division duplexing (FDD) systems. Existing works mainly focus on the implementation of autoencoder (AE) neural networks (NNs) for CSI compression, and consider straightforward quantization methods, e.g., uniform quantization, which are generally not optimal. With this strategy, it is hard to achieve a low reconstruction error, especially, when the available number of bits reserved for the latent space quantization is small. To address this issue, we recommend two different methods: one based on a post training quantization and the second one in which the codebook is found during the training of the AE. Both strategies achieve better reconstruction accuracy compared to standard quantization techniques.

Zheyu Wu, Matteo Nerini, Bruno Clerckx

This paper studies multi-operator wireless communication systems aided by general reconfigurable intelligent surface (RIS), including both conventional single-connected RIS and beyond-diagonal RIS (BD-RIS). Specifically, we consider a system where multiple operators coexist in the same area over different frequency bands, each with a single-antenna base station, while one operator serves its single-antenna user with the aid of an RIS. In such a system, the RIS may unintentionally reflect signals from the non-serving operators, leading to inter-operator interference and rapid fluctuations of their effective channels. To address this issue, we propose a practical RIS design framework that maximizes the received signal power of the serving operator while enforcing fixed RIS-reflected channels of the non-serving operators. We derive closed-form solutions to the resulting optimization problem, based on a novel technique to deal with the coupled unitary and linear equality constraints. We further give scaling law analysis of the received signal power. For a two-operator system, the received signal power scales quadratically with the number of RIS elements for group-connected BD-RIS with group size Gs>=2, whereas for conventional single-connected RIS it scales only linearly. More generally, for an L-operator system with L-1 non-serving operators, the scaling-law transition occurs at Gs=L, where quadratic scaling is achieved when Gs>=L, and linear scaling otherwise. These results demonstrate that, in a multi-operator system, quadratic scaling is achievable only with BD-RIS architectures having enough interconnections. Simulation results validate the analysis and show the significant gain of BD-RIS over conventional RIS in multi-operator systems. In particular, group-connected BD-RIS with Gs=2 achieves a 13dB gain over conventional RIS in a two-operator system with a 128-element RIS.

Matteo Nerini, Zheyu Wu, Shanpu Shen et al.

Reconfigurable intelligent surfaces (RISs) enable programmable control of the wireless propagation environment and are key enablers for future networks. Beyond-diagonal RIS (BD-RIS) architectures enhance conventional RIS by interconnecting elements through tunable impedance components, offering greater flexibility with higher circuit complexity. However, excessive interconnections between BD-RIS elements require multi-layer printed circuit board (PCB) designs, increasing fabrication difficulty. In this letter, we use graph theory to characterize the BD-RIS architectures that can be realized on double-layer PCBs, denoted as planar-connected RISs. Among the possible planar-connected RISs, we identify the ones with the most degrees of freedom, expected to achieve the best performance under practical constraints.

Zheyu Wu, Matteo Nerini, Bruno Clerckx

Reconfigurable intelligent surface (RIS) is a promising technology for future wireless communication systems. Conventional RIS is constrained to a diagonal scattering matrix, which limits its flexibility. Recently, beyond-diagonal RIS (BD-RIS) has been proposed as a more general RIS architecture class that allows inter-element connections and shows great potential for performance improvement. Despite extensive progress on BD-RIS, most existing studies rely on simplified channel models that ignore practical electromagnetic (EM) effects such as mutual coupling and impedance mismatching. To address this gap, this paper investigates the architecture design and optimization of BD-RIS under the general physics-consistent model derived with multiport network theory in recent literature. Building on a compact reformulation of this model, we show that band-connected RIS achieves the same channel-shaping capability as fully-connected RIS, which extends existing results obtained for conventional channel models. We then develop optimization methods under the general physics-consistent model; specifically, we derive closed-form solutions for single-input single-output (SISO) systems, propose a globally optimal semidefinite relaxation (SDR)-based algorithm for single-stream multi-input multi-output (MIMO) systems, and design an efficient alternating direction method of multipliers (ADMM)-based algorithm for multiuser MIMO systems. Using the proposed algorithms, we conduct comprehensive simulations to evaluate the impact of various EM effects and approximations. The results indicate that the commonly adopted unilateral approximation provides sufficient accuracy in RIS-aided systems and can therefore be readily adopted to simplify the channel model, whereas mutual coupling among RIS elements should be properly taken into account in channel modeling.

Ziang Liu, Zheyu Wu, Bruno Clerckx

Multiple-input multiple-output (MIMO) radar has waveform diversity and large spatial degrees of freedom (DoFs), making it attractive for high-resolution sensing. Scaling MIMO radar to massive arrays can further improve sensing performance, but it also increases hardware cost, power consumption, and digital processing complexity. The microwave linear analog computer (MiLAC) can tackle these challenges by moving linear operations from the digital domain to the analog domain. MiLAC has shown promising benefits for communications in recent studies and this paper identifies its potential for radar sensing. Specifically, we consider both MiLAC-aided transmit beamforming and receiver-side two-dimensional discrete Fourier transform (2D-DFT)-based direction-of-arrival (DoA) estimation. For transmit beamforming, we formulate a weighted Cramer Rao bound (CRB) minimization problem under lossless and reciprocal MiLAC constraints and propose a penalty dual decomposition (PDD)-based iterative algorithm to address the non-convex problem. We further prove that MiLAC-aided and fully-digital beamforming achieve the same CRB. For receiver processing, we show that the 2D DFT can be implemented by a lossless reciprocal MiLAC, which enables analog-domain DoA estimation without digital optimization. Numerical results confirm the theoretical finding and show that the MiLAC-aided approach achieves the same CRB and DoA estimation performance as the fully-digital benchmark. Meanwhile, hardware cost and power consumption are reduced because only low-resolution DACs are required at the transmitter, while RF chains and ADCs are eliminated at the receiver. Moreover, performing the 2D DFT in the analog domain eliminates all digital DFT operations for DoA estimation.

Zheyu Wu, Junjie Ma, Ya-Feng Liu et al.

Massive multiple-input multiple-output (MIMO) systems employing one-bit digital-to-analog converters offer a hardware-efficient solution for wireless communications. However, the one-bit constraint poses significant challenges for precoding design, as it transforms the problem into a discrete and nonconvex optimization task. In this paper, we investigate a widely adopted ``convex-relaxation-then-quantization" approach for nonlinear symbol-level one-bit precoding. Specifically, we first solve a convex relaxation of the discrete minimum mean square error precoding problem, and then quantize the solution to satisfy the one-bit constraint. Focusing on a real-valued system with an independently and identically distributed (i.i.d.) Gaussian channel, we develop a novel analytical framework based on approximate message passing (AMP) to characterize the high-dimensional asymptotic performance of the considered scheme. The key technical ingredient is an auxiliary AMP iteration that dedicatedly incorporates the nonlinear quantization function into the state evolution analysis. With the proposed framework, we derive a closed-form expression for the symbol error probability (SEP) at the receiver side in the large-system limit, which provides a quantitative characterization of how model and system parameters affect the SEP performance. Our empirical results suggest that the $\ell_\infty^2$ regularizer, when paired with an optimally chosen regularization parameter, achieves optimal SEP performance within a broad class of convex regularization functions. As a first step towards a theoretical justification, we prove the optimality of the $\ell_\infty^2$ regularizer within the mixed $\ell_\infty^2$-$\ell_2^2$ regularization functions.

Matteo Nerini, Xuekang Liu, Bruno Clerckx

Analog computing with microwave signals can enable exceptionally fast computations, potentially surpassing the limits of conventional digital computing. For example, by letting some input signals propagate through a linear microwave network and reading the corresponding output signals, we can instantly compute a matrix-vector product without any digital operations. In this paper, we investigate the computational capabilities of linear microwave networks made exclusively of two low-cost and fundamental components: hybrid couplers and phase shifters, which are both implementable in microstrip. We derive a sufficient and necessary condition characterizing the class of linear transformations that can be computed in the analog domain using these two components. Within this class, we identify three transformations of particular relevance to signal processing, namely the discrete Fourier transform (DFT), the Hadamard transform, and the Haar transform. For each of these, we provide a systematic design method to construct networks of hybrid couplers and phase shifters capable of computing the transformation for any size power of two. To validate our theoretical results, a hardware prototype was designed and fabricated, integrating hybrid couplers and phase shifters to implement the $4\times4$ DFT. A systematic calibration procedure was subsequently developed to characterize the prototype and compensate for fabrication errors. Measured results from the prototype demonstrate successful DFT computation in the analog domain, showing high correlation with theoretical expectations. By realizing an analog computer through standard microwave components, this work demonstrates a practical pathway toward low-latency, real-time analog signal processing.

Xuejun Cheng, Qian Zhang, Yunnuo Xu et al.

Reconfigurable intelligent surface (RIS)-aided rate-splitting multiple access (RSMA) systems have demonstrated remarkable potential in enhancing spectral efficiency. However, most existing works rely on ideal hardware, which is unrealistic.In practical deployments, RIS elements suffer from amplitude-phase coupling, where transceivers are subject to hardware impairments (HWI), and successive interference cancellation (SIC) in RSMA networks cannot achieve perfect interference elimination for decoded signals.To address these limitations, we investigate a robust beamforming design for RIS-aided RSMA systems under practical hardware imperfections. We first characterize the asymptotic signal-to-noise ratio (SNR) of practical RIS systems when the beamformer is designed based on ideal RIS model, thereby theoretically quantifying the resulting performance degradation. We then derive a closed-form expression for the distortion noise power induced by transceiver HWI, while also accounting for residual interference due to imperfect SIC. Building on these insights, we establish a comprehensive system model that jointly incorporates all hardware-induced impairments and formulate a multiuser sum rate maximization problem. To solve the resulting non-convex optimization problem, we develop an efficient block variable relaxation algorithm. Simulation results verify that the proposed scheme significantly outperforms conventional non-orthogonal multiple access (NOMA) approaches, and achieves superior robustness compared with benchmark schemes neglecting HWI, imperfect SIC, or amplitude-phase coupling.

Yiyang Peng, Zheyu Wu, Bruno Clerckx

Microwave linear analog computing (MiLAC) has recently emerged as a promising architecture for analog-domain beamforming. In particular, a hybrid digital-MiLAC architecture was proposed and was shown to achieve fully-digital beamforming flexibility in narrowband systems when the number of RF chains equals the number of data streams. However, its performance in wideband systems remains unexplored. This paper presents the first study of hybrid digital-MiLAC beamforming for wideband multi-user multiple-input single-output (MU-MISO) systems. We first characterize the minimum number of radio-frequency (RF) chains required for hybrid digital-MiLAC beamforming to realize an arbitrary set of fully-digital beamforming matrices across all subcarriers. It turns out that, unlike in the narrowband case, a larger number of RF chains is generally required in frequency-selective channels to achieve fully-digital beamforming flexibility, which may be unfavorable in practice. To study the performance of hybrid digital-MiLAC beamforming with a limited number of RF chains, we then formulate the average sum-rate maximization problem and develop an efficient weighted minimum mean-square error (WMMSE)-based algorithm for beamforming design. Simulation results show that hybrid digital-MiLAC beamforming consistently outperforms conventional hybrid digital-analog beamforming, and achieves $89.93\%$ of the fully-digital sum-rate while using only $12.5\%$ of the RF chains in highly frequency-selective channels.

Binggui Zhou, Bruno Clerckx

Beyond-diagonal reconfigurable intelligent surface (BD-RIS) has recently been introduced to enable advanced control over electromagnetic waves to further increase the benefits of traditional RIS in enhancing signal quality and improving spectral and energy efficiency for next-generation wireless networks. A significant issue in designing and deploying BD-RIS is the tradeoff between its performance and circuit complexity. Despite some efforts in exploring optimal architectures with the lowest circuit complexities for ideal BD-RIS, architecture discovery for non-ideal BD-RIS remains uninvestigated. Therefore, how non-idealities and circuit complexity jointly affect the performance of BD-RIS remains unclear, making it difficult to achieve the performance - circuit complexity tradeoff in the presence of non-idealities. Essentially, architecture discovery for non-ideal BD-RIS faces challenges from both the computational complexity of global architecture search and the difficulty in achieving global optima. To tackle these challenges, we propose a learning-based two-tier architecture discovery framework (LTTADF) consisting of an architecture generator and a performance optimizer to jointly discover optimal architectures of non-ideal BD-RIS given specific circuit complexities, which can effectively explore over a large architecture space while avoiding getting trapped in poor local optima and thus achieving near-optimal solutions for the performance optimization. Numerical results provide valuable insights for deploying non-ideal BD-RIS considering the performance - circuit complexity tradeoff.