arXiv subjects

Bruno Clerckx

Publications and source records attributed to Bruno Clerckx.

At least 19 recordsLinked to original sources

arXiv2026

Wideband Microwave Linear Analog Computer (MiLAC) for Frequency-Flat and Frequency-Selective Processing

Microwave linear analog computer (MiLAC) has been proposed as an analog processing architecture to perform efficient computation in the microwave domain. Consisting of reconfigurable impedance networks, a MiLAC can extract many of the gains of large multi-antenna systems without costly digital processing, e.g., achieving capacity in narrowband multiple-input single-output (MISO). However, the behavior of wideband MiLAC, required to support high data-rate transmissions, is widely unknown. The impedance components of MiLACs have non-trivial frequency-dependent response, requiring specific implementations to characterize it. In this work, we consider MiLAC implementations based on LC resonators with tunable capacitance, which allow synthesizing near-arbitrary passive lossless impedance matrices at individual frequencies using inductors and varactors. We characterize the mapping between optimal MISO precoding at a reference frequency, and the vector of capacitances configuring the MiLAC. We derive the degrees of freedom (DoFs) remaining after fixing such optimum precoding at the reference frequency, and show that these DoFs can be exploited to tune the frequency response of the MiLAC. We propose two techniques to exploit these DoFs: a closed-form approach for frequency-flat MiLAC processing, and a numerical approach for multi-frequency MiLAC processing, optimizing processing at frequencies other than the reference one. The frequency-flat approach shows satisfactory performance in a simulated frequency-flat millimeter-wave scenario, approaching the performance of digital processing. The multi-frequency approach can adapt to the frequency-selectivity of a simulated sub-6GHz scenario, attaining gains over frequency-flat digital processing. This constitutes the first demonstration that realistic MiLAC implementations can be configured to perform independent computations at different frequencies.

cs.IT↗

arXiv2026

Two-Layer Microwave Linear Analog Computer (MiLAC)-Aided Multi-User MIMO Networks

Microwave linear analog computer (MiLAC)-aided beamforming, which performs signal processing directly in the analog domain, has recently emerged as a promising alternative to fully digital and hybrid beamforming for multi-antenna systems. However, existing studies have shown that a single lossless and reciprocal MiLAC at the transmitter cannot, in general, attain the performance of fully digital beamforming in multi-user scenarios. To overcome this limitation, we propose a two-layer MiLAC-aided transmit beamforming architecture for downlink multi-user multiple-input multiple-output (MIMO) networks. Leveraging multiport microwave network theory, we first establish a general physics-compliant model of the proposed architecture, and then derive a simplified model under the assumptions of unilateral and perfectly matched amplifiers. We prove that, with lossless and reciprocal MiLACs, the two-layer MiLAC-aided transmitter can realize any fully digital transmit beamformer, while a single-layer MiLAC-aided receiver can attain the same achievable rate as a fully digital linear combiner. We then derive closed-form mappings from fully digital transmit beamformers and receive combiners to their corresponding MiLAC-aided analog implementations. Based on these equivalence results, we formulate a sum-rate maximization problem for the considered multi-user MIMO network and develop an optimization framework for jointly designing the power allocation and scattering matrices of the MiLAC-aided transceivers. Numerical results validate the theoretical analysis and show that the proposed two-layer MiLAC-aided design attains the same sum-rate performance as its fully digital counterpart.

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arXiv2026

Frequency-Dependent Hybrid Digital and Microwave Linear Analog Computer (MiLAC) Beamforming for Multiuser MIMO-OFDM Systems

Microwave linear analog computing (MiLAC) has recently emerged as a promising approach for reducing the hardware and digital-processing requirements of large-scale multiple-input multiple-output (MIMO) systems. In narrowband multiuser systems, hybrid digital-MiLAC beamforming can achieve digital beamforming flexibility with only as many radio-frequency (RF) chains as data streams. However, extending this advantage to wideband systems is nontrivial because practical MiLAC circuits exhibit frequency-dependent responses. In this paper, we investigate hybrid digital-MiLAC beamforming for multiuser MISO-OFDM systems with a frequency-dependent MiLAC circuit model. We characterize the frequency dependence of MiLAC by relating the susceptance of each tunable component across subcarriers to its center-frequency value. Under this frequency coupling, we show that a single MiLAC circuit generally cannot simultaneously match the desired beamforming directions across all subcarriers, highlighting the essential role of subcarrier-dependent digital precoding. We then develop a block coordinate descent (BCD) algorithm to jointly optimize the digital and MiLAC beamformers for average sum-rate maximization. In particular, an efficient alternating direction method of multipliers (ADMM) algorithm is custom-designed to handle the frequency-coupled circuit constraints in the MiLAC beamformer subproblem. Simulation results show that the proposed hybrid digital-MiLAC design outperforms conventional hybrid digital-analog beamforming, particularly when fewer RF chains are available and the channel is more frequency-selective. With $64$ transmit antennas and $4$ data streams, it attains $96.3\%$ of the digital sum-rate using only $8$ RF chains. Furthermore, under highly frequency-selective channels and using $4$ RF chains, it provides a $48\%$ sum-rate gain over the conventional hybrid design.

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arXiv2026

Can Reciprocal RIS Perform as Non-Reciprocal RIS?

Yes, if and only if some optimal non-reciprocal RIS (i.e., maximizing a given performance metric) makes the round-trip channel transmitter-RIS-transmitter symmetric, which holds if the channel transmitter-RIS has rank one or if single-stream transmission is optimal.

cs.IT↗

arXiv2026

Joint Training Scattering Matrix Learning and Channel Estimation for Beyond-Diagonal Reconfigurable Intelligent Surfaces

Beyond-diagonal reconfigurable intelligent surface (BD-RIS) generalizes the conventional diagonal RIS (D-RIS) by introducing tunable inter-element connections, offering enhanced wave manipulation capabilities. However, realizing the advantages of BD-RIS requires accurate channel state information (CSI), whose acquisition becomes significantly more challenging due to the increased number of channel coefficients, leading to prohibitively large pilot training overhead in BD-RIS-aided multi-user multiple-input multiple-output (MU-MIMO) systems. Existing studies reduce pilot overhead by exploiting the channel correlations induced by the Kronecker-product or multi-linear structure of BD-RIS-aided channels, which neglect the spatial correlation among antennas and the statistical correlation across RIS-user channels. In this paper, we propose a learning-based channel estimation framework, namely the joint training scattering matrix learning and channel estimation framework (JTSMLCEF), which jointly optimizes the BD-RIS training scattering matrix and estimates the cascaded channels in an end-to-end manner to achieve accurate channel estimation and reduce the pilot overhead. The proposed JTSMLCEF follows a two-phase channel estimation protocol to enable adaptive training scattering matrix optimization with a training scattering matrix optimizer (TSMO) and cascaded channel estimation with a dual-attention channel estimator (DACE). Specifically, the DACE is designed with intra-user and inter-user attention modules to capture the multi-dimensional correlations in multi-user cascaded channels. Simulation results demonstrate the superiority of JTSMLCEF. Compared with the current state-of-the-art method, it reduces the pilot overhead by $80\%$ while further reducing the normalized mean squared error (NMSE) by $82.6\%$ and $92.5\%$ in indoor and urban micro-cell (UMi) scenarios, respectively.

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arXiv2026

Beamforming Design for Stem-Connected Microwave Linear Analog Computer (MiLAC)-Aided Multiuser MISO Downlinks

A microwave linear analog computer (MiLAC) is a tunable microwave network that leverages wave propagation to perform computation directly in the analog domain. MiLAC finds promising applications in beamforming, where it can map the data streams to the antennas without a digital beamformer, using one radio-frequency chain per stream. A fully-connected MiLAC needs a number of tunable components that grows quadratically with the number of antennas, whereas a stem-connected MiLAC needs only a linearly growing number and still achieves the point-to-point capacity. For the multiuser multiple-input single-output downlink, we prove that the stem-connected MiLAC attains the maximum sum-rate of the fully-connected MiLAC whenever $N\ge 2K-1$, where $N$ and $K$ denote the numbers of antennas and users. The proof shows that restricting the design to beamformers with orthonormal columns, which the stem-connected MiLAC realizes in closed form, loses no sum-rate. Based on this restriction, we develop, for every $N\ge K$, a weighted minimum mean-square error algorithm with a Riemannian beamformer update and prove that its accumulation points are stationary. For the bounded, discrete susceptances of practical components, we then propose an alternating refinement that adjusts one susceptance at a time through rank-one updates and never decreases the sum-rate. With $64$ antennas, four users, and ideal components, the stem-connected MiLAC attains the fully-connected sum-rate with $4.5$ times fewer tunable components. With $3$-bit susceptances at a signal-to-noise ratio of $10$~dB, the refinement retains $90\%$ of this sum-rate.

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arXiv2026

Toward a Lean Formalization of Analog Computing with Microwaves

Analog computing with microwave signals can perform linear transformations directly in the analog domain, as the signals propagate through a microwave network. A fundamental question is which transformations can be computed with a given set of microwave components. In our previous work, we answered this question for networks of hybrid couplers and phase shifters by deriving a necessary and sufficient condition on the transformations these networks can compute, and we showed that the discrete Fourier transform (DFT) satisfies it. In this paper, we take a first step toward the formalization of analog computing with microwaves in Lean, a programming language and proof assistant that is increasingly adopted in mathematics. We formalize the considered components, their series and parallel connections, and the class of networks they can implement. Then, we formally prove the necessary and sufficient condition characterizing these networks, as well as the implementability of the DFT of any size power of two. All proofs are checked by the Lean kernel, and the code is openly available at: https://github.com/matteonerini/formalizing-analog-computing.

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arXiv2026

Finite-Resolution Microwave Linear Analog Computer (MiLAC)-Aided Multiuser Beamforming

Large-scale antenna arrays are essential to future wireless networks but impose significant hardware and digital-processing burdens. The microwave linear analog computer (MiLAC) offers a promising architecture for addressing these challenges. In a MiLAC, beamforming is realized entirely in the analog domain through a reconfigurable multiport microwave network comprising tunable admittance elements. However, existing studies assume that these elements are continuously tunable, whereas practical implementations can support only finitely many configurable states. This paper investigates finite-resolution MiLAC-aided multiuser beamforming under lossless and reciprocal constraints with prescribed connectivity patterns. Each tunable susceptance is selected from a symmetric uniform finite-resolution codebook. We formulate an online problem that jointly optimizes the discrete susceptances and power allocation for a prescribed codebook, and an offline problem that designs the codebook based on channel statistics. By exploiting the odd-uniform codebook structure, we express each multilevel susceptance as a weighted sum of two-level variables and develop exact continuous penalty models for both the online beamforming and offline codebook design problems. We prove that, for sufficiently large penalty parameters, these penalty models are globally equivalent to their original discrete counterparts. Building on these formulations, we develop efficient ADMM-based algorithms for solving the two problems. Numerical results demonstrate that the performance of an unquantized fully-connected MiLAC can be approached with substantially reduced connectivity and finite resolution. In particular, a 3-bit stem-connected MiLAC achieves more than 95% of the sum-rate performance of the unquantized fully-connected MiLAC while requiring only 22% of its tunable components.

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arXiv2026

Microwave Linear Analog Computer (MiLAC) for Simultaneous Active and Passive Beamforming

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.

cs.IT↗

arXiv2026

Channel Estimation in MIMO Systems Aided by Microwave Linear Analog Computers (MiLACs)

Microwave linear analog computers (MiLACs) have recently emerged as a promising solution for future gigantic multiple-input multiple-output (MIMO) systems, enabling beamforming with greatly reduced hardware and computational cost. However, channel estimation for MiLAC-aided systems remains an open problem. Conventional least squares (LS) and minimum mean square error (MMSE) estimation rely on intensive digital computation, which undermines the computational advantage offered by MiLACs. In this letter, we propose efficient LS and MMSE channel estimation schemes for MiLAC-aided MIMO systems. By designing the training precoder and combiner implemented by lossless and reciprocal MiLACs, the proposed schemes perform LS and MMSE estimation in the analog domain, leaving only simple digital scaling. They achieve identical estimation performance to their digital counterparts while significantly reducing computational complexity. Numerical results verify the effectiveness of the proposed schemes.

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arXiv2026

Active Beyond-Diagonal Reconfigurable Intelligent Surfaces: Modeling, Architecture Design, and Optimization

Beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) are an emerging RIS 2.0 technology for future wireless communication. However, BD-RISs are primarily passive without active amplification, suffering from severe multiplicative path loss. To address the concern of multiplicative path loss, in this work we investigate the active BD-RIS including the modeling, architecture design, and optimization. We first analyze the active BD-RIS using multiport network theory with scattering parameters and derive a physical and electromagnetic compliant active BD-RIS aided communication model. We also design two new active BD-RIS architectures, namely fully- and group-connected active BD-RISs. Based on the proposed model and architecture, we investigate the active BD-RIS aided single-input single-output system and derive the closed-form optimal solution and scaling law of the signal-to-noise ratio. We further investigate the active BD-RIS aided multiple-input multiple-output system and propose an iterative algorithm based on quadratically constrained quadratic programming to maximize the spectral efficiency. Numerical results are provided and show that the active BD-RIS can achieve higher spectral efficiency than the active/passive diagonal RIS and passive BD-RIS. For example, to achieve the same spectral efficiency, the number of elements required by active BD-RIS is less than half of that required by active diagonal RIS, showing the advantages of active BD-RIS.

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arXiv2026

Analog Computing with Hybrid Couplers and Phase Shifters

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.

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arXiv2026

Codeword-Segmentation Rate-Splitting Multiple Access and Evaluation under Suboptimal Decoding

Rate-Splitting Multiple Access (RSMA) has been recognized as a promising multiple access technique. We propose a novel architecture for downlink RSMA, namely Codeword-Segmentation RSMA (CS-RSMA). Different from conventional RSMA which splits users' messages into common and private parts before encoding, CS-RSMA encodes the users' messages directly, segments the codewords into common and private parts, and transmits the codeword segments using common and private streams. In addition to the principle of CS-RSMA, a novel performance analysis framework is proposed. This framework utilizes a recent discovery in mismatched decoding under finite-alphabet input and interference, and can better capture the receiver's complexity limits. Precoder optimization under finite alphabets and suboptimal decoders for conventional RSMA and CS-RSMA to maximize the Sum-Rate (SR) and the Max-Min Fairness (MMF) is also addressed. The numerical results reveal the theoretical performance of conventional RSMA and CS-RSMA. We observe that CS-RSMA leads to better performance than conventional RSMA in SR, and similar performance in MMF. Furthermore, a physical-layer implementation of CS-RSMA is proposed and evaluated through link-level simulations. Aside performance benefits, we also demonstrate that CS-RSMA brings significant benefits on the encoding/decoding, control signaling, and retransmission process compared to conventional RSMA.

cs.IT↗

arXiv2026

ETSI ISG MAT: Bridging Multiple Access Techniques Research and 6G Standardisation

Improved spectral efficiency and inter-user interference mitigation are important aspects of IMT-2030 and the ongoing 3GPP 6G study. ETSI established the Industry Specification Group on Multiple Access Techniques (ISG MAT) as a research and pre-standardisation activity to build wider consensus on downlink MAT for 3GPP-based 6G systems. Its first report, ETSI GR MAT 001 V1.1.1, provides a standards-oriented comparison of 3GPP-specified techniques, including OMA, MU-MIMO, and MUST, with candidate techniques comprising power-domain NOMA, RSMA, and cache-aided MU-MIMO. The report identifies operating conditions in which candidate MAT can improve spectral efficiency and assesses implications for transceiver processing, network assistance information, and reference-signal requirements. Ongoing work includes realistic 5G NR link-level evaluations and the study of MAT for non-terrestrial networks, providing timely technical evidence for 3GPP 6G standardisation discussions.

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arXiv2026

Microwave Linear Analog Computers (MiLACs) for Communications: Opportunities and Challenges

Future wireless systems will require ever larger antenna arrays and heavier signal processing, making conventional digital multiple-input multiple-output (MIMO) architectures difficult to scale. In this paper, we show that a possible solution is to offload part of the processing from the digital to the analog domain. This can be done through linear microwave networks designed to compute directly using the communication signals at radio frequency (RF). These networks, denoted as microwave linear analog computers (MiLACs), can perform useful matrix operations instantly through wave propagation. Remarkably, although MiLACs are linear, the output signals can depend nonlinearly on the tunable parameters of the network, enabling the computation of operations beyond simple linear transforms. In particular, MiLACs can realize matrix inversion and pseudo-inversion with complexity scaling quadratically with matrix size, rather than cubically, which is essential in zero-forcing beamforming. We then review how MiLAC-aided MIMO architectures can reduce the number of RF chains, relax the resolution requirements on digital-to-analog converters (DACs) and analog-to-digital converters (ADCs), and decrease the beamforming complexity. We finally discuss the main challenges related to MiLAC and promising directions for future research.

cs.IT↗

arXiv2026

Capacity of Two-User Wireless Systems Aided by Movable Signals

Movable signals have emerged as a third approach to enable smart radio environments (SREs), complementing reconfigurable intelligent surfaces (RISs) and flexible antennas. This paper investigates their potential to enhance multi-user wireless systems. Focusing on two-user systems in line-of-sight (LoS), we characterize the capacity regions of the multiple access channel (MAC) and broadcast channel (BC). Interestingly, movable signals can dynamically adjust the operating frequency to orthogonalize the user channels, thereby significantly expanding the capacity regions. We also study frequency optimization, constraining it in a limited frequency range, and show that movable signals provide up to 45% sum rate gain.

cs.IT↗

arXiv2026

Beyond-Diagonal RIS Under Non-Idealities: Learning-Based Architecture Discovery and Optimization

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. While existing studies have explored optimal architectures to minimize circuit complexity in ideal BD-RIS, architecture discovery for non-ideal BD-RIS remains uninvestigated. Consequently, 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 for 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.

cs.IT↗

arXiv2026

Channel Estimation and Beamforming for Microwave Linear Analog Computers (MiLACs)-Aided Multiuser MISO Systems

Microwave linear analog computers (MiLACs) have recently gained attention for future gigantic multiple-input multiple-output (MIMO) systems by enabling beamforming with greatly reduced hardware and computational cost. However, channel estimation for MiLAC-aided multiuser systems remains an open problem. Conventional channel estimation requires many radio-frequency (RF) chains to access full-dimensional received signals, followed by massive digital processing, which undermines the advantages of MiLAC-aided systems in reducing the number of RF chains and computational complexity. In this paper, we propose computationally efficient channel estimation and beamforming schemes for MiLAC-aided multiuser multiple-input single-output (MU-MISO) systems with a limited number of RF chains. We consider the general case where different user groups experience different channel correlation matrices. By exploiting the rank deficiency of these matrices, the proposed schemes use MiLAC to compress the full-dimensional received signals in the analog domain, making them compatible with the available RF chains while preserving the essential channel information. Then, in the digital domain, only low-dimensional channel estimation is performed based on these compressed observations, substantially reducing computational cost. We further show how regularized zero-forcing beamforming (R-ZFBF) can be efficiently realized from the low-dimensional channel estimates through a cascade of two MiLACs, which offers greater computational flexibility than a single MiLAC. Numerical results show that the proposed schemes reduce computational complexity up to $1540\times$ and $16108\times$, for channel estimation and beamforming, respectively, while achieving performance comparable to digital baselines.

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