Luc Le Magoarou

Taha Yassine, Luc Le Magoarou, Stéphane Paquelet et al.

Channel charting is an unsupervised learning method that aims at mapping wireless channels to a so-called chart, preserving as much as possible spatial neighborhoods. In this paper, a model-based deep learning approach to this problem is proposed. It builds on a physically motivated distance measure to structure and initialize a neural network that is subsequently trained using a triplet loss function. The proposed structure exhibits a low number of parameters and clever initialization leads to fast training. These two features make the proposed approach amenable to on-the-fly channel charting. The method is empirically assessed on realistic synthetic channels, yielding encouraging results.

Luc Le Magoarou, Taha Yassine, Stephane Paquelet et al.

Channel charting (CC) is an unsupervised learning method allowing to locate users relative to each other without reference. From a broader perspective, it can be viewed as a way to discover a low-dimensional latent space charting the channel manifold. In this paper, this latent modeling vision is leveraged together with a recently proposed location-based beamforming (LBB) method to show that channel charting can be used for mapping channels in space or frequency. Combining CC and LBB yields a neural network resembling an autoencoder. The proposed method is empirically assessed on a channel mapping task whose objective is to predict downlink channels from uplink channels.

Baptiste Chatelier, Luc Le Magoarou, Getachew Redieteab

In modern communication systems, channel state information is of paramount importance to achieve capacity. It is then crucial to accurately estimate the channel. It is possible to perform SISO-OFDM channel estimation using sparse recovery techniques. However, this approach relies on the use of a physical wave propagation model to build a dictionary, which requires perfect knowledge of the system's parameters. In this paper, an unfolded neural network is used to lighten this constraint. Its architecture, based on a sparse recovery algorithm, allows SISO-OFDM channel estimation even if the system's parameters are not perfectly known. Indeed, its unsupervised online learning allows to learn the system's imperfections in order to enhance the estimation performance. The practicality of the proposed method is improved with respect to the state of the art in two aspects: constrained dictionaries are introduced in order to reduce sample complexity and hierarchical search within dictionaries is proposed in order to reduce time complexity. Finally, the performance of the proposed unfolded network is evaluated and compared to several baselines using realistic channel data, showing the great potential of the approach.

Baptiste Chatelier, Luc Le Magoarou, Vincent Corlay et al.

Modern communication systems rely on accurate channel estimation to achieve efficient and reliable transmission of information. As the communication channel response is highly related to the user's location, one can use a neural network to map the user's spatial coordinates to the channel coefficients. However, these latter are rapidly varying as a function of the location, on the order of the wavelength. Classical neural architectures being biased towards learning low frequency functions (spectral bias), such mapping is therefore notably difficult to learn. In order to overcome this limitation, this paper presents a frugal, model-based network that separates the low frequency from the high frequency components of the target mapping function. This yields an hypernetwork architecture where the neural network only learns low frequency sparse coefficients in a dictionary of high frequency components. Simulation results show that the proposed neural network outperforms standard approaches on realistic synthetic data.

Taha Yassine, Luc Le Magoarou, Matthieu Crussière et al.

Channel charting (CC) consists in learning a mapping between the space of raw channel observations, made available from pilot-based channel estimation in multicarrier multiantenna system, and a low-dimensional space where close points correspond to channels of user equipments (UEs) close spatially. Among the different methods of learning this mapping, some rely on a distance measure between channel vectors. Such a distance should reliably reflect the local spatial neighborhoods of the UEs. The recently proposed phase-insensitive (PI) distance exhibits good properties in this regards, but suffers from ambiguities due to both its periodic and oscillatory aspects, making users far away from each other appear closer in some cases. In this paper, a thorough theoretical analysis of the said distance and its limitations is provided, giving insights on how they can be mitigated. Guidelines for designing systems capable of learning quality charts are consequently derived. Experimental validation is then conducted on synthetic and realistic data in different scenarios.

Lucas Polo-López, Luc Le Magoarou, Romain Contreres et al.

This work presents a deep learning surrogate model for the fast simulation of high-dimensional frequency selective surfaces. We consider unit-cells which are built as multiple concatenated stacks of screens and their design requires the control over many geometrical degrees of freedom. Thanks to the introduction of physical insight into the model, it can produce accurate predictions of the S-parameters of a certain structure after training with a reduced dataset.The proposed model is highly versatile and it can be used with any kind of frequency selective surface, based on either perforations or patches of any arbitrary geometry. Numeric examples are presented here for the case of frequency selective surfaces composed of screens with rectangular perforations, showing an excellent agreement between the predicted performance and such obtained with a full-wave simulator.

Nay Klaimi, Clément Elvira, Philippe Mary et al.

Sparse recovery methods are essential for channel estimation and localization in modern communication systems, but their reliability relies on accurate physical models, which are rarely perfectly known. Their computational complexity also grows rapidly with the dictionary dimensions in large MIMO systems. In this paper, we propose MOMPnet, a novel unfolded sparse recovery framework that addresses both the reliability and complexity challenges of traditional methods. By integrating deep unfolding with data-driven dictionary learning, MOMPnet mitigates hardware impairments while preserving interpretability. Instead of a single large dictionary, multiple smaller, independent dictionaries are employed, enabling a low-complexity multidimensional Orthogonal Matching Pursuit algorithm. The proposed unfolded network is evaluated on realistic channel data against multiple baselines, demonstrating its strong performance and potential.

Taha Yassine, Baptiste Chatelier, Vincent Corlay et al.

Channel charting builds a map of the radio environment in an unsupervised way. The obtained chart locations can be seen as low-dimensional compressed versions of channel state information that can be used for a wide variety of applications, including beam prediction. In non-standalone or cell-free systems, chart locations computed at a given base station can be transmitted to several other base stations (possibly operating at different frequency bands) for them to predict which beams to use. This potentially yields a dramatic reduction of the overhead due to channel estimation or beam management, since only the base station performing charting requires channel state information, the others directly predicting the beam from the chart location. In this paper, advanced model-based neural network architectures are proposed for both channel charting and beam prediction. The proposed methods are assessed on realistic synthetic channels, yielding promising results.

Baptiste Chatelier, José Miguel Mateos-Ramos, Vincent Corlay et al.

Direction of arrival (DoA) estimation is a common sensing problem in radar, sonar, audio, and wireless communication systems. It has gained renewed importance with the advent of the integrated sensing and communication paradigm. To fully exploit the potential of such sensing systems, it is crucial to take into account potential hardware impairments that can negatively impact the obtained performance. This study introduces a joint DoA estimation and hardware impairment learning scheme following a model-based approach. Specifically, a differentiable version of the multiple signal classification (MUSIC) algorithm is derived, allowing efficient learning of the considered impairments. The proposed approach supports both supervised and unsupervised learning strategies, showcasing its practical potential. Simulation results indicate that the proposed method successfully learns significant inaccuracies in both antenna locations and complex gains. Additionally, the proposed method outperforms the classical MUSIC algorithm in the DoA estimation task.

Baptiste Chatelier, Vincent Corlay, Matthieu Crussière et al.

Reaping the benefits of multi-antenna communication systems in frequency division duplex (FDD) requires channel state information (CSI) reporting from mobile users to the base station (BS). Over the last decades, the amount of CSI to be collected has become very challenging owing to the dramatic increase of the number of antennas at BSs. To mitigate the overhead associated with CSI reporting, compressed CSI techniques have been proposed with the idea of recovering the original CSI at the BS from its compressed version sent by the mobile users. Channel charting is an unsupervised dimensionality reduction method that consists in building a radio-environment map from CSIs. Such a method can be considered in the context of the CSI compression problem, since a chart location is, by definition, a low-dimensional representation of the CSI. In this paper, the performance of channel charting for a task-based CSI compression application is studied. A comparison of the proposed method against baselines on realistic synthetic data is proposed, showing promising results.

Nay Klaimi, Amira Bedoui, Clément Elvira et al.

Hybrid precoding is a key ingredient of cost-effective massive multiple-input multiple-output transceivers. However, setting jointly digital and analog precoders to optimally serve multiple users is a difficult optimization problem. Moreover, it relies heavily on precise knowledge of the channels, which is difficult to obtain, especially when considering realistic systems comprising hardware impairments. In this paper, a joint channel estimation and hybrid precoding method is proposed, which consists in an end-to-end architecture taking received pilots as inputs and outputting pre-coders. The resulting neural network is fully model-based, making it lightweight and interpretable with very few learnable parameters. The channel estimation step is performed using the unfolded matching pursuit algorithm, accounting for imperfect knowledge of the antenna system, while the precoding step is done via unfolded projected gradient ascent. The great potential of the proposed method is empirically demonstrated on realistic synthetic channels.

Baptiste Chatelier, Vincent Corlay, Musa Furkan Keskin et al.

The increasing deployment of large antenna arrays at base stations has significantly improved the spatial resolution and localization accuracy of radio-localization methods. However, traditional signal processing techniques struggle in complex radio environments, particularly in scenarios dominated by non line of sight (NLoS) propagation paths, resulting in degraded localization accuracy. Recent developments in machine learning have facilitated the development of machine learning-assisted localization techniques, enhancing localization accuracy in complex radio environments. However, these methods often involve substantial computational complexity during both the training and inference phases. This work extends the well-established fingerprinting-based localization framework by simultaneously reducing its memory requirements and improving its accuracy. Specifically, a model-based neural network is used to learn the location-to-channel mapping, and then serves as a generative neural channel model. This generative model augments the fingerprinting comparison dictionary while reducing the memory requirements. The proposed method outperforms fingerprinting baselines by achieving sub-wavelength localization accuracy, even in complex static NLoS environments. Remarkably, it offers an improvement by several orders of magnitude in localization accuracy, while simultaneously reducing memory requirements by an order of magnitude compared to classical fingerprinting methods.

Arad Gast, Luc Le Magoarou, Nir Shlezinger

The increasing demands for high-throughput and energy-efficient wireless communications are driving the adoption of extremely large antennas operating at high-frequency bands. In these regimes, multiple users will reside in the radiative near-field, and accurate localization becomes essential. Unlike conventional far-field systems that rely solely on DOA estimation, near-field localization exploits spherical wavefront propagation to recover both DOA and range information. While subspace-based methods, such as MUSIC and its extensions, offer high resolution and interpretability for near-field localization, their performance is significantly impacted by model assumptions, including non-coherent sources, well-calibrated arrays, and a sufficient number of snapshots. To address these limitations, this work proposes AI-aided subspace methods for near-field localization that enhance robustness to real-world challenges. Specifically, we introduce NF-SubspaceNet, a deep learning-augmented 2D MUSIC algorithm that learns a surrogate covariance matrix to improve localization under challenging conditions, and DCD-MUSIC, a cascaded AI-aided approach that decouples angle and range estimation to reduce computational complexity. We further develop a novel model-order-aware training method to accurately estimate the number of sources, that is combined with casting of near field subspace methods as AI models for learning. Extensive simulations demonstrate that the proposed methods outperform classical and existing deep-learning-based localization techniques, providing robust near-field localization even under coherent sources, miscalibrations, and few snapshots.

Cheima Hammami, Lucas Polo-López, Luc Le Magoarou

This paper introduces an innovative end-to-end model-based deep learning approach for efficient electromagnetic analysis of high-dimensional frequency selective surfaces (FSS). Unlike traditional data-driven methods that require large datasets, this approach combines physical insights from equivalent circuit models with deep learning techniques to significantly reduce model complexity and enhance prediction accuracy. Compared to previously introduced model-based learning approaches, the proposed method is trained end-to-end from the physical structure of the FSS (geometric parameters) to its electromagnetic response (S-parameters). Additionally, an improvement in phase prediction accuracy through a modified loss function is presented. Comparisons with direct models, including deep neural networks (DNN) and radial basis function networks (RBFN), demonstrate the superiority of the model-based approach in terms of computational efficiency, model size, and generalization capability.

Baptiste Chatelier, Vincent Corlay, Matthieu Crussière et al.

Years of study of the propagation channel showed a close relation between a location and the associated communication channel response. The use of a neural network to learn the location-to-channel mapping can therefore be envisioned. The Implicit Neural Representation (INR) literature showed that classical neural architecture are biased towards learning low-frequency content, making the location-to-channel mapping learning a non-trivial problem. Indeed, it is well known that this mapping is a function rapidly varying with the location, on the order of the wavelength. This paper leverages the model-based machine learning paradigm to derive a problem-specific neural architecture from a propagation channel model. The resulting architecture efficiently overcomes the spectral-bias issue. It only learns low-frequency sparse correction terms activating a dictionary of high-frequency components. The proposed architecture is evaluated against classical INR architectures on realistic synthetic data, showing much better accuracy. Its mapping learning performance is explained based on the approximated channel model, highlighting the explainability of the model-based machine learning paradigm.

Luc Le Magoarou, Taha Yassine, Stéphane Paquelet et al.

Massive MIMO systems are highly efficient but critically rely on accurate channel state information (CSI) at the base station in order to determine appropriate precoders. CSI acquisition requires sending pilot symbols which induce an important overhead. In this paper, a method whose objective is to determine an appropriate precoder from the knowledge of the user's location only is proposed. Such a way to determine precoders is known as location based beamforming. It allows to reduce or even eliminate the need for pilot symbols, depending on how the location is obtained. the proposed method learns a direct mapping from location to precoder in a supervised way. It involves a neural network with a specific structure based on random Fourier features allowing to learn functions containing high spatial frequencies. It is assessed empirically and yields promising results on realistic synthetic channels. As opposed to previously proposed methods, it allows to handle both line-of-sight (LOS) and non-line-of-sight (NLOS) channels.

Luc Le Magoarou

Channel charting is an unsupervised learning task whose objective is to encode channels so that the obtained representation reflects the relative spatial locations of the corresponding users. It has many potential applications, ranging from user scheduling to proactive handover. In this paper, a channel charting method is proposed, based on a distance measure specifically designed to reduce the effect of small scale fading, which is an irrelevant phenomenon with respect to the channel charting task. A nonlinear dimensionality reduction technique aimed at preserving local distances (Isomap) is then applied to actually get the channel representation. The approach is empirically validated on realistic synthetic \new{multipath} MIMO channels, achieving better results than previously proposed approaches, at a lower cost.

Luc Le Magoarou

In a wireless network, gathering information at the base station about mobile users based only on uplink channel measurements is an interesting challenge. Indeed, accessing the users locations and predicting their downlink channels would be particularly useful in order to optimize the network efficiency. In this paper, a supervised machine learning approach addressing these tasks in an unified way is proposed. It relies on a labeled database that can be acquired in a simple way by the base station while operating. The proposed regression method can be seen as a computationally efficient two layers neural network initialized with a non-parametric estimator. It is illustrated on realistic channel data, both for the positioning and channel mapping tasks, achieving better results than previously proposed approaches, at a lower cost.

Taha Yassine, Luc Le Magoarou

Massive multiple-input multiple-output (MIMO) communication systems have a huge potential both in terms of data rate and energy efficiency, although channel estimation becomes challenging for a large number of antennas. Using a physical model allows to ease the problem by injecting a priori information based on the physics of propagation. However, such a model rests on simplifying assumptions and requires to know precisely the configuration of the system, which is unrealistic in practice.In this paper we present mpNet, an unfolded neural network specifically designed for massive MIMO channel estimation. It is trained online in an unsupervised way. Moreover, mpNet is computationally efficient and automatically adapts its depth to the signal-to-noise ratio (SNR). The method we propose adds flexibility to physical channel models by allowing a base station (BS) to automatically correct its channel estimation algorithm based on incoming data, without the need for a separate offline training phase.It is applied to realistic millimeter wave channels and shows great performance, achieving a channel estimation error almost as low as one would get with a perfectly calibrated system. It also allows incident detection and automatic correction, making the BS resilient and able to automatically adapt to changes in its environment.

Luc Le Magoarou, Stéphane Paquelet

Channel estimation is a difficult problem in MIMO systems. Using a physical model allows to ease the problem, injecting a priori information based on the physics of propagation. However, such models rest on simplifying assumptions and require to know precisely the system configuration, which is unrealistic.In this paper, we propose to perform online learning for channel estimation in a massive MIMO context, adding flexibility to physical models by unfolding a channel estimation algorithm (matching pursuit) as a neural network. This leads to a computationally efficient neural network that can be trained online when initialized with an imperfect model. The method allows a base station to automatically correct its channel estimation algorithm based on incoming data, without the need for a separate offline training phase.It is applied to realistic channels and shows great performance, achieving channel estimation error almost as low as one would get with a perfectly calibrated system.

Luc Le Magoarou, Rémi Gribonval, Nicolas Tremblay

The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent research domain that generalizes classical signal processing tools, such as the Fourier transform, to situations where the signal domain is given by any arbitrary graph instead of a regular grid. Today, there is no method to rapidly apply graph Fourier transforms. We propose in this paper a method to obtain approximate graph Fourier transforms that can be applied rapidly and stored efficiently. It is based on a greedy approximate diagonalization of the graph Laplacian matrix, carried out using a modified version of the famous Jacobi eigenvalues algorithm. The method is described and analyzed in detail, and then applied to both synthetic and real graphs, showing its potential.

Luc Le Magoarou, Rémi Gribonval

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems.

Luc Le Magoarou, Rémi Gribonval

Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the dictionary. The resulting dictionary is in general a dense matrix, and its manipulation can be computationally costly both at the learning stage and later in the usage of this dictionary, for tasks such as sparse coding. Dictionary learning is thus limited to relatively small-scale problems. In this paper, inspired by usual fast transforms, we consider a general dictionary structure that allows cheaper manipulation, and propose an algorithm to learn such dictionaries --and their fast implementation-- over training data. The approach is demonstrated experimentally with the factorization of the Hadamard matrix and with synthetic dictionary learning experiments.