National audience

In systems operating with extremely large antenna arrays and high-frequency signaling, multiple users often reside in the radiative near-field, and accurate localization becomes essential. Unlike conventional far-field systems that rely solely on direction of arrival (DoA) estimation, near-field localization exploits spherical wavefront propagation to recover both DoA and range information. While subspace-based methods, such as MUltiple SIgnal Classification (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 artificial intelligence (AI)-aided subspace methods for near-field localization that enhance robustness to real-world challenges. Specifically, we introduceNF-SubspaceNet, a deep learning-augmented 2D MUSIC algorithm that learns a surrogate covariance matrix to improve localization under challenging conditions, andDCD-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.

Future wireless technologies will require accurate localization of multiple users in the radiative near-field. A leading approach employs subspace decomposition of the input covariance and localizes by peak-finding over the MUltiple SIgnal Classification (MUSIC) spectrum, which is suitable for non-coherent sources with sufficient snapshots and calibrated arrays. This work introduces deep-learning-aided cascaded differentiable MUSIC (DCD-MUSIC) that augments MUSIC near-field localization with dedicated deep neural networks (DNNs), allowing it to operate reliably and interpretably. DCD-MUSIC utilizes two DNNs trained to produce surrogate covariances, one from which the angles and number of sources are recovered, and one to compute the range MUSIC spectrum. This is achieved via a novel learning method that (i) facilitates division into signal and noise subspaces; and (ii) converts MUSIC into a differentiable machine learning model. Our results show that DCD-MUSIC successfully localizes multiple coherent near- and far-field sources.

Gain-phase impairments (GPIs) affect both communication and sensing in 6G integrated sensing and communication (ISAC). We study the effect of GPIs in a single-input, multiple-output orthogonal frequency-division multiplexing ISAC system and develop a model-based unsupervised learning approach to simultaneously (i) estimate the gain-phase errors and (ii) localize sensing targets. The proposed method is based on the optimal maximum a-posteriori ratio test for a single target. Results show that the proposed approach can effectively estimate the gain-phase errors and yield similar position estimation performance as the case when the impairments are fully known.

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.

We study model-based end-to-end learning in the context of integrated sensing and communication (ISAC) under hardware impairments. Hardware impairments are usually addressed by means of array calibration with a focus on communication performance. However, residual impairments may exist that affect sensing performance. This paper proposes a data-driven framework for mitigating such impairments. A monostatic orthogonal frequency-division multiplexing (OFDM) sensing and multiple-input single-output (MISO) communication scenario is considered, incorporating hardware imperfections at the ISAC transceiver antenna array. Since conventional ISAC signal processing algorithms rely on mathematical models of the wireless channel, a mismatch occurs between the assumed mathematical models and the underlying reality in the presence of hardware impairments. We first study the detrimental effects of such impairments at the transmitter and receiver side of the proposed scenario, showcasing different levels of degradation on communication and sensing performances. As the core contribution of this work, we propose a novel differentiable version of the orthogonal matching pursuit (OMP) algorithm that is suitable for multi-target sensing and allows for efficient end-to-end learning of the hardware impairments. Based on the differentiable OMP, we devise two model-based parameterization strategies of the ISAC beamformer and sensing receiver to account for hardware impairments: (i) learning a dictionary of steering vectors for different angles and (ii) learning the parameterized hardware impairments. We carry out a comprehensive performance analysis of the proposed model-based learning approaches and a strong baseline consisting of least-squares beamforming, conventional OMP, and maximum-likelihood symbol detection for communication. Results show that by parameterizing the hardware impairments, learning approaches offer gains in terms of higher detection probability, position estimation accuracy, and lower symbol error rate (SER) compared to the baseline. We demonstrate that learning the parameterized hardware impairments outperforms learning a dictionary of steering vectors, also exhibiting the lowest complexity.

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.

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

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 due to ambiguities is provided. Consequently, a new channel distance especially designed to remove ambiguities is proposed. Guidelines for designing systems capable of learning quality charts with the proposed distance are also derived. Experimental validation is then conducted on synthetic and realistic data in different scenarios.

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.

Integrated sensing and communication (ISAC) is envisioned to be one of the pillars of 6G. However, 6G is also expected to be severely affected by hardware impairments. Under such impairments, standard model-based approaches might fail if they do not capture the underlying reality. To this end, data-driven methods are an alternative to deal with cases where imperfections cannot be easily modeled. In this paper, we propose a model-driven learning architecture for joint single-target multi-input multi-output (MIMO) sensing and multi-input single-output (MISO) communication. We compare it with a standard neural network approach under complexity constraints. Results show that under hardware impairments, both learning methods yield better results than the model-based standard baseline. If complexity constraints are further introduced, model-driven learning outperforms the neural-network-based approach. Model-driven learning also shows better generalization performance for new unseen testing scenarios.

Massive MIMO systems are highly efficient but critically rely on accurate channel state information (CSI) at the base station in or-der 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 pre-coder 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.

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.

This paper deals with the computation of integrals of centred bivariate Gaussian densities over any domain defined as an angular sector of ℝ2. Based on an accessible geometrical approach of the problem, we suggest to transform the double integral into a single one, leading to a tractable closed-form expression only involving trigonometric functions. This solution can also be seen as the angular cumulative distribution of bivariate centered Gaussian variables (X, Y). We aim to provide a didactic approach of our results, and we validate them by comparing with those of the literature.

In a multiple-input-multiple-output (MIMO) communication system, the multipath fading tends to vanish with increasing number of radio links. This well-known channel hardening phenomenon plays a central role in the design of massive MIMO systems. It is quantified by the coefficient of variation of the channel gain. The aim of this paper is to study channel hardening using a physical channel model in which the influences of propagation rays and antenna array topologies are highlighted. Our analyses and closed form results extend the hardening properties beyond the classical Rayleigh fading models and offer further insights on the relationship with channel characteristics.

Signal processing on graphs is a recent research domain that seeks to extend classical signal processing tools such as the Fourier transform to irregular domains given by a graph. In such a graph setting, a way to rapidly apply the Fourier transform, i.e. a Fast Fourier Transform (FFT), is lacking. In this paper, we propose to leverage the recently introduced Flexible Approximate MUlti-layer Sparse Transforms (FAST) in order to compute approximate FFTs on graphs. The approach is first described, then validated on several types of classical graphs and finally used for fast filtering, showing good potential.

Dictionary learning aims at finding a frame (called dictionary) in which some training data admits a sparse representation. Traditional dictionary learning is limited to relatively small-scale problems, because high-dimensional dense dictionaries can be costly to manipulate, both at the learning stage and when used for tasks such as sparse coding. In this paper, inspired by usual fast transforms, we consider a multi-layer sparse dictionary structure allowing cheaper manipulation, and propose a learning algorithm imposing this structure. The approach is demonstrated experimentally with a factorization of the Hadamard matrix and on image denoising.