arXiv subjects

Maxime Guillaud

Publications and source records attributed to Maxime Guillaud.

At least 19 recordsLinked to original sources

arXiv2026

Leveraging von Mises Message-Passing for Massive MIMO Detection

Detection in massive multiple input multiple output (mMIMO) systems suffers from exponential complexity while using optimal decoders like maximum a posteriori (MAP). We propose a belief propagation-based detector based on directional statistics, applicable to mMIMO systems relying on PSK modulations. Thanks to a continuous relaxation of the PSK modulation to the unit circle, and to the use of von Mises parametric representations of the messages to obtain sparse representations of the (generally infinite dimensional) messages, the proposed method allows for approximate detection with a low complexity which does not depend on the PSK modulation order. Extensions of the algorithm to imperfect channel realizations are also present. We quantify the performance and complexity of the proposed approach and compare it with detection algorithms based on Gaussian approximation.

cs.IT↗

arXiv2026

An Experimental Assessment of the Spatial and Frequency Selectivity of Reconfigurable Intelligent Surfaces

This work investigates the impact of reconfigurable intelligent surfaces (RIS) on radio links other than the one for which the RIS configuration is optimized. We consider three different scenarios in which a secondary communication link could be affected by a RIS whose configuration is optimized for a primary communication link operating in the vicinity, on the same or on different frequencies. This question is investigated experimentally in the FR1 band, using the CorteXlab radio testbed and a Greenerwave RIS. We show that the impact, in terms of received power and impact on the channel phase of the secondary link, is significant even outside of the nominal frequency range of the RIS, and is not mitigated by carrier frequency separation between the two communication links.

cs.NI↗

arXiv2026

Tensor-Based Modulation on the Unit Circle: A Coding Perspective

Tensor-based modulation (TBM) provides a multi-linear spreading framework for blind multi-user separation in unsourced random access. In this paper, we show that TBM is a coded modulation built on a non-binary linear block code over $\mathbb{Z}_M$, whose symbols are mapped to $M$-PSK modulation, defining a geometrically uniform signal space code. We explicitly derive this generator matrix, characterize its rank deficiency, and show that reference symbols for tensor identifiability correspond to code shortening, producing a quasi-systematic or a systematic code, depending on the number of considered reference symbols for the TBM. Simulations in single-user AWGN and multi-user non-coherent multi-antenna fading channels demonstrate strong robustness and interference resilience, establishing TBM as a scalable, algebraically structured modulation-coding scheme bridging tensor representations and modern coding theory.

cs.IT↗

arXiv2023

Channel Charting for Streaming CSI Data

Channel charting (CC) applies dimensionality reduction to channel state information (CSI) data at the infrastructure basestation side with the goal of extracting pseudo-position information for each user. The self-supervised nature of CC enables predictive tasks that depend on user position without requiring any ground-truth position information. In this work, we focus on the practically relevant streaming CSI data scenario, in which CSI is constantly estimated. To deal with storage limitations, we develop a novel streaming CC architecture that maintains a small core CSI dataset from which the channel charts are learned. Curation of the core CSI dataset is achieved using a min-max-similarity criterion. Numerical validation with measured CSI data demonstrates that our method approaches the accuracy obtained from the complete CSI dataset while using only a fraction of CSI storage and avoiding catastrophic forgetting of old CSI data.

cs.IT↗

arXiv2023

On the Accuracy of Hotelling-Type Asymmetric Tensor Deflation: A Random Tensor Analysis

This work introduces an asymptotic study of Hotelling-type tensor deflation in the presence of noise, in the regime of large tensor dimensions. Specifically, we consider a low-rank asymmetric tensor model of the form $\sum_{i=1}^r \beta_i{\mathcal{A}}_i + {\mathcal{W}}$ where $\beta_i\geq 0$ and the ${\mathcal{A}}_i$'s are unit-norm rank-one tensors such that $\left| \langle {\mathcal{A}}_i, {\mathcal{A}}_j \rangle \right| \in [0, 1]$ for $i\neq j$ and ${\mathcal{W}}$ is an additive noise term. Assuming that the dominant components are successively estimated from the noisy observation and subsequently subtracted, we leverage recent advances in random tensor theory in the regime of asymptotically large tensor dimensions to analytically characterize the estimated singular values and the alignment of estimated and true singular vectors at each step of the deflation procedure. Furthermore, this result can be used to construct estimators of the signal-to-noise ratios $\beta_i$ and the alignments between the estimated and true rank-1 signal components.

stat.ML↗

arXiv2023

Hotelling Deflation on Large Symmetric Spiked Tensors

This paper studies the deflation algorithm when applied to estimate a low-rank symmetric spike contained in a large tensor corrupted by additive Gaussian noise. Specifically, we provide a precise characterization of the large-dimensional performance of deflation in terms of the alignments of the vectors obtained by successive rank-1 approximation and of their estimated weights, assuming non-trivial (fixed) correlations among spike components. Our analysis allows an understanding of the deflation mechanism in the presence of noise and can be exploited for designing more efficient signal estimation methods.

stat.ML↗

arXiv2023

Wireless Channel Charting: Theory, Practice, and Applications

Channel charting is a recently proposed framework that applies dimensionality reduction to channel state information (CSI) in wireless systems with the goal of associating a pseudo-position to each mobile user in a low-dimensional space: the channel chart. Channel charting summarizes the entire CSI dataset in a self-supervised manner, which opens up a range of applications that are tied to user location. In this article, we introduce the theoretical underpinnings of channel charting and present an overview of recent algorithmic developments and experimental results obtained in the field. We furthermore discuss concrete application examples of channel charting to network- and user-related applications, and we provide a perspective on future developments and challenges as well as the role of channel charting in next-generation wireless networks.

cs.IT↗

arXiv2022

On the Accuracy of Hotelling-Type Tensor Deflation: A Random Tensor Analysis

Leveraging on recent advances in random tensor theory, we consider in this paper a rank-$r$ asymmetric spiked tensor model of the form $\sum_{i=1}^r \beta_i A_i + W$ where $\beta_i\geq 0$ and the $A_i$'s are rank-one tensors such that $\langle A_i, A_j \rangle\in [0, 1]$ for $i\neq j$, based on which we provide an asymptotic study of Hotelling-type tensor deflation in the large dimensional regime. Specifically, our analysis characterizes the singular values and alignments at each step of the deflation procedure, for asymptotically large tensor dimensions. This can be used to construct consistent estimators of different quantities involved in the underlying problem, such as the signal-to-noise ratios $\beta_i$ or the alignments between the different signal components $\langle A_i, A_j \rangle$.

math.ST↗

arXiv2022

Delivering Ultra-Reliable Low-Latency Communications via Statistical Radio Maps

High reliability guarantees for Ultra-Reliable Low-Latency Communications (URLLC) require accurate knowledge of channel statistics, used as an input for rate selection. Exploiting the spatial consistency of channel statistics arises as a promising solution, allowing a base station to predict the propagation conditions and select the communication parameters for a new user from samples collected from previous users of the network. Based on this idea, this article provides a timely framework to exploit long-range channel spatial correlation through so-called statistical radio maps, enabling URLLC communications with given statistical guarantees. The framework is exemplified by predicting the channel capacity distribution both in a location-based radio map and in a latent space rendered by a channel chart, the latter being a localization-free approach based on channel state information (CSI). It is also shown how to use the maps to select the transmission rate in a new location that achieves a target level of reliability. Finally, several future directions and research challenges are also discussed.

cs.IT↗

arXiv2022

Constant Weight Codes with Gabor Dictionaries and Bayesian Decoding for Massive Random Access

This paper considers a general framework for massive random access based on sparse superposition coding. We provide guidelines for the code design and propose the use of constant-weight codes in combination with a dictionary design based on Gabor frames. The decoder applies an extension of approximate message passing (AMP) by iteratively exchanging soft information between an AMP module that accounts for the dictionary structure, and a second inference module that utilizes the structure of the involved constant-weight code. We apply the encoding structure to (i) the unsourced random access setting, where all users employ a common dictionary, and (ii) to the "sourced" random access setting with user-specific dictionaries. When applied to a fading scenario, the communication scheme essentially operates non-coherently, as channel state information is required neither at the transmitter nor at the receiver. We observe that in regimes of practical interest, the proposed scheme compares favorably with state-of-the art schemes, in terms of the (per-user) energy-per-bit requirement, as well as the number of active users that can be simultaneously accommodated in the system. Importantly, this is achieved with a considerably smaller size of the transmitted codewords, potentially yielding lower latency and bandwidth occupancy, as well as lower implementation complexity.

cs.IT↗

arXiv2021

When Random Tensors meet Random Matrices

Relying on random matrix theory (RMT), this paper studies asymmetric order-$d$ spiked tensor models with Gaussian noise. Using the variational definition of the singular vectors and values of (Lim, 2005), we show that the analysis of the considered model boils down to the analysis of an equivalent spiked symmetric \textit{block-wise} random matrix, that is constructed from \textit{contractions} of the studied tensor with the singular vectors associated to its best rank-1 approximation. Our approach allows the exact characterization of the almost sure asymptotic singular value and alignments of the corresponding singular vectors with the true spike components, when $\frac{n_i}{\sum_{j=1}^d n_j}\to c_i\in (0, 1)$ with $n_i$'s the tensor dimensions. In contrast to other works that rely mostly on tools from statistical physics to study random tensors, our results rely solely on classical RMT tools such as Stein's lemma. Finally, classical RMT results concerning spiked random matrices are recovered as a particular case.

math.PR↗

arXiv2021

Tensor Decomposition Bounds for TBM-Based Massive Access

Tensor-based modulation (TBM) has been proposed in the context of unsourced random access for massive uplink communication. In this modulation, transmitters encode data as rank-1 tensors, with factors from a discrete vector constellation. This construction allows to split the multi-user receiver into a user separation step based on a low-rank tensor decomposition, and independent single-user demappers. In this paper, we analyze the limits of the tensor decomposition using Cramér-Rao bounds, providing bounds on the accuracy of the estimated factors. These bounds are shown by simulation to be tight at high SNR. We introduce an approximate perturbation model for the output of the tensor decomposition, which facilitates the computation of the log-likelihood ratios (LLR) of the transmitted bits, and provides an approximate achievable bound for the finite-length error probability. Combining TBM with classical forward error correction coding schemes such as polar codes, we use the approximate LLR to derive soft-decision decoder showing a gain over hard-decision decoders at low SNR.

cs.IT↗

arXiv2021

How to Identify and Authenticate Users in Massive Unsourced Random Access

Identification and authentication are two basic functionalities of traditional random access protocols. In ALOHA-based random access, the packets usually include a field with a unique user address. However, when the number of users is massive and relatively small packets are transmitted, the overhead of including such field becomes restrictive. In unsourced random access (U-RA), the packets do not include any address field for the user, which maximizes the number of useful bits that are transmitted. However, by definition an U-RA protocol does not provide user identification. This paper presents a scheme that builds upon an underlying U-RA protocol and solves the problem of user identification and authentication. In our scheme, the users generate a message authentication code (MAC) that provides these functionalities without violating the main principle of unsourced random access: the selection of codewords from a common codebook is i.i.d. among all users.

cs.IT↗

arXiv2021

Triplet-Based Wireless Channel Charting: Architecture and Experiments

Channel charting is a data-driven baseband processing technique consisting in applying self-supervised machine learning techniques to channel state information (CSI), with the objective of reducing the dimension of the data and extracting the fundamental parameters governing its distribution. We introduce a novel channel charting approach based on triplets of samples. The proposed algorithm learns a meaningful similarity metric between CSI samples on the basis of proximity in their respective acquisition times, and simultaneously performs dimensionality reduction. We present an extensive experimental validation of the proposed approach on data obtained from a commercial Massive MIMO system; in particular, we evaluate to which extent the obtained channel chart is similar to the user location information, although it is not supervised by any geographical data. Finally, we propose and evaluate variations in the channel charting process, including the partially supervised case where some labels are available for part of the dataset.

eess.SP↗

arXiv2021

The Optimal DoF for the Noncoherent MIMO Channel with Generic Block Fading

The high-SNR capacity of the noncoherent MIMO channel has been derived for the case of independent and identically distributed (IID) Rayleigh block fading by exploiting the Gaussianity of the channel matrix. This implies the optimal degrees of freedom (DoF), i.e., the capacity pre-log factor. Nevertheless, as far as the optimal DoF is concerned, IID Rayleigh fading is apparently a sufficient but not necessary condition. In this paper, we show that the optimal DoF for the IID Rayleigh block fading channel is also the optimal DoF for a more general class of generic block fading channels, in which the random channel matrix has finite power and finite differential entropy. Our main contribution is a novel converse proof based on the duality approach.

cs.IT↗

arXiv2020

Joint Constellation Design for Noncoherent MIMO Multiple-Access Channels

We consider the joint constellation design problem for the noncoherent multiple-input multiple-output multiple-access channel (MAC). By analyzing the noncoherent maximum-likelihood detection error, we propose novel design criteria so as to minimize the error probability. As a baseline approach, we adapt several existing design criteria for the point-to-point channel to the MAC. Furthermore, we propose new design criteria. Our first proposed design metric is the dominating term in nonasymptotic lower and upper bounds on the pairwise error probability exponent. We give a geometric interpretation of the bound using Riemannian distance in the manifold of Hermitian positive definite matrices. From an analysis of this metric at high signal-to-noise ratio, we obtain further simplified metrics. For any given set of constellation sizes, the proposed metrics can be optimized over the set of constellation symbols. Motivated by the simplified metric, we propose a simple constellation construction consisting in partitioning a single-user constellation. We also provide a generalization of our previously proposed construction based on precoding individual constellations of lower dimensions. For a fixed joint constellation, the design metrics can be further optimized over the per-user transmit power, especially when the users transmit at different rates. Considering unitary space-time modulation, we investigate the option of building each individual constellation as a set of truncated unitary matrices scaled by the respective transmit power. Numerical results show that our proposed metrics are meaningful, and can be used as objectives to generate constellations through numerical optimization that perform better, for the same transmission rate and power constraint, than a common pilot-based scheme and the constellations optimized with existing metrics.

cs.IT↗

arXiv2020

Tensor-Based Modulation for Unsourced Massive Random Access

We introduce a modulation for unsourced massive random access whereby the transmitted symbols are rank-1 tensors constructed from Grassmannian sub-constellations. The use of a low-rank tensor structure, together with tensor decomposition in order to separate the users at the receiver, allows a convenient uncoupling between multi-user separation and single-user demapping. The proposed signaling scheme is designed for the block fading channel and multiple-antenna settings, and is shown to perform well in comparison to state-of-the-art unsourced approaches.

cs.IT↗

arXiv2020

Cube-Split: A Structured Grassmannian Constellation for Non-Coherent SIMO Communications

In this paper, we propose a practical structured constellation for non-coherent communication with a single transmit antenna over Rayleigh flat and block fading channel without instantaneous channel state information. The constellation symbols belong to the Grassmannian of lines and are defined up to a complex scaling. The constellation is generated by partitioning the Grassmannian of lines into a collection of bent hypercubes and defining a mapping onto each of these bent hypercubes such that the resulting symbols are approximately uniformly distributed on the Grassmannian. With a reasonable choice of parameters, this so-called cube-split constellation has higher packing efficiency, represented by the minimum distance, than the existing structured constellations. Furthermore, exploiting the constellation structure, we propose low-complexity greedy symbol decoder and log-likelihood ratio computation, as well as an efficient way to associate it to a multilevel code with multistage decoding. Numerical results show that the performance of the cube-split constellation is close to that of a numerically optimized constellation and better than other structured constellations. It also outperforms a coherent pilot-based scheme in terms of error probability and achievable data rate in the regime of short coherence time and large constellation size.

cs.IT↗