We consider the transmission of a continuous phase modulated (CPM) signal through a Gaussian channel affected by Doppler shifts. We propose a receiver robust to the Doppler shifts derived from a non-coherent detection criterion. We compare its performance to another non-coherent receiver based on a linear approximation of the CPM signal (Laurent decomposition) to which we add a Doppler compensation. Simulation results show that the first algorithm is robust to low-moderate Doppler shifts, while the second is robust to any one. We finally compare these two algorithms to delay-optimized differential detectors which do not require any Doppler shift estimation. We also provide complexity estimations to guide the possible complexity-performance trade-offs.

This is a supplementary material associated with the article "Untangling first and second order statistics contributions in multipath scenarios" that can be found, in the online version, at doi: https://doi.org/10.1016/j.sigpro.2022.108868.

We consider the transmission of a continuous phase modulated (CPM) signal through a Gaussian channel affected by Doppler shifts. We focus on a receiver robust to the Doppler shift by proposing two different types of receiver derived from a non-coherent detection criterion : one based on a linear approximation of the CPM signal (Laurent decomposition) and the other based on its exact expression. Simulation results show that the first algorithm is robust to low-moderate Doppler shifts, while the second is robust to any one.

Pendant plus de trente ans, les signaux Global Navigation Satellite System (GNSS) ont été utilisés comme signaux d’opportunité comme en GNSS Reflectometry (GNSS-R). L’étude de la réflexion de ces signaux sur le sol peut en effet conduire à l’estimation de paramètres sur la surface de réflexion ou sur la hauteur du récepteur. Lorsque cette hauteur est faible, le récepteur est à site bas et la proximité du sol entraîne de fortes interférences entre les signaux direct et réfléchi ce qui rend difficile une estimation non biaisée des différentes observables. Cette difficulté peut néanmoins être levée grâce à des signaux GNSS occupant des bandes de plus en plus larges. For more than three decades, Global Navigation Satellite System (GNSS) signals have been seen as signals of opportunity as in GNSS Reflectometry (GNSS-R). The study of the reflections from the ground of such signals can indeed lead to many features regarding the reflecting surface and the receiver’s height. When this height is small, the receiver is said ground-based and the vicinity to the ground induces important interferences between the direct and the reflected path which make it difficult to process to obtain an unbiased altimetry product. However, this difficulty can be leveraged thanks to recent wideband GNSS signals.

Cet article étudie une nouvelle architecture récurrente basée sur l’attention, plus légère et moins coûteuse en temps de calcul qu’un réseau d’attention global. Nous détaillons en quoi ce type d’architecture permet d’atteindre de meilleures performances que des réseaux récurrents plus classiques, dans le cas de la régression de séries temporelles. Nous montrons son intérêt pour la prédiction de l’état d’un réseau de communication, et plus particulièrement pour la détection de la congestion.

L’analyse multifractale est aujourd’hui un outil important de la caractérisation des dynamiques temporelles ou spatiales. Si l’estimation du paramètre de multifractalité peut se faire efficacement par des outils devenus standards, elle reste délicate pour des signaux et images de petites tailles. Le présent travail propose différents estimateurs construits sur des algorithmes Expectation-Maximization et compare leurs performances à l’aide de simulations de Monte Carlo contre les outils de l’état de l’art dans un contexte de signaux univariés de petites tailles.

Cet article présente une extension d'un algorithme EM (expectation maximization) publié récemment par les auteurs permettant d'estimer conjointement le centre et le rayon d'une hypersphère avec les hyperparamètres d'un modèle statistique prenant en compte le fait que les observations sont localisées sur une partie de l'hypersphère. La méthode proposée repose sur l'ajout de variables latentes ayant une loi a priori de von Mises-Fisher. Ce modèle statistique permet d'exprimer la vraisemblance complète des données, dont l'espérance conditionnée aux données observées possède une distribution connue conduisant à un algorithme EM simple et efficace. Les performances de cet algorithme d'estimation sont évaluées à l'aide de de simulations effectuées dans un cas bi-dimensionnel avec des résultats prometteurs.

In this article, we propose a new non-binary modulation which allows both Global Navigation Satellite Systems (GNSS) synchronization and the demodulation of non-binary symbols, without the need of a pilot signal, with the aim to provide a fast first position, velocity and time fix. The waveform is constructed as the product of i) a pseudo-random noise sequence with good auto-correlation and cross-correlation properties, and ii) a chirp spread spectrum family, which allows to demodulate non-binary symbols even if the signal phase is unknown. In order to demodulate the data, a bank of non-coherent matched filters is proposed. Because of the particular modulation structure, the receiver is capable to demodulate the navigation message faster while allowing the basic GNSS signal processing functionalities. Illustrative results are provided to support the discussion.

The Expectation-Maximization algorithm is a very popular approach for estimating the parameters of Gaussian mixture models (GMMs). A known issue with GMM estimation is its sensitivity to outliers, which can lead to poor estimation performance depending on the dataset under consideration. A common approach to deal with this issue is robust estimation, which typically consists of reducing the influence of the outliers on the estimators by weighting the impact of some samples of the dataset considered as outliers. In an unsupervised context, it is difficult to know which sample from the database corresponds to a normal observation. To that extent, we propose to use within the EM algorithm an outlier detection step that attributes an anomaly score to each sample of the database in an unsupervised way. A modified Bayesian Information Criterion is also introduced to efficiently select the appropriate amount of outliers contained in a dataset. The proposed method is tested on a benchmark remote sensing dataset coming from the UCI Machine Learning Repository. The experimental results show the interest of the proposed robustification when compared to other benchmark imputation procedures.

Multifractal analysis provides the theoretical and practical tools for describing the fluctuations of pointwise regularity in data and has led to many successful applications in signal and image processing. Originally limited to the analysis of single time series or images, a definition of multivariate multifractal analysis, i.e., the joint multifractal analysis of several data components, was recently proposed and was shown to effectively quantify local or transient dependencies in data regularity, beyond linear correlation. However, the accurate estimation of the associated matrix-valued joint multifractality parameters is notoriously difficult, thus limiting its practical usefulness. Leveraging a recent statistical model for bivariate multifractality, the goal of this work is to define and study Bayesian estimators designed to bypass this difficulty. Specifically, we study the original use of two different priors, combined with two different averages (arithmetic and Karcher means), for bivariate multifractal analysis. Monte Carlo simulations with synthetic data allow us to appreciate their relative performance and to conclude that our novel and original estimator based on a scaled inverse Wishart prior and the Karcher mean yields particularly favorable results with up to 5 times smaller rootmean-squared error than previous formulations.