Overview of Constrained PARAFAC Models

In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between different modes of the tensor which are captured by the equivalent core tensor. Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first introduced. This Kronecker product based approach is also formulated in terms of the index notation, which provides an original and concise formalism for both matricizing tensors and writing tensor models. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for $N^{th}$ order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models

Blind source separation of underdetermined mixtures of event-related sources

International audienceThis paper addresses the problem of blind source separation for underdetermined mixtures (i.e., more sources than sensors) of event-related sources that include quasi-periodic sources (e.g., electrocardiogram (ECG)), sources with synchronized trials (e.g., event-related potentials (ERP)), and amplitude-variant sources. The proposed method is based on two steps: (i) tensor decomposition for underdetermined source separation and (ii) signal extraction by Kalman filtering to recover the source dynamics. A tensor is constructed for each source by synchronizing on the ''event'' period of the corresponding signal and stacking different periods along the second dimension of the tensor. To cope with the interference from other sources that impede on the extraction of weak signals, two robust tensor decomposition methods are proposed and compared. Then, the state parameters used within a nonlinear dynamic model for the extraction of event-related sources from noisy mixtures are estimated from the loading matrices provided by the first step. The influence of different parameters on the robustness to outliers of the proposed method is examined by numerical simulations. Applied to clinical electroencephalogram (EEG), ECG and magnetocardiogram (MCG), the proposed method exhibits a significantly higher performance in terms of expected signal shape than classical source separation methods such as piCA and FastICA

Blind identification of possibly under-determined convolutive MIMO systems

Blind identi¯cation of a Linear Time Invariant (LTI) Multiple-Input Multiple-Output (MIMO) system is of great importance in many applications, such as speech processing, multi-access communication, multi-sensor sonar/radar systems, and biomedical applications. The objective of blind identi¯cation for a MIMO system is to identify an unknown system, driven by Ni unobservable inputs, based on the No system outputs. We ¯rst present a novel blind approach for the identi¯cation of a over-determined (No ¸ Ni) MIMO system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on Parallel Factorization (PARAFAC) of three- or four-way tensors constructed respectively based on third- or fourth-order cross-spectra of the system outputs. We show that the information available in the higher-order spectra allows for the system response to be identi¯ed up to a constant scaling and permutation ambiguities and a linear phase ambiguity. Important features of the proposed approaches are that they do not require channel length information, need no phase unwrapping, and unlike the majority of existing methods, need no pre-whitening of the system outputs.While several methods have been proposed to blindly identify over-determined convolutive MIMO systems, very scarce results exist for under-determined (No < Ni) case, all of which refer to systems that either have some special structure, or special No, Ni values. We propose a novel approach for blind identi¯cation of under-determined convolutive MIMO systems of general dimensions. As long as min(No;Ni) ¸ 2, we can always ¯nd the appropriate order of statistics that guarantees identi¯ability of the system response within trivial ambiguities. We provide the description of the class of identi¯able MIMO systems for a certain order of statistics K, and an algorithm to reach the solution.Finally we propose a novel approach for blind identi¯cation and symbol recovery of a distributed antenna system with multiple carrier-frequency o®sets (CFO), arising due to mismatch between the oscillators of transmitters and receivers. The received base-band signal is over-sampled, and its polyphase components are used to formulate a virtual MIMO problem. By applying blind MIMO system estimation techniques, the system response is estimated and used to subsequently decouple the users and transform the multiple CFOs estimation problem into a set of independent single CFO estimation problems.Ph.D., Electrical Engineering -- Drexel University, 200

Mobile and Wireless Communications

Mobile and Wireless Communications have been one of the major revolutions of the late twentieth century. We are witnessing a very fast growth in these technologies where mobile and wireless communications have become so ubiquitous in our society and indispensable for our daily lives. The relentless demand for higher data rates with better quality of services to comply with state-of-the art applications has revolutionized the wireless communication field and led to the emergence of new technologies such as Bluetooth, WiFi, Wimax, Ultra wideband, OFDMA. Moreover, the market tendency confirms that this revolution is not ready to stop in the foreseen future. Mobile and wireless communications applications cover diverse areas including entertainment, industrialist, biomedical, medicine, safety and security, and others, which definitely are improving our daily life. Wireless communication network is a multidisciplinary field addressing different aspects raging from theoretical analysis, system architecture design, and hardware and software implementations. While different new applications are requiring higher data rates and better quality of service and prolonging the mobile battery life, new development and advanced research studies and systems and circuits designs are necessary to keep pace with the market requirements. This book covers the most advanced research and development topics in mobile and wireless communication networks. It is divided into two parts with a total of thirty-four stand-alone chapters covering various areas of wireless communications of special topics including: physical layer and network layer, access methods and scheduling, techniques and technologies, antenna and amplifier design, integrated circuit design, applications and systems. These chapters present advanced novel and cutting-edge results and development related to wireless communication offering the readers the opportunity to enrich their knowledge in specific topics as well as to explore the whole field of rapidly emerging mobile and wireless networks. We hope that this book will be useful for students, researchers and practitioners in their research studies

Contributions à l’analyse des systèmes en réseau

La dernière décennie a vu l’émergence des travaux autour des systèmes dynamiques interconnectés (systèmes en réseaux ou systèmes cyberphysiques). Dans cette habilitation à diriger des recherches, je donne un aperçu des contributions qui ont été les miennes durant la dernière décennie sur : l’analyse des systèmes en réseaux (problème de consensus, observabilité et application à la préservation de la vie privée), le traitement des données de grandes dimensions (analyse tensorielle pour l’identification des systèmes non-linéaires, décomposition distribuée de tenseurs de grandes dimensions), et l’application à la mobilité intelligente (navigation en milieu urbain, prédiction et estimation de trafic, estimation d’attitude pour la navigation pédestre). Une prospective est ensuite développée autour de la sécurité des systèmes en réseaux, en se basant sur la théorie des systèmes, et sur l’analyse des données de grandes dimensions organisées dans des tenseurs de données avec des applications sur la mobilité intelligente

Extraction et débruitage de signaux ECG du foetus.

Les malformations cardiaques congénitales sont la première cause de décès liés à une anomalie congénitale. L electrocardiogramme du fœtus (ECGf), qui est censé contenir beaucoup plus d informations par rapport aux méthodes échographiques conventionnelles, peut être mesuré e par des électrodes sur l abdomen de la mère. Cependant, il est tres faible et mélangé avec plusieurs sources de bruit et interférence y compris l ECG de la mère (ECGm) dont le niveau est très fort. Dans les études précédentes, plusieurs méthodes ont été proposées pour l extraction de l ECGf à partir des signaux enregistrés par des électrodes placées à la surface du corps de la mère. Cependant, ces méthodes nécessitent un nombre de capteurs important, et s avèrent inefficaces avec un ou deux capteurs. Dans cette étude trois approches innovantes reposant sur une paramétrisation algébrique, statistique ou par variables d état sont proposées. Ces trois méthodes mettent en œuvre des modélisations différentes de la quasi-périodicité du signal cardiaque. Dans la première approche, le signal cardiaque et sa variabilité sont modélisés par un filtre de Kalman. Dans la seconde approche, le signal est découpé en fenêtres selon les battements, et l empilage constitue un tenseur dont on cherchera la décomposition. Dans la troisième approche, le signal n est pas modélisé directement, mais il est considéré comme un processus Gaussien, caractérisé par ses statistiques à l ordre deux. Dans les différentes modèles, contrairement aux études précédentes, l ECGm et le (ou les) ECGf sont modélisés explicitement. Les performances des méthodes proposées, qui utilisent un nombre minimum de capteurs, sont évaluées sur des données synthétiques et des enregistrements réels, y compris les signaux cardiaques des fœtus jumeaux.Congenital heart defects are the leading cause of birth defect-related deaths. The fetal electrocardiogram (fECG), which is believed to contain much more information as compared with conventional sonographic methods, can be measured by placing electrodes on the mother s abdomen. However, it has very low power and is mixed with several sources of noise and interference, including the strong maternal ECG (mECG). In previous studies, several methods have been proposed for the extraction of fECG signals recorded from the maternal body surface. However, these methods require a large number of sensors, and are ineffective with only one or two sensors. In this study, state modeling, statistical and deterministic approaches are proposed for capturing weak traces of fetal cardiac signals. These three methods implement different models of the quasi-periodicity of the cardiac signal. In the first approach, the heart rate and its variability are modeled by a Kalman filter. In the second approach, the signal is divided into windows according to the beats. Stacking the windows constructs a tensor that is then decomposed. In a third approach, the signal is not directly modeled, but it is considered as a Gaussian process characterized by its second order statistics. In all the different proposed methods, unlike previous studies, mECG and fECG(s) are explicitly modeled. The performances of the proposed methods, which utilize a minimal number of electrodes, are assessed on synthetic data and actual recordings including twin fetal cardiac signals.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Unified Framework for Multicarrier and Multiple Access based on Generalized Frequency Division Multiplexing

The advancements in wireless communications are the key-enablers of new applications with stringent requirements in low-latency, ultra-reliability, high data rate, high mobility, and massive connectivity. Diverse types of devices, ranging from tiny sensors to vehicles, with different capabilities need to be connected under various channel conditions. Thus, modern connectivity and network techniques at all layers are essential to overcome these challenges. In particular, the physical layer (PHY) transmission is required to achieve certain link reliability, data rate, and latency. In modern digital communications systems, the transmission is performed by means of a digital signal processing module that derives analog hardware. The performance of the analog part is influenced by the quality of the hardware and the baseband signal denoted as waveform. In most of the modern systems such as fifth generation (5G) and WiFi, orthogonal frequency division multiplexing (OFDM) is adopted as a favorite waveform due to its low-complexity advantages in terms of signal processing. However, OFDM requires strict requirements on hardware quality. Many devices are equipped with simplified analog hardware to reduce the cost. In this case, OFDM does not work properly as a result of its high peak-to-average power ratio (PAPR) and sensitivity to synchronization errors. To tackle these problems, many waveforms design have been recently proposed in the literature. Some of these designs are modified versions of OFDM or based on conventional single subcarrier. Moreover, multicarrier frameworks, such as generalized frequency division multiplexing (GFDM), have been proposed to realize varieties of conventional waveforms. Furthermore, recent studies show the potential of using non-conventional waveforms for increasing the link reliability with affordable complexity. Based on that, flexible waveforms and transmission techniques are necessary to adapt the system for different hardware and channel constraints in order to fulfill the applications requirements while optimizing the resources. The objective of this thesis is to provide a holistic view of waveforms and the related multiple access (MA) techniques to enable efficient study and evaluation of different approaches. First, the wireless communications system is reviewed with specific focus on the impact of hardware impairments and the wireless channel on the waveform design. Then, generalized model of waveforms and MA are presented highlighting various special cases. Finally, this work introduces low-complexity architectures for hardware implementation of flexible waveforms. Integrating such designs with software-defined radio (SDR) contributes to the development of practical real-time flexible PHY.:1 Introduction 1.1 Baseband transmission model 1.2 History of multicarrier systems 1.3 The state-of-the-art waveforms 1.4 Prior works related to GFDM 1.5 Objective and contributions 2 Fundamentals of Wireless Communications 2.1 Wireless communications system 2.2 RF transceiver 2.2.1 Digital-analogue conversion 2.2.2 QAM modulation 2.2.3 Effective channel 2.2.4 Hardware impairments 2.3 Waveform aspects 2.3.1 Single-carrier waveform 2.3.2 Multicarrier waveform 2.3.3 MIMO-Waveforms 2.3.4 Waveform performance metrics 2.4 Wireless Channel 2.4.1 Line-of-sight propagation 2.4.2 Multi path and fading process 2.4.3 General baseband statistical channel model 2.4.4 MIMO channel 2.5 Summary 3 Generic Block-based Waveforms 3.1 Block-based waveform formulation 3.1.1 Variable-rate multicarrier 3.1.2 General block-based multicarrier model 3.2 Waveform processing techniques 3.2.1 Linear and circular filtering 3.2.2 Windowing 3.3 Structured representation 3.3.1 Modulator 3.3.2 Demodulator 3.3.3 MIMO Waveform processing 3.4 Detection 3.4.1 Maximum-likelihood detection 3.4.2 Linear detection 3.4.3 Iterative Detection 3.4.4 Numerical example and insights 3.5 Summary 4 Generic Multiple Access Schemes 57 4.1 Basic multiple access and multiplexing schemes 4.1.1 Infrastructure network system model 4.1.2 Duplex schemes 4.1.3 Common multiplexing and multiple access schemes 4.2 General multicarrier-based multiple access 4.2.1 Design with fixed set of pulses 4.2.2 Computational model 4.2.3 Asynchronous multiple access 4.3 Summary 5 Time-Frequency Analyses of Multicarrier 5.1 General time-frequency representation 5.1.1 Block representation 5.1.2 Relation to Zak transform 5.2 Time-frequency spreading 5.3 Time-frequency block in LTV channel 5.3.1 Subcarrier and subsymbol numerology 5.3.2 Processing based on the time-domain signal 5.3.3 Processing based on the frequency-domain signal 5.3.4 Unified signal model 5.4 summary 6 Generalized waveforms based on time-frequency shifts 6.1 General time-frequency shift 6.1.1 Time-frequency shift design 6.1.2 Relation between the shifted pulses 6.2 Time-frequency shift in Gabor frame 6.2.1 Conventional GFDM 6.3 GFDM modulation 6.3.1 Filter bank representation 6.3.2 Block representation 6.3.3 GFDM matrix structure 6.3.4 GFDM demodulator 6.3.5 Alternative interpretation of GFDM 6.3.6 Orthogonal modulation and GFDM spreading 6.4 Summary 7 Modulation Framework: Architectures and Applications 7.1 Modem architectures 7.1.1 General modulation matrix structure 7.1.2 Run-time flexibility 7.1.3 Generic GFDM-based architecture 7.1.4 Flexible parallel multiplications architecture 7.1.5 MIMO waveform architecture 7.2 Extended GFDM framework 7.2.1 Architectures complexity and flexibility analysis 7.2.2 Number of multiplications 7.2.3 Hardware analysis 7.3 Applications of the extended GFDM framework 7.3.1 Generalized FDMA 7.3.2 Enchantment of OFDM system 7.4 Summary 7 Conclusions and Future work