Novel quaternion matrix factorisations

The recent introduction of η-Hermitian matrices A = AηH has opened a new avenue of research in quaternion signal processing. However, the exploitation of this matrix structure has been limited, perhaps due to the lack of joint diagonalisation methodologies of these matrices. As such, we propose novel decompositions of η- Hermitian matrices to address this shortcoming in the literature. As an application, we consider a blind source separation problem in the form of an Alamouti-based communication system. Simulation studies demonstrate the effectiveness of our proposed joint diagonalisation technique and indicate that our approach is particularly useful when the sources are correlated

Kurtosis-Based Blind Source Extraction of Complex Non-Circular Signals with Application in EEG Artifact Removal in Real-Time

A new class of complex domain blind source extraction algorithms suitable for the extraction of both circular and non-circular complex signals is proposed. This is achieved through sequential extraction based on the degree of kurtosis and in the presence of non-circular measurement noise. The existence and uniqueness analysis of the solution is followed by a study of fast converging variants of the algorithm. The performance is first assessed through simulations on well understood benchmark signals, followed by a case study on real-time artifact removal from EEG signals, verified using both qualitative and quantitative metrics. The results illustrate the power of the proposed approach in real-time blind extraction of general complex-valued sources

SMARAD - Centre of Excellence in Smart Radios and Wireless Research - Activity Report 2008 - 2010

Centre of Excellence in Smart Radios and Wireless Research (SMARAD), originally established with the name Smart and Novel Radios Research Unit, is aiming at world-class research and education in Future radio and antenna systems, Cognitive radio, Millimetre wave and THz techniques, Sensors, and Materials and energy, using its expertise in RF, microwave and millimetre wave engineering, in integrated circuit design for multi-standard radios as well as in wireless communications. SMARAD has the Centre of Excellence in Research status from the Academy of Finland since 2002 (2002-2007 and 2008-2013). Currently SMARAD consists of five research groups from three departments, namely the Department of Radio Science and Engineering, Department of Micro and Nanosciences, and Department of Signal Processing and Acoustics, all within the Aalto University School of Electrical Engineering. The total number of employees within the research unit is about 100 including 8 professors, about 30 senior scientists and about 40 graduate students and several undergraduate students working on their Master thesis. The relevance of SMARAD to the Finnish society is very high considering the high national income from exports of telecommunications and electronics products. The unit conducts basic research but at the same time maintains close co-operation with industry. Novel ideas are applied in design of new communication circuits and platforms, transmission techniques and antenna structures. SMARAD has a well-established network of co-operating partners in industry, research institutes and academia worldwide. It coordinates a few EU projects. The funding sources of SMARAD are diverse including the Academy of Finland, EU, ESA, Tekes, and Finnish and foreign telecommunications and semiconductor industry. As a byproduct of this research SMARAD provides highest-level education and supervision to graduate students in the areas of radio engineering, circuit design and communications through Aalto University and Finnish graduate schools such as Graduate School in Electronics, Telecommunications and Automation (GETA). During years 2008 – 2010, 21 doctor degrees were awarded to the students of SMARAD. In the same period, the SMARAD researchers published 141 refereed journal articles and 333 conference papers

Algorithmes pour la diagonalisation conjointe de tenseurs sans contrainte unitaire. Application à la séparation MIMO de sources de télécommunications numériques

This thesis develops joint diagonalization of matrices and third-order tensors methods for MIMO source separation in the field of digital telecommunications. After a state of the art, the motivations and the objectives are presented. Then the joint diagonalisation and the blind source separation issues are defined and a link between both fields is established. Thereafter, five Jacobi-like iterative algorithms based on an LU parameterization are developed. For each of them, we propose to derive the diagonalization matrix by optimizing an inverse criterion. Two ways are investigated : minimizing the criterion in a direct way or assuming that the elements from the considered set are almost diagonal. Regarding the parameters derivation, two strategies are implemented : one consists in estimating each parameter independently, the other consists in the independent derivation of couple of well-chosen parameters. Hence, we propose three algorithms for the joint diagonalization of symmetric complex matrices or hermitian ones. The first one relies on searching for the roots of the criterion derivative, the second one relies on a minor eigenvector research and the last one relies on a gradient descent method enhanced by computation of the optimal adaptation step. In the framework of joint diagonalization of symmetric, INDSCAL or non symmetric third-order tensors, we have developed two algorithms. For each of them, the parameters derivation is done by computing the roots of the considered criterion derivative. We also show the link between the joint diagonalization of a third-order tensor set and the canonical polyadic decomposition of a fourth-order tensor. We confront both methods through numerical simulations. The good behavior of the proposed algorithms is illustrated by means of computing simulations. Finally, they are applied to the source separation of digital telecommunication signals.Cette thèse développe des méthodes de diagonalisation conjointe de matrices et de tenseurs d’ordre trois, et son application à la séparation MIMO de sources de télécommunications numériques. Après un état, les motivations et objectifs de la thèse sont présentés. Les problèmes de la diagonalisation conjointe et de la séparation de sources sont définis et un lien entre ces deux domaines est établi. Par la suite, plusieurs algorithmes itératifs de type Jacobi reposant sur une paramétrisation LU sont développés. Pour chacun des algorithmes, on propose de déterminer les matrices permettant de diagonaliser l’ensemble considéré par l’optimisation d’un critère inverse. On envisage la minimisation du critère selon deux approches : la première, de manière directe, et la seconde, en supposant que les éléments de l’ensemble considéré sont quasiment diagonaux. En ce qui concerne l’estimation des différents paramètres du problème, deux stratégies sont mises en œuvre : l’une consistant à estimer tous les paramètres indépendamment et l’autre reposant sur l’estimation indépendante de couples de paramètres spécifiquement choisis. Ainsi, nous proposons trois algorithmes pour la diagonalisation conjointe de matrices complexes symétriques ou hermitiennes et deux algorithmes pour la diagonalisation conjointe d’ensembles de tenseurs symétriques ou non-symétriques ou admettant une décomposition INDSCAL. Nous montrons aussi le lien existant entre la diagonalisation conjointe de tenseurs d’ordre trois et la décomposition canonique polyadique d’un tenseur d’ordre quatre, puis nous comparons les algorithmes développés à différentes méthodes de la littérature. Le bon comportement des algorithmes proposés est illustré au moyen de simulations numériques. Puis, ils sont validés dans le cadre de la séparation de sources de télécommunications numériques