Simultaneous Source Localization and Polarization Estimation via Non-Orthogonal Joint Diagonalization with Vector-Sensors

Joint estimation of direction-of-arrival (DOA) and polarization with electromagnetic vector-sensors (EMVS) is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD). Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme. Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation. Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods

5G Positioning and Mapping with Diffuse Multipath

5G mmWave communication is useful for positioning due to the geometric connection between the propagation channel and the propagation environment. Channel estimation methods can exploit the resulting sparsity to estimate parameters(delay and angles) of each propagation path, which in turn can be exploited for positioning and mapping. When paths exhibit significant spread in either angle or delay, these methods breakdown or lead to significant biases. We present a novel tensor-based method for channel estimation that allows estimation of mmWave channel parameters in a non-parametric form. The method is able to accurately estimate the channel, even in the absence of a specular component. This in turn enables positioning and mapping using only diffuse multipath. Simulation results are provided to demonstrate the efficacy of the proposed approach

Advanced Algebraic Concepts for Efficient Multi-Channel Signal Processing

Unsere moderne Gesellschaft ist Zeuge eines fundamentalen Wandels in der Art und Weise wie wir mit Technologie interagieren. Geräte werden zunehmend intelligenter - sie verfügen über mehr und mehr Rechenleistung und häufiger über eigene Kommunikationsschnittstellen. Das beginnt bei einfachen Haushaltsgeräten und reicht über Transportmittel bis zu großen überregionalen Systemen wie etwa dem Stromnetz. Die Erfassung, die Verarbeitung und der Austausch digitaler Informationen gewinnt daher immer mehr an Bedeutung. Die Tatsache, dass ein wachsender Anteil der Geräte heutzutage mobil und deshalb batteriebetrieben ist, begründet den Anspruch, digitale Signalverarbeitungsalgorithmen besonders effizient zu gestalten. Dies kommt auch dem Wunsch nach einer Echtzeitverarbeitung der großen anfallenden Datenmengen zugute. Die vorliegende Arbeit demonstriert Methoden zum Finden effizienter algebraischer Lösungen für eine Vielzahl von Anwendungen mehrkanaliger digitaler Signalverarbeitung. Solche Ansätze liefern nicht immer unbedingt die bestmögliche Lösung, kommen dieser jedoch häufig recht nahe und sind gleichzeitig bedeutend einfacher zu beschreiben und umzusetzen. Die einfache Beschreibungsform ermöglicht eine tiefgehende Analyse ihrer Leistungsfähigkeit, was für den Entwurf eines robusten und zuverlässigen Systems unabdingbar ist. Die Tatsache, dass sie nur gebräuchliche algebraische Hilfsmittel benötigen, erlaubt ihre direkte und zügige Umsetzung und den Test unter realen Bedingungen. Diese Grundidee wird anhand von drei verschiedenen Anwendungsgebieten demonstriert. Zunächst wird ein semi-algebraisches Framework zur Berechnung der kanonisch polyadischen (CP) Zerlegung mehrdimensionaler Signale vorgestellt. Dabei handelt es sich um ein sehr grundlegendes Werkzeug der multilinearen Algebra mit einem breiten Anwendungsspektrum von Mobilkommunikation über Chemie bis zur Bildverarbeitung. Verglichen mit existierenden iterativen Lösungsverfahren bietet das neue Framework die Möglichkeit, den Rechenaufwand und damit die Güte der erzielten Lösung zu steuern. Es ist außerdem weniger anfällig gegen eine schlechte Konditionierung der Ausgangsdaten. Das zweite Gebiet, das in der Arbeit besprochen wird, ist die unterraumbasierte hochauflösende Parameterschätzung für mehrdimensionale Signale, mit Anwendungsgebieten im RADAR, der Modellierung von Wellenausbreitung, oder bildgebenden Verfahren in der Medizin. Es wird gezeigt, dass sich derartige mehrdimensionale Signale mit Tensoren darstellen lassen. Dies erlaubt eine natürlichere Beschreibung und eine bessere Ausnutzung ihrer Struktur als das mit Matrizen möglich ist. Basierend auf dieser Idee entwickeln wir eine tensor-basierte Schätzung des Signalraums, welche genutzt werden kann um beliebige existierende Matrix-basierte Verfahren zu verbessern. Dies wird im Anschluss exemplarisch am Beispiel der ESPRIT-artigen Verfahren gezeigt, für die verbesserte Versionen vorgeschlagen werden, die die mehrdimensionale Struktur der Daten (Tensor-ESPRIT), nichzirkuläre Quellsymbole (NC ESPRIT), sowie beides gleichzeitig (NC Tensor-ESPRIT) ausnutzen. Um die endgültige Schätzgenauigkeit objektiv einschätzen zu können wird dann ein Framework für die analytische Beschreibung der Leistungsfähigkeit beliebiger ESPRIT-artiger Algorithmen diskutiert. Verglichen mit existierenden analytischen Ausdrücken ist unser Ansatz allgemeiner, da keine Annahmen über die statistische Verteilung von Nutzsignal und Rauschen benötigt werden und die Anzahl der zur Verfügung stehenden Schnappschüsse beliebig klein sein kann. Dies führt auf vereinfachte Ausdrücke für den mittleren quadratischen Schätzfehler, die Schlussfolgerungen über die Effizienz der Verfahren unter verschiedenen Bedingungen zulassen. Das dritte Anwendungsgebiet ist der bidirektionale Datenaustausch mit Hilfe von Relay-Stationen. Insbesondere liegt hier der Fokus auf Zwei-Wege-Relaying mit Hilfe von Amplify-and-Forward-Relays mit mehreren Antennen, da dieser Ansatz ein besonders gutes Kosten-Nutzen-Verhältnis verspricht. Es wird gezeigt, dass sich die nötige Kanalkenntnis mit einem einfachen algebraischen Tensor-basierten Schätzverfahren gewinnen lässt. Außerdem werden Verfahren zum Finden einer günstigen Relay-Verstärkungs-Strategie diskutiert. Bestehende Ansätze basieren entweder auf komplexen numerischen Optimierungsverfahren oder auf Ad-Hoc-Ansätzen die keine zufriedenstellende Bitfehlerrate oder Summenrate liefern. Deshalb schlagen wir algebraische Ansätze zum Finden der Relayverstärkungsmatrix vor, die von relevanten Systemmetriken inspiriert sind und doch einfach zu berechnen sind. Wir zeigen das algebraische ANOMAX-Verfahren zum Erreichen einer niedrigen Bitfehlerrate und seine Modifikation RR-ANOMAX zum Erreichen einer hohen Summenrate. Für den Spezialfall, in dem die Endgeräte nur eine Antenne verwenden, leiten wir eine semi-algebraische Lösung zum Finden der Summenraten-optimalen Strategie (RAGES) her. Anhand von numerischen Simulationen wird die Leistungsfähigkeit dieser Verfahren bezüglich Bitfehlerrate und erreichbarer Datenrate bewertet und ihre Effektivität gezeigt.Modern society is undergoing a fundamental change in the way we interact with technology. More and more devices are becoming "smart" by gaining advanced computation capabilities and communication interfaces, from household appliances over transportation systems to large-scale networks like the power grid. Recording, processing, and exchanging digital information is thus becoming increasingly important. As a growing share of devices is nowadays mobile and hence battery-powered, a particular interest in efficient digital signal processing techniques emerges. This thesis contributes to this goal by demonstrating methods for finding efficient algebraic solutions to various applications of multi-channel digital signal processing. These may not always result in the best possible system performance. However, they often come close while being significantly simpler to describe and to implement. The simpler description facilitates a thorough analysis of their performance which is crucial to design robust and reliable systems. The fact that they rely on standard algebraic methods only allows their rapid implementation and test under real-world conditions. We demonstrate this concept in three different application areas. First, we present a semi-algebraic framework to compute the Canonical Polyadic (CP) decompositions of multidimensional signals, a very fundamental tool in multilinear algebra with applications ranging from chemistry over communications to image compression. Compared to state-of-the art iterative solutions, our framework offers a flexible control of the complexity-accuracy trade-off and is less sensitive to badly conditioned data. The second application area is multidimensional subspace-based high-resolution parameter estimation with applications in RADAR, wave propagation modeling, or biomedical imaging. We demonstrate that multidimensional signals can be represented by tensors, providing a convenient description and allowing to exploit the multidimensional structure in a better way than using matrices only. Based on this idea, we introduce the tensor-based subspace estimate which can be applied to enhance existing matrix-based parameter estimation schemes significantly. We demonstrate the enhancements by choosing the family of ESPRIT-type algorithms as an example and introducing enhanced versions that exploit the multidimensional structure (Tensor-ESPRIT), non-circular source amplitudes (NC ESPRIT), and both jointly (NC Tensor-ESPRIT). To objectively judge the resulting estimation accuracy, we derive a framework for the analytical performance assessment of arbitrary ESPRIT-type algorithms by virtue of an asymptotical first order perturbation expansion. Our results are more general than existing analytical results since we do not need any assumptions about the distribution of the desired signal and the noise and we do not require the number of samples to be large. At the end, we obtain simplified expressions for the mean square estimation error that provide insights into efficiency of the methods under various conditions. The third application area is bidirectional relay-assisted communications. Due to its particularly low complexity and its efficient use of the radio resources we choose two-way relaying with a MIMO amplify and forward relay. We demonstrate that the required channel knowledge can be obtained by a simple algebraic tensor-based channel estimation scheme. We also discuss the design of the relay amplification matrix in such a setting. Existing approaches are either based on complicated numerical optimization procedures or on ad-hoc solutions that to not perform well in terms of the bit error rate or the sum-rate. Therefore, we propose algebraic solutions that are inspired by these performance metrics and therefore perform well while being easy to compute. For the MIMO case, we introduce the algebraic norm maximizing (ANOMAX) scheme, which achieves a very low bit error rate, and its extension Rank-Restored ANOMAX (RR-ANOMAX) that achieves a sum-rate close to an upper bound. Moreover, for the special case of single antenna terminals we derive the semi-algebraic RAGES scheme which finds the sum-rate optimal relay amplification matrix based on generalized eigenvectors. Numerical simulations evaluate the resulting system performance in terms of bit error rate and system sum rate which demonstrates the effectiveness of the proposed algebraic solutions

Blind identification of mixtures of quasi-stationary sources.

由於在盲語音分離的應用，線性準平穩源訊號混合的盲識別獲得了巨大的研究興趣。在這個問題上，我們利用準穩態源訊號的時變特性來識別未知的混合系統系數。傳統的方法有二：i)基於張量分解的平行因子分析(PARAFAC);ii)基於對多個矩陣的聯合對角化的聯合對角化算法(JD)。一般來說，PARAFAC和JD 都採用了源聯合的提取方法；即是說，對應所有訊號源的系統係數在升法上是用時進行識別的。在這篇論文中，我利用Khati-Rao(KR)子空間來設計一種新的盲識別算法。在我設計的算法中提出一種與傳統的方法不同的提法。在我設計的算法中，盲識別問題被分解成數個結構上相對簡單的子問題，分別對應不同的源。在超定混合模型，我們提出了一個專門的交替投影算法(AP)。由此產生的算法，不但能從經驗發現是非常有競爭力的，而且更有理論上的利落收斂保證。另外，作為一個有趣的延伸，該算法可循一個簡單的方式應用於欠混合模型。對於欠定混合模型，我們提出啟發式的秩最小化算法從而提高算法的速度。Blind identification of linear instantaneous mixtures of quasi-stationary sources (BI-QSS) has received great research interest over the past few decades, motivated by its application in blind speech separation. In this problem, we identify the unknown mixing system coefcients by exploiting the time-varying characteristics of quasi-stationary sources. Traditional BI-QSS methods fall into two main categories: i) Parallel Factor Analysis (PARAFAC), which is based on tensor decomposition; ii) Joint Diagonalization (JD), which is based on approximate joint diagonalization of multiple matrices. In both PARAFAC and JD, the joint-source formulation is used in general; i.e., the algorithms are designed to identify the whole mixing system simultaneously.In this thesis, I devise a novel blind identification framework using a Khatri-Rao (KR) subspace formulation. The proposed formulation is different from the traditional formulations in that it decomposes the blind identication problem into a number of per-source, structurally less complex subproblems. For the over determined mixing models, a specialized alternating projections algorithm is proposed for the KR subspace for¬mulation. The resulting algorithm is not only empirically found to be very competitive, but also has a theoretically neat convergence guarantee. Even better, the proposed algorithm can be applied to the underdetermined mixing models in a straightforward manner. Rank minimization heuristics are proposed to speed up the algorithm for the underdetermined mixing model. The advantages on employing the rank minimization heuristics are demonstrated by simulations.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Lee, Ka Kit.Thesis (M.Phil.)--Chinese University of Hong Kong, 2012.Includes bibliographical references (leaves 72-76).Abstracts also in Chinese.Abstract --- p.iAcknowledgement --- p.iiChapter 1 --- Introduction --- p.1Chapter 2 --- Settings of Quasi-Stationary Signals based Blind Identification --- p.4Chapter 2.1 --- Signal Model --- p.4Chapter 2.2 --- Assumptions --- p.5Chapter 2.3 --- Local Covariance Model --- p.7Chapter 2.4 --- Noise Covariance Removal --- p.8Chapter 2.5 --- Prewhitening --- p.9Chapter 2.6 --- Summary --- p.10Chapter 3 --- Review on Some Existing BI-QSS Algorithms --- p.11Chapter 3.1 --- Joint Diagonalization --- p.11Chapter 3.1.1 --- Fast Frobenius Diagonalization [4] --- p.12Chapter 3.1.2 --- Pham’s JD [5, 6] --- p.14Chapter 3.2 --- Parallel Factor Analysis --- p.16Chapter 3.2.1 --- Tensor Decomposition [37] --- p.17Chapter 3.2.2 --- Alternating-Columns Diagonal-Centers [12] --- p.21Chapter 3.2.3 --- Trilinear Alternating Least-Squares [10, 11] --- p.23Chapter 3.3 --- Summary --- p.25Chapter 4 --- Proposed Algorithms --- p.26Chapter 4.1 --- KR Subspace Criterion --- p.27Chapter 4.2 --- Blind Identification using Alternating Projections --- p.29Chapter 4.2.1 --- All-Columns Identification --- p.31Chapter 4.3 --- Overdetermined Mixing Models (N > K): Prewhitened Alternating Projection Algorithm (PAPA) --- p.32Chapter 4.4 --- Underdetermined Mixing Models (N <K) --- p.34Chapter 4.4.1 --- Rank Minimization Heuristic --- p.34Chapter 4.4.2 --- Alternating Projections Algorithm with Huber Function Regularization --- p.37Chapter 4.5 --- Robust KR Subspace Extraction --- p.40Chapter 4.6 --- Summary --- p.44Chapter 5 --- Simulation Results --- p.47Chapter 5.1 --- General Settings --- p.47Chapter 5.2 --- Overdetermined Mixing Models --- p.49Chapter 5.2.1 --- Simulation 1 - Performance w.r.t. SNR --- p.49Chapter 5.2.2 --- Simulation 2 - Performance w.r.t. the Number of Available Frames M --- p.49Chapter 5.2.3 --- Simulation 3 - Performance w.r.t. the Number of Sources K --- p.50Chapter 5.3 --- Underdetermined Mixing Models --- p.52Chapter 5.3.1 --- Simulation 1 - Success Rate of KR Huber --- p.53Chapter 5.3.2 --- Simulation 2 - Performance w.r.t. SNR --- p.54Chapter 5.3.3 --- Simulation 3 - Performance w.r.t. M --- p.54Chapter 5.3.4 --- Simulation 4 - Performance w.r.t. N --- p.56Chapter 5.4 --- Summary --- p.56Chapter 6 --- Conclusion and Future Works --- p.58Chapter A --- Convolutive Mixing Model --- p.60Chapter B --- Proofs --- p.63Chapter B.1 --- Proof of Theorem 4.1 --- p.63Chapter B.2 --- Proof of Theorem 4.2 --- p.65Chapter B.3 --- Proof of Observation 4.1 --- p.65Chapter B.4 --- Proof of Proposition 4.1 --- p.66Chapter C --- Singular Value Thresholding --- p.67Chapter D --- Categories of Speech Sounds and Their Impact on SOSs-based BI-QSS Algorithms --- p.69Chapter D.1 --- Vowels --- p.69Chapter D.2 --- Consonants --- p.69Chapter D.1 --- Silent Pauses --- p.70Bibliography --- p.7

Contributions to measurement-based dynamic MIMO channel modeling and propagation parameter estimation

Multiantenna (MIMO) transceivers are a key technology in emerging broadband wireless communication systems since they facilitate achieving the required high data rates and reliability. In order to develop and study the performance of MIMO systems, advanced channel modeling that captures also the spatial characteristics of the radio wave propagation is required. This thesis introduces several contributions in the area of measurement-based modeling of wireless MIMO propagation channels. Measurement based modeling provides realistic characterization of the space, time and frequency dependency of the physical layer for both MIMO transceiver design and network planning. The focus in this thesis is on modeling and parametric estimation of mobile MIMO radio propagation channels. First, an overview of MIMO channel modeling approaches is given. A hybrid model for characterizing the spatio-temporal structure of measured MIMO channels consisting of a superposition of double-directional, specular-like propagation paths, and a stochastic process describing the diffuse scattering is formulated. State-space modeling approach is introduced in order to capture the dynamic channel properties from mobile channel sounding measurements. Extended Kalman filter (EKF) is employed for the sequential estimation problem and also statistical hypothesis testing for adjusting the model order are introduced. Due to the improved dynamic model of the mobile radio channel, the EKF approach outperforms maximum likelihood (ML) based batch solutions both in terms of lower estimation error as well as computational complexity. Finally, tensor representation for modeling multidimensional MIMO channels is considered and a novel sequential unfolding SVD (SUSVD) tensor decomposition is introduced. The SUSVD is an orthogonal tensor decomposition having several important applications in signal processing. The advantages of applying the SUSVD instead of other well known tensor models such as parallel factorization and Tucker-models, are illustrated using application examples in channel sounding data processing