16 research outputs found
Numerical performance of a tensor music algorithm based on HOSVD for a mixture of polarized sources
International audienceIn this paper, we develop an improved tensor MUSIC algorithm adapted to multidimensional data by means of multilinear algebra tools. This approach allows to preserve the multidimensional structure as the signal and the noise subspaces are estimated from the Higher Order Singular Value Decomposition (HOSVD) of the covariance tensor. The proposed algorithm is applied to a polarized source model. By computing the Mean Squared Error (MSE) for different scenarios, the performance of this method is compared to the classical MUSIC algorithm as well as the vector MUSIC algorithm that includes the polarization information. The simulations show that our algorithm outperforms the vector algorithms
Robust MIMO Channel Estimation from Incomplete and Corrupted Measurements
Location-aware communication is one of the enabling techniques for future 5G networks. It requires accurate temporal and spatial channel estimation from multidimensional data. Most of the existing channel estimation techniques assume that the measurements are complete and noise is Gaussian. While these approaches are brittle to corrupted or outlying measurements, which are ubiquitous in real applications. To address these issues, we develop a lp-norm minimization based iteratively reweighted higher-order singular value decomposition algorithm. It is robust to Gaussian as well as the impulsive noise even when the measurement data is incomplete. Compared with the state-of-the-art techniques, accurate estimation results are achieved for the proposed approach
Statistical Nested Sensor Array Signal Processing
Source number detection and direction-of-arrival (DOA) estimation are two major applications of sensor arrays. Both applications are often confined to the use of uniform linear arrays (ULAs), which is expensive and difficult to yield wide aperture. Besides, a ULA with N scalar sensors can resolve at most N â 1 sources. On the other hand, a systematic approach was recently proposed to achieve O(N 2 ) degrees of freedom (DOFs) using O(N) sensors based on a nested array, which is obtained by combining two or more ULAs with successively increased spacing.
This dissertation will focus on a fundamental study of statistical signal processing of nested arrays. Five important topics are discussed, extending the existing nested-array strategies to more practical scenarios. Novel signal models and algorithms are proposed.
First, based on the linear nested array, we consider the problem for wideband Gaussian sources. To employ the nested array to the wideband case, we propose effective strategies to apply nested-array processing to each frequency component, and combine all the spectral information of various frequencies to conduct the detection and estimation. We then consider the practical scenario with distributed sources, which considers the spreading phenomenon of sources.
Next, we investigate the self-calibration problem for perturbed nested arrays, for which existing works require certain modeling assumptions, for example, an exactly known array geometry, including the sensor gain and phase. We propose corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares is used to deal with the phase error issue.
We further propose a new class of nested vector-sensor arrays which is capable of significantly increasing the DOFs. This is not a simple extension of the nested scalar-sensor array. Both the signal model and the signal processing strategies are developed in the multidimensional sense. Based on the analytical results, we consider two main applications: electromagnetic (EM) vector sensors and acoustic vector sensors.
Last but not least, in order to make full use of the available limited valuable data, we propose a novel strategy, which is inspired by the jackknifing resampling method. Exploiting numerous iterations of subsets of the whole data set, this strategy greatly improves the results of the existing source number detection and DOA estimation methods
Advanced Algebraic Concepts for Efficient Multi-Channel Signal Processing
ï»żUnsere moderne Gesellschaft ist Zeuge eines fundamentalen Wandels in der Art und Weise
wie wir mit Technologie interagieren. GerĂ€te werden zunehmend intelligenter - sie verfĂŒgen
ĂŒber mehr und mehr Rechenleistung und hĂ€ufiger ĂŒber eigene Kommunikationsschnittstellen.
Das beginnt bei einfachen HaushaltsgerĂ€ten und reicht ĂŒber Transportmittel bis zu groĂen
ĂŒberregionalen 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 GerÀte heutzutage mobil und deshalb batteriebetrieben ist,
begrĂŒndet den Anspruch, digitale Signalverarbeitungsalgorithmen besonders effizient zu gestalten.
Dies kommt auch dem Wunsch nach einer Echtzeitverarbeitung der groĂen anfallenden
Datenmengen zugute.
Die vorliegende Arbeit demonstriert Methoden zum Finden effizienter algebraischer Lösungen
fĂŒr eine Vielzahl von Anwendungen mehrkanaliger digitaler Signalverarbeitung. Solche AnsĂ€tze
liefern nicht immer unbedingt die bestmögliche Lösung, kommen dieser jedoch hÀufig recht
nahe und sind gleichzeitig bedeutend einfacher zu beschreiben und umzusetzen. Die einfache
Beschreibungsform ermöglicht eine tiefgehende Analyse ihrer LeistungsfĂ€higkeit, was fĂŒr den
Entwurf eines robusten und zuverlÀssigen Systems unabdingbar ist. Die Tatsache, dass sie nur
gebrĂ€uchliche algebraische Hilfsmittel benötigen, erlaubt ihre direkte und zĂŒgige Umsetzung
und den Test unter realen Bedingungen.
Diese Grundidee wird anhand von drei verschiedenen Anwendungsgebieten demonstriert.
ZunÀchst 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 ĂŒber Chemie bis zur Bildverarbeitung. Verglichen mit existierenden
iterativen Lösungsverfahren bietet das neue Framework die Möglichkeit, den Rechenaufwand
und damit die GĂŒte der erzielten Lösung zu steuern. Es ist auĂerdem weniger anfĂ€llig gegen eine
schlechte Konditionierung der Ausgangsdaten. Das zweite Gebiet, das in der Arbeit besprochen
wird, ist die unterraumbasierte hochauflösende ParameterschĂ€tzung fĂŒr 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 natĂŒrlichere Beschreibung und eine
bessere Ausnutzung ihrer Struktur als das mit Matrizen möglich ist. Basierend auf dieser Idee
entwickeln wir eine tensor-basierte SchÀtzung 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, fĂŒr die verbesserte Versionen
vorgeschlagen werden, die die mehrdimensionale Struktur der Daten (Tensor-ESPRIT),
nichzirkulÀre Quellsymbole (NC ESPRIT), sowie beides gleichzeitig (NC Tensor-ESPRIT) ausnutzen.
Um die endgĂŒltige SchĂ€tzgenauigkeit objektiv einschĂ€tzen zu können wird dann ein
Framework fĂŒr die analytische Beschreibung der LeistungsfĂ€higkeit beliebiger ESPRIT-artiger
Algorithmen diskutiert. Verglichen mit existierenden analytischen AusdrĂŒcken ist unser Ansatz
allgemeiner, da keine Annahmen ĂŒber die statistische Verteilung von Nutzsignal und
Rauschen benötigt werden und die Anzahl der zur VerfĂŒgung stehenden SchnappschĂŒsse beliebig
klein sein kann. Dies fĂŒhrt auf vereinfachte AusdrĂŒcke fĂŒr den mittleren quadratischen
SchĂ€tzfehler, die Schlussfolgerungen ĂŒber 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-VerhÀltnis verspricht. Es wird gezeigt, dass sich die nötige Kanalkenntnis
mit einem einfachen algebraischen Tensor-basierten SchĂ€tzverfahren gewinnen lĂ€sst. AuĂerdem
werden Verfahren zum Finden einer gĂŒnstigen Relay-VerstĂ€rkungs-Strategie diskutiert. Bestehende
AnsÀtze basieren entweder auf komplexen numerischen Optimierungsverfahren oder auf
Ad-Hoc-AnsÀtzen die keine zufriedenstellende Bitfehlerrate oder Summenrate liefern. Deshalb
schlagen wir algebraische AnsÀtze zum Finden der RelayverstÀrkungsmatrix 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. FĂŒr den Spezialfall, in dem
die EndgerÀte nur eine Antenne verwenden, leiten wir eine semi-algebraische Lösung zum
Finden der Summenraten-optimalen Strategie (RAGES) her. Anhand von numerischen Simulationen
wird die LeistungsfĂ€higkeit dieser Verfahren bezĂŒglich Bitfehlerrate und erreichbarer
Datenrate bewertet und ihre EffektivitÀt 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
Advanced array signal processing algorithms for multi-dimensional parameter estimation
Multi-dimensional high-resolution parameter estimation is a fundamental problem in a variety of array signal processing applications, including radar, mobile communications, multiple-input multiple-output (MIMO) channel estimation, and biomedical imaging. The objective is to estimate the frequency parameters of noise-corrupted multi-dimensional harmonics that are sampled on a multi-dimensional grid. Among the proposed parameter estimation algorithms to solve this problem, multi-dimensional (R-D) ESPRIT-type algorithms have been widely used due to their computational efficiency and their simplicity. Their performance in various scenarios has been objectively evaluated by means of an analytical performance assessment framework. Recently, a relatively new class of parameter estimators based on sparse signal reconstruction has gained popularity due to their robustness under challenging conditions such as a small sample size or strong signal correlation. A common approach towards further improving the performance of parameter estimation algorithms is to exploit prior knowledge on the structure of the signals. In this thesis, we develop enhanced versions of R-D ESPRIT-type algorithms and the relatively new class of sparsity-based parameter estimation algorithms by exploiting the multi-dimensional structure of the signals and the statistical properties of strictly non-circular (NC) signals.
First, we derive analytical expressions for the gain from forward-backward averaging and tensor-based processing in R-D ESPRIT-type and R-D Tensor-ESPRIT-type algorithms for the special case of two sources. This is accomplished by simplifying the generic analytical MSE expressions from the performance analysis of R-D ESPRIT-type algorithms. The derived expressions allow us to identify the parameter settings, e.g., the number of sensors, the signal correlation, and the source separation, for which both gains are most pronounced or no gain is achieved.
Second, we propose the generalized least squares (GLS) algorithm to solve the overdetermined shift invariance equation in R-D ESPRIT-type algorithms. GLS directly incorporates the statistics of the subspace estimation error into the shift invariance solution through its covariance matrix, which is found via a first-order perturbation expansion. To objectively assess the estimation accuracy, we derive performance analysis expressions for the mean square error (MSE) of GLS-based ESPRIT-type algorithms, which are asymptotic in the effective SNR, i.e., the results become exact for a high SNR or a small sample size. Based on the performance analysis, we show that the simplified MSE expressions of GLS-based 1-D ESPRIT-type algorithms for a single source and two sources can be transformed into the corresponding Cramer-Rao bound (CRB) expressions, which provide a lower limit on the estimation error. Thereby, ESPRIT-type algorithms can become asymptotically efficient, i.e., they asymptotically achieve the CRB. Numerical simulations show that this can also be the case for more than two sources.
In the third contribution, we derive matrix-based and tensor-based R-D NC ESPRIT-type algorithms for multi-dimensional strictly non-circular signals, where R-D NC Tensor-ESPRIT-type algorithms exploit both the multi-dimensional structure and the strictly non-circular structure of the signals. Exploiting the NC signal structure by means of a preprocessing step leads to a virtual doubling of the original sensor array, which provides an improved estimation accuracy and doubles the number of resolvable signals. We derive an analytical performance analysis and compute simplified MSE expressions for a single source and two sources. These expressions are used to analytically compute the NC gain for these cases, which has so far only been studied via Monte-Carlo simulations. We additionally consider spatial smoothing preprocessing for R-D ESPRIT-type algorithms, which has been widely used to improve the estimation performance for highly correlated signals or a small sample size. Once more, we derive performance analysis expressions for R-D ESPRIT-type algorithms and their corresponding NC versions with spatial smoothing and derive the optimal number of subarrays for spatial smoothing that minimizes the MSE for a single source.
In the next part, we focus on the relatively new concept of parameter estimation via sparse signal reconstruction (SSR), in which the sparsity of the received signal power spectrum in the spatio-temporal domain is exploited. We develop three NC SSR-based parameter estimation algorithms for strictly noncircular sources and show that the benefits of exploiting the signalsâ NC structure can also be achieved via sparse reconstruction. We develop two grid-based NC SSR algorithms with a low-complexity off-grid estimation procedure, and a gridless NC SSR algorithm based on atomic norm minimization.
As the final contribution of this thesis, we derive the deterministic R-D NC CRB for strictly non-circular sources, which serves as a benchmark for the presented R-D NC ESPRIT-type algorithms and the NC SSR-based parameter estimation algorithms. We show for the special cases of, e.g., full coherence, a single snapshot, or a single strictly non-circular source, that the deterministic R-D NC CRB reduces to the existing deterministic R-D CRB for arbitrary signals. Therefore, no NC gain can be achieved in these cases. For the special case of two closely-spaced NC sources, we simplify the NC CRB expression and compute the NC gain for two closely-spaced NC signals. Finally, its behavior in terms of the physical parameters is studied to determine the parameter settings that provide the largest NC gain.Die hochauflösende ParameterschĂ€tzung fĂŒr mehrdimensionale Signale findet Anwendung in vielen Bereichen der Signalverarbeitung in Mehrantennensystemen. Zu den Anwendungsgebieten zĂ€hlen beispielsweise Radar, die Mobilkommunikation, die KanalschĂ€tzung in multiple-input multiple-output (MIMO)-Systemen und bildgebende Verfahren in der Biosignalverarbeitung. In letzter Zeit sind eine Vielzahl von Algorithmen zur ParameterschĂ€tzung entwickelt worden, deren SchĂ€tzgenauigkeit durch eine analytische Beschreibung der LeistungsfĂ€higkeit objektiv bewertet werden kann. Eine verbreitete Methode zur Verbesserung der SchĂ€tzgenauigkeit von ParameterschĂ€tzverfahren ist die Ausnutzung von Vorwissen bezĂŒglich der Signalstruktur. In dieser Arbeit werden mehrdimensionale ESPRIT-Verfahren als Beispiel fĂŒr Unterraum-basierte Verfahren entwickelt und analysiert, die explizit die mehrdimensionale Signalstruktur mittels Tensor-Signalverarbeitung ausnutzt und die statistischen Eigenschaften von nicht-zirkulĂ€ren Signalen einbezieht. Weiterhin werden neuartige auf Signalrekonstruktion basierende Algorithmen vorgestellt, die die nicht-zirkulĂ€re Signalstruktur bei der Rekonstruktion ausnutzen. Die vorgestellten Verfahren ermöglichen eine deutlich verbesserte SchĂ€tzgĂŒte und verdoppeln die Anzahl der auflösbaren Signale. Die Vielzahl der ForschungsbeitrĂ€ge in dieser Arbeit setzt sich aus verschiedenen Teilen zusammen.
Im ersten Teil wird die analytische Beschreibung der LeistungsfĂ€higkeit von Matrix-basierten und Tensor-basierten ESPRIT-Algorithmen betrachtet. Die Tensor-basierten Verfahren nutzen explizit die mehrdimensionale Struktur der Daten aus. Es werden fĂŒr beide Algorithmenarten vereinfachte analytische AusdrĂŒcke fĂŒr den mittleren quadratischen SchĂ€tzfehler fĂŒr zwei Signalquellen hergeleitet, die lediglich von den physikalischen Parametern, wie zum Beispiel die Anzahl der Antennenelemente, das Signal-zu-Rausch-VerhĂ€ltnis, oder die Anzahl der Messungen, abhĂ€ngen. Ein Vergleich dieser AusdrĂŒcke ermöglicht die Berechnung einfacher AusdrĂŒcke fĂŒr den SchĂ€tzgenauigkeitsgewinn durch den forward-backward averaging (FBA)-Vorverarbeitungsschritt und die Tensor-Signalverarbeitung, die die analytische AbhĂ€ngigkeit von den physikalischen Parametern enthalten.
Im zweiten Teil entwickeln wir einen neuartigen general least squares (GLS)-Ansatz zur Lösung der Verschiebungs-Invarianz-Gleichung, die die Grundlage der ESPRIT-Algorithmen darstellt. Der neue Lösungsansatz berĂŒcksichtigt die statistische Beschreibung des Fehlers bei der UnterraumschĂ€tzung durch dessen Kovarianzmatrix und ermöglicht unter bestimmten Annahmen eine optimale Lösung der Invarianz-Gleichung. Mittels einer Performanzanalyse der GLS-basierten ESPRIT-Verfahren und der Vereinfachung der analytischen AusdrĂŒcke fĂŒr den SchĂ€tzfehler fĂŒr eine Signalquelle und zwei zeitlich unkorrelierte Signalquellen wird gezeigt, dass die Cramer-Rao-Schranke, eine untere Schranke fĂŒr die Varianz eines SchĂ€tzers, erreicht werden kann.
Im nĂ€chsten Teil werden Matrix-basierte und Tensor-basierte ESPRIT-Algorithmen fĂŒr nicht-zirkulĂ€re Signalquellen vorgestellt. Unter Ausnutzung der Signalstruktur gelingt es, die SchĂ€tzgenauigkeit zu erhöhen und die doppelte Anzahl an Quellen aufzulösen. Dabei ermöglichen die vorgeschlagenen Tensor-ESPRIT-Verfahren sogar die gleichzeitige Ausnutzung der mehrdimensionalen Signalstruktur und der nicht-zirkulĂ€re Signalstruktur. Die LeistungsfĂ€higkeit dieser Verfahren wird erneut durch eine analytische Beschreibung objektiv bewertet und SpezialfĂ€lle fĂŒr eine und zwei Quellen betrachtet. Es zeigt sich, dass fĂŒr eine Quelle keinerlei Gewinn durch die nicht-zirkulĂ€re Struktur erzielen lĂ€sst. FĂŒr zwei nicht-zirkulĂ€re Quellen werden vereinfachte AusdrĂŒcke fĂŒr den Gewinn sowohl im Matrixfall also auch im Tensorfall hergeleitet und die AbhĂ€ngigkeit der physikalischen Parameter analysiert. Sind die Signale stark korreliert oder ist die Anzahl der Messdaten sehr gering, kann der spatial smoothing-Vorverarbeitungsschritt mit den verbesserten ESPRIT-Verfahren kombiniert werden. Anhand der Performanzanalyse wird die Anzahl der Mittellungen fĂŒr das spatial smoothing-Verfahren analytisch fĂŒr eine Quelle bestimmt, die den SchĂ€tzfehler minimiert.
Der nĂ€chste Teil befasst sich mit einer vergleichsweise neuen Klasse von ParameterschĂ€tzverfahren, die auf der Rekonstruktion ĂŒberlagerter dĂŒnnbesetzter Signale basiert. Als Vorteil gegenĂŒber den Algorithmen, die eine SignalunterraumschĂ€tzung voraussetzen, sind die Rekonstruktionsverfahren verhĂ€ltnismĂ€Ăig robust im Falle einer geringen Anzahl zeitlicher Messungen oder einer starken Korrelation der Signale. In diesem Teil der vorliegenden Arbeit werden drei solcher Verfahren entwickelt, die bei der Rekonstruktion zusĂ€tzlich die nicht-zirkulĂ€re Signalstruktur ausnutzen. Dadurch kann auch fĂŒr diese Art von Verfahren eine höhere SchĂ€tzgenauigkeit erreicht werden und eine höhere Anzahl an Signalen rekonstruiert werden.
Im letzten Kapitel der Arbeit wird schlieĂlich die Cramer-Rao-Schranke fĂŒr mehrdimensionale nicht-zirkulĂ€re Signale hergeleitet. Sie stellt eine untere Schranke fĂŒr den SchĂ€tzfehler aller Algorithmen dar, die speziell fĂŒr die Ausnutzung dieser Signalstruktur entwickelt wurden. Im Vergleich zur bekannten Cramer-Rao-Schranke fĂŒr beliebige Signale, zeigt sich, dass im Fall von zeitlich kohĂ€renten Signalen, fĂŒr einen Messvektor oder fĂŒr eine Quelle, beide Schranken Ă€quivalent sind. In diesen FĂ€llen kann daher keine Verbesserung der SchĂ€tzgĂŒte erzielt werden. ZusĂ€tzlich wird die Cramer-Rao-Schranke fĂŒr zwei benachbarte nicht-zirkulĂ€re Signalquellen vereinfacht und der maximal mögliche Gewinn in AbhĂ€ngigkeit der physikalischen Parameter analytisch ermittelt. Dieser Ausdruck gilt als MaĂstab fĂŒr den erzielbaren Gewinn aller ParameterschĂ€tzverfahren fĂŒr zwei nicht-zirkulĂ€re Signalquellen
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
Linear Transmit-Receive Strategies for Multi-user MIMO Wireless Communications
Die Notwendigkeit zur Unterdrueckung von Interferenzen auf der einen Seite
und zur Ausnutzung der durch Mehrfachzugriffsverfahren erzielbaren Gewinne
auf der anderen Seite rueckte die raeumlichen Mehrfachzugriffsverfahren
(Space Division Multiple Access, SDMA) in den Fokus der Forschung. Ein
Vertreter der raeumlichen Mehrfachzugriffsverfahren, die lineare
Vorkodierung, fand aufgrund steigender Anzahl an Nutzern und Antennen in
heutigen und zukuenftigen Mobilkommunikationssystemen besondere Beachtung,
da diese Verfahren das Design von Algorithmen zur Vorcodierung
vereinfachen. Aus diesem Grund leistet diese Dissertation einen Beitrag zur
Entwicklung linearer Sende- und Empfangstechniken fuer MIMO-Technologie mit
mehreren Nutzern. Zunaechst stellen wir ein Framework zur Approximation des
Datendurchsatzes in Broadcast-MIMO-Kanaelen mit mehreren Nutzern vor. In
diesem Framework nehmen wir das lineare Vorkodierverfahren regularisierte
Blockdiagonalisierung (RBD) an. Durch den Vergleich von Dirty Paper Coding
(DPC) und linearen Vorkodieralgorithmen (z.B. Zero Forcing (ZF) und
Blockdiagonalisierung (BD)) ist es uns moeglich, untere und obere Schranken
fuer den Unterschied bezueglich Datenraten und bezueglich Leistung zwischen
beiden anzugeben. Im Weiteren entwickeln wir einen Algorithmus fuer
koordiniertes Beamforming (Coordinated Beamforming, CBF), dessen Loesung
sich in geschlossener Form angeben laesst. Dieser CBF-Algorithmus basiert
auf der SeDJoCo-Transformation und loest bisher vorhandene Probleme im
Bereich CBF. Im Anschluss schlagen wir einen iterativen CBF-Algorithmus
namens FlexCoBF (flexible coordinated beamforming) fuer
MIMO-Broadcast-Kanaele mit mehreren Nutzern vor. Im Vergleich mit bis dato
existierenden iterativen CBF-Algorithmen kann als vielversprechendster
Vorteil die freie Wahl der linearen Sende- und Empfangsstrategie
herausgestellt werden. Das heisst, jede existierende Methode der linearen
Vorkodierung kann als Sendestrategie genutzt werden, waehrend die Strategie
zum Empfangsbeamforming frei aus MRC oder MMSE gewaehlt werden darf. Im
Hinblick auf Szenarien, in denen Mobilfunkzellen in Clustern
zusammengefasst sind, erweitern wir FlexCoBF noch weiter. Hier wurde das
Konzept der koordinierten Mehrpunktverbindung (Coordinated Multipoint
(CoMP) transmission) integriert. Zuletzt stellen wir drei Moeglichkeiten
vor, Kanalzustandsinformationen (Channel State Information, CSI) unter
verschiedenen Kanalumstaenden zu erlangen. Die Qualitaet der
Kanalzustandsinformationen hat einen starken Einfluss auf die Guete des
Uebertragungssystems. Die durch unsere neuen Algorithmen erzielten
Verbesserungen haben wir mittels numerischer Simulationen von Summenraten
und Bitfehlerraten belegt.In order to combat interference and exploit large multiplexing gains of the
multi-antenna systems, a particular interest in spatial division multiple
access (SDMA) techniques has emerged. Linear precoding techniques, as one
of the SDMA strategies, have obtained more attention due to the fact that
an increasing number of users and antennas involved into the existing and
future mobile communication systems requires a simplification of the
precoding design. Therefore, this thesis contributes to the design of
linear transmit and receive strategies for multi-user MIMO broadcast
channels in a single cell and clustered multiple cells. First, we present a
throughput approximation framework for multi-user MIMO broadcast channels
employing regularized block diagonalization (RBD) linear precoding.
Comparing dirty paper coding (DPC) and linear precoding algorithms (e.g.,
zero forcing (ZF) and block diagonalization (BD)), we further quantify
lower and upper bounds of the rate and power offset between them as a
function of the system parameters such as the number of users and antennas.
Next, we develop a novel closed-form coordinated beamforming (CBF)
algorithm (i.e., SeDJoCo based closed-form CBF) to solve the existing open
problem of CBF. Our new algorithm can support a MIMO system with an
arbitrary number of users and transmit antennas. Moreover, the application
of our new algorithm is not only for CBF, but also for blind source
separation (BSS), since the same mathematical model has been used in BSS
application.Then, we further propose a new iterative CBF algorithm (i.e.,
flexible coordinated beamforming (FlexCoBF)) for multi-user MIMO broadcast
channels. Compared to the existing iterative CBF algorithms, the most
promising advantage of our new algorithm is that it provides freedom in the
choice of the linear transmit and receive beamforming strategies, i.e., any
existing linear precoding method can be chosen as the transmit strategy and
the receive beamforming strategy can be flexibly chosen from MRC or MMSE
receivers. Considering clustered multiple cell scenarios, we extend the
FlexCoBF algorithm further and introduce the concept of the coordinated
multipoint (CoMP) transmission. Finally, we present three strategies for
channel state information (CSI) acquisition regarding various channel
conditions and channel estimation strategies. The CSI knowledge is required
at the base station in order to implement SDMA techniques. The quality of
the obtained CSI heavily affects the system performance. The performance
enhancement achieved by our new strategies has been demonstrated by
numerical simulation results in terms of the system sum rate and the bit
error rate
Advanced RFI detection, RFI excision, and spectrum sensing : algorithms and performance analyses
Because of intentional and unintentional man-made interference, radio frequency interference (RFI) is causing performance loss in various radio frequency operating systems such as microwave radiometry, radio astronomy, satellite communications, ultra-wideband communications, radar, and cognitive radio. To overcome the impact of RFI, a robust RFI detection coupled with an efficient RFI excision are, thus, needed. Amongst their limitations, the existing techniques tend to be computationally complex and render inefficient RFI excision. On the other hand, the state-of-the-art on cognitive radio (CR) encompasses numerous spectrum sensing techniques. However, most of the existing techniques either rely on the availability of the channel state information (CSI) or the primary signal characteristics. Motivated by the highlighted limitations, this Ph.D. dissertation presents research investigations and results grouped into three themes: advanced RFI detection, advanced RFI excision, and advanced spectrum sensing.
Regarding advanced RFI detection, this dissertation presents five RFI detectors: a power detector (PD), an energy detector (ED), an eigenvalue detector (EvD), a matrix-based detector, and a tensor-based detector. First, a computationally simple PD is investigated to detect a brodband RFI. By assuming Nakagami-m fading channels, exact closed-form expressions for the probabilities of RFI detection and of false alarm are derived and validated via simulations. Simulations also demonstrate that PD outperforms kurtosis detector (KD). Second, an ED is investigated for RFI detection in wireless communication systems. Its average probability of RFI detection is studied and approximated, and asymptotic closed-form expressions are derived. Besides, an exact closed-form expression for its average probability of false alarm is derived. Monte-Carlo simulations validate the derived analytical expressions and corroborate that the investigated ED outperforms KD and a generalized likelihood ratio test (GLRT) detector. The performance of ED is also assessed using real-world RFI contaminated data. Third, a blind EvD is proposed for single-input multiple-output (SIMO) systems that may suffer from RFI. To characterize the performance of EvD, performance closed-form expressions valid for infinitely huge samples are derived and validated through simulations. Simulations also corroborate that EvD manifests, even under sample starved settings, a comparable detection performance with a GLRT detector fed with the knowledge of the signal of interest (SOI) channel and a matched subspace detector fed with the SOI and RFI channels. At last, for a robust detection of RFI received through a multi-path fading channel, this dissertation presents matrix-based and tensor-based multi-antenna RFI detectors while introducing a tensor-based hypothesis testing framework. To characterize the performance of these detectors, performance analyses have been pursued. Simulations assess the performance of the proposed detectors and validate the derived asymptotic characterizations.
Concerning advanced RFI excision, this dissertation introduces a multi-linear algebra framework to the multi-interferer RFI (MI-RFI) excision research by proposing a multi-linear subspace estimation and projection (MLSEP) algorithm for SIMO systems. Having employed smoothed observation windows, a smoothed MLSEP (s-MLSEP) algorithm is also proposed. MLSEP and s-MLSEP require the knowledge of the number of interferers and their respective channel order. Accordingly, a novel smoothed matrix-based joint number of interferers and channel order enumerator is proposed. Performance analyses corroborate that both MLSEP and s-MLSEP can excise all interferers when the perturbations get infinitesimally small. For such perturbations, the analyses also attest that s-MLSEP exhibits a faster convergence to a zero excision error than MLSEP which, in turn, converges faster than a subspace projection algorithm. Despite its slight complexity, simulations and performance assessment on real-world data demonstrate that MLSEP outperforms projection-based RFI excision algorithms. Simulations also corroborate that s-MLSEP outperforms MLSEP as the smoothing factor gets smaller.
With regard to advanced spectrum sensing, having been inspired by an Fâtest detector with a simple analytical false alarm threshold expression considered an alternative to the existing blind detectors, this dissertation presents and evaluates simple Fâtest based spectrum sensing techniques that do not require the knowledge of CSI for multi-antenna CRs. Exact and asymptotic analytical performance closed-form expressions are derived for the presented detectors. Simulations assess the performance of the presented detectors and validate the derived expressions. For an additive noise exhibiting the same variance across multiple-antenna frontends, simulations also corroborate that the presented detectors are constant false alarm rate detectors which are also robust against noise uncertainty
Employing data fusion & diversity in the applications of adaptive signal processing
The paradigm of adaptive signal processing is a simple yet powerful method for the class of system identification problems. The classical approaches consider standard one-dimensional signals whereby the model can be formulated by flat-view matrix/vector framework. Nevertheless, the rapidly increasing availability of large-scale multisensor/multinode measurement technology has render no longer sufficient the traditional way of representing the data. To this end, the author, who from this point onward shall be referred to as `we', `us', and `our' to signify the author myself and other supporting contributors i.e. my supervisor, my colleagues and other overseas academics specializing in the specific pieces of research endeavor throughout this thesis, has applied the adaptive filtering framework to problems that employ the techniques of data diversity and fusion which includes quaternions, tensors and graphs. At the first glance, all these structures share one common important feature: invertible isomorphism. In other words, they are algebraically one-to-one related in real vector space. Furthermore, it is our continual course of research that affords a segue of all these three data types. Firstly, we proposed novel quaternion-valued adaptive algorithms named the n-moment widely linear quaternion least mean squares (WL-QLMS) and c-moment WL-LMS. Both are as fast as the recursive-least-squares method but more numerically robust thanks to the lack of matrix inversion. Secondly, the adaptive filtering method is applied to a more complex task: the online tensor dictionary learning named online multilinear dictionary learning (OMDL). The OMDL is partly inspired by the derivation of the c-moment WL-LMS due to its parsimonious formulae. In addition, the sequential higher-order compressed sensing (HO-CS) is also developed to couple with the OMDL to maximally utilize the learned dictionary for the best possible compression. Lastly, we consider graph random processes which actually are multivariate random processes with spatiotemporal (or vertex-time) relationship. Similar to tensor dictionary, one of the main challenges in graph signal processing is sparsity constraint in the graph topology, a challenging issue for online methods. We introduced a novel splitting gradient projection into this adaptive graph filtering to successfully achieve sparse topology. Extensive experiments were conducted to support the analysis of all the algorithms proposed in this thesis, as well as pointing out potentials, limitations and as-yet-unaddressed issues in these research endeavor.Open Acces