45 research outputs found
Deterministic Cramer-Rao bound for strictly non-circular sources and analytical analysis of the achievable gains
Recently, several high-resolution parameter estimation algorithms have been
developed to exploit the structure of strictly second-order (SO) non-circular
(NC) signals. They achieve a higher estimation accuracy and can resolve up to
twice as many signal sources compared to the traditional methods for arbitrary
signals. In this paper, as a benchmark for these NC methods, we derive the
closed-form deterministic R-D NC Cramer-Rao bound (NC CRB) for the
multi-dimensional parameter estimation of strictly non-circular (rectilinear)
signal sources. Assuming a separable centro-symmetric R-D array, we show that
in some special cases, the deterministic R-D NC CRB reduces to the existing
deterministic R-D CRB for arbitrary signals. This suggests that no gain from
strictly non-circular sources (NC gain) can be achieved in these cases. For
more general scenarios, finding an analytical expression of the NC gain for an
arbitrary number of sources is very challenging. Thus, in this paper, we
simplify the derived NC CRB and the existing CRB for the special case of two
closely-spaced strictly non-circular sources captured by a uniform linear array
(ULA). Subsequently, we use these simplified CRB expressions to analytically
compute the maximum achievable asymptotic NC gain for the considered two source
case. The resulting expression only depends on the various physical parameters
and we find the conditions that provide the largest NC gain for two sources.
Our analysis is supported by extensive simulation results.Comment: submitted to IEEE Transactions on Signal Processing, 13 pages, 4
figure
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 hochauflÜsende Parameterschätzung fßr mehrdimensionale Signale findet Anwendung in vielen Bereichen der Signalverarbeitung in Mehrantennensystemen. Zu den Anwendungsgebieten zählen beispielsweise Radar, die Mobilkommunikation, die Kanalschätzung in multiple-input multiple-output (MIMO)-Systemen und bildgebende Verfahren in der Biosignalverarbeitung. In letzter Zeit sind eine Vielzahl von Algorithmen zur Parameterschätzung entwickelt worden, deren Schätzgenauigkeit durch eine analytische Beschreibung der Leistungsfähigkeit objektiv bewertet werden kann. Eine verbreitete Methode zur Verbesserung der Schätzgenauigkeit von Parameterschätzverfahren ist die Ausnutzung von Vorwissen bezßglich der Signalstruktur. In dieser Arbeit werden mehrdimensionale ESPRIT-Verfahren als Beispiel fßr Unterraum-basierte Verfahren entwickelt und analysiert, die explizit die mehrdimensionale Signalstruktur mittels Tensor-Signalverarbeitung ausnutzt und die statistischen Eigenschaften von nicht-zirkulären Signalen einbezieht. Weiterhin werden neuartige auf Signalrekonstruktion basierende Algorithmen vorgestellt, die die nicht-zirkuläre Signalstruktur bei der Rekonstruktion ausnutzen. Die vorgestellten Verfahren ermÜglichen eine deutlich verbesserte Schätzgßte und verdoppeln die Anzahl der auflÜsbaren Signale. Die Vielzahl der Forschungsbeiträge in dieser Arbeit setzt sich aus verschiedenen Teilen zusammen.
Im ersten Teil wird die analytische Beschreibung der Leistungsfähigkeit von Matrix-basierten und Tensor-basierten ESPRIT-Algorithmen betrachtet. Die Tensor-basierten Verfahren nutzen explizit die mehrdimensionale Struktur der Daten aus. Es werden fßr beide Algorithmenarten vereinfachte analytische Ausdrßcke fßr den mittleren quadratischen Schätzfehler fßr zwei Signalquellen hergeleitet, die lediglich von den physikalischen Parametern, wie zum Beispiel die Anzahl der Antennenelemente, das Signal-zu-Rausch-Verhältnis, oder die Anzahl der Messungen, abhängen. Ein Vergleich dieser Ausdrßcke ermÜglicht die Berechnung einfacher Ausdrßcke fßr den Schätzgenauigkeitsgewinn durch den forward-backward averaging (FBA)-Vorverarbeitungsschritt und die Tensor-Signalverarbeitung, die die analytische Abhängigkeit von den physikalischen Parametern enthalten.
Im zweiten Teil entwickeln wir einen neuartigen general least squares (GLS)-Ansatz zur LÜsung der Verschiebungs-Invarianz-Gleichung, die die Grundlage der ESPRIT-Algorithmen darstellt. Der neue LÜsungsansatz berßcksichtigt die statistische Beschreibung des Fehlers bei der Unterraumschätzung durch dessen Kovarianzmatrix und ermÜglicht unter bestimmten Annahmen eine optimale LÜsung der Invarianz-Gleichung. Mittels einer Performanzanalyse der GLS-basierten ESPRIT-Verfahren und der Vereinfachung der analytischen Ausdrßcke fßr den Schätzfehler fßr eine Signalquelle und zwei zeitlich unkorrelierte Signalquellen wird gezeigt, dass die Cramer-Rao-Schranke, eine untere Schranke fßr die Varianz eines Schätzers, erreicht werden kann.
Im nächsten Teil werden Matrix-basierte und Tensor-basierte ESPRIT-Algorithmen fßr nicht-zirkuläre Signalquellen vorgestellt. Unter Ausnutzung der Signalstruktur gelingt es, die Schätzgenauigkeit zu erhÜhen und die doppelte Anzahl an Quellen aufzulÜsen. Dabei ermÜglichen die vorgeschlagenen Tensor-ESPRIT-Verfahren sogar die gleichzeitige Ausnutzung der mehrdimensionalen Signalstruktur und der nicht-zirkuläre Signalstruktur. Die Leistungsfähigkeit dieser Verfahren wird erneut durch eine analytische Beschreibung objektiv bewertet und Spezialfälle fßr eine und zwei Quellen betrachtet. Es zeigt sich, dass fßr eine Quelle keinerlei Gewinn durch die nicht-zirkuläre Struktur erzielen lässt. Fßr zwei nicht-zirkuläre Quellen werden vereinfachte Ausdrßcke fßr den Gewinn sowohl im Matrixfall also auch im Tensorfall hergeleitet und die Abhängigkeit 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 fßr das spatial smoothing-Verfahren analytisch fßr eine Quelle bestimmt, die den Schätzfehler minimiert.
Der nächste Teil befasst sich mit einer vergleichsweise neuen Klasse von Parameterschätzverfahren, die auf der Rekonstruktion Ăźberlagerter dĂźnnbesetzter Signale basiert. Als Vorteil gegenĂźber den Algorithmen, die eine Signalunterraumschätzung voraussetzen, sind die Rekonstruktionsverfahren verhältnismäĂig 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 zusätzlich die nicht-zirkuläre Signalstruktur ausnutzen. Dadurch kann auch fĂźr diese Art von Verfahren eine hĂśhere Schätzgenauigkeit erreicht werden und eine hĂśhere Anzahl an Signalen rekonstruiert werden.
Im letzten Kapitel der Arbeit wird schlieĂlich die Cramer-Rao-Schranke fĂźr mehrdimensionale nicht-zirkuläre Signale hergeleitet. Sie stellt eine untere Schranke fĂźr den Schätzfehler aller Algorithmen dar, die speziell fĂźr die Ausnutzung dieser Signalstruktur entwickelt wurden. Im Vergleich zur bekannten Cramer-Rao-Schranke fĂźr beliebige Signale, zeigt sich, dass im Fall von zeitlich kohärenten Signalen, fĂźr einen Messvektor oder fĂźr eine Quelle, beide Schranken äquivalent sind. In diesen Fällen kann daher keine Verbesserung der SchätzgĂźte erzielt werden. Zusätzlich wird die Cramer-Rao-Schranke fĂźr zwei benachbarte nicht-zirkuläre Signalquellen vereinfacht und der maximal mĂśgliche Gewinn in Abhängigkeit der physikalischen Parameter analytisch ermittelt. Dieser Ausdruck gilt als MaĂstab fĂźr den erzielbaren Gewinn aller Parameterschätzverfahren fĂźr zwei nicht-zirkuläre Signalquellen
Advanced Algebraic Concepts for Efficient Multi-Channel Signal Processing
ďťżUnsere moderne Gesellschaft ist Zeuge eines fundamentalen Wandels in der Art und Weise
wie wir mit Technologie interagieren. Geräte werden zunehmend intelligenter - sie verfßgen
ßber mehr und mehr Rechenleistung und häufiger ßber eigene Kommunikationsschnittstellen.
Das beginnt bei einfachen Haushaltsgeräten und reicht Ăźber Transportmittel bis zu groĂen
Ăźberregionalen 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,
begrĂźndet 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 LĂśsungen
fßr eine Vielzahl von Anwendungen mehrkanaliger digitaler Signalverarbeitung. Solche Ansätze
liefern nicht immer unbedingt die bestmÜgliche LÜsung, kommen dieser jedoch häufig recht
nahe und sind gleichzeitig bedeutend einfacher zu beschreiben und umzusetzen. Die einfache
Beschreibungsform ermÜglicht eine tiefgehende Analyse ihrer Leistungsfähigkeit, was fßr den
Entwurf eines robusten und zuverlässigen Systems unabdingbar ist. Die Tatsache, dass sie nur
gebräuchliche algebraische Hilfsmittel benÜtigen, erlaubt ihre direkte und zßgige 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 Ăźber Chemie bis zur Bildverarbeitung. Verglichen mit existierenden
iterativen LĂśsungsverfahren bietet das neue Framework die MĂśglichkeit, den Rechenaufwand
und damit die GĂźte der erzielten LĂśsung zu steuern. Es ist auĂerdem weniger anfällig gegen eine
schlechte Konditionierung der Ausgangsdaten. Das zweite Gebiet, das in der Arbeit besprochen
wird, ist die unterraumbasierte hochauflÜsende Parameterschätzung fßr 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 natĂźrlichere Beschreibung und eine
bessere Ausnutzung ihrer Struktur als das mit Matrizen mĂśglich 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, fĂźr 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 endgßltige Schätzgenauigkeit objektiv einschätzen zu kÜnnen wird dann ein
Framework fßr die analytische Beschreibung der Leistungsfähigkeit beliebiger ESPRIT-artiger
Algorithmen diskutiert. Verglichen mit existierenden analytischen AusdrĂźcken ist unser Ansatz
allgemeiner, da keine Annahmen Ăźber die statistische Verteilung von Nutzsignal und
Rauschen benĂśtigt werden und die Anzahl der zur VerfĂźgung stehenden SchnappschĂźsse beliebig
klein sein kann. Dies fĂźhrt auf vereinfachte AusdrĂźcke fĂźr den mittleren quadratischen
Schätzfehler, die Schlussfolgerungen ßber 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 nÜtige Kanalkenntnis
mit einem einfachen algebraischen Tensor-basierten Schätzverfahren gewinnen lässt. AuĂerdem
werden Verfahren zum Finden einer gßnstigen 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. FĂźr den Spezialfall, in dem
die Endgeräte nur eine Antenne verwenden, leiten wir eine semi-algebraische LÜsung zum
Finden der Summenraten-optimalen Strategie (RAGES) her. Anhand von numerischen Simulationen
wird die Leistungsfähigkeit dieser Verfahren bezßglich 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
Biologically Inspired Sensing and MIMO Radar Array Processing
The contributions of this dissertation are in the fields of biologically inspired sensing and multi-input multi-output: MIMO) radar array processing. In our research on biologically inspired sensing, we focus on the mechanically coupled ears of the female Ormia ochracea. Despite the small distance between its ears, the Ormia has a remarkable localization ability. We statistically analyze the localization accuracy of the Ormia\u27s coupled ears, and illustrate the improvement in the localization performance due to the mechanical coupling. Inspired by the Ormia\u27s ears, we analytically design coupled small-sized antenna arrays with high localization accuracy and radiation performance. Such arrays are essential for sensing systems in military and civil applications, which are confined to small spaces. We quantitatively demonstrate the improvement in the antenna array\u27s radiation and localization performance due to the biologically inspired coupling. On MIMO radar, we first propose a statistical target detection method in the presence of realistic clutter. We use a compound-Gaussian distribution to model the heavy tailed characteristics of sea and foliage clutter. We show that MIMO radars are useful to discriminate a target from clutter using the spatial diversity of the illuminated area, and hence MIMO radar outperforms conventional phased-array radar in terms of target-detection capability. Next, we develop a robust target detector for MIMO radar in the presence of a phase synchronization mismatch between transmitter and receiver pairs. Such mismatch often occurs due to imperfect knowledge of the locations as well as local oscillator characteristics of the antennas, but this fact has been ignored by most researchers. Considering such errors, we demonstrate the degradation in detection performance. Finally, we analyze the sensitivity of MIMO radar target detection to changes in the cross-correlation levels: CCLs) of the received signals. Prior research about MIMO radar assumes orthogonality among the received signals for all delay and Doppler pairs. However, due to the use of antennas which are widely separated in space, it is impossible to maintain this orthogonality in practice. We develop a target-detection method considering the non-orthogonality of the received data. In contrast to the common assumption, we observe that the effect of non-orthogonality is significant on detection performance
Compact Formulations for Sparse Reconstruction in Fully and Partly Calibrated Sensor Arrays
Sensor array processing is a classical field of signal processing which offers various applications in practice, such as direction of arrival estimation or signal reconstruction, as well as a rich theory, including numerous estimation methods and statistical bounds on the achievable estimation performance. A comparably new field in signal processing is given by sparse signal reconstruction (SSR), which has attracted remarkable interest in the research community during the last years and similarly offers plentiful fields of application. This thesis considers the application of SSR in fully calibrated sensor arrays as well as in partly calibrated sensor arrays. The main contributions are a novel SSR method for application in partly calibrated arrays as well as compact formulations for the SSR problem, where special emphasis is given on exploiting specific structure in the signals as well as in the array topologies
Characterisation and Modelling of Indoor and Short-Range MIMO Communications
Over the last decade, we have witnessed the rapid evolution of Multiple-Input Multiple-Output
(MIMO) systems which promise to break the frontiers of conventional architectures and deliver
high throughput by employing more than one element at the transmitter (Tx) and receiver (Rx)
in order to exploit the spatial domain. This is achieved by transmitting simultaneous data
streams from different elements which impinge on the Rx with ideally unique spatial signatures
as a result of the propagation pathsâ interactions with the surrounding environment. This thesis
is oriented to the statistical characterisation and modelling of MIMO systems and particularly
of indoor and short-range channels which lend themselves a plethora of modern applications,
such as wireless local networks (WLANs), peer-to-peer and vehicular communications.
The contributions of the thesis are detailed below. Firstly, an indoor channel model is proposed
which decorrelates the full spatial correlation matrix of a 5.2 GHzmeasuredMIMO channel and
thereafter assigns the Nakagami-m distribution on the resulting uncorrelated eigenmodes. The
choice of the flexible Nakagami-m density was found to better fit the measured data compared
to the commonly used Rayleigh and Ricean distributions. In fact, the proposed scheme captures
the spatial variations of the measured channel reasonably well and systematically outperforms
two known analytical models in terms of information theory and link-level performance.
The second contribution introduces an array processing scheme, namely the three-dimensional
(3D) frequency domain Space Alternating Generalised Expectation Maximisation (FD-SAGE)
algorithm for jointly extracting the dominant pathsâ parameters. The scheme exhibits a satisfactory
robustness in a synthetic environment even for closely separated sources and is applicable
to any array geometry as long as its manifold is known. The algorithm is further applied to the
same set of raw data so that different global spatial parameters of interest are determined; these
are the multipath clustering, azimuth spreads and inter-dependency of the spatial domains.
The third contribution covers the case of short-range communications which have nowadays
emerged as a hot topic in the area of wireless networks. The main focus is on dual-branch
MIMO Ricean systems for which a design methodology to achieve maximum capacities in the
presence of Line-of-Sight (LoS) components is proposed. Moreover, a statistical eigenanalysis
of these configurations is performed and novel closed-formulae for the marginal eigenvalue
and condition number statistics are derived. These formulae are further used to develop an
adaptive detector (AD) whose aim is to reduce the feasibility cost and complexity of Maximum
Likelihood (ML)-based MIMO receivers.
Finally, a tractable novel upper bound on the ergodic capacity of the above mentioned MIMO
systems is presented which relies on a fundamental power constraint. The bound is sufficiently
tight and applicable for arbitrary rank of the mean channel matrix, Signal-to-Noise ratio (SNR)
and takes the effects of spatial correlation at both ends into account. More importantly, it
includes previously reported capacity bounds as special cases
Machine learning algorithms for cognitive radio wireless networks
In this thesis new methods are presented for achieving spectrum sensing in cognitive radio wireless networks. In particular, supervised, semi-supervised and unsupervised machine learning based spectrum sensing algorithms are developed and various techniques to improve their performance are described.
Spectrum sensing problem in multi-antenna cognitive radio networks is considered and a novel eigenvalue based feature is proposed which has the capability to enhance the performance of support vector machines algorithms for signal classification. Furthermore, spectrum sensing under multiple primary users condition is studied and a new re-formulation of the sensing task as a multiple class signal detection problem where each class embeds one or more states is presented. Moreover, the error correcting output codes based multi-class support vector machines algorithms is proposed and investigated for solving the multiple class signal detection problem using two different coding strategies.
In addition, the performance of parametric classifiers for spectrum sensing under slow fading channel is studied. To address the attendant performance degradation problem, a Kalman filter based channel estimation technique is proposed for tracking the temporally correlated slow fading channel and updating the decision boundary of the classifiers in real time. Simulation studies are included to assess the performance of the proposed schemes.
Finally, techniques for improving the quality of the learning features and improving the detection accuracy of sensing algorithms are studied and a novel beamforming based pre-processing technique is presented for feature realization in multi-antenna cognitive radio systems. Furthermore, using the beamformer derived features, new algorithms are developed for multiple hypothesis testing facilitating joint spatio-temporal spectrum sensing. The key performance metrics of the classifiers are evaluated to demonstrate the superiority of the proposed methods in comparison with previously proposed alternatives
Ultra wideband antenna array processing under spatial aliasing
Given a certain transmission frequency, Shannon spatial sampling limit deÂŻnes
an upper bound for the antenna element spacing. Beyond this bound, the exceeded
ambiguity avoids correct estimation of the signal parameters (i.e., array manifold
crossing). This spacing limit is inversely proportional to the frequency of transmis-
sion. Therefore, to meet a wider spectral support, the element spacing should be
decreased. However, practical implementations of closely spaced elements result in a
detrimental increase in electromagnetic mutual couplings among the sensors. Further-
more, decreasing the spacing reduces the array angle resolution. In this dissertation,
the problem of Direction of Arrival (DOA) estimation of broadband sources is ad-
dressed when the element spacing of a Uniform Array Antenna (ULA) is inordinate.
It is illustrated that one can resolve the aliasing ambiguity by utilizing the frequency
diversity of the broadband sources. An algorithm, based on Maximum Likelihood
Estimator (MLE), is proposed to estimate the transmitted data signal and the DOA
of each source. In the sequel, a subspace-based algorithm is developed and the prob-
lem of order estimation is discussed. The adopted signaling framework assumes a
subband hopping transmission in order to resolve the problem of source associations
and system identiÂŻcation. The proposed algorithms relax the stringent maximum
element-spacing constraint of the arrays pertinent to the upper-bound of frequency
transmission and suggest that, under some mild constraints, the element spacing can be conveniently increased. An approximate expression for the estimation error has
also been developed to gauge the behavior of the proposed algorithms. Through con-
ÂŻrmatory simulation, it is shown that the performance gain of the proposed setup
is potentially signiÂŻcant, speciÂŻcally when the transmitters are closely spaced and
under low Signal to Noise Ratio (SNR), which makes it applicable to license-free
communication