392 research outputs found
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
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
On the SNR Variability in Noisy Compressed Sensing
Compressed sensing (CS) is a sampling paradigm that allows to simultaneously
measure and compress signals that are sparse or compressible in some domain.
The choice of a sensing matrix that carries out the measurement has a defining
impact on the system performance and it is often advocated to draw its elements
randomly. It has been noted that in the presence of input (signal) noise, the
application of the sensing matrix causes SNR degradation due to the noise
folding effect. In fact, it might also result in the variations of the output
SNR in compressive measurements over the support of the input signal,
potentially resulting in unexpected non-uniform system performance. In this
work, we study the impact of a distribution from which the elements of a
sensing matrix are drawn on the spread of the output SNR. We derive analytic
expressions for several common types of sensing matrices and show that the SNR
spread grows with the decrease of the number of measurements. This makes its
negative effect especially pronounced for high compression rates that are often
of interest in CS.Comment: 4 pages + reference
R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis
High-resolution parameter estimation algorithms designed to exploit the prior
knowledge about incident signals from strictly second-order (SO) non-circular
(NC) sources allow for a lower estimation error and can resolve twice as many
sources. In this paper, we derive the R-D NC Standard ESPRIT and the R-D NC
Unitary ESPRIT algorithms that provide a significantly better performance
compared to their original versions for arbitrary source signals. They are
applicable to shift-invariant R-D antenna arrays and do not require a
centrosymmetric array structure. Moreover, we present a first-order asymptotic
performance analysis of the proposed algorithms, which is based on the error in
the signal subspace estimate arising from the noise perturbation. The derived
expressions for the resulting parameter estimation error are explicit in the
noise realizations and asymptotic in the effective signal-to-noise ratio (SNR),
i.e., the results become exact for either high SNRs or a large sample size. We
also provide mean squared error (MSE) expressions, where only the assumptions
of a zero mean and finite SO moments of the noise are required, but no
assumptions about its statistics are necessary. As a main result, we
analytically prove that the asymptotic performance of both R-D NC ESPRIT-type
algorithms is identical in the high effective SNR regime. Finally, a case study
shows that no improvement from strictly non-circular sources can be achieved in
the special case of a single source.Comment: accepted at IEEE Transactions on Signal Processing, 15 pages, 6
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Barriers and Incentives to the Adoption of ISO 14001 by Firms in the United States
This paper summarizes four novel advanced antenna concepts explored in the framework of the WINNER+ project. The concepts are related to multiuser MIMO communication in cellular networks, focusing on the acquisition and application of channel state information (CSI) at the transmitter in time-division-duplex (TDD) mode. The concepts include new ideas for CSI modeling and sounding for the purposes of multiuser precoding, and methods for pilot signal design with the aim to support the estimation of different CSI quantities. Furthermore, a new relaying strategy for terminal-to-terminal communication is described. All the ideas are feasible for adoption into practical upcoming communication systems such as LTE-Advanced, and most of the proposed concepts have only a minor impact on standards. Our study indicates that the CSI at its best is not only about estimating the channel responses between different antenna pairs. What counts is the nature of the intended communication link as well as the form in which CSI is applied.QC 20111102</p
HTMT2– an improved criterion for assessing discriminant validity in structural equation modeling
Roemer, E., Schuberth, F., & Henseler, J. (2021). HTMT2– an improved criterion for assessing discriminant validity in structural equation modeling. Industrial Management and Data Systems, 121(12), 2637-2650. https://doi.org/10.1108/IMDS-02-2021-0082Purpose: One popular method to assess discriminant validity in structural equation modeling is the heterotrait-monotrait ratio of correlations (HTMT). However, the HTMT assumes tau-equivalent measurement models, which are unlikely to hold for most empirical studies. To relax this assumption, the authors modify the original HTMT and introduce a new consistent measure for congeneric measurement models: the HTMT2. Design/methodology/approach: The HTMT2 is designed in analogy to the HTMT but relies on the geometric mean instead of the arithmetic mean. A Monte Carlo simulation compares the performance of the HTMT and the HTMT2. In the simulation, several design factors are varied such as loading patterns, sample sizes and inter-construct correlations in order to compare the estimation bias of the two criteria. Findings: The HTMT2 provides less biased estimations of the correlations among the latent variables compared to the HTMT, in particular if indicators loading patterns are heterogeneous. Consequently, the HTMT2 should be preferred over the HTMT to assess discriminant validity in case of congeneric measurement models. Research limitations/implications: However, the HTMT2 can only be determined if all correlations between involved observable variables are positive. Originality/value: This paper introduces the HTMT2 as an improved version of the traditional HTMT. Compared to other approaches assessing discriminant validity, the HTMT2 provides two advantages: (1) the ease of its computation, since HTMT2 is only based on the indicator correlations, and (2) the relaxed assumption of tau-equivalence. The authors highly recommend the HTMT2 criterion over the traditional HTMT for assessing discriminant validity in empirical studies.publishersversionpublishe
Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems
Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input
multiple-output (MIMO) relaying belongs to the class of difference-of-convex
functions (DC) programming problems. DC programming problems occur as well in
other signal processing applications and are typically solved using different
modifications of the branch-and-bound method. This method, however, does not
have any polynomial time complexity guarantees. In this paper, we show that a
class of DC programming problems, to which the sum-rate maximization in two-way
MIMO relaying belongs, can be solved very efficiently in polynomial time, and
develop two algorithms. The objective function of the problem is represented as
a product of quadratic ratios and parameterized so that its convex part (versus
the concave part) contains only one (or two) optimization variables. One of the
algorithms is called POlynomial-Time DC (POTDC) and is based on semi-definite
programming (SDP) relaxation, linearization, and an iterative search over a
single parameter. The other algorithm is called RAte-maximization via
Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors
method and an iterative search over two (or one, in its approximate version)
optimization variables. We also derive an upper-bound for the optimal values of
the corresponding optimization problem and show by simulations that this
upper-bound can be achieved by both algorithms. The proposed methods for
maximizing the sum-rate in the two-way AF MIMO relaying system are shown to be
superior to other state-of-the-art algorithms.Comment: 35 pages, 10 figures, Submitted to the IEEE Trans. Signal Processing
in Nov. 201
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