Helmut Bölcskei: Katalogdaten im Frühjahrssemester 2015

Auszeichnung: Die Goldene Eule
NameHerr Prof. Dr. Helmut Bölcskei
LehrgebietMathematische Informationswissenschaften
Adresse
Professur Math. Informationswiss.
ETH Zürich, ETF E 122
Sternwartstrasse 7
8092 Zürich
SWITZERLAND
Telefon+41 44 632 34 33
E-Mailhboelcskei@ethz.ch
URLhttps://www.mins.ee.ethz.ch/people/show/boelcskei
DepartementInformationstechnologie und Elektrotechnik
BeziehungOrdentlicher Professor

NummerTitelECTSUmfangDozierende
227-0434-00LHarmonic Analysis: Theory and Applications in Advanced Signal Processing Information 6 KP2V + 2UH. Bölcskei
KurzbeschreibungThis course is an introduction to the field of applied harmonic analysis with emphasis on applications in signal processing such as transform coding, inverse problems, imaging, signal recovery, and inpainting. We will consider theoretical, applied, and algorithmic aspects.
LernzielThis course is an introduction to the field of applied harmonic analysis with emphasis on applications in signal processing such as transform coding, inverse problems, imaging, signal recovery, and inpainting. We will consider theoretical, applied, and algorithmic aspects.
InhaltFrame theory: Frames in finite-dimensional spaces, frames for Hilbert spaces, sampling theorems as frame expansions

Spectrum-blind sampling: Sampling of multi-band signals with known support set, density results by Beurling and Landau, unknown support sets, multi-coset sampling, the modulated wideband converter, reconstruction algorithms

Sparse signals and compressed sensing: Uncertainty principles, recovery of sparse signals with unknown support set, recovery of sparsely corrupted signals, orthogonal matching pursuit, basis pursuit, the multiple measurement vector problem

High-dimensional data and dimension reduction: Random projections, the Johnson-Lindenstrauss Lemma, the Restricted Isometry Property, concentration inequalities, covering numbers, Kashin widths
SkriptLecture notes, problem sets with documented solutions.
LiteraturS. Mallat, ''A wavelet tour of signal processing: The sparse way'', 3rd ed., Elsevier, 2009

I. Daubechies, ''Ten lectures on wavelets'', SIAM, 1992

O. Christensen, ''An introduction to frames and Riesz bases'', Birkhäuser, 2003

K. Gröchenig, ''Foundations of time-frequency analysis'', Springer, 2001

M. Elad, ''Sparse and redundant representations -- From theory to applications in signal and image processing'', Springer, 2010
Voraussetzungen / BesonderesThe course is heavy on linear algebra, operator theory, and functional analysis. A solid background in these areas is beneficial. We will, however, try to bring everybody on the same page in terms of the mathematical background required, mostly through reviews of the mathematical basics in the discussion sessions. Moreover, the lecture notes contain detailed material on the advanced mathematical concepts used in the course. If you are unsure about the prerequisites, please contact C. Aubel or H. Bölcskei.
227-0438-00LFundamentals of Wireless Communication Information
Findet dieses Semester nicht statt.
6 KP2V + 2UH. Bölcskei
KurzbeschreibungThe class focuses on fundamental communication-theoretic aspects of modern wireless communication systems. The main topics covered are the system-theoretic characterization of wireless channels, the principle of diversity, information theoretic aspects of communication over fading channels, and the basics of multi-user communication theory and cellular systems.
LernzielAfter attending this lecture, participating in the discussion sessions, and working on the homework problem sets, students should be able to
- understand the nature of the fading mobile radio channel and its implications for the design of communication systems
- analyze existing communication systems
- apply the fundamental principles to new wireless communication systems, especially in the design of diversity techniques and coding schemes
InhaltThe goal of this course is to study the fundamental principles of wireless communication, enabling students to analyze and design current and future wireless systems. The outline of the course is as follows:

Wireless Channels
What differentiates wireless communication from wired communication is the nature of the communication channel. Motion of the transmitter and the receiver, the environment, multipath propagation, and interference render the channel model more complex. This part of the course deals with modeling issues, i.e., the process of finding an accurate and mathematically tractable formulation of real-world wireless channels. The model will turn out to be that of a randomly time-varying linear system. The statistical characterization of such systems is given by the scattering function of the channel, which in turn leads us to the definition of key propagation parameters such as delay spread and coherence time.

Diversity
In a wireless channel, the time varying destructive and constructive addition of multipath components leads to signal fading. The result is a significant performance degradation if the same signaling and coding schemes as for the (static) additive white Gaussian noise (AWGN) channel are used. This problem can be mitigated by diversity techniques. If several independently faded copies of the transmitted signal can be combined at the receiver, the probability of all copies being lost--because the channel is bad--decreases. Hence, the performance of the system will be improved. We will look at different means to achieve diversity, namely through time, frequency, and space. Code design for fading channels differs fundamentally from the AWGN case. We develop criteria for designing codes tailored to wireless channels. Finally, we ask the question of how much diversity can be obtained by any means over a given wireless channel.

Information Theory of Wireless Channels
Limited spectral resources make it necessary to utilize the available bandwidth to its maximum extent. Information theory answers the fundamental question about the maximum rate that can reliably be transmitted over a wireless channel. We introduce the basic information theoretic concepts needed to analyze and compare different systems. No prior experience with information theory is necessary.

Multiple-Input Multiple-Output (MIMO) Wireless Systems
The major challenges in future wireless communication system design are increased spectral efficiency and improved link reliability. In recent years the use of spatial (or antenna) diversity has become very popular, which is mostly due to the fact that it can be provided without loss in spectral efficiency. Receive diversity, that is, the use of multiple antennas on the receive side of a wireless link, is a well-studied subject. Driven by mobile wireless applications, where it is difficult to deploy multiple antennas in the handset, the use of multiple antennas on the transmit side combined with signal processing and coding has become known under the name of space-time coding. The use of multiple antennas at both ends of a wireless link (MIMO technology) has been demonstrated to have the potential of achieving extraordinary data rates. This chapter is devoted to the basics of MIMO wireless systems.

Cellular Systems: Multiple Access and Interference Management
This chapter deals with the basics of multi-user communication. We start by exploring the basic principles of cellular systems and then take a look at the fundamentals of multi-user channels. We compare code-division multiple-access (CDMA) and frequency-division multiple access (FDMA) schemes from an information-theoretic point of view. In the course of this comparison an important new concept, namely that of multiuser diversity, will emerge. We conclude with a discussion of the idea of opportunistic communication and by assessing this concept from an information-theoretic point of view.
SkriptLecture notes will be handed out during the lectures.
LiteraturA set of handouts covering digital communication basics and mathematical preliminaries is available on the website. For further reading, we recommend
- J. M. Wozencraft and I. M. Jacobs, "Principles of Communication Engineering," Wiley, 1965
- A. Papoulis and S. U. Pillai, "Probability, Random Variables, and Stochastic Processes," McGraw Hill, 4th edition, 2002
- G. Strang, "Linear Algebra and its Applications," Harcourt, 3rd edition, 1988
- T.M. Cover and J. A. Thomas, "Elements of Information Theory," Wiley, 1991
Voraussetzungen / BesonderesThis class will be taught in English. The oral exam will be in German (unless you wish to take it in English, of course).

A prerequisite for this course is a working knowledge in digital communications, random processes, and detection theory.