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# Module Overview

## 1. Mathematics of Machine Learning

Module Components:

Learning Objectives:
After completing the module the students will have a solid understanding of theoretical foundations of Machine Learning and will be able to develop, apply, and analyze the complexity of the resulting learning algorithms. Moreover, a special emphasis will be put on applications of Machine Learning in areas such as Signal Processing and Wireless Communications and the students will be able to theoretically analyze and algorithmically solve learning problems arising in these fields.
Content:
Learning Model, Learning via Uniform Convergence, Bias-Complexity Tradeoff, Stochastic Inequalities and Concentration of Measure, Suprema of empirical Processes, Vapnik- Chervonenkis Dimension (VC Dimension), Nonuniform Learning, Runtime of Learning, Hilbert Spaces and Projection Methods, Kernel and Multi-Kernel Methods, Information Innovation, Regularization, Dimension Reduction and Compressive Sensing

## 2. Modern Signal Processing for Communications

Module Components:

Learning Objectives:
After completion of this module, the students have the ability to apply various methods and tools of modern signal processing to solve problems in a broad area of wireless communications. Moreover, they will better understand the fundamental relationships in wireless networks and obtain valuable insights into the design and operation of such networks. Finally the lecture intends to convey a comprehensive understanding of selected theoretical concepts used in wireless network optimization such as random matrix theory and non-linear Perron-Frobenius theory.
Content:
- Modern signal processing methods for interference reduction in spread spectrum and MIMO systems, adaptive beamforming, PAPR reduction in OFDM systems, acoustic source localization with wireless sensor networks, environmental modeling in wireless multi-agent systems
- Fundamentals of (convex) optimization theory, projection methods, principles of convex relaxation
- Axiomatic framework for interference modeling, existence and uniqueness of fixed points, fixed-point algorithms, applications of standard interference functions
- Non-linear Perron-Frobenius theory
- (Non-asymptotic) random matrix theory

## 3. Modern Wireless Communications

Module Components:

Learning Objectives:
After completing this module, the students will have a basic knowledge of wireless communications systems and they will be able to master some fundamental mathematical methods that are widely used in the analysis and optimization of modern wireless communications systems. In particular, the students will learn how to model the wireless channel and how to exploit the spatial diversity using multiple antenna systems. Further the lectures intends to convey a basic understanding of modern modulation and multiple access techniques such as CDMA and OFDMA. Regarding the mathematical methods for the analysis and optimization of wireless communications systems, the students will learn how to use mathematical methods when designing modern wireless communications networks. In doing so the lectures will combine the mathematical precision with practical examples. As a result, the acquired knowledge will enable the students to better understand complex interdependencies in such networks, which is essential for efficient design and operation of wireless networks.
Content:
- A brief overview of typical wireless communications scenarios, the main challenges and differences when compared with wired communications
- Wireless channel as a time-varying linear system (time-varying impulse response), large-scale and small-scale fading, multi-path fading, existing approaches to modeling of wireless channels
- Basic principles of stochastic modeling for wireless channels, Rayleigh and Rician channels, log-normal shadowing
- Time-frequency correlation functions, wide-sense stationary uncorrelated scattering model, Doppler spread and coherence time, delay spread and coherence bandwidth, flat versus frequency-selective fading
- Performance measures used in wireless communications: signal-to-noise ratio, rate, ergodic capacity, outage capacity, delay-limited capacity
- Definitions of time, frequency and spatial diversity, other notions of diversity
- Some basic diversity techniques including repetition coding, maximal ratio combiner (RAKE receiver), receive antenna diversity (SIMO), transmit antenna diversity (MISO), the impact of channel state information
- Principlesofspread-spectrumtechniques and orthogonal frequency division multiplex(OFDM)
- Basic multiaccess techniques including TDMA, FDMA, DS-CDMA and OFDMA
- Mathematical methods that are used to solve many real-world problems in modern wireless communications systems/networks. As concrete applications that are in the focus of the lectures, we cite interference reduction in spread spectrum and MIMO systems, adaptive beamforming, PAPR reduction in OFDM systems. In particular, a special attention is attached to the following topics: basic principles of (functional) analysis that are relevant in the design of modern communications systems, fundamentals of matrix analysis, fundamentals of (convex) optimization theory, projection methods, principles of convex relaxation, algorithm design, convergence properties.

## 4. Introduction to Game Theory with Engineering Applications

Module Components:

• Link to the module in MOSES
• 6 Credit Points
• 4 SWS
• Module No.: #40884 / #3
• Person in Charge: Prof. Dr.-Ing. Setareh Maghsudi
• Cycle: only in winter semester
• Course Name:

Learning Objectives:
The module provides an introduction to game theory and mechanism design, with an emphasis on applications in science engineering. After the lecture, the students know the basic concepts of game theory and learning in games. Moreover, the students can do self-study for expanding their knowledge of game theory. Besides, they can model various engineering scenarios as multi-agent systems, and use game theory to solve the underlying problem. Based on the selected type of the project, they can implement of game-theoretical multi-agent systems using conventional programming languages such as MATLAB, and they can analyze the system using simulation or theory.
Content:
A. Introductory Theory:
1. Strategic Form Games
2. Equilibrium Concepts (Nash and Correlated Equilibrium)
3. Potential Games
4. Learning in Games
5. Repeated Games
6. Extensive Form Games
7. Games with Incomplete Information
8. Nash Bargaining Solution
9. Auction Theory and Mechanism Design
10. Cooperative Games
11. Behavioral Game Theory
12. Exchange Economy (Tentative)
13. Evolution (Tentative)
14. Multi-Agent Systems

B. Application Examples:
1. Wireless Communications (Radio and Computational Resource Management)
2. Vehicular Networks (Traffic Control)
3. Economics (Portfolio Selection)