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1. Mathematics of Machine Learning


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, BiasComplexity 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 MultiKernel Methods, Information Innovation, Regularization, Dimension Reduction and Compressive Sensing 
2. Modern Signal Processing for Communications


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 nonlinear PerronFrobenius 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 multiagent systems  Fundamentals of (convex) optimization theory, projection methods, principles of convex relaxation  Axiomatic framework for interference modeling, existence and uniqueness of fixed points, fixedpoint algorithms, applications of standard interference functions  Nonlinear PerronFrobenius theory  (Nonasymptotic) random matrix theory 
3. Modern Wireless Communications


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 timevarying linear system (timevarying impulse response), largescale and smallscale fading, multipath fading, existing approaches to modeling of wireless channels  Basic principles of stochastic modeling for wireless channels, Rayleigh and Rician channels, lognormal shadowing  Timefrequency correlation functions, widesense stationary uncorrelated scattering model, Doppler spread and coherence time, delay spread and coherence bandwidth, flat versus frequencyselective fading  Performance measures used in wireless communications: signaltonoise ratio, rate, ergodic capacity, outage capacity, delaylimited 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  Principlesofspreadspectrumtechniques and orthogonal frequency division multiplex(OFDM)  Basic multiaccess techniques including TDMA, FDMA, DSCDMA and OFDMA  Mathematical methods that are used to solve many realworld 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. Master Project Network Information Systems


Learning Outcomes: Students acquire methods and skills to solve a scientific question in the area of network information systems. They can formulate scientific questions as well as to proof or disprove a hypothesis in this field. In particular, they can systematically produce and publish results to validate the thesis and derive conclusions for further studies in this research area. Furthermore, students are able to pursue research approaches independently and to critically review related work in this field. 
Content: Network information systems are continuously improved to connect an everincreasing number of computing devices and to fulfil a wide range of different requirements. In particular, higher throughput, lower latency, and higher reliability paved the the way for future application scenarios, e.g., augmented reality, autonomous driving, and reliable industrial communication. However, new use cases often come with new requirements implying that wireless communication systems need to be adapted continuously. In the project, students will develop solutions for selected topics in the area of network information systems. Students work with a member of our institute on a current research topic. In particular, students will design, implement, and evaluate prototypes improving network information systems. 
Teaching and Learning Methods: Topics will be individually determined based on skills and capacity. A researcher of our group will supervise the project. We expect students to have prior experience in network information systems. Moreover, good analytical and programming skills are required. Students realize a prototype in the area of network information systems. Students will write a technical report and present their results. 
Assigned Degree Programs:

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