course: Optimization in Information Engineering

number:
141217
teaching methods:
lecture with tutorials
media:
computer based presentation, black board and chalk
responsible person:
Prof. Dr.-Ing. Aydin Sezgin
Lecturers:
Prof. Dr.-Ing. Aydin Sezgin (ETIT), M. Sc. Aya Ahmed (ETIT), M. Sc. Sampath Thanthrige (ETIT)
language:
german
HWS:
4
CP:
5
offered in:
summer term

dates in summer term

  • start: Tuesday the 07.04.2020
  • lecture Tuesdays: from 10:15 to 11.45 o'clock in ID 03/463
  • tutorial Tuesdays: from 12:15 to 13.45 o'clock in ID 03/463

Exam

Form of exam:written
Registration for exam:FlexNow
Date:12.02.2020
Begin:13:30
Duration:120min
Room : ID 04/413

goals

Modern communication technology is an interdisciplinary field that requires both in-depth knowledge and concepts from various disciplines. This lecture will teach students various concepts from multiple disciplines that are essential in understanding reliable communication subjected to noise.

content

The lecture mainly focuses on convex optimization. In every lecture, new methods from the field of convex optimization are introduced and exemplified through practical engineering examples, mainly from the field of communications. The introduced methods are universally applicable to many other disciplines.

Summary of Content:

Motivation: * Cocktail party problem or power allocation problem of 2-user interference channel

Fundamentals: Linear Algebra & Optimization * Convex sets * Convex functions * Eigenvalues and eigenvectors * Linear independence * Rank, subspaces, nullspaces * Optimization with Lagrange multipliers * Quadratic optimization * Semi-definite relaxation

Use case 1: Information-theoretic metrics * Discrete entropy: Optimal distribution * Differential entropy: Optimal distribution

Use case 2: Gaussian channel * Point-to-point channel * Parallel channels with waterfilling * MIMO: Optimization of covariance matrix * MISO broadcast channel: Optimal beamforming with convex optimization * MIMO MAC: Iterative waterfilling

Use case 3: Information security * SISO wiretap channel * MISO wiretap channel

Use case 4: Fourth industrial revolution * Cyber physical systems * Kalman filter as quadratic optimization problem * Machine learning

Appendix:

Fundamentals probability theory: * Gauss Signals * Weak law of large numbers * Central limit theorem * AEP

Fundamentals communication channels: * Complex baseband * Statistic channels * Deterministic model

Use case: Achieving capacity of discrete memoryless channels * Achievability * Converse * Blahut-Arimoto algorithm

Use case: Degrees of Freedom (DoF) * Sampling theorem, Nyquist rate, capacity of bandlimited channels * DoF MIMO, MIMO MAC, MIMO BC, MIMO IC and MIMO X-channels * Interference alginment * Asymmetric signalling

requirements

keine

recommended knowledge

Content of the lectures

  • Mathematics 1-4
  • System Theory 1-2
  • Com­mu­ni­ca­ti­on En­gi­nee­ring

materials

presentation slides:

miscellaneous: