The course "Analog Radio Systems" introduces analog signal processing and analog system theory on the basis of radio systems. The focus is initially on the theoretical description of components of practice-relevant radio systems which, in addition to classical linear and time-invariant (sub)systems, also contain time-variant and nonlinear sub-systems to a considerable extent. These include, for example, time-invariant, linear but direction-dependent antennas, time-variant and/or nonlinear modulators, and time-variant radio channels. After explaining all relevant subsystems, the analog radio system as a whole is discussed.

The course "Modern Radio Systems" first explains common terminology (diversity, MIMO), performance limits (bit error curves, channel capacities) and linear estimation methods (Least Mean Error, Kalman Filter) of modern radio systems in a compact way. Then, various mathematical methods for radio channel estimation, time-invariant and also time-varying radio channel equalization, and design of simple multi-antenna systems are presented. In the last learning block, current research topics such as Massive Multiantenna Systems as well as Millimeter Wave Radio Systems are discussed.

The course "Passive Radio Systems" covers analog and digital signal processing of passive radio systems. Passive radio systems are described by different transmitting and receiving devices, where at least one device is powered by the radio channel and has no other power supply. Such radio systems are usually used to identify objects ("Internet of Things", "Radio Frequency Identification"), but also to locate them. In addition to identification and localization, another focus of the lecture is energy harvesting from the transmitted signal in the passive device.

The experiments are used to program simple but also advanced algorithms of signal processing using MATLAB/SIMULINK. The main focus of the course is the structured and well-documented implementation and simulation of analog systems with discrete-time and discrete-value methods as well as the simulation of digital systems. This elective course teaches practical fundamentals to support the lectures Analog, Modern
and Passive Radio Systems.

The course begins with a review of elementary mathematical principles,
especially because some students have studied mathematics for a longer period of time before and therefore a refresher course is useful. The focus is then on other important mathematical basics (differential equations, integral transformations, function theory), which are a prerequisite for the master's program, but which some students did not acquire or not covered at an appropriate level in the earlier studies.

This course covers mathematical fundamentals useful for the HFS and IEN majors and largely assumed in electromagnetic field theory.
Contents:
1 Additions to vector calculus
1.1 Coordinate systems (cartesian, cylindrical, spherical) and coordinate transformations
1.2 Products of three and more scalar and vectorial factors
(spar product, double cross product, scalar product of two vector products)
1.3 Rotation of vectors
1.4 Differentiation of vectors
2 Vector analysis
2.1 Scalar and vector functions
2.2 Gradient, divergence and rotation
2.3 Nabla operator and calculation with Nabla operator
2.4 Displacement, area and volume integrals, contour and envelope integrals
2.5 Fundamental theorems for grad, div, rot
2.6 Partial integration
2.7 Cylindrical and spherical coordinates: Areas, volumes, grad, div, red
2.8 Dirac's delta function
2.9 Vector fields: Helmholtz theorem, potentials (vortex freedom), source freedom