Home » Lehre » Lehrveranstaltungen » Analysis of Wireless Information Systems using MATLAB

Analysis of Wireless Information Systems using MATLAB

You will only have access to the moodle course room and the course materials with successful registration and approval via LSF.


The course on Analysis of Wireless Information Systems using MATLAB is organized into the following chapters:

  1. Theory of probability
  • Finite fields of probability (set calculus, random experiment, conditional probability, total probability, Bayes’s theorem, independence, permutations and combinations, Markov chains)
  • Borel fields of probability
  • Random variables and distribution functions
  • Abstract Lebesgue integrals
  • Mathematical expectations
  • Functions of random variables (determining the distribution function; simulation lemma; examples: uniformly distributed phase angles, classically distributed Doppler frequencies, exponentially distributed delays)
  • Conditional probability in infinite fields of probability
  • Bayes‘s theorem in Borel fields of probability
  • Multidimensional random variables (marginal probality, total probability, Bayes’s theorem, conditional expectation)
  • Stochastic processes (stationarity, Wiener-Chintchin-Theorem)
  • Selected discrete distributions (two-point, binomial, Poisson)
  • Selected continuous distributions (uniform, exponential Gaussian)
  • Selected stochastic processes (white noise, Poisson, exponentially distributed interarrival times, simulation of a Poisson process, pure ALOHA, slotted ALOHA, possible MATLAB implementation)
  1. A Primer on Information Theory
  • Mutual information and self-information
  • Entropy and average mutual information
  • Channel capacity (AWGN, MIMO)
  • Formula collection: computing determinants
  1. A Primer on Generating Functions in Discrete Mathematics – Paving the Way to the Channel Capacity of Discrete Channels 
  2. Simulating the fast fading mobile radio channel
  • WSSUS model (correlation functions, scattering function, power delay profile, Doppler spectrum)
  • Simulation model
  • Discrete-time discrete-frequency simulation model
  • Probability density functions of phases, Doppler frequencies and delays
  1. Receiver with Multiple Receive Antannas
  • System model and likelihood functions
  • Matrix-vector calculus using Hermitian matrices
  • Sufficient statistics
  • Matched filter (ourput noise, signa-to-noise ratio, noise whitening using Cholesky decomposition or Karhunen-Loève transformation)
  • Optimum receivers (Bayes detection, MAP detection, ML detection)
  • Maximum-likelihood sequence detection (detection rule, Viterbi algorithm, a provincial posse, soft-output Viterbi algorithm, SIMPLE RULE, HUBER RULE, BATTAIL RULE)
  1. Polar Codes
  • History
  • Construction (channel polarization paradigm, channel combining, channel splitting)
  • Useful matrix manipulation (Kronecker product, permutation matrices)
  • Binary erasure channel (channel capacity, Bhattacharyya bound
  • Polar code examples
  1. Problems and Excercises
  • Computing and simulating a discrete stochastic process
  • Computing and simulating a continuous stochastic process
  • Computing and simulating a Poisson process
  • Simulating the mobile radio channel
  • Evaluating the generating function of the Fibonacci sequence – on our way towards the channel capacity of a discrete noiseless channel
  • Evaluating the number of possibilities to return change in coins – on our way towards the channel capacity of a discrete noiseless channel
  • Evaluating the channel capacity of a simple discrete noiseless channel
  • Evaluating the channel capacity of the telegraph channel using the Morse code