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Analysis of Wireless Information Systems using MATLAB

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Contents

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

STUDENTS ARE EXPECTED TO PRESENT THEIR SOLUTIONS IN A PRESENTATION.