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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
• 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
• 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.