Contents
The course on Analysis of Wireless Information Systems using MATLAB is organized into the following chapters:
1. Theory of probability
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Finite fields of probability (set calculus, random experiment, conditional probability, total probability, Bayes’s theorem, independence, permutations and combinations, Markov chains)
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Borel fields of probability
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Random variables and distribution functions
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Abstract Lebesgue integrals
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Mathematical expectations
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Functions of random variables (determining the distribution function; simulation lemma; examples: uniformly distributed phase angles, classically distributed Doppler frequencies, exponentially distributed delays)
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Conditional probability in infinite fields of probability
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Bayes‘s theorem in Borel fields of probability
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Multidimensional random variables (marginal probality, total probability, Bayes’s theorem, conditional expectation)
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Stochastic processes (stationarity, Wiener-Chintchin-Theorem)
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Selected discrete distributions (two-point, binomial, Poisson)
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Selected continuous distributions (uniform, exponential Gaussion)
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Selected stochastic processes (white noise, Poisson, exponentially distributed interarrival times, simulation of a Poisson process, pure ALOHA, slotted ALOHA, possible MATLAB implementation)
2. Simulating the fast fading mobile radio channel
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WSSUS model (correlation functions, scattering function, power delay profile, Doppler spectrum)
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Simulation model
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Discrete-time discrete-frequency simulation model
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Probability density functions of phases, Doppler frequencies and delays
3. A Primer on Generating Functions in Discrete Mathematics - Paving the Way to the Channel Capacity of Discrete Channels
4. A Primer on Information Theory
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Mutual information and self-information
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Entropy and average mutual information
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Channel capacity (AWGN, MIMO)
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Formula collection: computing determinants
5. Receiver with Multiple Receive Antannas
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System model and likelihood functions
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Matrix-vector calculus using Hermitian matrices
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Sufficient statistics
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Matched filter (ourput noise, signa-to-noise ratio, noise whitening using Cholesky decomposition or Karhunen-Loève transformation)
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Optimum receivers (Bayes detection, MAP detection, ML detection)
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Maximum-likelihood sequence detection (detection rule, Viterbi algorithm, a provincial posse, soft-output Viterbi algorithm, SIMPLE RULE, HUBER RULE, BATTAIL RULE)
6. Problems and Excercises
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Computing and simulating a discrete stochastic process
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Computing and simulating a continuous stochastic process
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Computing and simulating a Poisson process
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Simulating the mobile radio channel
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Evaluating the generating function of the Fibonacci sequence - on our way towards the channel capacity of a discrete noiseless channel
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Evaluating the number of possibilities to return change in coins - on our way towards the channel capacity of a discrete noiseless channel
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Evaluating the channel capacity of a simple discrete noiseless channel
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Evaluating the channel capacity of the telegraph channel using the Morse code
STUDENTS ARE EXPECTED TO PRESENT THEIR SOLUTIONS IN A PRESENTATION.
This lecture will be held in the "inverted classroom model" at https://moodle.uni-due.de/course/view.php?id=21653 in the summer semester 2020.