# Analysis of Wireless Information Systems using MATLAB

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 Gaussion)
• Selected stochastic processes (white noise, Poisson, exponentially distributed interarrival times, simulation of a Poisson process, pure ALOHA, slotted ALOHA, possible MATLAB implementation)

• 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

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

• Mutual information and self-information
• Entropy and average mutual information
• Channel capacity (AWGN, MIMO)
• Formula collection: computing determinants

• 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)

6. 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.

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.