__ __

Martial Coulon
is an assistant professor with the department of Telecommunications &
Networking of the engineering school INP-ENSEEIHT, Toulouse (France). He
is responsible or involved in the teaching of the following courses at an
undergraduate level:

- Measure theory
- Lebesgue integrals
- Fourier transforms
- Distribution theory

**Probability**

- Discrete and continuous
random variables
- Mathematical expectation
- Change of variables
- Extension to random vectors
- Properties of Gaussian
vectors

- The statistical model
- Estimation theory

- Maximum likelihood method
- Moment method
- Bayesian estimation

- Hypothesis testing

- Neyman-Pearson
- Generalized likelihood
ratio
- Goodness-of-fit
tests (Kolmogorov, Chi-Square)

**Probability**** and Statistics with Matlab**

- Introduction to Matlab

- building vectors and matrices
- arithmetic operators
- control flow
- script files and functions
- plotting

- Introduction to Matlab: building vectors
- Random variables generation
- Probability density
estimation: histogram
- Application
to estimation and detection theory
- Initiation to simulation

**Optimization**

- first- and second-order derivatives
- convexity
- first-
and second-order optimality conditions
- quadratic forms
and applications
- optimization algortihms
(steepest-descent, Gauss-Newton, BFGS,...)
- applications: GPS, Support Vector
Machines

- Path Loss
- Shadowing
- Fast fading
- Doppler effect
- LOS and NLOS channels
- Diversity methods
- Introduction to MIMO systems

- conventional receiver
- optimal receivers
- Decorrelating receivers
- MMSE/LMS receivers
- SIC receivers

- Impulse/Multi-band UWB
- Small-scale
and large-scale channel modelling
- I-UWB
and MC-UWB receivers
- Interference with
narrow-band systems

- Channel modeling
- Equalization
- Spectrum spreading
- OFDM
- Diversity
- Mobile systems

**Communications systems****Sampling****/Quantization****Digital Modulations****Nyquist****criterion****Optimum receivers for AWGN channels****Inter-symbol interference and equalization**

**Deterministic****and random signals****Linear****filtering****Sampling****Poisson Processes**

**FIR/IIR Filtering (synthesis, windowing, stability...)**