Advanced Topics in Signal Processing

The course focuses on understanding basic definitions of digital signals as well as on representative mathematical tools for their processing. The topics covered are chosen from a large pool of techniques and methodologies in order to be aligned with the students’ needs (ie, weaknesses and targeted applications). The topics’ pool includes: stochastic processes and parametric models for their characterization (ΑR, MA, ARMA), optimum linear minimum mean squared error, normal equations and their geometric representation, minimum unbiased variance estimator, maximum likelihood, Bayesian estimation, adaptive algorithms (steepest descent algorithm, Robbins Monro stochastic approximation, LMS) affine projection algorithms, distributed algorithms, least-squares method: asymptotic properties , RLS algorithm, signals over graphs (definitions, Laplacian, signal frequency over graphs, filters over graphs). Emphasis is given in signal processing applications (eg, estimation of wireless channels, localization/positioning, interference management, spatial precoding/combining, beamforming) in 5G and beyond communication systems.