Maximally sparse convex estimation and equalizationMaximally sparse convex estimation and equalization Διπλωματική Εργασία Diploma Work 2014-10-062014enSparse multipath channels are wireless links commonly found in communication systems such as High Frequency radio channels, horizontal and vertical underwater acoustic channels and terrestrial broadcasting channels for High Definition Television. Their impulse responses are characterized by a few significant terms that are widely separated in time. With high speed transmission, the length of a sampled sparse channel can reach hundreds of symbol interval. Thus, the amount of Intersymbol Interference (ISI) at the receiver is very high. Consequently, the presence of an ISI mitigating structure at the receiver, such as the Decision Feedback Equalizer (DFE) is essential. Due to the sparse impulse responses of these channels, traditional estimation techniques such as Least Squares (LS) result in over-parameterization and thus poor performance of the estimator. Also, classical equalizers become too complex for tackling these channels. The problem of estimating and equalizing sparse multipath channels is considered in this thesis. We formulate the sparse channel estimation and the computation of the sparse DFE filters as sparse approximation problems. A usual approach in sparse approximation problems is regularization with an l_1 norm penalty term and usage of convex optimization techniques in order to acquire a solution. Other sparsity promoting penalty functions are available, but the l_1 norm has the advantage to be a convex function, making the l_1 norm regularized approximation problem a convex one. When a problem is formulated as a convex optimization problem, it can be solved by very fast, efficient and reliable algorithms. In order to achieve sparser solutions and still gain from the benefits of the convex optimization theory, the Maximally Sparse Convex (MSC) algorithm utilizes a non-convex regularization term, that promotes sparsity more strongly than the l_1 norm, but chosen such that the total cost function remains convex.http://creativecommons.org/licenses/by/4.0/Πολυτεχνείο Κρήτης::Σχολή Ηλεκτρονικών Μηχανικών και Μηχανικών ΥπολογιστώνLourakis_Georgios_Dip_2014.pdfChania [Greece]Library of TUC2014-10-06application/pdf1.7 MBfree Lourakis Georgios Λουρακης Γεωργιος Liavas Athanasios Λιαβας Αθανασιος Digalakis Vasilis Διγαλακης Βασιλης Bletsas Aggelos Μπλετσας Αγγελος Πολυτεχνείο Κρήτης Technical University of Crete Convex optimization Communication systems, Wireless Wireless data communication systems Wireless information networks Wireless telecommunication systems wireless communication systems communication systems wireless wireless data communication systems wireless information networks wireless telecommunication systems