Transform Domain LMS/F Algorithms, Performance Analysis and Applications
Azzedine Zerguine, Murwan Mohamed Elmahdi Bashir
كلية الهندسة-جامعة الملك فهد للبترول والمعادن · السعودية
Adaptive Filtering Algorithms are known to suffer in terms of convergence under highly correlated inputs. In this work we investigate the Transform DomainLMF algorithm. The Fourth Moments family of adaptive algorithms is known tohave better steady state and convergence properties compared to the LMS family, under Non-Gaussian noise environments. The second scope of the thesis isto study the problem of sparse system identification, that is, when the number ofactive elements in the linear system under consideration is small. We proposedthe Zero-Attractor (ZA-TD-LMF) algorithm to solve the problem under the highlycorrelated environments and non-Gaussian noise. Furthermore to deal the prob-lem of variable sparsity, we employed the convex combination filter to design analgorithms that can solve the problem of moving sparse elements. The first convex filter, called ZA-LMF and LMF convex, is designed to alleviate the choice ofwhich algorithm we should use (LMF or ZA-LMF) if we do not have previousinformation about the level of sparsity of the system under consideration. Similarly, a transform Domain LMS and ZA-LMS convex is proposed and studied toendow the designer with more freedom in system designing. The Computer Simulations confirm that the convex is universal and always offer the best performanceavailable and chooses the best performing algorithm.