Adaptive algorithms, combinations and applications in deconvolution

Abstract

Filter combinations running in parallel have been used to improve the performance of adaptive filters related to the choice of the fixed parameters, tracking capability, stability, steady-state solution, initialization, among other factors. Although many results related to this topic had been published in the literature, there are still many open problems, which will be addressed in this research project, that is: (i) combinations of two NLMS (normalized least mean square) filters with different orders for sparse acoustic echo cancellation; (ii) analysis of the transient of the convex combination; (iii) reduction of the computational cost of the combination; (iv) comparison of the convex, affine and linear combinations in different simulation scenarios; and (v) use of the affine combination in adaptive distributed processing with applications in sensor networks. We also intend to address the use of blind equalization algorithms for QAM (quadrature amplitude modulation) signals in image restoration. Some works in the literature propose the use of the constant modulus algorithm (CMA) for image blind deconvolution. However, its performance is not good enough since the image pixels cannot be interpreted as a constant modulus signal. In this work, we will use efficient blind equalization algorithms for image deconvolution. Finally, we will study equalization in communication systems based in chaos. Due to the lack of robustness of chaos synchronization, even minor channel imperfections are enough to hinder communication. Therefore, the equalizer plays an important role in these systems. Firstly, we will extend the NLMS algorithm to adapt the equalizer and in the sequel we will investigate a possible blind solution. (AU)