Adaptive filters for sparse system identification

Sparse system identification has attracted much attention in the field of adaptive algorithms, and the adaptive filters for sparse system identification are studied. Firstly, a new family of proportionate normalized least mean square (PNLMS) adaptive algorithms that improve the performance of identifying block-sparse systems is proposed. The main proposed algorithm, called block-sparse PNLMS (BS-PNLMS), is based on the optimization of a mixed ℓ2,1 norm of the adaptive filter\u27s coefficients. A block-sparse improved PNLMS (BS-IPNLMS) is also derived for both sparse and dispersive impulse responses. Meanwhile, the proposed block-sparse proportionate idea has been extended to both the proportionate affine projection algorithm (PAPA) and the proportionate affine projection sign algorithm (PAPSA). Secondly, a generalized scheme for a family of proportionate algorithms is also presented based on convex optimization. Then a novel low-complexity reweighted PAPA is derived from this generalized scheme which could achieve both better performance and lower complexity than previous ones. The sparseness of the channel is taken into account to improve the performance for dispersive system identification. Meanwhile, the memory of the filter\u27s coefficients is combined with row action projections (RAP) to significantly reduce the computational complexity. Finally, two variable step-size zero-point attracting projection (VSS-ZAP) algorithms for sparse system identification are proposed. The proposed VSS-ZAPs are based on the approximations of the difference between the sparseness measure of current filter coefficients and the real channel, which could gain lower steady-state misalignment and also track the change in the sparse system --Abstract, page iv

Contribuições à modelagem estocástica de algoritmos adaptativos normalizados

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Elétrica, Florianópolis, 2015.Este trabalho de pesquisa trata da modelagem estocástica de três algoritmos adaptativos bem conhecidos da literatura, a saber: o algoritmo NLMS (normalized least-mean-square), o algoritmo IAF PNLMS (individual-activation-factor proportionate NLMS) e o algoritmo TDLMS (transform-domain least-mean-square). Particularmente para o algoritmo NLMS, um modelo estocástico analítico é obtido levando em conta um ambiente não estacionário e sinais de entrada gaussianos complexos. Baseado nas expressões de modelo, o impacto dos parâmetros do algoritmo sobre o seu desempenho é discutido, evidenciando algumas das características de rastreamento do algoritmo NLMS frente ao ambiente não estacionário considerado. Para o algoritmo IAF-PNLMS, assumindo um ambiente estacionário, um modelo estocástico mais preciso do que os até então disponíveis na literatura é apresentado, considerando sinais de entrada gaussianos correlacionados tanto complexos quanto reais. Com respeito ao algoritmo TDLMS, um modelo estocástico melhorado é derivado focando em um ambiente não estacionário e sinais de entrada gaussianos correlacionados reais. A partir das expressões de modelo obtidas, o impacto dos parâmetros do algoritmo TDLMS sobre o seu desempenho é discutido. Resultados de simulação para diferentes cenários de operação são mostrados, confirmando a precisão dos modelos estocásticos propostos tanto na fase transitória quanto em regime permanente.Abstract : This research work focuses on the stochastic modeling of three well-known adaptive algorithms from the literature, namely: the normalized least-mean-square (NLMS) algorithm, the individual-activation-factor proportionate NLMS (IAF-PNLMS) algorithm, and the transform-domain least-mean-square (TDLMS) algorithm. Particularly for the NLMS algorithm, an analytical stochastic model is obtained taking into account a nonstationary environment and complex-valued Gaussian input data. Based on the obtained model expressions, the impact of the algorithm parameters on its performance is discussed, clarifying some of the tracking properties of the NLMS algorithm vis-à-vis the nonstationary environment considered. For the IAF-PNLMS algorithm, assuming a stationary environment, a more accurate stochastic model than those available so far in the literature is presented considering both complex- and real-valued Gaussian correlated input data. Regarding the TDLMS algorithm, an improved stochastic model is derived focusing on a nonstationary environment and real-valued Gaussian correlated input data. From the obtained model expressions, the impact of the TDLMS algorithm parameters on its performance is discussed. Simulation results for different operating scenarios are shown, confirming the accuracy of the proposed stochastic models for both transient and steady-state phases