Análise de Transiente do Algoritmo ℓ0-sign-LMS

Sparse systems are common in the most diverse areas of application of adaptive filtering, in- cluding control, biomedical engineering and echo can- cellation. Algorithms capable of using this property to accelerate convergence and/or improve steady state error are gaining increasing prominence in the acade- mic community. Motivated by these experiences, this work presents a theoretical analysis of the transient and steady-state performances of the ℓ0-sign-LMS algo- rithm, which presents the desired convergence proper- ties for sparse systems, as well as robustness to impul- sive noise and reduced computational complexity. The analysis is performed through the recursive calculation of the autocorrelation matrix of the coefficient deviati- ons, adopting some assumptions commonly used in the literature, but not the very frequent hypothesis that the input signal is white. At the end, several simulation results are presented to evaluate the performance of the proposed stochastic model.