Output signal based combination of two NLMS adaptive filters – transient analysis

Abstract

A combination of two complex normalized least mean square (NLMS) adaptive filters that adapt on the same input signal at the same time is investigated. One of the filters has a large and the other one has a small step size. The outputs of the filters are combined together through a mixing parameter A. This combination is an interesting new way of achieving simultaneously a fast initial convergence and a small steady state error of an adaptive algorithm. The mixing parameter is computed from the output signals of the individual filters. The expressions characterizing the time evolution of the mean square deviation and the excess mean square error of the combination scheme are derived. The theoretical results are verified by simulations.

Considerações sobre a Modelagem Estocástica da Combinação de Filtros Adaptativos Usando o Algoritmo NLMS

“…sendo a parcela decorrente de cada filtro componente dada por Portanto, a curva de aprendizagem pode ser predita através de (14), (15)…”

“…Contudo, apesar dos esforços até então despendidos, pouco se tem desenvolvido em relação à modelagem da combinação de filtros adaptativos operando especificamente com o algoritmo NLMS, podendo-se citar apenas os modelos derivados em [8], [13] e [14]. Entretanto, esses modelos focam particularmente em sinais de entrada reais não-correlacionados e/ou consideram aproximações grosseiras para o cálculo das matrizes de autocorrelação normalizadas surgidas na derivação do modelo (para detalhes, veja a discussão em [15] e [16]).…”

A novel sign adaptation scheme for convex combination of two adaptive filters

“…Following these works, García new plant identification method by using two or three LMS filters with large and small step sizes to gain fast convergence and low misadjustment [11]. Also, the convex combination strategy can be extended to the recursive least squares (RLS) [11], NLMS algorithm [13], APA [14], subband adaptive filter (SAF) [15], Shalvi-Weinstein algorithm (SWA) [16] and the constant-modulus algorithm (CMA) [16], etc. To achieve more strong robustness than the basic-CLMS algorithm, Ruiz et al presented a new normalized rule of the CLMS algorithm when the signal-to-noise ratio (SNR) is time varying [17].…”

Novel Sparse Algorithms based on Lyapunov Stability for Adaptive System Identification

“…The affine combination as a generalization of the convex combination is studied in [24], and in [25] affine combination analysis was extended for colored inputs and nonstationary environments. In [26], transient analysis for the affine combination of two NLMS adaptive filters is studied. In [27], [28], it is demonstrated that affine combination results in faster convergence than the convex combination of two adaptive filters.…”