l ₀ ‐norm penalised shrinkage linear and widely linear LMS algorithms for sparse system identification

Abstract

In this study, the authors propose an l 0-norm penalised shrinkage linear least mean squares (l 0-SH-LMS) algorithm and an l 0-norm penalised shrinkage widely linear least mean squares (l 0-SH-WL-LMS) algorithm for sparse system identification. The proposed algorithms exploit the priori and the posteriori errors to calculate the varying step-size, thus they can adapt to the time-varying channel. Meanwhile, in the cost function they introduce a penalty term that favours sparsity to enable the applicability for sparse condition. Moreover, the l 0-SH-WL-LMS algorithm also makes full use of the non-circular properties of the signals of interest to improve the tracking capability and estimation performance. Quantitative analysis of the convergence behaviour for the l 0-SH-WL-LMS algorithm verifies the capabilities of the proposed algorithms. Simulation results show that compared with the existing least mean squares-type algorithms, the proposed algorithms perform better in the sparse channels with a faster convergence rate and a lower steady-state error. When channel changes suddenly, a filter with the proposed algorithms can adapt to the variation of the channel quickly.

Sparsity-aware subband adaptive algorithms with adjustable penalties

“…As a consequence, the transient MSD behavior of the sparsity-aware NSAF algorithms can be described by (28) with the recursions (18) and (26). However, it still requires the computation of the moments (18) and (26) in advance.…”

“…Since the matrices () k Η and () k Θ are also bounded (see [19], [24] for details) , we can use theorem 2 in [28] to obtain the mean square convergence condition of the sparsity-aware NSAF algorithms from (26). Specifically, the matrix 1 F given by (27)…”

Implementation of LMS algorithm for system identification

“…The difference between the LMS and GAL is only in underlying filtering structure, LMS uses transversal structure and GAL uses lattice structure. The LMS algorithm has an inherent limitation that it can search local minima only but not global minima [8]. However, this limitation can be overcome by simultaneously initializing the search at multiple points.…”

EEG Sinyallerinden EOG Gürültülerini Yok Etmek için Lineer ve Geniş Lineer Kompleks Değerli En Küçük Ortalama Kare Algoritmaları Tabanlı Bir Adaptif Gürültü Yok Etme Sistemi

“…Özellikle [16]'da ki çalışmada, artırılmış kompleks istatistik kavramı ortaya konulmuştur ve bu kapsamda hem kovaryans matrisi hem de sözde-kovaryans matrisi, artırılmış kovaryans matrisi içerisinde birleştirilmiştir. Artırılmış kompleks istatistik yani geniş lineer model yaklaşımı, LMS tabanlı adaptif filtreleme algoritmalarının tasarımlarında oldukça yaygın ve etkin bir şekilde kullanılmıştır [14,[17][18][19][20][21][22][23][24]. Örneğin, [14,[17][18][19][20][21][22][23][24]'de yer alan çalışmalarda; WL (veya artırılmış) kompleks değerli LMS (WL-CLMS) algoritması, kompleks değerli dairesel ve dairesel olmayan sinyallerin işlenebilmesi için önerilmiştir.…”