An Exact Expectation Model for the LMS Tracking Abilities

Silva, Thiago T. P.; Lara, Pedro; Igreja, Filipe; Oliveira, Fernanda D. V. R.; Tarrataca, Luís; Haddad, Diego B.

doi:10.1109/tsp.2020.3028993

Cited by 14 publications

(4 citation statements)

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“…The model utilizes the ubiquitous independence assumption [40], which implies that vectors x(k) are independent and identically distributed. The eigendecomposition of the input autocovariance matrix R (43) emphasizes two import quantities for the following analysis: the eigenvalues λ i ∈ R+ (for i ∈ {0, 1, .…”

Section: Transient Analysismentioning

confidence: 99%

“…The ability to operate in a nonstationary setting is one of the most desirable features of adaptive filtering algorithms [40].…”

Section: Trackingmentioning

confidence: 99%

“…Its suitability is discussed in more detail in [43]. It should be noted that first-order perturbations (69) are encountered in applications such as acoustic echo cancellation and transmission systems [40], in such a manner that its use is not due solely to analytical convenience. Under (69), a new formulation is called for Equation (22):…”

Section: Trackingmentioning

confidence: 99%

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Stochastic Modeling of the Set-Membership- Sign-NLMS Algorithm

De Souza,

Henriques,

Siqueira

et al. 2024

IEEE Access

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This paper proposes the Set-Membership sign-NLMS (SM-sign-NLMS) adaptive filter, which combines the ability for data censoring (offered by Set-Membership schemes) with robustness against impulsive noise (provided by signed schemes). The algorithm can present a much lower steady-state probability of update than the standard SM-NLMS algorithm when impulsive noise is present in the system. It is derived from a local deterministic optimization problem modulated by a minimum disturbance cost function combined with a bounded error criterion. Several stochastic models are proposed in order to extract insights and a time-variant step size extension of the algorithm. The first of them, based on energy conservation arguments, leads to a fixed-point analytic equation whose solution predicts the asymptotic performance of the algorithm. Further, a transient analysis based on a statistical decoupling of the radial and (discrete) angular distributions of the input vector is derived. Based on such an analysis, an efficient time-variant step-size version of the algorithm is proposed. Additionally, such an analysis is also utilized to obtain a fixed-point formula whose solution describes the asymptotic performance when the unknown plant that the filter intends to match varies according to a first-order Markovian model. Lastly, a novel stochastic model is advanced for the description of the algorithm learning behavior under a deficient-length scenario for a white input signal, which provides some insights about the asymptotic performance of the algorithm. The findings are confirmed by extensive simulations.

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Section: Transient Analysismentioning

confidence: 99%

“…The ability to operate in a nonstationary setting is one of the most desirable features of adaptive filtering algorithms [40].…”

Section: Trackingmentioning

confidence: 99%

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Stochastic Modeling of the Set-Membership- Sign-NLMS Algorithm

De Souza,

Henriques,

Siqueira

et al. 2024

IEEE Access

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“…It is important to obtain performance guarantees in nonstationary settings, which occur when the ideal plant to be identified is time variant. In this section, the tracking capability of the BC-LMS is analyzed when the coefficients of ideal plant vary slowly, according to a first-order Markovian model [10], [11]:…”

Section: Tracking Analysismentioning

confidence: 99%

Transient Analysis of the Bias-Compensated LMS Algorithm

Pimenta

Siqueira

Petraglia

et al. 2021

JCIS

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In most supervised adaptive filtering settings, only the additive noise of the reference signal is taken into account. However, in many practical situations the excitation data is also immersed in noise, which leads to a bias in the estimation procedure. In order to mitigate such issue, adaptive algorithms with bias compensation schemes have been proposed. This paper advances for the first time a stochastic model that predicts the average and mean-square learning behavior of the biascompensated least mean squares algorithm in the transient region. Asymptotic predictions can also be obtained as a result of the devised analysis. Tracking capabilities and the impact of employing sub-optimal length adaptive filter are also considered, without restricting the input signal to be white. Results indicate that the proposed analysis reveals accurate agreement with simulation results.

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