Exact Expectation Evaluation and Design of Variable Step-Size Adaptive Algorithms

Lara, Pedro; Igreja, Filipe; Tarrataca, Luís; Haddad, Diego B.; Petraglia, M.R.

doi:10.1109/lsp.2018.2880084

Cited by 28 publications

(18 citation statements)

References 16 publications

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“…Remark 1 Popular in the field of stochastic approximations, IA usually provides accurate predictions when the step size value is vanishingly small [5 ].…”

Section: First‐order Analysismentioning

confidence: 99%

“…Using the previous definitions, the update equation of the standard FX‐LMS algorithm can be expressed as

w false(k + 1 false) = w false(k false) + β e^{normal′} false(k false) {bold-italicu}_{f} false(k false),

where the step size

β \in R_{+}

is an adjustable parameter that engenders a trade‐off between convergence rate, steady‐state performance, divergence probability and tracking capabilities [5 ]. Equation (7 ) reveals that the FX‐LMS is a modified version of the popular LMS algorithm, and that analysis and behaviour of the former are more complicated due to the presence of additional filters in the adaptation procedure [4 ].…”

Section: Introductionmentioning

confidence: 99%

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Bias‐compensated FX‐LMS algorithm

et al. 2020

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Active noise control is an expanding field that requires a suitable synthesis of secondary perturbations. Unfortunately, most schemes for noise cancelling do not take into account that the input signal that drives the adaptive filter can be noisy. In this Letter, it is theoretically shown that noise perturbations in the excitation data degrade the performance of the standard filtered‐x least mean squares (FX‐LMS) algorithm. Furthermore, a method that compensates such an issue is devised, and a first‐order stochastic analysis of the resulting algorithm is performed. The results reveal that the proposed scheme outperforms the standard FX‐LMS algorithm, even when the variance of the additive noise in the input is not accurately estimated.

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“…Remark 1 Popular in the field of stochastic approximations, IA usually provides accurate predictions when the step size value is vanishingly small [5 ].…”

Section: First‐order Analysismentioning

confidence: 99%

“…Using the previous definitions, the update equation of the standard FX‐LMS algorithm can be expressed as

w false(k + 1 false) = w false(k false) + β e^{normal′} false(k false) {bold-italicu}_{f} false(k false),

where the step size

β \in R_{+}

Section: Introductionmentioning

confidence: 99%

Bias‐compensated FX‐LMS algorithm

et al. 2020

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“…Such an assumption, popular in the field of stochastic approximations, turns the mathematics tractable, and thereby more accurate when the step size is not large. It is noteworthy that this presumption can be circumvented by the exact expectation analysis method, which requires a cumbersome number of algebraic manipulations, even for small-length filters [18]- [20].…”

Section: Bc-bs-nlmsmentioning

confidence: 99%

A Block-Sparsity Induced NLMS Algorithm with Bias Compensation

Pimenta¹,

Resende²,

Silva³

et al. 2020

Anais De XXXVIII Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

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Adaptive filtering algorithms are flexible mechanisms that adapt themselves to the environment statistics in which they are immersed. It is known that in practice several transfer functions are sparse, in the sense that their energy is concentrated in a few (sometimes clustered) coefficients. In this paper, a new normalized adaptive algorithm tailored to identifying block-sparse systems using a mixed ℓ2,0-norm of the adaptive coefficients is devised. Since the presence of noise in the input signal may induce an additional asymptotic bias in the estimation procedure, a compensation scheme is also advanced to address such an issue. At last, the computational burden is controlled by the adoption of a selective partial-update strategy. Simulated results indicate that the proposed algorithms present good performance compared to state-of-the-art alternatives, and allows the designer the choice of a convenient point regarding the trade-off between computational cost and convergence rate.

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“…The avoidance of IA engineers the exact expectation technique [11][12][13], which is also able to provide a proper step-size upper bound that guarantees convergence [12]. Furthermore, it can be employed in the derivation of a deterministic theoretical step-size sequence that optimises performance [14].…”

mentioning

confidence: 99%

Exact expectation analysis of the LMS adaptive identification of non‐linear systems

et al. 2020

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Most adaptive filtering schemes employ the tapped-delay line. In part, such a fact can be explained by the assumption that the plant they intend to estimate is linear. Although such a hypothesis can be reasonable if the input signal is constrained to a certain range, sometimes it may not be valid. In this last case, the performance and stability guarantees provided by stochastic models that presume linearity of the ideal system are no longer valid. This Letter advances an analytic model of the least-mean-square (LMS) learning capabilities when the ideal system is not linear, with the additive noise including nonlinear functions of the input samples. The proposed analysis does not assume neither that the excitation signal is statistically independent of the adaptive weights, nor that the additive noise is white and/or independent of input data. Furthermore, it can be applied to non-Gaussian and/or non-white input signals. Simulations show that the advanced model is more accurate than traditional approaches. CAPES, CNPq, and FAPERJ for supporting this research.

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Exact Expectation Evaluation and Design of Variable Step-Size Adaptive Algorithms

Cited by 28 publications

References 16 publications

Bias‐compensated FX‐LMS algorithm

Bias‐compensated FX‐LMS algorithm

A Block-Sparsity Induced NLMS Algorithm with Bias Compensation

Exact expectation analysis of the LMS adaptive identification of non‐linear systems

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