Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian Inputs

Bershad, N.J.; Eweda, Eweda; Bermudez, J.C.M.

doi:10.1109/tsp.2014.2307278

Cited by 59 publications

(44 citation statements)

References 24 publications

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“…Consequently, the presented performance analysis quantifies the effect of these periodic dynamic on the performance of the LMS filter, compared to the JWSS setup. Finally, note that the deviation vector g[n] does not appear in [21]. This is due to the fact that for the specific system model and the additive noise considered in [21], it can be shown that the LMMSE estimator of the SOI is LTI, thus g[n] is the zero vector.…”

Section: Discussionmentioning

confidence: 99%

“…(15)]. We note that this specialization holds only when the random walk effect in [21] is neglected, i.e., the system considered in [21] becomes…”

Section: A Time-evolution Of the Msementioning

confidence: 95%

“…Specifically, [18] focused on interference rejection in the presence of cyclostationary digitally modulated signals; The work [19] proposed a scheme for blind adaptation of FRESH filters using the LMS and the recursive least-squares algorithms; The work [20] studied the effect of errors in the frequency shifts on the performance of LMS-based adaptive FRESH filters with a temporally independent input signal. In [21], the LMS performance was studied for the identification of a linear system whose coefficients obey a random walk model with a WSCS Gaussian input and an additive wide-sense stationary (WSS) Gaussian noise. We note that when the random walk effect is negligible, the linear system considered in [21] becomes linear time-invariant (LTI).…”

Section: Introductionmentioning

confidence: 99%

“…In [21], the LMS performance was studied for the identification of a linear system whose coefficients obey a random walk model with a WSCS Gaussian input and an additive wide-sense stationary (WSS) Gaussian noise. We note that when the random walk effect is negligible, the linear system considered in [21] becomes linear time-invariant (LTI). The work [22] analyzed the LMS performance when applied to adaptive line enhancement/cancellation for a WSCS input consisting of a Gaussian process with periodic variance plus a sine wave with random phase.…”

Section: Introductionmentioning

confidence: 99%

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Performance analysis of LMS filters with non-Gaussian cyclostationary signals

Shlezinger

Todros

2019

Signal Processing

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The least mean-square (LMS) filter is one of the most common adaptive linear estimation algorithms.In many practical scenarios, e.g., digital communications systems, the signal of interest (SOI) and the input signal are jointly wide-sense cyclostationary. Previous works analyzing the performance of LMS filters for this important case assume Gaussian probability distributions of the considered signals. In this work, we provide a transient and steady-state performance analysis that applies to non-Gaussian cyclostationary signals. In the considered analysis, the SOI is modeled as a perturbed response of a linear periodically time-varying system to the input signal. We obtain conditions for convergence and derive analytical expressions for the non-asymptotic and steady-state mean-squared error. We then show how the theoretical analysis can be effectively applied for two common non-Gaussian classes of input distributions, the class of compound Gaussian distributions, and the class of Gaussian mixture distributions. The accuracy of our analysis is illustrated for system identification and signal recovery scenarios that involve linear periodically time variant systems and non-Gaussian inputs.

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Section: Discussionmentioning

confidence: 99%

“…(15)]. We note that this specialization holds only when the random walk effect in [21] is neglected, i.e., the system considered in [21] becomes…”

Section: A Time-evolution Of the Msementioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Performance analysis of LMS filters with non-Gaussian cyclostationary signals

Shlezinger

Todros

2019

Signal Processing

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“…Least mean square (LMS) and normalized least mean square (NLMS) algorithms in the cyclostationary regime are analyzed in [25]. A periodic Levinson-Durbin algorithm for entropy maximization is derived in [35].…”

Section: Mmse Linear Filteringmentioning

confidence: 99%

Cyclostationarity: New trends and applications

Napolitano

2016

Signal Processing

183

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Stochastic analysis of the diffusion least mean square and normalized least mean square algorithms for cyclostationary white Gaussian and non‐Gaussian inputs

Eweda

Bershad

Bermudez

2021

Adaptive Control & Signal

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The diffusion least mean square (DLMS) and the diffusion normalized least mean square (DNLMS) algorithms are analyzed for a network having a fusion center. This structure reduces the dimensionality of the resulting stochastic models while preserving important diffusion properties. The analysis is done in a system identification framework for cyclostationary white nodal inputs. The system parameters vary according to a random walk model. The cyclostationarity is modeled by periodic time variations of the nodal input powers. The analysis holds for all types of nodal input distributions except for distributions with infinite variance. The derived models consist of simple scalar recursions. These recursions facilitate the understanding of the network mean and mean-square dependence upon the 1) nodal weighting coefficients, 2) nodal input kurtosis and cyclostationarities, 3) nodal noise powers, and 4) the unknown system mean-square parameter increments. Optimization of the node weighting coefficients is studied. Also investigated is the stability dependence of the two algorithms upon the nodal input kurtosis and weighting coefficients. Significant differences are found between the behaviors of the DLMS and DNLMS algorithms for non-Gaussian nodal inputs. Simulations provide strong support for the theory.

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Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian Inputs

Cited by 59 publications

References 24 publications

Performance analysis of LMS filters with non-Gaussian cyclostationary signals

Performance analysis of LMS filters with non-Gaussian cyclostationary signals

Cyclostationarity: New trends and applications

Stochastic analysis of the diffusion least mean square and normalized least mean square algorithms for cyclostationary white Gaussian and non‐Gaussian inputs

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