Performance analysis of LMS filters with non-Gaussian cyclostationary signals

Abstract

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.

Transient Theoretical Analysis of Diffusion RLS Algorithm for Cyclostationary Colored Inputs

“…, σ x,k (n−L+1) a diagonal matrix, and R u,k = E{u k,n u k,n } the autocorrelation matrix. The sinusoidal and pulsed variation models [16]- [21] are often adopted for the periodic sequences σ 2…”

“…Nevertheless, cyclostationary inputs with periodical variations are ubiquitous in real-world applications [14], [15]. In that way, the theoretical performance of LMS-type algorithms were studied further based on this assumption [16]- [21]. Then, the convergence behavior of the diffusion LMS (DLMS) was also analyzed for cyclostationary inputs in [22]- [24].…”

An Alternative Approach to Obtain a New Gain in Step-Size of LMS Filters Dealing with Periodic Signals

“…Very different fields of knowledge such as underwater communications [4] or ultrawide bandwidth systems [5] make use of the LMS algorithm to optimize an objective function by iteratively minimizing the error signal. Apart from the classical performance analysis of the LMS algorithm, one may find recent relevant references about stochastic analysis of the LMS algorithm for non-Gaussian [6], white Gaussian [7], and colored Gaussian [8] cyclostationary input signals.…”

Security‐aware authorization and verification based data aggregation model for wireless sensor networks

“…[10][11][12][13] The adaptive linear estimation of a signal of interest (SOI) is based on an input signal. 14 WSN can also be used in various environmental hazards, namely nuclear power plants. Due to the major advantages, more attention is devoted to the WSN, and various models are adopted for the WSN network.…”

“…WSN with the highly‐constrained, cheap, and small sensor nodes effectively senses the physical environment, 7 which includes large application prospects 8 in both the civilian and military usages, like military target surveillance and tracking, health monitoring system, tracking critical facilities, 9 and animal habitats monitoring 10‐13 . The adaptive linear estimation of a signal of interest (SOI) is based on an input signal 14 . WSN can also be used in various environmental hazards, namely nuclear power plants.…”