Energy Conservation and the Learning Ability of LMS Adaptive Filters

Sayed, Ali H.; Nascimento, Vítor H.

doi:10.1002/0471461288.ch3

Cited by 5 publications

(6 citation statements)

References 10 publications

(19 reference statements)

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“…The evolution of the error s[n] = U H F x[n] in the compact transformed domain is totally equivalent to the behavior of x[n] from a mean-square error point of view. Thus, using energy conservation arguments [57], we consider a general weighted squared error sequence s…”

Section: B Mean-square Analysismentioning

confidence: 99%

Adaptive Least Mean Squares Estimation of Graph Signals

Lorenzo

Barbarossa

Banelli

et al. 2016

IEEE Trans. on Signal and Inf. Process. over Networks

106

168

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The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment

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Section: B Mean-square Analysismentioning

confidence: 99%

Adaptive Least Mean Squares Estimation of Graph Signals

Lorenzo

Barbarossa

Banelli

et al. 2016

IEEE Trans. on Signal and Inf. Process. over Networks

106

168

View full text Add to dashboard Cite

show abstract

“…In particular, it is immediate to see that (48) can be obtained from ( 44)-(45), by substituting the terms p i in (46) with p 2 i , for the case i = j. Such approximation appears in (48) only in the term O(µ 2 ) and, under Assumption 3, it is assumed to a negligible deviation from (43). Now, we proceed by showing stability conditions for recursion (42).…”

Section: Discussionmentioning

confidence: 99%

“…(48) only in the term O(µ 2 ) and, under Assumption 3, it is assumed to produce a negligible deviation from (43). Now, we proceed by showing the stability conditions for recursion (42).…”

Section: Appendix a Proof Of Theoremmentioning

confidence: 99%

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Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies

Lorenzo

Banelli

Isufi

et al. 2018

IEEE Trans. Signal Process.

128

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The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly time-varying) subset of vertices. We recast two classical adaptive algorithms in the graph signal processing framework, namely, the least mean squares (LMS) and the recursive least squares (RLS) adaptive estimation strategies. For both methods, a detailed mean-square analysis illustrates the effect of random sampling on the adaptive reconstruction capability and the steady-state performance. Then, several probabilistic sampling strategies are proposed to design the sampling probability at each node in the graph, with the aim of optimizing the tradeoff between steady-state performance, graph sampling rate, and convergence rate of the adaptive algorithms. Finally, a distributed RLS strategy is derived and is shown to be convergent to its centralized counterpart. Numerical simulations carried out over both synthetic and real data illustrate the good performance of the proposed sampling and reconstruction strategies for (possibly distributed) adaptive learning of signals defined over graphs.

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“…Subsequently, the mean-square performance of the algorithm is analyzed based on an energy conservation relation [104], [106], [107], [108], [110], [131], [132]. Stability bounds for the step size and an expression for the steady-state MSE are determined by manipulating various error quantities in the energy conservation relation.…”

Section: Chapter 5 Stability and Performance Analysismentioning

confidence: 99%

Subband adaptive algorithms for high-order transversal filters

Lee¹

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Adaptive filters have been employed in wide range of applications where signal characteristics are not available, or are time-varying, such as acoustic echo cancellation and adaptive noise cancellation. Despite their widespread use, performance of the adaptive filters is degraded in some applications by two major factors, namely, (i) coloring of the input signal, and (ii) long impulse response of the unknown system. The classical least-mean-square (LMS) algorithm is computationally efficient but its convergence speed deteriorates as the eigenvalue spread of the input autocorrelation matrix increases due to the coloring of the input signal. The convergence problem worsens when the order of the adaptive filter is increased in order to model the unknown system with sufficient accuracy. In contrast, recursive least-squares (RLS) algorithm is adequate in dealing with colored excitation with large spectral dynamic range. Nevertheless, high computational complexity renders the algorithm not applicable in real-time for the case of high-order adaptive filter. Those problems have motivated various approaches of employing subband and multirate techniques in designing computationally efficient adaptive algorithms with improved convergence performance against high eigenvalue disparity. Conventional subband adaptive filters (SAFs) decompose the input signal and desired response into multiple contiguous spectral bands, decimate the subband signals, process each subband with separate adaptive subfilters, and finally interpolate and recombine the resulting subband signals to obtain a filtered output. Intuitively, faster convergence is possible because the spectral dynamic range is greatly reduced in each subband. Furthermore, the computational burden can be reduced by decimating both the order and adaptation rate of the subfilters. Yet, detailed analysis shows that the convergence ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library viii rate of the conventional SAF is limited by aliasing and band-edge effects, in spite of a number of modifications that have been proposed, such as, introducing adaptive cross-filters or spectral gaps between adjacent subfilters, as well as oversampled scheme. This thesis describes, analyzes, and generalizes a new class of SAFs, called the normalized SAF (NSAF), whereby the adaptive filter is no longer separated into subfilters. Instead, subband signals, which are normalized by their respective subband input variance, are used to adapt the fullband tap weights of a modeling filter. The

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Energy Conservation and the Learning Ability of LMS Adaptive Filters

Cited by 5 publications

References 10 publications

Adaptive Least Mean Squares Estimation of Graph Signals

Adaptive Least Mean Squares Estimation of Graph Signals

Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies

Subband adaptive algorithms for high-order transversal filters

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