Adaptive sparse Volterra system identification with ℓ0‐norm penalty

Shi, Kun; Shi, Peng

doi:10.1016/j.sigpro.2011.04.028

Cited by 33 publications

(14 citation statements)

References 6 publications

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“…Both modeling vehicles introduce massive over-parametrization to capture the nonlinear dynamics that results in identifiability issues. Sparse estimation in Volterra models [5], [4], [18] and pruning in neural networks [19] are commonly enforced to keep model complexity reasonably low.…”

Section: Introductionmentioning

confidence: 99%

Constrained SPICE in Volterra-Laguerre modeling of human smooth pursuit

Bro

Medvedev

2017

2017 IEEE Conference on Control Technology and Applications (CCTA)

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Abstract-The Volterra model is a well-established option in nonlinear black-box system identification. However, the estimated model is often over-parametrized. This paper presents an approach to reducing the number of parameters of a Volterra model with the kernels parametrized in the orthonormal basis of Laguerre functions by estimating it with a sparse estimation algorithm subject to constraints. The resulting parameter estimates are scrutinized for parameter redundancy and functional dependence by principal component analysis. The benefits of this approach are illustrated by identifying the human smooth pursuit system. Previous studies have suggested that the Volterra model structure is suitable for modeling the human smooth pursuit system both in health and disease. The data sets are obtained by eye tracking in a study performed on 7 test subjects diagnosed with Parkinson's disease and 22 healthy control subjects. In terms of output error, the reduced model has similar performance to that of the full model.

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Section: Introductionmentioning

confidence: 99%

Constrained SPICE in Volterra-Laguerre modeling of human smooth pursuit

Bro

Medvedev

2017

2017 IEEE Conference on Control Technology and Applications (CCTA)

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“…We consider a typical CS scenario, which is also considered in [1][2][3][4][13][14][15]. The goal is to reconstruct a lengthsparse signal from observations, where < .…”

Section: Examplementioning

confidence: 99%

“…From [1][2][3][4], we know that the above problem is difficult to solve in a straight way. In order to solve the 0 -norm problem effectively, an approximation model is to replace the 0 -norm by the 1 -norm to solve the Basis Pursuit problem, such as in [5,6]:…”

Section: Introductionmentioning

confidence: 99%

“…For some > 0, (1/2)‖ − ‖ 2 2 + ‖ ‖ 1 is a convex function but not a differentiable function. Recently, many scholars have studied the method for solving (3). For instance, gradient projection for sparse reconstruction was proposed by Figueiredo et al in [9], a two-step iterative shrinkage thresholding (IST) method was proposed by Bioucas-Dias and Figueiredo in [10], a fast IST algorithm was presented by Beck and Teboulle in [11], SPGL1 (A solver for large-scale sparse reconstruction) was proposed by Ewout and Friedlander in [12], who consider a least-squares problem with 1 -norm constraint and use a spectral gradient projection method, and ADM method was proposed by Yang and Zhang in [13].…”

Section: Introductionmentioning

confidence: 99%

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The Smoothing FR Conjugate Gradient Method for Solving a Kind of Nonsmooth Optimization Problem with l1-Norm

Chen

2018

Mathematical Problems in Engineering

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We study the method for solving a kind of nonsmooth optimization problems with 1 -norm, which is widely used in the problem of compressed sensing, image processing, and some related optimization problems with wide application background in engineering technology. Transformated by the absolute value equations, this kind of nonsmooth optimization problem is rewritten as a general unconstrained optimization problem, and the transformed problem is solved by a smoothing FR conjugate gradient method. Finally, the numerical experiments show the effectiveness of the given smoothing FR conjugate gradient method.

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“…Such an approach is known as LASSO [27]; in the view of the principle of parsimony [36], such sparse model representations must be preferred. These techniques have been used successfully in SISO Volterra basis selection and polynomial models [28,37,38]. The large number of coefficients of the predistorter or equalizer limits its applicability to only low nonlinear orders, short memory depth, and a few carriers.…”

Section: Complexity Reductionmentioning

confidence: 99%

Low complexity predistortion and equalization in nonlinear multicarrier satellite communications

Zenteno

Piazza

Shankar

et al. 2015

EURASIP J. Adv. Signal Process.

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Aiming to reduce the power/mass requirements in satellite transponders and to reduce mission costs, joint amplification of multiple carriers using a single high-power amplifier (HPA) is being considered. In this scenario, a careful investigation of the resulting power efficiency is essential as amplification is nonlinear, and multicarrier signals exhibit enlarged peak-to-average power ratio. Thus, operating the amplifier close to saturation vastly increases signal distortion resulting in a severe degradation of performance, especially for higher order modulations. This paper proposes a reduced-complexity digital predistortion (DPD) scheme at the transmitter and a corresponding equalizer (EQ) at the receiver to mitigate these nonlinear effects. Scenarios include both the forward as well as the return links. In particular, the paper exploits the MIMO Volterra representation and builds on a basis pursuit approach using a LASSO (least absolute shrinkage and selection operator) algorithm to achieve an efficient basis representation, avoiding large computational complexity, to describe the selection of predistorter/equalizer model. The work further compares and contrasts the two mitigation techniques taking various system aspects into consideration. The gains in performance and amplification efficiency demonstrated by the use of DPD/ EQ motivate their inclusion in next-generation satellite systems.

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Adaptive sparse Volterra system identification with ℓ0‐norm penalty

Cited by 33 publications

References 6 publications

Constrained SPICE in Volterra-Laguerre modeling of human smooth pursuit

Constrained SPICE in Volterra-Laguerre modeling of human smooth pursuit

The Smoothing FR Conjugate Gradient Method for Solving a Kind of Nonsmooth Optimization Problem with l1-Norm

Low complexity predistortion and equalization in nonlinear multicarrier satellite communications

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