144 research outputs found
Sparse Nonlinear MIMO Filtering and Identification
In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation
Statistical efficiency of structured cpd estimation applied to Wiener-Hammerstein modeling
Accepted for publication in the Proceedings of the European Signal Processing Conference (EUSIPCO) 2015.International audienceThe computation of a structured canonical polyadic decomposition (CPD) is useful to address several important modeling problems in real-world applications. In this paper, we consider the identification of a nonlinear system by means of a Wiener-Hammerstein model, assuming a high-order Volterra kernel of that system has been previously estimated. Such a kernel, viewed as a tensor, admits a CPD with banded circulant factors which comprise the model parameters. To estimate them, we formulate specialized estimators based on recently proposed algorithms for the computation of structured CPDs. Then, considering the presence of additive white Gaussian noise, we derive a closed-form expression for the Cramer-Rao bound (CRB) associated with this estimation problem. Finally, we assess the statistical performance of the proposed estimators via Monte Carlo simulations, by comparing their mean-square error with the CRB
State–of–the–art report on nonlinear representation of sources and channels
This report consists of two complementary parts, related to the modeling of two important sources of nonlinearities in a communications system. In the first part, an overview of important past work related to the estimation, compression and processing of sparse data through the use of nonlinear models is provided. In the second part, the current state of the art on the representation of wireless channels in the presence of nonlinearities is summarized. In addition to the characteristics of the nonlinear wireless fading channel, some information is also provided on recent approaches to the sparse representation of such channels
Overview of Constrained PARAFAC Models
In this paper, we present an overview of constrained PARAFAC models where the
constraints model linear dependencies among columns of the factor matrices of
the tensor decomposition, or alternatively, the pattern of interactions between
different modes of the tensor which are captured by the equivalent core tensor.
Some tensor prerequisites with a particular emphasis on mode combination using
Kronecker products of canonical vectors that makes easier matricization
operations, are first introduced. This Kronecker product based approach is also
formulated in terms of the index notation, which provides an original and
concise formalism for both matricizing tensors and writing tensor models. Then,
after a brief reminder of PARAFAC and Tucker models, two families of
constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models,
are described in a unified framework, for order tensors. New tensor
models, called nested Tucker models and block PARALIND/CONFAC models, are also
introduced. A link between PARATUCK models and constrained PARAFAC models is
then established. Finally, new uniqueness properties of PARATUCK models are
deduced from sufficient conditions for essential uniqueness of their associated
constrained PARAFAC models
The Kolmogorov mapping theorem in signal processing
Since the publication in 1957 of the work of Andrei
Kolmogorov 181 in mapping a function of multiple variables
by means functions of a single variable, many
mathematicians and engineers try , with different degree of
success and not without controversy 1191. to find the direct
application of it to multiple extremes problems, rooting of
multivariate polynomials, neural networks and pattern
recognition. This paper revisits the theorem from the optic
of a generalised architecture for signal processing 1281. It is
envisaged the high potential of the theorem to handle either
linear or non-linear processing problems. A specific
implementation following the main guide-lines of the
theorem is reported, as well as some preliminary results
concerning the design, implementation and performance of
non-linear systems. The applications cover non linear
transmission channels for communications, instantaneous
companders and prediction of chaotic series.Peer ReviewedPostprint (published version
Nonlinear Blind Identification with Three-Dimensional Tensor Analysis
This paper deals with the analysis of a third-order tensor composed of a fourth-order output cumulants used for blind identification of a second-order Volterra-Hammerstein series. It is demonstrated that this nonlinear identification problem can be converted in a multivariable system with multiequations having the form of +=. The system may be solved using several methods. Simulation results with the Iterative Alternating Least Squares (IALS) algorithm provide good performances for different signal-to-noise ratio (SNR) levels. Convergence issues using the reversibility analysis of matrices and are addressed. Comparison results with other existing algorithms are carried out to show the efficiency of the proposed algorithm
Enhanced Nonlinear System Identification by Interpolating Low-Rank Tensors
Function approximation from input and output data is one of the most
investigated problems in signal processing. This problem has been tackled with
various signal processing and machine learning methods. Although tensors have a
rich history upon numerous disciplines, tensor-based estimation has recently
become of particular interest in system identification. In this paper we focus
on the problem of adaptive nonlinear system identification solved with
interpolated tensor methods. We introduce three novel approaches where we
combine the existing tensor-based estimation techniques with multidimensional
linear interpolation. To keep the reduced complexity, we stick to the concept
where the algorithms employ a Wiener or Hammerstein structure and the tensors
are combined with the well-known LMS algorithm. The update of the tensor is
based on a stochastic gradient decent concept. Moreover, an appropriate step
size normalization for the update of the tensors and the LMS supports the
convergence. Finally, in several experiments we show that the proposed
algorithms almost always clearly outperform the state-of-the-art methods with
lower or comparable complexity.Comment: 12 pages, 4 figures, 3 table
Restoration of ultrasonic images using non-linear system identification and deconvolution
This paper studies a new ultrasound image restoration method based on a non-linear forward model. A Hammerstein polynomial-based non-linear image formation model is considered to identify the system impulse response in baseband and around the second harmonic. The identification process is followed by a joint deconvolution technique minimizing an appropriate cost function. This cost function is constructed from two data fidelity terms exploiting the linear and non-linear model components, penalized by an additive-norm regularization enforcing sparsity of the solution. An alternating optimization approach is considered to minimize the penalized cost function, allowing the tissue reflectivity function to be estimated. Results on synthetic ultrasound images are finally presented to evaluate the algorithm performance
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