Volterra filter equalization: a fixed point approach

Nowak, Robert; Veen, B.D. Van

doi:10.1109/78.554302

Cited by 62 publications

(45 citation statements)

References 16 publications

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“…Still, it has been applied successfully to oversampled nonlinear receiver front ends in [19]. In other works, the equalization problem has been formulated as a fixed point problem [20], [21] where a solution for the equalizer is found iteratively. This is possible as long as the mapping between the iteration steps is contractive.…”

Section: Introductionmentioning

confidence: 99%

Minimum Mean-Square Error Equalization for Second-Order Volterra Systems

Krall

Witrisal

Leus

et al. 2008

IEEE Trans. Signal Process.

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Abstract-In this paper, a novel nonlinear Volterra equalizer is presented. We define a framework for nonlinear second-order Volterra models, which is applicable to different applications in engineering. We use this framework to define the channel and to model the equalizer. We then solve the minimum mean-square error (MMSE) problem explicitly for the tandem connection of the two second-order Volterra systems. Optimal solutions for a simplified, linear version of the MMSE equalizer are also presented. The novel equalizer was tested when applied to a nonlinear ultra-wideband transmitted reference receiver front end. As a comparison, a least mean squares (LMS) equalizer with a training sequence has been used to verify the performance of the newly proposed equalizer. The simulation results show that the LMS equalizer is only able to attain the proposed MMSE equalizer after very long training, which might not be desirable in a communication system. Index Terms-Nonlinear MMSE equalizer, second-order systems, Volterra systems.

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Section: Introductionmentioning

confidence: 99%

Minimum Mean-Square Error Equalization for Second-Order Volterra Systems

Krall

Witrisal

Leus

et al. 2008

IEEE Trans. Signal Process.

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show abstract

“…An iterative pre-distortion algorithm based on the Newton algorithm was developed and compared with a successive approximation method based on an fixed-point equation, investigated in [5]. The complexity of the Newton method is higher than the complexity of the successive approximation method, but still grows linearly with the number of iterations.…”

Section: Discussionmentioning

confidence: 99%

“…The method converges if T(·) is a contraction mapping for the signals involved [5]. The complexity (e.g.…”

Section: A Successive Approximationmentioning

confidence: 99%

“…This can be solved in an iterative way, using a known successive approximation method [5], based on a fixed-point equation, and a Newton method, developed in this contribution. Given a model N of a nonlinear system, a structure P is searched which, placed before the nonlinear system, linearizes the signal path as good as possible.…”

Section: Iterative Linearizationmentioning

confidence: 99%

“…Two methods, one based on successive approximation, investigated in [5], and one based on a Newton method are compared.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Iterative linearization methods suited for digital pre-distortion of power amplifiers

Aschbacher¹,

Steinmair²,

Rupp³

Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004.

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Abstract-This paper deals with iterative linearization of a nonlinear dynamical system. The methods proposed are suited for digital pre-distortion of power amplifiers working close to saturation, as it is common for efficiency reasons. Two methods (a well known successive approximation method based on a fixed-point formulation and a Newton method) are compared with respect to convergence speed, robustness against model uncertainties, and complexity. The presented methods are used to linearize a Volterra model of a measured power amplifier.

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Adaptive least mean squares block Volterra filters

Haweel

2001

Circuit Theory & Apps

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SUMMARYAdaptive ÿltering has found many applications in situations where the underlying signals are changing or unknown. While linear ÿlters are simple from implementation and conceptual points of view, many signals are non-linear in nature. Non-linear ÿlters based on truncated Volterra expansions can e ectively model a large number of systems. Unfortunately, the resulting input auto-moment matrix is ill conditioned, which results in a slow convergence rate. This paper proposes a class of block adaptive Volterra ÿlters in which the input sequences are Hadamard transformed to improve the condition number of the input auto-moment matrix and consequently improve the convergence rate. This is achieved by the decorrelation e ect produced by the orthogonality of the transform. Since Hadamard transformation employs only ±1's, the additional required computational and implementation burdens are few. The e ect of additive white Gaussian noise is introduced. Simulation experiments are given to illustrate the improved performance of the proposed method over the conventional Volterra LMS method.

show abstract

Volterra filter equalization: a fixed point approach

Cited by 62 publications

References 16 publications

Minimum Mean-Square Error Equalization for Second-Order Volterra Systems

Minimum Mean-Square Error Equalization for Second-Order Volterra Systems

Iterative linearization methods suited for digital pre-distortion of power amplifiers

Adaptive least mean squares block Volterra filters

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