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The Volterra and Wiener Theories of Nonlinear Systems
01 Jan 1980-
TL;DR: In this article, a complete and detailed development of the analysis, design and characterization of non-linear systems using the Volterra and Wiener theories, as well as gate functions, is presented.
Abstract: This text presents a complete and detailed development of the analysis, design and characterization of non-linear systems using the Volterra and Wiener theories, as well as gate functions, thus yielding new insights and a better comprehension of the subject. The Volterra and Wiener theories are useful in the study of systems in biological, mechanical, and electrical fields.
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TL;DR: This paper relates the general Volterra representation to the classical Wiener, Hammerstein, Wiener-Hammerstein, and parallel Wiener structures, and describes some state-of-the-art predistortion models based on memory polynomials, and proposes a new generalizedMemory polynomial that achieves the best performance to date.
Abstract: Conventional radio-frequency (RF) power amplifiers operating with wideband signals, such as wideband code-division multiple access (WCDMA) in the Universal Mobile Telecommunications System (UMTS) must be backed off considerably from their peak power level in order to control out-of-band spurious emissions, also known as "spectral regrowth." Adapting these amplifiers to wideband operation therefore entails larger size and higher cost than would otherwise be required for the same power output. An alternative solution, which is gaining widespread popularity, is to employ digital baseband predistortion ahead of the amplifier to compensate for the nonlinearity effects, hence allowing it to run closer to its maximum output power while maintaining low spectral regrowth. Recent improvements to the technique have included memory effects in the predistortion model, which are essential as the bandwidth increases. In this paper, we relate the general Volterra representation to the classical Wiener, Hammerstein, Wiener-Hammerstein, and parallel Wiener structures, and go on to describe some state-of-the-art predistortion models based on memory polynomials. We then propose a new generalized memory polynomial that achieves the best performance to date, as demonstrated herein with experimental results obtained from a testbed using an actual 30-W, 2-GHz power amplifier
1,305 citations
Cites background or methods from "The Volterra and Wiener Theories of..."
...The most general form of nonlinearity with -tap memory is described by the Volterra series, which consists of a sum of multidimensional convolutions [9], which in discrete time can be written...
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...Within the general framework of Volterra systems, there is a technique known as the th-order inverse [9] that accomplishes this....
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...The number of terms in (4) can be greatly reduced [10] by eliminating redundancies associated with the various index permutations of (6) and assuming, without loss of generality [9], that the kernels are symmetric....
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TL;DR: A memory polynomial model for the predistorter is proposed and implemented using an indirect learning architecture and linearization performance is demonstrated on a three-carrier WCDMA signal.
Abstract: Power amplifiers (PAs) are inherently nonlinear devices and are used in virtually all communications systems. Digital baseband predistortion is a highly cost-effective way to linearize PAs, but most existing architectures assume that the PA has a memoryless nonlinearity. For wider bandwidth applications such as wideband code-division multiple access (WCDMA) or wideband orthogonal frequency-division multiplexing (W-OFDM), PA memory effects can no longer be ignored, and memoryless predistortion has limited effectiveness. In this paper, instead of focusing on a particular PA model and building a corresponding predistorter, we focus directly on the predistorter structure. In particular, we propose a memory polynomial model for the predistorter and implement it using an indirect learning architecture. Linearization performance is demonstrated on a three-carrier WCDMA signal.
1,160 citations
Cites methods from "The Volterra and Wiener Theories of..."
...Volterra series is a general nonlinear model with memory [3] and has been used to model PAs with mild nonlinearities [4]....
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...Predistortion of the Volterra model is usually implemented using the th-order inverse technique [3], which is complicated....
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TL;DR: In this article, a review of the past and recent developments in system identification of nonlinear dynamical structures is presented, highlighting their assets and limitations and identifying future directions in this research area.
1,000 citations
TL;DR: In this paper, it is shown that the NARMAX (Non-linear AutoRegressive Moving Average with eXogenous inputs) model is a general and natural representation of non-linear systems and contains, as special cases, several existing nonlinear models.
Abstract: Input-output representations of non-linear discrete-time systems are discussed. It is shown that the NARMAX (Non-linear AutoRegressive Moving Average with eXogenous inputs) model is a general and natural representation of non-linear systems and contains, as special cases, several existing non-linear models. The problem of approximating non-linear input-output systems is also addressed and several properties of non-linear models are highlighted using simple examples.
912 citations