28,734 research outputs found
Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS
Over the last decade, kernel methods for nonlinear processing have
successfully been used in the machine learning community. The primary
mathematical tool employed in these methods is the notion of the Reproducing
Kernel Hilbert Space. However, so far, the emphasis has been on batch
techniques. It is only recently, that online techniques have been considered in
the context of adaptive signal processing tasks. Moreover, these efforts have
only been focussed on real valued data sequences. To the best of our knowledge,
no adaptive kernel-based strategy has been developed, so far, for complex
valued signals. Furthermore, although the real reproducing kernels are used in
an increasing number of machine learning problems, complex kernels have not,
yet, been used, in spite of their potential interest in applications that deal
with complex signals, with Communications being a typical example. In this
paper, we present a general framework to attack the problem of adaptive
filtering of complex signals, using either real reproducing kernels, taking
advantage of a technique called \textit{complexification} of real RKHSs, or
complex reproducing kernels, highlighting the use of the complex gaussian
kernel. In order to derive gradients of operators that need to be defined on
the associated complex RKHSs, we employ the powerful tool of Wirtinger's
Calculus, which has recently attracted attention in the signal processing
community. To this end, in this paper, the notion of Wirtinger's calculus is
extended, for the first time, to include complex RKHSs and use it to derive
several realizations of the Complex Kernel Least-Mean-Square (CKLMS) algorithm.
Experiments verify that the CKLMS offers significant performance improvements
over several linear and nonlinear algorithms, when dealing with nonlinearities.Comment: 15 pages (double column), preprint of article accepted in IEEE Trans.
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Finding Structural Information of RF Power Amplifiers using an Orthogonal Non-Parametric Kernel Smoothing Estimator
A non-parametric technique for modeling the behavior of power amplifiers is
presented. The proposed technique relies on the principles of density
estimation using the kernel method and is suited for use in power amplifier
modeling. The proposed methodology transforms the input domain into an
orthogonal memory domain. In this domain, non-parametric static functions are
discovered using the kernel estimator. These orthogonal, non-parametric
functions can be fitted with any desired mathematical structure, thus
facilitating its implementation. Furthermore, due to the orthogonality, the
non-parametric functions can be analyzed and discarded individually, which
simplifies pruning basis functions and provides a tradeoff between complexity
and performance. The results show that the methodology can be employed to model
power amplifiers, therein yielding error performance similar to
state-of-the-art parametric models. Furthermore, a parameter-efficient model
structure with 6 coefficients was derived for a Doherty power amplifier,
therein significantly reducing the deployment's computational complexity.
Finally, the methodology can also be well exploited in digital linearization
techniques.Comment: Matlab sample code (15 MB):
https://dl.dropboxusercontent.com/u/106958743/SampleMatlabKernel.zi
Modeling of complex-valued Wiener systems using B-spline neural network
In this brief, a new complex-valued B-spline neural network is introduced in order to model the complex-valued Wiener system using observational input/output data. The complex-valued nonlinear static function in the Wiener system is represented using the tensor product from two univariate Bspline neural networks, using the real and imaginary parts of the system input. Following the use of a simple least squares parameter initialization scheme, the GaussāNewton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first-order derivatives recursion. Numerical examples, including a nonlinear high-power amplifier model in communication systems, are used to demonstrate the efficacy of the proposed approaches
Adaptive Bayesian decision feedback equalizer for dispersive mobile radio channels
The paper investigates adaptive equalization of time dispersive mobile ratio fading channels and develops a robust high performance Bayesian decision feedback equalizer (DFE). The characteristics and implementation aspects of this Bayesian DFE are analyzed, and its performance is compared with those of the conventional symbol or fractional spaced DFE and the maximum likelihood sequence estimator (MLSE). In terms of computational complexity, the adaptive Bayesian DFE is slightly more complex than the conventional DFE but is much simpler than the adaptive MLSE. In terms of error rate in symbol detection, the adaptive Bayesian DFE outperforms the conventional DFE dramatically. Moreover, for severely fading multipath channels, the adaptive MLSE exhibits significant degradation from the theoretical optimal performance and becomes inferior to the adaptive Bayesian DFE
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