2,115 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.
Sig. Pro
Detection for 5G-NOMA: An Online Adaptive Machine Learning Approach
Non-orthogonal multiple access (NOMA) has emerged as a promising radio access
technique for enabling the performance enhancements promised by the
fifth-generation (5G) networks in terms of connectivity, low latency, and high
spectrum efficiency. In the NOMA uplink, successive interference cancellation
(SIC) based detection with device clustering has been suggested. In the case of
multiple receive antennas, SIC can be combined with the minimum mean-squared
error (MMSE) beamforming. However, there exists a tradeoff between the NOMA
cluster size and the incurred SIC error. Larger clusters lead to larger errors
but they are desirable from the spectrum efficiency and connectivity point of
view. We propose a novel online learning based detection for the NOMA uplink.
In particular, we design an online adaptive filter in the sum space of linear
and Gaussian reproducing kernel Hilbert spaces (RKHSs). Such a sum space design
is robust against variations of a dynamic wireless network that can deteriorate
the performance of a purely nonlinear adaptive filter. We demonstrate by
simulations that the proposed method outperforms the MMSE-SIC based detection
for large cluster sizes.Comment: Accepted at ICC 201
A stochastic behavior analysis of stochastic restricted-gradient descent algorithm in reproducing kernel Hilbert spaces
This paper presents a stochastic behavior analysis of a kernel-based
stochastic restricted-gradient descent method. The restricted gradient gives a
steepest ascent direction within the so-called dictionary subspace. The
analysis provides the transient and steady state performance in the mean
squared error criterion. It also includes stability conditions in the mean and
mean-square sense. The present study is based on the analysis of the kernel
normalized least mean square (KNLMS) algorithm initially proposed by Chen et
al. Simulation results validate the analysis
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