9,389 research outputs found
Nonparametric Independent Component Analysis for the Sources with Mixed Spectra
Independent component analysis (ICA) is a blind source separation method to
recover source signals of interest from their mixtures. Most existing ICA
procedures assume independent sampling. Second-order-statistics-based source
separation methods have been developed based on parametric time series models
for the mixtures from the autocorrelated sources. However, the
second-order-statistics-based methods cannot separate the sources accurately
when the sources have temporal autocorrelations with mixed spectra. To address
this issue, we propose a new ICA method by estimating spectral density
functions and line spectra of the source signals using cubic splines and
indicator functions, respectively. The mixed spectra and the mixing matrix are
estimated by maximizing the Whittle likelihood function. We illustrate the
performance of the proposed method through simulation experiments and an EEG
data application. The numerical results indicate that our approach outperforms
existing ICA methods, including SOBI algorithms. In addition, we investigate
the asymptotic behavior of the proposed method.Comment: 27 pages, 10 figure
On asymptotics of ICA estimators and their performance indices
Independent component analysis (ICA) has become a popular multivariate
analysis and signal processing technique with diverse applications. This paper
is targeted at discussing theoretical large sample properties of ICA unmixing
matrix functionals. We provide a formal definition of unmixing matrix
functional and consider two popular estimators in detail: the family based on
two scatter matrices with the independence property (e.g., FOBI estimator) and
the family of deflation-based fastICA estimators. The limiting behavior of the
corresponding estimates is discussed and the asymptotic normality of the
deflation-based fastICA estimate is proven under general assumptions.
Furthermore, properties of several performance indices commonly used for
comparison of different unmixing matrix estimates are discussed and a new
performance index is proposed. The proposed index fullfills three desirable
features which promote its use in practice and distinguish it from others.
Namely, the index possesses an easy interpretation, is fast to compute and its
asymptotic properties can be inferred from asymptotics of the unmixing matrix
estimate. We illustrate the derived asymptotical results and the use of the
proposed index with a small simulation study
An OFDM Signal Identification Method for Wireless Communications Systems
Distinction of OFDM signals from single carrier signals is highly important
for adaptive receiver algorithms and signal identification applications. OFDM
signals exhibit Gaussian characteristics in time domain and fourth order
cumulants of Gaussian distributed signals vanish in contrary to the cumulants
of other signals. Thus fourth order cumulants can be utilized for OFDM signal
identification. In this paper, first, formulations of the estimates of the
fourth order cumulants for OFDM signals are provided. Then it is shown these
estimates are affected significantly from the wireless channel impairments,
frequency offset, phase offset and sampling mismatch. To overcome these
problems, a general chi-square constant false alarm rate Gaussianity test which
employs estimates of cumulants and their covariances is adapted to the specific
case of wireless OFDM signals. Estimation of the covariance matrix of the
fourth order cumulants are greatly simplified peculiar to the OFDM signals. A
measurement setup is developed to analyze the performance of the identification
method and for comparison purposes. A parametric measurement analysis is
provided depending on modulation order, signal to noise ratio, number of
symbols, and degree of freedom of the underlying test. The proposed method
outperforms statistical tests which are based on fixed thresholds or empirical
values, while a priori information requirement and complexity of the proposed
method are lower than the coherent identification techniques
Stochastic trapping in a solvable model of on-line independent component analysis
Previous analytical studies of on-line Independent Component Analysis (ICA)
learning rules have focussed on asymptotic stability and efficiency. In
practice the transient stages of learning will often be more significant in
determining the success of an algorithm. This is demonstrated here with an
analysis of a Hebbian ICA algorithm which can find a small number of
non-Gaussian components given data composed of a linear mixture of independent
source signals. An idealised data model is considered in which the sources
comprise a number of non-Gaussian and Gaussian sources and a solution to the
dynamics is obtained in the limit where the number of Gaussian sources is
infinite. Previous stability results are confirmed by expanding around optimal
fixed points, where a closed form solution to the learning dynamics is
obtained. However, stochastic effects are shown to stabilise otherwise unstable
sub-optimal fixed points. Conditions required to destabilise one such fixed
point are obtained for the case of a single non-Gaussian component, indicating
that the initial learning rate \eta required to successfully escape is very low
(\eta = O(N^{-2}) where N is the data dimension) resulting in very slow
learning typically requiring O(N^3) iterations. Simulations confirm that this
picture holds for a finite system.Comment: 17 pages, 3 figures. To appear in Neural Computatio
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