9,389 research outputs found

    Nonparametric Independent Component Analysis for the Sources with Mixed Spectra

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    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

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    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

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    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

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    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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