Stationary points of a kurtosis maximization algorithm for blind signal separation and antenna beamforming

Ding, Zhi; Nguyen, Tuan Dung

doi:10.1109/78.845917

Cited by 63 publications

(8 citation statements)

References 14 publications

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“…One of the main benefits of kurtosis lies in the absence of spurious local extrema for infinite sample size when the noiseless observation model is fulfilled. This attractive feature leads to globally convergent source extraction algorithms, from which full source separation can be performed by using some form of deflation procedure [11], [12], [13], [14], even in the convolutive MIMO case [15]. Although the adequacy of kurtosis as a contrast may be objected on the basis of statistical efficiency and robustness against outliers [16], its widespread use is justified by mathematical tractability, computational convenience and robustness to finite sample effects.…”

Section: B Kurtosis As a Contrast Functionmentioning

confidence: 99%

“…The search direction g is typically (but not necessarily) the gradient, g = ∇ w K(w), which is given by (cf. [13], [15]):…”

Section: A Exact Line Search On the Kurtosis Contrastmentioning

confidence: 99%

“…The CFPA [33] and nc-FastICA [34] algorithms [eqn. (13)] have essentially the same cost as FastICA in the complex case; it suffices to add an initial burden of L(2L + 1)T flops due to the computation of the pseudo-covariance matrix. The KM-F algorithm [36] [eqn.…”

Section: E Computational Complexitymentioning

confidence: 99%

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Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast With Algebraic Optimal Step Size

Zarzoso

Comon

2010

IEEE Trans. Neural Netw.

241

213

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Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the independent components one after another. A novel method for deflationary ICA, referred to as RobustICA, is put forward in this paper. This simple technique consists of performing exact line search optimization of the kurtosis contrast function. The step size leading to the global maximum of the contrast along the search direction is found among the roots of a fourth-degree polynomial. This polynomial rooting can be performed algebraically, and thus at low cost, at each iteration. Among other practical benefits, RobustICA can avoid prewhitening and deals with real- and complex-valued mixtures of possibly noncircular sources alike. The absence of prewhitening improves asymptotic performance. The algorithm is robust to local extrema and shows a very high convergence speed in terms of the computational cost required to reach a given source extraction quality, particularly for short data records. These features are demonstrated by a comparative numerical analysis on synthetic data. RobustICA's capabilities in processing real-world data involving noncircular complex strongly super-Gaussian sources are illustrated by the biomedical problem of atrial activity (AA) extraction in atrial fibrillation (AF) electrocardiograms (ECGs), where it outperforms an alternative ICA-based technique.

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Section: B Kurtosis As a Contrast Functionmentioning

confidence: 99%

“…The search direction g is typically (but not necessarily) the gradient, g = ∇ w K(w), which is given by (cf. [13], [15]):…”

Section: A Exact Line Search On the Kurtosis Contrastmentioning

confidence: 99%

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Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast With Algebraic Optimal Step Size

Zarzoso

Comon

2010

IEEE Trans. Neural Netw.

241

213

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“…Now define a subset of P i,j,l,m as Q i,j,l,m = {(i, j, l, m) , (i, j, l, m) ∈ P i,j,l,m and i ≤ j, l ≤ m} . f (u) − τ can be written into two ways as follows (35) and…”

Section: Semidefinite Programing Solutionmentioning

confidence: 99%

“…In Each of the 4 channel outputs has AWG noise with SNR of 10dB. We apply the CMA algorithms without cross-cumulant jointly with the Gram-Schmidt orthogonalization process to separate different sources [35]. For BGD algorithms, the initial values for {w…”

Section: B Blind Source Separation Problemmentioning

confidence: 99%

A Convex Relaxation Approach to Higher-Order Statistical Approaches to Signal Recovery

Han

Ding

Muhammad

2016

IEEE Trans. Veh. Technol.

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In this work, we investigate an efficient numerical approach for solving higher order statistical methods for blind and semi-blind signal recovery from non-ideal channels. We develop numerical algorithms based on convex optimization relaxation for minimization of higher order statistical cost functions. The new formulation through convex relaxation overcomes the local convergence problem of existing gradient descent based algorithms and applies to several well-known cost functions for effective blind signal recovery including blind equalization and blind source separation in both single-input-single-output (SISO) and multi-input-multi-output (MIMO) systems. We also propose a fourth order pilot based cost function that benefits from this approach. The simulation results demonstrate that our approach is suitable for short-length packet data transmission using only a few pilot symbols. Keywords: Blind signal recovery, semi/blind channel equalization, convex optimization, semidefinite programming, rank 1 approximation. 4 Let J b,i denote a blind cost function, for examples, CMA, SWA, or MED, to recover the source i, the cost function for multiple blind source recovery (BSR) is [23], [24] J bsr = NT i=1 J b,i + λ cr · NT i =j Huy-Dung Han Huy-Dung Han received B.S. in

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MIMO Blind Equalization Algorithms

Blind Equalization and System Identification

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Stationary points of a kurtosis maximization algorithm for blind signal separation and antenna beamforming

Cited by 63 publications

References 14 publications

Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast With Algebraic Optimal Step Size

Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast With Algebraic Optimal Step Size

A Convex Relaxation Approach to Higher-Order Statistical Approaches to Signal Recovery

MIMO Blind Equalization Algorithms

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