A Fast Fixed-Point Algorithm for Independent Component Analysis of Complex Valued Signals

Abstract

Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article, it is assumed that the original, complex valued source signals are mutually statistically independent, and the problem is solved by the independent component analysis (ICA) model. ICA is a statistical method for transforming an observed multidimensional random vector into components that are mutually as independent as possible. In this article, a fast fixed-point type algorithm that is capable of separating complex valued, linearly mixed source signals is presented and its computational efficiency is shown by simulations. Also, the local consistency of the estimator given by the algorithm is proved.

Target detection algorithm using independent component analysis for pulse Doppler radar

“…The ICA is one useful tool used in blind source separation, and requires only the statistical independence of the source signals for signal reconstruction. As the target signal has a complex sinusoidal signal in the time domain, previous methods such as those using algorithms FastICA [5] or MLICA [6], specifying the sinusoidal wave separation, are also useful in target signal separation. Initially, to obtain multiply observed signals in mono-static observations, the observed signal matrix X is generated with a time shift of…”

“…The whitened signal Z is decomposed by PCA processing described in [4]. In this method, the FastICA algorithm based on maximizing the non-Gaussianity is applied to Z [5] to obtain the reconstruction matrix W Fast . The reconstruction signal matrix after FastICA is defined as Here, we empirically demonstrate that this FastICA-based separation is often insufficient to recognize a target signal in an extremely lower SCR cases.…”

“…Thus, this paper proposes a novel target detection method based on the independent component analysis (ICA) scheme, which is extended to the complex-valued signal separation model [5,6]. In this method, quasi-multichannels are generated using a time shift of the received signal with a single sensor.…”

New Negentropy Optimization Schemes for Blind Signal Extraction of Complex Valued Sources

“…2) have the potentiality of two-dimensional optimization. However, for classical methods such as complex fast independent component analysis (FastICA) algorithm [16] and complex maximization of non-Gaussianity (CMN) algorithm [15], with contrast function of only one variable, the optimization algorithms have to be one-dimensional. .…”

“…Several contrast functions and algorithms have been proposed based on the nonlinearities of the outputs. In [16], an extension of the well known negentropy-based FastICA to the complex case by Bingham and Hyvarinen was proposed using the modulus information. Novey and Adali proposed in [17] a complex-FastICA algorithm for non-circular sources using the information of pseudo-covariance matrix.…”