In this study, we propose a robust approach for blind source separation (BSS) by using radial basis function networks (RBFNs) and higher-order statistics (HOS). The RBFN is employed to estimate the inverse of a hypothetical complicated mixing procedure. It transforms the observed signals into high-dimensional space, in which one can simply separate the transformed signals by using a cost function. Recently, Tan et al. proposed a nonlinear BSS method, in which higher-order moments between source signals and observations are matched in the cost function. However, it has a strict restriction that it requires the higher-order statistics of sources to be known. We propose a cost function that consists of higher-order cumulants and the second-order moment of signals to remove the constraint. The proposed approach has the capacity of not only recovering the complicated mixed signals, but also reducing noise from observed signals. Simulation results demonstrate the validity of the proposed approach. Moreover, a result of application to X-ray image separation also shows its practical applicability.

In this study, a fourth-order cumulants based iterative algorithm for blind channel equalization is introduced, which is robust with respect to the existence of heavy Gaussian noise in a channel and does not require the minimum phase characteristic of the channel. The transmitted signals at the receiver are over-sampled to ensure the channel described by a full-column rank matrix. It changes a single-input/single-output (SISO) finite-impulse response (FIR) channel to a single-input/multi-output (SIMO) channel. Based on the properties of the fourth-order cumulants of the over-sampled channel inputs, the iterative algorithm is derived to estimate the deconvolution matrix which makes the overall transfer matrix transparent, i.e., it can be reduced to the identity matrix by simple reordering and scaling. In simulation studies, both a closed-form and a stochastic version of the proposed algorithm are tested with three-ray multi-path channels, and their performances are compared with the methods based on conventional second-order statistics and higher-order statistics (HOS) as well. Relatively good results with fast convergence speed are achieved, even when the transmitted symbols are significantly corrupted with Gaussian noise.

This study is aimed to explore a fast convergence method of blind equalization using higher order statistics (cumulants). The efforts are focused on deriving new theoretical solutions for blind equalizers rather than investigating practical algorithms. Under the common assumptions for this framework, it is found that the condition for blind equalization is directly associated with an eigenproblem, i. e. the lag coefficients of the equalizer can be obtained from the eigenvectors of a higher order statistics matrix. A method of blind phase recovery is also proposed for QAM systems. Computer simulations show that very fast convergence can be achieved based on the approach.

This letter presents a new algorithm for improving the Signal to Noise Ratio (SNR) of complex sinusoidal signals contaminated by additive Gaussian noises using sum of Higher-Order Statistics (HOS). We conduct some computer simulations to show that the proposed algorithm can improve the SNR more than 7 dB compared with the conventional coherent integration when the SNR of the input signal is -10 dB.

This paper addresses the problem of estimating the parameters of multivariate ARMA processes by using higher-order statistics called cumulants. The main objective in this paper is to extend the idea of the q-slice algorithm in univariate ARMA processes to multivariate ARMA processes. It is shown for a multivariate ARMA process that the MA coefficient matrices can be estimated up to postmultiplication of a permutation matrix by using the third-order cumulants and of an extended permutation matrix by using the fourth-order cumulants. Simulation examples are included to demonstrate the effectiveness of the proposed method.