Whitening transformation

About: Whitening transformation is a research topic. Over the lifetime, 195 publications have been published within this topic receiving 2560 citations.

Analysis of covariance using the rank transformation.

Abstract: The rank transformation refers to the replacement of data by their ranks, with a subsequent analysis using the usual normal theory procedure, but calculated on the ranks rather than on the data. Rank transformation procedures have previously been shown by the authors to have properties of robustness and power in both regression and analysis of variance. It seems natural to consider the use of the rank transformation in analysis of covariance, which is a combination of regression and analysis of variance. In this paper the rank transformation approach to analysis of covariance is presented and examined. Comparisons are made with the rank transformation procedure given by Quade (1967, Journal of the American Statistical Association 62, 1187-1200), and some 'standard' data sets are used to compare the results of these two procedures. A Monte Carlo simulation study examines the behavior of these methods under the null hypothesis and under alternative hypotheses, with both normal and nonnormal distributions. All results are compared with the usual analysis of covariance procedure on the basis of robustness and power.

Robust whitening procedure in blind source separation context

Abstract: An efficient algorithm is presented for robust whitening in the presence of temporally uncorrelated additive noise that may be spatially correlated. This whitening is introduced as a pre-processing step in the blind source separation process. The robust whitening consists in the eigenvalue decomposition of a positive definite linear combination of a set a correlation matrices taken at nonzero lags. The coefficients of the linear combination are computed by a finite step global convergence algorithm. Some numerical simulations are provided to illustrate the effectiveness of the solution.

A unitary transformation method for angle-of-arrival estimation

Abstract: Eigenstructure methods for estimating angles of arrival of radiation sources generally require complex computations in computing eigencomponents of the covariance matrix and calculating the search function. A unitary transformation method that transforms the complex covariance matrix of an equally spaced linear array, which is Hermitian persymmetric, and the complex search vector into a real symmetric matrix and a real vector, respectively is presented. Both tasks can be accomplished by real computations. The sampled covariance matrix available is not persymmetric. To suit the unitary transformation method, a persymmetrized estimator of the sampled covariance matrix, which is optimal in the sense of Euclidean distance, is proposed. >

Optimal whitening and decorrelation

Abstract: Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there is a diverse range of sphering methods in use, for example based on principal component analysis (PCA), Cholesky matrix decomposition and zero-phase component analysis (ZCA), among others. Here we provide an overview of the underlying theory and discuss five natural whitening procedures. Subsequently, we demonstrate that investigating the cross-covariance and the cross-correlation matrix between sphered and original variables allows to break the rotational invariance and to identify optimal whitening transformations. As a result we recommend two particular approaches: ZCA-cor whitening to produce sphered variables that are maximally similar to the original variables, and PCA-cor whitening to obtain sphered variables that maximally compress the original variables.

Whitening-rotation-based semi-blind MIMO channel estimation

Abstract: This paper proposes a whitening-rotation (WR)-based algorithm for semi-blind estimation of a complex flat-fading multi-input multi-output (MIMO) channel matrix H. The proposed algorithm is based on decomposition of H as the matrix product H=WQ/sup H/, where W is a whitening matrix and Q is unitary rotation matrix. The whitening matrix W can be estimated blind using only received data while Q is estimated exclusively from pilot symbols. Employing the results for the complex-constrained Cramer-Rao Bound (CC-CRB), it is shown that the lower bound on the mean-square error (MSE) in the estimate of H is directly proportional to its number of unconstrained parameters. Utilizing the bounds, the semi-blind scheme is shown to be very efficient when the number of receive antennas is greater than or equal to the number of transmit antennas. Closed-form expressions for the CRB of the semi-blind technique are presented. Algorithms for channel estimation based on the decomposition are also developed and analyzed. In particular, the properties of the constrained maximum-likelihood (ML) estimator of Q for an orthogonal pilot sequence is examined, and the constrained estimator for a general pilot sequence is derived. In addition, a Gaussian likelihood function is considered for the joint optimization of W and Q, and its performance is studied. Simulation results are presented to support the algorithms and analysis, and they demonstrate improved performance compared to exclusively training-based estimation.