Mmse Whitened Least Squares Estimator and It's Applications

Abstract

ABSTRACT The objective of this work is to study and present the information about linear estimators, wherein, we study whitening for improved performance. Data whitening is incorporated in MMSE context to ensure that the data set elements are uncorrelated , and simultaneously the whitened data set is as informative as the original one. Common estimators suffer large noise variance because white noise in measurement space gets colored due to inverse transformation into parameter space. Whitening transformati on spreads the colored noise over the entire vector space, thus reducing the noise variance. This makes a whitened estimator to perform better than other estimators. MMSE whitening applied to least squares estimator results in whitened least squares estimator. The WTLS estimator can be represented by a LS estimator followed by a whitening transformation and can be used in most applications where LS estimator is used. The performance of WTLS estimator is analyzed in different contexts like linear regression, system identification and linear multiuser detection. The analysis suggest that under certain conditions, namely low signal to noise ratios, WTLS estimator works significantly better than its counterparts. Simulation results are presented to support the analysis and to compare the performance of WTLS estimator with other linear estimators.