Covariance shaping approach to linear least-squares estimation

A new biased linear estimator referred to as the covariance shaping least-squares (CSLS) estimator is proposed for estimating a set of unknown deterministic parameters in a linear model. The CSLS estimator is directed at improving the performance of the least-squares (LS) estimator by choosing the estimate to minimize the error variance in the observations subject to a constraint on its covariance. The CSLS estimator is shown to achieve the Cramer-Rao bound for biased estimators. Furthermore, the covariance of the estimate can be chosen such that there is a threshold SNR, below which the CSLS estimator yields a lower MSE than the LS estimator for all values of the parameters. Based on the concept of CSLS estimation, we propose a new linear receiver for multiuser detection in CDMA systems.