An MSE-tunable linear estimator with conditional dominance over least-squares estimation

In the paper, we propose a conditionally biased linear estimator to estimate a deterministic vector h subjected to a linear transformation M and corrupted by zero-mean additive white Gaussian noise, w. We begin by drawing inspiration from the rank shaping idea of the Rank Shaped Least Squares (RSLS) estimator. We then incorporate the estimator into the Covariance Shaping Least Squares (CSLS) framework, which results in inheritance of attractive properties, such as achieving the Cramer-Rao Lower Bound for biased estimators (B-CRLB) and conditional dominance over the Least Squares Estimator (LSE). We further introduce a bias control parameter that not only allows elegant control of the trade-off between the bias and the MSE floor, but also helps in elucidating the common framework that binds the proposed estimator, RSLS, CSLS and LS estimators. We conclude by applying the proposed estimator for pilot-aided channel estimation in OFDM systems.