  In this work, we propose low-complexity adaptive biased estimation
algorithms, called group-based shrinkage estimators (GSEs), for parameter
estimation and interference suppression scenarios with mechanisms to
automatically adjust the shrinkage factors. The proposed estimation algorithms
divide the target parameter vector into a number of groups and adaptively
calculate one shrinkage factor for each group. GSE schemes improve the
performance of the conventional least squares (LS) estimator in terms of the
mean-squared error (MSE), while requiring a very modest increase in complexity.
An MSE analysis is presented which indicates the lower bounds of the GSE
schemes with different group sizes. We prove that our proposed schemes
outperform the biased estimation with only one shrinkage factor and the best
performance of GSE can be obtained with the maximum number of groups. Then, we
consider an application of the proposed algorithms to single-carrier
frequency-domain equalization (SC-FDE) of direct-sequence ultra-wideband
(DS-UWB) systems, in which the structured channel estimation (SCE) algorithm
and the frequency domain receiver employ the GSE. The simulation results show
that the proposed algorithms significantly outperform the conventional unbiased
estimator in the analyzed scenarios.
