Investigation of Some Bias and MSE Issues in Block-Component-Wise Conditionally Unbiased LMMSE

Imposing a joint conditionally unbiasedness constraint on a vector of parameters reduces Bayesian estimation to deterministic parameter estimation. In component-wise conditionally unbiased (CWCU) Bayesian parameter estimation, every parameter in turn is treated as deterministic while the others are being treated as Bayesian. If the parameters are transmitted symbols, the CWCU approach corresponds to unbiased symbol detection whereas joint deterministic unbiasedness leads to a zero-forcing approach. In this paper we consider an intermediate approach corresponding to Block-CWCU (BCWCU) LMMSE estimation. We investigate the interplay between block-size, joint bias and prior covariance rank. We also investigate two sequential interference cancellation (SIC) implementations of BCWCU-LMMSE estimation. The results are illustrated with concrete examples.