Notes on Lattice-Reduction-Aided MMSE Equalization

Over the last years, novel low-complexity approaches to the equalization of MIMO channels have gained much attention. Thereby, methods based on lattice basis reduction are of special interest, as they achieve the optimum diversity order. In this paper, a tutorial overview on LRA equalization optimized according to the MMSE criterion is given. It is proven that applying the zero-forcing BLAST algorithm to a suitably augmented channel matrix—the inverse of the square root of the correlation matrix of the data symbols times the noise variance forms its lower part—results in the optimum solution. This fact is already widely used but lacks a formal proof. It turns out that it is more important to take the correlations of the data correctly into account than what type of lattice reduction actually is used.