Notes on Lattice-Reduction-Aided MMSE Equalization

TL;DR

This paper provides a formal proof that lattice-reduction-aided MMSE equalization achieves optimal performance in MIMO systems, emphasizing the importance of accounting for data correlations over the specific lattice reduction method used.

Contribution

It offers a formal proof that applying zero-forcing BLAST to an augmented channel matrix yields the optimal MMSE solution, highlighting the significance of data correlation considerations.

Findings

Zero-forcing BLAST applied to augmented matrix achieves optimal MMSE equalization.

Correctly accounting for data correlations is more crucial than the specific lattice reduction method.

Formal proof clarifies the optimality of lattice-reduction-aided MMSE equalization.

Abstract

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.