Lattice-reduction-aided (LRA) equalization is a very interesting multi-user equalization technique as it enables a lowcomplexity full-diversity detection. To this end, the multipleinput/ multiple-output channel is factorized into a reduced variant and a unimodular integer matrix. Inspired by the closely related finite-field processing strategy of integer-forcing (IF) equalization, this factorization task has recently been relaxed to nonunimodular integer matrices. In this paper, the claim of a significant performance gain induced by the IF philosophy is revisited. For that purpose, lattice-basis-reduction approaches are reviewed; the optimal one with respect to channel equalization is identified. A fair comparison between unimodular LRA and IF strategy is given, complemented by detailed numerical results.
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