Lattice reduction does not change the solution vector for many algorithms in vector perturbation precoding due to a unique lattice structure, and LLL-aided nearest plane methods do not beat conventional THP under mutual information.
Sum rates, rate allocation, and user scheduling for multi-user MIMO vector perturbation precoding,
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Is Lattice Reduction Necessary for Vector Perturbation Precoding?
Lattice reduction does not change the solution vector for many algorithms in vector perturbation precoding due to a unique lattice structure, and LLL-aided nearest plane methods do not beat conventional THP under mutual information.