Is Lattice Reduction Necessary for Vector Perturbation Precoding?

TL;DR

This paper investigates whether lattice reduction enhances vector perturbation precoding in terms of mutual information, revealing that for certain lattice structures, LR does not improve the solution, challenging previous performance assumptions.

Contribution

The study provides a structural analysis showing LR's limited impact on solution vectors in VP, and re-evaluates popular LR-aided algorithms, highlighting the effectiveness of Tomlinson-Harashima precoding.

Findings

LR does not impact the solution vector for a class of lattice problems.

LR-aided algorithms do not outperform Tomlinson-Harashima precoding based on mutual information.

Popular LR-aided methods like LLL-aided NP are not superior to conventional THP.

Abstract

Vector perturbation (VP) precoding is an effective nonlinear precoding technique in the downlink (DL) with modulo channels, providing an approximation of dirty paper coding (DPC) which is capacity-achieving. Especially, when combined with Lattice reduction (LR), low-complexity algorithms achieve a very promising performance, outperforming other popular non-linear precoding techniques like Tomlinson-Harashima precoding (THP). However, these results are based on the symbol error rate (SER) or bit error rate (BER). When shifting the focus to the mutual information as the figure of merit, we show that this is different and that the underlying lattice problem has a unique structural property. For lattice problems with this special structure, we show for a whole class of algorithms that LR does not have any impact on the solution vector. At the same time, algorithms are identified which benefit from LR, even if this lattice structure arises. The provided structural analysis has strong implications on the performance evaluation of VP. In particular, we re-evaluate popular Lenstra-Lenstra-Lov\'asz (LLL)-aided methods like the LLL-aided nearest plane (NP) algorithm and show that they do not outperform conventional THP, highlighting the effectiveness of the THP method. This is in contrast to the existing results based on SER and BER where these methods clearly outperform THP.