Proximity Factors of Lattice Reduction-Aided Precoding for Multiantenna Broadcast

TL;DR

This paper analyzes the efficiency of lattice reduction-aided precoding in multiantenna broadcast systems by deriving bounds on proximity factors related to the closest vector problem, highlighting its power efficiency advantages.

Contribution

It introduces the concept of proximity factors for lattice precoding and derives their bounds, providing a theoretical measure of power efficiency loss.

Findings

Proximity factors are bounded, quantifying worst-case power loss.

Approximate lattice precoding relates to the $ ext{CVP}$ problem.

Analysis avoids boundary effects due to infinite lattice assumption.

Abstract

Lattice precoding is an effective strategy for multiantenna broadcast. In this paper, we show that approximate lattice precoding in multiantenna broadcast is a variant of the closest vector problem (CVP) known as $\eta$-CVP. The proximity factors of lattice reduction-aided precoding are defined, and their bounds are derived, which measure the worst-case loss in power efficiency compared to sphere precoding. Unlike decoding applications, this analysis does not suffer from the boundary effect of a finite constellation, since the underlying lattice in multiantenna broadcast is indeed infinite.