Asymptotic Analysis of Random Lattices in High Dimensions

TL;DR

This paper analyzes the asymptotic properties of high-dimensional random lattices, revealing their distance characteristics, convergence behavior, and implications for sphere-decoding complexity and error probability in large antenna systems.

Contribution

It provides the first detailed asymptotic analysis of random lattices in high dimensions, linking lattice geometry to decoding complexity and error performance.

Findings

Asymptotic value for lattice point distances in high dimensions

Convergence behavior of distance approximation

Insights into sphere-decoding complexity and PEP asymptotics

Abstract

This paper presents the asymptotic analysis of random lattices in high dimensions to clarify the distance properties of the considered lattices. These properties not only indicate the asymptotic value for the distance between any pair of lattice points in high-dimension random lattices, but also describe the convergence behavior of how the asymptotic value approaches the exact distance. The asymptotic analysis further prompts new insights into the asymptotic behavior of sphere-decoding complexity and the pairwise error probability (PEP) with maximum-likelihood (ML) detector for a large number of antennas.