Asymptotic analysis of random lattices in high dimensions

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 (with and without noise corruption) in high-dimension random lattices, but also describe the convergence behavior of how the asymptotic value approaches the exact distance. Besides, we provide a discussion on further extensions and potential applications of the derived results regarding the lattice theory and multiple-input multiple-output (MIMO) technology.