  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.
