Some n×n lattice space-time codes with large normalized diversity products and high ranks

A lattice space-time code over C is a set A consisting of matrices in M
_n
(C) such that A is a free abelia group under the matrix addition. Based on lattice space-time block codes design, a large number of signal are applied to the motives constellation design to realize the diversity of signal space technologies such as Rayleigh fading channel. In this paper, we constructed a new 3×3 lattice space-time code with a large normalized diversity product d
_g
≈ 0.607126, and a new 4×4 lattice space-time code with a large normalized diversity product d
_g
≈ 0.328018. As a corollary, we give a 3×3 lattice space-time code of rank 12 with a positive diversity product, and a 4×4 lattice space-time code of rank 20 with a positive diversity product.