Cross-packing lattices for the Rician fading channel

We introduce cross-packing lattices for Rician fading channels, motivated by a geometric interpretation stemming from the pairwise error probability analysis. We approximate the star bodies arising from the pairwise error probability analysis with n-dimensional crosses of radius t, consisting of 2nt + 1 unit cubes, for some positive integer t. We give a construction for a family of cross-packing lattices for all dimensions and any minimum cross distance 2t + 1. We show by simulations how our new cross-packing lattices perform compared to other known lattices over the Rician fading channel, for different values of the Rician K-factor.