Good Lattice Constellations for Both Rayleigh Fading and Gaussian Channels

Recent work on lattices matched to the Rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency. In this paper we present a new family of lattice constellations, based on complex algebraic number fields, which have good performance on Rayleigh fading channels. Some of these lattices also present a reasonable packing density and thus may be used at the same tune over a Gaussian channel. Conversely, we show that particular versions of the best lattice packings (D4, Er, E8, K12, A16, A24), constructed from totally complex algebraic cyclotomic fields, present better performance over the Rayleigh fading channel. The practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links. Index Terms.