Four antenna space-time lattice constellations from division algebras

Rate one full-diversity orthogonal designs for four transmit antennas are known not to exist so either rate, orthogonality or diversity is compromised. Use of algebraic number theory has lead to full-diversity, rate one code constructions. The use of regular representations of certain rings of algebraic integers and their Hamiltonian quaternionic counterparts to construct lattices of rank 8 that yield rate one full-diversity lattice constellation codes for four transmitting antennas is presented in this paper. The resulting codes require less transmission power per bit. Using number theoretic tools a general lower bound to the minimum Euclidean distance within the received constellation is computed