Quaternion-Valued Multi-User MIMO Transmission via Dual-Polarized Antennas and QLLL Reduction

In this paper, quaternion-valued multi-user MIMO equalization is studied for the case of dual-polarized antennas. Given the multi-user MIMO uplink scenario, the relationship or transition between quaternion-valued arithmetic in transmitter/receiver processing and both vertically-and horizontally-polarized electromagnetic waves is discussed. A quaternion-valued system and channel model as well as related signal constellations are presented. Both linear and lattice-reduction-aided linear equalization are extended to the problem in hand. For that purpose, a quaternion-valued variant of the famous LLL lattice-reduction algorithm is proposed, which we call QLLL. Its gains in transmission performance and computational complexity over real-and complex-valued LLL reduction are discussed. Besides, the respective diversity orders are generalized to cope with the quaternion-valued channel model. The theoretical studies are complemented by results obtained from numerical simulations.