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 transmit-ter/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.

[1]  Ralf R. Müller,et al.  Channel modelling of MU-MIMO systems by quaternionic free probability , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[2]  RongLin Li,et al.  A Broadband Dual-Polarized Planar Antenna for 2G/3G/LTE Base Stations , 2014, IEEE Transactions on Antennas and Propagation.

[3]  Wai Ho Mow,et al.  Complex Lattice Reduction Algorithm for Low-Complexity Full-Diversity MIMO Detection , 2009, IEEE Transactions on Signal Processing.

[4]  Amir K. Khandani,et al.  LLL Reduction Achieves the Receive Diversity in MIMO Decoding , 2006, IEEE Transactions on Information Theory.

[5]  Gregory W. Wornell,et al.  Lattice-reduction-aided detectors for MIMO communication systems , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[6]  B.J. Wysocki,et al.  Modeling dual polarization wireless fading channels using quaternions , 2006, Joint IST Workshop on Mobile Future, 2006 and the Symposium on Trends in Communications. SympoTIC '06..

[7]  Robert F. H. Fischer,et al.  Factorization Approaches in Lattice-Reduction-Aided and Integer-Forcing Equalization , 2016 .

[8]  Robert F. H. Fischer,et al.  Multilevel Codes in Lattice-Reduction-Aided Equalization , 2018 .

[9]  Tianbing Xia,et al.  The Theory of Quaternion Orthogonal Designs , 2008, IEEE Transactions on Signal Processing.

[10]  Huguette Napias,et al.  A generalization of the LLL-algorithm over euclidean rings or orders , 1996 .

[11]  Wei Liu.  Channel equalization and beamforming for quaternion-valued wireless communication systems , 2018 .

[12]  G. Dixon,et al.  On quaternions and octonions: Their geometry, arithmetic, and symmetry , 2004 .

[13]  Robert F. H. Fischer,et al.  Low-complexity near-maximum-likelihood detection and precoding for MIMO systems using lattice reduction , 2003, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

[14]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[15]  Ming-Yang Li,et al.  Eight-Port Orthogonally Dual-Polarized Antenna Array for 5G Smartphone Applications , 2016, IEEE Transactions on Antennas and Propagation.

[16]  Robert F. H. Fischer,et al.  V-BLAST in lattice reduction and integer forcing , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[17]  Robert F. H. Fischer,et al.  Complexity-performance trade-off of algorithms for combined lattice reduction and QR decomposition , 2012 .