Communication over Hypercomplex Kähler Manifolds: Capacity of Multidimensional-MIMO Channels

We consider the single-user communications scenario over joint space, pattern and polarization diversity providing dual-polarized multidimensional-MIMO (PMD-MIMO) channels established by the use of multiple dual-polarized transmit/receive antennas in the form of uniformly-spaced 1D, 2D and/or 3D MIMO arrays. Based on the equivalent channel-models formulated on hypercomplex manifolds, we subsequently identify the decomposition of dual-polarized PMD-MIMO channels into multiple independently-fading and attenuated classical MIMO channels in parallel through the algebraic properties of hypercomplex Kähler manifolds and consequently derive the corresponding ergodic capacities analytically. We show in essence via the diversity-reception over independent channels perspective deduction of the decomposition into parallel MIMO channels observation that the capacity gains achievable by PMD-MIMO Tx/Rx over classical single-polarized linear antenna array MIMO Tx/Rx may be notably large with equal number of transmit and/or receive antenna locuses and under same resource requirements/channel conditions whenever the cross-polar discrimination between dual antennas is good.

[1]  T. Svantesson.  On capacity and correlation of multi-antenna systems employing multiple polarizations , 2002, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313).

[2]  Reinaldo A. Valenzuela,et al.  V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel , 1998, 1998 URSI International Symposium on Signals, Systems, and Electronics. Conference Proceedings (Cat. No.98EX167).

[3]  S. Thorbjørnsen,et al.  Random matrices with complex Gaussian entries , 2003 .

[4]  A. Robert Calderbank,et al.  Space-Time Codes for High Data Rate Wireless Communications : Performance criterion and Code Construction , 1998, IEEE Trans. Inf. Theory.

[5]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

[6]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[7]  Partha P. Mitra,et al.  Tripling the capacity of wireless communications using electromagnetic polarization , 2001, Nature.

[8]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[9]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[10]  Yves Talpaert.  Differential geometry with applications to mechanics and physics , 2000 .

[11]  Dennis Goeckel,et al.  On the asymptotic capacity of MIMO systems with fixed length linear antenna arrays , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[12]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[13]  A. Robert Calderbank,et al.  Space-time block coding for wireless communications: performance results , 1999, IEEE J. Sel. Areas Commun..

[14]  Beza Negash Getu,et al.  The MIMO cube - a compact MIMO antenna , 2005, IEEE Transactions on Wireless Communications.

[15]  William C. Y. Lee,et al.  Mobile Communications Engineering , 1982 .