Communication over Hypercomplex Kähler Manifolds: Capacity of Dual-Polarized 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.