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

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Abstract

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.

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Correspondence to Özgür Ertuğ.

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özgür Ertuğ has received his B.Sc. degree in electrical engineering from University of Southern California, Los Angeles in 1997. As research assistant, he pursued his M.Sc. degree at William Marsh Rice University, Houston in electrical and computer engineering and graduated in 1999. Between August 1999 and April 2000, he was a research and development engineer at Turkish Scientific and Technological Research Council - BILTEN Electronics and Informatics Research Institute in Ankara, Turkey. He then pursued his Ph.D. studies as research and teaching assistant at Middle East Technical University, Ankara, Turkey in electrical and electronics engineering specializing on telecommunications and signal processing, and graduated in December 2005 with his dissertation on information-theoretic analysis of finite-dimensional randomly-spread CDMA systems over GWSSUS fading channels. He joined the faculty of Gazi University, Electrical and Electronics Engineering Department, Ankara, Turkey in early 2006. He is a member of IEEE since 2000 and actively serves as a reviewer for major IEEE conferences and journals. His major research interests lie in the broad areas of communication and information theories, networking, signal processing and system implementation. He is the author of around 20 papers in these areas and is listed in Marquis Who's Who in Science and Engineering in 2005 for his contributions.

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Ertuğ, Ö. Communication over Hypercomplex Kähler Manifolds: Capacity of Multidimensional-MIMO Channels. Wireless Pers Commun 41, 155–168 (2007). https://doi.org/10.1007/s11277-006-9135-5

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  • DOI: https://doi.org/10.1007/s11277-006-9135-5

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