On the decomposition of the MIMO channel correlation tensor

While the knowledge about the spatial eigenstructure of multiple-input multiple-output is well understood, no respective concept has yet been proposed for MIMO (multiple-input multiple-output) channels. The existing literature also lacks attempts to exhaustively identify analytical tools for characterizing, analyzing and synthesizing the spatial structure of MIMO channels. This work introduces the novel concept of a fourth-order MIMO correlation tensor. In contrast to conventional matrix representations of MIMO correlations, the correlation tensor preserves the inherent spatial structure of MIMO channels and gives rise to three different decomposition methods: The eigendecomposition exploits the Hermitian symmetry of the correlation tensor and yields matrix valued eigenmodes which are of the same size as the channel realizations. The Kronecker mode decomposition makes use of the link-end-oriented structure of the correlation tensor. The resulting Kronecker modes are Hermitian and related to a single link-end. As a third method, an approximate decomposition into vector valued components is presented. Each of the above decompositions can be utilized for providing further insights into the spatial structure of MIMO channels, or for creating spatial channel models. Finally, we will discuss existing channel models from literature in the context of the newly presented analytical tools.