Multilinear Generalized Singular Value Decomposition (Ml-Gsvd) With Application To Coordinated Beamforming In Multi-User Mimo Systems

In this paper, we propose a new Multilinear Generalized Singular Value Decomposition (ML-GSVD) which allows to jointly factorize a set of matrices with one common dimension. The ML-GSVD is an extension of the Generalized Singular Value Decomposition (GSVD) for more than two matrices. In comparison with other approaches that extend the GSVD, the proposed tensor decomposition preserves the essential properties of the original GSVD, such as orthogonality of the second mode factor matrices. In this work, we introduce two algorithms to compute the ML-GSVD. In addition, we present an application of the ML-GSVD to compute the beamforming matrices for the multi-user MIMO downlink channel with more than two users in wireless communications.