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.

[1]  M. Saunders,et al.  Towards a Generalized Singular Value Decomposition , 1981 .

[2]  R. Harshman.  The differences between analysis of covariance and correlation , 2001 .

[3]  C. Loan.  Generalizing the Singular Value Decomposition , 1976 .

[4]  D. Botstein,et al.  Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organisms , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[5]  R. Bro,et al.  PARAFAC2—Part I. A direct fitting algorithm for the PARAFAC2 model , 1999 .

[6]  O. Alter,et al.  Platform-Independent Genome-Wide Pattern of DNA Copy-Number Alterations Predicting Astrocytoma Survival and Response to Treatment Revealed by the GSVD Formulated as a Comparative Spectral Decomposition , 2016, PloS one.

[7]  Martin Haardt,et al.  Efficient Computation of the PARAFAC2 Decomposition via Generalized Tensor Contractions , 2018, 2018 52nd Asilomar Conference on Signals, Systems, and Computers.

[8]  Chintha Tellambura,et al.  GSVD Beamforming for Two-User MIMO Downlink Channel , 2013, IEEE Transactions on Vehicular Technology.

[9]  Ami Wiesel,et al.  On the Gaussian MIMO Wiretap Channel , 2007, 2007 IEEE International Symposium on Information Theory.

[10]  Orly Alter,et al.  GSVD Comparison of Patient-Matched Normal and Tumor aCGH Profiles Reveals Global Copy-Number Alterations Predicting Glioblastoma Multiforme Survival , 2012, PloS one.

[11]  Orly Alter,et al.  Tensor GSVD of Patient- and Platform-Matched Tumor and Normal DNA Copy-Number Profiles Uncovers Chromosome Arm-Wide Patterns of Tumor-Exclusive Platform-Consistent Alterations Encoding for Cell Transformation and Predicting Ovarian Cancer Survival , 2015, PloS one.

[12]  Chintha Tellambura,et al.  Generalized Singular Value Decomposition for Coordinated Beamforming in MIMO Systems , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[13]  R. Bro,et al.  A fast non‐negativity‐constrained least squares algorithm , 1997 .

[14]  O. Alter,et al.  A Higher-Order Generalized Singular Value Decomposition for Comparison of Global mRNA Expression from Multiple Organisms , 2011, PloS one.

[15]  P. Schönemann,et al.  A generalized solution of the orthogonal procrustes problem , 1966 .