A central concept in matrix analysis is the decomposition of a matrix into a product of orthogonal (or unitary) matrices and a diagonal/triangular one, e.g., unitary diagonalization of a symmetric matrix, and more generally the singular-value decomposition, and the QR decomposition. Such decompositions are of particular importance for multi-antenna point-to-point physical-layer communications, where the channel gains are represented by a (channel) matrix. Transforming the channel matrix into diagonal/triangular forms, in this case, allows to reduce the coding task to that of coding for scalar (single-antenna) channels. Thus, the modulation and coding tasks are effectively decoupled and the performance is dictated by the diagonal values. In this work we develop new joint matrix decompositions of several matrices using the same unitary matrix on one side (corresponding to a joint transmitter or receiver) to achieve desired properties for the resulting diagonals. An important special case is a transformation leading to equal diagonals for all matrices simultaneously. This, in turn, allows to construct practical schemes for various communications settings, as well as deriving new theoretic bounds for others.
natoly Khina received the B.Sc. and M.Sc. degrees in electrical engineering (both summa cum laude) from Tel Aviv University in 2006 and 2010, respectively, where he is currently working towards completing his Ph.D. degree. His research interests include information theory, signal processing, digital communications and matrix analysis. In parallel to his studies, Anatoly has been working as an engineer in various algorithms, software and hardware R&D positions. He is a recipient of the Rothschild fellowship, Clore scholarship, Trosky Award, Weinstein Prize for research in signal processing, and the first prize for outstanding research work of the Advanced Communication Center, Israel.