A central concept in matrix analysis is the decomposition of a matrix into a product of orthogonal (or unitary) matrices and a diagonaltriangular 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 diagonaltriangular 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.
In parallel to his studies, Dr. Khina had been working as an engineer in various algorithms, software and hardware R&D positions. He is a recipient of the Fulbright, Rothschild and Marie Skłodowska-Curie Postdoctoral Fellowships, Clore Scholarship, Trotsky Award, Weinstein Prize (M.Sc., Ph.D., and publication) in signal processing, Intel award for Ph.D. research, and the first prize for outstanding research work in the field of communication technologies of the Advanced Communication Center (ACC) Feder Family Award.