Non-separable matrix builders for signal processing, quantum information and mimo applications

Hurley, Ted; Hurley, Barry

doi:10.22108/ijgt.2023.136437.1824

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	Non-separable matrix builders for signal processing, quantum information and mimo applications
International Journal of Group Theory
مقاله 7، دوره 13، شماره 3، آذر 2024، صفحه 271-291 اصل مقاله (502.83 K)
نوع مقاله: 2022 CCGTA IN SOUTH FLA
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.136437.1824
نویسندگان
Ted Hurley^* ¹؛ Barry Hurley²
¹University of Galway (Formerly National University of Ireland Galway), Ireland
²Friar's Hill, Galway, Ireland
چکیده
Matrices are built and designed by applying procedures from lower order matrices. Matrix tensor products, direct sums or multiplication of matrices are such procedures and a matrix built from these is said to be a separable matrix. A non-separable matrix is a matrix which is not separable and is often referred to as an entangled matrix. The matrices built may retain properties of the lower order matrices or may also acquire new desired properties not inherent in the constituents. Here design methods for non-separable matrices of required types are derived. These can retain properties of lower order matrices or have new desirable properties. Infinite series of required type non-separable matrices are constructible by the general methods. Non-separable matrices of required types are required for applications and other uses; they can capture the structure in a unique way and thus perform much better than separable matrices. General new methods are developed with which to construct multidimensional entangled paraunitary matrices; these have applications for wavelet and filter bank design. The constructions are used to design new systems of non-separable unitary matrices; these have applications in quantum information theory. Some consequences include the design of full diversity constellations of unitary matrices, which are used in MIMO systems, and methods to design infinite series of special types of Hadamard matrices.
کلیدواژه‌ها
Non-separable؛ signal processing؛ quantum؛ mimo

مراجع
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Non-separable matrix builders for signal processing, quantum information and mimo applications