SYNTHESIS OF SYSTEMS OF CORRELATED SIGNALS USING A SUPPLEMENTATION FOR THE GRAM-SCHMIDT ORTHOGONALIZATION PROCEDURE - Голубничий, О. Г. (Science-based technologies, 2019)
The synthesis of systems of correlated signals, which can be used in signal and data processing techniques for information and communication systems, is considered in the paper. The Gram–Schmidt procedure is a well-known method for orthogonalization of a basis of a vector space, which can represent signal constructions in different signal processing applications. A supplementation for the Gram-Schmidt orthogonalization procedure, which allows controlling the correlations between signal components in a system of signals in condition of equality of these correlations, is justified and formalized in the paper. The presented solution is performed by methods of linear algebra using transformations of signals when representing them in vector spaces. The formation of a new system of non-orthogonal vectors, which corresponds to a system of correlated signals, is implemented through additive transformations in a system of orthogonal vectors, which corresponds to a system of non-correlated signals, after the Gram–Schmidt procedure. The proposed calculation procedure contains an additional interior parameter, which depends both on the number of signal components and on correlations between them. An evaluation procedure for the value of this parameter is formalized and analyzed in the paper. The calculation procedure is adapted for stochastic signals and their processing, which takes into account standard deviations for evaluation of norms of vectors when representing signals in vector spaces. The solution for the synthesis of systems of correlated signals is characterized by a suitable algorithmic and computational complexity, which is important for its practical implementation in real-time signal processing applications. The results obtained in the paper can be used for solving the problems of analysis, synthesis and simulations of non-orthogonal multiple access (NOMA) schemes for the fifth generation (5G) mobile communications.