NUMERICAL SOLUTION OF MULTIDIMENSIONAL THOMSON PROBLEM FOR VECTORS PACKAGING ON HYPERSPHERE IN BROADBAND RADIOCOMMUNICATION PROBLEMS

Subject of Research. The paper presents a method for numerical solution of the multidimensional Thomson Problem for packing signals interpreted as vectors on the hypersphere in broadband radio communication problems. Method. The implementation of the numerical solution of the multidimensional Thomson Problem for the packing of hypersphere vectors in radio communication problems is carried out. The developed method of packing wideband radio signals is as follows: first, the vectors are packed on the hypersphere in accordance with the formulation of the Thomson Problem, then the resulting vectors are transformed into a spectrum and on its basis the resulting signals are obtained using the inverse Fourier transform. Main Results. The paper considers the mathematical apparatus of the developed method of packing vectors on the hypersphere, as well as some results of its research for convergence and stability. The paper describes the principle of the developed method implementation based on a set of vectors packed on the hypersphere and presents some research results of synthesis method for spherical packed broadband radio signals. Practical Relevance. Studies show that the practical significance of the developed method for spherical signal packaging lies in the possibility of increasing the transmission speed of information messages and improving the efficiency of frequency-time resource usage, for example, compared with orthogonal coding. The method for packaging wideband communication signals to hypersphere meets the demands of different consumers deciding between speed and the noise stability. The developed method provides additional design possibilities for protected communication channels by increasing the power of broadband signal ensembles with noise-like character.

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