Artificial intelligence

Abstract: The paper addresses the problem of geometric design of multidimensional signal configurations in signal space under energy, amplitude, and geometric constraints. It is shown that the formation of efficient signal configurations in multidimensional Euclidean spaces can be appropriately interpreted as a problem of controlled spatial placement of points, whose geometry directly determines the noise immunity and energy characteristics of an information transmission system. A geometrically oriented approach to the synthesis of signal configurations is proposed, in which the design problem is reduced to an optimization model of packing equal non-overlapping spheres in a multidimensional signal space. Such a formulation makes it possible to consistently take into account the mutual distances between codewords, constraints on the average and peak signal energy, as well as the spatial uniformity of point placement. To implement the design process, inteligent optimization strategies are employed, combining localized improvement methods, multistart search schemes, and incremental configuration construction. Unlike classical regular constructions based on lattice structures, the proposed approach enables the generation of irregular multidimensional signal configurations adapted to specific channel characteristics and communication system requirements. A method for analyzing the noise immunity of the obtained configurations is proposed, based on the study of the minimum pairwise distance, the local geometry of neighborhood, and normalized energy metrics. It is shown that in high-dimensional spaces the effectiveness of geometric design is determined not only by global distance-related characteristics, but also by the local geometric properties of the signal space. The obtained results provide a methodological basis for the geometric design of multidimensional signal configurations and can be used in the development of modern multichannel and multidimensional information transmission systems.

Keywords: multidimensional signal configurations, sphere packing, geometric design, noise immunity, optimization-based synthesis

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