Models of optimum radio-systems on the vector combinatorial configurations

Abstract

Method for construction of optimum radio systems, based on a new conceptual model of the systems - Ideal Ring Vector structures (clusters of the IRV) is proposed. IRV clusters are cyclic ordered sequences of t- integer sub-sequences of the sequence which form perfect relationships of t-dimensional partitions over a virtual t-dimensional lattice covered surface of a finite space interval. The sums of connected sub-sequences of an IRV enumerate the set of tcoordinates specified with respect to cyclic frame reference exactly R-times. This property makes IRVs useful in applications which need to partition multidimensional objects with the smallest possible number of intersections. This sort of models can be used for finding optimal solution for wide classes of technological problems based on the idea of “perfect” vector combinatorial constructions, and expanding the applicability of two-, three- and multidimensional IRV as multidimensional cyclic relationships for fundamental and applied research in systems engineering, for improving such quality indices as vector data coding and signal reconstruction, resolving ability and low side lobe antenna design. There are regarded basic properties these models and made comparative analysis of the models with difference sets. It is shown that the IRVs to be in exceed of difference sets multiply, and set of the classical difference sets is subset of the IRVs. Short review of the methods relating to constructing of the optimum models of non-uniform antenna arrays with respect to low side lobe is given. The problem statement involves development the regular method for construction of the optimum radio-systems using two- and three-dimensional IRVs, and some examples are regarded for illustration its technical merits including algorithm of synthesis of two-dimensional symmetric antenna with 12 elements which provides sufficiently low side lobe radiation levels and shows a flat gain over the frequency range is presented. Method for design of two- or multidimensional vector signals coded based on the optimum binary monolithic code is presented.