Multi-station access based on circular matrices of multi-position linear recurrence sequences
Svetlana F. Gorgadze, Anastasia V. Ermakova, Anastasia Yu. Kudryashova · T-Comm - Телекоммуникации и Транспорт · 2025
Variants of the construction of orthogonal signature systems based on circular matrices of multiposition linear recurrence sequences of maximum period are developed. It is shown that any matrix of this class is reduced to the matrix of Vilenkin-Krestenson functions by means of a unique linear operator whose basis is the permutation of rows and columns of the circular matrix by increasing values of the elements of the multiplicative group of the extended Galois field modulo an irreducible primitive polynomial used in the formation of the initial sequence. It is established that the transmission in a radio channel of a stream of information symbols on the basis of any system of the above signatures and the fast pro-cessing of the resulting signal in the receiver on the basis of the generalised fast Fourier transform on the basis of the Vilenkin-Krestenson functions are associated with several variants of the interleaving of the transmitted information symbols. It is shown that the use of several different systems of developed orthogonal signatures for simultaneous infor-mation transmission in combination with a fast algorithm for compensation of their mutual interference on the basis of generalised fast Fourier transform in the basis of Vilenkin-Krestenson functions allows to increase the bandwidth of the communication channel in the number of times equal to the number of simultaneously used systems in comparison with the method of information transmission on the basis of one system of orthogonal functions and to fully compensate mutual interference. The new method of mutual interfer-ence compensation is a result of previously unknown properties of the systems of pro-posed orthogonal signals revealed in this work. This increase in link capacity is made pos-sible by common interference compensation.