Group signals based on symmetric orthogonal matrices and multipath signal processing

Abstract

In the construction of group signals for radio access systems, we consider the use of both traditional symmetric orthogonal matrices, such as the discrete exponential function matrix that forms the basis for OFDM signals, as well as their variants, such as matrix circulants of multiposition linear recurrence sequences. It is shown that the advantage of the latter variant of symmetric orthogonal matrices is the ability to use a generalized fast Fourier transform to process the corresponding group signals. This allows for a threefold increase in the number of elementary arithmetic operations compared to the traditional fast Fourier transform, which forms and processes OFDM signals. This circumstance enables the formation of group signals based on matrices of large dimensions compared to OFDM signals with the same computational complexity of the formation and processing algorithms. Additionally, unlike discrete exponential functions, there are no restrictions on the frequency grid step value of the subcarriers of the formed group signal when using matrix-circulants of linear recurrence sequences. This is because the latter are noise-like signals that occupy the entire allocated frequency band. Consequently, it is theoretically possible to transmit the same number of subcarriers simultaneously in one frequency band, proportionally increasing their transmission time. These circumstances allow for the use of matrices of different dimensions within a frame to form a group signal. This allows for the flexible distribution of channel resources and increases the efficiency of multipath communication channels. In the case of using cyclic prefixes throughout the frame, the total duration is reduced by approximately three times compared to forming a group signal based on matrices of the same dimension. Another important advantage of using symmetric, orthogonal matrices based on matrix circulants of linear recurrence sequences is the ability to attach a synchronous signal to them. This signal can be detected using a generalized fast Fourier transform, which is the same type of transform used to process the group signal of the communication channel. In this paper, we explore different ways to integrate the synchronous signal into the fundamental system of discrete orthogonal functions, which are used to create both the uplink and downlink channels. Synchronizing the frequency and time delay of synchronous signals in a multi-beam communication channel results in Gaussian interference at the solver's input when processing a group information signal. This also results in the absence of Rayleigh fading in the communication channel and the communication system's insensitivity to Doppler frequency shift. Because the circulant matrix of a linear recurrent sequence preserves symmetry and orthogonality under cyclic permutation of its columns and rows, the generalized fast Fourier transform can be used to process multibeam channel signals and eliminate interference from subcarrier signals of neighboring beams, unlike with OFDM signals.

Topics & Concepts