ALGEBRAIC DIGITAL SIGNAL PROCESSING AS A MEANS TO ACHIEVE NEW RESULTS IN MOBILE COMMUNICATIONS

The arguments for the relevance of searching for new promising directions for the possible search for methods to radically increase the efficiency (speed and reliability) of telecommunication systems are considered. In contrast to traditional developments of combinatorial methods for detecting and correcting errors in received data, which are usually used at the channel and network levels of telecommunication protocols, the paper presents the results of the development of new algebraic algorithms for digital signal processing implemented at the lowest (physical) level. At the same time, detailed mathematical models are presented for the practical implementation of a new technology for receiving signals with quadrature amplitude modulation (QAM) at the output of a Gaussian channel under conditions of extremely low signal-to-noise ratios (SNR). The models considered are characterized by a comprehensive mathematical description of all linear transformations, which provides convenience for checking the correctness and reproducing calculations. Conclusions from the analysis of the results of the application of the new technology open up virtually unlimited possibilities for increasing the specific speed and reliability of data transmission without increasing the physical frequency and energy resources of communication channels in future-generation 5G/6G telecommunication systems.