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Introduction. The growth in the volume of information transmitted through communication channels leads to their significant congestion. Almost all methods conventionally used to increase the data transfer rate in given frequency bands have been exhausted. In this regard, it is of interest to use new approaches aimed at improving the spectral efficiency of radio engineering and telecommunication systems by applying optimal signals that make it possible to use the bandwidth reserves of transmission channels given by Shannon's theory.Aim. Improvement of the spectral efficiency of digital messaging systems by using signals with a compact spectrum and increased volume of the channel alphabet at the same time as minimizing energy losses.Materials and methods. When searching for optimal signals, the mathematical apparatus of communication theory and functional analysis, as well as the methods of calculus of variations, were used. The evaluation of bit error rate performance of the obtained optimal signals transmitted in a channel with additive white Gaussian noise was performed in the MatLab environment. Results. It was established that, in a channel with additive white Gaussian noise, optimal signals with a signal constellation size of 64 in the case of quadrature amplitude-phase modulation provide an energy gain of more than 1 dB relative to signals obtained by narrowband filtering under the conditions of uncontrolled intersymbol interference. Optimal signals were shown to provide for an energy gain of 4.9 dB with respect to signals based on narrow-band filtering at a fixed spectral efficiency of 7 (bit/s)/Hz.Conclusion. The paper proposes a method for improving the spectral efficiency of quadrature signals with amplitudephase modulation, based on the use of optimal pulse shapes obtained as a result of solving an optimization problem. The optimization problem was solved according to the criterion of minimizing out-of-band emissions with the constraint on bit error rate performance in case of amplitude-phase modulation. The energy and spectral efficiency of signals with optimal pulse shapes and signals based on narrow-band filtering were compared.

Introduction. Spectrally efficient frequency division multiplexing (SEFDM) is a promising technology for improving spectral efficiency. Since SEFDM signals transmitted on subcarriers are not orthogonal, interchannel interference occurs due to the mutual influence of signals transmitted on adjacent subcarriers. Algorithms for receiving SEFDM signals can be distinguished into element-by-element coherent detection and maximum-likelihood sequence estimation (MLSE). The former method, although being simpler, is characterized by a low bit error rate performance. The latter method, although providing for a higher energy efficiency, is more complicated and does not allow high absolute message rates.Aim. To consider a trade-off solution to the problem of coherent detection of SEFDM signals under the condition of significant interchannel interference, namely, the use of an iterative algorithm of element-by-element processing with decision feedback at each subcarrier frequency.Materials and methods. Analytical expressions for the operation of a demodulator solver were derived. A simulation model for transmission of SEFDM signals was built in the MatLab environment, including element-by-element detection with decision feedback.Results. The simulation results confirmed the efficiency of the proposed algorithm. For error probabilities p =102…103, the energy gains reach values from 0.2 to 7.5 dB for different values of the non-orthogonal subcarrier spacing. At the same time, the efficiency of the detection algorithm with decision feedback turns out to be significantly lower than that when using the detection algorithm MLSE.Conclusion. The proposed detection algorithm can be used in future generations of mobile communications, which require high transmission rates. By reducing the computational complexity of the algorithm, it is possible to provide for a lower power consumption of mobile devices.