Energy Efficiency for Faster-than-Nyquist Data Transmission Using Processing Algorithms with Decision Feedback  
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1 School of Physics and Electronic Information, Yantai University, Yantai 264005, China; [EMAIL_ADDRESS]  
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2 Institute of Electronics and Telecommunications, Higher School of Applied Physics and Space Technologies, Peter the Great St. Petersburg Polytechnic University (SPPU), Polytechnicheskaya, 29, 195251 St. Petersburg, Russia; lavrenyuk.idsppsku.ru (LL. ); [EMAIL_ADDRESS] (S.M. ); ovsyannikova,astsppsku.ru (A.O. ); [EMAIL_ADDRESS] (S.Z)  
[PERSON]  
2 Institute of Electronics and Telecommunications, Higher School of Applied Physics and Space Technologies, Peter the Great St. Petersburg Polytechnic University (SPPU), Polytechnicheskaya, 29, 195251 St. Petersburg, Russia; lavrenyuk.idsppsku.ru (LL. ); [EMAIL_ADDRESS] (S.M. ); ovsyannikova,astsppsku.ru (A.O. ); [EMAIL_ADDRESS] (S.Z)  
[PERSON]  
2 Institute of Electronics and Telecommunications, Higher School of Applied Physics and Space Technologies, Peter the Great St. Petersburg Polytechnic University (SPPU), Polytechnicheskaya, 29, 195251 St. Petersburg, Russia; lavrenyuk.idsppsku.ru (LL. ); [EMAIL_ADDRESS] (S.M. ); ovsyannikova,astsppsku.ru (A.O. ); [EMAIL_ADDRESS] (S.Z)  
[PERSON]  
2 Institute of Electronics and Telecommunications, Higher School of Applied Physics and Space Technologies, Peter the Great St. Petersburg Polytechnic University (SPPU), Polytechnicheskaya, 29, 195251 St. Petersburg, Russia; lavrenyuk.idsppsku.ru (LL. ); [EMAIL_ADDRESS] (S.M. ); ovsyannikova,astsppsku.ru (A.O. ); [EMAIL_ADDRESS] (S.Z)  
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3 Hubei Key Laboratory of Marine Electromagnetic  
shape. The duration of FTN signals is longer than the duration of the message bit. The correlation properties of signals are determined by the level of intersymbol interference, which is caused by the superposition of neighboring signals on each other [4; 5; 6]. Methods for constructing FTN signals are described in detail in [2; 4; 6; 7; 8] and can be divided into two groups: filtering methods and optimization methods of the signal envelope shape [9; 10; 11; 12; 13; 14]. Their common feature is that the duration of the signals is significantly (8-16 times) greater than the duration of message bits for the binary channel alphabet. The energy efficiency of using such signals is determined by their correlation properties and is characterized by energy costs for various processing algorithms. Modern trends in increasing the data transmission rate in cases of limited frequency bands are implemented by increasing the bit rate and by increasing the volume of the channel alphabet [4; 6; 7]. In this case, it is necessary to separate the concepts of the absolute data transmission rate and the transmission rate normalized to the frequency band. Restrictions on the computational complexity of the FTN signal demodulation algorithms are imposed for real-time data transmission systems. At the same time, when the data rate normalized to the band increases, there is no such limitation. An indicator of the effectiveness of the application of FTN signals in such conditions is the approach to the Shannon limit for continuous channels with additive Gaussian noise. However, even in this case, the issue of computational complexity of FTN signal demodulation algorithms is debated. This is because additional intersymbol interference occurs as the bit rate of FTN signals increases. This interference leads to an increase in energy costs, the specific value of which is determined by the reception algorithms. Moreover, in this regard, most of the attention is paid to developing and obtaining the most effective algorithms, from the point of view of obtaining maximum reception reliability and ensuring minimal computational complexity in their implementation. It is advisable to compare the reception efficiency under conditions of limited computational complexity of the proposed algorithms.