## 1 Introduction  
Both single-carrier signals with multilevel modulation and multi-carrier signals with orthogonal frequency division multiplexing (OFDM) [1, 2] have significant drawbacks. Such random signals have a high peak-to-average power ratio (PAPR), reaching a value of more than 10-15 dB. At the same time, in digital television and radio broadcasting (DVB) transmission equipment, especially that used in DVB-S2X satellite applications, traveling-wave tube (TWT) amplifiers with power of up to 1 kW and powerful transistors having power of up to 100 W [3, 4, 5, 6] are used. These devices have a nonlinear frequency response with a relatively small linear region. Therefore, the developers of such equipment tend to develop signals able to satisfy the requirements not only for transmitting the maximum amount of information in the allocated frequency band but also for effective use of amplifying devices. The second requirement can be met by the application of signalswith a reduced PAPR compared to known cases. In such conditions, the use of signals with a reduced PAPR increases the average power of the radiated oscillations while maintaining the same total operating energy costs. Therefore, either the quality of information detection may be improved or the distance between transmitting and receiving stations may be increased. Recently, the option of using Faster-than-Nyquist (FTN) signals in DVB-S2X satellite application systems have been actively considered [7; 8; 9; 10; 11]. Typically, FTN signals are formed with the use of filtering method. It is based on the method of forming root raised cosine (RRC) pulses with time and spectral characteristics determined by the type of frequency response of the shaping filter with a roll-off factor \(0\leq\alpha\leq 1\). The energy efficiency is determined by the correlation properties of random FTN signals based on RRC pulses. In turn, the correlation properties of FTN signals depend on the frequency response of the filter. Long pulse duration \(T_{s}\) significantly exceeds the symbol transmission time \(T\) and therefore causes random intersymbol interference (ISI) in signal packet. As a result, ISI leads to energy losses. Random signal packet based on RRC pulses has high PAPR. PAPR value depends on several factors: the depth of random ISI influenced by the duration of the applied pulses, the pulse shape, and the transmission rate of the channel symbols. For instance, a bandpass signal packet with binary phase shift keying (BPSK), pulse duration \(T_{s}=10T\) and roll-off factor \(\alpha=1\) transmitted at the rate \(R=1/T\) has PAPR equal to 6 dB. Reducing roll-off factor to zero results into PAPR equal to 7 dB. An increase in pulse duration to \(T_{s}=16T\) causes an increase in PAPR by about 0.5 dB. To reduce the PAPR, as a rule, the amplitude limitation of the emitted oscillations or clipping is used [12; 13; 14]. However, joint application of clipping and preamplifier increase the average power of oscillations emitted by the transmitter and cause significant increases in the level of out-of-band emissions and correlation coefficient. Another method for FTN signal generation assumes the synthesis of optimal pulse shapes. Optimal FTN signals obtained as the mathematical solution to the optimization problem [8; 15; 16; 17] can provide high information transmission rates [18]. An integral part of the optimization process includes requirements for signal spectrum compactness, detection reliability, and technical and economic constraints. These requirements determine the time and spectral parameters of optimal pulses and random signal sequences. The duration of such signals exceeds the time interval of one information bit (for binary transmission without coding). The emerging ISI in the signal sequence is not random but controllable. The ISI level can be controlled at the stage of the optimization problem solving by introducing the constraint on the cross-correlation coefficient.