Optimizing the Shape of Faster-Than-Nyquist (FTN) Signals With the Constraint on Energy Concentration in the Occupied Frequency Bandwidth

The achievement of the boundary values of spectral efficiency is associated with the development of methods for generating and receiving signals with a compact spectrum. The reason is a constant increase in the capacity of existing communication channels caused by an increase in the volume of transmitted information. Moreover, the allocated frequency bandwidths have natural limitations, and they are almost all reached. The effective way to approach the boundary values of spectral efficiency is the application of spectrally efficient signals, such as FTN (Faster-Than-Nyquist) signals. This article proposes to synthesize optimal FTN signals that are more compact in the spectrum than RRC (root raised cosine) pulses-based signals. The criterion of maximum energy concentration in the occupied frequency bandwidth and the constraint on the cross-correlation coefficient are used to solve the optimization problem. The contribution of this work is the optimization of FTN signal shape. The obtained optimal FTN signals provide a 24% increase in spectral efficiency compared to the RRC pulses-based signals. At the same time, the energy loss stays almost unchanged. To the best of authors' knowledge, this is the first case when the frequency bandwidth reduction is achieved at practically no energy loss. The simulation modeling in channels with additive white Gaussian noise and fading channels is done with regard to the FTN-SC-FDE (Faster-Than-Nyquist - Single Carrier system with Frequency Domain Equalization) structure. The optimal FTN signals presented in this work can be used to increase the spectral efficiency of satellite broadcasting systems, such as DVB-S2/S2X.