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

Sergey B Makarov,Junwei Qi,Ilya I Lavrenyuk,Mingxin Liu,Anna S Ovsyannikova,Wei Xue,Sergey V Zavjalov

doi:10.1109/access.2020.3009213

Abstract

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.

Highlights

It is never possible to reach the performance boundaries of spectral and energy efficiency in existing communication systems
The comparison of the bandwidth occupied by optimal FTN signals and FTN signals based on RRC pulses (Fig. 4) shows the following
When cross-correlation coefficient K0 = 0.1 is chosen, the optimal FTN signals based on the pulses of duration from Ts = 8T to Ts = 16T have a narrower band than the FTN signals based on RRC pulses

Summary

Introduction

It is never possible to reach the performance boundaries of spectral and energy efficiency in existing communication systems. These boundaries are determined by the Shannon formula for the channel capacity [1]–[3]. The approach to the boundaries of spectral and energy efficiency is associated with an increase in the volume of the channel alphabet and a combination of signal generation. At the same time, according to Shannon [7], an additional way for increasing the efficiency of information systems is to approach the boundaries of the channel capacity using a mathematical solution to the optimization problem [8]–[10]. An integral part of this optimization problem refers to the requirement for a fixed frequency bandwidth, BER (bit error rate) performance, and technical and economic limitations on the time parameters of signals and their random sequences.

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Results

Conclusion