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

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. INDEX TERMS Faster than Nyquist signaling; maximum band energy concentration criterion; optimization methods; spectral efficiency

Generalized Approximate Message Passing Equalization for Multi-Carrier Faster-Than-Nyquist Signaling

“…In this correspondence, we employ a root-raised cosine (RRC) shaping pulse p(t) with a roll-off factor β. For other non-orthogonal signaling schemes [19]- [21], the shaping pulse p(t) can be adjusted and the following derivations are still valid.…”

A Reduction of Peak-to-Average Power Ratio Based Faster-Than-Nyquist Quadrature Signals for Satellite Communication

“…The shape of function a(t) in time interval T s = LT (L = 1,2,...) is determined as a solution to the optimization problem [8,19]. The main requirement of the optimal signal generation is the requirement for the maximum spectral filling of the allocated frequency band.…”

“…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.…”

“…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.…”

A Transmission Scheme Based on Uniform Shortening LDPC Codes for Performance Improvement in Faster-Than-Nyquist Systems

“…To the best of our knowledge, rRC pulse shaping is very popular for FTN signaling. So, this pulse is utilized to conduct almost the researches in this field [4], [5], [8]- [10]. Note that the improvement of symbol rates discussed here is ideal, i.e., theoretical upper bound for noiseless case with optimal receiver design.…”