A Study of the Extremum of the Total Energy of the Selective Signals Constructed by Quadratic Splines

Abstract

The development of mobile communication networks in the direction of 5G networks implies the use of the radio interface that is based on new signal-code structures, the choice of which will determine their further development and the ability of operators to provide innovative services. The use of quadratic splines for the synthesis of selective signals with a finite spectrum, free from intersymbol interference, is proposed. An analytical expression for the synthesized signal in the time and frequency domains is obtained. A study was made of the dependence of the total energy of a selective signal on the parameters of a quadratic spline, which is used to interpolate the spectral density in the transition region using the methods of differential calculus of functions of several variables. To study the extremum of the total energy of a selective signal, the parameters of the width of the transition area α was used and the coefficient of rounding the spectrum ρ, the variation of whose spectral density allowed us to establish the limits of the change in the total energy of the signal in question. Conducted studies allow us to synthesize the signal and formulate recommendations on how by changing the parameters of the signal, you can get a signal with the desired properties. This will allow to obtain the optimal waveform in accordance with the selected criteria, providing for the required energy performance of the signal in the radio interface of 5G networks.