The properties of time-frequency localization of basis functions used in OFTDM communication systems

Abstract

This article investigates the properties of time-frequency localization (TFL) of various basis functions, such as rectangular function, the function of half cosine, isotropic orthogonal transform algorithm (IOTA) function and extended Gaussian function used in OFTDM communication systems. The aim is to study the properties of time-frequency localization of basis functions used in OFTDM communication systems which is a prerequisite for creating information communication system based on new basis functions that are well localized both in frequency and in time domain, with good suppression of intersymbol (ISI) and interchannel (ICI) interference. The results presented in the article are obtained by the method of mathematical modeling. The paper presents several different types of forming impulses with the further use of the Heisenberg parameter ξ as an indicator of TFL properties. The higher ξ is, the better the joint time-frequency localization of basis function. Two parameters affect the effectiveness of extended Gaussian function. One of them is α and the other is the number of filter M units. The properties of time-frequency localization described by Heisenberg parameter, uncertainty function and interference function and instantaneous correlation function allow to describe how signals at different carrier frequencies and with different characters interact with each other. By using different basis functions with different properties of TFL dynamic spectrum distribution can be achieved more naturally because the transmitter and receiver quickly adapt to different channel conditions and environmental obstacles. Thus, we can expect higher reliability and spectral efficiency of communications system. Also a lower sensitivity to time and frequency shift can be expected at simplifying the synchronization.