Third, their measures give a better description of the system than other linear approaches. The Lyapunov exponent, for example, is a quantity that characterizes the average stretching or shrinking of phase space in a specific direction. It is negative, zero, and positive for dissipative, conservative, and chaotic systems, respectively. This approach has been used in many fields, including atmospheric physics and geospace [18]. Chaos theory has been used to investigate nonlinear processes in the ionosphere in different regions of the world [19; 20; 21; 22; 23]. There is varied use and application of the term nonlinearity. Generally, it implies a more advanced concept compared to linearity. This is true for nonlinear optimization and nonlinear waves. The use of \"nonlinear\" in this paper has a completely unique and different concept. We use it in terms of chaos theory, where the dynamics of a system are sensitive to initial conditions. This entails using analyses such as the Lyapunov exponent and correlation dimension. Similar concepts, applications, and definitions can be seen in other publications [24; 25]. We examined the scenario where we can analyze a time series in phase space to ascertain whether stochastic or chaotic processes govern its dynamics. The ionosphere is used to propagate long-range terrestrial communication, but it also causes delays in satellite-to-ground communication systems. However, there has been no data-driven analysis of such a connection in the literature. There exist nonlinear tools for the investigation of causality between two signals. [PERSON] et al. [26] used nonlinear tools to unveil the connection between rain and signal attenuation, which was not evident from correlation studies. In a similar approach, the connection between large-scale oscillations revealed weak relationships using nonlinear approaches [24]. The influence of external connections, such as teleconnections and solar activity, has been explored using a nonlinear causality approach [27]. Exploring these nonlinear connections at different timescales allows for an investigation of the role of solar activity on the ionosphere-radio signal relationship. The idea of \"nonlinear interaction\" implies that the relationship between two variables (VTEC and DFS) is more than linear. For example, the connection between the two can be a quadratic representation or a more general relationship. Linear approaches cannot determine this type of connection; hence, we need to investigate the nonlinear interactions. Consider the effect of the ionosphere on radio signals. This effect varies depending on several factors, including the time of day, ionosphere state, tropospheric weather, and so on. We can assert the existence of a nonlinear interaction between these effects if we can mathematically summarize them as a nonlinear equation. From the foregoing reasons, the intrinsic and external influences make the ionosphere a complex system. It is of interest to ionospheric scientists due to the numerous complexities associated with it [28]. High-latitude stations or short time periods in the tropics have been the focus of most studies on complex structures. There is a need to study the long-term evolution and complexities of the ionosphere in the tropical region. Furthermore, the evolving interaction of the ionosphere with signal quality at different time scales will be of interest to the scientific community. Predicting the behavior of the ionosphere on space and time scales has continued to attract attention due to the crucial role it plays in our everyday lives. The goals of this study are to (1) determine the level of complexity in both the ionosphere and signal quality and (2) find the complex interactions (if there are any) between VTEC and the DFS between Abuja and Lagos using some nonlinear tools.