The fifth generation (5G) of mobile communications systems plans to support different types of applications, where each of these applications may have different requirements. For this reason, the main characteristic of 5G mobile communications systems is the flexibility of their architecture. An interesting proposal that can meet the requirements of these applications is the multi-carrier waveform Generalized Frequency Division Multiplexing (GFDM). However, due to its multi-carrier nature, this new waveform is highly sensitive to non-linear distortions arising mainly from high-power amplifiers (HPA). In addition, the wideband characteristics of multi-carrier signals result in frequency-dependent distortions, typically know as memory effects. This paper presents the development of closed-form analytical expressions that could be used to evaluate the impact of the distortions induced by non-linearities with memory in the outof-band emissions and the bit error rate performance of GFDM-based systems. The resulting analytical expressions are general enough to obtain numerical results for different parameters of the GFDM-based system.

The rapid growth of the Internet of Things (IoT) has extended its concept to underwater environments. However, the implementation of these systems via wired communication still represents a technological challenge, mainly due to the high cost of their deployment. Therefore, wireless communications are seen as an interesting solution for the deployment of underwater communications systems. Preliminary research indicated that underwater acoustic wireless communication could be used for some Internet of Underwater Things applications, mainly due to the wide range of communications involved. However, a significant disadvantage of acoustic systems is their low transmission data rate; thus, studies and analyses to improve this disadvantage must be carried out. Considering that new waveforms have been proposed to improve the performance of terrestrial wireless communications systems, this work presents the development of general analytical expressions that allow the performance evaluation of the Generalized Frequency Division Multiplexing (GFDM) waveform in underwater environments. These analytical expressions were obtained considering a continuous-time model for the GFDM signal and modeling the underwater acoustic communication channel as a time-varying multipath channel. Numerical results were obtained for many different systems and channel parameters, allowing a quantitative evaluation of the system performance degradation.