## 2 Related Works
### CFO Case Studies in Multicarrier Modulations
The simulation was performed usingthe CP-based technique, Moose (preamble-based techniques) and Classen (pilot-based techniques). The results showed that the Classen estimation technique was much more efficient than the other ones. In 2015, the efficiency of OFDM systems with CFO estimation errors was measured in terms of spectral efficiency [26]. That work was performed regarding both the degradation in Signal-to-Interference-plus-Noise Ratio (SINR) due to the residual CFO, and the penalty of the extra power and spectral resources allocated to achieve the desired CFO estimation accuracy. Indeed, there still was a residual CFO after CFO estimation and compensation at the receiver which may degrade OFDM system performance. The authors of [26] presented a modified formula for the spectral efficiency of OFDM systems by making the trade-off between the following two conflicting factors related to the estimation-based CP and the training sequence method. Using too few training symbols induced an increase in CFO estimator errors while too many training symbols induced a loss of power and bandwidth system resources. During the same year (2015), two ML CFO estimated methods called stochastic ML (SML) and deterministic ML (DML) were investigated by modeling the DVB-T2 transmitted signal as a stochastic and a deterministic unknown waveform, respectively, and assuming an unknown fading channel scenario [1] in contrast to the method developed in [4]. It was shown that the proposed deterministic ML method was more flexible and presented a lower computational complexity compared to the SML method but at the cost of reduced estimation accuracy. Numerical results demonstrated that both methods outperformed the cross-correlation-based method. In 2016, the Symbol Error Rate (SER) vs. SNR of UFMC and OFDM was evaluated in a 5G framework assuming the presence of a CFO or not and using mobile network system transmission parameters [27]. UFMC and OFDM performance was first compared. The results demonstrated that UFMC outperformed OFDM by 0.8 dB at an SER of \(2\times~{}10^{-3}\). Simulations were pursued, and it was demonstrated that the CFO estimator errors varied among these values: 10%, 20% and 50%. It was observed that for both OFDM and UFMC, the CFO estimation error critically diminished the SER performance of the system. In 2017, other authors also studied UFMC and OFDM performance by evaluating the CFO impact on these multicarrier modulations [28]. Two different detection techniques such as Minimum Mean Square Error (MMSE) and Zero Forcing (ZF) were used. A simulation was performed by explicitly inserting a CFO on the receiver side and calculating the SER vs. SNR. Single-user and multi-user UFMCs were investigated. Also, a MIMO technique was applied to the UFMC system. The results illustrated the good performance of UFMC when compared to OFDM without any CFO and with a CFO for a single user and multiple users in different communication environments. In 2021, [29] explored the challenges in applying Orthogonal Frequency-Division Multiplexing (OFDM) to full-duplex (FD) cellular systems. This concerned the OFDM's vulnerability to interference due to frequency offsets. The authors compared FBMC with f-OFDM, UFMC, and GFDM. In this section, related works about multicarrier modulations in DVB-T2 and CFO case studies in multicarrier modulations were presented. It was noticed that many papers presented CFO estimation and compensation algorithms in OFDM and DVB-T2. Only two papers addressed the impact of a CFO in OFDM and UFMC, respectively. Tables 1 and 2 summarize the papers by presenting their advantages and their limitations. Table 1 summarizes papers that studied multicarrier modulations in DVB-T2 and Table 2 summarizes papers that presented CFO case study in multicarrier modulations. To the best of our knowledge, there is no work that addresses the CFO impact on UFMC-based DVB-T2. This work fills this gap by evaluating the CFO impact on the received signal quality using UFMC- and NUC-based DVB-T2.