## 2 Related Works
### CFO Case Studies in Multicarrier Modulations  
A CFO results in Intercarrier Interference (ICI) by breaking the orthogonality between subcarriers. This part presents papers that investigated CFO case studies in multicarrier modulations and DVB-T2 in particular. In 2006, a suboptimal scheme was proposed for OFDM systems to estimate the CFO using null subcarriers (i.e., subcarriers with no data transmitted) [24]. This scheme was based on the exploitation of one OFDM training sequence in which the use of odd subcarrier indexes like null subcarriers was imposed first and where even subcarriers indexes carried pilot tones. The work was performed assuming that the guard interval was longer than the Channel Impulse Response (CIR) length and the time synchronization was perfect. The specificity of that scheme was a reduced implementation complexity compared to previous work as the main required component was a simple correlator. Furthermore, null subcarrier allocation for the optimal maximum likelihood CFO estimation was also investigated using an extended m-sequence. It was demonstrated that that method presented improved performance compared to the previous one based on the principle of null subcarriers with distinct spacing. In 2012, an optimum maximum likelihood (ML) synchronization method for P1 symbols was proposed [7]. Indeed, the P1 symbol was obtained in a similar way to that for an OFDM symbol. However, its features were different from a classical OFDM symbol and therefore were not really exploited by synchronization algorithms developed for multicarrier systems. The authors of that paper exploited the tripartite structure of the P1 symbol and the presence of null subcarriers in the vector transformed by an inverse Fourier transform. For the purpose of complexity reduction, ML synchronization for OFDM systems with no training sequence was used in parallel with the implementation of null subcarriers in OFDM symbols. Furthermore, the Cramer-Rao lower bound for the new scheme CFO estimator was investigated. That solution presented optimal performance while having a much lower complexity than that of the classical ML solution. In the same year (2012), an ICI cancellation method was studied for a DVB-T2 system including the MISO technique [3]. Indeed, the P1 symbol inserted at the beginning of each T2 frame was used to estimate the CFO. That symbol presented a frequency-shifted guard interval at both ends which improved the correlation between the central part of the P1 symbol and the two intervals. Then, the estimation was performed by correlating the received P1 symbol and by recovering the argument of the correlator output's peak. When the MISO technique was exploited in DVB-T2, the signal and a slightly modified version of that signal were transmitted at the same time by two spatially separated transmitters having their own oscillators. That technique improved signal performance. However, two distinct CFOs, called dual CFOs, may appear in the received signal, one for each transmitter. In [3], the authors presented a method to mitigate Intercarrier Interference (ICI) occurring due to the dual CFOs after performing dual CFO compensation. They also proposed an iterative detection and ICI cancellation technique with the presence of a large CFO. Using that technique, the ICI was eliminated in a successive and iterative manner using the previously detected data samples and a priori LLR (Log-Likelihood Ratio) values fed from the LDPC decoder. The BER vs. SNR simulation results showed that the proposed DVB-T2 receiver outperformed the case in which dual CFOs were perfectly known and came closer to the performance of the ideal dual-CFO-free case. Moreover, CFO estimation techniques were presented, and their performance was evaluated using the Mean Square Error (MSE) [25]. The main estimation techniques presented were time-domain estimation (use of a cyclic prefix or training sequence) and frequency-domain estimation (pilot tone techniques).