# Extreme Learning Machines to Combat Phase Noise in RoF-OFDM Schemes
## 7 Conclusions  
In our work, without increasing the OFDM modem complexity and decreasing the effective bit rate, we introduced novel phase noise mitigation techniques employing fully-real and fully-complex ELMs in order to reduce amplitude and phase noises effectively and, then, enhance the system performance significantly. In a standard SLFN composed by one input and one output and prone to the ELM algorithm, the training set corresponded to the pilots for diminishing the rotation and dispersion effects on data-carrying subcarriers (testing set). As the pilot subcarriers were exploited, the learning phase happened in real-time, and additionally, the general throughput was not decreased. According to BER minimization purposes, the number of hidden nodes and the activation function for each ELM were initially found. Afterward, the effectiveness of the ELM algorithm in the complex domain was demonstrated regarding the feasible pilot-assisted equalization and real ELM techniques for a QPSK-OFDM based RoF scheme taking into account the following parameters: fiber length, radio frequency, laser linewidth, SNR, and OFDM symbol period. For any duration of an OFDM symbol, this superiority increased as the chromatic dispersion effect increased, laser phase noise decreased, and AWGN disappeared, which made the cost of RoF-OFDM schemes lower by the use of noisier lasers, for instance. As the heterodyning tones became phase-decorrelated, the system performance lost its dependence on the product between the laser linewidth and the OFDM symbol period. For phase-uncorrelated fields, the BER remained invariant to this relationship. In particular, for a 64-ns RoF-OFDM signal, the SNR requirement at a BER threshold of \(10^{-3}\) was relaxed by a factor near 1 dB for any laser linewidth and/or time delay by using the real and complex ELMs. For comparison purposes, also, the results in the worst scenario, with phase-insensitive methods and with the CPE compensation, were depicted. The complex ELM almost matched the CPE compensation in terms of combating phase and amplitude noises. However, the CPE compensation technique required an additional preamble for each OFDM frame, i.e., the transmission rate decreased. Finally, the less computational complexity of the fully-complex ELM among the pilot-based equalizer and the real ELM was shown. Instead, the real-fully ELM demanded more computational effort. In summary, the fully-complex ELM was suitable for RoF-OFDM systems because it minimized the BER, as well as reduced the complexity of the equalizer. Investigations regarding these novel phase noise methods can be directed towards the study of the ELM algorithm under the semi-supervised learning, by keeping in mind that phase noise in data and pilot subcarriers comes from the same source. It could be expected that with the assistance of a certain number of unlabeled samples (data subcarriers), the accuracy increases in the test stage, namely the BER enhances. The reasons behind the diverse performance regimes for the ELMs as a function of the chromatic dispersion effect are also open questions (refer to Figures 7 and 8). Finally, in the case of partially-phase-decorrelated fields, the explanation about the effectiveness of the phase noise reduction mechanisms given a relationship between the laser phase noise and the OFDM symbol period is left as a pending task (see Section 6). **Author Contributions:** Conceptualization, D.Z.-B. ; methodology, D.Z.-B. ; software, D.Z.-B. and M.M. ; formal analysis, D.Z.-B. ; investigation, D.Z.-B. ; resources, D.Z.-B. and M.M. ; writing, original draft preparation, D.Z.-B. ; writing, review and editing, D.Z.-B., M.M., C.A.A.-M., and A.D.F. ; project administration, D.Z.-B. ; funding acquisition, M.M. **Funding:** This research was funded by Vicerrectoria de Investigacion y Postgrado and Faculty of Engineering Science of the Universidad Catolica del Maule. **Acknowledgments:** This work was supported by the Laboratory of Technological Research in Pattern Recognition (LITRP), Project FONDECYT Iniciacion No.