# Extreme Learning Machines to Combat Phase Noise in RoF-OFDM Schemes
## 6 Discussion  
It is well known that the most important measurement in the telecommunication industry is the BER vs. SNR curve. For this metric, results are now exposed and evaluated with the \(Lf_{RF}\) relationship (i.e., the phase-decorrelation degree between the fields at the base station) as the parameter for overall design purposes. Novel methods and the pilot-based equalizer were only taken into account. In order to expand the observations for various RoF-OFDM signals, the next laser linewidths and OFDM symbol periods respectively were simulated: (a) 0.5 MHz and 32 ns, (b) 0.5 MHz and 64 ns, (c) 0.5 MHz and 128 ns, (d) 1 MHz and 32 ns, (e) 1 MHz and 64 ns, and (f) 1 MHz and 128 ns for Figure 9 and (a) 5 MHz and 3.2 ns, (b) 5 MHz and 6.4 ns, (c) 5 MHz and 12.8 ns, (d) 10 MHz and 3.2 ns, (e) 10 MHz and 6.4 ns, and (f) 10 MHz and 12.8 ns for Figure 10. Keeping in mind the values of the laser phase noise and the duration of a single OFDM symbol, three time delays were chosen to expose each of the system performances distinguished by the complex ELM (see Section 5), as well as the pilot-based channel correction [9]. As noted before, the BER minimized as the product between the fiber length and radio frequency decreased, the laser linewidth tended to 0 Hz, and/or the SNR increased. As the \(Lf_{RF}\) parameter increased, the BER value subject to phase noise compensation did not change in terms of the laser linewidth times the OFDM symbol period (\(\Delta vT_{s}\)). To the best of the authors' knowledge, this behavior was exclusively noticed for phase-uncorrelated tones (where the system performance exclusively depended on the \(\Delta vT_{s}\) relationship, instead of the laser linewidth and the OFDM symbol period independently) [35; 36]. In the partial phase-decorrelation situation, however, it was revealed for the first time that given a certain \(\Delta vT_{s}\), the phase noise mitigation techniques were more beneficial as the laser phase noise diminished or the duration of an OFDM symbol augmented. The previous results can be seen via the contrast of Figure 9b-e, whose \(\Delta vT_{s}\) parameters were. The corresponding Figure 10 exhibits the same observation. The reasons behind these results were beyond the purpose of the current investigation (the introduction of real and complex ELMs for diminishing phase noise in direct-detection OFDM-based RoF schemes, by exploiting the information in-phase and amplitude that provided the unmodulated subcarriers); nonetheless, they could be explained by calculating the residual phase error of a multicarrier signal characterized by partial phase-decorrelation. Note that without reducing phase noise, the system performance did not depend on the OFDM symbol period [9]. Regarding the effectiveness of the phase error compensation mechanisms, the ELM algorithm in the complex domain was the best choice for all OFDM symbol periods, which was followed by the fully-real ELM in the situation of a 3.75 Gbps OFDM signal (see Figure 9b,e) and as noticed in the preceding section. For OFDM symbol periods less than 64 ns, the pilot-assisted equalization outperformed the real ELM (see Figures 9a,c and 10); otherwise, the opposite occurred as long as AWGN decreased (see Figure 9d,f). \begin{table}
\begin{tabular}{c c} \hline \hline
**Phase Error Correction Scheme** & **Time (ms)** \\ \hline Pilot-assisted equalization & 64.44 \(\pm\) 0.46 \\ Real ELM & 135.42 \(\pm\) 2.44 \\ Complex ELM & 56.20 \(\pm\) 1.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Complexity evaluation. For the above phase error correction methods and an OFDM-based RoF signal of 64 ns, Figure 11 exhibits finally the SNR and laser linewidth requirements at the FEC threshold with the \(Lf_{RF}\) relationship as the parameter. These requirements decreased as the amount of phase-correlation between the beating tones diminished, being more relaxed via the fully-complex ELM.