## 4 Results and Discussion
### Performance Evaluation
for BPSK and QPSK subcarrier modulation formats. This competitiveness does not happen for the 16 QAM constellation, where the C-ELM must be highlighted by its superiority. Finally, even without AWGN, the R-ELM presents incapacity to follow phase noise fluctuations in a single OFDM symbol. For example, the \(log_{10}\)(BER) corresponds to \(-2.65\), \(-2.8\), and \(2.85\) by using the CPE compensation, C-ELM, and RC-ELM, respectively, according to an SNR equals to \(15\) dB and a 2-MHz combined linewidth for the QPSK format (see blue curves in Figure 8b). Meanwhile, the FEC limit remains unreachable in the case of adoption of the PAE and R-ELM, whose \(log_{10}\)(BERs) respectively result in \(-1.9\) and \(-0.6\). Notice that if the ratio between data and pilots tends to be \(1\), the BERs provided by PAE and CPE compensation techniques could be similar (the interpolation and mean operations to obtain the corrected symbols converge to the same result). Because this situation does not happen in our work (refer to Table 1), their BER values differ even under an AWGN channel without phase noise. In the absence of phase noise, the required SNR to overcome the FEC threshold increases as the constellation symbols augments, simply meaning that higher spectral efficiency formats have poorer sensitivity. Instead, without any phase-noise reduction technique, the BER reaches its maximum value for any SNR value (refer to the uncorrected constellation of Figure 1b), by showing that phase error is especial detrimental. A better understanding of the performance behavior may be accomplished by studying the constellations (after the PAE, R-ELC, C-ELM, RC-ELM, or CPE compensation) for (a) BPSK, (b) QPSK, and (c) 16 QAM subcarrier modulation formats, refer to Figure 8. For that end, the SNR value is fixed to \(20\) dB and the RF-linewidth parameter varies as a function of the modulation in order to clearly perceive the system deterioration. Looking at the point dispersion, it can be seen that whereas for the CPE compensation, the constellation shape remains notorious, the R-ELM practically leads to a stain. The PAE, C-ELM, and CPE compensation produce quasi-circular constellations for all subcarrier modulation formats. Their symbols then suffer a uniform distortion and standard decision regions do not affect the system performance. On the other hand, the constellation shape of the novel ELM changes as a function of its number of symbols. The constellation degradation only happens in the real dimension for BPSK. While the variance noise comes from a non-Gaussian distribution in the QPSK constellation. Finally, the constellation dispersion in 16 QAM is determined by the symbol power as follows: the inner points seem to possess a Gaussian degradation, in contrast to the symbol shapes in the periphery that are elliptical with semi-minor and semi-major axes dependent on the magnitude of the complex point. Consequently, in order to broaden the laser oscillators in CO-OFDM schemes, the RC-ELM should be included the demapping process by providing non-rectangular boundaries. However, this improved ELM is left as a pending task.