## 5 Performance Analyses
### Bit Error Probability Comparison  
This section focuses on the performance analysis in terms of BEP when the square 16-QAM constellation is used to transmit data (adaptive modulation). In other words, the CSI is not available at the transmitter side, and, as a consequence, subcarriers, subchirps, subslots, and subtiles transmit the same integer number of bits, which is equal to \(b=\log_{2}16=4\). Note that this performance analysis is different from the one based on the use of UA, since the latter allocates \(b\in\mathbb{R}\) in accordance with the nSNR, which is different from the adaptive modulation, in which \(b\in\mathbb{Z}\). Figure 13 displays the graphs of \(\mathbb{P}_{\mathrm{e}}\times P_{\mathrm{T}}\) (dBm) while considering the PLC channel corrupted by AWGN, in which the constant lines refer to the lower bound BEP, \(\mathbb{P}_{\mathrm{e}}^{\mathrm{LB}}\) for each data communication scheme. Note that, in this figure, each row of subfigures has a different \(L_{\mathrm{CP}}\) from the others, and each column has a different \(\Delta\); moreover, the results are in accordance with Section 5.1. Meaning that, regardless of the scheme, each row of subfigures has a \(\Delta\) that yields the lowest values of \(\mathbb{P}_{\mathrm{e}}\). For instance, for the row with \(L_{\mathrm{CP}}=14\), the \(\mathbb{P}_{\mathrm{e}}^{\mathrm{LB}}\) for the OCDM scheme is equal to \(1.54\times 10^{-4}\), \(6.63\times 10^{-5}\), and \(1.37\times 10^{-5}\) when \(\Delta\) is equal to 0, 3, and 7, respectively, showing that STO can be helpful to mitigate interference caused by a CP length violation. Regarding the performance of each scheme, when considering the scenario free of interference, the OCDM scheme and SCCP yield the best results, requiring only require \(P_{\mathrm{T}}=23\) dBm to achieve \(\mathbb{P}_{\mathrm{e}}=10^{-6}\), while the HS-OFDM scheme and OTFDM require \(P_{\mathrm{T}}\) equal to 33 and 25 dBm, respectively. Moreover, as the interference starts to rise, the performance of all data communication schemes decreases. For example, for the simulations with \(L_{\mathrm{CP}}=18\) and AWGN, to achieve a \(\mathbb{P}_{\mathrm{e}}=10^{-4}\), the HS-OFDM scheme requires values of \(P_{\mathrm{T}}\) equal to 40 and 30 for \(\Delta\) equal to 0 and 3, respectively. For the OCDM scheme, we  
Figure 12: \(R\) (Mpbs ) \(\times P_{\mathrm{T}}\) (dBm) and \(R^{\mathrm{UB}}\) for the HS-OFDM scheme, OCDM, and SCCP schemes while considering \(L_{\mathrm{CP}}=30\), \(\Delta\in\{0,3,7\}\), and both types of additive noise. can see that \(\mathbb{P}_{\rm e}=10^{-4}\) when \(P_{\rm T}\) is equal to 23, 21, and 23 dBm for \(\Delta\) equal to 0, 3, and 7, respectively. Furthermore, for \(L_{\rm CP}=14\), the OCDM scheme continues to yield better values of \(\mathbb{P}_{\rm e}\) compared to the other data communication schemes. Moreover, the OCDM scheme is the only one to reach \(\mathbb{P}_{\rm e}\) values lower than \(2\times 10^{-4}\) for all \(\Delta\) considered. In other words, the OCDM scheme offers a better (higher) performance loss in terms of \(\mathbb{P}_{\rm e}\) than the others as the interference increases. In contrast, the SCCP scheme and OTFDM are proven to be the most fragile to interference in terms of \(\mathbb{P}_{\rm e}\). Note that SCCP and OCDM share the same nSNR; however, the difference between their time-frequency domain occupation indicates that the former is less resilient to interference. This leads to the conclusion that  
Figure 13: \(\mathbb{P}_{\rm e}\times P_{\rm T}\) (dBm) and \(\mathbb{P}_{\rm e}^{\rm LB}\) for the HS-OFDM scheme, OCDM, and SCCP when \(L_{\rm CP}\in\{14,18,30\}\), \(\Delta\in\{0,3,7\}\), and the additive noise is AWGN. the CSS-based data communication scheme is less impacted than the others regarding the interference caused by the CP length violation and the STO.