## 5 Performance Analyses
### Achievable Data Rate Comparison
A comparison in terms of te achievable data rate for the two types of additive noise shows that with \(P_{\text{T}}=30\) dBm, the HS-OFDM scheme yields a rate \(R\) equal to 4.97 and 4.22 Mbps for the AWGN and ACGN, respectively, while the OTFDM scheme provides the second best achievable data rate, producing values of \(R\) equal to 4.67 and 3.96 Mbps. Furthermore, the OCDM scheme and SCCP yield 4.26 Mbps and 3.71 Mbps, respectively, for the aforementioned additive noises. Moreover, even though the HS-OFDM scheme is more fragile to interference than the others, it yields better data rate results for most of the considered \(P_{\text{T}}\) values in comparison to the other data communication schemes. Indeed, the HS-OFDM scheme might not be the best when \(P_{\text{T}}\) is high and there is interference. This occurs when the interference compromises the data rate performance of the HS-OFDM scheme more than the others. For instance, with \(L_{\text{CP}}=14\) (i.e., a strong CP length violation), the HS-OFDM scheme still generates better achievable data rate results among thefour data communication schemes for the values of \(P_{\rm T}\leq 25\) dBm for both additive-type noises. To put into numbers, when \(P_{\rm T}=20\) dBm, \(\Delta=0\), and AWGN, the HS-OFDM scheme yields a rate \(R\) close to 3.23 Mbps, the OCDM scheme attains \(R=2.67\) Mpbs, the SCCP scheme yields 2.71 Mbps, and the OTFDM scheme attains \(R=3.07\) Mbps. Performance comparisons in terms of \(R\) (Mbps) \(\times\)\(P_{\rm T}\) (dBm) while considering OA, through the water-filling technique, are in the plots shown in Figure 12. The nSNRs used to perform the power allocation is in Table 1 since we assume the transmitter does not know the existence of interference, but it knows PLC CIR and the additive noise. The knowledge of PLC CIR allows the receiver to use the correct value of \(L_{\rm CP}\). In other words, the system does not face interference caused by CP length violation. The plots show that the OCDM scheme and SCCP attain the same performance for both resource allocation  
Figure 10: \(R\) (Mbps) \(\times\)\(P_{\rm T}\) (dBm) and \(R^{\rm UB}\) 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. techniques since their nSNR are equal. In contrast, the HS-OFDM scheme and OTFDM with OA offer higher data rates than with UA when \(-20\leq P_{\rm T}\leq 0\) dBm for AWGN and \(-15\leq P_{\rm T}\leq 5\) dBm for ACGN. For example, while considering ACGN and \(\Delta=7\), the HS-OFDM scheme reaches a value of \(R=0.27\) Mbps when adopting \(P_{\rm T}\) equal to \(-4\) and \(-1\) dBm with OA and UA, respectively. On the other hand, the OTFDM scheme requires greater values of \(P_{\rm T}\) than the HS-OFDM scheme to achieve the same \(R\), reaching a data rate equal to 0.27 Mbps when \(P_{\rm T}=0\) dBm with OA and \(P_{\rm T}=2\) dBm with UA. Furthermore, the HS-OFDM scheme attains the highest achievable data rate for all values of \(P_{\rm T}\) in most scenarios (with and without interference). The exception is for high values of total power transmission (\(P_{\rm T}\geq 25\) dBm for AWGN and \(P_{\rm T}\geq 30\) dBm for ACGN), where the interference starts to harm the HS-OFDM scheme more than the other multiplexing techniques. Figure 11: \(R\) Mbps) \(\times P_{\rm T}\) (dBm) and \(R^{\rm UB}\) 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 ACGN.