## 5 Performance Analyses
### Achievable Data Rate Comparison  
This section discusses achievable data rates when UA and OA are considered. For the simulations based on UA, \(P_{\text{T}}\in[-20,40]\) (dBm) is equally divided among the subcarriers, subchirps, subslots, and subtiles. On the other hand, the simulations using OA consider that the transmitter has complete knowledge of CSI to perform the water-filling algorithm to allocate \(P_{\text{T}}\in[-20,40]\) (dBm) among the subcarriers, subchirps, subslots, and subtiles. Moreover, we consider \(L_{\text{CP}}\in\{14,18,30\}\) and \(\Delta\in\{0,3,7\}\). Regardless of the resource allocation technique (i.e., UA and OA), the nSNR value for OCDM and SCCP are the same for all subchirps and subslots, meaning that the total transmission power is equally distributed among the subchirps and subslots. The numerical results in terms of \(R\) (Mbps) \(\times\)\(P_{\text{T}}\) (dBm), while adopting UA and AWGN, are illustrated in Figure 10, with the constant lines being the achievable upper bound data rate, \(R^{\text{UB}}\). Note that Figure 10 depicts the results of the simulations performed while varying \(L_{\text{CP}}\) and \(\Delta\), with each row of subfigures having a fixed \(L_{\text{CP}}\) and each column a fixed \(\Delta\). Moreover, there is a \(\Delta\) returning the best achievable data rate for each \(L_{\text{CP}}\), which agrees with the results discussed in Section 5.1. For instance, the use of \(\Delta\) equal to 7, 3, and 0 results in the best curves for all schemes when \(L_{\text{CP}}\) is equal to 14, 18, and 30, respectively (i.e., the diagonal subfigures). Indeed, varying \(\Delta\) for each value of \(L_{\text{CP}}<L_{h}-1\), we can see that \(\Delta=0\) might not be the best choice for symbol synchronization under the interference caused by the CP length violation. This can be noticed by taking the \(R^{\text{UB}}\) as a parameter of the comparison. For example, with \(L_{\text{CP}}=18\), the \(R^{\text{UB}}\) for the OTFDM scheme is equal to 6.88, 8.03, and 6.77 Mbps with \(\Delta\) equal to 0, 3, and 7, respectively. For the simulations without any form of interference, Figure 10i shows that the HS-OFDM scheme yields the best \(R\) for all values of \(P_{\text{T}}\), reaching a value of 6.54 Mbps with \(P_{\text{T}}=40\) dBm, while OCDM, SCCP, and OTFDM reach 5.83, 5.83, and 6.23 Mbps, respectively. However, with a growing interference, HS-OFDM experiences a greater loss of the achievable data rate. Indeed, HS-OFDM attains the lowest \(R^{\text{UB}}\) in the simulations with \(L_{\text{CP}}\
eq 30\) and \(\Delta\in\{0,3,7\}\), while SCCP, OTFDM, and OCDM have the first-, second-, and third-highest \(R^{\text{UB}}\). Even though SCCP presents a higher \(R^{\text{UB}}\), OTFDM yields a better data rate than the other schemes when \(P_{\text{T}}=40\) dBm, \(L_{\text{CP}}\
eq 30\), and \(\Delta\in\{0,3,7\}\). For example, with \(L_{\text{CP}}=18\), \(\Delta=7\), and \(P_{\text{T}}=40\) dBm OTFDM yields \(R=5.70\) Mbps while HS-OFDM, OCDM, and SCCP reach \(R\) equal to 4.75, 4.93, and 5.32 Mbps, respectively. Figure 11 displays the numerical results pertaining to UA and ACGN following the same structure of subfigures as Figure 10. Based on the curves, we can state that the analysis associated with UA and AWGN also applied to UA and ACGN. Indeed, without interference, the HS-OFDM scheme still attains the best achievable data rate. With interference, the SCCP scheme has the higher \(R^{\text{UB}}\) and the OTFDM scheme has the best data rate for \(P_{\text{T}}=40\) dBm. For example, with \(L_{\text{CP}}=0\) and \(\Delta=0\), HS-OFDM, OCDM, SCCP, and OTFDM generate \(R\) equal to 5.79, 5.28, 5.28, and 5.53 Mbps, respectively, for \(P_{\text{T}}=40\) dBm. Furthermore, with \(L_{\text{CP}}=18\) and \(\Delta=7\), HS-OFDM and OCDM yield \(R=4.64\) Mbps, while SCCP and OTFDM generate \(R\) equal to 4.63 and 5.25 Mbps, respectively.