## 6 Simulation Results
The proposed process may also be useful for classic single-hop SC-FDMA operations. It is sufficient to eliminate the channel impulse response between the relay and the base station. This recommended detector, however, functions exactly akin to the ordinary one in this case. Figure 7 compares the BER quality of the planned AF SC-FDMA scheme with the single-hop transmission coupled to the proposed estimator at round 8. The results demonstrate that the dual-hop system is far better than the single-hop one. This is because the dual-hop system maximizes diversity benefits by transmitting waveforms across both main and relayed channels. It is well-known that SAGE-based strategies depend critically on having an efficient starting point. Figure 8 illustrates the BER effectiveness of the mentioned detector and estimator as a function of the training symbols length, \(T\), at \(\text{SNR}=4\) and 8 dB. The proposed estimator clearly has a convergence level of more than 60 known symbols. It is worth noting that, depending on the transmission parameters and the linkages, the basic requirement of pilots needed to provide accurate initial estimations may change. The designer can put the offered estimation method to work across a broad variety of network and link parameters to find out how few pilots are required to meet all the requirements. The findings are recorded in look-up tables for later use in the actual hardware. Additionally, the designer can pick a sufficiently large random sample of pilots to account for many different configurations of the network and its links. Figure 9 presents the BER performance of the proposed approach as a function of the number of operating users at SNR = 8 dB. The findings show that, when the number of users increases, the suggested method's BER performance degrades marginally. This is due to the fact that increasing the number of active users increases the residual multiple access interference, which reduces BER performance. Furthermore, we observed a substantial performance boost compared to the algorithms described in [50; 51]. This is because the aforementioned algorithms do not profit from the features inherent in channel coding transmissions. Figure 6: BER efficiency comparison of various schemes. Blue color with solid line represents the performance without IQM being estimated and corrected, green color with dashed line represents the performance of the algorithm reported in [50], red color with dashed line represents the performance of the algorithm reported in [51], brown color with solid line describes the performance of the proposed algorithm, and black color with solid line represents the performance of perfect case. In prior discussions, it was presumed that the wireless channels remained constant during the observation period, i.e., their coherence times approached infinity. Figure 10 illustrates the impact of the maximum Doppler shift, \(d_{s}\), on the BER performance of the proposed approach at \(\text{SNR}=8\) dB. Here, \(d_{s}\) was normalized to the sampling frequency. An improved version of the Jakes model [69] was used to represent the time-selective nature of the wireless links. We also display the results of the methods described in [50; 51] for the purpose of comparison. The results indicate that the proposed approach achieves adequate BER performance when \(d_{s}\leq 10^{-4}\). This demonstrates that the suggested technique works well in quasi-stationary settings. However, the algorithms reported in [50; 51] are unable to provide acceptable outcomes. Figure 8: The effect of the training symbol’s length on the system efficiency. Figure 7: BER of the dual-hop and single-hop schemes.