## 6 Simulation Results  
The developed estimation and detection methods were evaluated using Monte Carlo simulations to confirm their reliability. We explored a multi-user upstream SC-FDMA system that used a coded AF dual-hop transmission. Unless otherwise indicated explicitly in the article, the following transmission parameters were employed for simulations. * There were \(K=8\) operating users. * There were \(N=1024\) subcarriers in all. * The number of allotted subcarriers per user was \(M=1024/8=128\). * The cyclic prefix length was \(\
u=10\). * The localized mapper subcarriers distribution was employed. * Each user was appointed one of four possible signal architectures, \(\Omega^{(k)}\), (16-QAM, 64-QAM, 128-QAM, 512-QAM). * Each user adopted a convolutional code with a rate of 0.5, a constraint size of 7, and generating polynomials of 25 and 37. * Training symbols of length 60 were supplied to kick-start the suggested estimate procedure. * Wireless links between user \(k\) and the relay node, \(\mathbf{h}_{R}^{(k)}\), and user \(k\) and the destination, \(\mathbf{h}_{D}^{(k)}\), were created using nine taps where each one was modelled as a complex random variable with a profile being [72] \[\sigma_{\text{B}}^{(k)2}(l)=\Gamma_{B}^{(k)}\exp(l/10),l=0,\cdots,9,\] (42) where \(B\in\{R,D\}\) and \(\Gamma_{B}^{(k)}\) were chosen in such a manner that the mean energy per subcarrier was set to a certain value chosen at random from an interval of \([1,2]\). * IQM parameters of the users, relay, and destination nodes were selected at random as follows: \(\rho^{(k)},\rho^{(R)},\rho^{(D)}\in[0.91,1.6]\) and \(\theta^{(k)},\theta^{(R)},\theta^{(D)}\in[0,25^{o}]\). Here, \(\rho^{(k)}\), \(\rho^{(R)}\) and \(\rho^{(D)}\) are the IQM gains while \(\theta^{(k)}\), \(\theta^{(R)}\) and \(\theta^{(D)}\) are the IQM phases at the relay, destination, and user \(k\) terminals, respectively. * For the presented data detector, the bit-error-rate (BER) was employed as a measure of performance, whereas for the IQM and channel assessment, the mean-square-estimation error (MSE) was adopted. The BER of the provided detector is shown in Figure 4 as a function of the signal-to-noise ratio (SNR), and the MSE of the described estimator is demonstrated in Figure 5. The MSE of a predictor that is fully aware of all information symbols is also illustrated as a reference in Figure 5. This produces a performance limit on MSE. In addition, Figure 4 displays the BER efficacy when all channel impulse responses between terminals and IQM parameters are considered to be perfectly estimated. As can be seen, both the MSE and BER efficiency keep getting better as the repetition approach continues. After eight rounds, the effectiveness of the indicated detector and estimator is remarkably near to that acquired under ideal circumstances of complete channel state information and IQM parameters awareness. The reason for this behavior is elaborated as follows. As the prediction technique is founded on a limited number of pilots, the soft information provided by the supplied detector is untrustworthy in the first iteration. In contrast to the data-assisted scenario, a higher number of iterations leads to the use of more trustworthy information, which improves the accuracy of both the estimation and detection processes. Figure 6 compares the BER efficiency for the proposed design to that of several other systems. There is a situation with ideal forecasting and compensation for IQM at all nodes of the considered system, as well as the case with no IQM correction. It is clear that IQM, if unadjusted for, would lead to subpar BER efficiency. By all appearances, the presented scheme not only achieves a BER quality that is much better than that reported in [50,51], but it also produces an efficiency that is within 1 dB of the optimum. Figure 4: The provided data detector’s BER when used with the proposed channel impulse response and IQM parameters’ estimator. Figure 5: MSE efficiency of the calculated channel impulse response along with IQM parameters.