## 4 Simulation Results  
The recognition efficiency of the offered approach was evaluated via Monte Carlo simulations. Unless otherwise declared, we assume that the OFDM scheme is operating at \(N=512\), \(\
u=7\), and 16 QAM. The SFBC collection under examination is [SFBC1, SFBC2, SFBC3, and SFBC4] with their broadcast matrices being defined as indicated in (1)-(4). A convolutional code is adopted with a rate of \(1/2\), 16 states memory elements, and generator polynomials of 32 and 37 with a base of 8 [40]. The suggested recognizer is launched utilizing 70 dispersed known symbols. The proposed method is flexible because there are no predetermined positions for the pilot symbols. The radio connection between each broadcast and receiver antenna is assumed to be multiple taps, with a length of \(L=6\) and a power delay profile of  
\[\sigma^{(f)2}(l)=q\exp(-l/6), \tag{30}\]  
where \(q\) is chosen to have a mean power per subcarrier of one [39]. The IQD parameters of the broadcaster and receiver are chosen at random as follows: \(\rho_{tx}^{(f)},\rho_{rx}\in[0.92,1.5]\), and \(\theta_{tx}^{(k)},\theta_{rx}\in[0,20^{o}]\). The probability of false recognition \(P_{f}\) is utilized as an efficiency indicator for the suggested recognizer,  
\[ \begin{array}{l}P_{f}=1-\big{[}\Pr(\text{SFBC1}|\text{SFBC1})+\Pr(\text{SFBC2 }|\text{SFBC2})\\ \hskip 14.226378 pt+\Pr(\text{SFBC3}|\text{SFBC3})+\Pr(\text{SFBC4}|\text{SFBC4 })\big{]}.\end{array}  \tag{31}\]  
Figure 2: The basic structure of the solution being offered. The main contributing blocks are the channel and IQD estimator and SFBC recognizer along with a posteriori data expectation. Note that the previous formulation of \(P_{f}\) was constructed assuming that four SFBC signals are used. For any other set of SFBC signals, an equivalent expression can be simply obtained. In addition, the bit error rate (BER) is used as a quality metric of the entire system, whereas the mean square estimation error (MSE) is utilized to assess the offered estimation of the IQD parameters and radio links. Figures 3-5 illustrate the \(P_{f}\), MSE, and BER, respectively, of the proposed approach as a function of the signal-to-noise ratio (SNR). Observably, the effectiveness of the offered strategy improves as the iteration process proceeds. The results reveal that the proposed method converges after around seven iterations. The following is an explanation for this tendency. The detector's soft information is imprecise in the first round since the recognition and prediction methods are based on a small number of known symbols. In contrast to the data-assisted situation, the estimate and recognition accuracies rise with an increase in the number of iterations since more reliable information is incorporated by the error control decoder. Furthermore, it is evident that the first five iterations generate the best and most efficient results with minimal delay. In practice, the mode of operation with the smallest delay and the highest impact could be attributed to the fourth iteration. This is also consistent with the results shown in [41]. Figure 4: Mean square estimation error of the proposed estimator as a function of the SNR. Figure 3: Probability of false recognition of the proposed recognizer as a function of the SNR. Figures 6-8 depict \(P_{f}\), MSE, and BER, respectively, of a number of different systems for the sake of comparison. The first system is based on the assumption that the IQD parameters are not be calculated and adjusted. The performances of the systems introduced in [42; 43] are also shown. Furthermore, we highlight the system's efficiency under the presumption that its input data are completely known. This functions as a benchmark for the proposed estimation and recognition processes. In addition, we display the BER performance under perfect circumstances where unknown parameters can be precisely estimated and identified. As is evident, the performance is poor if the IQD is not resolved.