## 4 Simulation Results and Discussion
### BER Performances: JISB_DSICED3_versus SB_DSICED3_W/OF  
First of all, the impact of different code rates such as (\(R\in\{1/3,1/2,2/3,3/4,5/6\}\)) on the BER performance of SB_DSICED3_W/OF and JISB_DSICED3 schemes is shown in Figures 7 and 8, respectively. It can be seen that the relative behaviour of the algorithm with feedback JISB_DSICED3 with respect to the code rate behaved in the same way as the conventional algorithm without feedback SB_DSICED3_W/OF, that is when the code rate R increased, this led to a decrease in the BER performance. Therefore, the code rate should be chosen carefully based on the purposes and applications. Because the code rates can lead to either a significant loss in terms of performance (code rate \(R\in\{2/3,3/4,5/6\}\)) or too great a loss of throughput (code rate \(R=1/3,1/2\)), for the rest of this paper, the code rate was fixed at \(1/2\) as a particular example in order to illustrate the out-performance of the proposed with feedback algorithm JISB_DSICED3 over the conventional without feedback algorithm SB_DSICED3_W/OF. Figure 9 shows the BER of the semi-blind scheme versus the number of pilot symbols \(\beta E\) for different values of the SNR, \(p_{B}/\sigma_{w}^{2}\), where \(p_{S1}/\sigma_{w}^{2}=30\) dB and \(E=128\) symbols. It can be seen that only a minimum of four pilot symbols (\(\beta E=4\) symbols or \(\beta=1/32\)) was needed for the semi-blind channel estimation to achieve the saturation level. Thus,  
Figure 8: \(BER\) versus SNR, \(p_{B}/\sigma_{w}^{2}\) for different code rates \(R\) of the JISB_DSICED3 scheme; \(i_{max}=4\), \(j_{max}=1\), \(p_{S1}/\sigma_{w}^{2}=30\) dB, \(\beta E=4\) symbols, and \(E=128\) symbols. the minimum required pilot symbols made the semi-blind scheme favourable in practical implementations for short-packet transmission. Figure 10 illustrates the BER performance of the semi-blind scheme JISB_DSICED3 versus the SNR, \(p_{B}/\sigma_{w}^{2}\), for different maximum numbers of joint iterations \(i_{max}\). A BPS scheme for the BER was also calculated, which was achieved by using the best channel estimation of the SI channel and intended channel in Figures 5 and 6, respectively, for the SI cancellation and SPA decoding processes with one iteration (\(j_{max}=1\)). It can be seen that the system achieved the convergence level when \(i_{max}=4\), and the BER of the proposed JISB_DSICED3 scheme was also close to that of the lower bound (the BPS scheme). Figure 10: BER versus SNR, \(p_{B}/\sigma_{w}^{2}\) for different values of \(i_{max}\); \(R=1/2\), \(p_{SI}/\sigma_{w}^{2}=30\) dB, \(\beta E=4\) symbols, and \(E=128\) symbols. Figure 11 compares the BERs of the semi-blind scheme JISB_DSICED3 and the conventional semi-blind without feedback scheme SB_DSICED3_W/OF versus the SNR, \(p_{B}/\sigma_{w}^{2}\), for different values of \(E\in\{32,64,128\}\) symbols, \(\beta E=4\) symbols, and \(p_{SI}/\sigma_{w}^{2}=30\) dB. It can be seen that, at a low SNR (\(\leq\)5 dB), the BER of the JISB_DSICED3 scheme was slightly lower than that of the SB_DSICED3_W/OF scheme regardless of the total number of transmitted symbols. However, at a high SNR (\(\geq\)5 dB), the semi-blind scheme JISB_DSICED3 showed its out-performance with faster convergence. This was due to the use of a minimum of four pilot symbols, which were added to the information sequence, for better performance in the semi-blind scheme. Last but not least, Figure 12 shows the BER performance versus different values of \(E\) symbols, where \(\beta E=4\) symbols. The result indicated that the semi-blind scheme JISB_DSICED3 had better performance than the conventional semi-blind without feedback scheme SB_DSICED3_W/OF, regardless of the total number of transmitted symbols and the SNR level. It also showed that when the number of symbols \(E\) and the value of SNR increased, the gaps between the two schemes were bigger, which was shown clearly when \(SNR=10\) dB. This was due to the advantage of having known pilot symbols and the feedback loops.