## 5 Results and Discussion
Figure 12 exhibits the BER performance comparison for ATC-SM based on the CMI with different modulation schemes over the slow Rayleigh fading channel. The antenna configuration of Nr = Nt = 8 was adopted. Moreover, the information length was taken as K = 1024. The simulated results illustrate that the scheme in 16 QAM outperformed its counterpart in 32 QAM in terms of BER performance under identical conditions. Similarly, the configuration with 32 QAM was better than that of 64 QAM. This was due to the fact that high-order modulation was more sensitive against bit errors, thus causing system degradation, as compared with a lower order modulation. Figure 9: Bit error rate (BER) performance of the two-source ATCC-SM scheme under a non-ideal inter-user channel scenario and ATC-SM based on the CMI over the slow Rayleigh fading channel, K = 1024, 16 QAM, Nt = 8 and different numbers of receive antennas. Figure 13 shows the BER performance of the two-source ATCC-SM over 16 QAM based on the CMI and the random interleaver (RI) with K = 50, 100 and 1024 under a non-ideal inter-user channel scenario, i.e., \(\chi_{\text{S}_{1}\text{-S}_{2}}=~{}\chi_{\text{S}_{2}\text{-S}_{1}}=~{}5\) dB over the slow Rayleigh fading channel. The antenna configuration \(\text{N}_{\text{r}}=~{}\text{N}_{\text{t}}=~{}8\) was employed. The Monte Carlo simulated results clearly demonstrate that the system with the CMI offered a superior performance as compared to its counterpart with an RI at a whole SNR range over the same block length. This was based on the fact that the CMI effectively broke the short weight sequences by increasing the minimum free distance of the turbo codes. Furthermore, we can observe from Figure 13 that the gains of 0.5, 0.4, and 0.25 dB were obtained at BER \(\approx\) 10\({}^{-5}\) for K = 50, 100 and 1024 relative to the RI, respectively. This implies that the CMI can be used to effectively improve short packet communication scenarios, such as K \(<\) 200. In Figure 14, the BER performance of the two-source ATCC-SM over 16 QAM based on the CMI for \(\text{K}~{}=~{}512\), 1024, 2048 and 4096 under \(\chi_{\text{S}_{1}\text{-S}_{2}}=~{}\chi_{\text{S}_{2}\text{-S}_{1}}=~{}5\) dB through the slow Rayleigh fading channel are shown. The antenna configuration was taken as \(\text{N}_{\text{r}}=~{}\text{N}_{\text{t}}=~{}8\). The simulated results reveal that the system performance improved as the information length increased under identical conditions. Figure 10: BER performance of the two-source ATCC-SM scheme under a non-ideal inter-user channel scenario and ATC-SM based on the CMI over the slow Rayleigh fading channel, K = 1024, 32 QAM, \(\text{N}_{\text{t}}=~{}8\) and different numbers of receive antennas. Figure 11: BER performance of the two-source ATCC-SM scheme under a non-ideal inter-user channel scenario and ATC-SM based on the CMI over the slow Rayleigh fading channel, K = 1024, 64 QAM, N\({}_{t}=~{}8\) and different numbers of receive antennas. Figure 12: BER performance comparison of the ATC-SM scheme based on the CMI with different modulation schemes over the slow Rayleigh fading channel, K = 1024 and N\({}_{r}=~{}\text{N}_{t}=~{}8\). Figure 14: BER performance of two-source ATCC-SM based on the CMI under a non-ideal inter-user channel scenario over the slow Rayleigh fading channel, 16 QAM, \(\rm{N_{r}=N_{t}=8}\), and different information lengths such as K = 512, 1024, 2048 and 4096. Figure 13: BER performance of two-source ATCC-SM based on the CMI and the RI under a non-ideal inter-user channel scenario over the slow Rayleigh fading channel, 16 QAM, \(\rm{N_{r}=N_{t}=8}\), and information length such as K = 50, 100 and 1024.