## 5 Results and Discussion  
The simulation results of ATC-SM, ATC-VBLAST, ATCC-SM and ATCC-VBLAST are discussed in this section. The slow Rayleigh fading channel was assumed for all the schemes. Two source nodes and a destination node were equipped with multiple antennas, and the two sources had an identical number of antennas. Monte Carlo simulations were executed in a MATLAB environment. Different numbers of receive antennas, modulation schemes, and various information lengths were chosen in different scenarios. During the simulation, all the schemes were required to achieve a very low BER such as \(10^{-6}\). Therefore, the running of all the simulations of the proposed schemes under different conditions needed to take some time. Furthermore, the execution times may have varied when using different computers to run the simulations. For a fair comparison, the log-MAP decoding algorithm was employed in all simulations. All the schemes adopted RSC encoders with the same generator polynomial \((11/13;15/13)\). The number of decoding iterations was four. The overall code rate at the destination node was the same, i.e., R = 1/3 between the non-cooperative and cooperative schemes. In the coded cooperative scheme, we supposed that S\({}_{2}\) was placed near to the destination than S\({}_{1}\) such that a 1 dB gain in SNR was given to S\({}_{2}\), i.e., \(\chi_{\text{S}_{2}-\text{D}}=\chi_{\text{S}_{1}-\text{D}}+1\). Moreover, a non-ideal inter-user channel was assumed for all coded-cooperative simulations. Figure 9 demonstrates the BER performance of the two-source ATCC-SM scheme under the non-ideal inter-user channel scenario and the ATC-SM scheme based on the CMI over the slow Rayleigh fading channel. 16 QAM was chosen as the modulation scheme. The number of antennas at the sources was N\({}_{\text{t}}=~{}8\), and the number of receive antennas at the destination was taken as N\({}_{\text{r}}=5\), 6, 7 and 8. Furthermore, the information length was taken as K = 1024 in the simulation. Through the simulated results, it can be evidently observed that the cooperative scheme outperformed its counterpart non-cooperative scheme under identical conditions. We assumed that the inter-user channel had a 5 dB gain, i.e., \(\chi_{\text{S}_{1}-\text{S}_{2}}=~{}\chi_{\text{S}_{2}-\text{S}_{1}}=~{}5\) dB. For the case of N\({}_{\text{r}}\)= 6, the proposed two-source ATCC-SM achieved a performance gain of about 0.5 dB at BER of \(10^{-6}\) over ATC-SM. The prominent performance improvement was made possible due to the deployment of the joint ATC decoder at the destination. In addition, the system performance improved as the number of the receive antennas increased. For the case of the eight receive antennas, both the ATC-SM and two-source ATCC-SM configurations were superior to that of the seven receive antennas in the whole SNR range, as depicted in Figure 9. The phenomenon can be explained by the fact that deploying more receive antennas yielded the additional spatial diversity gain in the MIMO system. To confirm the effectiveness of the cooperative system, we further investigated the BER performance of the proposed two-source ATCC-SM scheme under a non-ideal inter-user channel scenario and ATC-SM based on the CMI in 32 QAM and 64 QAM over the slow Rayleigh fading channel, as shown in Figures 10 and 11, respectively. The parameters K = 1024, Nt= 8 and different numbers of receive antennas, i.e., Nr = 5, 6, 7 and 8, were employed in the simulations. It was assumed that the link between two sources had an SNR of \(\chi_{\text{S}_{1}\text{-S}_{2}}=~{}\chi_{\text{S}_{2}\text{-S}_{1}}=~{}6\) dB and \(\chi_{\text{S}_{1}\text{-S}_{2}}=~{}\chi_{\text{S}_{2}\text{-S}_{1}}=~{}8\) dB for 32 QAM and 64 QAM, respectively. The simulated results demonstrate the superiority of the cooperative system as compared to the non-cooperative system. Furthermore, the BER performance obtained an obvious improvement with the increase of the number of receive antennas under identical conditions, as expected.