## 3 Two-Source Asymmetric Turbo-Coded Cooperative (ATCC) Scheme Based on CMI
### Two-Source Asymmetric Turbo-Coded Cooperative Spatial Modulation (ATCC-SM) Scheme Based on CMI  
This subsection describes the two-source ATCC-SM scheme with the CMI. The block diagram of the two-source ATCC-SM scheme is illustrated in Figure 6, where two sources employ a full duplex mode and can simultaneously transmit and receive data. The two-source ATCC-SM scheme needs to take two time slots to accomplish a complete transmission process. The solid and dashed lines with arrows represent the first and second time slots, respectively, as illustrated in Figure 6. During the first time slot, the input sequences \(\mathbf{q^{\prime}}_{1}\) and \(\mathbf{q^{\prime}}_{2}\) of length K at the source 1 (S\({}_{1}\)) node and the source 2 (S\({}_{2}\)) node are separately fed into the RSC-1 of the ATC encoder that generates the codeword \(\mathbf{v^{S_{1}}}\) and \(\mathbf{v^{S_{2}}}\) of length 2K. After that, the obtained \(\mathbf{v^{S_{1}}}\) and \(\mathbf{v^{S_{2}}}\) are given to SM to output the following vectors:  
\[\mathbf{v^{S_{1}}_{l_{1}r_{1}}}(\mathbf{m}_{1})\ =\ [0,\ \ldots,\ 0,\ \mathbf{v^{S_{1}}_{r_{1}}}( \mathbf{m}_{1})\,\ 0,\ \ldots,\ 0]^{\mathrm{T}},\ \ \ \ \mathbf{v^{S_{2}}_{l_{2}r_{2}}}(\mathbf{m}_{2})\ =\ [0,\ \ldots,\ 0,\ \mathbf{v^{S_{2}}_{r_{2}}}( \mathbf{m}_{2}),\ 0,\ldots,\ 0]^{\mathrm{T}} \tag{16}\]  
The operation of SM is discussed in Section 2.2 of this manuscript. The output vector \(\mathbf{v^{S_{1}}_{l_{1}r_{1}}}(\mathbf{m}_{1})\) is broadcasted to the S\({}_{2}\) and the destination node over the slow Rayleigh fading MIMO channel. Similarly, the vector \(\mathbf{v^{S_{2}}_{l_{2}r_{2}}}(\mathbf{m}_{2})\) is propagated to S\({}_{1}\) and the destination node over the slow Rayleigh fading MIMO channel. During the first time slot, S\({}_{2}\) and S\({}_{1}\) get the received vectors \(\mathbf{z_{S_{1},S_{2}}}(\mathbf{m}_{1})\) and \(\mathbf{z_{S_{2}S_{1}}}(\mathbf{m}_{1})\), which can be mathematically modeled as:  
\[\mathbf{z_{S_{1},S_{2}}}(\mathbf{m}_{1})=\ \mathbf{H_{S_{1},S_{2}}}\mathbf{v^{S_{1}}_{ l_{1}r_{1}}}(\mathbf{m}_{1})+\mathbf{n_{S_{1},S_{2}}}(\mathbf{m}_{1})=\ \mathbf{h^{I_{1}(m_{1})}_{S_{1},S_{2}}}\ \mathbf{v^{S_{1}}_{r_{1}}}(\mathbf{m}_{1})+\mathbf{n_{S_{1},S_{2}}}( \mathbf{m}_{1}), \tag{17}\]  
\[\mathbf{z_{S_{2}S_{1}}}(\mathbf{m}_{1})=\ \mathbf{H_{S_{2}S_{1}}}\mathbf{v^{S_{2}}_{ l_{2}r_{2}}}(\mathbf{m}_{1})+\mathbf{n_{S_{2}S_{1}}}(\mathbf{m}_{1})=\ \mathbf{h^{I_{2}(m_{1})}_{S_{2}S_{1}}}\mathbf{v^{S_{2}}_{r_{2}}}(\mathbf{m}_{1}) +\mathbf{n_{S_{2}S_{1}}}(\mathbf{m}_{1}) \tag{18}\]  
where \(\mathbf{H_{S_{1},S_{2}}}\) and \(\mathbf{H_{S_{2}S_{1}}}\) represent the channel matrices of S\({}_{1}\)-S\({}_{2}\), and S\({}_{2}\)-S\({}_{1}\), respectively. \(\mathbf{H_{S_{1},S_{2}}}\) and \(\mathbf{H_{S_{2},S_{1}}}\) are defined similarly to \(\mathbf{H}\) in Equation (13). \(\mathbf{h^{I_{1}(m_{1})}_{S_{1},S_{2}}}\) and \(\mathbf{h^{I_{2}(m_{1})}_{S_{2}S_{1}}}\) represent the I\({}_{1}\)(m\({}_{1}\))th and I\({}_{2}\)(m\({}_{1}\))th columns of \(\mathbf{H_{S_{1},S_{2}}}\) and \(\mathbf{H_{S_{2},S_{1}}}\), respectively, and they are defined similarly to \(\mathbf{h^{I(j)}}\) in Equation (13). The vectors \(\mathbf{n_{S_{1},S_{2}}}(\mathbf{m}_{1})\) and \(\mathbf{n_{S_{2},S_{1}}}(\mathbf{m}_{1})\) denote the complex additive Gaussian noise from S\({}_{1}\) to S\({}_{2}\). Figure 6: Two-source asymmetric turbo-coded cooperative (ATCC)-SM scheme with the CMI. \(S_{2}\), and from \(S_{2}\) to \(S_{1}\), respectively. Both of them are defined like \(\mathbf{n}(\mathrm{j})\) in Equation (13). Afterwards, the vectors \(\mathbf{z}_{S_{1}S_{2}}(\mathrm{m}_{1})\) and \(\mathbf{z}_{S_{2}S_{1}}(\mathrm{m}_{1})\) enter the SM demodulator of \(S_{2}\) and \(S_{1}\), respectively. As a result, the LLRs \(\gamma_{S_{1}S_{2}}(\mathbf{v}^{S_{1}})\) and \(\gamma_{S_{2}S_{1}}(\mathbf{v}^{S_{2}})\) are obtained and are further given to the RSC-1 decoder to get the estimations \(\hat{\mathbf{q}}_{1}^{\prime}\) and \(\hat{\mathbf{q}}_{2}^{\prime}\) during the second time slot.