## 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
It is worth mentioning that SM demodulator is made up of an SM demapper, a bit combiner and bit ungrouping blocks. Through the CMI, the generated estimations \(\hat{\mathbf{q}}_{1}^{\prime}\) and \(\hat{\mathbf{q}}_{2}^{\prime}\) are interleaved as \(\hat{\mathbf{q}}_{1}^{\prime\mathrm{1}}\) and \(\hat{\mathbf{q}}_{2}^{\prime\mathrm{1}}\), respectively, which are re-encoded into codewords \(\overline{\mathbf{v}}^{S_{2}}\) and \(\overline{\mathbf{v}}^{S_{1}}\) by the RSC-2 encoder. Here, only the length \(K\) parity sequences \(\overline{\mathbf{v}}^{S_{2}}\) and \(\overline{\mathbf{v}}^{S_{1}}\) of \(\overline{\mathbf{v}}^{S_{2}}\) and \(\overline{\mathbf{v}}^{S_{1}}\) are employed by SM to produce vectors: \(\overline{\mathbf{v}}^{S_{2}}_{\overline{1}_{\overline{1}_{\overline{1}_{ \overline{1}}}}}(\mathrm{m}_{1}^{\prime})=\left[0,\,\ldots,\,0,\,\overline{ \mathbf{v}}^{S_{2}}_{\overline{1}_{\overline{2}}}(\mathrm{m}_{1}^{\prime}),\,0, \ldots,\,0\right]^{\mathrm{T}}\) and \(\overline{\mathbf{v}}^{S_{1}}_{\overline{1}_{\overline{1}_{\overline{1}}}}( \mathrm{m}_{2}^{\prime})=\left[0,\,\ldots,\,0,\,\overline{\mathbf{v}}^{S_{1}}_{ \overline{1}_{\overline{1}}}(\mathrm{m}_{2}^{\prime}),\,0,\,\ldots,\,0\right]^ {\mathrm{T}}\), respectively, sent to the corresponding destination node over the slow Rayleigh fading MIMO channel, where \(\overline{\mathbf{v}}^{S_{2}}_{\overline{2}}(\mathrm{m}_{1}^{\prime})\) and \(\overline{\mathbf{v}}^{S_{1}}_{\overline{1}}(\mathrm{m}_{1}^{\prime})\) with normalized transmission powers are in the \(\overline{\mathrm{I}}_{2}(\mathrm{m}_{2}^{\prime})\)th and \(\overline{\mathrm{I}}_{2}(\mathrm{m}_{2}^{\prime})\)th positions, with \(\overline{\mathrm{r}}_{2}\), \(\overline{\mathrm{r}}_{2}\in\left\{1,\,2,\ldots,\mathrm{M}\right\}\), \(\overline{\mathrm{I}}_{2}(\mathrm{m}_{1}^{\prime})\), \(\overline{\mathrm{I}}_{1}(\mathrm{m}_{2}^{\prime})\in\left\{1,\,2,\ldots, \mathrm{N}_{\mathrm{T}}\right\}\), \(\mathrm{m}_{1}^{\prime}\in\left\{1,\,2,\,3,\ldots,\,K/d_{1}^{\prime}\right\}\) and \(\mathrm{m}_{2}^{\prime}\in\left\{1,\,2,\,3,\ldots,\,K/d_{2}^{\prime}\right\}\) for \(d_{1}^{\prime}=\,d_{2}^{\prime}\) and \(\mathrm{m}_{1}^{\prime}=\,m_{2}^{\prime}\). During the first time slot, the destination accepts the vectors \(\mathbf{z}_{S_{1}D}(\mathrm{m}_{1})\) and \(\mathbf{z}_{S_{2}D}(\mathrm{m}_{1})\). Moreover, the destination also gets \(\overline{\mathbf{z}}_{S_{1}D}(\mathrm{m}_{1}^{\prime})\) and \(\overline{\mathbf{z}}_{S_{2}D}(\mathrm{m}_{1}^{\prime})\) during the second time slot. The received vectors at the destination can be mathematically modeled as  
\[\mathbf{z}_{S_{1}D}(\mathrm{m}_{1})= \ \mathbf{H}_{S_{1}D}\mathbf{v}^{S_{1}}_{\overline{1}  
requires two time slots to complete transmission. The solid and dashed lines with arrows indicate the first and the second time slots, respectively.  
At the \(\mathsf{S_{1}}\) node, the input sequence \(\mathbf{a^{\prime}_{1}}\) of length \(\mathsf{K}\) is firstly converted by \(\mathsf{S/P}\) conversion into length \(\mathsf{K}/\mathsf{N_{T}}\) parallel sequences \(\mathbf{a^{\prime}_{1}}\), \(\mathbf{a^{\prime}_{1}}^{2}\),..., and \(\mathbf{a^{\prime}_{1}}^{N_{\mathrm{T}}}\) in the first time slot. The resulting sequence is passed to RSC-1 encoder and the M-PSK/QAM modulator that produces the modulated sequences \(\mathbf{v^{S_{1}}_{1,\mathrm{m}}}\), \(\mathbf{v^{S_{1}}_{2,\mathrm{m}^{\prime}}}\),..., and \(\mathbf{v^{S_{1}}_{N_{\mathrm{T}},\mathrm{m}}}\) with dimension \(1\times\mathrm{L_{1}}\). The following transmission matrix  
\[\mathbf{V^{S_{1}}_{m}}=\bigg{[}\big{(}\mathbf{v^{S_{1}}_{1,m}}\big{)}^{ \mathsf{T}},\,(\mathbf{v^{S_{1}}_{2,m}}\big{)}^{\mathsf{T}},\,\ldots,\,( \mathbf{v^{S_{1}}_{N_{\mathrm{T}},m}})^{\mathsf{T}}\bigg{]}^{\mathsf{T}}, \tag{23}\]  
which consists of the modulated sequences, is broadcasted to \(\mathsf{S_{2}}\) and the destination node through the slow Rayleigh fading MIMO channel.