# An Interference Cancellation Scheme for High Reliability Based on MIMO Systems
## 3 Proposed Scheme
\begin{array}{c}\delta_{\delta_{1}}(n-1)\\ \delta_{\delta_{2}}(n-1)\end{array} \right]}_{\text{IRI}}, \tag{16}\]  
where \(h_{\text{SR}_{1},ij}\) is a channel coefficient from the \(j\)-th transmit antenna at S to the \(i\)-th receive antenna at R\({}_{1}\) and \(h_{\text{R}_{2}\text{R}_{1},ij}\) is a channel coefficient from the \(j\)-th transmit antenna at R\({}_{2}\) to the \(i\)-th receive antenna at R\({}_{1}\). Using the property of Equation (13), Equation (16) is represented as follows,  
\[\left[ \begin{array}{c}y_{\text{R}_{1},1}(n)\\ y_{\text{R}_{1},2}(n)\end{array} \right]=\left[ \begin{array}{cc}h_{\text{SR}_{1 },11}+e^{-j\frac{2\pi k_{2}}{N}}h_{\text{SR}_{1},12}&h_{\text{R}_{2}\text{R}_{ 1},11}+e^{-j\frac{2\pi k_{2}}{N}}h_{\text{R}_{2}\text{R}_{1},12}\\ h_{\text{SR}_{1},21}+e^{-j\frac{2\pi k_{2}}{N}}h_{\text{SR}_{1},22}&h_{\text{R}_ {2}\text{R}_{1},21}+e^{-j\frac{2\pi k_{2}}{N}}h_{\text{R}_{2}\text{R}_{1},12} \end{array} \right]\left[ \begin{array}{c}\underbrace{x(n)}_{\text{Desired}}\\ \underbrace{\hat{x}(n-1)}_{\text{IRI}}\end{array} \right]. \tag{17}\]  
Likewise, received symbols at R\({}_{2}\) for an even \(n\) are as follows,  
\[\left[ \begin{array}{c}y_{\text{R}_{2},1}(n)\\ y_{\text{R}_{2},2}(n)\end{array} \right]=\underbrace{\left[ \begin{array}{cc}h_ {\text{SR}_{2},11}&h_{\text{SR}_{2},12}\\ h_{\text{SR}_{2},21}&h_{\text{SR}_{2},22}\end{array} \right]\left[ \begin{array} []{c}x_{\delta_{1}}(n)\\ x_{\delta_{2}}(n)\end{array} \right]}_{\text{Desired}}+\underbrace{\left[ \begin{array}{cc}h_{\text{R}_{1}\text{R}_{2},11}&h_{\text{R}_{1}\text{R}_{2}, 12}\\ h_{\text{R}_{1}\text{R}_{2},21}&h_{\text{R}_{1}\text{R}_{2},22}\end{array}  \right]\left[ \begin{array}{c}\hat{x}_{\delta_{1}}(n+1)\\ \hat{x}_{\delta_{2}}(n+1)\end{array} \right]}_{\text{IRI}}, \tag{18}\]  
where \(h_{\text{SR}_{2},ij}\) is a channel coefficient from the \(j\)-th transmit antenna at S to the \(i\)-th receive antenna at R\({}_{2}\) and \(h_{\text{R}_{1}\text{R}_{2},ij}\) is a channel coefficient from the \(j\)-th transmit antenna at R\({}_{1}\) to the \(i\)-th receive antenna at R\({}_{2}\). Like Equation (17), Equation (18) is represented as follows,  
\[\left[ \begin{array}{c}y_{\text{R}_{2},1}(n)\\ y_{\text{R}_{2},2}(n)\end{array} \right]=\left[ \begin{array}{cc}h_{\text{SR}_{2 },11}+e^{-j\frac{2\pi k_{2}}{N}}h_{\text{SR}_{2},12}&h_{\text{R}_{1}\text{R}_ {2},11}+e^{-j\frac{2\pi k_{2}}{N}}h_{\text{R}_{1}\text{R}_{2},12}\\ h_{\text{SR}_{2},21}+e^{-j\frac{2\pi k_{2}}{N}}h_{\text{SR}_{2},22}&h_{\text{R}_ {1}\text{R}_{2},21}+e^{-j\frac{2\pi k_{2}}{N}}h_{\text{R}_{1}\text{R}_{2},22} \end{array} \right]\left[ \begin{array}{c}\underbrace{x(n)}_{\text{Desired}}\\ \underbrace{\hat{x}(n+1)}_{\text{IRI}}\end{array} \right]. \tag{19}\]  
For obtaining desired symbols, the proposed scheme removes IRI and R\({}_{1}\) and R\({}_{2}\) using MIMO signal detection scheme. Among several signal detections, the proposed scheme uses low-complexity  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Time Slot** & & **S** & & **R\({}_{1}\)** & & **R\({}_{2}\)** \\ \hline \multirow{4}{*}{\(t=1\)} & Tx\({}_{1}\) & Tx\({}_{2}\) & Tx\({}_{1}\) & Tx\({}_{2}\) & Tx\({}_{1}\) & Tx\({}_{2}\) \\ \cline{2-6}  & Tx\({}_{1}\) & Tx\({}_{2}\) & Tx\({}_{1}\) & Tx\({}_{2}\) & Tx\({}_{1}\) & Tx\({}_{2}\) \\ \hline \multirow{2}{*}{\(t=2\)} & Tx\({}_{1}\) & Tx\({}_{1,\delta}\) & & & & \\  & (S \(\rightarrow\) R\({}_{1}\)) & (S \(\rightarrow\) R\({}_{1}\)) & (S \(\rightarrow\) R\({}_{1}\)) & & & \\ \hline \multirow{2}{*}{\(t=3\)} & Tx\({}_{2}\) & Tx\({}_{2,\delta}\) & Tx\({}_{1}\) & Tx\({}_{1,\delta}\) & & & \\  & (S \(\rightarrow\) R\({}_{2}\)) & (S \(\rightarrow\) R\({}_{2}\)) & (S \(\rightarrow\) R\({}_{2}\)) & (R\({}_{1}\rightarrow\) D\({}_{2}\)) & (R\({}_{1}\rightarrow\) D\({}_{2}\)) & & \\ \hlineQRD-\(M\) which has optimal error performance. The QRD-\(M\) is reduced complexity of the ML.