## 5 Conclusions
### Notations  
The following notations are used in this manuscript:  
\[\begin{array}{ll}N&N\geq 1\\ R_{1},R_{2}&\\ d_{R_{1}},d_{R_{2}}&\\ \mathcal{R}&\mathcal{R}=\{R_{1},R_{2}\}\\ D_{n}&n\in N\\ d_{n}&n\in N\\ v_{n}&n\in N\\ A_{0},A_{1},A_{2}&A_{0}>1,A_{1}>1,A_{2}>1\\ \omega&\\ \mathbf{H_{0}},\mathbf{G_{0}}&\\ h_{0}^{(a_{0},a_{1})},\delta_{0}^{(a_{0},a_{1})}&a_{0}\in A_{0},a_{1}\in A_{1} \\ \mathbf{H_{n}},\mathbf{G_{n}}&\\ \theta&\theta=\{odd,even\}\\ T^{(\theta)}&\theta=\{odd,even\}\\ h_{n}^{(a_{0},a_{1})},\delta_{n}^{(a_{0},a_{1})}&n\in N,a_{0}\in A_{0},a_{1} \in A_{1}\\ T_{1}^{(\theta)},T_{2}^{(\theta)}&\\ \lambda&0\leq\lambda\leq 1\\ \eta&0\leq\eta\leq 1\\ P_{\mathcal{S}},P_{\mathcal{R}}&\\ \rho_{\mathcal{S}}\rho_{\mathcal{R}}&\\ a_{i}&i\in N,\sum\limits_{i}a_{i}=1,\alpha_{1}<\ldots<\alpha_{N}\\ x_{i}&i\in N\\ n_{\mathcal{R}},n_{\mathcal{R}}&n\in N\\ \Upsilon_{\mathcal{R}}^{(\pi\theta)}&\theta=\{odd,even\},\,\mathcal{R}=\{R_{1 },R_{2}\}\\ \Upsilon_{\mathcal{R}}^{(\pi\theta)}&\theta=\{odd,even\},\,n\in N\\ R_{i}^{*}&i\in N\\ \Upsilon_{i}^{(\pi\theta)}&i\in N\\ \Upsilon_{i}^{(\pi\theta)}&i\in N\\ \Upsilon_{i}^{(\pi\theta)}&i\in N\\ \Upsilon_{i}^{(\pi\theta)}&i\in N\\ \Upsilon_{i}^{(\pi\theta)}&i\in N\\ \Upsilon_{i}^{(\pi\theta)}&\theta=\{odd,even\},\,\mathcal{R}=\{R_{1},R_{2}\},i\in N\\ \Upsilon_{i}^{(\pi\theta)}&\theta=\{odd,even\},\,\mathcal{R}=\{R_{1},R_{2}\},i\in N\\ \Upsilon_{i}^{(\pi\theta)}&\theta=\{odd,even\},\,n\in N,i\in n\\ \Upsilon_{i}^{(\pi\theta)}&\theta=\{odd,even\},\,\mathcal{R}=\{R_{1},R_{2} \},i\in N\\ \Upsilon_{i}^{(\pi\theta)}&\theta=\{odd,even\},\,n\in N,i\in n\\ \Upsilon_{i}^{(\pi\theta)}&\theta=\{odd,even\},\,\mathcal{R}=\{R_{1},R_{2} \}\\ OP_{\mathcal{R}}^{(\pi\theta)}&\theta=\{odd,even\},\,n\in N\\ TP^{(\theta)}&\theta=\{odd,even\}\\ EE^{(\theta)}&\theta=\{odd,even\}\\ \end{array}\]  
Number of devices  
Coupled relays  
Distances from BS to relays  
Set of relays  
Deviates from relay \(R_{1}\) to devices  
Distances from relay \(R_{2}\) to devices  
Distances from relay \(R_{1}\) to devices  
Distances from relay \(R_{2}\) to devices  
Distances from relay \(R_{1}\) to devices  
Distances from relay \(R_{1}\) and \(R_{2}\) to devices
From PDF expressions [23] (Equations (59) and (60)), we obtain  
\[\begin{split}&\begin{split} L_{\begin{subarray}{c}\text{$T_{1}^{( \rho)}$}\\ \text{$R$}-x_{i}\\ i=\{\text{$N$},...,\text{$1$}\}\end{subarray}}^{\text{$A_{0}$}}=\prod_{a_{0} =1}^{A_{0}}\prod_{a_{1}=1}^{A_{1}}\int\limits_{0}^{\frac{\gamma_{i}^{*}}{(1- \lambda)\beta_{i}\rho_{S}}}\frac{\exp(-x/\sigma_{\mathcal{R}}^{2})}{\sigma_{ \mathcal{R}}^{2}}dx\underbrace{\prod_{k=N}^{i+1}\prod_{a_{0}}^{A_{1}}\prod_{a_ {1}}^{A_{1}}\int\limits_{\frac{\gamma_{k}^{*}}{(1-\lambda)\beta_{k}\rho_{S}}} ^{\infty}\frac{\exp(-y/\sigma_{\mathcal{R}}^{2})}{\sigma_{\mathcal{R}}^{2}}dy }_{i<N}\\ &=\prod_{a_{0}=1}^{A_{0}}\prod_{a_{1}=1}^{A_{1}}\left(1-\exp\left( -\frac{\gamma_{i}^{*}}{(1-\lambda)\beta_{i}\rho_{S}\sigma_{\mathcal{R}}^{2}} \right)\right)\underbrace{\prod_{k=N}^{i+1}\left(1-\prod_{a_{0}}^{A_{0}}\prod_{ a_{1}}^{A_{1}}\left(1-\exp\left(-\frac{\gamma_{k}^{*}}{(1-\lambda)\beta_{k}\rho_{S} \sigma_{\mathcal{R}}^{2}}\right)\right)\right)}_{i<N}.\end{split}\] (A3)  
By substituting (A3) into (30), we obtain the expression of OP at coupled relays \(\mathcal{R}\), as shown in (31).  
From (34), we obtain  
\[Q_{i}=\Pr\Biggl{\{}\max_{[A_{0}\times A_{1}]}\Biggl{\{}\mathbf{R}_{\mathcal{R} -x_{i}}^{\left(\tau_{1}^{(\rho)}\right)}\Biggr{\}}\geq R_{i}^{*}\Biggr{\}}= \Pr\Biggl{\{}\max_{[A_{0}\times A_{1}]}\Biggl{\{}\gamma_{\mathcal{R}-x_{i}}^{ \left(\tau_{1}^{(\rho)}\right)}\Biggr{\}}\geq\gamma_{i}^{*}\Biggr{\}}.\] (A4)