## 2 System Model and Problem Formulation
\begin{table}
\begin{tabular}{c c} \hline \hline
**Variables** & **Definition** \\ \hline M-SN\({}_{mt}\) & the \(m\)-th M-SN \\ HP-SN\({}_{k}\) & the \(k\)-th HP-SN \\ LP-SN\({}_{l}\) & the \(l\)-th LP-SN \\ \(\mathbf{s}_{mt}\) & the transmit signal from macrocell sink node to M-SN\({}_{mt}\) \\ \(\mathbf{x}_{s}\) & the transmit signal from femtocell sink node \\ \(\mathbf{v}_{m}\) & the transmit beamforming vector from macrocell sink node aiming at M-SN\({}_{m}\) \\ \(\mathbf{w}_{k}\) & the transmit beamforming vector from femtocell sink node aiming at HP-SN\({}_{k}\) \\ \(s_{p,m},s_{s,k}\) & the information-bearing signal intended for M-SN\({}_{m}\) and HP-SN\({}_{k}\) \\ \(\mathbf{z}\) & the energy-carrying AN \\ \(\mathbf{g}_{m}\) & the channel between macrocell sink node and M-SN\({}_{m}\) \\ \(\mathbf{g}_{c,k}\) & the channel between macrocell sink node and HP-SN\({}_{k}\) \\ \(\mathbf{G}_{e,l}\) & the channel between macrocell sink node and LP-SN\({}_{l}\) \\ \(\mathbf{h}_{m}\) & the channel between femtocell sink node and M-SN\({}_{m}\) \\ \(\mathbf{h}_{c,k}\) & the channel between femtocell sink node and HP-SN\({}_{k}\) \\ \(\mathbf{H}_{e,l}\) & the channel between femtocell sink node and LP-SN\({}_{l}\) \\ \(n_{m},n_{c,k},n_{e,l}\) & the complex Gaussian noise at the M-SN\({}_{m}\), the HP-SN\({}_{k}\) and the LP-SN\({}_{l}\) \\ \(n_{a,k}\) & the additional noise introduced from the RF-to-signal conversion in the ID part at the HP-SN\({}_{k}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System Parameters  
Figure 2: Power splitting scheme in each HP-SN. Therefore, the received signal at the M-SN\({}_{m}\), the HP-SN\({}_{k}\), and the LP-SN\({}_{l}\) can be given by, respectively,  
\[y_{m} = \underbrace{\mathbf{g}_{m}^{H}\mathbf{v}_{m}s_{m}}_{\text{ desired signal}}+\underbrace{\mathbf{g}_{m}^{H}\sum_{i=1,i\
eq m}^{M}(\mathbf{v}_{i}s_{p,i})}_{ \text{intra-tier interference}}+\underbrace{\mathbf{h}_{m}^{H}(\sum_{k=1}^{K} \mathbf{w}_{k}s_{s,k}+\mathbf{z})}_{\text{inter-tier interference}}+n_{m},m=1,...,M,\] \[y_{c,k} = \underbrace{\mathbf{h}_{c,k}^{H}\mathbf{w}_{k}s_{s,k}}_{\text{ desired signal}}+\underbrace{\mathbf{h}_{c,k}^{H}\mathbf{z}+\mathbf{h}_{c,k}^{H}\sum_{i=1,i \
eq k}^{K}(\mathbf{w}_{i}s_{s,i})}_{\text{intra-tier interference}}+ \underbrace{\mathbf{g}_{c,k}^{H}\sum_{m=1}^{M}\mathbf{v}_{m}s_{m}}_{\text{ inter-tier interference}}+n_{c,k},k=1,...,K,\] \[\mathbf{y}_{c,l} = \underbrace{\mathbf{H}_{c,l}^{H}\mathbf{w}_{l}s_{s,l}}_{\text{ desired signal}}+\underbrace{\mathbf{H}_{c,l}^{H}\mathbf{z}+\mathbf{H}_{c,l}^{H}\sum_{i=1,i \
eq l}^{K}(\mathbf{w}_{i}s_{s,i})}_{\text{intra-tier interference}}+ \underbrace{\mathbf{G}_{c,l}^{H}\sum_{m=1}^{M}\mathbf{v}_{m}s_{m}}_{\text{ inter-tier interference}}+\mathbf{n}_{e,l},l=1,...,L,\]  
where \(\mathbf{g}_{m}\in\mathbb{C}\) and \(\mathbf{h}_{m}\in\mathbb{C}^{N_{S}}\) are denoted by the channel between macrocell sink node and M-SN\({}_{m}\) as well as that between femtocell sink node and M-SN\({}_{m}\), \(\mathbf{g}_{c,k}\in\mathbb{C}^{N_{p}\times N_{\mathbb{C}}}\) and \(\mathbf{h}_{c,k}\in\mathbb{C}^{N_{S}\times N_{\mathbb{C}}}\) indicate the channel vectors between macrocell sink node and HP-SN\({}_{k}\) as well as that between the femtocell sink node and the HP-SN\({}_{k}\), \(\mathbf{G}_{c,l}\in\mathbb{C}^{N_{p}\times N_{E}}\) and \(\mathbf{H}_{e,l}\in\mathbb{C}^{N_{S}\times N_{E}}\) are the channel vectors between the macrocell sink node and LP-SN\({}_{l}\) as well as that between the femtocell sink node and LP-SN\({}_{l}\), \(s_{m}\) is confidential information-bearing signal for M-SN\({}_{m}\) from the macrocell sink node satisfying \(\mathbb{E}\{s_{m}^{2}\}=1\). In addition, \(n_{m}\sim\mathcal{CN}(0,\sigma_{m}^{2})\), \(n_{a,k}\sim\mathcal{CN}(0,\sigma_{a,k}^{2})\) and \(\mathbf{n}_{e,l}\sim\mathcal{CN}(0,\sigma_{e,l}^{2}\mathbf{I})\) denote the complex AWGN at the M-SN\({}_{m}\), the HP-SN\({}_{k}\) and the LP-SN\({}_{l}\), respectively.