# Coverage and Rate Analysis for Location-Aware Cross-Tier Cooperation in Two-Tier HetNets
## 2 System Model
### Location-Aware Cross-Tier Cooperation Scheme
Note that the prescribed value \(D\) is decided by the MBSs. In the current operation of cellular networks, a user will periodically feed back the measurement reports, including the user's location information, to its serving BS for assisting the serving BS selection procedure [35]. Thus the MBSs classify the users as MIUs and MEUs through this procedure. Meanwhile, the FBSs use the pilot signals combined with a positive cooperation threshold to convince the vulnerable users to connect to both tiers of the BSs. The BSs use backhaul links (e.g., digital subscriber line (DSL)) [3; 36] to exchange/share the users' data and the control information, namely, the prescribed value \(D\) and the cooperation threshold. It is assumed that the users are stationary in this paper, that is, handoffs (HOs) do not occur for the BSs. This assumption is widely adopted in the extensive literature. When taking the mobility of users into account, the HO procedure will occur between different BSs such that different user association schemes are adopted. However, the high mobility users, such as users driving cars on the highways or taking high-speed trains, will have higher HO interruptions, which will degrade the network performance. To mitigate the HO effect, a location-aware HO skipping scheme for the macro tier can be adopted, which is similar to the scheme proposed in [37]. Additionally, our proposed LA-CTC scheme should be revised. In detail, it is assumed that the trajectory within the target MBS footprint is a priori via some trajectory estimation techniques [38; 39]. Thus the HO skips associating to the target MBS if the user trajectory passes through the outer region of its target MBS; that is, when the minimum distance between the user trajectory and its target MBS exceeds the same predefined threshold value \(D\), the HO occurs. However, the high-mobility users will skip HOs to the entire femto tier to avoid the excessive HOs because the FBS coverage area is too small [40]. The high-mobility users will be served directly by their un-skipped MBSs which are their trajectories pass through the inner region of the target MBSs. We let \(\mathcal{Q}_{M,in}\), \(\mathcal{Q}_{M,out}\), \(\mathcal{Q}_{F}\) and \(\mathcal{Q}_{C}\) denote the probabilities that a typical user belongs to each of the above four disjoint user sets, respectively. Mathematically, this is \(\mathcal{Q}_{l}=\mathbb{P}\left(u\in\ U_{l}\right)\), where \(l\in\{M,in;\ M,out;\ F;\ C\}\). On the basis of the ergodicity of the PPP, these probabilities are derived in the following lemma. **Lemma 1**. : \(\mathcal{Q}_{M,in}\)_, \(\mathcal{Q}_{M,out}\), \(\mathcal{Q}_{F}\) and \(\mathcal{Q}_{C}\) are given as follows:_  
\[\mathcal{Q}_{M,in}=1-\exp\left(-\pi\lambda_{1}D^{2}\right) \tag{3}\]  
\[\mathcal{Q}_{M,out}\approx 2\pi\lambda_{1}\int_{D}^{\infty}r\exp\left(-\pi \left(\lambda_{1}r^{2}+\lambda_{2}\left(\frac{\beta P_{2}}{P_{1}}\right)^{2/ \alpha_{2}}r^{2\alpha_{1}/\alpha_{2}}\right)\right)dr \tag{4}\]  
\[\mathcal{Q}_{F}\approx\exp\left(-\pi\lambda_{1}D^{2}\right)-2\pi\lambda_{1} \int_{D}^{\infty}r\exp\left(-\pi\left(\lambda_{1}r^{2}+\lambda_{2}\left(\frac {P_{2}}{P_{1}}\right)^{2/\alpha_{2}}r^{2\alpha_{1}/\alpha_{2}}\right)\right)dr \tag{5}\]  
\[\mathcal{Q}_{C}=\exp\left(-\pi\lambda_{1}D^{2}\right)-\mathcal{Q}_{M,out}- \mathcal{Q}_{F} \tag{6}\]  
_If the path loss exponents are equal, that is, \(\alpha_{i}\equiv\alpha\), \(\mathcal{Q}_{M,out}\), then \(\mathcal{Q}_{F}\) can be reduced to a closed-form expression as:_  
\[\mathcal{Q}_{M,out}\approx\left(\lambda_{1}/\lambda_{1}^{\prime}\right)\exp \left(-\pi\lambda_{1}^{\prime}D^{2}\right) \tag{7}\]  
\[\mathcal{Q}_{F}\approx\exp\left(-\pi\lambda_{1}D^{2}\right)-\left(\lambda_{1} /\lambda_{1}^{\prime\prime}\right)\exp\left(-\pi\lambda_{1}^{\prime\prime}D ^{2}\right) \tag{8}\]  
Figure 1: Illustration of the proposed location-aware cross-tier cooperation (LA-CTC) scheme.