# Coverage and Rate Analysis for Location-Aware Cross-Tier Cooperation in Two-Tier HetNets
## 1 Introduction
### Related Work  
Lately, the modeling of the increasing irregularity in BS locations as a Poisson point process (PPP) and the utilizing of stochastic geometry to study HetNets have been used extensively. The pioneering works in [10; 11] have shown that the PPP model is tractable, yet accurate for providing important performance metrics for cellular networks in terms of coverage and rate. The key performance metrics such as the coverage probability and the average rate are essential for characterizing the performance of a HetNet, which has been well investigated in the literature [10; 11; 12; 13]. For example, the effect of typical frequency reuse on the coverage and the rate for conventional single-tier networks was discussed in [10]. The baseline model in [10] was further extended to a general \(K\)-tier case of a downlink HetNet, and its coverage and rate were also analyzed in [11]. Furthermore, the coverage and rate analyses for a typical user with different path-loss exponents in the HetNet, taking into account more practical propagation environments, were modeled and analyzed in [12; 13]. The authors in [12] investigated the impact of the dual-slope path loss on the coverage probability and capacity of mmWave networks. In [13], the authors considered various indoor and outdoor propagation environments for a HetNet, and a heuristic algorithm for the power allocation at the tiered cells was also developed. In addition, this random spatial model in [11] has been further extended to many scenarios of interest for HetNets, such as user association [14; 15; 16], fractional frequency reuse [17; 18], CoMP transmission [19; 20; 21; 22; 23], and so on. As mentioned above, the gains from load balancing through CRE user association should be guaranteed by suitable enhanced inter-cell interference coordination (eICIC) techniques [24]. The CRE, in conjunction with suitable eICIC techniques, has been presented in previous works, such as for resource partitioning [25; 26], fractional frequency reuse [27] and reduced power subframes [28]. However, the CRE with CoMP transmission is not yet well captured. The CoMP transmission is of great importance to HetNets, which have been extensively studied in the literature. Accordingly, [19; 20; 21; 22; 23] extended the PPP model to capture the performance of the HetNets by deploying CoMP transmission. The authors in [19] analyzed the coverage probability for CoMP transmission in HetNets, for which the set of cooperating BSs was determined. The impact of the overhead delay introduced by CoMP transmission on the performance of HetNets was studied in [20]. In [21], the authors focused on a pairwise BS cooperation scheme based on a user's first and second closest geographic BSs. The coherent joint-transmission with limited information exchange between BSs through Willems' encoding was considered. Moreover, the dirty paper coding (DPC) orthogonal transmission was also adopted to tackle the intra-cell interference for the cooperating pair. The authors in [22] presented a tractable model for analyzing non-coherent joint-transmission BS cooperation under user-centric BS clustering and channel-dependent cooperation activation. Further, the authors in [23] proposed a location-aware cross-tier BS cooperation scheme, and evaluated the performance in terms of the outage probability and the achievable average rate. The proposed scheme in [23] outperforms both the conventional MRP and CRE. In [29], the authors considered the overlapping expanded region (ER) of the microcells for employing CoMP joint transmission. The authors in [30] investigated the cross-tier BS cooperation in HetNets for which the locations of PBSs were modelled as a Neyman-Scott cluster process. An edge-aware cross-tier BS cooperation scheme for the cell-edge hotspot users was proposed. In [31], the authors proposed a cross-tier BS cooperation scheme to improve the coverage performance of MEUs in non-uniform HetNets, which has also been investigated in [32], considering that the small cells are deployed farther away from the MBSs.