# Performance of Dense Wireless Networks in 5G and beyond Using Stochastic Geometry
## 1 Introduction  
The fifth-generation (5G) cellular network has been recently deployed with unprecedented communication performance, i.e., a 10-100 times higher data rate, 1 ms latency, and much higher area throughput [1; 2]. The upcoming sixth-generation (6G) cellular network promises to further improve current performance by at least one order of magnitude [3]. To meet such requirements, it is necessary to operate on multiple frontiers, e.g., increase the bandwidth, cell density, and transceiver efficiency. Current cellular networks operate at the sub-6 GHz band, which is heavily congested [3]. Recently, millimeter waves (mmW) and sub-THz frequencies (30-300 GHz) have enjoyed substantial interest due to the large unexploited spectrum [4; 5; 6]. However, propagation at these frequencies experiences higher path and penetration loss, making the links prone to blockage [7]. A solution to these challenges is to use a beam-type communication based on massive multiple-input multiple-output (mMIMO) systems and increase the cell density [8]. However, as the device density increases, interference emerges as one of the main challenges to be characterized and mitigated. The characterization of the aggregate interference power and coverage analysis in millimeter-wave (mmW) networks has been investigated in recent years but only in some specialized settings, under line-of-sight (LOS) and non-line-of-sight (NLOS) propagation. Among different models [9], \(\alpha\)-stable distribution has been widelyaccepted for modeling the aggregated interference power in a wireless network generated by PPP-distributed UEs [10; 11]. The heavy-tailed behavior has been validated experimentally in the context of the Internet of Things (IoT) [12; 13]. Generally, \(\alpha\)-stable distribution does not have a defined PDF model, except for specific cases. In [14], the exact PDF for some of the values of \(\alpha\) has been derived in the context of wireless communications. The \(\alpha\)-stable distribution when the interferers transmit in multiple sub-bands is studied in [15]. In all of these studies, the considered scenario is a PPP on a 2D plane. The case of PPP in a 3D volume has also been modeled as an \(\alpha\)-stable distribution in [10]. However, in cellular networks, the distribution of the UEs is not a homogeneous PPP in a 3D volume, but rather a PPP distribution of UEs on a 2D plane, where the AP is placed at an arbitrary height \(h\). When the height of the AP is considered, the heavy tail of the distribution becomes much shorter, similar to the interference power in cognitive radio networks, where the secondary UEs are not allowed to transmit when they are within the interference region [16; 17]. The impact analysis of the user's height was studied in Ref. [18]. The array's height \(h\) plays an important role that needs to be analyzed, namely, in view of the 5G mmW and 6G use cases. Therefore, it is necessary to extend the Stochastic Geometry (SG) framework to the 3D framework of antennas and user equipments (UEs) (see e.g., [19]). SG provides a preferred framework in network modeling to perform coverage and rate performance analysis [17; 20; 21; 22; 23]. The impact of the antennas' height in a 3D SG for ultra-dense networks proves an upper limit on network performance that depends on the path-loss model parameters [24]. Although the impact of the antenna and user equipment (UE) height difference has been studied [25], the existence of an optimum array height has not been deduced in dense networks. Here, we derive the analytical model of aggregated interference and show that the optimum array height depends on the path-loss model but also on the user's density, array type, and size. Similarly, the impact of the height on low-altitude aerial platforms [26; 27] and in unmanned aerial vehicles [28; 29] proves that there are optimum altitudes maximizing the coverage probability according to some specific scenarios.