# Performance of Dense Wireless Networks in 5G and beyond Using Stochastic Geometry
## 1 Introduction
In the literature, it is common to assume that the fading follows Rayleigh distribution (or at least the interference link has a Rayleigh distribution) or Nakagami-m distribution. The coverage probability has a tractable form as a Laplace function of the aggregate interference power (see, e.g., [17; 30; 31; 32]). However, for general fading, using the Laplace function of the aggregate interference is not possible anymore, and thus, the coverage and rate analysis cannot be expressed in a tractable way. To overcome this problem, in ref. [20], multiple techniques are introduced, including some methods to find the probability density function (PDF) of the aggregate interference calculated from the corresponding characteristic function (CF). In previous works, interference distribution for single antennas and the uniform linear array (ULA) (e.g., in [30]) configuration was investigated most. The contribution of this paper is the usage of the 3D SG framework in the uplink for homogeneous Poisson point process (PPP) with a density \(\lambda\) on a pseudo-3D geometry (sometimes referred to as 2.5D geometry [33; 34]) where UEs lie in a plane (say ground) and the access point (AP) with \(N_{c}\times N_{v}\) uniform cylindrical array (UcylA) (i.e., a set of \(N_{v}\) half-wavelength rings of \(N_{c}\) uniform circular array (UCA) antennas/each) has the height \(h\geq 0\). Figure 1 illustrates the setup for the computation of the properties of the aggregate interference from the ensemble of \(UE_{1},UE_{2},\ldots UE_{i},\ldots\) when the array at the AP is pointing toward the user of interest \(UE_{0}\). We show that by being able to characterize the aggregated interference, one can optimally adjust the configurations of the AP to increase the number of users served and, accordingly, the coverage probability. We analytically prove in Section 4 that the aggregated interference power onto an array of antennas located at an arbitrary height \((h)\) has a CF is decomposable into a mixture of two stable distributions (a skewed alpha-stable and a Gaussian distribution). The closed-form CF for \(h>0\) is another novelty to compute the PDF or cumulative density function (CDF) of the aggregated interference power, without cumbersome numerical integration. The scenario considered herein for users and interferers accounts for either LOS or NLOS propagation, and also the possibility of link blockage as is typical in mmW and sub-THz systems. The analytical model enables (Section 3.4) the evaluation of the trade-off in array height selection and the impact of the propagation scenarios. The UcylA with \(h>0\) generalizes the previous works on ULA configuration, which was investigated mostly using coverage analysis (see, e.g., [30; 35]). In array engineering, UcylA can be designed using multifaceted array in a far more practical way, and the results in [36] support the conclusion that any results for curved arrays apply to faceted ones. Based on the analytical model, the main results can be summarized as follows: (i) in most scenarios with small interferers' density, it is more beneficial to adopt a UCA rather than UcylA, while for large interferer density a UcylA would be preferred; (ii) there is an optimum AP height that depends on propagation and interferer density \(\lambda\); (iii) at AP height \(h=0\), the aggregated interference power is alpha-stable distributed, and for \(h\to\infty\), the limit becomes Gaussian, but for any arbitrary height \(h\), it is decomposable into two stable distributions; (iv) blockage probability impacts the service probability for small \(\lambda\), but less if counting the average number of users served within a region; (v) a connection with multiple paths (LOS and NLOS) is more beneficial for small \(\lambda\), as for large \(\lambda\), the interference is too large. This paper is organized as follows. We present the system model, including the signal and array gain models, in Section 2. The CF of the aggregate interference for UcylA in LOS links is described in Section 3.