**1. Introduction**

The opportunities offered by unmanned aerial vehicles (UAVs) in a wide variety of fields have led to a dramatic increase in their production and deployment. Initially utilized in the military, UAVs today are applied in many fields including communications networks [1]. Specifically, UAVs can be used in wireless communications systems to reliably support connectivity in disaster management, public safety, and rescue operations [2–4].

The support of UAVs as a new network user in fifth generation (5G) systems opens up new opportunities related to the organization of services such as delivery, security surveillance, mapping navigation, and many others [5–7]. Furthermore, UAVs can be utilized by the network operator as repeaters and mobile base stations (BS). However, UAVs are characterized by the new unique properties compared to classic users (higher

**Citation:** Begishev, V.; Moltchanov, D.; Gaidamaka, A.; Samouylov, K. Closed-Form UAV Blockage Probability in Ground- and Rooftop-Mounted Urban mmWave NR Deployments. *Sensors* **2022**, *22*, 977. https://doi.org/10.3390/ s22030977

Academic Editor: Alberto Gotta

Received: 27 December 2021 Accepted: 25 January 2022 Published: 27 January 2022

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speed, higher position relative to the ground, etc.) and thus require new mechanisms to support them in 5G systems.

Many factors such as selected frequency range, line-of-sight (LoS) range, and signal attenuation play an important role in UAV communications. The work within 3GPP related to integration of UAV to 5G systems started with 3GPP SP-180909 (see Section 2 for a detailed overview of 3GPP standardization efforts) outlining requirements for communication delay, rate, and reliability as key performance indicators (KPI), for UAV applications. For example, security surveillance requires very high data rates in the downlink for airto-ground communications [8]. Services such as private property monitoring, flying BSs, and mobile integrated access and backhaul (IAB) nodes also require high bandwidth at the air interface [9]. It is worth noting that some missions cannot be completed by one UAV. In such cases, a swarm of UAVs are needed, resulting in additional communications overheads [10]. Specifically, as a result of the movement of UAVs, the structure of the swarm may change dynamically, requiring regular updates.

Based on the abovementioned application requirements, UAVs need to be supported by all radio access technologies (RAT) within 5G systems. Within the range of technologies, the most challenging is the support of UAVs in the millimeter wave (mmWave) bands [11]. The rationale is that this band is highly susceptible to a blockage by buildings. A feasible solution to this problem would be to support the multi-connectivity functionality standardized for 5G NR systems [12]. According to it, when blockage occurs, it is possible to switch to another BS that is currently non-blocked. This technique has been shown to drastically improve performance of conventional terrestrial users, see, e.g., [13,14]. To assess the coverage of 5G mmWave NR deployments with multiconectivity functionality for UAV users, simple and accurate line-of-sight (LoS) blockage models are thus required [15].

The conventional approach to analyzing the coverage/outage phenomenon in the presence of blockage is to utilize the tools of stochastic geometry, see, e.g., [16–18] among others for human body blockage models. The core of the analysis is to estimate the probability that a LoS path between user equipment (UE) and BS is not blocked by obstacles having a certain shape. The major step is thus to determine the number of blockers falling to the so-called LoS blockage zone, see [19] for details. The approach has proved itself as a versatile tool for analysis of human blockage in mmWave systems with purely random deployments of blockers, where the dimensions of obstacles are negligible compared to the length of the path between communicating entities.

Analyzing regular deployments, where dimensions of the obstacles are not negligible as compared to the LoS path between the communicating entities, the described approach results in a number of inherent limitations. In particular, the probability that a LoS path is blocked by an obstacle depending on relative positions of obstacles with respect to each other leading to complex expressions for coverage/outage probabilities that cannot be provided in closed-form. When dealing with such deployments the results are often provided in product form either having infinite sums [20] or involving integration [21]. An alternative approach is to utilize field measurements of LoS blockage, see, e.g., [22]. The latter approach is mainly dictated by the simplicity of the final expression but is limited to those conditions where the measurements data have been gathered. Thus, there is a need for a model providing simple closed-form approximation for UAV LoS blockage probability accounting for both system and environment characteristics.

In this paper, we will target the abovementioned two challenges. Specifically, we first provide closed-form approximation for LoS blockage probability of UAVs in urban terrestrial deployments of mmWave systems. To this end, we utilize the tools of integral geometry rather than stochastic geometry. Then, we proceed to apply the proposed methodology to estimate the UAV LoS blockage probability in the rooftop deployment of BSs. The proposed approach allows for the providing of UAV LoS probability in closedform in grounded, rooftop, and mixed grounded-rooftop deployments as a function of environmental characteristics.

Our main contributions can be summarized as follows:


The rest of the paper is organized as follows. First, we overview recent efforts in the analysis of UAV blockage probability in Section 2. The system model utilized in our study is introduced in Section 3. UAV LoS blockage probability for grounded and rooftop deployments is derived in Section 4. Numerical results are provided in Section 5. Conclusions are provided in the last section.
