**5. Numerical Results**

In this section, we first assess the accuracy of the model identifying its application range, and then proceed to report on the impact of system parameters on the UAV blockage probability. Finally, we evaluate the effect of rooftop-mounted BSs. The values of input system parameters are provided in Table 1.

**Table 1.** Summary of notation and parameters.


## *5.1. Accuracy Assessment*

To identify the application range of the developed closed-form approximation, we start assessing the accuracy of the model by comparing its results to those obtained using the computer simulations. To this end, Figure 4 shows the UAV LoS blockage probability obtained using the proposed model and computer simulations for various UAV altitudes and BS heights *hU* and *hA*, respectively, street width *l* = 20 m, mean building height and standard deviation *E*[*HB*] = 30 m and *σ*[*HB*] = 10 m, block width and length of

*bw* = *bl* = 100 m. The considered region of interest is formed by considering 10 horizontal and vertical building blocks interchanged with streets.

**Figure 4.** Comparison of the developed model and computer simulations.

By analyzing the results shown in Figure 4, one may deduce that the proposed model allows for the approximation of the results obtained via computer simulations quite closely. Similar observations have been made for rooftop-mounted mmWave BSs. Notably, the developed model slightly overestimates the actual value of the probability. This is explained by the inherent structure of the model that assumes that all the LoS visibility regions are completely independent. This observation allows us to identify the applicability regions of the model. First of all, observe that due to the abovementioned property the model always provides the upper bound on the UAV LoS blockage probability. Secondly, the results become more accurate as of the area of the zone and/or the density of the mmWave BSs increase. Based on these results, when discussing the response of the UAV blockage probability to system parameters and assessing the effect of rooftop-mounted mmWave BSs, we thus utilize the developed model.

#### *5.2. Effects of System Parameters*

We now proceed to evaluating the effect of system parameters on the UAV blockage probability including the BS height and altitude of UAV, the mean and variance of building height and, finally, the street width and building block's width and length.

We start with an assessment of the effects of mmWave height and UAV flying altitude. To this aim, Figure 5 shows UAV LoS blockage probability as a function of these parameters for street width *l* = 20 m, mean building height and standard deviation *E*[*HB*] = 30 m and *σ*[*HB*] = 10 m, block width and length of *bw* = *bl* = 100 m. By analyzing the presented results, we see that higher BS heights result in lower UAV LoS blockage probability, see Figure 5a. Particularly, the gain of changing mmWave BS height from 5 m to just 15 m leads to the decrease of UAV LoS blockage probability by approximately 0.15 for 20 mmWave BS deployed in the area. The rationale for these improvements is that higher mmWave BS heights make the visible regions at the UAV flying altitude larger, see Figure 2. Furthermore, this effect is non-linear as the area increases faster when the mmWave BS height increases. We also note that these gains depend heavily on BS deployment density and are minimal highly dense deployments.

Analyzing the effect of UAV flying altitude in Figure 5b, qualitatively similar conclusions can be made. More specifically, the higher the altitude the smaller the UAV LoS blockage probability. Specifically, for the density of 20 mmWave BS in the considered area, the gain of changing the altitude from 100 to 200 m is approximately 0.15 and is comparable to that of the change in BS height from 5 to 15 m. We also note that in practice this parameter should be tuned with care. The reason is that higher altitudes may lead to much lower

received power, especially for ground-mounted mmWave BS that is usually downtilted to provide better coverage for terrestrial users, e.g., pedestrians.

**Figure 5.** UAV blockage probability as a function of BS height and UAV altitude. (**a**) Various BS heights; (**b**) Various UAV altitudes.

In dense city deployments of mmWave BS, the characteristics of building block height may produce a significant impact on UAV LoS blockage probability. We investigate this hypothesis in Figure 6, where we illustrate the UAV LoS blockage probability as a function of the number of deployed mmWave BS for UAV altitude *hU* = 150 m, BS height *hA* = 5 m, street width *l* = 20 m, block width and length of *bw* = *bl* = 100 m. Here, in Figure 6a we show the effect of different mean values by keeping the standard deviation constant at *σ*[*HB*] = 10, while in Figure 6b we vary standard deviation and keep the mean constant at *E*[*HB*] = 30 m.

**Figure 6.** UAV blockage probability as a function of building block height parameters. (**a**) Various mean heights; (**b**) Various standard deviations.

By analyzing the presented data, we may conclude that the mean building height logically produces a significant effect on the UAV LoS blockage probability. The magnitude of this effect is comparable to that of BS height or UAV altitude. Particularly, when considering districts with high building heights, e.g., city centers, one needs to utilize additional ways to improve UAV LoS blockage probability. However, at the same time, the effect of standard deviation is rather limited, leading to differences in the range of 0.05–0.1 for the considered range of the number of deployed mmWave BS.

Finally, we consider the effect of street and building block widths on UAV LoS blockage probability illustrated in Figure 7 for UAV altitude *hU* = 150 m, BS height *hA* = 5 m, mean building height and standard deviation *E*[*HB*] = 30 m and *σ*[*HB*] = 10 m, respectively, block width and length of *bw* = *bl* = 100 m. As one may observe, both parameters

drastically affect the considered metric of interest. However, the effects are different. Specifically, by increasing the street width the UAV LoS blockage probability drastically increases, see Figure 7a. The rationale is that this leads to much larger areas of LoS visibility zones, see Figure 2. At the same time, one may observe that by increasing the street and building block widths, the considered area increases as the number of streets and building blocks in both horizontal and vertical directions are kept constant. Thus, logically, larger building blocks dimensions lead to higher UAV LoS blockage probability, see Figure 7b. Nevertheless, this effect is attributed to the increase of the considered area.

**Figure 7.** UAV blockage probability as a function of street and building block widths. (**a**) Various street widths; (**b**) Various building block width.

#### *5.3. The Effect of Rooftop-Mounted BSs*

Finally, we highlight the effect of rooftop-mounted BS on the UAV blockage probability. To this aim, Figure 8 shows the effect of rooftop-mounted mmWave BSs on the UAV blockage probability for UAV altitude *hU* = 150 m, BS height *hA* = 5 m, street width *l* = 20 m, mean building height and standard deviation *E*[*HB*] = 30 m and *σ*[*HB*] = 10 m, block width and length of *bw* = *bl* = 100 m. By analyzing the presented data, one may observe that mounting BSs on rooftops allows us to greatly reduce the BS blockage probability. More specifically, adding just three rooftop-mounted mmWave BSs to the considered area allows for the reduction of the UAV LoS blockage probability by multiple times. Recall that in the considered deployment the deployment area is (*bl* + *l*)*MV* × (*bw* + *l*) ∗ *MH* ≈ 1.44 × 10<sup>6</sup> m2, implying that the density of rooftop BS is just ≈2 ×10−<sup>6</sup> BS/km2. Specifically, by comparing the horizontal and vertical distances between lines in Figure 8, we observe that in terms of UAV LoS blockage probability, adding additional BS at the rooftop is equivalent to deploying 10 more ground-mounted mmWave BSs. This value is affected by system parameters and environmental characteristics of the deployment and may vary between six and twelve.

**Figure 8.** The effect of the rooftop-mounted BSs.

#### *5.4. Discussion, Limitations and Applications*

The presented results illustrate that out of all considered deployment parameters, street width and building block length are the ones impacting the UAV LoS blockage probability the most. The impact of BS and UAV heights as well as the mean building block height is also noticeable. These parameters all need to be accounted for when estimating the required density of BSs to support UAVs in mmWave 5G systems. Note that in real deployments, these parameters are not independent as specified in [20]. Thus, in general, in city centers, where the mean building heights and width are larger, much higher BS deployment density will be required for the same target UAV LoS blockage probability as compared to the suburbs.

We specifically emphasize the importance of rooftop-mounted BS. As we have observed, qualitatively, the density of ground-mounted BS deployment has to be extremely high, especially in city center deployment conditions. Here, to support the uninterrupted connectivity, it is much more economically sustainable for network operators to deploy dedicated BSs having almost unobstructed coverage for UAV. Our results demonstrate that one rooftop-mounted BS is equivalent to six to twelve ground-mounted ones in terms of UAV LoS blockage probability.

Although the proposed model by design can capture the specifics of different deployments, it also has its limitations. Specifically, as the model assumes that visibility areas are all convex, the visibility areas created by BSs deployed on the crossroads need to be treated as two independent rectangular visibility areas. This implies that the accuracy of the model increases as the size of the analyzed regions with homogeneous building deployments increases. Furthermore, the independence of all visibility areas also implies that the BS locations should be close to the Poisson point process (PPP, [32]). Note that due to restrictions of BS locations in the city center and also due to the need for high densification to satisfy the growing customer needs, BS deployment locations are far from regular cellular structures. Specifically, many studies assume PPP as the deployment process for 4G/5G systems.

The proposed model is especially usable in system-level simulations of mmWave NR deployments supporting UAVs. As noticed in [33], the handling of dynamic blockage events is one of the most time-consuming operations. Associating UAVs with the blockage process having the fraction of time in blockage coinciding with the UAV LoS blockage probability may efficiently address this challenge. Furthermore, the proposed model can be utilized by network operators at the network deployment phase to assess the density of mmWave BSs providing the required level of UAV coverage.
