3D Placement and Orientation of mmWave-based UAVs for Guaranteed LoS Coverage

Unmanned Aerial Vehicles (UAVs), also known as drones, have numerous applications in telecommunications, rescue operations, aerial sensing, to name a few. Significant research efforts have gone into understanding the role of UAVs as aerial base stations (BSs) to complement the coverage and capacity of terrestrial wireless networks. mmWave and future teraHertz communications with orders of magnitude larger bandwidths than the conventional sub-6 GHz systems are expected to play a pivotal role in supporting emerging applications, such as extended reality, in UAV-assisted communications networks [1]. However, characterized by very high path loss in non-line-of-sight (NLoS) conditions, it is critical that mmWave (and teraHertz) based UAV communications always have a line-of-sight (LoS) coverage to wireless devices  [2][3].

To provision high quality wireless LoS coverage to wireless devices (or users), UAVs should jointly adjust their coordinates and the orientations of their directional antennas. There exist some work  [4, 5, 6, 7, 8, 9] that study the problem of communication coverage for UAVs, however, there are several limitations: (i) Existing work consider wireless devices on the ground (i.e., horizontal plane) whereas our work considers wireless devices in 3D space. (ii) Existing work model air-to-ground path loss model as a probabilistic LoS and NLoS model in sub-6 GHz communications. However, as discussed in [3, 2], to fully take advantage of mmWave-based communication, especially for UAVs, the receiver must be located such that it can secure a LoS communication with the transmitter. Our 3D LoS coverage model attempts to always guarantee LoS, a key requirement of mmWave communications. (iii) And finally, most of existing works build UAV wireless coverage model as a disk. In this paper, we propose to utilize 3D directional coverage model [10] to realistically model mmWave-based UAV LoS and user direct line-of-view (LoV) coverage (See Fig. 1). Following this, we investigate the joint problem of 3D placement and orientation of UAVs such that (i) users with limited direct LoV region have guaranteed LoS coverage¹¹1Note that this work only considers LoS paths, however, they may be some strong NLoS paths and is left for future studies. by at least one UAV, (ii) the SNR between the UAV and its associated users are maximized, and (iii) the number of UAVs required is minimized. To our understanding, this is the first work which studies the guaranteed LoS coverage problem for UAV mmWave communications, where users are considered in 3D space and has limited directed LoV region.

The key contributions of this work are as follows:

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  We first present LoS and LoV coverage model for UAVs and users respectively, which realistically model mmWave based UAV systems.

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  We formulate the problem of determining the 3D placement and antenna orientations of UAVs as an integer linear programming optimization problem. Then, we prove that it is NP-Hard. Next, we propose a low-complexity geometric approach for solving the problem efficiently.

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  Our extensive experimental results depict that the proposed algorithm (almost) always guarantees LoS coverage to all users irrespective of its limited LoV region, compared to that of the baseline approach²²2The baseline algorithm is similar to the proposed algorithm in pseudocode  1 except that the antenna orientation is fixed.. Furthermore, we notice that compared to the baseline approach, the proposed algorithm incurs fewer number of UAVs and achieves much higher average SNR under scenarios where the user’s LoV are higher and both the approaches can provide LoS coverage to the majority of users.

The rest of the paper is organised as follows: In Section II, we model the considered UAV-based mmWave wireless system and formulate the problem. In Section III, we discuss the proposed solution approach. In Section IV, we present the experimental results, followed by conclusion in Section V.

Let us consider a mmWave-based UAV communication system with $|C|$ UAVs and $|U|$ users (i.e., wireless devices, such as, aerial sensing drones, mobile terminals etc.) both deployed in 3D space (See Fig. 1). We assume that each user $\hat{u}_{j}\in U$ is located at a known 3D location $u_{j}$ in the region. Since, there may be buildings, trees or other objects on the side, top or bottom of any given user $\hat{u}_{j}$ (at location $u_{j}$), it is quite likely $\hat{u}_{j}$ may not always have a LoV from all directions. Let vector direction $\vv{d}_{u_{j}}=(\vv{x_{j}},\vv{y_{j}},\vv{z_{j}})$ with angle-of-view (AoV), $\theta_{j}$ (where $0^{\circ}<\theta_{j}\leq 180^{\circ}$) denotes the user LoV for the considered user $\hat{u}_{j}$, and is known a priori.

Let $c_{i}$ denote the 3D location of UAV $\hat{c}_{i}\in C$ (in case of deployment in the 3D space). We assume that UAV $\hat{c}_{i}$ is equipped with a directional antenna. Furthermore, we consider that the antenna can face any direction $\vv{d}_{c_{i}}$ that can be defined by two angles in 3D space (2D azimuth and elevation angles [11]) or a 3D Cartesian vector $(\vv{\hat{x}_{i}},\vv{\hat{y}_{i}},\vv{\hat{z}_{i}})$. Moreover, UAV’s directional antenna half power beamwidth (HPBW) $\phi$ is a prespecified value between $(0^{\circ},180^{\circ})$. However, this limitation has no influence to the coverage orientation, because UAV can hover in the air and rotate itself to face any orientation $\vv{d}_{c_{i}}$. So in other words, considering $\vv{d}_{c_{i}}$ as a 3D Cartesian vector $(\vv{\hat{x}_{i}},\vv{\hat{y}_{i}},\vv{\hat{z}_{i}})$ provides $360^{\circ}$ rotation capability to a certain UAV in our system model.

Just like terrestrial cellular networks, we assume that neighboring UAVs transmit on orthogonal frequencies and hence do not interfere with each other. Also, our problem setup is general and is applicable to any multiple access scheme, such as time/frequency division multiple access or orthogonal frequency division multiple access.

In this section, we propose a low-complexity greedy algorithm based on the aforementioned geometric approach to solve the problem efficiently.

As depicted in pseudocode 1, the algorithm computes the set of all users, $U_{c_{k}}$, that can be LoS covered by a UAV placed at a discrete candidate location $k\in\mathbb{K}$ with at least one feasible antenna orientation $(\vv{\hat{x}_{k}},\vv{\hat{y}_{k}},\vv{\hat{z}_{k}})$. Let $\mathbb{K}_{LoV}\subseteq\mathbb{K}$ denote the set of such candidate grid locations (See Observation 1 and lines 3-7). Notice that, UAV $\hat{c}_{k}$ may not necessarily provide LoS coverage to all the users in $U_{c_{k}}$ with any one unique orientation (among all possible orientations). Thus, the algorithm further computes the subset of users $U_{<c_{k},d^{u_{i}}_{c_{k}}>}\in U_{c_{k}}$ LoS covered by orientation $d^{u_{i}}_{c_{k}}$ that cover the largest possible subset of $U_{c_{k}}$ while necessarily a user $\hat{u}_{i}$ is being covered (See lines 11 - 12). To compute $U_{<c_{k},d^{u_{i}}_{c_{k}}>}$ and $d^{u_{i}}_{c_{k}}$, the algorithm uses the geometric approach described previously in subsection II-e.

By repeating this procedure for every single user $\hat{u}_{i}\in U_{c_{k}}$, the algorithm selects the case in which the most number of users can be covered by grid location $k$, i.e., subset $U^{max}_{c_{k}}$, and corresponding orientation $\vv{d}^{max}_{c_{k}}$. We also compute the average of SNR between the UAV $\hat{c}_{k}$ and each user $\hat{u}_{j}\in U^{max}_{c_{k}}$, and term it $\gamma^{avg}_{c_{k}}$ for a UAV at grid location $k$ and selected orientation $\vv{d}^{max}_{c_{k}}$ (See lines 9-14 of pseudocode 1). After repeating this procedure for all grid locations, among the cases that cover maximum number of users, we will pick the case which has the largest $\gamma^{avg}_{c_{k}}$ (See lines 15-18 of pseudocode 1). We delete associated users to the selected grid location $c_{sel}$, which is $U^{max}_{c_{sel}}$, from all $U_{k}$s (See lines 19-21 of pseudocode 1). It means that each user’s coverage ensures only once in the proposed algorithm. These steps will be repeated until no users remains such that could be covered by grid candidate locations in the space or the total number of UAVs $C$ has been deployed. It is worth mentioning that $|\cup_{k}{U_{c_{k}}}|$ will be a decreasing quantity after each iteration, and thus will reach zero in countable number of iterations. Therefore, the algorithm 1 is terminated in a polynomial-time running complexity as also analyzed in Theorem 2. In our work, we consider $C$ to be sufficiently large (i.e., $|C|>\mathbb{K}$), however, a certain network provider may consider lesser value of $C$ for enormous cost reasons. Nevertheless, the proposed algorithm will always provide a solution with minimum number of UAVs ($\leq|C|$) with LoS coverage to almost all users and also, high SNR between UAV and users.

In this section, we discuss the comparative analysis of proposed algorithm against a simple baseline approach (discussed below) in terms of key performance metrics, namely, percentage of users LoS covered, number of UAVs needed and average SNR achieved. For the baseline approach, we consider that the UAV antenna is always facing downward (i.e., azimuth angle to $0^{\circ}$ and elevation angle to $-90^{0}$ or 3D cartesian vector is $(0,0,-1)$), which is usually considered in the literature [14]. Notice that this baseline approach does not take into account the limited LoV region of each user, and thus, has limitations in providing guaranteed LoS coverage to all users as discussed later in this section.

Note using the parameters listed in Table I, the SNR $\gamma_{ij}$ between a UAV $\hat{c}_{i}$ and user $\hat{u}_{j}$ can be computed using Eq. 2. Now given $\gamma_{ij}$, known user $\hat{u}_{j}$’s AoV ($\theta_{j}$), UAV antenna HPBW $\phi$, the maximum 3D distance ($D_{max}$) between UAV $\hat{c}_{i}$ and user $\hat{u}_{j}$ can be calculated, where $D_{max}$ is $\approx 80$ m.

Average percentage of users LoS covered. As shown in Fig. 3(a), the percentage of LoS covered users increases with increasing user AoV. This is intuitive as the probability of a user to be in LoS coverage by a certain UAV increases with increasing user AoV, given the other parameters (i.e., SNR threshold and UAV HPBW) are constant (See Equation 5). It is important to note that the proposed approach significantly outperforms the baseline approach, particularly for limited user AoV (e.g., $[15^{\circ},45^{\circ}]$). This is because unlike the baseline approach, the proposed approach specifically accounts for users’ LoV, and chooses (sub)optimal 3D placement and antenna orientation of UAVs to guarantee LoS coverage to (almost) all users.

Average number of UAVs needed per number of users LoS covered. Fig 3(b) shows that, with increasing user AoV, the proposed algorithm requires fewer number of UAVs to provide guaranteed LoS coverage to all users. This is again because a certain UAV can cover larger number of users when user AoV is larger (See Eq. 5), and thus, on average fewer UAVs are required to cover all users in the considered 3D region. Besides providing LoS coverage to less number of users in the baseline approach compared to the proposed approach (as shown in Fig. 3(a)), the average number of UAVs needed per number of users LoS covered in the proposed algorithm is significantly less than the baseline approach, thus showcasing the superiority of the proposed algorithm.

Average SNRs achieved. As shown in Fig. 3(c), by considering an SNR of zero for the users out of the coverage (or in other words, users in NLoS region), our approach experiences significantly higher average SNR at users when compared to that of the baseline approach. This is expected as the proposed algorithm determines the suitable 3D placement and antenna orientation for UAVs such that the average SNR experienced by users are maximized (See Obj. function in Equation 6).

In this letter, we investigated the design of joint 3D placement and orientation of high frequency band (e.g., mmWave or teraHertz) UAVs which require guaranteed line-of-sight (LoS) coverage to users – with limited direct line-of-view (LoV) due to various blocking objects around it. We first formulated the aforestated joint problem as an integer linear programming (ILP) optimization problem and proved its NP-Hardness. By utilizing the geometric properties of the setup, a low-computational complexity algorithm was presented to solve the problem. Our comprehensive evaluations showed the superiority of the proposed algorithm in providing LoS coverage for a near $100\%$ of the users while experiencing significantly higher SNRs, when compared to that of baseline approach, for all considered simulation setting.