1 Efficient Deployment of Multiple Unmanned Aerial Vehicles for Optimal Wireless Coverage Mohammad Mozaffari1, Walid Saad1, Mehdi Bennis2, and M´erouane Debbah3 1 Wireless@VT, Electrical and Computer Engineering Department, Virginia Tech, VA, USA, Emails: mmozaff,walids @vt.edu 2 CWC - Centre for Wireless Communications, Oulu, Finland, Email: [email protected].fi{ } 3 Mathematical and Algorithmic Sciences Lab, Huawei France R & D, Paris, France, and CentraleSupelec, Universite Paris-Saclay, Gif-sur-Yvette, France, Email: [email protected] Abstract—In this paper, the efficient deployment of multiple [6], the authors used evolutionary algorithms in order to find unmanned aerial vehicles (UAVs) with directional antennas acting the optimal placement of low altitude platforms (LAPs) and as wireless base stations that provide coverage for ground users portable base stations for disaster relief scenarios. However, is analyzed. First, the downlink coverage probability for UAVs as a function of the altitude and the antenna gain is derived. the model of [6] assumes that overlapping LAPs’ coverage Next, using circle packing theory, the three-dimensional locations areas is allowed by using inter-cell interference coordination of the UAVs is determined in a way that the total coverage (ICIC). However, ICIC requires further communications be- area is maximized while maximizing the coverage lifetime of the tween LAPs. UAVs. Our results show that, in order to mitigate interference, The main contribution of this paper is to investigate the op- the altitude of the UAVs must be properly adjusted based on the beamwidth of the directional antenna as well as coverage timal 3D deployment of multiple UAVs in order to maximize requirements. Furthermore, the minimum number of UAVs the downlink coverage performance while using a minimum needed to guarantee a target coverage probability for a given transmit power. Given a target geographical area, the coverage geographical area is determined. Numerical results evaluate the requirements of the ground users, and a number of UAVs various tradeoffs involved in various UAV deployment scenarios. that use directional antennas, we develop a novel framework I. INTRODUCTION to determine the optimal 3D locations of the UAVs. First, The use of wireless aerial platforms is a promising ap- we derive the downlink coverage probability for a UAV proach to improve the performance of wireless communication as a function of the UAV’s altitude and the antenna gain. networks. In particular, unmanned aerial vehicles (UAVs) Next, using circle packing theory [7], we propose an efficient can act as flying base stations to enhance the coverage and deployment method which leads to the maximum coverage rate performance of wireless networks in different scenarios performance while ensuring that the coverage areas of UAVs such as temporary hotspots and emergency situations [1]. In do not overlap. Our results show that, considering the size addition, mobile UAVs can establish efficient communications of the desired area, the number of available UAVs and the with ground sensors for alarm messages delivery scenarios [2]. gain (or beamwidth) of the directional antennas, the altitude Indeed, using UAVs as aerial base stations provides several and locations of the UAVs can be appropriately adjusted for advantages compared to the terrestrial base stations. First, due satisfying the coverage requirements. In addition, our results to their higher altitude, aerial base stations have a higher reveal the minimum number of UAVs required to guarantee a chance of line-of-sight (LoS) links to ground users. Second, target coverage for a given geographical area. UAVs can easily move and have a flexible deployment, and The rest of this paper is organized as follows. In Section II, hence, they can provide rapid, on-demand communications. we present the system model and describe the air-to-ground Finally, using directional antennas, one can further enhance channel model. Section III presents the coverage analysis and arXiv:1606.01962v1 [cs.IT] 6 Jun 2016 the UAV-based communications due to the possibility of using the proposed deployment method. In Section IV, we provide effective beamforming schemes [3]. the simulation results, and Section V concludes the paper. Despite the numerous advantages for using UAVs as flying base stations, one must overcome a number of technical chal- II. SYSTEM MODEL lenges. These challenges include the optimal 3D deployment Consider a circular geographical area of radius R , as illus- of UAVs, energy limitations, interference management, and c trated in Figure 1, within which M UAVs must be deployed to path planning [1]–[5]. In particular, the deployment problem provide wireless coverage for ground users located within the is of paramount importance as it highly impacts the energy area. In this model, we consider a stationary low altitude aerial consumption as well as the interference generated by UAVs. platform such as quadrotor UAVs. The UAVs are assumed to However, only a limited number of existing literature have be symmetric having the same transmit power and altitude. addressed the interplay between UAV deployment and wireless We denote the UAV’s directional antenna half beamwidth by performance [1], [4]–[6]. For instance, in [5], the use of θ , and, thus, the antenna gain can be approximated by [8]: multiple UAVs as wireless relays in order to provide service B G θB ≤ ϕ ≤ θB , for ground sensors is investigated. This work addressed the G = 3dB, −2 2 (1) g(ϕ), otherwise, tradeoff between connectivity among the UAVs and maximiz- 29000 ing the area covered by the UAVs. However, the work in [5] where ϕ is the sector angle, G3dB ≈ 2 with θB in degrees, θB does not consider the use of UAVs as aerial base stations is the main lobe gain [9]. Also, g(ϕ) is the antenna gain outside and their mutual interference in downlink communications. In of the main lobe. For the air-to-ground channel modeling, a 2 Theorem 1. The coverage probability for a ground user, located at a distance r ≤ h.tan(θB/2) from the projection of the UAV j on the desired area, is given by: Pmin + LdB Pt G3dB + µLoS Pcov = PLoS,j Q − − σLoS Pmin + LdB Pt G3dB + µNLoS + PNLoS,j Q − − , (7) σNLoS where Pmin = 10 log βN + βI¯ is the minimum received power requirement (in dB) for a successful detection, N is Fig. 1: System model. the noise power, β is the signal-to-interference-plus-noise-ratio common approach is to consider the LoS and non-line-of- (SINR) threshold. I¯ is the mean interference power received sight (NLoS) links between the UAV and the ground users from the nearest UAV k which is given by: − − µLoS,k µNLoS,k n separately [10]. Each link has a specific probability of occur- ¯ 10 10 4πfcdk − I Ptg(ϕk) 10 PLoS,k + 10 PNLoS,k c . rence which depends on the elevation angle, environment, and ≈ Also, Q(.) is the Q function. relative location of the UAV and the users. Clearly, for NLoS links the shadowing and blockage loss is higher than the LoS Proof. The downlink coverage probability for a ground user links. Therefore, the received signal power from UAV j at a considering the mean value of interference between UAVs can be written as: user’s location can be given by [10]: Pr,j Pt + G3dB − LdB − ψLoS, LoS link, Pcov = P β = P [Pr,j (dB) Pmin] Pr,j (dB)= (2) N + I¯ ≥ ≥ Pt + G3dB − LdB − ψNLoS, NLoS link, = PLoS,j P [Pr,j (LoS) Pmin]+ PNLoS,j P [Pr,j (NLoS) Pmin] ≥ ≥ where Pr,j is the received signal power, Pt is the UAV’s trans- (a) = PLoS,j P [ψLoS Pt + G3dB Pmin LdB ] mit power, and G3dB is the UAV antenna gain in dB. Also, LdB ≤ − − + PNLoS,j P [ψNLoS Pt + G3dB Pmin LdB] is the path loss which for the air-to-ground communication is: ≤ − − (b) Pmin + LdB Pt G3dB + µLoS 4πfcdj = PLoS,j Q − − LdB = 10nlog , (3) σ c LoS Pmin + LdB Pt G3dB + µNLoS where fc is the carrier frequency, c is the speed of light, + PNLoS,j Q − − , (8) σNLoS dj is the distance between UAV j and a ground user, and 2 P n ≥ 2 is the path loss exponent. Also, ψLoS ∼ N(µLoS, σLoS) where [.] is the probability notation, and Pmin = 2 ¯ and ψNLoS ∼ N(µNLoS, σNLoS) are shadow fading with normal 10 log βN + βI . Clearly, due to the use of directional anten- distribution in dB scale for LoS and NLoS links. The mean nas, interference received from the nearest UAV k is dominant. and variance of the shadow fading for LoS and NLoS links Hence, I¯ can be written as: are (µ , σ2 ), and (µ , σ2 ). As shown in [10], the LoS LoS NLoS NLoS I¯ ≈ P E [P (LoS)] + P E [P (NLoS)] variance depends on the elevation angle and type of the LoS,k r,k NLoS,k r,k − − n µLoS µNLoS 4πf d − environment as follows: 10 10 c k = Ptg(ϕk) 10 PLoS,k + 10 PNLoS,k . σLoS(θj )= k1 exp(−k2θj ), (4) h i c E σNLoS(θj )= g1 exp(−g2θj ), (5) where [.] is the expected value over the received interference power. The mean interference is a reasonable approximation 1 where θj = sin− (h/dj ) is the elevation angle between the for the interference and leads to a tractable coverage probabil- UAV and the user, k1, k2, g1, and g2 are constant values which ity expression. In (8), (a) is a direct result of (2), and (b) comes depend on environment. Finally the LoS probability is given from the complementary cumulative distribution distribution γ by [10]: 180 function (CCDF) of a Gaussian random variable. Furthermore, PLoS,j = α θj − 15 , (6) π r ≤ h.tan(θB/2) implies that a user can be covered only if it is where α and γ are constant values reflecting the environment in the coverage range of a directional antenna with beamwidth impact.