3D Placement of a New Tethered UAV to UAV Relay System for Coverage Maximization

In this paper, a new relay system that uses the UAV as a relay station between the tethered UAV and ground user (TU2U2G) is proposed. The TU2U2G system uses a TUAV as a viable alternative to replace BS and provide seamless service over a cable that simultaneously supplies stable power and a reliable wired data-link connection from a ground control station. Compared to the BS, TUAV improves system coverage due to its high altitude. Also, it overcomes the antenna down-tilting, which increases the path loss between BS and UAV in the cellular system. In addition, it overcomes the UAV drawback of the batteries’ limited capacity. Therefore, TUAV can achieve the main requirements of a reliable cellular BS in terms of endurance, backhaul link quality, and the advantage of the UAV’s high altitude. After that, the optimization problem is formulated to maximize UAV relay station coverage under the power budget and maximum UAV height constraints. For simplicity, the 3D placement of the UAV is decoupled to the vertical and horizontal placement. Then, a 3D placement algorithm for the system is proposed. The UAV placement in the TU2U2G system compared to the cellular system shows better results in terms of optimum UAV height, maximum coverage radius, and maximum relaying distance.

approach to find the optimum altitude of UAV that minimizes power loss, outage probability, and BER is presented in [21] while an approach to optimize the overall network delays is proposed in [22] All these works are proposed for UAV to assist the cellular network. However, the antenna down-tilting and low height of the cellular base station (BS) limits the ability of the UAV relay station to reach high altitudes due to the power constraint on the path between UAV and BS [23]. In other words, using the UAV as a relay station in the cellular system makes the UAV lose the advantage of deployment at optimum altitude which reflects directly on the coverage [7]. On the other hand, using UAV as an alternative to cellular BS is not a realistic solution because UAV has a drawback of the batteries' limited capacity which poses a challenge for the lifetime of its operation. Therefore, a UAV cannot be available for the entire duration of the operation as it is necessary to return for charging or replacing the battery. In this paper, Tethered UAV (TUAV) is proposed as an alternative to BS. TUAV is a UAV supplied by both power and data over a cable from a ground station (GS) as shown in Fig. 1. TUAV can achieve the main requirements of a reliable cellular BS in terms of endurance and backhaul link quality and the advantage of the UAV's high altitude as shown in Fig. 2. Recently, AT&T's deployed the first TUAV to provide cellular coverage in Puerto Rico for the suffered regions after Hurricane Maria [24] which means that, TUAV can be a realistic alternative to the cellular BS. Therefore, we propose the TU2U2G system to replace the BS in the cellular system with TUAV to maximize the UAV relay station coverage. The contribution of this paper resides in several aspects: • Propose a new relay system TU2U2G system. It uses the TUAV as a viable alternative to replace BS and provide seamless service over a cable that simultaneously supplies a stable power and a reliable wired data-link connection from a ground control station [6]. Compared to the BS, TUAV improves the system coverage due to its high attitude. Also, it overcomes the antenna down-tilting which increases the path loss between BS and UAV in the cellular System [3].
• Formulate the optimization problem to maximize UAV relay station coverage under the power budget and maximum UAV height constraints for the TU2U2G system. For simplicity, the 3D placement of the UAV is decoupled to the vertical and horizontal placement. Then, a 3D placement algorithm for the system is proposed.
• Numerical results are presented. TU2U2G the system shows better results than the cellular system in terms of optimum UAV height, maximum coverage radius, and maximum distance between BS and UAV.
The structure of the paper is organized as follows: Section 2 presents the system models. The 3D placement of UAV for maximum coverage is proposed in section 3. Numerical results are discussed in section 4. Finally, concluding remarks are in section 5.

. System models
The proposed TU2U2G system consists of TUAV, UAV, and MS. The ground distance between UAV and MS is R and θ is the elevation angle. The ground distance between ground TUAV and UAV is d and α is the elevation angle. TU2U2G communication links are the A2G link and the TU2U link. The A2G link is between UAV and MS. TU2U link is between TUAV and UAV as shown in Fig.3. The UAV acts as an aerial base station or a relay to extend the wireless coverage. To formulate the optimization problem, it is essential to adopt the appropriate path loss models for the systems communication Links.

A2G Channel
The A2G path loss can be calculated by [4]: FSPL represents the free space path loss between the UAV and a ground receiver. refers to LOS and NLOS excess path loss. The value of depends on the environment types [4]. The probability of having a LOS connection between the ground user and a UAV is given by [4]: Where a and b are constants that depend on the environment. Total path loss of the A2G link is presented in (4) by substituting with (2)

U2U Channel
The TU2U path loss can be represented by a simple free-space propagation model [26], [27]. The free space path loss (FSPL) depends on the frequency and the distance between the transmitter and the receiver. The log-distance equation of FSPL is presented in (5).
Where (L) is the distance in meters, and (f) is the frequency in (Hz), and −147.55 is −20 log ( 4 ) where C is the speed of light. The distance (L) in (5) can be represented as a function of the ground distance between TUAV and UAV ( 2 ) and elevation angle as in (6).

UAV transmission power, SNR, and probability of coverage
The transmit power of UAV can be written as Where is the received power (in dBm). is the path loss.
Therefore, the downlink SNR in dB is calculated as Where 2 is noise power. The coverage probability is the probability that a user can achieve SNR above the threshold (T). Therefore, the user coverage probability can be defined as Besides the SNR-based coverage approach, the coverage can be defined through path loss [7] [10].
Here, a user is considered to be covered by the UAV if 2 < ℎ ( 2 ) . Therefore, the UAV coverage radius can be mathematically defined as R| 2 = ℎ ( 2 ) . It means that users at the distance R will have the same path loss ℎ( 2 ) , while users with a radius less than will experience path loss less than ℎ( 2 ) .

Problem formulation
In this paper, the coverage is maximized by jointly optimizing the coverage radius of UAV (R) and the distance between the TUAV and UAV( 2 ). In other words, our target is to maximize the number of covered users (N) per UAV under the power budget and maximum UAV height constraints. The problem is formally written as follows: Subject to constraints: C4: C5: C6: We aim to maximize the number of users (N) covered by UAV in (14)

. The proposed 3d placement of UAV
It can be noticed that the UAV height is a joint variable between constrains equations of each optimization problem. Therefore, the 3D placement of the UAV is decoupled to the vertical and horizontal placement for simplicity. First, the vertical placement aims to find the optimum UAV heights for the maximum coverage radius. Since the coverage area of a UAV is considered as a circular disc. Therefore, the horizontal placement aims to find the center of the circular disc.

Altitude Optimization for Maximum Coverage
In the case of the TU2U2G system, the optimum height of the UAV is constrained by the maximum allowable path losses of the A2G link and TU2U link. Therefore, in the following the optimum UAV height for each communication link is separately obtained. Then, the final optimum UAV height for each system is obtained using the proposed algorithm.

Finding the UAV height for maximum coverage radius between UAV and ground user
The optimal altitude that results in the maximum coverage region can be found by the first derivative = 0. The optimal elevation angle depends on the type of environment [4]. The radius of the coverage area at can be calculated from (4) .The ℎ that maximizes the coverage region is given by (24).

Finding the UAV height for maximum distance between TUAV and UAV
For a maximum allowable path loss between TUAV and UAV, the optimum angle that maximizes 2 can be calculated from (25). The value of =0 which means that the maximum distance between TUAV and UAV is achieved when they are at the same level. The maximum distance of 2 at can be calculated by (6). Then, optimum altitude difference between TUAV and UAV (∆h) is obtained by (26).

Horizontal placement of UAV
The proposed horizontal placement aims to maximize the possible number of enclosed users considering the maximum allowable distance of 2 . This is done by searching for the center of the coverage region under Constraints C3, C4. C3 assures that the user is inside the UAV coverage when located within the distance R from the UAV center. While C4 assures that the UAV is inside the TUAV coverage when located within the distance 2 from the TUAV center.

3D placement algorithm
In the proposed Algorithm, step (1) obtains the optimum h UAV for maximum coverage radius R under constraint C1. It is calculated from A2G path loss by finding θ OPT which is obtained by solving the problem in (23). Then, substituting by θ OPT in (24) to calculate R. Then, substituting by θ OPT and R in (24) to calculate h UAV .
Step (2) obtains the optimum ∆h for maximum distance between UAV and TUAV under constraint C2. It is calculated by solving the problem in (25). Then, substituting by α OPT in (6) to calculate 2 .Then, substituting by α OPT and d TU2U (26) to calculate ∆h.
Step (3) calculates ℎ and ℎ to satisfy the constraints C7 and C8. First, the maximum altitude difference between TUAV and UAV (∆ℎ ) is calculated by: Where ℎ is the maximum altitude of TUAV. Then, the optimum of ℎ and ℎ are found under the constraints of maximum and allowable height.
Step (6) solves the problem (14) under constraints C3 and C4 to find the UAV horizontal placement. This is done by searching for the coverage region center ( , ) that maximizes the number of users (N).it is solved by branch and cut method [10].
Then, substituting by θ OPT in (24) to calculate R.
Then, substituting by θ OPT and R in (24) to calculate ℎ .

Obtain∆ℎ
Finding by solving the problem in (25).
The worst-case complexity of the proposed algorithm is analyzed as follows. The complexity of Steps 1 to 5 is ( ), Step 6 which is implements the branch and cut method is (2 ) and each branching node complexity is ( 3.5 log ( −1 )) where is the accepted duality gap. Therefore, the complexity of Algorithms is ( + 2 3.5 log ( −1 )).

. Numerical results
In this section, numerical results of UAV placement for the TU2U2G system are presented. The optimum values of the distance between TUAV and UAV, and distance between BS and UAV, and the coverage Radius of the UAV are discussed. In addition to that, a comparison between the TU2U2G and cellular systems is presented. The system parameters are listed in Table1.

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To compare the TU2U2G system with the cellular system, both are simulated at different allowable path losses. Fig.4 shows that, at the same allowable path loss, the distance between TUAV and UAV in the TU2U2G system is greater than the distance between BS and UAV in the cellular system. Also, the coverage radius of the UAV in the TU2U2G system is greater than the cellular system as shown in Fig. 5.
It means that the TU2U2G system can extend the coverage better than the cellular system.  Fig. 7 show the 3D placement for the TU2U2G system and the cellular system respectively. The simulation is done at The A2G path loss = 100 dB. While A2A is set to different Path loss values 110 dB, 115 dB, 120 dB, and 125 dB. The optimum altitude of the A2G link for PL=100 dB is 225.9m and the coverage radius is 208.7 m. In the TU2U2G system, using TUAV with variable and high altitude allows the UAV to reach the optimum altitude of the A2G link. However, in the cellular system, the maximum coverage of the UAV is 70m. Fig. 8 shows the increase of UAV height and coverage with the increase of the TUAV height. On the other hand, the antenna down tilting and the low height of the Base station limit the UAV height to a max of 70 m which reduces the coverage radius of the UAV.

. Conclusion
A new relay system TU2U2G that replaces BS with TUAV is proposed. In the proposed system, the TUAV has advantages of variable height up to 100m and overcoming the problem of antenna down tilting. The 3D placement algorithm of UAV relay stations that jointly optimize the transmitting power and relaying distance for the coverage maximization is proposed. TU2U2G the system shows better results than the cellular system in terms of optimum UAV height, maximum coverage radius, and maximum distance between BS and UAV.