The Outage-Free Replacement Problem in Unmanned Aerial Vehicle Base Stations

Thanks to the feature of on-demand and flexible deployment, unmanned aerial vehicle base stations (UAV-BS) can enhance coverage and capacity beyond current 5 G cellular networks. The main challenge in deploying UAV-BS lies in the fact that the limited battery in UAB-BS cannot support long-time reliable services. Therefore, a serving UAV-BS being running out its power needs to be replaced with a new fully-charged UAV-BS. This is called UAV-BS replacement process. However, most existing UAV-BS replacement methods ignore the link outage problem during the replacement. Thus the outage-free replacement problem (OFRP) for UAV-BSs arises. We provide a method to calculate the outage probability of the UAV replacement approach. We further formulate the Outage Probability Minimization Problem (OPMP) for UAV-BS replacement. To solve this problem, a 3-Dimensional Outage-Free Replacement Approach (3D-OFRA) is presented, which exploits different heights of swapping UAV-BSs during the replacement process. More importantly, we provide the guidelines of determining the distance between two UAV-BSs to minimize the link outage possibility during the UAV-BS replacement process. Our numerical results show that with the recommended distance between two UAV-BSs based on 3D-OFRA, the outage probability of the served UEs approaches to zero, compared with 40% of the traditional direct replacement approach.

However, UAV-BS faces many challenges, especially battery capacity issues. Generally, the service time of UAV-BS is about 15 to 30 minutes only [1], so cellular operators need to prepare a backup UAV-BS to replace the UAV-BS before its battery runs out. The replacement UAB-BS has become necessary for long-term communication services.
In the literature, the UAV-BS replacement is a hot research topic [10] [11]. The authors in [10] proposed a scheduler aorithm to schedule multiple UAV-BS replacements for long-term (several hours) UAV-BS communication services to the users in the hot spots. In order to increase the service time of the UAV-BS group, [11] proposed a model of swapping the positions of the UAV-BS with low residual battery and the adjacent UAV-BS with high remaining battery.
Nevertheless, the existing UAV-BS replacement approaches cannot provide reliable communication services during the UAV-BS replacement process. As shown in Fig. 1, due to the mobility/movement of UAV-BSs during the replacement procedure, UEs in the shaded area will be covered by none of UAVs for a short period of time and then experience the link outage issue. Such a problem is called Outage-Free Replacement Problem (OFRP).
To solve OFRP, we propose a 3-Dimensional Outage-Free Replacement Approach (3D-OFRA), which utilizes the height of UAV-BS to ensure that all ground hotspot users can always connect to UAV-BS. In the proposed OFRA, we first analyze the outage probability of the direct replacement approach, and then formulate the OFRP as an Outage Probability Minimization Problem (OPMP). After that, we also suggest a condition, this is the upper limit of the horizontal distance between two UAV-BSs, so that the outage probability can be zero during the entire UAV-BS replacement process. In this way, all users in the hotspot area can seamlessly transfer the association to the new upcoming UAV-BS.
Numerical results show that there is usually a nonlinear relationship between the outage probability and the horizontal distance between two UAV-BSs. In addition, the results verify that the outage probability is zero when the recommended distance condition is met. This means that the proposed OFRA can effectively solve OPMP.
The main contributions of this paper are summarized as follows: r Compare with the existing solutions of UAV replacement, this work is the first one to identify and solve the Outage-Free Replacement Problem (OFRP), and we believe that this work can lead an important contribution to related research field.
r We suggest a horizontal distance condition between two UAV-BSs for ensuring the proposed 3-Dimensional Outage-Free Replacement Approach (3D-OFRA) can guarantee zero outage to UEs in the target hotspot area.
r With the proposed 3D-OFRA, the collision problem of UAV-BSs during the replacement procedure can be avoided since two UAV-BSs fly at different altitudes and follow the suggested horizontal distance condition.
r The simulation result indicates that the proposed 3D-OFRA indeed provides the optimal solution for the Outage Probability Minimization Problem (OPMP) modeled from OFRP, under the suggested (upper-bound) horizontal distance condition. The rest of letter is organized as follows. Section II presents considered system model with some assumptions. Section III presents the This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ Fig. 1. The scenario of coverage outage (shaded area) during the replacement process, where red dot circle is the target hotspot area, the blue circle is the coverage of the leaving UAV-BS, the green circle is the coverage of the upcoming fully charged UAV-BS, the black arrows indicate that the two UAV-BS are moving in the same direction and speed. problem formulation. Section IV explains the proposed approach with the algorithm, example, and analysis in detail. In Section V, we show the simulation results and validate the performance of the proposed algorithm in various situations. Finally, the conclusion remarks of this work are given in Section VI.

II. SYSTEM MODEL
As shown in Fig. 2, we consider the scenario that the centralized network controller/cellular operator wants to replace the UAV-BS U 1 with a fully charged UAV-BS U 2 . We assume that the target hotspot area is given as a circular coverage area, is the horizontal coordinates of T A and r A is the coverage radius. A set of stationary user equipments (UEs), E = {u 1 , u 2 , . . . , u M }, are uniformly distributed in T A . We denote u m = (x m , y m ) as the coordinates of a ground UE, where m = 1, 2, . . . , M. UAV-BS U i is allowed to fly within a predefined allowable altitudes, where T is the complete time of the UAV-BS replacement.
In this work, we adopt the air-to-ground channel model [12], so the average path loss of the LoS and non-LoS (NLoS) signals respectively are is the elevation angle of the UAV-BS; a and b are the constant factors depend on the different environments (rural, urban, dense urban, etc.); and r i, In summary, the average path loss of the signal from U i and u m will be where α = η LoS − η NLoS and β = 20 log 10 ( 4πfc c ) + η NLoS . For simplicity, we assume that the operating UAV-BS uses a fixed power P transmit to transmit signals, and the power received by UE u m is P receive In the considered scenario, we assume that the allowable path loss (ψ) is predefined by the cellular operator. According to [12], we can find the optimal elevation angle (θ opt ) of the UAV-BS by solving the following partial differential equation, ∂r ∂h = ∂r ∂θ ∂θ ∂h = 0. With the optimal elevation angle (θ opt ) and the allowable path loss (ψ), the allowable Euclidean distance between a UAV-BS and its covered UE (d max ) can be obtained from (1). Thus, the maximum altitude and the maximum coverage radius of the UAV-BS are h max = d max sin θ opt and r max = d max cos θ opt , respectively.

III. OUTAGE PROBABILITY MINIMIZATION PROBLEM
Considering the UAV-BS replacement scenario using a straightforward approach in Fig. 3, two UAV-BSs U 1 and U 2 fly at the same altitude and provide the identical coverage size with the radius r. The size of hotspot area, |T A | = πr 2 A , is equal to the coverage of U 1 in this scenario. The replacement procedure will be triggered when the horizontal distance between two UAV-BSs meets the given distance constraint d U 1 ,U 2 = U 1 U 2 . In this straightforward replacement scenario, U 1 is leaving the hotspot area with a fixed speed v and U 2 is going to the horizontal location of U 1 with the same speed and direction. It is clear that only the UE in the Street of Coverage [13] [14] region can seamlessly hands over its association to the new UAV-BS. Conversely, the separated shaded regions do not be covered by U 1 and U 2 simultaneously during the entire replacement process. It means that the UEs in shaded regions will not be covered by any one UAV for a certain time period, so we denote these separated shaded regions as unguaranteed regions. Consider the triangle U 1 BC, we can obtain the angle ∠BU 1 C = ) and the angle ∠AU 1 C = 2∠BU 1 C. Then, we can calculate the size of sector , the size of triangle AU 1 C can be obtained by Then, the size of the shaded area can be derived by Finally, the outage probability of the replacement approach is However, for the above straightforward replacement approach, P outage = 0 is impossible to be achieved since P outage = 0 holds only if θ = 0 and d U 1 ,U 2 = 0. In practice, the collision of two UAV-BSs will occur if d U 1 ,U 2 = 0. Hence, the objective of this work is to minimize outage probability during UAV-BS replacement procedure within the allowable constraint, h min ≤ h i,t ≤ h max , where i ∈ {1, 2}. In this letter, we only consider the case of r A < r max , where r A is the radius of the hotspot area and r max is the maximum radius provided by a UAV-BS.
With the above assumptions, the OFRP problem under consideration can be formulated as an Outage Probability Minimization Problem (OPMP), which can be defined as where

IV. THE PROPOSED 3-DIMENSIONAL OUTAGE-FREE UAV-BS REPLACEMENT APPROACH
In this section, we present the procedure of the proposed 3-Dimensional Outage-Free Replacement Approach (3D-OFRA), for provisioning reliable communications to the hotspot UEs. The proposed model aims to achieve zero outage coverage during the UAV-BS replacement procedure. Fig. 4 depicts the steps of proposed replacement approach and Algorithm 1 shows the proposed procedure. The detailed explanations are addressed below.

A. The Proposed Procedure of 3D-OFRA
The required input information includes (T A , ψ, h min , v), where T A is the target hotspot area, ψ is the predefined allowable path loss, h min is the minimum altitude of a UAV-BS redefined by local laws, and v is the fixed horizontal flying speed of a UAV-BS. The controllable parameters includes U 1,t and U 2,t , which are the coordinates of two UAV-BSs. The output of this algorithm is the outage probability of T A . At the first step, the system gets following important constraints, h max , r max , and r min , by the operations from lines 1 and 3. With h max , the system increases the altitude of UAV-BS U 1 until h 1,t=1 = h max at line 4. Since the maximum altitude h max is derived by (1) with the given allowable path loss, the communication outage of all the UEs in T A will not occur. The operation at line 5 flies the fully charged UAV-BS U 2 with a predefined speed v to the T A . UAV-BS U 2 will fly at the appropriate altitude based on the radius of given hotspot area, r A . At the second step, when d U 1 ,U 2 = d upperbound U 1 ,U 2 , UAV-BS U 1 starts leaving T A with the same speed v as UAV-BS U 2 coming. Such an operation is executed at line 6 of Algorithm 1. After the second step, both U 1 and U 2 simultaneously move with the same speed and direction until U 2 cover the whole hotspot area T A as shown in step 4 of Fig. 4. During the time period of the UAV-BS replacement, all the UEs, covered by U 1 and U 2 at the same time, hand over their associations to U 2 . The operation of step 3 is executed at line 7. After U 2 covers the whole T A at step 4, the system keeps U 1 leaving T A with the speed v for charging where U 1 and U 2 represent the horizontal locations of two UAV-BSs, respectively.
Input: T A , ψ, h min , v, U 1,t and U 2,t Output: P outage (T A ) 1: Use (1) with the given ψ to derive d max ; 2: Solve the partial differential equation ∂r/∂θ = 0 of (1) with ψ and then get θ opt ; 3: Obtain h max = d max sin θ opt , r max = d max cos θ opt , and r min = h min cot θ opt ; /*Step 1 (t = 1)*/ 4: UAV-BS U 1 increases h 1,t=1 of itself until h 1,t=1 = h max ; 5: UAV-BS U 2 starts moving to the coordinates of with a given fixed speed v, and altitude of U 2 is h 2,t=1 = r A tan θ opt ; /*Step 2 (t = 2)*/ 6: When d U 1 ,U 2 = d upperbound U 1 ,U 2 , UAV-BS U 1 starts leaving T A with the same speed v; /*Steps 3 and 4(t = 3)*/ 7: The UEs, simultaneously covered by T A , U 1 , and U 2 , hand over the associations to U 2 ; /*Steps 4(t = 4)*/ 8: After U 2 covers the whole area of T A , U 1 keeps leaving T A with the speed v for charging/replacing the battery; 9: Calculate P outage (T A ) during the time period of above operations; 10: return P outage (T A ); its battery at line 8. The system monitors and calculates the average outage probability P outage (T A ) during the time period of executing the above operations at line 9. Finally, the system outputs the obtained P outage (T A ) at line 10.

B. Outage Probability Analysis
The key issue is how to determine the appropriate horizontal distance d U 1 ,U 2 (at line 6) so as to achieve P outage (T A ) = 0 during the entire replacement process. According to our design, UAV-BS U 1 will increase the altitude of itself to h max to provide the maximum allowable coverage radius r max and wait for the upcoming fully charged UAV-BS U 2 . Since each UAV-BS can move with a fixed horizontal speed, the horizontal distance d U 1 ,U 2 between U 1 and U 2 will be a constant while both UAV-BSs moves simultaneously. Fig. 5(a) and Fig. 5(b) show that the outage probability is zero (P outage ( The reason is that all the UEs in T A are always covered by U 1 or U 2 until finishing the UAV-BS replacement. Outage only occurs under the case of d U 1 ,U 2 > r 2 max − r 2 A as shown in Fig. 5(c). Hence, the upper bound of the horizontal distance between U 1 and U 2 for guaranteeing zero outage probability is d upperbound By observing the scenario depicted in Fig. 5(c), we can formulate the outage probability of the case d U 1 ,U 2 > r 2 max − r 2 A . Note that r 2 = r A in this case. First, by law of cosines, we can calculate Because ∠P 1 U 1 I 1 = ∠P 1 U 1 U 2 , we can obtain P 2 I 2 = P 1 I 1 = r max · sin ∠P 1 U 1 I 1 . Second, we can get ∠P 2 U 1 I 2 = sin −1 ( P 2 I 2 r A ) and ∠P 2 U 1 P 4 = 180 − 2∠P 2 U 1 I 2 . Then, the size of the shaded area can be derived by Finally, the outage probability of the proposed 3D-OFRA can expressed as (8).

C. Complexity Analysis
The proposed 3D-OFRA is based on some analytical models. For instance, the maximum altitude of the UAV-BS is determined by the air-to-ground channel model discussed in [12] and the outage probability is derived by (8). A mathematical computation only costs O(1) complexity and the procedure of 3D-OFRA takes T seconds, so the time complexity of 3D-OFRA is O(T ). To validate the correctness of (8), some simulations are needed to observe the performance gap between the simulation results and the analysis results. The simulation based 3D-OFRA is implemented to solve problem (P1) directly and the program needs to use (3) and (4)

D. Design Discussion
In this subsection, we summarize the benefits of 3D-OFRA's design as follows: 1) Seamless Handover: In the proposed 3D-OFRA, we only allow U 1 to increase its altitude and U 2 flies at a relatively low altitude during the replacement procedure. Such a design makes it easy for a UE to receive stronger signals from the new UAV-BS U 2 and then the UE will hands its association over to U 2 .

V. NUMERICAL RESULTS
We consider the urban scenario and the environmental parameters are (a, b, η LoS , η NLoS ) = (9.61, 0.16, 1, 20) given by [12]. We assume that the used spectrum frequency is f c = 2.4 (GHz), the maximum allowable path-loss of the received signals UAV-BS to the UE link is ψ = 119 (dB), and the transmit power of a UAV is P transmit = 20 (dBm). We conduct several simulations to verify the performance of the proposed model and compare our approach with the conventional/straightforward replacement method. The simulations are implemented in MATLAB R2019a and the program will observe the performance of comparison approaches per second.
We first observe how the horizontal distance between two UAV-BSs, d U 1 ,U 2 , affects the outage probability. In Fig. 6, we use (7) and (8) to show the outage probability of the proposed 3D-OFRA while varying the radius of hotspot area, r A = [1,200], and the distance between two UAV-BSs, d U 1 ,U 2 = [1, 350]. The red line indicates the suggested/optimal values of d U 1 ,U 2 that guarantee zero outage probability to the users in the target area T A with different radius r A .
Second, we consider the case of r A = 100 (m). In Fig. 7, the conventional replacement approach based on our analytical model, denoted as Conventional (Analytical) using black-dashed line, shows that the average outage probability increases as d U 1 ,U 2 increases. The conventional approach can achieve zero outage probability only if d U 1 ,U 2 = 0. However, in practice, the UAV-BS collision will occur if two UAV-BSs fly at the same altitude using the conventional replacement approach. In the proposed 3D-OFRA, we can derive the optimal (or upper-bound/maximum) horizontal distance d U 1 ,U 2 by (7). In Fig. 7, the analytical model of 3D-OFRA, denoted as 3D-OFRA (Analytical) using red-dashed line, indicates that 3D-OFRA can guarantee the zero outage probability until d U 1 ,U 2 > d upperbound Fig. 6. The performance of the proposed replacement approach in terms of outage probability by (8) while varying the radius of hotspot area, r A , and the horizontal distance between two UAV-BSs, d U 1 ,U 2 . We also conduct some simulations with Monte Carlo method to observe the performance of conventional approach and the proposed 3D-OFRA in terms of outage probability. We uniformly spread 1,000 UEs in T A and execute the simulation 10,000 runs to get the average result. For validating the correctness of our proposed analytical model in 3D-OFRA, we then simulate both conventional approach and 3D-OFRA with two different flying speeds v ∈ {5, 25} (m/s) of UAV-BS. According to the result in Fig. 7, we find that the high-speed replacement method leads to a small outage probability while the low-speed replacement method will have the performance results close to the proposed analytical model. However, it does not means that the high-speed replacement has a better performance. The reason is that a lot of outage events cannot be well-observed in the considered discrete-time observing/simulation system, especially for the high-speed replacement approaches.
In practice, the interference from different UAV-BSs will make both conventional approach and 3D-OFRA have a worse outage performance than the analytical result. Although we do not consider interference in the proposed 3D-OFRA, the effect of interference can be solved by applying a simple fractional power control scheme. For example, the leaving UAV-BS uses less transmit power than the new UAV-BS.

VI. CONCLUSION
In this work, we proposed a new UAV-BS replacement approach for providing reliable communications coverage to service the users in the hotspot. The proposed 3-Dimensional Outage-Free Replacement Approach (3D-OFRA) utilizes the altitude of a UAV-BS to provide a larger coverage with the allowable path loss for the hotspot users. In this way, the users in the hotspot area can always be covered by at least one UAV-BS before the UAV-BS replacement is finished. Compared to the straightforward approach, the simulation results validate that the proposed approach not only can avoid the UAV-BS collision but also can effectively provide reliable communications with zero outage probability. An interesting work that be extended from the work is the design of collaborative replacement for a group of UAV-BSs while considering joint energy efficiency and trajectory optimization.