Throughput Improvement for Multi-Hop UAV Relaying

Unmanned aerial vehicle (UAV) relaying is one of the main technologies for UAV communications. It uses UAVs as relays in the sky to provide reliable wireless connection between remote users. In this paper, we consider a multi-hop UAV relaying system. To improve the spectrum efficiency of the system, we maximize the average end-to-end throughput from the source to the destination by jointly optimizing the bandwidth allocated to each hop, the transmit power for the source and relays, and the trajectories of the UAVs, subject to constraints on the total spectrum bandwidth, the average and peak transmit power, the UAV mobility and collision avoidance, and the information-causality of multi-hop relaying. The formulated optimization is non-convex. We propose an efficient algorithm to approximate and solve it, using the alternating optimization and successive convex optimization methods. Numerical results show that the proposed optimization significantly outperforms other benchmark schemes, verifying the effectiveness of our scheme.

hand, disadvantages also exist. First, a UAV has limited on-board energy, which is used not only for its communication mission but also for propulsion, so the working time of a UAV communication system is limited. Second, interference to other unintended users may be caused, due to the high probability of LoS links. Therefore, careful design is required for UAV wireless communication to achieve high performance in practice [3], [4]. In general, there are three typical use cases in UAV wireless communications. First, UAVs can serve as aerial base stations (BSs) to assist overloaded or malfunctioning ground BSs [5]- [13]. Second, UAVs can be dispatched to send/collect data to/from widespread nodes in wireless sensor networks (WSNs) for Internet of things (IoT) [14], [15]. Third, UAVs can serve as aerial relays to provide reliable wireless connection for remote users [16]- [30]. In this paper, we focus on UAV-assisted relaying.
Works on this topic can be categorized depending on the number of UAVs used. In the first case, a single UAV is deployed as relay [16]- [24]. The single UAV relay case is channels with equal bandwidth. Since the number of orthogonal channels is proportional to the number of hops, when the number of hops is large and the total bandwidth of the available spectrum is limited, equal bandwidth allocation limits the throughput of each hop and thus limits the end-to-end throughput of the system. Therefore, bandwidth allocation needs to be studied to increase the spectrum efficiency of multi-hop UAV relaying.
In this paper, we consider bandwidth allocation to improve the overall spectrum efficiency of a multi-hop UAV relaying system, as shown in Fig. 1. Specifically, we maximize the end-to-end throughput from the source to the destination by jointly optimizing the transmit powers of the source and the UAV relays, the channel bandwidths allocated to different hops, and the trajectories of all UAV relays, subject to constraints on the mobility, the collision avoidance, the total spectrum bandwidth, the average and peak transmit power, and the information-causality of relaying. The main contributions of this paper are summarized as follows: • Unlike the equal bandwidth allocation scheme in existing works that may limit the throughput of the multi-hop UAV relaying system, we adapt the channel bandwidth of each hop to the dynamic of the system in order to improve throughput. Specifically, we optimize the bandwidth of each hop along with the transmit power of each transmitting node and trajectories of the UAV relays to maximize the end-to-end throughput.
• The resultant optimization problem is difficult to solve due to its non-convexity. To tackle this difficulty, we propose an efficient iterative suboptimal algorithm to solve the problem, by using the alternating optimization and successive convex optimization methods.
• Computer simulation results show that the proposed joint bandwidth, transmit power and trajectory optimization algorithm achieves significantly higher throughput than other benchmark schemes. The remainder of the paper is organized as follows. Section II introduces the considered system model and presents the problem formulation. Section III presents the VOLUME 7, 2019 proposed effective algorithm to solve the formulated problem. Section IV shows the simulation results to verify the performance of the proposed algorithm. Section V concludes this paper.

II. SYSTEM MODEL AND PROBLEM FORMULATION A. SYSTEM MODEL
As shown in Fig. 1, a source needs to communicate with a destination that is far away. The source and the destination are both fixed on the ground, and the distance between them is D in meter (m). It is assumed that there is no direct link between the source and the destination, which is reasonable when D is large and/or there are obstacles between them. M UAVs are deployed as multi-hop relays to assist the communication from the source to the destination. The source, destination, and UAV relays are all equipped with a single antenna. All UAV relays fly at a fixed altitude H in meters in the sky, determined by the minimum altitude for terrain avoidance or by UAV safety regulation of the government [18]. 1 Throughout this paper, we express location in a threedimension (3D) Cartesian coordinate system. The 3D coordinates of the source and the destination are [w T s , 0] T and [w T d , 0] T , respectively, where w s and w d are 2 × 1 vectors denoting their respective horizontal coordinates, the superscript T denotes the transpose operation and 0 represents their height. The coordinate of UAV relay m (m = 1, . . . , M ) at time t can be expressed by [q T m (t), H ] T , 0 ≤ t ≤ T , where q m (t) is a 2 × 1 vector denoting its horizontal coordinate and T in second (s) denotes the flight duration. To facilitate the UAV trajectory optimization, we discretize the flight duration T into N time slots with equal length, and the length of each time slot is denoted by t , i.e., t = T N . The value of t is small enough so that the distance between any two nodes (the source, the destination, or the UAV relays) can be regarded as approximately constant within each time slot. With the discretization, the trajectory of UAV relay m in the horizontal plane can be expressed by discrete variables {q m [n], n = 1, . . . , N }. We assume that the initial location and the final location of UAV relay m are [q T 0,m , H ] T and [q T F,m , H ] T , respectively, and its maximum speed is v max . Thus, the mobility constraints of UAV relay m can be expressed as where · denotes the Euclidean norm and S v max t is the maximum distance that a UAV can travel within one time slot. In addition, since all UAVs fly at the same altitude, we set collision avoidance constraints for all UAV 1 Here, we assume that all UAVs fly at the same altitude H for simplicity. The considered model with this assumption can be extended to the scenario where different UAVs fly at different altitudes by adding the altitudes of the UAVs as variables to be optimized, and the resultant problem can be solved by a method similar to that in this paper. relays as where L min denotes the minimum allowable distance between any two UAVs.
The M UAV relays assist the communication from the source to the destination in the following manner: the source sends data to UAV relay 1, UAV relay 1 forwards its received data to UAV relay 2, and so on, until UAV relay M forwards data to the destination. Each UAV relay works in the full-duplex mode, which allows it to receive and transmit data at the same time at different frequencies, as described in the next paragraph. The wireless channels from the source to UAV relay 1, from UAV relay m to UAV relay m + 1, m = 1, . . . , M − 1, and from UAV relay M to the destination are assumed to be LoS channels, which has been verified by recent measurement results [31]. Thus, the power gain of the channel from the source to UAV relay 1 in time slot n follows the free space path loss model and can be written as where L s, 1 [n] denotes the distance between the source and UAV relay 1 in time slot n, and α 0 denotes the power gain of a wireless channel at a reference distance of 1 m. Similarly, the power gains of the channels from UAV relay m to UAV relay m + 1 and from UAV relay M to the destination respectively, are Since the source and the UAV relays may transmit signal at the same time, to avoid interference in the relaying process, a frequency reuse scheme is applied, which divides the total bandwidth B in Hertz (Hz) into M + 1 orthogonal channels. Specifically, in time slot n, channel 1 with bandwidth Ba s,1 [n] in Hz is allocated to the 1st hop (from the source to UAV The transmit powers of the source and the UAV relays are subject to both average constraints and peak constraints. We denote the transmit powers of the source and UAV relay m in time slot n by P s [n] and P m [n], respectively, and write the constraints on transmit powers of the source and UAV relay m in (7) and (8), respectively, as follows.
whereP s andP m denote the average powers of the source and UAV relay m, respectively, and P s,max and P m,max denote their peak powers, respectively. To make the constraints (7a) and (8a) non-trivial, we assume thatP s < P s,max and P m < P m,max . With the above notations, the achievable rate from the source to UAV relay 1 in time slot n over unit bandwidth in bits/second/Hertz (bps/Hz) can be expressed as where ξ 0 = α 0 BN 0 and N 0 denotes the power spectral density of the additive white Gaussian noise (AWGN) at the receivers. Similarly, the achievable rates from UAV relay m to UAV relay m + 1 and from UAV relay M to the destination in time slot n over unit bandwidth in bps/Hz can be expressed as We consider DF relaying. Thus, the multi-hop relaying process is subject to the ''information-causality'' constraint [18], [19], [30], which means that in each time slot, UAV relay 1 can only forward the data that it has already received from the source, and UAV relay m+1 can only forward the data that it has already received from UAV relay m, m = 1, . . . , M −1.
Assuming the processing and forwarding delay at each UAV relay is one time slot, we express the information-causality constraints as Furthermore, note that since the data processing and forwarding delay from the source to the destination via M hops is M time slots, there is no point for the source to transmit within the last M time slots. In addition, since the data processing and forwarding delays from the source to UAV relay m and from UAV relay m to the destination are m and M − m time slots, respectively, there is no point for UAV relay m to transmit within the first m time slots and the last M − m time slots. Therefore, there are additional constraints on transmit powers and channel bandwidths: Since the end-to-end throughput of a multi-hop DF relaying system is limited by the rate of the weakest hop, according to the information-causality constraints (12) and (13), the average end-to-end throughput from the source to the destination over the whole flight duration, denoted byR thr , is limited by the average achievable rate from UAV relay M to the destination asR
Since the objective function in (16) is not concave and the constraints in (2), (12), and (13) are not convex, (16) is not a VOLUME 7, 2019 convex optimization problem. In the next section, we propose an efficient algorithm to solve it suboptimally.

III. EFFICIENT SOLUTION TO PROBLEM (16)
We first partition the optimization variables of problem (16) into two blocks, one for the bandwidth and transmit power variables (A, P) and the other for the UAV trajectory variables Q. With the variable partition, we propose an efficient algorithm to solve (16) by applying the alternating optimization method. Specifically, we divide problem (16) into two subproblems: sub-problem 1 optimizes (A, P) under given Q, and sub-problem 2 optimizes Q under given (A, P). We solve these two sub-problems alternatively until the objective value of problem (16) converges. In the following, we first show how to solve sub-problems 1 and 2 efficiently, and then show the overall algorithm in the end.
It can be shown that there exists an optimal solution to (21) such that the constraints (21e) and (21f) are satisfied with equality. This can be proved as follows. Suppose that for ∀l = 1, . . . , M − 1 and ∀n, P l [n] is an optimal solution to problem (21), which satisfies constraint (21e) with strict inequality. We can always find a solutionP l [n] that is strictly smaller than P l [n] and satisfies constraint (21e) with equality without decreasing the optimal value in (21). Similarly, we can also prove that there exists an optimal solution satisfying constraint (21f) with equality. Therefore, problem (21) has the same optimal solution of A and P as problem (20). Thus, we can obtain the optimal solution to problem (20) by solving problem (21). Since the objective function of problem (21) is linear and the feasible region of it is convex, problem (21) is a convex optimization problem and can be solved optimally by using the interior-point method [32].
Since the objective function of problem (26) and the LHSs of the constraint (2) are non-concave with respect to Q, and the LHSs of the constraints (26b)-(26d) are non-convex with respect to Q, problem (26) where (27g) is from constraint (2). Similar to sub-problem 1, it can be proved that there exists an optimal solution to problem (27) that satisfy the constraints (27e) and (27f) with equality, and thus problem (27) has the same optimal solution of Q as problem (26). Therefore, we can find Q by solving problem (27). However, it is still difficult to obtain the optimal solution to problem (27) due to the following two reasons. First, the terms R s (q 1 [n]) in (27b), R m (q m [n], q m+1 [n]) in (27e), and R M (q M [n]) in (27f) are non-convex with respect to Q. Second, the term q m [n] − q k [n] in (27g) is non-concave with respect to Q.
In the following, we propose an efficient algorithm to find an approximate solution to problem (27), using the successive convex optimization method. The algorithm successively maximizes the objective function of problem (27) where η (l)
After the approximation, we note that the objective function of problem (38)  ) in (38f) are concave with respect to Q, and the right hand side of (38g) is linear with respect to Q. Therefore, problem (38) is convex and can be solved optimally by the interior-point method [32]. Since the constraints (38b), (38e), (38f), and (38g) of problem (38) imply the constraints (27b), (27e), (27f), and (27g) of problem (27), respectively, the solution obtained by solving problem (38) is guaranteed to be a feasible solution to problem (27). Furthermore, since problem (38) can be optimally solved and problem (38) and problem (27) have the same objective function, the objective value of problem (27) with the solution obtained by solving problem (38) in the (l + 1)th iteration Q (l+1) must be no less than that with the solution obtained in the lth iteration Q (l) . As the objective value of problem (27) is bounded from above, the iteration of solving problem (27) is guaranteed to converge.

C. OVERALL ALGORITHM
The overall algorithm solves sub-problems 1 and 2 alternately until (16) converges. We summarize it in Algorithm 1, where θ > 0 and > 0 are thresholds indicating the convergence of (27) and (16), respectively. Since the value of (16) is non-decreasing over iterations, and it is bounded from the above, Algorithm 1 is guaranteed to converge. Algorithm 1 has a polynomial-time complexity O(K ite (MN ) 3.5 ), where K ite denotes the iteration number.

IV. NUMERICAL RESULTS AND DISCUSSION
We have conducted computer simulation to verify the performance of our proposed algorithm (denoted by ''joint optimization'') and compared it with three benchmark schemes described as follows. Update i = i + 1.

4:
For given trajectory variables Q (i−1) , update the bandwidth and transmit power variables (A (i) , P (i) ) by solving problem (21).

5:
For given bandwidth and transmit power variables (A (i) , P (i) ), update the trajectory variables Q (i) by the following iteration process. Set initial variablesQ (0) = Q (i−1) , and set l = 0. 6: repeat 7: Update l = l + 1. 8: ObtainQ (l) by solving problem (38). 9: until The fractional increase of the objective value of problem (27) withQ (l) is smaller that a given threshold θ > 0. Set Q (i) =Q (l) . 10: until The fractional increase of the objective value of problem (16) with A (i) , P (i) , Q (i) is smaller than a given threshold > 0.
trajectory optimization and power allocation algorithm proposed in [30].    Fig. 3 shows the trajectories of the UAV relays in the horizontal plane when the UAV flight duration is T = 40 s, whereP = 10 dBm. It is observed that the UAV trajectories obtained by the benchmark ''fixed BW'' and ''fixed BW and power'' schemes are similar, where the two UAV relays fly from the initial location to the final location in arc paths, and during their flights, UAV relay 1 and UAV relay 2 are close to the source and the destination, respectively. It is also observed that the UAV trajectories obtained by the proposed scheme is slightly different from those by the benchmark ''fixed BW'' and ''fixed BW and power'' schemes, where the two UAV relays are closer with each other during the flight.   Fig. 4 is larger than that of Fig. 3, more degree of freedom is available for UAV trajectory optimization. It is observed that the trends of the UAV trajectories of the benchmark ''fixed BW and power'' and ''fixed BW'' schemes are similar. Specifically, in these two schemes, UAV relay 1 first flies towards a point close to the source, then flies towards the destination, and finally flies to the final location; UAV relay 2 first flies towards the destination for a short period of time, then turns and flies towards a point near the source, and then flies towards the destination and finally towards the final location. It is also observed that the UAV trajectories obtained by the proposed joint optimization scheme are significantly different from that obtained by the above two benchmark schemes. To show the UAV trajectories more clearly, corresponding time variables are marked on the trajectories, where solid line and dash line arrows are for UAV relay 1 and UAV relay 2, respectively. It can be seen that UAV relay 1 first flies towards a point close to the source in order to receive as much data from the source as possible; from t = 34 s to t = 70 s, it flies towards the destination along the line connecting the source and the destination, in this way, it can receive as much data from the source as possible and send as much data to UAV relay 2 as possible; from t = 70 s on, it flies to the final location following an arc path to get close to UAV relay 2 in order to send as much data to it as possible. On the other hand, UAV relay 2 first flies together with UAV relay 1 towards the source and then turns its direction and flies towards the destination at t = 10 s; from t = 10 s to t = 44 s, it flies towards a point close to the destination in order to send the data it received so far to the destination; from t = 44 s to t = 60 s it flies towards UAV relay 1 in order to receive as much data from it as possible; from t = 60 s to t = 86 s, UAV relay 2 flies towards a point close to the destination in order to send as much data to the destination as possible; finally from t = 86 s on, it flies directly towards the final location, and it keeps sending data to the destination till the end of the flight.  The corresponding channel bandwidth allocation and transmit power allocation results obtained by the proposed joint optimization scheme when T = 120 s andP = 10 dBm are shown in Figs. 5 and 6, respectively, where the former figure shows the bandwidth of the channels from the source to UAV relay 1, from UAV relay 1 to UAV relay 2, and from UAV relay 2 to the destination normalized by the total bandwidth B versus time t, and the latter figure shows the corresponding transmit power of the source, UAV relay 1, and UAV relay 2 versus time t. It is observed that from t = 0 s to t = 18 s, during which UAV relay 1 and UAV relay 2 are getting close to the source as shown in Fig. 4, the source and UAV relay 1 have non-zero bandwidth and power allocation, which means that during this period, the source sends data to UAV relay 1 and UAV relay 1 sends data to UAV relay 2 at the same time. Furthermore, the bandwidth and power allocated to the source are significantly greater than that allocated to UAV relay 1, which means the joint optimization scheme mainly focuses on data transmission from the source to UAV relay 1 in this period. From t = 18 s to t = 44 s, all bandwidth and power are allocated to the source for its data transmission to UAV relay 1. At t = 44 s, all bandwidth and power allocation are allocated to UAV relay 2, because it arrives at a location close to the destination and it is a right time for it to send its received data to the destination. After the data transmission of UAV relay 2 is completed, all bandwidth and power allocation are allocated to the source again, and it continues to send data to UAV relay 1 until t = 56 s. From t = 56 s to t = 72 s, all bandwidth and power are allocated to UAV relay 1 for its data transmission to UAV relay 2. From t = 72 s to t = 96 s, during which UAV relay 2 is close to the destination, all bandwidth and power are allocated to it for its data transmission to the destination. At t = 96 s, as shown in Fig. 4, UAV relay 1 reach a location close to UAV relay 2, and from then on bandwidth and power are allocated to both UAV relay 1 and UAV relay 2 for the data transmissions from UAV relay 1 to UAV relay 2 and from UAV relay 2 to the destination. Fig. 7 shows the throughput of different schemes versus UAV flight duration T whenP = −5 dBm andP = 10 dBm. It is observed that the throughput of all schemes increases with T . It is also observed that the proposed joint optimization scheme always achieves the highest throughput, and the ''fixed BW'' scheme always outperforms the ''fixed BW and power'' scheme. This is because the more degree of freedom is available for resource allocation, the higher throughput performance can be achieved. Furthermore, the ''line trajectory'' scheme has higher throughput than the ''fixed BW'' and ''fixed BW and power'' schemes in the regime of T ≤ 120 s whenP = −5 dBm, and has lower throughput than these two benchmark schemes in the regime of T ≥ 60 s whenP = 10 dBm. These results show that bandwidth and power allocation is more effective in improving throughput performance whenP is low, and UAV trajectory optimization is more effective in improving throughput performance when P is high.
The above results demonstrate that the proposed joint optimization scheme can strike a balance among the data transmissions from the source to UAV relay 1, from UAV relay 1 to UAV relay 2, and from UAV relay 2 to the destination, and thus is effective in improving the end-to-end throughput from the source to the destination.

V. CONCLUSION
In this paper, we have studied deploying M UAVs as multi-hop relays to assist the communication from the source to the destination. To fully exploit all available degree of freedom for spectrum efficiency improvement, we have maximized the end-to-end throughput from the source to the destination by jointly optimizing the transmit powers of the source and all UAV relays, the channel bandwidths of the M + 1 hops, and the trajectories of all UAV relays, subject to the mobility constraints and the collision avoidance constraints of the UAVs, the channel bandwidth and transmit power constraints, and the information-causality constraints of the source and UAV relays. Although the optimal solution of the considered throughput maximization problem is difficult to obtain, we have proposed an efficient algorithm to find a high-quality suboptimal solution to it, which achieves significantly higher throughput as compared to some benchmark schemes. In the future, it will be interesting to study multi-hop UAV relaying in the scenario where all UAVs can use the same spectrum to forward data when the interference is weak or when the interference from the previous UAVs could be canceled.