NOMA-Aided UAV Data Collection System: Trajectory Optimization and Communication Design

Unmanned aerial vehicle (UAV) communication has been deemed as a promising technology to collect data for the Internet of Things (IoT) in inaccessible areas. However, due to the limited UAV flight time, traditional UAV communication may not be competent for large-scale IoT data collection. This paper considers integrating non-orthogonal multiple access (NOMA) into UAV communication systems to collect data for large-scale IoT devices within UAV flight time. We aim to minimize the total energy consumption of IoT devices while ensuring data collection, by jointly optimizing UAV trajectory, IoT device scheduling and transmit power. The formulated problem is a mixed integer non-convex problem, which is challenging to solve in general. We propose a data collection optimization algorithm (DCOA) to solve it by applying the Generalized Benders Decomposition (GBD) and successive convex approximation (SCA) techniques. Then, a greedy algorithm (GA) is also proposed to reduce complexity by simplifying the optimization of UAV trajectory and IoT device scheduling. Finally, the numerical results demonstrate that, compared with traditional UAV communication systems, the NOMA-aided UAV system performs better in terms of data collection and lower total energy consumption of IoT devices can be achieved by DCOA.


I. INTRODUCTION A. MOTIVATION
The Internet of Things (IoT) with powerful connection and data interaction, is promoting the development of energy, medical, agriculture and other fields, which has dramatically changed our daily life [1]- [4]. According to Cisco, 500 billion devices are expected to be connected to the Internet by 2030 [5], sensing or interacting with the internal state or the external environment and communicating over the IoT. The data collected by IoT devices (IoTDs) can be processed by IoT applications to provide insights and help make decisions and actions. However, with the expansion of the application scale, defects of IoT in data collection gradually emerge, restricting its further development.
Data collection is an essential function of IoT and the basis of IoT applications. Limited by the energy consumption, The associate editor coordinating the review of this manuscript and approving it for publication was Praveen Gunturi. quantity and distribution of IoTDs, data collection has always been a challenge for IoT. Nowadays, the common data collection technologies are Narrow Band IoT (NB-IoT) and Long Range (LoRa), due to their advantages of wide coverage, large-scale connection and low device power consumption [6], [7]. However, both of them rely heavily on the infrastructure, such as base stations and signal towers, making them hard to catch up with the development of IoT, where more and more IoTDs are deployed in inaccessible areas, for example, in the forest to monitor the environment. It is infeasible either technically or economically to construct infrastructure in inaccessible areas. Therefore, effective data collection schemes for IoT in inaccessible areas are urgently needed.
In this context, Unmanned aerial vehicle (UAV) communication is considered as a promising technology to solve the above problem, due to its high mobility, low cost and flexible deployment [8]. UAV can be deployed flexibly in inaccessible areas at any time, significantly reducing the 1 The flight time of UAV is closely related to the energy consumption of UAV. As the energy consumption of UAV is affected by many factors, such as UAV load, flight speed, flight altitude, wind speed, etc., in practical, UAV flight time is more often mentioned as an important parameter of UAV. Therefore we pay more attention to UAV flight time.
of UAV-based aerial small cells [17]. Energy limitation is a major bottleneck in UAV communication. Zeng et al. derived the propulsion power consumption model of the rotary-wing UAV and found the optimized hovering locations and durations to minimize the propulsion and communication energy of UAV [18]. In particular, Sun et al. proposed the solar-powered UAV, which effectively solved the limitation of UAV energy and greatly improved the stability and sustainability of UAV communication. And they maximized the system sum throughput by optimizing the 3D aerial trajectory and the wireless resource allocation [19]. In terms of enhancing user performance, Zhan et al. jointly optimized the wake-up schedule and UAV trajectory to minimize the maximum energy consumption of users [20]. Mozaffari et al. proposed a novel framework to minimize the total transmit power of devices under their SINR constraint [21]. Lin et al. maximized the energy efficiency of sensors by adaptively tuning the frame length at MAC layer according to UAV flying speed [22]. Wu et al. investigated new type of multi-UAV enabled wireless networks to maximize the minimum average rate among all users, by jointly optimizing user scheduling and association, UAV trajectory and transmit power [23]. UAV has become an indispensable part of the future communication system. It is worth noting that the above studies are based on OMA while we study the UAV communication systems with the power domain NOMA. The power domain NOMA separates the signals of multiple IoTDs at the expense of IoTD power, which leads to the coupling of IoTD scheduling and power. In addition, SIC in NOMA is generally conducted according to the descending order of the channel gain, which is affected by UAV trajectory. Therefore, the optimization of UAV trajectory, IoTD scheduling and transmit power in this paper will be much complicated.

2) NOMA
Saito et al. firstly presented the concept of NOMA in [24] and they investigated the system level performance of NOMA with ideal SIC in [25]. Then researchers analyzed the performance of the NOMA system in the actual communication system [26], [27]. Wang et al. considered the downlink of NOMA systems with statistical channel state information, deriving the ergodic data rate, the outage probability and the sum throughput of NOMA systems [26]. Ding et al. investigated the performance of NOMA in a cellular downlink scenario with randomly deployed users [27]. The data rate of uplink and downlink was optimized in [28] and [29]. Zhu et al. optimized the achievable sum rate with minimum rate constraint in a downlink 2-user NOMA network, considering user pairing and power allocation [28]. Sedagha et al. maximized the sum rate of single antenna multiple subcarriers NOMA uplinks under frequency-flat fading and frequency-selective fading [29]. Since the power domain NOMA is realized via different power level of users in the same frequency, the studies in [30] and [31] focused on energy efficiency of the NOMA system. Fang et al.
aimed to maximize the system energy efficiency in a NOMA HetNet via subchannel allocation and power allocation [30]. Zeng et al. optimized power and sub-channel allocation to maximize the energy efficiency of multi-carrier uplink NOMA systems considering the user power restriction [31]. Pischella et al. paid more attention to the proportional fairness of NOMA. They proposed a graph-based clustering and resource allocation algorithm to optimize the time-based proportional fairness in the multi-carrier uplink networks [32].
Recently, some researchers considered integrating NOMA into UAV communication systems to improve UAV performance. Hou et al. proposed a NOMA-aided UAV network by utilizing a stochastic geometry model for providing wireless service to randomly roaming users [33]. They also proposed two connection strategies in NOMA-assisted multi-UAV communication system, user-centric strategy and UAV-centric strategy, and derived interference and coverage probability in the imperfect successive interference cancelation scenario [34]. Sohail et al. optimized the energy efficiency of the multi-user NOMA assisted UAV communication system by a computationally efficient method amid multi-QoS constraints [35]. Zhao et al. maximized the sum rate of the network served users by optimizing UAV trajectory and precoding vectors [36]. Cui et al. paid more attention to user fairness. They jointly optimized the trajectory design and resource allocation to maximize the minimum average rate between multiple users with the constraints of UAV flight speed and transmit power [37]. The number of users with satisfactory QoS experience was maximized in [38], by optimizing UAV deployment, admission control and power allocation. The above studies proposed some solutions to improve the performance of NOMA aided UAV communication systems. However, it is worth mention that these studies aim at the long-term benefits of the system without considering the effect of UAV flight time, which may not be applicable to the scenarios where the primary goal is to accomplish data collection of large-scale IoTDs within UAV flight time.

C. CONTRIBUTIONS AND ORGANIZATION
In this paper, we propose the NOMA-aided UAV communication system to collect data for large-scale IoTDs in inaccessible areas. The main contributions are as follows. 1) We aim to complete data collection within UAV flight time and reduce the total energy consumption of IoTDs, by jointly optimizing UAV trajectory, IoTD scheduling and transmit power, which is a challenging problem to solve due to the coupling of the variables. A data collection optimization algorithm (DCOA) is proposed to obtain a suboptimal solution.
2) The formulated problem is a mixed integer non-convex problem, which is difficult to tackle due to the coupling variables. The Generalized Benders Decomposition (GBD) is used to decouple IoTD scheduling and transmit power and get the optimal IoTD scheduling.
Then, with the given IoTD scheduling, we propose a two-step iterative optimization algorithm to get the optimal UAV trajectory and IoTD transmit power by applying the successive convex approximation (SCA) technique. In addition, in order to reduce complexity, a greedy algorithm (GA) is proposed by simplifying the optimization of UAV trajectory and IoTD scheduling. 3) Numerical results show that the NOMA-aided UAV system performs better in terms of the data collection success rate of large-scale IoTDs compared with traditional UAV communication systems. Besides, numerical results also reveal that lower total energy consumption of IoTDs can be achieved by DCOA. And the greedy algorithm can greatly reduce the runtime of algorithm. The rest of this paper is organized as follows. Section II introduces the system model and the problem formulation. In Section III, we present DCOA algorithm and GA algorithm in detail and analyze the computational complexity of these two algorithms. The numerical results are investigated in Section IV. Finally, we conclude this paper in Section V.

II. SYSTEM MODEL AND PROBLEM FOMULATION
A. SYSTEM MODEL In this paper, as shown in Figure 1, we focus on a NOMA-aided UAV data collection system for large-scale IoTDs in inaccessible areas. IoTDs are distributed in inaccessible areas, denoted as K = {1, 2, . . . k, . . . K }. UAV is deployed to collect data from IoTDs, denoted as u. The radius of the inaccessible areas is denoted as R.

1) MODEL OF IoT DEVICES AND UAV
It is assumed that the location and data volume of IoTDs are known. The parameters of IoTD k can be expressed by the matrix M k = {D k , C k , P k , P max }. D k = (x k , y k ) is the coordinate of IoTD. C k is the amount of uploaded data. P k is the transmit power, and the maximum power is denoted as P max .
The parameters of UAV can be expressed by the matrix

2) CHANNEL MODEL
The UAV communication channel is divided into M subchannels, expressed as M = {1, 2, . . . m, . . . M }. The subchannel bandwidth is W . Referring to [20], [23], [39], we assume that the communication channel is a line-of-sight (LOS) channel, and the channel gain follows the free space path loss model. 2 h k [n] represents the channel gain of IoTD k in time slot n. The channel gain can be assumed constant in each time slot because the position of UAV is assumed to remain approximately unchanged in each time slot in UAV model.
where β 0 represents the channel gain at the reference distance d = 1 m and d u,k [n] represents the distance between IoTD k and UAV in time slot n.

3) NOMA MODEL
As shown in Figure 1, we divide IoTDs into two sets K Referring to [24] and [25], SIC is conducted according to the descending order of channel gain at the receiver. Since the channel gain of external IoTD is less than the channel gain of internal IoTD, the signal-to-interference and noise ratio of IoTD k can be expressed as ∀n ∈ N , ∀m ∈ M, (5) where σ 2 represents the power spectral density of noise.
The trajectory optimization and communication design problem of the NOMA-aided UAV data collection system can be formulated as  [n] are coupled in (9b). So problem P is a mixed integer non-convex problem. In addition, K I and K O are determined by the position of UAV, which cannot be presented by formula. Thus solving problem P optimally is challenging in general.

III. PROPOSED ALGORITHM
Notation: For variable A, A * represents the optimal value. A,Ā orÂ represent the feasible value. In this section, we discuss the proposed DCOA algorithm for solving problem P. The block diagram of DCOA is illustrated in Figure 2. We first initialize UAV trajectory D u [n] with a clustering method. Then, Generalized Benders Decomposition is used to get the optimal IoTD scheduling α * k [n][m] with given D u [n]. Next, we formulate problem P2 with the goal of maximizing the amount of uploaded data and problem P3 with the goal of minimizing the total energy consumption of IoTDs. Finally, UAV trajectory and transmit power are optimized by iteratively solving P2 and P3 under the condition that the amount of uploaded data is increased and the total energy consumption is reduced.

A. UAV TRAJECTORY INITIALIZATION
UAV trajectory is initialized based on the position and the uploaded data of IoTDs. Specifically, the initial UAV trajectory is designed as a circle. The center is expressed as where k = C k K k=1 C k . The radius is denoted by where ς(0 < ς < 1) is the parameter to regulate UAV trajectory. Thus, the initial position of UAV in time slot n can be expressed as Therefore, radius r u of the internal IoTD area is denoted as

B. IoTD SCHEDULING OPTIMIZATION
With given D u [n] and r u , IoTD scheduling and transmit power can be optimized by solving problem P1.

P1
: min is a mixed integer nonlinear programming problem (MINLP). We intend to solve this problem with Generalized Benders Decomposition [40], [41]. P1 can be decomposed into two sub-problems, the primal problem with only continuous variables P k [n] and the master problem with only integer variables α k [n][m]. By iteratively solving these two sub-problems, the optimal solution is obtained. Specifically, in the v-th iteration of GBD, the upper bound of problem P1 can be updated by solving the primal problem, and optimality cut or feasibility cut can be obtained as the constraints of master problem. By solving the master problem, the lower bound of problem P1 can be updated, and the optimal α [m] can be obtained for the primal problem of the next iteration. When the difference between the upper bound and lower bound is less than the threshold δ, the iteration converges.

1) SOLVING THE PRIMAL PROBLEM
In the v-th iteration of GBD, with given integer variable α , the primal problem can be expressed as is a non-convex problem due to the non-convex constraint (15b). We apply dual decomposition and SCA to relax (15) into a convex problem. VOLUME 8, 2020 Dual Decomposition: With the Lagrange dual, the Lagrange function of (15) can be denoted as where η = [η 1 , . . . , η k , . . . , η K ] T , η k 0 is the Lagrange multiplier vector. Problem (15) can be written as The dual problem can be expressed as (18) can be decomposed into a two-layer optimization problem, the inner layer minimization problem with variable P k [n] and the outer layer maximization problem with variable η. By iteratively solving these two problems, the optimal solution of problem (18) is obtained.

a: INNER LAYER MINIMIZATION
In the u-th iteration, with given η (u) , the inner layer minimization problem is expressed as where Since R I k [n][m] is a non-concave function with respect to P k [n], (19) is not a convex minimization problem. Referring to [23], we get the sub-optimal solution of problem (19) wherē In order to tackle the non-concave function [25], in the r-th iteration of SCA, we perform the first-order Taylor Then (22) can be transformed into the following convex function.
The key to the transformation is thatR I k [n][m] is a concave function with respect to P k [n]. According to [42], the first-order Taylor expansion of the concave function at any point is the global upper bound of the function. Therefore, [m] and L 2 L 2 . Thus, the transformation will not expand the range of problem (19).
Thus, the inner layer minimization problem (19) can be rewritten as It can be found that the first derivative of the function L(P k [n], η (u) ) with respect to P k [n] is an increasing function, so the optimal solution of (29) can be denoted as The SCA algorithm for problem (19) is shown in Algorithm 1.
is the optimal solution of the inner layer minimization problem (19). With givenP (u) k [n], the outer layer maximization problem is expressed as Since L(η,P ) is differentiable with respect to η k , the gradient method can be applied to solve the multiplier η where ϕ(ϕ > 0) is the step size in the u-th iteration. The iteration terminates when L (u+1) − L (u) κ, where κ is the threshold.
Hence, the optimal solution of the primal problem in the vth iteration of GBD can be obtained by solving problem (19) and (32).P (v) =η (u) . The Algorithm 2 for the primal problem is as follows. , and calculate η (u+1) according to (33). 6:

2) FEASIBILITY CHECK FOR THE PRIMAL PROBLEM
In the v-th iteration of GBD, α If the primal problem is feasible in the v-th iteration, we can get the optimality cut and add it as a constraint of the master problem.

b: THE PRIMAL PROBLEM IS INFEASIBLE
If the primal problem is infeasible, define a set ofη (v) The calculation ofη (v) is presented in APPENDIX A. By solving (35), the optimalP is obtained. The feasibility cut can be denoted as

3) SOLVING THE MASTER PROBLEM
With the given optimality cut and feasibility cut, the master problem can be expressed as where v 1 is the number of times the primal problem is feasible, and v 2 is the number of times the primal problem programming problem, which can be solved by the branch and bound method or the cut plane method [43], [44].
With the dual decomposition and the first-order Taylor expansion, the primal problem is transformed into a convex optimization problem. Therefore, according to [45], the convergence of GBD algorithm can be guaranteed. In addition, it should be noted that the primal problem must be feasible in the first iteration of GBD algorithm [41].
GBD algorithm for problem P1 is shown in Algorithm 3. if (15) is feasible then 5: Get the optimal transmit powerP (v) k [n],η (v) and the optimal objective valueẼ. 6: Obtain the optimality cut with dual decomposition. 7: The upper bound value is updated with UB(v) = min UB(v − 1),Ẽ . Obtain the feasibility cut according to (37). 11: end if 12: Add the optimality cut or the feasibility cut to the master problem. 13: Solve the master problem (38) with branch and bound method, and get α  if |UB(v) − LB(v)| ε then 15: Global optimal solution = true; 16

Algorithm 3 Generalized Benders Decomposition for Solv
(39d) (39b) and (39c) are convex sets, because UAV trajectory in other time slots is available when optimizing UAV trajectory in time slot n. (39a) is a non-convex constraint, so (39) is not a concave maximization problem, which cannot be solved directly in general.

R I k [n][m] in (39a) can be expressed as
wherē Referring to [23], we introduce the relaxation variable S.
Therefore (39) It can be proved that (45b) holds with equality when problem (45) [42], the first-order Taylor expansion of the convex function at any point is the global lower bound of the function. Therefore, this transformation does not expand the feasible region of problem (45).

Specifically,R I k [n][m] can be transformed tō
where B I (r) where J I (r) In the same way, because D u [n] − D i Therefore, problem (45) (53e) VOLUME 8, 2020 Problem (53) is a convex optimization problem, which can be solved with CVX [42]. Due to the function relaxation, the optimal solution of problem (53) is the lower bound of the optimal solution of problem P2. And the optimal UAV trajectory of problem (53) can be denoted asD u [n]. The Algorithm 4 for problem P2 is presented as follows.  P3 : min s.t. 0 P k [n] P max , ∀k ∈ K, ∀n ∈ N , (54a) Problem P3 is similar to problem (15), so Algorithm 2 can be applied to solve it. The optimal IoTD transmit power of problem (54) is denoted asP k [n]. In summary, data collection optimization algorithm shown in Figure 2 is shown in Algorithm 5.

E. DESIGN OF GREEDY ALGORITHM
In order to reduce algorithm complexity, we propose a greedy algorithm for the NOMA-aided UAV data collection system. As shown in Algorithm 6, we propose an IoTD pairing scheme based on the amount of uploaded data and channel gain of IoTDs to optimize IoTD scheduling, and the initial UAV position is taken as the optimal UAV trajectory. In addition, more than two IoTDs are allowed to reuse the same channel in the same time slot in the greedy algorithm. 14: else 15:

F. COMPUTATIONAL COMPLEXITY ANALYSIS
The computational complexity of the proposed algorithm DCOA and GA is analyzed as follows. The computational complexity of DCOA depends on Algorithm 2, 3 and 4. In the worst case, the computational complexity of Algorithm 2 is roughly estimated as O u max r max K 2 M N 2 . The primal problem of Algorithm 3 is solved by Algorithm 2. The master problem of Algorithm 3 is solved by the branch and bound method or the cut plane method, so its computational complexity is O (4KMN ) 3 [44], [46]. In the worst case, the computational complexity of Algorithm 3 is roughly estimated as O 64v max (KMN ) 3 . The computational complexity of Algorithm 4 in the worst case is roughly estimated as O max 3r max KM N 2 , 8r max N 4 [42]. Assume that the loop number of Algorithm 2 and Algorithm 4 in DCOA is L. The computational complexity of DCOA algorithm in the worst case is roughly estimated as (55). The GA algorithm consists of the following three parts: UAV trajectory optimization, IoTD scheduling and power optimization. The computational complexity of the three parts are roughly estimated as O (N ), O 2K 3 and O u max r max K 2 M N 2 respectively. Therefore, the computational complexity of the proposed GA algorithm in the worst case is roughly estimated as Assign channel for IoTDs inK Y according to their sequence number. 15: For k ∈K Y , α k [n][m] = 1. IoTD k is closest to UAV in time slot n. m is the channel number of idle channel in time slot n. 16: until All channels are assigned. 17: repeat 18: Let P k = P max . According to (6) and (7), calculatẽ . 19:Ĉ k = C k −C k . 20: ifĈ k > 0 then 21: Let k ∈ K Y . C k =Ĉ k . 22: else 23: Let k ∈ K N . 24: end if 25: GetK Y by sequencing IoTDs in K Y from large to small according to C k . 26: GetK N by sequencing IoTDs in K N from small to large according to C k . 27: Assign channel according to the sequence number of IoTD k inK Y . 28: For k ∈K Y , α k [n][m] = 1. The time slot n and the channel number m are the same as those of IoTD j (j ∈ K N ), and the sequence number of IoTD j in step 26 is same as the sequence number of IoTD k in step 25. 29

IV. NUMERICAL RESULTS
In this section, numerical results are presented to demonstrate the performance of the proposed algorithm. In the simulation, we assume that IoTDs are randomly distributed in a circular area with radius R = 70 m. The amount of uploaded data C k varies randomly from 1 Mbit to 5 Mbit. The maximum transmit power is P max = 4 W. The flight height and maximum flight speed of UAV are H = 50 m and V max = 7 m/s. The trajectory initialization parameter is set as ς = 0.7. Furthermore, assuming the number of system channels is M = 7 and the bandwidth of sub-channel is W = 30 kHz. The normalized channel gain is β 0 = −50 dB. The noise power is σ 2 = −100 dBm.  In Figure 3 and Figure 4, we evaluate the convergence performance of GBD algorithm and the two-step iterative optimization algorithm for problems P2 and P3 in DCOA. We set N = 6, K = 70 and T = 60s. As shown in Figure 3, for GBD algorithm, the initial upper bound is set to the maximum energy consumption of IoTDs (2 · 6 · 7 · 10s · 4W = 3360 J), and the lower bound is 0 J. It can be found that the difference between the upper bound and the lower bound gradually decreases and GBD algorithm converges after 13 iterations. For the two-step iterative optimization algorithm shown in Figure 4, the initial value is the total energy consumption optimized by GBD algorithm, and it converges after 6 iterations. It can be seen that the minimum energy consumption can be obtained with several iterations in DCOA, which shows that DCOA is effective.  Figure 5 shows the distribution of IoTDs and UAV trajectory optimized by GA and DCOA, respectively, when N = 6, K = 60 and T = 60s. The GA UAV trajectory is the initial UAV trajectory according to (12), and the DCOA UAV trajectory is the UAV trajectory optimized by DCOA algorithm. In this paper, the GA UAV trajectory is designed based on the amount of uploaded data and the location of IoTDs, with the goal of ensuring IoTDs fairness. Moreover, it can be observed that the DCOA UAV trajectory is around the GA UAV trajectory. This is due to the fact that the DCOA UAV trajectory is optimized based on the GA UAV trajectory. Because the increase in the channel gain difference of IoTDs which access the same channel in NOMA is conducive to the reduction of energy consumption. In order to minimize the total energy consumption of IoTDs, UAV tends to be close to IoTDs with large amount of uploaded data and away from IoTDs with small amount.
In Figure 6, we compare the total energy consumption of IoTDs achieved by GA algorithm and DCOA algorithm under different numbers of IoTDs when N = 6 and T = 60s, 70s, 80s. It can be observed that the total energy consumption presents an exponential growth with the increase in the number of IoTDs. This is because that the power domain NOMA scheme is realized at the cost of increasing of IoTDs power. In addition, in terms of NOMA, interference from co-channel IoTDs is much greater than noise. Thus, according to equations (6) and (7), the power of internal IoTD needs to be increased several times to ensure the data rate. Therefore, when the number of IoTDs is less than the number of channels (K = 30, 40), IoTDs are more likely to upload data by OMA to reduce energy consumption. As the number of IoTDs increases (K = 60, 70, 80), the number of NOMA IoTDs increases, resulting in the exponential growth of IoTDs energy consumption.
In addition, compared with GA algorithm, DCOA algorithm can effectively reduce the total energy consumption when K = 60, 70, 80. The more IoTDs, the more obvious the advantages of DCOA. The reason is that the pairing of IoTDs can affect the transmit power of IoTDs greatly, and DCOA algorithm optimizes IoTD scheduling by GBD algorithm. And the distance between UAV and paired IoTDs is optimized to reduce the interference from external IoTD by optimizing UAV trajectory.
Note: When K = 80, we set P max = 10W to get a generalized simulation result, which can intuitively show the impact of the increased number of IoTDs on the total energy consumption. Figure 7 shows the total energy consumption versus UAV flight time optimized by DCOA algorithm and GA algorithm when N = 6, K = 60, 70, 80 and r u = 23.3958m. It can be observed that the total energy consumption decreases exponentially with UAV flight time increasing. The reason is as follows. First, according to constraint (9b), P ∝ Tn √ 2 c and c = C k /W . So, IoTD transmit power decreases rapidly with the increase of flight time, especially when T n or c is large. Second, when the power of external IoTDs decreases, its interference with internal IoTDs also decreases, according to equation (6), which can significantly reduce the power of the internal IoTDs. Therefore, as presented in Figure 7, although communication time increases linearly, the total energy consumption of IoTDs decreases exponentially. From the numerical results, it can be found that increasing UAV flight time will greatly improve the performance of the proposed NOMA-aided UAV data collection system in terms of the total energy consumption of IoTDs.
In fact, UAV flight time is generally unchangeable, but T n can be changed with the value of N . Therefore, in Figure 8, we analyze the impact of N on total energy consumption. In Figure 8, we simulate the total energy consumption optimized by DCOA algorithm and GA algorithm when K = 60, T = 70s and R = 60m, 70m, 80m. It can be observed that with unchangeable UAV flight time, the total energy consumption increases significantly as N increases. Therefore, combining with the results of Figure 7, we can conclude as follows. For the proposed NOMA-aided UAV data collection system, in terms of reducing total energy consumption of IoTDs, reducing N to increase the length of one time slot T n is more effective than increasing N to increase the number of subchannels. In addition, as shown in Figure 8, small change of the radius R has little effect on the total energy consumption. In Figure 9, we analyze the impact of the amount of IoTD uploaded data on the total energy consumption optimized by DCOA algorithm. We set N = 6, T = 60s and the number of IoTD uploaded data is 1 Mbit ∼ 5 Mbit or 2 Mbit ∼ 5 Mbit. It can be observed that when the number of IoTD is large, the range of data volume of IoTDs will greatly affect the total energy consumption. And the larger the range of data volume changes, the lower the total energy consumption. Therefore, based on numerical results, we can find that the proposed UAV-aided NOMA data collection system is suitable for collecting data in inaccessible areas where multiple IoTDs with large differences in data volume coexist. Furthermore, we compare the runtime of GA algorithm and DCOA algorithm under the same computer configuration when N = 6, R = 70m and T = 60s. As shown in Table 1, the runtime of GA algorithm is greatly shortened since the optimization of UAV trajectory and IoTD scheduling is simplified. Combining the results of Figure 6 and Figure 7, compared with DCOA algorithm, the performance of GA algorithm decreases little when the number of IoTDs is small or UAV flight time is long. Therefore, in the above situation, GA algorithm may be more advantageous.
Finally, we compare the impact of NOMA and OMA on the success rate of data collection when T = 70s. For NOMA, we set N = 6. For OMA, in order to ensure the access of IoTDs, the number of subchannels should be more than the number of IoTDs. So, we set N = 8 when K = 50 and N = 9 when K = 60. As shown in Table 2, NOMA technology is more suitable than OMA technology for collecting data within limited time.

V. CONCLUSION
In this paper, we have investigated a NOMA-aided UAV communication system to collect data within UAV flight time for large-scale IoTDs in inaccessible areas. Specifically, UAV trajectory, IoTD scheduling and transmit power are jointly optimized to minimize the total energy consumption of IoTDs while ensuring data collection. Then data collection optimization algorithm is proposed to get the sub-optimal solution relying on the Generalized Benders Decomposition and successive convex approximation techniques. And we propose the greedy algorithm to reduce complexity by simplifying the optimization of UAV trajectory and IoTD scheduling. Finally, the numerical results demonstrate that, compared with the traditional UAV communication systems, the proposed NOMA-aided UAV system performs better in terms of the data collection and DCOA can effectively reduce the total energy consumption of IoTDs.

APPENDIX A SOLUTION OF THE FEASIBILITY CUT
The calculation ofη (v) andP k [n] can be achieved by solving the following 1 ∼ norm problem when the primal problem is infeasible.