In this paper, we consider a ground terminal (GT) to an unmanned aerial vehicle (UAV) wireless communication system where data from GTs are collected by an unmanned aerial vehicle. We propose to use the ground terminal-UAV (G-U) region for the energy consumption model. In particular, to fulfill the data collection task with a minimum energy both of the GTs and UAV, an algorithm that combines optimal trajectory design and resource allocation scheme is proposed which is supposed to solve the optimization problem approximately. We initialize the UAV’s trajectory firstly. Then, the optimal UAV trajectory and GT’s resource allocation are obtained by using the successive convex optimization and Lagrange duality. Moreover, we come up with an efficient algorithm aimed to find an approximate solution by jointly optimizing trajectory and resource allocation. Numerical results show that the proposed solution is efficient. Compared with the benchmark scheme which did not adopt optimizing trajectory, the solution we propose engenders significant performance in energy efficiency.

With series of features such as low cost, long duration, high flexibility, and high adaptability, extensive research endeavour has been rendered to exploring the application of UAV. In [

As we discussed previously, energy efficiency is a factor that cannot be ignored for UAV due to the limited on-board power. He et al. [

In this paper, a flexible UAV is deployed to collect data from a group of ground terminals at known location in ground terminals to a UAV (G2U) system. Intuitively, the study needs to jointly consider the uplink transmission energy of GTs and the UAV’s propulsion energy consumption. To obtain the most fundamental insights, we focus on a G2U wireless communication system, where a group of ground terminals are collected data by a UAV, as shown in Figure

A UAV-enabled data collection system.

The rest of this paper is organized as follows. Section

We consider a wireless system consisting of

We assume that the UAV flying at a fixed altitude

We assume that the channels between the UAV and the ground nodes are dominated by LoS links. Furthermore, we assume that the Doppler effect due to the UAV mobility can be perfectly compensated. Thus, the channel coefficient from the ground terminal

There are two parts of energy consumption in the UAV-enabled data collection system:

For fixed-wing UAVs, the total propulsion energy

The energy consumption

Note that the achievable data rate for each ground terminal is a function of total operating time

Consider the data collection system which both ground terminals and UAV would consume energy to support the data transmission and UAV flying. There are two parts of energy consumption: (1) ground terminal energy

The outer boundary of this region is called the

An energy pair

The Pareto boundary of the energy region characterizes that the minimum energy consumption for UAV and ground terminal for data collection task. It can be adopted to evaluate the trade-off of the energy consumption in the data collection system. It is an interesting topic to investigate the UAV trajectory strategy and resource allocation scheme for UAV and ground terminals to finish the data collection task cooperatively.

In this section, we address the data collection system in a general scenario where there are multiple ground terminals which is served by a flexible flying UAV. We first formulate the optimization problem to describe the Pareto boundary of the energy region. Then, we investigate the optimal solution of the optimization problem for this scenario, from which we obtain an upper bound for the achievable energy consumption pairs in the G-U region. Then, we propose an alternating iterative method to derive the optimal resource allocation scheme and optimal trajectory design strategy.

In order to characterize the trade-off of the energy region effectively, we adopt the strategy to minimize the ground terminal energy consumption with fixed UAV energy consumption. By traversing

The constraint

Note that the problem (

For ease of exposition, the time horizon

Correspondingly, the spectrum and power allocation

For the problem (

The constraint

Problem (

In this section, an efficient algorithm that combines optimal trajectory design and resource allocation scheme is proposed to approximately solve the original optimization problem. The sequential convex optimization method is applied to meet the optimized goal by iteratively obtaining the optimal trajectory and allocating the wireless resource to the ground terminals.

The original optimization problem can be classified into two subproblems: (1) wireless resource allocation issue for the multiple ground nodes and (2) the UAV trajectory optimization problem. To make the optimization problem more trackable, we propose to adopt the iteratively optimization method which assumes that one issue is determined when the other issue is considered to be optimized, and vice versa.

Firstly, we should find a feasible solution for the UAV flight trajectory from the initial point to the final location by the predefined available energy

It is noted that the constraints

The UAV energy consumption of the objective function can be upper-bounded by the following equation:

Considering the function is still a nonconvex set for the variable

It can be shown that we must have

Then, the inequality in first-order Taylor expansion shows that the new constructed convex constraint

Then, the optimization problem (

Based on the previous discussions, the optimal solution of (

For the wireless resource allocation issue, it is proposed to minimize the ground nodes transmit power under the fixed UAV trajectory

This subproblem may correspond to the practical scenario when the UAV’s trajectory is predetermined due to other tasks (e.g., surveillance) rather than data collection. In this case, the optimal solution of the subproblem (

Since the trajectory

Substitute the optimal

It is proposed to adopt an iterative subgradient method (Algorithm

Initialize

Obtain the optimal power

Get the subgradient

Update the dual variable according the equation (

Update

The optimal solution includes two steps: (1) each of subproblem in slot

Since the ground node has been allocated with fixed frequency band and power resource, we should adopt a dual problem to achieve the optimization goal by optimizing the UAV trajectory. In this section, we consider the issue to maximize the total rate of ground nodes by optimizing the UAV’s trajectory with fixed frequency band and power allocation. It is noted that maximizing the total rate of ground nodes can minimize the total energy consumption of ground nodes with the rate constraints. They are dual problems with each other. The optimization subproblem (

It is noted that the constraints

Firstly, to tackle the nonconvexity of the objective function, for any local point

Note that

Therefore, the optimization problem (

Secondly, considering the constraint set is still a nonconvex set for the variable

Then, all the constraints are convex set. Until now, we reformulate the optimization problem for any given local point

Based on the previous discussions, the optimal solution of (

Initialize

Solve problem (

Update the local point

Update

In summary, through adopting the relaxation method and sequential convex optimization technique, an efficient solution is proposed to solve the UAV trajectory optimization problem which is guaranteed that the optimal point is fulfill the Karush–Kuhn–Tucker conditions of the original nonconvex problem (

Until now, we have solved the issues of UAV trajectory optimal design and resource allocation for ground terminals when one of them is fixed. In order to obtain the optimal solution for the original optimization problem (

The proposed optimal solution can be summarized as follows (Algorithm

Let

Go to

Solve problem (

Update the fixed resource allocation solution

Solve problem (

Update the fixed UAV trajectory

Note that the solution for problem (

In this part, we provide numerical results to prove the reliability of the proposed algorithm. We assume that

Firstly, we evaluate the energy trade-off between the consumption of ground terminals and UAV.

We consider a certain trajectory. Multiple ground terminal and UAV energy region are shown in Figure

Multiple GTs and UAV energy region. (a)

By comparing with the resource allocation optimization shown in Figure

Energy consumption for GTs of different

Total energy consumption for ground terminals with

Next, we study the UAV trajectory optimization.

As shown in Figure

Trajectories in different iterations. (a) Five iterations. (b) Seven iterations.

Schedule for each GT.

We also collect the UAV trajectory optimization results. In multiuser scenario, we obtained the UAV trajectory under the constraints of limited flight energy and data collection rate, minimizing the energy consumption problem of user communication. The UAV trajectories under different UAV energy consumption are shown in Figure

Trajectories under different UAV energy consumption. (a) Δ

In this paper, we have studied the optimal resource allocation scheme and optimal trajectory design strategy for multiple ground terminals with UAV arbitrary flight. First, UAV’s energy consumption and GT’s energy consumption are derived, and we describe their Pareto optimal trade-offs and adopt the strategy to minimize the ground terminal energy consumption with fixed UAV energy consumption and consider rate constraints of ground terminals. Second, through calculating minimum energy consumption for constrained UAV flight, we gain the initial UAV flight in the G-U system. Next, we propose to get the optimal resource allocation under the fixed flight. Then, through maximizing the total rate of ground nodes by optimizing the UAVs trajectory with fixed frequency band and power allocation. Finally, we use an alternate iterative solution to optimize the UAV trajectory and resource allocation. Simulation results show the alternate solution we proposed can significantly improve the performance in energy efficiency compared with the scheme without optimizing trajectory. Through this paper, we consider a point-to-point G2U communication scheme formerly [

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Dingcheng Yang and Qingmin Zhao are contributed equally to this work.

This work was supported in part by the National Natural Science Foundation of China (grant nos. 61703197, 61561032, and 61461029), Graduate Student Innovation Special Funds of Nanchang University (grant no. CX2019077), and Key Research and Development Program of Jiangxi Province (grant no. 20182ABC28008).