This paper focuses on the secrecy efficiency maximization in intelligent reflecting surface (IRS) assisted unmanned aerial vehicle (UAV) communication. With the popularization of UAV technology, more and more communication scenarios need UAV support. We consider using IRS to improve the secrecy efficiency. Specifically, IRS and UAV trajectories work together to counter potential eavesdroppers, while balancing the secrecy rate and energy consumption. The original problem is difficult to solve due to the coupling of optimization variables. We first introduce secrecy efficiency as an auxiliary variable and propose relaxation optimization problem, and then prove the equivalence between relaxation problem and the original problem. Then an iterative algorithm is proposed by applying the block coordinate descent (BCD) method and the inner approximation method. The simulation results show that the proposed algorithm converges fast and is superior to the existing schemes. In addition, in order to improve the robustness of the algorithm, we also pay attention to the case of obtaining imperfect channel state information (CSI).

In recent years, the increase of wireless devices and the requirements of intelligent terminals for quality of service have promoted the development of 5G network technology [

UAV can be used as air relay and air base station, and has good performance in military and commercial fields [

As a new technology, UAV communication also has its inherent shortcomings, first of all, the energy problem of UAV [

In recent years, the intelligent reflector (IRS) has attracted extensive attention in the field of wireless communication. Its ability to reset the transmission characteristics of signals can improve system performance in a low-power mode. In [

Specifically, the intelligent reflector can rectify and retransmit the signals transmitted from the UAV to the ground or from the ground to the UAV, and improve the power of the signals received by users through interaction with the environmental channel [

In the multi-user system, another widely concerned technology is orthogonal multiple access [

In UAV communication, we can also use NOMA technology to improve transmission efficiency. To the author’s knowledge, there are only a few studies on safety based energy efficiency [

Consider a more realistic scenario. Since different users are trusted communication nodes, that is, the channel between users and IRS can be acquired in advance through pilot signals or other means. However, users are usually unable to obtain potential eavesdropper information. UAV estimates the air to ground channel by observing the position of the eavesdropper. However, due to the greater impact of the environment on the ground channel, it is impossible to obtain accurate channel state information through distance alone. Therefore, it is generally assumed that the channel for untrusted users is imperfect.

In recent years, the research on imperfect channel has also made some progress. Continuous interference canceller (SIC), imperfect channel estimation (ICSI) and hardware damage of transceiver (HWI) are considered [

In this paper, we would like to maximize the security transmission rate in the uplink network. Our concern is that in a communication area, there are multiple users who need to transmit information to the UAV. Due to the complexity of the geographical environment and potential eavesdroppers, the uplink network uses an IRS for assistance. We jointly optimize the trajectory of UAV, the phase shift matrix of IRS, and the beam design of multiple users to maximize the safety rate. The proposed optimization variables are highly coupled. We propose an iterative algorithm based on the block coordinate descent method. The simulation results show that the proposed scheme has higher security transmission rate than the traditional schemes.

As shown in

It is assumed that the UAV flies at a fixed altitude

The starting point and ending point constraints of UAV are expressed as follows:

Since the energy carried by UAV is limited, the power constraint of UAV includes two parts: the power constraint in each time slot and the power constraint in the whole flight cycle.

The air to ground channel can be approximately represented by the distance from the reference point to the corresponding node. However, the composition of the ground channel is usually more complex than air to ground channel. We assume that different users, users and potential eavesdroppers, and channels from users to the IRS all follow the free space path loss model. Specifically, we believe that all channels are the product of large-scale fading and small-scale fading. Therefore,

The transmission rate of

In the scenario considered in this paper, the eavesdropper is silent. The eavesdropper can passively obtain user information rather than actively attack users. The eavesdropping rate of the potential eavesdropper is thus defined as

Due to its structure and weight limitations, the UAV cannot carry a large number of energy equipment, so its maximum power will be strictly limited. Therefore, it is necessary to comprehensively consider the demand for safe communication and the minimization of power. We consider safety energy efficiency in this paper, which is defined as follows:

According to above discussing, we formulate the original problem as

In this section, we first decompose the original problem, and propose an approximate problem to relax the original problem. Then, we designed the beam vector, UAV trajectory and IRS reflection phase, respectively. Finally, we propose a joint optimization algorithm and analyze its complexity.

Note that the original problem is highly nonconvex, especially in its goal. Maximizing the safe rate is obviously contrary to minimizing the power. In order to seek an equilibrium effect, we introduce the power into a constant to express it, and propose the following lemma:

The optimal solution of

We then assume that the optimal solution of

According to Lemma 1, we obtain an equivalence problem of the original problem. In the following subsections, we would propose the solution of

Because of the non convexity of the objective function and the coupling of the optimization variables, it is challenging to solve P0. The block coordinate descent method is used to decompose the problem into three subproblems, which can effectively solve the problem. This leads us to propose an algorithm based on alternating optimization (AO), which solves the sub optimization problem by iterating one of the optimizations, and fixes the other two optimizations in each iteration until convergence is achieved.

We use the following combination to represent the current state of UAV trajectory:

By substituting

Note that problem

It is obvious that the optimal solution of

Based on the above discussion, we transform the trajectory optimization problem

Problem

In this section, we show the beamforming design of

It should be noted that the optimal target value of

In this subsection, we would show the phase-shift matrix design for the original problem with fixed trajectory and beamforming. First, we reformulate the original problem as

Then we take the trajectory and beamforming as fixed ones. The optimization of phase-shift matrix is simplified as

We then introduce the vector variable

To solve

It is worth noting that

In this section, we consider combining the above alternative optimization algorithms to obtain a general algorithm for the joint design of all optimization variables. In addition, we discuss the complexity of the proposed algorithm.

We first focus on the complexity in each iteration. Each iteration of Algorithm 1 involves the following computations:

In the above algorithm, we have made a strong assumption that the channel state information of the eavesdropper is perfectly obtained, which is actually difficult to achieve. When the eavesdropping channel is different from our assumption, the performance of the proposed algorithm will also be affected. In order to improve the robustness of the proposed algorithm, we have improved the algorithm in this chapter, that is, to consider imperfect channel state information.

In the actual communication environment, it is very difficult to obtain a perfect eavesdropping channel due to the lack of specific link information of potential eavesdroppers. On the other hand, we assume that imperfect CSI can be obtained through the vision advantage of UAV, that is, the eavesdropping channel can be approximately estimated by the location of the eavesdropper. Further, we assume that the approximate eavesdropping channel is an imperfect CSI, which satisfies the following conditions:

We first record the S-procedure. For a function

It can be obtained that the condition

Conversely,

By introducing S-procedure to equivalently transform (

It can be observed that

According to the above discussion, we could replace the non-convex constraints in the original problem, i.e., the constraints about the imperfect CSI as following:

Note that

In this paper, we pay attention to the UAV-NOMA system supported by IRS for the first time, and jointly design the trajectory of UAV and the phase shift matrix of IRS. Different from the goal of maximizing the communication rate or minimizing the power consumption in previous studies, we balance them to flexibly meet the needs of different scenarios.

We design the known perfect CSI and imperfect CSI at the same time. For the perfect CSI, we use the classical alternating optimization algorithm and analyze its complexity; For the case of imperfect CSI, we use S-lemma to transform and solve the original problem.

Some unfinished work is left for future work, such as 3-D trajectory design of UAV. At present, the flight design of UAV at fixed altitude is mainly for the safety consideration of collision prevention. However, extending the UAV trajectory to the 3-D range will undoubtedly increase the design difficulty, but it will also bring higher design freedom. And the introduction of UAV group will be our follow-up work.

First, we simulate the simulation environment proposed in the paper. As shown in

In the fourth chapter, we propose a method based on alternating optimization, and analyze the complexity of the algorithm. From the analysis of algorithm complexity, it can be concluded that the time consumption of alternative optimization is linear with the number of iteration convergence. Therefore, we verified the number of iterations of the algorithm and compared it with other existing algorithms. The results are as follows:

It can be seen from

In

We show the curve of energy efficiency

In

In

It can be seen from

In this section, we simulate the proposed scheme of imperfect CSI. To facilitate comparison, we still choose other existing schemes as comparison schemes.

For the completeness of the experimental results, we obtain that the results of perfect CSI are compared with the results of imperfect CSI. As the number of users increases, the energy efficiency inevitably decreases. The robust algorithm we proposed can well reduce the performance loss caused by imperfect CSI. As shown in

Finally, we also simulated the influence of noise in

In this paper, we focus on the issue of maximizing energy efficiency based on security in UAV communication network. We assume that there is a potential eavesdropper trying to obtain the information sent by the user to the UAV. On the other hand, multiple users are in the NOMA working mode, and there is an IRS to help improve secure communication. By designing the user’s transmission beam and the IRS reflection phase matrix, we can maximize the energy efficiency on the premise of ensuring a certain security rate. Compared with the existing algorithms, the proposed scheme can better utilize energy. In addition, we also consider a wider range of imperfect known CSIs, and propose an optimization scheme for this case, which shows the robustness of the scheme.

The authors wish to express their appreciation to the reviewers for their helpful suggestions which greatly improved the presentation of this paper.

This work was supported in part by the Key Scientific and Technological Project of Henan Province (Grant Nos. 212102210558, 222102210212), Doctoral Research Start Project of Henan Institute of Technology (Grant No. KQ1852).

The authors declare that they have no conflicts of interest to report regarding the present study.