Power Control Algorithm Based on a Cooperative Game in User-Centric Unmanned Aerial Vehicle Group

School of Information and Communication Engineering, Beijing Information Science & Technology University, Beijing 100101, China Key Laboratory of Modern Measurement & Control Technology, Ministry of Education, Beijing Information Science & Technology University, Beijing 100101, China Beijing Key Laboratory of High Dynamic Navigation Technology, University of Beijing Information Science & Technology, Beijing, 100101, China


Introduction
With the rapidly increasing number of wireless devices and growth of user traffic demand, improving the throughput of a communication system has gained considerable attention [1]. Wireless networks are effective solutions to improve system throughput because a large number of unmanned aerial vehicles (UAVs) groups can be deployed. e usercentric UAV group (UUAVG) can not only improve system capacity but also achieve seamless coverage and enhance the quality of service (QoS) of the system [2]. e UUAVG network organises a dynamic UAVG for each user; the unmanned aerial vehicles group (UAVG) is composed of all potential UAVs near a user, so that the user can perceive that the network follows them [3]. UUAVG is defined as the network architecture of serving user by the "decellular" method [4]. When the user moves, the UAVG will dynamically add and delete UAV members according to the user location to meet user requirements in the UAVG network centre [5]. Compared with traditional cellular network, UUAVG network structure can effectively improve network coverage, reduce the interrupt probability by 30%, and improve the spectrum efficiency by 5%-15% [6,7]. Although the UUAVG improves the system throughput by deploying a large number of UAVs, the cochannel interference problem is severe and reduces the QoS for the users. erefore, it is essential to realise methods to reduce this cochannel interference.
At present, many scholars have studied the complex interference problem of UUAVG, and power control is regarded as the most effective interference suppression method. In [8], an orthogonal frequency division multiplexing-(OFDM-) based UAVG communication link resource allocation algorithm was introduced.
is algorithm considers subcarrier and power allocations. It maximises the system capacity, while accounting for user fairness. However, the algorithm is complicated and has a low convergence speed. In [9], the local optimal solution is obtained by joint optimisation of uplink cell association and power allocation, which effectively improves the network performance. In [10], aiming at the problem of UAV access and base station bandwidth allocation, a hierarchical game power control algorithm is proposed. is algorithm can effectively solve the problem of UAV access and base station bandwidth allocation. Nash equilibrium is proved by theory, but the problem is modeled as a noncooperative game, sacrificing the overall performance of the system. In [11], a power control algorithm based on mean field game and deep reinforcement learning is proposed. e algorithm first transforms the power control problem into discrete mean constant game and then uses neural network to solve the optimal transmit power. Although this algorithm can effectively improve the energy efficiency of UAV, its complexity is much higher than those of other algorithms. In [12], a noncooperative game distributed power control algorithm was introduced, which could effectively improve the system throughput and reduce cochannel interference; however, the proposed algorithm cannot achieve optimal system capacity. In [13], a power control algorithm based on noncooperative game is proposed. e algorithm adopts a nonuniform pricing method and sets different prices for different base stations. e scheme can effectively improve the system performance in UAVG network structure. Although the above studies reduce interference to a certain extent, they are not user-centric and cannot achieve optimal system throughput.
To solve the above problems, a cooperative game power control algorithm in UUAVG is proposed by this study. First, the system model of the UUAVG downlink power control is established. Considering the interference to user QoS and service UAV to edge users, a new cooperative game utility function is proposed, and the optimal power control scheme is solved using the Lagrange function. e simulation results show that the cooperative game power control (CGPC) algorithm can reduce the user transmitted power and interuser interference and improve system throughput.

System Model
e model of UUAVG downlink power control system is shown in Figure 1. Assuming that there is a service user (SU) in the model, the dynamic UAVG is formed with the SU as the centre, and the coverage range of the UAVG available to the SU is represented by the dotted circle. It is assumed that there is only one service unmanned aerial vehicle (SUAV) in the UAVG. Suppose that there are n cooperative unmanned aerial vehicles (CUAV), denoted as CUAVi (i � 1, 2, . . . , i, . . . , j, . . . , N); in the coverage of the UAVG, assume that there are n edge users (EU) at the same time, denoted as EUi (i � 1, 2, . . . , i, . . . , j, . . . , N), and that they are far away from the SUAV, with the service base station of EUi represented as CUAVi. Let the vertical height of the SUAV and CUAV from the ground be H 0 . Owing to the scarcity of spectrum availability and to improve frequency utilisation, when deploying the UAVG, the downlink communication frequencies of the SUAV and SU are the same as those of the CUAVi and EUi. erefore, the interference between the SUAV and CUAV and those between the CUAVs are inevitable.
For each user, they are in the center of the network, and UAVs around the user are dynamically composed of UAVG. Each user has a unique UAVG to provide services, but each UAV may belong to a different UAVG at the same time.
erefore, each UAV may be both a user's SUAV and another user's CUAV at the same time. For users, if a UAVG is the user's own UAVG, it is called a service user of this UAVG; otherwise, it is called an edge user of this UAVG.
Let p t and p i denote the transmitted power levels of SUAV and CUAVi, and let c i denote the signal to interference noise ratio (SINR) of the corresponding EUi.
(1) e downlink channel gain between CUAVi and EUi is denoted as h ii , the channel gain between CUAV and EUi is denoted as h ji , and the channel gain between SUAV and EUi is denoted as g si . e power of the additive white Gaussian noise on EUi is σ 2 . e distance between CUAVi and EUi is denoted as d ii and that between SUAV and EUi is denoted as r si . e horizontal distance between CUAVi and EUi is denoted as D ii and that between SUAV and EUi is denoted as R si . Using the triangle Pythagorean theorem, we can get d ii and r si .  Complexity (2)

CGPC Game Elements.
In the noncooperative game, each participant will choose selfishness to maximise their benefits, thereby causing interference to the other participants and reducing the benefits to other users. Meanwhile, a cooperative game is meant to maximise the interests of the collective and is a competition model in which the participants seek to maximise their interests. erefore, a cooperative game will bring more benefits to the system. e three basic elements of the cooperative game are the participants, strategy set, and utility function. Participants in the game are represented as I: the set of CUAVs participating in the game, where I � 1, 2, . . . , N { }. e strategy set is represented as Ω i : decision of each participant can be expressed as p 1 , p 2 , . . . , p i , . . . , p n , 0 ≤ p i ≤ p max CUAV (here, p max CUAV represents the maximum allowable transmitted power of the CUAV), and each decision is independent of the others. e utility function is given as U i , which represents the preference of EUi for a certain strategy.

Utility Function.
In the traditional cooperative game algorithm, the utility function only considers the user SINR. In this study, we consider not only the SINR of users but also the influence of SUAV on EUi. A new utility function is divided into two types according to whether the SINR of users is greater than the threshold SINR: In the first case, when user e objective function of power control based on the cooperative game in CGPC can be expressed as follows: Here, T is the threshold value for which EUi can withstand interference from the UAVG. In theory, we set c min EU and determine the interference threshold T according to the channel gain and transmit power from EUi to CUAV.
EU , if and only if c i � c min EU ; we can calculate the threshold T � (p i h ii /c min EU ). e physical meaning of power control in CGPC indicates that the utility function of the EU reaches the maximum when the interference from CUAV to SU does not exceed the maximum interference threshold that the SU can bear. (4) can be further modified by considering the logarithm of the objective function of (4) and using the properties of logarithmic functions, ln N i�1 c i � N i�1 ln c i , as follows:

Nash Solution. Equation
erefore, the problem of U i (p i , c i ) maximisation is now transformed into the problem of u i (p i , c i ) maximisation, and u i � ln U i .

Theorem 1. Model equivalence theorem. Suppose that the decision set for the utility function set has a one-to-one mapping relationship that satisfies the concave function characteristics; that is, u i � ln U i satisfies the characteristics of the concave function. us, it can be concluded that the models in (4) and (5) are equivalent, and the same solution is obtained.
Equation (5) is an optimisation problem with multiple constraints, and the Lagrange factor λ, μ i , η i , ε i is introduced to construct a Lagrange function. Among them, Lagrange factor is the limiting factor set when solving Lagrange function. rough Lagrange factor, the objective function Complexity 3 and constraint conditions are connected together to construct a new Lagrange function. Therefore, Lagrange function can be expressed as follows: According to (6), the partial derivative of the Lagrange function p i is calculated, and the optimal solution is obtained by setting (zL(p i , c i )/zp i ) � 0; so we can get p i as follows: According to the SINR definition, (zc i /zp i ) � (c i /p i ) holds. e fixed-point iterative method is used for iteration; after k iterations, the transmitted power of CUAVi is as follows: According to (8), the first term (c min EU /c i )p (k) i on the right is consistent with the traditional SINR balancing algorithm [12], and it is expressed that p (k+1) i will gradually stabilise when c i approaches c min EU .
is a fine-tuning term comprising the Lagrangian factors, channel gain, and current SINR. is proves the correctness of the algorithm. It not only ensures that it is similar to the traditional SINR balancing algorithm but also makes fine-tuning on the basis of the traditional SINR balancing algorithm. e algorithm in this paper is based on UAV transmit power polling, not on time.
In this paper, the throughput of the system is characterised by the sum of the average reachable rates of all users, where the average reachable rate of each user can be expressed as where R i is the user reachable rate and the bandwidth is B � 1 Hz. erefore, the system throughput of each iteration can be expressed as follows: where S (k) t is the throughput of the k-th iteration. R (k) i is the user reachable rate of user i at the k-th iteration.

Performance Evaluation
In this section, we present verification of the feasibility of the CGPC algorithm through simulations and calibrations for the theoretical analysis results and simulation results.

Simulation Configuration and Parameters.
According to [11][12][13], the height of the UAVG is selected as H 0 � 80 m, and the horizontal projection coverage area of the UAVG is selected in a circular area of radius 300 m, where the horizontal distance from the SU to SUAV is set as [0, 100 m], and the horizontal distance from EU to SUAV is set as (100, 300]. Suppose that there is one SUAV and four CUAVs, namely, CUAV1, CUAV2, CUAV3, and CUAV4, in this circular area. In the circular region, there is one SU and four EU, namely, EU1, EU2, EU3, and EU4. e distance relationship between the EUs and SUAV is expressed Suppose that the transmitted power of the SUAV is 30 dBm, and the initial transmitted power of the CUAV is 20 dBm. Assuming noise threshold T � 1 × 10 − 10 W, the Lagrange factors are obtained as λ � 1 × 10 16 and μ i � η i � ε i � 10 [11][12][13]. Figure 2 illustrates the curves for the CUAV transmitted power changing with the number of iterations. e abscissa in the figure is the number of iterations, and the ordinate is the transmitted power from the CUAV. It can be observed from the figure that the initial transmitting power of CUAVs is 0.1 W. With the increase of iteration times, the transmitting power of CUAV decreases gradually and reaches a stable state after many games. e attenuation rate of CUAV1 is the fastest and that of CUAV4 is the slowest. is is due to the different distances between EU and SU. e distance between EU1 and SU is relatively close, and the downlink communication power of CUAV1 and EU1 has a greater impact on SU. e power attenuation of CUAV1 is relatively large. e distance between EU4 and SU is relatively long, and the influence of CUAV 4 and EU4 downlink communication power on SU is relatively small. erefore, the power attenuation of CUAV 4 is relatively small. is is consistent with the result of formula (3). Figure 3 presents a comparison of the CUAV transmitted power for different algorithms. e abscissa is the distance between the EU and SUAV, and the ordinate is the transmitted power from the CUAV. e curves in the figure represent the results of the K-G algorithm [12] and CGPC algorithm. It can be observed that the transmitted power of the CUAV increases with the distance between the EU and SUAV. When the distance between EU and CUAV is close, the effect of the proposed algorithm is equivalent to that of the traditional K-G algorithm. However, after 60 meters, it obviously reflects the advantages of this algorithm, which can effectively reduce the transmission power of CUAV. is is because the design of utility function considers not only the user's QoS but also the influence of different distance EU on CUAV. e farther the distance between EU and CUAV, the more obvious the advantages of this algorithm. Comparing these two algorithms under the same conditions, the transmitted power of the CUAV based on the CGPC algorithm is observed to be lower than that of the K-G algorithm, which reduces the cofrequency interference. Figure 4 demonstrates the curves for the system average throughput according to the number of CUAVs for different algorithms; the abscissa is the number of CUAVs, and the ordinate is the average throughput of the system. e curves represent results for the Stackelberg Game based Nonunified Pricing Power Control (SGNPPC) algorithm [13] and CGPC algorithm for the average system throughput. It can be observed that the average throughput of the two systems increases as the number of CUAVs increases. When the number of CUAVs reaches 24, the average throughput of the system is close to saturation. ereafter, the system throughput of the SGNPPC algorithm gradually decreases with increase in the number of CUAVs; this is because more interference is inserted with the increase in the number of CUAVs; conversely, the throughput of the CGPC algorithm increases with the increase in the number of CUAVs, but the rate of increase is reduced.

Simulation Results and Analysis.
is deceleration can be attributed to the adoption of cooperative games to reduce the interference between the CUAVs. Compared with the SGNPPC algorithm, the average throughput of the CGPC algorithm increased by 10.32%.

Conclusion
In this study, a CGPC algorithm is proposed in the scenario of the UUAVG. e algorithm considers not only the SINR of the user but also the influence of the different distances between the EU and SUAV on the EU. e complex Nash theorem utility function is transformed into an easily solved optimisation problem using the principle of model equivalence; further, the Lagrange function is constructed, and the optimal transmitted power is obtained iteratively. e convergence of the algorithm is proven by simulation, and the average throughput of the system is improved. In the future work, we will consider the joint optimisation of distributed power control and user rate control, as well as the trajectory design and layout design of UAV.

Data Availability
No data were used to support this study.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.