Multi-objective optimization method for trade-off energy efficiency and spectrum efficiency of space-air-ground internet of things

Abstract

The application discloses a multi-objective optimization method for trade-off energy efficiency and spectrum efficiency of space-air-ground-thing Internet of Things, and belongs to the field of communication resource allocation.The application realizes the method as follows: constructing a space-air-ground-thing Internet of Things model, constructing a multi-objective optimization problem of maximizing system energy efficiency and system spectrum efficiency according to the space-air-ground-thing Internet of Things model; introducing an energy efficiency and spectrum efficiency trade-off coefficient, and converting the multi-objective optimization problem of trade-off energy efficiency and spectrum efficiency in the space-air-ground-thing Internet of Things network into a single-objective optimization problem by using a constraint method; dividing the complex single-objective optimization problem into three sub-problems of sub-channel selection, unmanned aerial vehicle and Internet of Things device power control and unmanned aerial vehicle position deployment, and further improving optimization efficiency; and adopting a block coordinate descent method to iteratively solve the three sub-problems in turn to obtain a solution of the multi-objective optimization problem of trade-off energy efficiency and spectrum efficiency, until a multi-objective optimization result is obtained.The application is suitable for the case that there are obstacles between unmanned aerial vehicles and Internet of Things devices, and can improve the energy efficiency and spectrum efficiency of the system.

Description

Technical Field

[0001] This invention relates to a multi-objective optimization method for balancing energy efficiency and spectral efficiency in the context of the Internet of Things (IoT) between air, space, and ground, and belongs to the field of communication resource allocation. Background Technology

[0002] In recent years, the Internet of Things (IoT) has received widespread attention and has been applied in various fields such as agriculture and healthcare due to its ability to enhance communication between people and things, and between things themselves, improve data collection, increase resource utilization, and reduce costs. With the booming development of IoT, the number of connected devices has increased dramatically, leading to continuously rising communication demands. Traditional terrestrial communication is no longer suitable, necessitating expansion into space communication. Integrated space-air-ground networks are considered an effective solution and have gained widespread attention. In integrated space-air-ground networks, satellites offer wide coverage and large communication capacity, providing services to remote areas such as deserts and rural areas; the air segment network assists satellite communication, providing higher-quality communication services; and the densely deployed ground segment system supports high data rate access. Therefore, relying on integrated space-air-ground networks, the connectivity, capacity, and energy efficiency of IoT can be significantly improved.

[0003] Unmanned aerial vehicles (UAVs), due to their high maneuverability, high line-of-sight (LoS) probability, flexible deployment, and low cost, are the main information carriers in the air segment of integrated air-space-ground networks and have received widespread attention and research. However, the limited energy of UAVs has always made their duration a key constraint on communication performance. Many scholars have focused on this issue, maximizing UAV energy efficiency through optimizing power allocation and UAV trajectory. In air-space-ground networks, researchers have also conducted studies on system energy efficiency. However, most current research assumes a line-of-sight channel between the UAV and ground equipment. In reality, obstructions are likely to exist between the UAV and ground equipment, leading to additional losses; therefore, it is necessary to consider non-line-of-sight channels as well.

[0004] However, improving system energy efficiency may very well mean reducing system spectral efficiency. In air-to-ground networks, due to the large distance between UAVs and satellites, communication links need to allocate a significant amount of bandwidth for data transmission, consuming a large portion of the already limited spectrum resources. Therefore, while considering system energy efficiency, it is also necessary to consider system spectral efficiency, requiring a trade-off optimization. Currently, there is no multi-objective optimization method in air-to-ground IoT networks that comprehensively considers both energy efficiency and spectral efficiency. Summary of the Invention

[0005] The main objective of this invention is to provide a multi-objective optimization method for balancing energy efficiency and spectral efficiency in the context of the air-space-ground Internet of Things (IoT). This method constructs an air-space-ground IoT model and, based on this model, establishes a multi-objective optimization problem maximizing system energy efficiency and spectral efficiency. It introduces an energy efficiency and spectral efficiency tradeoff coefficient ∈, and uses the ∈ constraint method to transform the multi-objective optimization problem in the air-space-ground IoT network into a single-objective optimization problem. The complex single-objective optimization problem is further divided into three sub-problems: sub-channel selection, power control of UAVs and IoT devices, and UAV location deployment. These three sub-problems are jointly optimized using a block coordinate descent method, further improving optimization efficiency. This invention is applicable not only to the ideal situation where there are no obstructions between IoT devices and UAVs, but also to situations where there are obstacles between UAVs and IoT devices. It can balance system energy efficiency and spectral efficiency according to actual conditions, thereby improving both.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] The multi-objective optimization method for balancing energy efficiency and spectral efficiency in a space-air-ground Internet of Things (IoT) network disclosed in this invention includes the following steps:

[0008] Step 1: For the air-to-ground IoT network where UAVs collect data from ground-based IoT devices and transmit the data to low-Earth orbit satellites, the channel between the UAV and the satellite is equivalent to a line-of-sight (LAS) channel. Due to the actual situation of obstacles obstructing the connection between the UAV and the IoT devices, the channel is also equivalent to a probabilistic LAS channel. Based on this, an air-to-ground IoT model is constructed. Based on the constructed air-to-ground IoT model, a multi-objective optimization function is built to maximize system energy efficiency and system spectral efficiency. Given constraints on the number of communication devices for UAVs and IoT devices, the maximum transmit power of UAVs and IoT devices, the minimum transmission rate, and the minimum distance between UAVs, a multi-objective optimization problem balancing energy efficiency and spectral efficiency is constructed in the air-to-ground IoT network.

[0009] Step 1.1: Construct an air-space-ground IoT model, where the number of IoT devices in the network is U, and the number of drones is I, using... and This is represented by a low-Earth orbit satellite covering these IoT devices and drones, providing them with services. Introducing a Cartesian coordinate system, the positions of the i-th IoT device and drone are represented as follows: and Where h u A fixed flight altitude is set for the drone. To support simultaneous transmission from multiple IoT devices, orthogonal frequency division access (OFDM) technology is employed. The channel between the drone and the IoT devices is divided into K sub-channels, where K = U / I, and the bandwidth of each sub-channel is B. The channel bandwidth between each drone and the satellite is W.

[0010] Calculate the data transmission rate r from IoT device i to drone u. iu The presence of obstacles incurs additional losses between IoT devices and drones; therefore, the channel between the drone and the IoT device is equivalent to a probabilistic line-of-sight channel. The average path loss between the IoT device and the drone is...

[0011]

[0012] Among them, f c Let η be the carrier frequency, v be the speed of light in a vacuum, and η be the speed of light in a vacuum. LOS η represents the average additional loss caused by free-space path loss in line-of-sight links. NLOS This represents the average additional loss caused by free-space path loss in non-line-of-sight links. P represents the distance between IoT devices and drones. iu The probability of line-of-sight distance is obtained from the following equation (2).

[0013]

[0014] Where φ and It is a constant greater than 0, determined by the environment, θ iu It is the elevation angle between the equipment and the drone, expressed as

[0015]

[0016] The gain between IoT devices and drones is obtained.

[0017]

[0018] Since an IoT device can only communicate with one drone, its transmission rate is expressed as...

[0019]

[0020] Where p i Where N is the transmit power of the IoT device, N0 is the noise power spectral density, and a iu Let a be a binary variable consisting of 0 and 1. iu =1 indicates that IoT device i selects drone u for communication, otherwise it indicates that there is no communication.

[0021] Calculate the data transmission rate r between the UAV u and the satellite. us Because it is a line-of-sight channel, the gain between the UAV and the satellite is [value missing].

[0022]

[0023] Among them, G tx and G rxd represents the antenna gain of the drone and the satellite, respectively. us The distance between a drone and a satellite is usually approximated by the satellite's orbital altitude h. s .

[0024] The data transmission rate between the UAV and the satellite was obtained as follows:

[0025]

[0026] Where, p u N is the drone's transmit power, and N1 is the noise power spectral density.

[0027] By combining formulas (1) to (7), we can obtain the air-space-ground Internet of Things model.

[0028] Step 1.2: Based on the space-air-ground IoT model obtained in Step 1.1, form the energy efficiency η. EE and spectral efficiency η SE The expression for is the objective function of the multi-objective optimization problem that balances energy efficiency and spectral efficiency.

[0029] Energy efficiency is the ratio of effective information transmission rate to power. The data transmitted to the satellite is data sent by the drone, and the energy efficiency η is... EE Represented as

[0030]

[0031] Where, p h It is the power required for a single drone to remain suspended in the air.

[0032] Spectral efficiency is the ratio of effective information transmission rate to channel bandwidth, expressed as:

[0033]

[0034] To simplify the symbols, let and In addition, make the drone's position variable Sub-channel selection variable A = {a iu The transmit power variable P of IoT devices I ={p i} and the UAV transmit power variable P U ={p u}. Combine formulas (8) and (9) to construct the optimization objective function.

[0035] Step 1.3: Given constraints, construct a multi-objective optimization problem that balances energy efficiency and spectral efficiency. Based on the condition that an IoT device can only communicate with one UAV at a time and an aircraft can only communicate with K IoT devices simultaneously, constraints are given on the number of communication devices for both UAVs and IoT devices. Since the energy available for signal transmission by UAVs and IoT devices is limited, constraints are given on the maximum transmit power of both UAVs and IoT devices. The data transmission rate of IoT devices needs to meet the minimum transmission rate requirement to ensure normal communication; therefore, a minimum transmission rate constraint is given. UAVs will collide when they are too close; therefore, a minimum distance constraint between UAVs is given. Using formulas (8) and (9) as the optimization objective function, a multi-objective optimization problem balancing energy efficiency and spectral efficiency in the air-space-ground IoT network is constructed as shown in formula (10).

[0036]

[0037] Where r min For the minimum transmission rate, p imax and p umax For the maximum transmit power of IoT devices and drones, d min This is the minimum distance for the drone.

[0038] Step 2 addresses the high complexity of the multi-objective problem constructed in Step 1, which makes it difficult to directly determine sub-channel selection, UAV and IoT device transmit power, and UAV deployment schemes to achieve suitable energy efficiency and spectral efficiency. By introducing an energy efficiency and spectral efficiency tradeoff coefficient ∈, and utilizing the ∈ constraint method, the multi-objective optimization problem of balancing energy efficiency and spectral efficiency in the air-space-ground IoT network constructed in Step 1 is transformed into a single-objective optimization problem, reducing the complexity of solving the optimization problem. The energy efficiency objective function, containing variables such as IoT device transmit power, UAV transmit power, and sub-channel selection, is retained as the objective function of the single-objective optimization problem. Through the energy efficiency and spectral efficiency tradeoff coefficient ∈, the relatively simple spectral efficiency function is transformed into a new constraint condition, thus converting the multi-objective optimization problem of balancing energy efficiency and spectral efficiency in the air-space-ground IoT network into a single-objective optimization problem, facilitating the solution of the optimization problem.

[0039] The transformed single-objective optimization problem is expressed as:

[0040]

[0041] Where ∈ is the energy efficiency and spectral efficiency tradeoff coefficient.

[0042] Step 3: Divide the single-objective optimization problem obtained in Step 2 into three sub-problems: channel selection, power control of the UAV and IoT devices, and UAV deployment, to further improve the solution efficiency. The channel selection sub-problem contains a binary variable 'a' indicating whether communication exists between the UAV and the IoT devices. iuThis problem is difficult to solve directly using convex optimization methods. Therefore, a matching algorithm is adopted to quickly obtain suitable sub-channels and improve the data transmission rate between UAVs and IoT devices. For the non-convex sub-problem of power control for UAVs and IoT devices, the objective function in fractional form containing the UAV's transmit power and the IoT device's transmit power is transformed into a difference form using the Dinkelbach algorithm for easier solution; and the method of successive convex approximation is used to transform the objective function containing the transmission rate r us Non-convex constraints are transformed into convex constraints; the Lagrange duality algorithm is used to transform unmanned...

[0043] The power control subproblem for both the drone and IoT devices is transformed into its corresponding dual problem, yielding optimal solutions for both drone and IoT device transmission power to minimize system energy consumption. The drone deployment subproblem is difficult to solve; therefore, an angle relaxation variable Θ = {θ} is introduced. iu}, and the distance between UAVs is calculated using a successive convex approximation algorithm. Transmission rate r iu By approximating the problem, the drone deployment subproblem is transformed into a convex problem, reducing computational complexity.

[0044] Step 3.1: Given other conditions, the IoT device selects a suitable sub-channel for communication with the drone; this is the sub-channel selection problem. The drone's position D is fixed, and the IoT transmit power P... I and UAV transmission power P U When variable A satisfies the constraints, it does not affect the objective function. Therefore, when the constraints are satisfied, maximizing the total transmission rate of IoT devices is taken as the objective function to improve the throughput of IoT devices. The sub-channel selection subproblem is expressed as follows:

[0045]

[0046] The sub-channel selection subproblem contains binary integer variables, making it difficult to obtain the optimal result using convex optimization methods. A many-to-one matching algorithm is employed to solve this problem, constructing a preference list of drones and IoT devices in descending order of transmission rate. First, the IoT devices select the first drone from the preference list. Then, the number of IoT devices already communicating with this drone is checked; if it is less than K, communication is successfully established. iu =1. If it equals K, then compare the priority of the IoT device with the IoT device that has already established communication with it in the drone's preference list. If the IoT device has a higher priority, then it replaces the IoT device with the lowest speed to establish communication with the drone, and puts the IoT device with the lowest speed into the waiting list for rematching. Otherwise, the IoT device fails to establish communication, a iu=0, remove the drone from the device preference list, add it to the match list and match again until a communication solution between the drone and the IoT device is obtained.

[0047] Step 3.2: Deploy the drone at a fixed location and select sub-channels to optimize the transmission power of the IoT and the drone, which is the power control sub-problem of the drone and IoT devices. The resulting power control sub-problem of the drone and IoT devices is non-convex, so the energy efficiency objective function and the constraint C7 related to the drone's data transmission rate need to be transformed into a convex form suitable for solving.

[0048] Since energy efficiency is the ratio of data transmission rate to the energy consumed during data transmission, it contains power variables in both the numerator and denominator, making it difficult to solve directly. The Dinkelbach algorithm is used to transform the energy efficiency function into a difference form that relates to the power of the drone and the IoT device.

[0049] Introducing a nonnegative parameter λ to represent the ratio of transmission rate to energy consumption, we have:

[0050]

[0051] The function in fractional form is transformed into difference form, expressed as:

[0052]

[0053] The objective function is transformed into a difference form for easier solution. Besides the objective function, constraint C7 is non-convex, but the data transmission rate r from the UAV to the satellite... us It's about the drone's transmit power p u The concave function is thus obtained through a first-order Taylor expansion, yielding the UAV data transmission rate r. us The upper bound is denoted as

[0054]

[0055] Constraint C7 is transformed into a convex constraint, which is

[0056]

[0057] Therefore, the power control subproblem of drones and IoT devices can be written in the following convex form, which is suitable for solving.

[0058]

[0059] Since the problem involves two variables, the Lagrange duality method is used to solve the convex form of the power control subproblem for UAVs and IoT devices. By representing the power control subproblem as its corresponding dual problem, the transmit power schemes for the UAV and IoT devices that satisfy the constraints can be quickly obtained. The Lagrange dual function is...

[0060]

[0061] Where μ,υ,ω,ε,τ are Lagrange dual variables.

[0062] The Lagrange duality problem is expressed as

[0063]

[0064] Due to constraint C4, the optimal solution... The following conditions must be met.

[0065]

[0066] Optimal solution The following conditions must be met.

[0067]

[0068] Since the Lagrange function has a non-differentiable probability, the subgradient method is used to update the Lagrange multipliers, as expressed below.

[0069]

[0070]

[0071]

[0072]

[0073] in, n is the number of iterations, γ is the iteration step size, and we have

[0074]

[0075] Step 3.3: Given the sub-channel selection and the transmit power of the UAV and IoT devices, optimize the deployment location of the UAV. Maximizing the transmission rate of the IoT devices is used as the objective function, but the UAV deployment subproblem is difficult to solve. To transform the problem into a convex problem, we first introduce an angle variable Θ = {θ}. iu}, thus obtaining the new constraint C9 representing the elevation angle of the IoT device, which is

[0076]

[0077] The constraint given in equation (28) is a non-affine constraint, which can be relaxed to

[0078]

[0079] Although the constraint remains non-convex, it applies to the horizontal distance between the drone and the IoT device. It is convex, therefore the elevation angle θ iu exist The lower bound of the location is represented as

[0080]

[0081] in

[0082]

[0083] For constraint C8, the minimum distance between UAVs is obtained using a successive convex approximation algorithm. exist and The lower bound of the location is

[0084]

[0085] Due to the IoT transmission rate r iu Since the objective function related to the physical network transmission rate is non-convex, constraints C6 and C7 are also non-convex. However, the transmission rate r is derived from this. iu Distance between IoT devices and drones and It is a concave function. Let For x, Let y be the IoT transmission rate r. iu In x 0 and y 0 The lower bound of the location is

[0086]

[0087] in

[0088]

[0089]

[0090] in

[0091]

[0092]

[0093] Therefore, based on (29) to (37), we obtain the UAV location deployment subproblem in convex form, denoted as:

[0094]

[0095] Step 4: Using the block coordinate descent method, first solve the sub-channel selection sub-problem. Based on the solution to the sub-channel selection sub-problem, solve the UAV and IoT device transmit power sub-problem. Then, based on the solutions to the obtained sub-channel and UAV and IoT device transmit power sub-problems, solve the UAV location deployment sub-problem. Based on the solutions to the UAV and IoT device transmit power sub-problem and the UAV location deployment sub-problem, resolve the sub-channel selection sub-problem. Iterate and alternately solve the three sub-problems—sub-channel selection, UAV and IoT device transmit power, and UAV location deployment—to obtain a solution to the multi-objective optimization problem that balances energy efficiency and spectral efficiency, until the multi-objective optimization result balancing energy efficiency and spectral efficiency in the air-space-ground IoT network is obtained.

[0096] The implementation method for step four is as follows: Using the block coordinate descent method, firstly, the sub-channel selection sub-problem is solved according to step 3.1. Then, based on the solution to the sub-channel selection sub-problem obtained in step 3.1, the UAV and IoT device transmit power sub-problem given in step 3.2 is solved. Next, based on the solutions to the obtained sub-channel sub-problem and the UAV and IoT device transmit power sub-problem, the UAV location deployment sub-problem given in step 3.3 is solved. Then, based on the solutions to the UAV and IoT device transmit power sub-problem and the UAV location deployment sub-problem, the sub-problem given in step 3.1 is solved again. This iterative process of alternately solving the three sub-problems—sub-channel selection, UAV and IoT device transmit power, and UAV location deployment—results in a solution to the multi-objective optimization problem that balances energy efficiency and spectral efficiency, thus obtaining the multi-objective optimization result of balancing energy efficiency and spectral efficiency in the air-space-ground IoT network.

[0097] The process also includes step five: Based on the multi-objective optimization results of the air-space-ground IoT network obtained in step four, which balance energy efficiency and spectral efficiency, a communication scheme between the UAV and IoT devices is designed using the sub-channel selection result A. Suitable UAVs and IoT devices are selected for communication to improve the throughput of both. The optimized IoT device transmit power P is then utilized. I and UAV transmission power P U Adjust the transmission power of IoT devices and drones in the air-space-ground IoT system to minimize energy consumption while meeting communication spectral efficiency requirements, thereby improving system energy efficiency. Utilize the drone deployment results (D) to plan drone positions, further enhancing data transmission rates for IoT devices and drones. Furthermore, the optimization results obtained in step four apply not only to situations where there are no obstructions between IoT devices and drones but also to situations where obstacles exist, improving both system energy efficiency and spectral efficiency.

[0098] Beneficial effects:

[0099] 1. This invention discloses a multi-objective optimization method for balancing energy efficiency and spectral efficiency in the context of the air-to-ground Internet of Things (IoT). Addressing the limitations of limited spectrum resources, limited UAV energy, and obstruction between UAVs and IoT devices in the air-to-ground IoT, an air-to-ground IoT model is constructed. By comprehensively considering both system energy efficiency and spectral efficiency, a multi-objective optimization problem balancing energy efficiency and spectral efficiency is established. The resulting optimization is applicable not only to the ideal scenario where there is no obstruction between UAVs and IoT devices, but also to scenarios where obstacles exist between IoT devices and UAVs. By balancing the system's energy efficiency and spectral efficiency, both aspects of the system's energy efficiency and spectral efficiency are improved.

[0100] 2. The multi-objective optimization method for balancing energy efficiency and spectral efficiency in the context of the air-space-ground Internet of Things (IoT) disclosed in this invention introduces a trade-off coefficient e between energy efficiency and spectral efficiency, transforming the relatively simple spectral efficiency objective function into a new constraint. This converts the multi-objective optimization problem into a single-objective optimization problem involving only energy efficiency, thereby improving solution efficiency. Furthermore, the single-objective optimization problem with multiple variables is divided into three sub-problems: channel selection, UAV and IoT device transmit power, and UAV location deployment, each with fewer variables. These sub-problems are solved using the block coordinate descent method, further improving optimization efficiency.

[0101] 3. The multi-objective optimization method for balancing energy efficiency and spectral efficiency in the context of the air-space-ground Internet of Things (IoT) disclosed in this invention employs a many-to-one matching algorithm to solve a sub-channel selection sub-problem containing binary integer variables indicating whether communication exists between UAVs and IoT devices. This reduces computational complexity and improves data transmission rates between UAVs and IoT devices. For the non-convex UAV and IoT device transmit power sub-problem, the Dinkelbach algorithm is used to transform the fractional energy efficiency objective function, which contains power variables in both the numerator and denominator, into a difference form related to the transmit power of both the IoT devices and the UAVs. A successive convex approximation algorithm is used to obtain the upper bound of the UAV transmission rate, transforming the problem into a convex form that is easier to solve. The Lagrange dual algorithm is then used to transform the convex problem into a corresponding dual problem, quickly obtaining the optimal solutions for UAV and IoT transmit power. This approach minimizes the transmit power of both UAVs and IoT devices while meeting spectral efficiency requirements, thereby improving energy efficiency. For the UAV deployment sub-problem, the non-convex part of the problem is transformed into a convex form for easier solution by introducing angle relaxation variables and using successive convex approximations to obtain approximate values ​​for the distance between UAVs and the transmission rate of IoT devices. By optimizing the drone location deployment sub-problem, the drone deployment results are obtained, thereby improving the transmission rate between drones and IoT devices. Attached Figure Description

[0102] Figure 1This is a flowchart of the multi-objective optimization method for balancing energy efficiency and spectral efficiency for the space-air-ground Internet of Things of the present invention.

[0103] Figure 2 This is a diagram of the air-space-ground Internet of Things (IoT) network structure;

[0104] Figure 3 This is a graph showing the change in system energy efficiency with the number of iterations under different trade-off coefficients.

[0105] Figure 4 This is a graph showing the change of the system spectral efficiency with the number of iterations under different tradeoff coefficients ∈. Detailed Implementation

[0106] To better illustrate the purpose and advantages of this invention, a simulation analysis of a multi-objective optimization method balancing energy efficiency and spectral efficiency for the space-air-ground Internet of Things (IoT) is presented below to provide a detailed explanation. The invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0107] Example 1

[0108] This embodiment details the specific steps of implementing the multi-objective optimization method for balancing energy efficiency and spectral efficiency for the space-air-ground Internet of Things (IoT) of the present invention.

[0109] This case study considers the limited energy and spectrum resources of UAVs in an air-to-ground IoT environment. Therefore, a multi-objective optimization method balancing energy efficiency and spectral efficiency for air-to-ground IoT is adopted to improve the system's energy efficiency and spectral efficiency while meeting communication requirements. The multi-objective optimization method balancing energy efficiency and spectral efficiency for air-to-ground IoT disclosed in this example is as follows: Figure 1 As shown, the specific implementation steps are as follows:

[0110] Step 1: For the air-to-ground IoT network, the channel between the UAV and the satellite is equivalent to a line-of-sight channel, and the channel between the UAV and IoT devices is equivalent to a probabilistic line-of-sight channel. Based on this, an air-to-ground IoT model is constructed. Based on the constructed air-to-ground IoT model, a multi-objective optimization function maximizing system energy efficiency and system spectral efficiency is built. Given constraints, a multi-objective optimization problem balancing energy efficiency and spectral efficiency in the air-to-ground IoT network is constructed.

[0111] Step 1.1: Construct an air-space-ground IoT model, such as... Figure 1 As shown, the number of IoT devices in the network is U, and the number of drones is I, respectively represented by... and This is represented by a low-Earth orbit satellite providing services to these drones and devices. Introducing a Cartesian coordinate system, the positions of the i-th IoT device and drone are represented as follows: and Where h uA fixed flight altitude is set for the drones. Orthogonal frequency division access (OFDM) technology is used, dividing the channel between the drones and IoT devices into K sub-channels, where K = U / I, and each sub-channel has a bandwidth of B. The channel bandwidth between each drone and the satellite is W. In Example 1, eight IoT devices are randomly distributed within a 1km × 1km square area. Two drones provide the service, there are four sub-channels, and the flight altitude is 100m. The channel bandwidth between each drone and the IoT devices, as well as with the satellite, is 1MHz.

[0112] Calculate the data transmission rate r from IoT device i to drone u. iu The average path loss between IoT devices and drones is

[0113]

[0114] Among them, f c Let η be the carrier frequency, v be the speed of light in a vacuum, and η be the speed of light in a vacuum. LOS η represents the average additional loss caused by free-space path loss in line-of-sight links. NLOS This represents the average additional loss caused by free-space path loss in non-line-of-sight links. P represents the distance between IoT devices and drones. iu The probability of sight distance is obtained from the following equation (40).

[0115]

[0116] Where φ and It is a constant greater than 0, determined by the environment, θ iu It is the elevation angle between the equipment and the drone, expressed as

[0117]

[0118] The gain between IoT devices and drones is obtained.

[0119]

[0120] In Example 1, the carrier center frequency is 5 GHz. Environmental variables. The values ​​are (4.88, 0.43, 0.1, 21).

[0121] The rate at which IoT devices transmit data to drones is expressed as:

[0122]

[0123] Where p i Where N is the transmit power of the IoT device, N0 is the noise power spectral density, and a iu Let a be a binary variable consisting of 0 and 1.iu =1 indicates that IoT device i selects drone u for communication, otherwise it indicates that no communication exists. In Example 1, the noise power spectral density is -169dBm / Hz.

[0124] Calculate the data transmission rate r between the UAV u and the satellite. us Because it is a line-of-sight channel, the gain between the UAV and the satellite is [value missing].

[0125]

[0126] Among them, G tx and G rx d represents the antenna gain of the drone and the satellite, respectively. us The distance between a drone and a satellite is usually approximated by the satellite's orbital altitude h. s In Example 1, the low-Earth orbit satellite has an orbital altitude of 500 km, and the UAV antenna is an omnidirectional antenna; therefore, G... tx =1, the satellite's antenna gain is 15dBi.

[0127] Data transmission rate between drones and satellites is

[0128]

[0129] Where, p u N is the drone's transmit power, and N1 is the noise power spectral density.

[0130] Step 1.2: Based on the space-air-ground IoT model obtained in Step 1.1, form the energy efficiency η. EE and spectral efficiency η SE The expression for is the objective function of the multi-objective optimization problem that balances energy efficiency and spectral efficiency.

[0131] Energy efficiency is the ratio of effective information transmission rate to power, η. EE Represented as

[0132]

[0133] Where, p h This is the power required for a single drone to remain suspended in the air, which is 2W in Example 1.

[0134] Spectral efficiency is the ratio of effective information transmission rate to channel bandwidth, expressed as:

[0135]

[0136] To simplify the symbols, let and In addition, make the drone's position variable Sub-channel selection variable A = {a iu The transmit power variable P of IoT devices I ={p i} and the UAV transmit power variable P U ={p u}

[0137] Step 1.3: Given constraints, construct a multi-objective optimization problem that balances energy efficiency and spectral efficiency. Based on the condition that an IoT device can only communicate with one UAV at a time and an aircraft can only communicate with K IoT devices simultaneously, constraints are given on the number of communication devices for both UAVs and IoT devices. Since the energy available for signal transmission by UAVs and IoT devices is limited, constraints are given on the maximum transmit power of both UAVs and IoT devices. The data transmission rate of IoT devices needs to meet the minimum transmission rate requirement to ensure normal communication; therefore, a minimum transmission rate constraint is given. UAVs will collide when they are too close; therefore, a minimum distance constraint between UAVs is given. Using formulas (46) and (47) as the objective function, a multi-objective optimization problem balancing energy efficiency and spectral efficiency in the air-space-ground IoT network is constructed as shown in formula (48).

[0138]

[0139] Where r min For the minimum transmission rate, p imax and p umax For the maximum transmit power of IoT devices and drones, d min The minimum distance between drones is specified. In Example 1, the maximum transmit power of the IoT device is 0.1W, and the minimum data rate requirement is 15kbps. The maximum transmit power of the drone is 8W, and the minimum distance between drones is 50m.

[0140] Step 2: Introduce the energy efficiency and spectral efficiency tradeoff coefficient ∈, and use the ∈ constraint method to transform the multi-objective optimization problem of balancing energy efficiency and spectral efficiency in the air-space-ground IoT network constructed in Step 1 into a single-objective optimization problem, reducing the complexity of solving the optimization problem. The energy efficiency objective function is retained as the objective function of the single-objective optimization problem. Through the energy efficiency and spectral efficiency tradeoff coefficient ∈, the relatively simple spectral efficiency function is transformed into a new constraint condition, which facilitates the solution of the optimization problem.

[0141] The transformed single-objective optimization problem is expressed as:

[0142]

[0143] Wherein, ∈ represents the energy efficiency and spectral efficiency tradeoff coefficient. In this embodiment, we consider three cases where ∈ takes the values ​​of 0.35, 0.40, and 0.45.

[0144] Step 3: The single-objective optimization problem obtained in Step 2 is divided into three sub-problems: sub-channel selection, UAV and IoT device power control, and UAV deployment, to further improve the solution efficiency. A matching algorithm is used to solve the sub-channel selection problem containing binary integer variables, quickly obtaining suitable sub-channels and improving the data transmission rate between the UAV and IoT devices. For the non-convex sub-problem of UAV and IoT device power control, the Dinkelbach algorithm is used to transform the fractional objective function containing the UAV's transmit power and the IoT device's transmit power into a difference form for solution; a successive convex approximation method is used to transform the sub-problem containing the transmission rate r... us The non-convex constraints are transformed into convex constraints; the power control subproblem of UAVs and IoT devices is transformed into a corresponding dual problem using the Lagrange dual algorithm, yielding the optimal solutions for the UAV and IoT device transmission power. The UAV deployment subproblem is difficult to solve, so an angle relaxation variable Θ={θ iu}, and the distance between UAVs is calculated using a successive convex approximation algorithm. Transmission rate r iu By approximating the problem, the drone deployment subproblem is transformed into a convex problem, reducing computational complexity.

[0145] Step 3.1: Given other conditions, the IoT device selects a suitable sub-channel for communication with the drone; this is the sub-channel selection problem. The drone's position D is fixed, and the IoT transmit power P... I and UAV transmission power P U When variable A satisfies the constraints, it does not affect the objective function. Therefore, when the constraints are satisfied, maximizing the total transmission rate of IoT devices is taken as the objective function to improve the throughput of IoT devices. The sub-channel selection subproblem is expressed as follows:

[0146]

[0147] The sub-channel selection subproblem contains binary integer variables, making it difficult to obtain the optimal result using convex optimization methods. A many-to-one matching algorithm is employed to solve this problem, constructing a preference list of drones and IoT devices in descending order of transmission rate. First, the IoT devices select the first drone from the preference list. Then, the number of IoT devices already communicating with this drone is checked; if it is less than K, communication is successfully established. iu =1. If it equals K, then compare the priority of the IoT device with the IoT device that has already established communication with it in the drone's preference list. If the IoT device has a higher priority, then it replaces the IoT device with the lowest speed to establish communication with the drone, and puts the IoT device with the lowest speed into the waiting list for rematching. Otherwise, the IoT device fails to establish communication, a iu=0, remove the drone from the device preference list, add it to the match list and match again until a communication solution between the drone and the IoT device is obtained.

[0148] Step 3.2: Deploy the drone at a fixed location and select sub-channels to optimize the transmission power of the IoT and the drone, which is the power control sub-problem of the drone and IoT devices. The resulting power control sub-problem of the drone and IoT devices is non-convex, so the energy efficiency objective function and the constraint C7 related to the drone's data transmission rate need to be transformed into a convex form suitable for solving.

[0149] Since energy efficiency is the ratio of data transmission rate to the energy consumed during data transmission, it contains power variables in both the numerator and denominator, making it difficult to solve directly. The Dinkelbach algorithm is used to transform the energy efficiency function into a difference form that relates to the power of the drone and the IoT device.

[0150] Introducing a nonnegative parameter λ to represent the ratio of transmission rate to energy consumption, we have:

[0151]

[0152] The function in fractional form is transformed into difference form, expressed as:

[0153]

[0154] The objective function is transformed into a difference form for easier solution. Besides the objective function, constraint C7 is non-convex, but the data transmission rate r from the UAV to the satellite... us It's about the drone's transmit power p u The concave function is thus obtained through a first-order Taylor expansion, yielding the UAV data transmission rate r. us The upper bound is denoted as

[0155]

[0156] Constraint C7 is transformed into a convex constraint, which is

[0157]

[0158] Therefore, the power control subproblem of drones and IoT devices can be written in the following convex form, which is suitable for solving.

[0159]

[0160] Since the problem involves two variables, the Lagrange duality method is used to solve the convex form of the power control subproblem for UAVs and IoT devices. By representing the power control subproblem as its corresponding dual problem, the transmit power schemes for the UAV and IoT devices that satisfy the constraints can be quickly obtained. The Lagrange dual function is...

[0161]

[0162] Where μ,υ,ω,ε,τ are Lagrange dual variables.

[0163] The Lagrange duality problem is expressed as

[0164]

[0165] Due to constraint C4, the optimal solution... The following conditions must be met.

[0166]

[0167] Optimal solution The following conditions must be met.

[0168]

[0169] Since the Lagrange function has a non-differentiable probability, the subgradient method is used to update the Lagrange multipliers, as expressed below.

[0170]

[0171]

[0172]

[0173]

[0174] in, n is the number of iterations, γ is the iteration step size, and we have

[0175]

[0176] Step 3.3: Given the sub-channel selection and the transmit power of the UAV and IoT devices, optimize the deployment location of the UAV. Maximizing the transmission rate of the IoT devices is used as the objective function, but the UAV deployment subproblem is difficult to solve. To transform the problem into a convex problem, we first introduce an angle variable Θ = {θ}. iu}, thus obtaining the new constraint C9 representing the elevation angle of the IoT device, which is

[0177]

[0178] The constraint given by equation (66) is a non-affine constraint, which can be relaxed to

[0179]

[0180] Although the constraint remains non-convex, it applies to the horizontal distance between the drone and the IoT device. It is convex, therefore the elevation angle θ iu exist The lower bound of the location is represented as

[0181]

[0182] in

[0183]

[0184] For constraint C8, the minimum distance between UAVs is obtained using a successive convex approximation algorithm. exist and The lower bound of the location is

[0185]

[0186] Due to the IoT transmission rate r iu Since the objective function related to the physical network transmission rate is non-convex, constraints C6 and C7 are also non-convex. However, the transmission rate r is derived from this. iu Distance between IoT devices and drones and It is a concave function. Let For x, Let y be the IoT transmission rate r. iu In x 0 and y 0 The lower bound of the location is

[0187]

[0188] in

[0189]

[0190]

[0191] in

[0192]

[0193]

[0194] At this point, the drone location deployment subproblem has been transformed into a convex problem, represented as:

[0195]

[0196] Step 4: Using the block coordinate descent method, first solve the sub-channel selection sub-problem according to Step 3.1. Then, based on the solution to the sub-channel selection sub-problem obtained in Step 3.1, solve the UAV and IoT device transmit power sub-problem given in Step 3.2. Next, based on the solutions to the obtained sub-channel sub-problem and the UAV and IoT device transmit power sub-problem, solve the UAV location deployment sub-problem given in Step 3.3. Then, based on the solutions to the UAV and IoT device transmit power sub-problem and the UAV location deployment sub-problem, resolve the sub-problem given in Step 3.1. Iterate and alternately solve the three sub-problems of sub-channel selection, UAV and IoT device transmit power, and UAV location deployment to obtain the solution to the multi-objective optimization problem that balances energy efficiency and spectral efficiency, thus obtaining the multi-objective optimization result of balancing energy efficiency and spectral efficiency in the air-space-ground IoT network.

[0197] Through steps one through four, we obtained the energy efficiency and spectral efficiency of the system in Example 1. The energy efficiency changes with the number of iterations as follows: Figure 3 As shown, the spectral efficiency changes with the number of iterations as follows: Figure 4 As shown. According to Figure 3 and Figure 4 It is evident that this method eventually converges to at least one local optimum, and the improvement in system energy efficiency leads to a decrease in spectral efficiency. This method can consider the energy efficiency and spectral efficiency of the system through a trade-off coefficient, providing an optimization scheme that meets practical needs. This method has guiding significance for the rational selection of energy efficiency and spectral efficiency in space-air-ground IoT systems.

[0198] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structure or process made using the content of the present invention specification and drawings, or directly or indirectly applied to other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A multi-objective optimization method for balancing energy efficiency and spectral efficiency in space-air-ground Internet of Things (IoT) networks, characterized by: Includes the following steps, Step 1: For the air-space-ground IoT network where UAVs collect data from ground-based IoT devices and transmit the data to low-Earth orbit satellites, the channel between the UAV and the satellite is equivalent to a line-of-sight channel. Due to the actual situation of obstacles obstructing the UAV and IoT devices, the channel between the UAV and IoT devices is equivalent to a probabilistic line-of-sight channel. Based on this, an air-space-ground IoT model is constructed. Based on the constructed air-space-ground IoT model, a multi-objective optimization function that maximizes the system's energy efficiency and spectral efficiency is constructed. Given constraints on the number of communication devices for UAVs and IoT devices, the maximum transmit power of UAVs and IoT devices, the minimum transmission rate of data transmitted by IoT devices, and the minimum distance between UAVs, a multi-objective optimization problem that balances energy efficiency and spectral efficiency in the air-space-ground IoT network is constructed. Step 2: Introduce energy efficiency and spectral efficiency tradeoff coefficients ,use The constraint method transforms the multi-objective optimization problem of balancing energy efficiency and spectral efficiency in the air-space-ground IoT network constructed in step one into a single-objective optimization problem, reducing the complexity of solving the optimization problem; it retains the energy efficiency objective function containing variables such as IoT device transmit power, UAV transmit power, and sub-channel selection as the objective function of the single-objective optimization problem; and it uses energy efficiency and spectral efficiency tradeoff coefficients... The relatively simple spectral efficiency function is transformed into a new constraint, that is, the multi-objective optimization problem of balancing energy efficiency and spectral efficiency in the air-space-ground Internet of Things network is transformed into a single-objective optimization problem, which is conducive to solving the optimization problem; Step 3: Divide the single-objective optimization problem obtained in Step 2 into three sub-problems: channel selection, power control of UAV and IoT devices, and UAV location deployment, to further improve the solution efficiency; the channel selection sub-problem contains a binary variable indicating whether there is communication between the UAV and the IoT device. A matching algorithm is employed to quickly obtain suitable sub-channels, improving the data transmission rate between drones and IoT devices. For the non-convex sub-problem of drone and IoT device power control, the Dinkelbach algorithm is used to transform the fractional objective function containing both drone and IoT device transmit power into a difference form for solution. A successive convex approximation method is then used to further refine the sub-problem involving drone and IoT device power control. Data transmission rate with satellite The non-convex constraints are transformed into convex constraints; the power control subproblem of UAV and IoT devices is transformed into a corresponding dual problem using the Lagrangian dual algorithm, obtaining the optimal solutions for the transmission power of the UAV and IoT devices, minimizing the energy consumption of the system; the UAV location deployment subproblem is difficult to solve, so angle relaxation variables are introduced. And the distance between UAVs is determined by a successive convex approximation algorithm. Internet of Things (IoT) devices To drones Data transmission rate By approximating the problem, the drone deployment subproblem is transformed into a convex problem, reducing computational complexity; Step 4: Using the block coordinate descent method, first solve the sub-channel selection sub-problem. Based on the solution to the sub-channel selection sub-problem, solve the UAV and IoT device transmit power sub-problem. Then, based on the solutions to the obtained sub-channel selection sub-problem and the UAV and IoT device transmit power sub-problem, solve the UAV location deployment sub-problem. Based on the solutions to the UAV and IoT device transmit power sub-problem and the UAV location deployment sub-problem, solve the sub-channel selection sub-problem again. Iterate and alternately solve the three sub-problems of sub-channel selection, UAV and IoT device transmit power, and UAV location deployment to obtain the solution to the multi-objective optimization problem that balances energy efficiency and spectral efficiency, until the multi-objective optimization result that balances energy efficiency and spectral efficiency in the air-space-ground IoT network is obtained.

2. The method of claim 1, wherein: The process also includes step five, which involves using the multi-objective optimization results of the air-space-ground IoT network, which balances energy efficiency and spectral efficiency, obtained in step four, to select sub-channels based on the sub-channel selection results. Design a communication scheme between drones and IoT devices, select suitable drones and IoT devices for communication, and improve the throughput of both IoT devices and drones; utilize the optimized transmission power of IoT devices. and drone launch power Adjust the transmission power of IoT devices and drones in the air-space-ground IoT system to minimize the energy consumption of IoT devices and drones while meeting the communication spectrum efficiency requirements, thereby improving the system's energy efficiency. Utilizing drone location deployment results Planning drone locations further improves data transfer rates for IoT devices and drones.

3. The multi-objective optimization method for tradeoff between energy efficiency and spectrum efficiency in space-air-ground internet of things network according to claim 1 or 2, characterized in that: The implementation method for step one is as follows: Step 1.1: Construct a space-air-ground IoT model, with the number of IoT devices in the network being [number missing]. The number of drones is , respectively and This indicates that a low-Earth orbit satellite covers these IoT devices and drones, providing them with services; a Cartesian coordinate system is introduced, the first... The locations of the IoT devices and drones are respectively represented as follows: and ,in To maintain a fixed flight altitude for the drone, and to support simultaneous transmission from multiple IoT devices, orthogonal frequency division access (OFDM) technology is employed, dividing the channel between the drone and the IoT devices into [specific parameters]. There are 1 sub-channels, of which The bandwidth of each sub-channel is The channel bandwidth between each drone and the satellite is ; Computing IoT devices To drones Data transmission rate The presence of obstacles causes additional losses between IoT devices and drones; therefore, the channel between drones and IoT devices is equivalent to a probabilistic line-of-sight channel. The average path loss between IoT devices and drones is... (1) wherein, is the carrier frequency, is the speed of light in vacuum, is the average additional loss due to free space path loss of line of sight link, is the average additional loss due to free space path loss of non-line of sight link, is the distance between the IoT device and the UAV, is the line of sight probability, obtained from the following equation (2) (2) wherein and is a constant greater than 0 determined by the environment, is the elevation angle between the device and the drone, expressed as (3) The gain between IoT devices and drones is obtained. (4) Since an IoT device can only communicate with one drone, its transmission rate is expressed as... (5) wherein is a transmit power for the internet of things device, is a noise power spectral density, is a 0, 1 binary variable, denotes an internet of things device selecting a drone communicates, and otherwise denotes an absence of communication; Computational drones Data transmission rate with satellite Because it is a line-of-sight channel, the gain between the UAV and the satellite is [value missing]. (6) wherein, and Gup and Gsp represent the antenna gains of the UAV and the satellite, respectively, d represents the distance between the UAV and the satellite; The data transmission rate between the UAV and the satellite was obtained as follows: (7) wherein, P is the drone transmit power, N is the noise power spectral density; By combining formulas (1) to (7), the air-space-ground Internet of Things model is obtained; Step 1.2: Based on the space-air-ground-terrestrial IoT model obtained in Step 1.1, form expressions for energy efficiency and spectral efficiency , i.e., objective functions for the multi-objective optimization problem that trades off energy efficiency and spectral efficiency; The energy efficiency is the ratio of the effective information transmission rate to the power, the data transmitted to the satellite is the data sent by the unmanned aerial vehicle, and the energy efficiency is represented as (8) wherein, is the power required for a single drone to remain airborne; Spectral efficiency is the ratio of effective information transmission rate to channel bandwidth, expressed as: (9) For simplifying the symbols, let and ; in addition, let the UAV position , the subchannel selection variable , the IoT device transmit power variable , and the UAV transmit power variable ; the optimization objective function is constructed by combining equations (8) and (9); Step 1.3: Given the constraints, construct a multi-objective optimization problem that balances energy efficiency and spectral efficiency; based on the fact that an IoT device can only communicate with one drone at a time and an aircraft can only communicate with one drone at a time. Given the communication scenarios of various IoT devices, the number of communication devices for both UAVs and IoT devices is constrained; since the energy available for signal transmission by UAVs and IoT devices is limited, the maximum transmission power of UAVs and IoT devices is constrained; the data transmission rate of IoT devices needs to meet the minimum transmission rate requirement to ensure normal communication, therefore a minimum transmission rate constraint is given; UAVs may collide when they are too close, therefore a minimum distance constraint between UAVs is given; using formulas (8) and (9) as the optimization objective function, a multi-objective optimization problem balancing energy efficiency and spectral efficiency in the air-space-ground IoT network is constructed as shown in formula (10). (10) wherein is the minimum transmission rate, and is the maximum transmission power of the IoT device and the drone, is the minimum distance of the drone.

4. The method of claim 3, wherein: The transformed single-objective optimization problem in step two is expressed as follows: (11) wherein, is the energy efficiency and spectral efficiency trade-off coefficient.

5. The method of claim 4, wherein: The method for implementing step three is as follows: Step 3.1: Under the given other conditions, the Internet of Things device selects a suitable unmanned aerial vehicle subchannel for communication, i.e., the subchannel selection problem; fixed unmanned aerial vehicle location , Internet of Things transmission power and unmanned aerial vehicle transmission power , the variable does not affect the objective function when the constraint condition is met, so as to maximize the total transmission rate of the Internet of Things device as the objective function when the constraint condition is met, and improve the throughput of the Internet of Things device; the subchannel selection subproblem is expressed as (12) The sub-channel selection subproblem contains binary integer variables, making it difficult to obtain the optimal result using convex optimization methods. A many-to-one matching algorithm is employed to solve this problem, constructing a preference list of drones and IoT devices in descending order of transmission rate. First, the IoT devices select the first drone from the preference list. Then, the number of IoT devices already communicating with this drone is checked; if it is less than [a certain number], [the selection process continues]. Then communication is successfully established. If equal to Then, the priority of the IoT device with the lowest speed among the IoT devices that have already established communication with the drone is compared in the drone preference list. If the IoT device has a higher priority, it will replace the IoT device with the lowest speed to establish communication with the drone, and put the IoT device with the lowest speed into the waiting list for rematching. Conversely, the IoT device fails to establish communication, The UAV is deleted from the device preference list and put into the list to be matched for re-matching until a communication scheme of the UAV and the IoT device is obtained. Step 3.2: Deploy the drone at a fixed location and select a sub-channel to optimize the transmission power of the IoT and the drone, which is the power control sub-problem of the drone and IoT devices. The obtained power control sub-problem of the drone and IoT devices is non-convex, so the energy efficiency objective function and the constraint C7 related to the data transmission rate of the drone need to be transformed into a convex form suitable for solving. Since energy efficiency is the ratio of data transmission rate to energy consumed during data transmission, and both the numerator and denominator contain power variables, it is difficult to solve directly. The Dinkelbach algorithm is used to transform the energy efficiency function into a difference form of a function related to the power of the drone and the power of the IoT device. A non-negative parameter representing the ratio of transmission rate to consumed energy is introduced For (13) The function in fractional form is transformed into difference form, expressed as: (14) The objective function is transformed into a difference form for ease of solution; the constraint C7 is non-convex except for the objective function, but the rate at which the UAV transmits data to the satellite is a concave function in terms of the UAV transmit power , so by first-order Taylor expansion, an upper bound on the UAV transmit data rate is obtained, denoted as (15) Constraint C7 is transformed into a convex constraint, which is (16) Therefore, the power control subproblem of drones and IoT devices can be written in the following convex form, which is suitable for solving. (17) Since the problem involves two variables, the Lagrange duality method is used to solve the convex form of the power control subproblem for UAVs and IoT devices. By representing the power control subproblem for UAVs and IoT devices as their corresponding dual problems, the UAV and IoT device transmit power schemes that satisfy the constraints can be quickly obtained; the Lagrange dual function is... (18) wherein is a Lagrangian dual variable; The Lagrange duality problem is expressed as (19) Due to constraint C4, the optimal solution The following conditions need to be met (20) optimal solution the following conditions need to be met (21) Since the Lagrange function has a non-differentiable probability, the subgradient method is used to update the Lagrange multipliers, as expressed below. (22) (23) (24) (25) (26) wherein , is the number of iterations, is the iteration step size, and has (27) Step 3.3: Given the sub-channel selection and the transmit power of the UAV and IoT devices, optimize the deployment location of the UAV; maximizing the transmission rate of the IoT devices is used as the objective function, but the UAV deployment subproblem is difficult to solve; to transform the problem into a convex problem, an angle variable is first introduced. This yields a new constraint C9 representing the elevation angle of IoT devices, which is... (28) The constraint given in equation (28) is a non-affine constraint, which is relaxed to (29) While this constraint is still non-convex, it is convex with respect to the horizontal distance between the UAV and the IoT device, so the upper bound on the elevation angle at is expressed as (30) in (31) For constraint C8, the minimum value of the distance between UAVs is obtained using a successive convex approximation algorithm, the distance between UAVs At and the lower bound is (32) Due to the transmission speed of the Internet of Things Since the objective function related to the physical network transmission rate is non-convex, constraints C6 and C7 are also non-convex; however, the transmission rate is derived... Distance between IoT devices and drones and It is a concave function; let for , for This allows us to obtain the IoT transmission rate. exist and The lower bound of the location is (33) in (34) (35) in (36) (37) Therefore, based on (29) to (37), we obtain the UAV location deployment subproblem in convex form, denoted as: (38)。

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