A 3D Deployment Method for UAV Base Stations in Post-Disaster Communication Recovery

Abstract

The present invention belongs to the field of communication technologies, and particularly relates to a three-dimensional deployment method of an unmanned aerial vehicle (UAV) base station in post-disaster communication restoration. Based on minimizing the required number of UAVs and maximizing the overall quality of service measured by the received power of all users, a problem of obtaining the optimal decision for UAV deployment is constructed. During the process of solving the problem of obtaining the optimal decision for UAV deployment, a greedy search algorithm is used to find a sub-optimal solution for the minimum number and positions of UAVs, and then an artificial electric field algorithm is used to optimize the problems of position and load balancing, so as to obtain an optimal UAV deployment scheme. The present invention combines a greedy search algorithm and a meta-heuristic artificial electric field algorithm, takes into account minimizing the number of UAV deployments and meeting QoS requirements, can be continuously deployed in three-dimensional space, can quickly adapt to autonomous positioning in a dynamic network, and has a low complexity.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies, and particularly relates to a three-dimensional deployment method for an unmanned aerial vehicle base station in post-disaster communication restoration. Background Art

[0002] In recent years, natural disasters such as earthquakes and floods have occurred frequently, causing huge property and life losses. Most disasters are often unpredictable, and their sudden occurrence may cause unimaginable damage to humans. In such cases, effective disaster management and rapid response are key tasks for mitigating the impact of disasters. In addition, effective information management and rapid communication restoration are important components of disaster response and relief. However, in most post-disaster situations, traditional ground wireless infrastructure is often unavailable or may be severely damaged, preventing victims from communicating with each other or with the outside world. The first 72 hours after a disaster are the most critical, and there is a need to quickly deploy a wireless network to restore connectivity and provide assistance to rescue personnel or teams in the affected area.

[0003] In recent years, unmanned aerial vehicle (UAV) communication systems have received extensive attention from researchers in academia and industry due to their advantages such as wide coverage, strong data transmission capabilities, low capital costs, and short deployment times. UAVs can serve as flying base stations to provide wireless coverage for ground devices in disasters due to their inherent flexibility and mobility advantages. UAVs can achieve exploration of affected areas and rapid communication connections, playing an important role in disasters.

[0004] Currently, the main communication platform for emergency communication systems is the ground emergency communication platform. However, ground emergency communication vehicles have low flexibility and are greatly affected by terrain and road conditions, making it difficult to reach the target area in the first place. In addition, the equipment and deployment costs of ground emergency communication vehicles are very high, and the ground communication links established by them have higher fading compared to the air-ground (ATG) links established by low-altitude platforms (LAPs). Air-ground links have advantages such as small fading and a high probability of line-of-sight (LoS) links. LAPs can also achieve maximum coverage of users by adjusting their three-dimensional spatial positions and provide services to more users.

[0005] Regarding the deployment of Unmanned Aerial Vehicle (UAV) base stations (UAV-BS), most of the current related research focuses on deploying a single UAV in three-dimensional space or multiple UAVs in 2D space, with less consideration of the three-dimensional space jointly. The deployment of UAV base stations needs to jointly consider factors such as signal-to-noise ratio, relative positions between UAV base stations, and three-dimensional spatial positions, which is an NP-hard problem. Currently, there are mainly numerical methods, (meta)heuristic methods, and artificial intelligence methods. However, numerical algorithms are difficult to handle NP-hard problems. The post-disaster environment is often sudden and unknown. Artificial intelligence algorithms rely on prior datasets, and the capabilities and computing power constraints of UAVs all indicate that artificial intelligence algorithms are not the optimal solution in the current scenario. Summary of the Invention

[0006] To address the above problems, the present invention proposes a three-dimensional deployment method for UAV base stations in post-disaster communication recovery. Based on minimizing the required number of UAVs and maximizing the overall quality of service measured by the received power of all users, a problem of obtaining the optimal decision for UAV deployment is constructed, which is expressed as:

[0007]

[0008] Constraints:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014] Among them, N D represents the number of UAV base stations; K T represents the total number of ground users in the area; λ represents the balance between maximizing the quality of network performance and minimizing the number of deployed ABSs. Here, through experiments, it is recommended to choose 0.6, which can better achieve the balance between the two components of the objective function. Those skilled in the art can flexibly set this parameter according to the actual situation; u i represents the binary variable indicating whether the i-th UAV base station is deployed; P i,k represents the transmit power from UAV i to UE k ; P T represents the transmit power; a i,k represents UAV i and UEk The binary value of whether it is associated; UAV max Indicates the maximum capacity that the UAV can serve; β represents the environmental factor; p i,k Represents the transmission power from the i-th UAV to the k-th user; Λ th Represents UE k Received from UAV i The threshold of the signal-to-interference-plus-noise ratio; g j,k Represents the channel gain between the j-th UAV and the k-th user equipment; N gw Represents the power of Gaussian white noise; In a three-dimensional Cartesian coordinate system, use x j , y j Represents the horizontal position of the UAV base station, z j Represents the height; θ represents the safety distance between two UAVs.

[0015] Furthermore, in order to solve the problem of obtaining the optimal decision for UAV deployment, the greedy search algorithm is used to find the sub-optimal solution of the minimum number and position of UAVs, and then the artificial electric field algorithm is used to optimize the problems of position and load balancing to obtain the optimal UAV deployment plan.

[0016] Furthermore, the process of using the greedy search algorithm to find the sub-optimal solution of the minimum number and position of UAVs includes the following steps:

[0017] 101. Deploy candidate UAV base stations to cover all user equipment, ensure that each user equipment has at least one UAV base station to serve, and at the same time set all decision variables to 1, and measure and obtain the signal strength of other UAVs received.

[0018] 102. Calculate the signal-to-interference-plus-noise ratio between each UAV base station and the user, and determine whether the signal-to-interference-plus-noise ratio exceeds the set threshold. If it exceeds, there is a connection relationship between the UAV base station and the user, otherwise there is no connection relationship, so as to construct a connection graph.

[0019] 103. Delete the redundant connections existing in the connection graph.

[0020] 104. Check whether there is a UAV base station with a degree of 0 in the connection graph. If it exists and deleting this UAV base station does not affect the communication of other UAV base stations, then delete this UAV base station.

[0021] 105. According to the degree of the UAV, delete the n UAVs with the smallest degree, and try to re-associate the user equipment corresponding to the deleted UAVs to the adjacent UAV base stations; when the signal-to-interference-plus-noise ratio threshold condition for the connection between the UAV base station and the user equipment in step S102 is satisfied, and the capacity that the current UAV can serve after connection does not exceed the maximum capacity that the UAV can serve, the association can be successful.

[0022] 106. Determine whether the current UAV base station covers all user devices. If it does, complete the greedy search algorithm to obtain a certain number of UAV base stations and their initial positions. Otherwise, return to step 105.

[0023] Further, the process of deleting redundant connections existing in the connection graph includes the following steps:

[0024] For user devices served by multiple UAV base stations simultaneously, retain the connection with the UAV base station with the largest degree and delete the connections with other UAV base stations;

[0025] For UAV base stations exceeding the service quantity, iteratively delete the UAV base station with the highest degree connected to this UAV.

[0026] Further, the process of optimizing the problems of position and load balancing through the artificial electric field algorithm includes the following steps:

[0027] 201. Obtain the position of a particle in the three-dimensional search space according to the greedy search algorithm, denoted as X i =(x, y, z), where x, y, and z are the coordinates of a particle on the x, y, and z axes of the three-dimensional coordinate system respectively; in the present invention, the UAV base station or the user device is taken as a particle, and the geographical coordinates of the UAV base station or the user device are the positions in the three-dimensional search space;

[0028] 202. Determine whether there are unassociated user devices. If there are, let the base station or the UAV re-establish a connection with this UE;

[0029] 203. Based on the artificial electric field algorithm, calculate the acceleration of a particle at time t;

[0030] 204. Update the velocity at the current time according to the acceleration at the previous time, and update the position of the current particle in the three-dimensional space according to the velocity;

[0031] 205. Determine whether the current is the maximum number of iterations. If so, end the iteration and obtain the optimal position of the particle; otherwise, return to step 202;

[0032] where i = 1, 2, 3,......, N, N represents the minimum number of UAVs obtained by the greedy search algorithm; x i is the position of the i-th particle in the three-dimensional search space.

[0033] Further, the solution process for calculating the acceleration of a particle at time t:

[0034] Calculate the force between two particles, denoted as:

[0035] Calculate the resultant force acting on a particle, expressed as: This resultant force is the acceleration of the particle at time t;

[0036] Among them, Q i represents the electric charge of the i-th particle. The charge of the drone base station is the service capacity of the base station, and the charge of the user equipment is the service capacity it needs to occupy; R i,j is the signal strength received between the i-th particle and the j-th particle, is the unit vector of direction. The unit vector of direction between two drone base stations is the negative direction, that is, the force between drone base stations is a repulsive force. The unit vector of direction between a drone base station and a user equipment is the positive direction, that is, the force between a drone base station and a user equipment is an attractive force; The resultant force received by the particle.

[0037] Furthermore, the process of updating the velocity at the current moment according to the acceleration at the previous moment and updating the position of the current particle in the d-dimensional space according to the velocity includes the following steps:

[0038]

[0039]

[0040] Among them, represents the velocity of the i-th particle in the three-dimensional space at time t + 1; rand() represents obtaining a random number uniformly distributed in [0, 1]; represents the acceleration of the i-th particle in the three-dimensional space at time t; x i (t + 1) represents the position of the i-th particle in the three-dimensional space at time t + 1.

[0041] The present invention combines a greedy search algorithm with a relatively new artificial electric field algorithm of adaptive metaheuristics, considers minimizing the number of drone deployments and maximizing the received power, can be continuously deployed in three-dimensional space, can quickly adapt to the autonomous positioning of a dynamic network, and has a low complexity. It has better effects compared with other metaheuristic algorithms such as particle swarm and genetic algorithms; the greedy search algorithm can quickly complete the initialization to give the required number of drones and the initial positions, and the artificial electric field algorithm is suitable for solving the many-to-many problem of drone coverage of end users, autonomously uses a dynamic network, and at the same time, due to the characteristics of the algorithm, it can better achieve the load of drone base station coverage. Description of the Drawings

[0042] Figure 1 is a schematic diagram of the drone deployment system model in a three-dimensional deployment method of drone base stations in post-disaster communication recovery according to the present invention;

[0043] Figure 2This is a flowchart of a three-dimensional deployment method for UAV base stations in post-disaster communication recovery according to the present invention. Detailed implementation manners

[0044] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0045] The present invention proposes a three-dimensional deployment method for UAV base stations in post-disaster communication recovery. Based on minimizing the required number of UAVs and maximizing the overall service quality measured by the received power of all users, a problem of obtaining the optimal decision for UAV deployment is constructed, and this problem is expressed as:

[0046]

[0047] Constraint conditions:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] Among them, P i,k represents the transmission power from the UAV i to the UE k ; P T represents the transmission power; a i,k represents the binary value indicating whether the UAV i and the UE k are associated; UAV max represents the maximum capacity that the UAV can serve; β represents the environmental factor; p i,k represents the transmission power from the i-th UAV to the k-th user; Λ th represents the threshold of the signal-to-interference-plus-noise ratio received by the UE k from the UAV i ; g j,k represents the channel gain between the j-th UAV and the k-th user terminal; N gw represents the power of Gaussian white noise; in a three-dimensional Cartesian coordinate system, using x j , y jrepresents the horizontal position of the UAV base station, z j represents the height; θ represents the safety distance between two UAVs.

[0054] This embodiment describes the implementation of the present invention from five aspects: the adopted system model, channel model, problem modeling, greedy search algorithm, and artificial electric field algorithm.

[0055] 1. System model

[0056] When the existing network infrastructure fails, for example, when a natural disaster causes the network to collapse, in this case, this embodiment considers a group of UAV base stations to quickly cover the network blank area. The key in network recovery is to provide coverage for disconnected users while meeting the relevant constraints of the target QoS (Quality of Service), and the goal is to determine the minimum number of ABSs required and their optimized 3D positions to provide effective connections to the uncovered users in the disaster area. Figure 1 An example system model is given. In the considered scenario, there are three communication objects: user equipment (UE), fixed ground base stations, and UAV base stations. In this work, this embodiment assumes that the UAV-BS can be reliably connected to the backbone network through some existing wireless technologies without interfering with the link from the UAV base station (UAV-BS) to the user, that is, the air-to-ground link.

[0057] 2. Channel model

[0058] The communication network considered in this embodiment includes two channel models, namely the air-to-air (A2A) channel model and the air-to-ground channel model (A2G).

[0059] 2.1 A2A channel model

[0060] Considering the open space of A2A communication, the channel between air-to-air is mainly dominated by the LOS link. Therefore, the path loss between UAVs can be simulated by the free space propagation loss (FSPL), and the path loss between UAVs is expressed as:

[0061]

[0062] where d i,j is the distance between the i-th UAV base station UAV i and the j-th UAV base station UAV j , f 0 is the carrier frequency of the UAV-to-UAV channel, and c is the speed of light.

[0063] In this embodiment, it is assumed that the channel is symmetric, and the transmission power and the receiving sensitivities of the two UAVs in the backbone network are the same. Since the received signal strength is inversely proportional to the first power of the distance, let R i,j represent the received signal strength between the i-th particle and the j-th particle, and the path loss between UAVs is expressed as:

[0064]

[0065] 2.2 A2G Channel Model

[0066] Generally, considering the complex terrain of the disaster area, the air-to-ground propagation channel is modeled by jointly considering the LOS and NLOS components and their occurrence probabilities. Note that for non-line-of-sight links, due to the shadowing effect and signal reflection from obstacles, the path loss is higher than that of line-of-sight links. The probability that the i-th UAV base station UAV i at the elevation angle (see θ in Figure 1 ) has a LOS connection with the k-th user equipment UE i,k is expressed as: k

[0067]

[0068] where α and β are environmental factors, and their values are constants depending on the environment (rural, urban, dense urban, etc.); the elevation angle is expressed as h represents the vertical distance between the i-th UAV base station UAV i and the k-th user equipment UE k , and r represents the distance between the UAV i and the UE k . i

[0069] Therefore, the path loss between the i-th UAV base station UAV i and the k-th user equipment UE k can be expressed as:

[0070]

[0071] The average path loss of LOS and NLOS links is expressed as:

[0072]

[0073]

[0074] where and They are the average path losses of LOS and NLOS links respectively; ηLOS and ηNLOS are the average additional path losses to the free space propagation loss under LOS and NLOS respectively, which depend on the environment; f is the channel carrier frequency from the UAV to the user equipment.

[0075] Since the UAV uses the same frequency band as the ground base station, there is co-frequency channel interference between UAVs and between the UAV and the ground base station. Assume that the k-th user equipment UE k receives a signal-to-interference-plus-noise ratio (SINR) from the i-th unmanned aerial vehicle base station UAV i exceeding the threshold Λ th , then the UE k is covered, and its transmission rate and QoS can be supported by the UAV i . The calculation method of SINR is:

[0076]

[0077] where p i,k is the transmission power of the i-th unmanned aerial vehicle base station UAV i to the k-th user equipment UE k , g i,k is the channel gain between the i-th unmanned aerial vehicle base station UAV i and the k-th user equipment UE k , N gw represents the power of Gaussian white noise, j≠i represents all other UAVs and ground base stations except the i-th unmanned aerial vehicle base station UAV i ; the value of the threshold Λ th is set according to the experience of those skilled in the art. The minimum value of the threshold Λ th is -5 dB, and only when it is at least greater than this value is it considered that there is a possibility of communication.

[0078] 3. Problem Modeling

[0079] The main objectives of this embodiment include:

[0080] (1) Minimize the deployment cost by minimizing the required number of UAVs;

[0081] (2) Intelligently deploy UAV-BS to maximize the overall quality of service measured by the received power of all users.

[0082] For the above objectives, a decision variable u is introduced i, to indicate whether the ground user equipment is covered by a certain UAV-BS. This value is a boolean variable, where 1 represents being covered by the service and 0 represents the opposite. Based on this, K can be defined T (N T +1) associated matrix A, where a i,k represents whether the UAV i is associated with the UE k is a boolean variable. If associated, it represents 1, otherwise it represents 0, i ∈ [1, N T , k ∈ [1, K T .

[0083] The power budget set by the UAV for each covered user is expressed as where P max is the maximum transmission power of the UAV, and UAV max is the maximum capacity that the UAV can serve. Based on the above, this embodiment models the problem of obtaining the optimal UAV deployment decision as:

[0084]

[0085] Constraint conditions:

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] The objective function minimizes the number of deployed ABSs and places them in high-demand areas to minimize the deployment cost, and also improves the network quality by maximizing the received power of each user. The first part in equation (8) represented by u i is responsible for minimizing the number of deployed UAV-BSs, and the second part explains the total received power normalized by the transmission power P T . Since the objective function consists of two parts, this embodiment introduces a new parameter λ to balance the need between maximizing the network performance quality and minimizing the number of deployed ABSs. This parameter can be configured by the deployed disaster relief personnel according to the situation to facilitate minimizing the number of ABSs or maximizing the total received power.

[0092] The constraint represented by equation (9) ensures that the wireless node will only link to the available UAV-BS;

[0093] The constraint defined in Equation (10) states that each UE should be served by a single UAV-BS;

[0094] The constraint defined in Equation (11) ensures that the number of users connected to each UAV-BS does not exceed the defined capacity, where UAV max represents the maximum number of users that a single UAV-BS can serve;

[0095] The constraint in Equation (12) ensures that the number of uncovered users does not exceed the allowable outage ratio represented by β;

[0096] The constraint in Equation (13) ensures the minimum SINR threshold for the ground users served by the UAV i ;

[0097] The last constraint in Equation (14) enforces the safety distance between any pair of deployed UAV-BSs;

[0098] This embodiment uses Taylor series linearization to handle the non-linearity in (13) and (14).

[0099] 4. Greedy Search Algorithm

[0100] To quickly deploy the minimum number of UAVs at the optimal positions, the search space is reduced by specifying the initial search space of the continuous deployment process to sub-optimal positions. These sub-optimal positions can be obtained from the given discontinuous space by using a low-complexity greedy algorithm. The basic idea of the specific deployment scheme is as follows: First, use the greedy search algorithm to obtain the minimum number of UAVs and their sub-optimal positions from the given candidate positions; then use the meta-heuristic artificial electric field algorithm to simultaneously achieve load balancing by finding the optimal positions of each UAV in the continuous space. The flow chart of the entire hybrid algorithm is as Figure 2 shown.

[0101] The greedy search method in this embodiment specifically includes the following steps:

[0102] 1) Initialization: Deploy a sufficient number of candidate UAV-BSs to cover all UEs, ensuring that at least each UE is served by one UAV-BS, and at the same time set all u i to 1, and then calculate the distances between the UAVs.

[0103] 2) Establish links: By calculating the SINR between the UAV and the UE, compare whether it exceeds the threshold Λ th to construct a connection graph.

[0104] 3) Delete redundant connections: Redundant connections exist when at least one UE is associated with more than one UAV. The specific process is as follows:

[0105] · For a UE served by multiple UAVs simultaneously, retain the connection to the UAV with the highest degree and delete the connections to other UAVs.

[0106] · For UAVs exceeding the service quantity, i.e., not satisfying (11), iteratively delete the connections of the UEs with the highest degree because these UEs have more options to connect to other UAV-BSs.

[0107] · After deletion, the number of UEs served by each UAV and BS should be below the threshold, i.e., satisfy (11).

[0108] 4) Check for idle UAVs: If after step 3, the degree of a UAV becomes 0, then after attempting to delete the UAV, check whether the other associated UAVs can still communicate. If so, delete the UAV.

[0109] Delete associated replaceable UAVs: If without violating the constraint conditions, select the UAV with a lower degree, attempt to delete all associated UEs and make them re-associate to adjacent UAV-BSs. If the attempt is successful, delete the UAV. Then return to step 5. After the end, the approximate value of the minimum number of UAVs is expected to cover all UEs and their initial positions.

[0110] 5. Artificial Electric Field Algorithm

[0111] Obtain a sub-optimal solution for the minimum number and positions of UAV-BSs through a greedy search algorithm, and then further optimize the positions and load balancing through the artificial electric field algorithm; this algorithm utilizes the artificial electric field law to place at the optimal positions.

[0112] 5.1 Modeling of the Artificial Electric Field Algorithm

[0113] According to Coulomb's law, the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. There are two types of electrostatic forces: attractive force and repulsive force. The force between objects with different charges is attractive, and the force between two objects with the same charge is repulsive. Each UAV-BS carries K d positive charges, and each UE carries a negative charge. The forces formed between different UAV-BSs are repulsive, while the forces formed between UAV-BS and UE are attractive. The UAV-BS approaching charge balance attracts less strongly, while the UAV-BS with a larger charge difference attracts more strongly, thus achieving load balancing.

[0114] Charged Q i and Q j The magnitude of the electrostatic force between two objects is:

[0115]

[0116] Among them, is the magnitude of the electrostatic force, K is the Coulomb constant, Q i and Q j are the charges of the i-th and j-th objects respectively, and d is the distance between the two charges Q i and Q j .

[0117] 5.2 Initialization

[0118] In this step, according to the greedy search algorithm, set the corresponding number of UAV-BSs, and deploy the UAV-BSs to the corresponding positions to associate the corresponding UEs, denoted as X i =(x, y, z), i = 1, 2, 3,......, N, x i is the position of the i-th particle in the three-dimensional search space.

[0119] 5.3 Associate UEs

[0120] After the first run after initialization, there are no UEs to be associated. However, as the iteration progresses, there will be cases where UEs are not associated, and connections need to be re-established by re-association.

[0121] 5.3 Calculate the superimposed force

[0122] The force between two particles can be obtained from Coulomb's law and the fact that the signal strength is proportional to the first power of the distance:

[0123]

[0124] where K(t) represents the Coulomb constant; Q i and Q j represent the electric charges of the particles, which are the service capacities of the particles in the present invention. For the UAV base station, it is its total service capacity, and for the user equipment, it is the user capacity it needs; R i,j is the signal strength received between the i-th particle and the j-th particle, is the unit vector of the direction.

[0125] In this embodiment, the calculation of forces, etc. are all represented by vectors. Therefore, the total force finally calculated is the superposition in the three-dimensional space, which fits the movement of the continuous deployment of UAVs in the three-dimensional space. The total force acting on particle i is given by the following formula:

[0126]

[0127] According to Newton's second law:

[0128]

[0129] In the present invention, the UAVs are of the same specification, so "the masses are the same", and thus the acceleration is equivalent to the resultant force.

[0130] The distance between two charged particles and the Coulomb constant K(t) are as follows:

[0131]

[0132] where K 0 and α are two constant parameters. Generally, K 0 and α are taken as 200 and 30 respectively. As the number of iterations increases, the Coulomb constant becomes smaller, and then the movement amplitude of each time also becomes smaller, approaching the optimal solution; maxitr is the maximum number of iterations, and itr is the current iteration.

[0133] 5.4 Update the position and velocity

[0134] Through movement, the velocity of each charged particle is updated by its previous velocity and acceleration, and then this velocity is used to update the position of the charged particle.

[0135]

[0136]

[0137] 5.5 Determine whether the number of iterations is satisfied

[0138] Through a certain number of current iterations, UAV-BS tends to force balance, and the resulting revenue efficiency is relatively low. Therefore, when the iteration reaches the preset number of times, it stops and outputs the current position.

[0139] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A three-dimensional deployment method of UAV base stations in post-disaster communication restoration, characterized in that, Based on minimizing the required number of UAVs and maximizing the overall service quality measured by the received power of all users, a problem of obtaining the optimal decision for UAV deployment is constructed, which is expressed as: Constraints: Among them, N D represents the available number of UAVs; K T represents the total number of ground users in the area; λ represents the balance between maximizing the control network performance quality and minimizing the number of deployed ABSs; u i represents the binary variable indicating whether the i-th UAV base station is deployed; P i,k represents the transmission power from UAV i to UE k ; P T represents the transmission power; a i,k represents the binary value indicating whether UAV i and UE k are associated; UAV max represents the maximum capacity that the UAV can serve; β represents the environmental factor; p i,k represents the transmission power from the i-th UAV to the k-th user; Λ th represents the threshold of the signal-to-interference-plus-noise ratio received by UE k from UAV i ; g j,k represents the channel gain between the j-th UAV and the k-th user equipment; N gw represents the power of Gaussian white noise; in a three-dimensional Cartesian coordinate system, x j , y j represent the horizontal position of the UAV base station, and z j represents the height; θ represents the safety distance between two UAVs; To solve the problem of obtaining the optimal decision for UAV deployment, a greedy search algorithm is used to find a sub-optimal solution for the minimum number and location of UAVs, specifically including:

101. Deploy candidate UAV base stations to cover all user equipment, ensure that each user equipment has at least one UAV base station service, and at the same time set all decision variables to 1, and measure and obtain the signal strength of other UAVs received; 102. Calculate the signal-to-interference-plus-noise ratio (SINR) between each UAV base station and the user, and determine whether the SINR exceeds the set threshold. If it exceeds, there is a connection relationship between the UAV base station and the user, otherwise there is no connection relationship, and a connection graph is constructed accordingly; 103. Delete the redundant connections existing in the connection graph; 104. Check whether there is a UAV base station with a degree of 0 in the connection graph. If it exists and deleting this UAV base station does not affect the communication of other UAV base stations, then delete this UAV base station; 105. According to the degree of the UAV, delete the n UAVs with the smallest degree, and try to re-associate the user equipment corresponding to the deleted UAVs to the adjacent UAV base stations; 106. Determine whether the current UAV base stations cover all user equipment. If they cover, the greedy search algorithm is completed to obtain a certain number of UAV base stations and their initial positions, otherwise return to step 105; Then, the artificial electric field algorithm is used to optimize the problems of position and load balancing to obtain the optimal UAV deployment plan, specifically including:

201. Obtain the position of a particle in a three-dimensional search space according to the greedy search algorithm, denoted as X i =(x, y, z), where x, y, and z are the coordinates of a particle on the x, y, and z axes of a three-dimensional coordinate system, respectively; 202. Determine whether there are unassociated user equipment. If there are, let the base station or UAV re-establish a connection with this UE; 203. Based on the artificial electric field algorithm, calculate the acceleration of a particle at time t; 204. Update the velocity at the current time according to the acceleration at the previous time, and update the position of the current particle in three-dimensional space according to the velocity; 205. Determine whether the current is the maximum number of iterations. If so, end the iteration and obtain the optimal position of the particle; otherwise return to step 202; where \(i = 1, 2, 3,\cdots, N\), \(N\) represents the minimum number of UAVs obtained by the greedy search algorithm; \(x\) i is the position of the \(i\)-th particle in the three-dimensional search space.

2. A three-dimensional deployment method of UAV base stations in post-disaster communication restoration according to claim 1, characterized in that, The process of deleting the redundant connections existing in the connection graph includes the following steps: For user equipment served by multiple UAV base stations simultaneously, retain its connection with the UAV base station with the largest degree, and delete the connections with other UAV base stations; For UAV base stations exceeding the service quantity, iteratively delete the UAV base station with the highest degree connected to this UAV.

3. A three-dimensional deployment method of UAV base stations in post-disaster communication restoration according to claim 1, characterized in that, The solution process for calculating the acceleration of a particle at time t: Calculate the force between two particles, expressed as: Calculate the resultant force acting on the i-th particle, expressed as: This resultant force is the acceleration of the i-th particle at time t; Among them, Q i represents the electric charge of the i-th particle, and R i,j is the signal strength received between the i-th particle and the j-th particle; is the unit vector of direction. The unit vector of direction between two UAV base stations is the negative direction, and the unit vector of direction between a UAV base station and a user equipment is the positive direction; represents the resultant force received by the particle; K(t) represents the Coulomb constant between two charged particles at time t.

4. A three-dimensional deployment method of UAV base stations in post-disaster communication restoration according to claim 1, characterized in that, The Coulomb constant between two charged particles at time t is expressed as: where K 0 and α are two constant parameters, itr is the current iteration number, and maxitr is the maximum iteration number.

5. A three-dimensional deployment method of an unmanned aerial vehicle base station in post-disaster communication restoration according to claim 1, characterized in that, the process of updating the velocity at the current moment according to the acceleration at the previous moment and updating the position of the current particle in the d-dimensional space according to the velocity includes the following steps: Among them, represents the velocity of the $i$-th particle in three-dimensional space at time $t + 1$; rand() represents obtaining a random number uniformly distributed in [0, 1]; represents the acceleration of the $i$-th particle in three-dimensional space at time $t$; $x$ i (t + 1) represents the position of the $i$-th particle in three-dimensional space at time $t + 1$.

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