Energy Minimization Method and System for Unmanned Aerial Vehicle-Assisted Multi-Cluster NOMA Networks

Abstract

This invention relates to the field of communication technology, specifically disclosing a method and system for minimizing energy consumption in a UAV-assisted multi-cluster NOMA network. The method constructs a UAV-assisted multi-cluster NOMA network and, with the objective of maximizing the total energy consumption of the UAVs while satisfying the constraints of the UAV-assisted multi-cluster NOMA network, establishes a first optimization problem that jointly optimizes the UAV's hovering point access order, transmission power allocation, transmission duration allocation, and total duration. Solving this first optimization problem yields the hovering point access order, transmission power allocation, transmission duration allocation, and total duration that minimize the total energy consumption of the UAVs. Simulation results verify that this invention significantly outperforms traditional benchmark schemes in terms of energy saving and system efficiency improvement, while effectively meeting the QoS requirements of all ground users.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and in particular to a method and system for minimizing energy consumption in unmanned aerial vehicle-assisted multi-cluster NOMA networks. Background Technology

[0002] In recent years, drones have been increasingly used in low-altitude applications, encompassing a variety of tasks such as aerial inspection, video transmission, photography, and package delivery. Leveraging their superior maneuverability and flexibility, drones have played a crucial role in enhancing terrestrial network capabilities, particularly in scenarios where traditional infrastructure is lacking or damaged, such as during natural disasters or in remote areas where communication needs require improvement. Furthermore, the high-quality line-of-sight (LoS) communication channels between drones and ground users significantly improve transmission efficiency and reliability, enabling drones to demonstrate strong potential in a wide range of applications, including emergency response, real-time data acquisition, and monitoring.

[0003] The rapid development of mobile internet and the widespread adoption of smart devices have fueled a surge in mobile multimedia services, leading to an exponential increase in mobile communication traffic. Furthermore, the rise of the Internet of Things (IoT) has prompted the deployment of numerous IoT devices, all requiring wireless connectivity. This growing demand places higher performance requirements on wireless communication systems to cope with the increasing traffic and user connectivity needs. Non-Orthogonal Multiple Access (NOMA) has emerged as a key technology, offering high-speed data transmission, low latency, high reliability, and massive connectivity. NOMA utilizes serial interference cancellation to decode overlapping signals, enabling multiple ground users to simultaneously share communication resources, significantly improving spectral efficiency and system throughput, and achieving seamless integration with 5G (5th Generation Mobile Communication Technology). Numerous studies have demonstrated the enormous potential of NOMA in improving spectral efficiency, network throughput, and overall performance. For example, in multi-input multiple output (MIMO) NOMA networks, passive beamforming technology using reconfigurable intelligent surfaces (RIS) effectively optimizes signal quality and reduces interference. Furthermore, millimeter-wave NOMA frameworks improve network security and performance through strategic user grouping and power allocation. In two-hop mobile edge computing systems, NOMA-based resource allocation schemes achieve a balance between latency and energy consumption.

[0004] Combining NOMA technology with UAV-assisted communication represents a significant advancement in improving system performance. This combination has attracted widespread attention in academia, with numerous studies demonstrating its significant advantages in improving the efficiency and reliability of communication systems. For example, research has shown that NOMA technology can significantly enhance network security in UAV-supported wireless networks; and an analytical framework built for Coordinated Multipoint (CoMP) NOMA-integrated UAV cellular networks has proven further performance improvements. Furthermore, hybrid aerial networks constructed using a combination of Reconfigurable Intelligent Surfaces (RIS) and NOMA have also achieved optimization of key network parameters. It should be noted that NOMA's efficiency can be fully realized when the number of users in each cluster is limited; however, when UAVs need to provide services to a large number of users, a single NOMA group may be insufficient, often requiring users to be divided into multiple clusters, with NOMA technology applied separately within each cluster. To address this issue, one paper proposes a method to optimize user clustering, routing, transmission power, hovering position, and time to improve network performance, while another study focuses on improving quality of service (QoS) through similar optimization measures.

[0005] Meanwhile, a significant shortcoming in most existing studies is the neglect of energy consumption in drone networks. Effective energy management is crucial for operational efficiency, especially considering the physical limitations of drones. For example, rotorcraft drones typically have a flight time of only about 30 minutes, requiring frequent battery changes or recharging, thus highlighting the necessity of optimizing energy management strategies. Some literature has focused on minimizing total energy consumption in drone-based patrol and detection scenarios by optimizing task completion time, communication scheduling, computational resource allocation, and drone trajectories. Similarly, some literature has developed a framework to optimize the data collection process from IoT devices using energy-constrained drones, maximizing data volume while effectively managing energy usage.

[0006] In multi-cluster environments, energy management in UAV-NOMA networks faces numerous complex challenges. One key issue is how to plan the optimal order in which UAVs visit each cluster to minimize flight time and energy consumption. This requires designing an efficient flight path. However, this optimization faces a significant trade-off: increasing UAV flight speed can shorten flight time, allowing more time for data transmission and hovering within the cluster, but this also leads to a significant increase in flight energy consumption. Therefore, achieving a balance between reducing flight time and minimizing energy consumption has become an important and yet under-researched topic in UAV-assisted multi-cluster NOMA networks. Summary of the Invention

[0007] This invention provides a method and system for minimizing energy consumption in UAV-assisted multi-cluster NOMA networks. The technical problem it solves is how to jointly optimize the UAV's hovering point access sequence, transmission power allocation, and transmission duration to minimize the UAV's total energy consumption.

[0008] To address the above technical problems, this invention provides a method for minimizing energy consumption in UAV-assisted multi-cluster NOMA networks, comprising the following steps:

[0009] Construct an unmanned aerial vehicle (UAV) assisted multi-cluster NOMA network, where NOMA refers to Non-Orthogonal Multiple Access; the UAV assisted multi-cluster NOMA network includes unmanned aerial vehicles (UAVs) and is divided into... Clusters For each ground user, the drone's flight altitude is fixed at [missing information]. The drone starts from the starting position Starting from the designated hovering point, the drone sequentially visits the hovering points of each cluster to provide NOMA services to the clusters, and finally returns to the designated destination. ;

[0010] With the objective of minimizing the total energy consumption of the UAV and the constraint of the UAV-assisted multi-cluster NOMA network, a joint optimization mechanism is constructed to optimize the UAV's hovering point access order, transmission power allocation P, transmission duration allocation T, and total duration. The first optimization problem;

[0011] Solving the first optimization problem yields the UAV's hovering point access order, transmission power allocation P, transmission duration allocation T, and total duration. .

[0012] Furthermore, the total energy consumption of the drone includes the drone's hovering energy consumption. Transmission energy consumption of drones and the propulsion energy consumption of drones .

[0013] Furthermore, the constraints of the UAV-assisted multi-cluster NOMA network include the first to seventh constraints. The first constraint is that the set of hovering points of the UAV must include the centroid coordinates of each cluster. The second constraint is that the flight speed of the UAV is not less than the maximum speed. The third constraint is the given start and end positions of the UAV. The fourth constraint is that the throughput of each ground user is not less than a defined throughput threshold. The fifth constraint is that the decoded SINR of each ground user reaches at least a defined decoded SINR threshold. SINR refers to the signal-to-noise ratio. The sixth constraint is that the order of power allocation is consistent with the distance order between the UAV and the ground users. The seventh constraint is that the total transmission power of all users in each cluster does not exceed the power limit of the UAV. .

[0014] Furthermore, by solving the first optimization problem, we obtain the UAV's hovering point access order, transmission power allocation P, transmission duration allocation T, and total duration. The specific steps include:

[0015] To minimize the flight propulsion energy consumption of drones The goal is to optimize the drone's flight speed and hovering point access order, which means optimizing the drone's flight duration and flight trajectory.

[0016] Based on the determined access order of hovering points, to minimize the transmission energy consumption of the drone. and hovering energy consumption Optimize the transmission power allocation of the UAV with the sum of its components as the objective. and transmission duration allocation Allocation based on drone flight time and transmission time Obtain the total duration of the drone Furthermore, to minimize the flight propulsion energy consumption of the drone. To achieve this, optimize the drone's flight speed and hovering point access sequence, specifically including the following steps:

[0017] To minimize the flight propulsion energy consumption of drones With the objective as the objective and the first to third constraints as the constraints, the first optimization problem is transformed into a second optimization problem that optimizes the flight speed and hovering point access order of the UAV.

[0018] Based on the speed range of the drone The optimal flight speed of the UAV was determined using the golden ratio search method. And determine the optimal flight trajectory It consists of line segments connecting the hovering points;

[0019] Rearrange The order in which the hovering points are visited yields an ordered sequence of waypoints. ,make , Define the access order for flight energy consumption Represented as , express The propulsion energy consumption between them This represents finding the Euclidean distance, transforming the second optimization problem into minimizing... To achieve the goal, to satisfy To optimize only the hover point access order under constraints The third optimization problem;

[0020] The flight path of the UAV is represented by a weighted graph, and virtual nodes are introduced that are zero distance from the start and end points but infinite distance from all other points. Improvements were made to the algorithm for the Traveling Salesman Problem;

[0021] The third optimization problem is solved using an improved algorithm for the Traveling Salesman Problem.

[0022] Furthermore, the constructed weighted graph , where the vertex set edge set , Represents any two distinct vertices and The edge between, For the weight function, ;

[0023] The improved algorithm for the Traveling Salesman Problem includes the following steps:

[0024] Construct a weighted graph ;

[0025] Add virtual nodes arrive ;

[0026] Set the edge weights to: , , , ;

[0027] From virtual node To begin, execute the standard Traveling Salesman Problem algorithm to determine the initial order of visits. ;

[0028] from Remove from and its related edges; determine the final access order as follows .

[0029] Furthermore, based on the determined access sequence of hovering points, the transmission energy consumption of the drone is minimized. and hovering energy consumption Optimize the transmission power allocation of the UAV with the sum of its components as the objective. and transmission duration allocation The specific steps include:

[0030] Based on the determined flight speed and hovering point access sequence of the drone, the goal is to minimize the drone's transmission energy consumption. and hovering energy consumption With the sum of the values ​​as the objective and the fourth to seventh constraints as conditions, the first optimization problem is transformed into optimizing the transmission power allocation of the UAV. and transmission duration allocation The fourth optimization problem;

[0031] The fourth optimization problem is decomposed into optimizing transmission duration allocation. The fifth optimization problem and optimized transmission power allocation The sixth optimization problem;

[0032] The fifth and sixth optimization problems are solved iteratively, alternating between them, to obtain the UAV's transmission power allocation. and transmission duration allocation .

[0033] Furthermore, the optimization objective of the fifth optimization problem is to minimize the transmission energy consumption of the UAV. and hovering energy consumption The sum of these constraints constitutes the fourth constraint.

[0034] The solution to the fifth optimization problem is: , This represents the transmission duration allocated to the m-th cluster. This represents the k-th ground user in the m-th cluster. throughput threshold, express The downlink achievable rate, min indicates taking the minimum value.

[0035] Furthermore, the optimization objective of the sixth optimization problem is to minimize the transmission energy consumption of the UAV. and hovering energy consumption The sum of these constraints is subject to the fourth to seventh constraints.

[0036] Solving the sixth optimization problem includes the following steps:

[0037] The fourth constraint Transformation into , It is about non-concave functions, It is a non-convex function;

[0038] Will At a given local point Performing a first-order Taylor expansion at the given location yields its upper bound. ;

[0039] The fourth constraint condition is rewritten as follows: ;when hour, ;

[0040] Rewrite the fifth constraint as a linear constraint;

[0041] Based on the sixth and seventh constraints, and the rewritten fourth and fifth constraints, the sixth optimization problem is transformed into the seventh optimization problem.

[0042] The seventh optimization problem is solved using a convex optimization problem solver to obtain the UAV's transmission power allocation. .

[0043] This invention also provides an energy minimization system for UAV-assisted multi-cluster NOMA networks. This system applies the energy minimization method for UAV-assisted multi-cluster NOMA networks, and its key features are: the system includes a network construction module, a problem construction module, and a problem solving module; the network construction module is used to construct a UAV-assisted multi-cluster NOMA network, the problem construction module is used to construct a first optimization problem, and the problem solving module is used to solve the first optimization problem.

[0044] This invention provides a method and system for minimizing energy consumption in a UAV-assisted multi-cluster NOMA network. It constructs a UAV-assisted multi-cluster NOMA network and, with the objective of minimizing the total energy consumption of the UAVs while satisfying the constraints of the UAV-assisted multi-cluster NOMA network, establishes a first optimization problem that jointly optimizes the UAV hovering point access order, transmission power allocation, transmission duration allocation, and total duration. Solving this first optimization problem yields the hovering point access order, transmission power allocation, transmission duration allocation, and total duration that minimize the total energy consumption of the UAVs. Simulation results verify that this invention significantly outperforms traditional benchmark schemes in terms of energy saving and system efficiency improvement, while effectively meeting the QoS requirements of all ground users. Attached Figure Description

[0045] Figure 1 This is a flowchart of the energy consumption minimization method for UAV-assisted multi-cluster NOMA networks provided in this embodiment of the invention;

[0046] Figure 2 This is a UAV flight trajectory map optimized by the improved TSP algorithm provided in this embodiment of the invention;

[0047] Figure 3This is a diagram illustrating the convergence process of the golden section algorithm provided in this embodiment of the invention.

[0048] Figure 4 This is a diagram illustrating the convergence process of Algorithm 3 provided in this embodiment of the invention;

[0049] Figure 5 This is a process diagram of optimizing flight speed using the golden section search method provided in an embodiment of the present invention;

[0050] Figure 6 This is a graph showing the relationship between UAV propulsion energy consumption and flight time provided in an embodiment of the present invention;

[0051] Figure 7 This is a graph showing the relationship between UAV flight speed and flight time provided in an embodiment of the present invention;

[0052] Figure 8 This is a comparison chart of the propulsion energy consumption of UAVs under different schemes provided in the embodiments of the present invention;

[0053] Figure 9 This is a diagram showing the optimized power allocation of user equipment in different clusters provided in an embodiment of the present invention;

[0054] Figure 10 The transmission and hovering energy consumption and throughput thresholds provided in this embodiment of the invention. Relationship diagram;

[0055] Figure 11 This is a graph showing the relationship between transmission and hovering energy consumption and the number of user devices, provided in an embodiment of the present invention. Detailed Implementation

[0056] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are given for illustrative purposes only and should not be construed as limiting the present invention. The accompanying drawings are for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0057] The energy consumption minimization method for UAV-assisted multi-cluster NOMA networks provided in this embodiment of the invention, such as... Figure 1 As shown in the flowchart, this embodiment includes the following steps:

[0058] Constructing a drone-assisted multi-cluster NOMA network;

[0059] With the goal of minimizing the total energy consumption of UAVs and under the constraint of UAV-assisted multi-cluster NOMA networks, a joint optimization mechanism is constructed to optimize the UAV hovering point access order, transmission power allocation P, transmission duration allocation T, and total duration. ;

[0060] Solving the first optimization problem yields the UAV's hovering point access order, transmission power allocation P, transmission duration allocation T, and total duration. .

[0061] (1) Unmanned Aerial Vehicle-Assisted Multi-Cluster NOMA Network

[0062] 11) Network Model

[0063] In the network model of a drone-assisted multi-cluster NOMA network (UAV-NOMA network), the drone (UAV) acts as a mobile base station. Services are provided to ground users, who are divided into: To achieve efficient user clustering, this paper employs the K-means algorithm, which has fast convergence characteristics, to cluster users into clusters. Ground users are divided into Clusters. Define the set of clusters as... In the first Cluster In China, there are a total of A ground user, using The total number of users in all clusters is indicated. ,satisfy The drone starts from the starting position. Starting from the designated destination, the system follows the trajectory to the hovering point of each cluster in sequence, eventually returning to the designated endpoint. Specifically, each cluster The hovering point is set as its cluster center. (Excluding horizontal position at altitude). During this process, the drone transmits only while hovering to reduce the impact of the Doppler effect. To meet the demands of large-scale connectivity and optimize spectral efficiency, the drone employs NOMA technology within each cluster to provide services to users. Furthermore, the total duration... Including transmission duration and flight duration ,Right now Assigned to the first The transmission time of each cluster is ,satisfy .set up Indicates the first The th cluster A user, and the hover point The distance between them is expressed as Drones are always The horizontal position is Therefore, there is hovering point Included in drones in 0 to In the various horizontal positions between.

[0064] Assuming the drone flies at an altitude of ,user The position is ,but The calculation is as follows: , This represents the calculation of Euclidean distance. It is usually assumed that the m-th element... In this process, the distance between each user and the drone meets the following requirements. .

[0065] 12) Communication model

[0066] Air-to-ground communication channels are typically assumed to be LoS channels. Ground users... The channel gain between the drone and the UAV is expressed as ,in For reference distance The average channel gain at a distance of meters. In a NOMA system, the receiver employs serial interference cancellation technology to ensure fairness among ground users. Specifically, users with weaker channel conditions (weak users) are allocated more transmission power, while users with better channel quality (strong users) are allocated less power. Let... Indicates user The transmission power. Sorted according to the distance from the ground user to the drone. Must meet Furthermore, the total transmission power of all ground users within each cluster must not exceed the power limit of the drone. ,Right now In a NOMA system, each ground user first decodes the stronger signal from the channel, removes it from the received combined signal, and then decodes its own signal. Therefore, based on distance ordering, when ,user The signal-to-noise ratio expression is:

[0067]

[0068] in This indicates the noise power at the receiving end.

[0069] when At that time, its SINR is:

[0070]

[0071] Furthermore, users with better channel conditions also need to accurately decode messages from users with weaker channel conditions, thus requiring them to meet certain constraints. ,in Indicates user Decoding requirements. Therefore, users The downlink reachable rate is expressed as:

[0072]

[0073] in This refers to the channel bandwidth.

[0074] 13) Energy consumption model

[0075] This paper divides the energy consumption of UAVs into two parts: flight propulsion energy consumption and transmission energy consumption, and analyzes them separately. The energy consumption of UAVs during flight is denoted as... The energy consumption during transmission is denoted as According to existing literature, the propulsion power consumption of a rotary-wing UAV in horizontal flight can be expressed as:

[0076]

[0077] in, Indicates the horizontal flight speed of the drone. and These represent the average rotor induced velocity and rotor tip velocity of the UAV, respectively. and These represent the hovering induced power and rotor profile power of the UAV, respectively. Furthermore, , , and These represent the drone's fuselage drag coefficient, rotor solid fraction, rotor disk area, and air density, respectively. Therefore, the drone's propulsion energy consumption... It can be represented as:

[0078]

[0079] On the other hand, the total transmission energy consumption of the drone can be expressed as:

[0080]

[0081] In addition, the energy consumption during the drone's hovering period is recorded as , define when The drone is currently hovering. Energy consumption during hovering is calculated as follows:

[0082]

[0083] Ultimately, the total energy consumption of the system is defined as:

[0084]

[0085] (2) Constructing the optimization problem

[0086] 21) Objective function

[0087] To maximize resource efficiency, the optimization objective established in this method is to jointly optimize the UAV trajectory. Transmission power and transmission duration allocation Total duration To minimize (min) the total energy consumption of the system. Therefore, the objective function is: Total duration =Transmission duration +Flight duration Transmission time (i.e., transmission duration allocation) ) has already been used as an optimization variable, while flight time Optimization is equivalent to optimizing flight speed.

[0088] 22) Constraints

[0089] Based on the network and communication models of UAV-assisted multi-cluster NOMA networks, the constraints of UAV-assisted multi-cluster NOMA networks include:

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] Equations (9) to (15) represent the first to seventh constraints, respectively. Constraint (9) requires that the set of hovering points of the UAV must include the centroid coordinates of each cluster. Constraint (10) requires that the flight speed of the UAV is not less than the maximum speed. Constraint (11) defines the starting and ending positions of the UAV. Constraint (12) ensures that the throughput of each ground user is not less than a defined threshold. Constraint (13) guarantees that the decoded SINR of each ground user reaches at least the defined threshold. Constraint (14) restricts the order of power allocation to be consistent with the distance order between the UAV and ground users. Constraint (15) ensures that the total transmission power of all users within each cluster does not exceed the power limit of the UAV. .

[0098] 23) Optimization problem

[0099] By combining the objective function and constraints, we obtain the first optimization problem (P1).

[0100] Due to the high coupling of variables in nonconvex constraints (12) and (13) and the complexity of selective constraint (9), directly solving the nonconvex optimization problem (P1) is extremely challenging.

[0101] (3) Solving the optimization problem

[0102] This invention addresses the first optimization problem through a two-stage approach, aiming to minimize the total energy consumption of the UAV by comprehensively considering propulsion and transmission energy consumption. In the first stage, the UAV's flight speed and hovering point access sequence are optimized to reduce propulsion energy consumption, and the optimal flight trajectory is proven. It consists of line segments connecting hovering points. In the second stage, based on the determined hovering point access order (i.e., flight path or flight trajectory), the transmission power allocation of the UAV is optimized. and transmission duration allocation To minimize the transmission and hovering energy consumption of the UAV, the first optimization problem is solved to obtain the UAV's hovering point access order, transmission power allocation P, transmission duration allocation T, and total duration. The specific steps include:

[0103] To minimize the flight propulsion energy consumption of drones The goal is to optimize the drone's flight speed and hovering point access order, which means optimizing the drone's flight duration and flight trajectory.

[0104] Based on the determined access order of hovering points, to minimize the transmission energy consumption of the drone. and hovering energy consumption Optimize the transmission power allocation of the UAV with the sum of its components as the objective. and transmission duration allocation Allocation based on drone flight time and transmission time Obtain the total duration of the drone .

[0105] 31) Phase 1: Optimization of UAV flight speed and hovering point access order

[0106] In the first phase, the goal is to minimize the drone's propulsion energy consumption. The first optimization problem is transformed into a second optimization problem:

[0107]

[0108]

[0109] To address problem P2, this invention employs a two-step optimization strategy. First, the optimal flight speed of the UAV is determined using the golden section search method, and it is rigorously proven that the optimal flight trajectory consists of several line segments. Second, the traveling salesman problem algorithm is used to optimize the order in which the UAV visits hovering points, thereby further reducing flight energy consumption.

[0110] ① Determination of optimal flight speed

[0111] This invention first considers designing the minimum energy flight trajectory between any two points, for example, from... arrive The path discretization method is used to divide the UAV trajectory into... Each segment, thus obtaining The waypoint. The drone was at the... The location information of the starting point of the segment is denoted as The flight time for this segment is expressed as Suppose that for any ,have ,in Choose a value small enough that the drone's flight speed can be approximated as constant within each segment. Given , The selection is large enough that... ,in From arrive The upper bound of the required total flight distance. Therefore, the drone in the... The flight speed of the segment can be expressed as Total flight time for ,in Therefore, the first The propulsion energy consumption of a segment can be approximated as:

[0112]

[0113] in, .therefore, The total propulsion energy consumption of each segment is .

[0114] It is important to note that, given and Under the conditions, depending on ,in It is the only variable, and its value range lies within the interval. Therefore, this section uses the golden section search method to obtain... The minimum value.

[0115] The golden ratio search method achieves its goal by progressively narrowing the search interval until it is small enough. For example, for a given interval... unimodal function on The search range is updated by comparison. and This is accomplished using the function value at that point. For any interval... In each iteration, the update boundary of the interval can be represented as follows:

[0116]

[0117] The specific search process of the golden section search method is shown in Table 1 below, Algorithm 1:

[0118] Table 1

[0119]

[0120] The golden section search method can be used to determine that for any straight road segment... Its optimal flight speed It is the same in all road sections, that is... This uniform optimal speed is independent of the start and end points of the road segment. The time complexity of the golden section search method depends on the required accuracy. Instead of the size of the initial interval, the time complexity is O(n). By employing the golden ratio search method, the optimal speed for each UAV flight segment can be efficiently determined, thereby minimizing energy consumption. Next, we will continue with Proposition 1 to further determine the optimal flight trajectory of the UAV.

[0121] Proposition 1: To minimize flight propulsion energy consumption, the UAV should start from a designated origin. and finish line They fly in a straight line.

[0122] Proof: This proposition is proved by contradiction. Assume that the optimal flight trajectory designed to minimize propulsion energy consumption includes the point... and The curved path between them. Therefore, waypoints can always be found. and Replace any curved path with a straight path and follow this path at the optimal speed. Flight, thus obtaining alternative trajectories with lower energy consumption. Due to ,in It is a constant. Minimize The premise is that Reduce to the minimum value. Clearly, the shortest path between two points is a straight line. Therefore, the drone should follow the connecting... and The straight segment, at the optimal speed Flight, thus completing the proof.

[0123] Based on proposition 1, the most energy-efficient flight mode for a drone is from the starting point. and finish line Maintain a constant speed along a straight path This method demonstrates that energy consumption is closely related to flight distance, thus highlighting the importance of the shortest flight path. To achieve this goal, this paper employs an improved traveling salesman problem algorithm to determine the optimal order in which the UAV visits hovering points.

[0124] ② Access order optimization

[0125] By rearranging The order in which each hovering point is visited yields an ordered sequence of waypoints. ,in yes An arrangement. Let , Access order Defined as Flight energy consumption Represented as: Therefore, the second optimization problem (P2) can be reformulated as the third optimization problem:

[0126]

[0127]

[0128] To clarify the issue (P3), this paper constructs a weighted graph. To optimize the flight path of drones, Represents a set of vertices. Denotes the set of edges. It is a weighted function. , For any two distinct vertices and ,in There exists an edge in each. Define the weight function. (Positive real numbers), in particular, .

[0129] By constructing a weighted graph The problem (P3) is identified based on the graph. This paper presents an improved algorithm for the Traveling Salesman Problem (P3) that focuses on reaching a specific destination without returning to the starting point. To efficiently solve this problem, this paper introduces a virtual node. The node is configured to be zero distance from the start and end points, but infinite distance from all other points.

[0130] When solving the Traveling Salesman Problem (TSP) using the improved algorithm, the UAV first follows the traditional TSP strategy, starting from the virtual node. Start by traversing all points, and finally return to the node. Due to virtual nodes and and The distance is zero, minimizing the total flight distance of the UAV requires selecting from... arrive and from arrive The path is determined. Finally, by removing virtual nodes and their associated edges, the target access order of the UAV is obtained.

[0131] The detailed process of the improved algorithm for the Traveling Salesman Problem is summarized in Algorithm 2, as shown in Table 2 below.

[0132] Table 2

[0133]

[0134] 32) Second Phase: Optimization of UAV Transmission Power and Transmission Duration Allocation

[0135] Optimizing the UAV's flight propulsion energy consumption allows for the attainment of optimal flight speed and access sequence. Building upon the results of this optimization phase, the next step is to minimize the energy consumption for communication and hovering. The fourth optimization problem is formulated as follows:

[0136]

[0137]

[0138] Question (P4) because and The coupling between the components results in a non-convex problem, making direct solutions challenging. To simplify the problem (P4), it is divided into two sub-problems: transmission duration optimization and transmission power optimization. A closed-form solution can be derived for transmission duration optimization. For the non-convex power optimization problem, a first-order Taylor approximation is applied to approximate it as a convex problem. Subsequently, this embodiment proposes an algorithm that effectively handles these two sub-problems through iterative solutions.

[0139] ① Optimization of transmission time

[0140] At a given transmission power In this case, problem (P4) can be decomposed into a fifth optimization problem:

[0141]

[0142]

[0143] To solve this problem, we will obtain a closed-form solution using Proposition 2 and provide a proof.

[0144] Proposition 2: For drones, shorter transmission time means lower energy consumption. Therefore, under the constraints, the solution to problem (P5) can be expressed in closed-form as:

[0145]

[0146] Proof: Since the objective function is The increasing function, therefore minimizing This helps to reduce the value of the objective function. Furthermore, considering constraint (12), The optimal value is the minimum value that satisfies the constraint. This shows that the closed-form expression in equation (19) provides the optimal transmission time. This is related to minimizing This aligns with the principle of reducing energy consumption.

[0147] ② Transmission power optimization

[0148] Given transmission duration In this case, problem (P4) can be decomposed into the sixth optimization problem:

[0149]

[0150]

[0151] Due to the existence of constraints (12) and (13), this problem is difficult to solve directly. Therefore, the continuous convex approximation method is used to approximate the non-convex constraints as convex constraints. For constraint (12), we have:

[0152] (20)

[0153] It can be further elaborated as follows:

[0154] (twenty one)

[0155] because The existence of It is about Non-concave functions. To handle non-convex terms. For a non-convex function at a given local point Performing a first-order Taylor expansion at this point, we obtain its upper bound:

[0156] (twenty two)

[0157] This will It is approximated as a concave function. Therefore, constraint (12) can be approximated as:

[0158]

[0159] In particular, when hour, The following conditions must be met:

[0160]

[0161] Similarly, constraint (13) is transformed into the following form:

[0162]

[0163] Transform it into the form of linear constraints:

[0164]

[0165] Therefore, the sixth optimization problem (P6) can be approximated as the seventh optimization problem:

[0166]

[0167]

[0168] Problem (P7) is a standard convex optimization problem, which can be solved using a convex optimization problem solver (CVX solver).

[0169] ③ Overall Algorithm and Complexity Analysis

[0170] Based on the above discussion, to solve problem (P4), it is decomposed into two subproblems: one can be expressed as a closed-form solution, and the other is transformed into a convex optimization problem. Table 3 shows Algorithm 3, which summarizes the detailed process of solving problem (P4) using an iterative algorithm.

[0171] Table 3

[0172] ,

[0173] The core step of Algorithm 3 is solving a convex optimization problem; therefore, its complexity is mainly affected by the number of optimization variables. Given a certain solution accuracy, its complexity can be expressed as: .

[0174] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved. This embodiment does not impose any limitations on these steps.

[0175] (4) Analysis of simulation results

[0176] 41) Simulation Settings

[0177] This embodiment employs extensive simulation experiments to verify the effectiveness of the proposed algorithm. First, consider a UAV-assisted multi-cluster NOMA network, which includes... There are 10 user devices, which are uniformly and randomly distributed in an area of ​​1. Within the square area. The relevant parameter settings are as follows: Assuming that all user devices have the same throughput threshold and decoding signal-to-noise ratio requirement, i.e. The maximum flight speed of the drone is set to... For parameters related to the energy consumption of rotary-wing drones, set... The initial and final positions of the drone are set as follows: and Specifically, drones from The flight begins, passing each cluster center, and finally returns. .

[0178] By using the K-means algorithm to transform the randomly distributed The user equipment is divided into five different clusters, such as Figure 2 As shown. The center point of each cluster represents the geometric center of all ground user locations within that cluster, ensuring fairness within each cluster. Meanwhile, Figure 2 The study also showcased the drone's flight trajectory optimized using the improved TSP algorithm. Figure 2 The effectiveness of Algorithm 2 was verified, demonstrating a trajectory that minimizes flight energy consumption during UAV flight.

[0179] 42) Convergence Analysis

[0180] Figure 3 The performance of Algorithm 1 at different numbers of iterations is shown. Figure 3The results show that energy consumption decreases significantly with increasing iterations and stabilizes near the 14th iteration. This curve highlights the effectiveness of the golden section search method in rapidly converging to the minimum energy consumption. The peak energy consumption in the second iteration can be attributed to the inherent mechanism of the method, which evaluates extreme points within the search interval to determine the search direction; that is, the method seeks the minimum by alternately evaluating the left and right segments of the interval. During this process, it is likely that extreme values ​​on the higher energy consumption side were tested, leading to the observed peak—a typical phenomenon in the golden section search method. Furthermore, Figure 4 The convergence of Algorithm 3 is demonstrated. It can be observed that both the outer and inner iterations converge quickly, thus verifying the effectiveness of the proposed algorithm.

[0181] 43) Analysis of the propulsion energy consumption performance of unmanned aerial vehicles (UAVs)

[0182] Figure 5 The flight performance of the UAV at a standard flight altitude of 100 meters was analyzed, demonstrating the relationship between flight speed and energy consumption. Figure 5 The results show that Algorithm 1 successfully converged and achieved the lowest flight energy consumption during flight. Figure 6 and Figure 7 This further reveals the inherent trade-off between UAV speed and flight time, and its impact on propulsion energy consumption. This example introduces two benchmark scenarios for comparison: a UAV flight time minimization scenario, where the UAV flies at maximum speed to shorten the total flight time; and a UAV power minimization scenario, where the UAV flies at maximum endurance speed to reduce propulsion power consumption. Figure 6 The data shows that the curve for the drone flight time minimization scheme exhibits a sharp upward trend, indicating that increasing flight speed to minimize runtime significantly increases propulsion energy consumption. In contrast, the drone power minimization scheme shows lower power consumption in the initial stage, but due to the extended runtime, it results in additional energy expenditure. Figure 7 The paper demonstrates the change in UAV speed over time after optimization, showing how different strategies balance energy efficiency and runtime by maintaining or adjusting flight speed. The method proposed in this invention effectively addresses this trade-off, significantly reducing energy consumption by balancing flight speed and runtime, and outperforming the two benchmark schemes mentioned above.

[0183] Figure 8 The energy consumption performance of the UAV under three strategies was compared: Algorithm 2, random access order, and cluster index access order. A bar chart shows the energy consumption comparison of Algorithm 1, the UAV flight time minimization scheme, and the power minimization scheme. Notably, the improved TSP method achieved the lowest energy consumption in all scenarios, fully demonstrating its superior performance in optimizing UAV flight paths and improving energy efficiency. Figure 8 The results further demonstrate that, especially when combined with the golden section search method, the improved TSP algorithm provides structured path planning that significantly enhances energy savings.

[0184] 44) Analysis of UAV communication and hovering energy consumption performance

[0185] Figure 9 This paper demonstrates the optimized power allocation for user equipment within different clusters in a UAV-NOMA network. It can be observed that the power allocation varies across clusters because power needs to be adjusted based on distance to ensure successful SIC decoding. User equipment farther from the drone is allocated more power to effectively meet decoding requirements. Figure 10 The throughput threshold was compared under three strategies. The trends in transmission and hovering energy consumption were analyzed using three strategies: Algorithm 3, the equal power allocation scheme, and the TDMA (Time Division Multiple Access) scheme. Algorithm 3 exhibited a moderate and stable energy consumption increase; in contrast, the equal power allocation scheme showed a steeper energy consumption increase, indicating lower energy allocation efficiency as throughput demand increased. The TDMA scheme showed an energy consumption increase between the two, being more efficient than the equal power allocation scheme but still less efficient than the proposed Algorithm 3. The results demonstrate that Algorithm 3, when utilizing the NOMA scheme, can more effectively manage the energy consumption issues arising from increased throughput demand.

[0186] Figure 11 A comparative analysis was conducted on the communication and hovering energy consumption performance of Algorithm 3, the equal power allocation scheme, and the TDMA scheme under the condition of increasing number of user devices. The energy consumption of all strategies increased with the increase in the number of user devices. However, the proposed scheme exhibited the lowest energy consumption increase with the increase in the number of user devices, demonstrating superior efficiency. In contrast, the equal power allocation scheme showed a significant linear increase in energy consumption, indicating that uniformly allocating power to each user significantly improves overall communication and hovering energy consumption. The TDMA scheme allocated the maximum allowable power within a specified time slot for each user, leading to a significant increase in communication and hovering energy consumption with the increase in the number of users. However, although its energy consumption increase was more controllable than that of the equal power allocation scheme, it was still higher than that of the proposed algorithm. Overall, Algorithm 3 effectively optimized communication and hovering energy consumption, outperforming traditional strategies.

[0187] Based on the above-mentioned method for minimizing the energy consumption of UAV-assisted multi-cluster NOMA networks, this embodiment also provides a system for minimizing the energy consumption of UAV-assisted multi-cluster NOMA networks, which includes a network construction module, a problem construction module, and a problem solving module; the network construction module is used to construct the UAV-assisted multi-cluster NOMA network, the problem construction module is used to construct a first optimization problem, and the problem solving module is used to solve the first optimization problem.

[0188] The embodiments described in this invention can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with the embodiments of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0189] Computer programs for implementing the methods and systems of the present invention may be written in any combination of one or more programming languages ​​and stored in a computer-readable storage medium. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0190] Computer-readable storage media can be tangible media that may contain or store computer programs for use by or in conjunction with an instruction execution system, apparatus, or device. Computer-readable storage media can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. Alternatively, computer-readable storage media can be machine-readable signal media. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, optical disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0191] In summary, the embodiments of the present invention aim to minimize the overall energy consumption of multi-cluster UAV-NOMA networks by jointly optimizing the flight trajectory, power allocation, and transmission duration of UAVs. The main contributions of the present invention can be summarized as follows:

[0192] (1) A novel multi-cluster UAV-NOMA network framework is proposed, aiming to meet the user's requirements for decoding signal and interference-to-noise ratio using limited resources. This framework significantly improves the network's energy efficiency by optimizing the allocation of UAV flight trajectory, transmission power, and transmission duration. The problem is formalized as a non-convex optimization problem with selective constraints, and solving this problem is quite challenging.

[0193] (2) To address this challenge, this invention proposes a two-stage algorithm. The first stage combines an improved traveling salesman problem method with the golden section search algorithm, focusing on reducing propulsion energy consumption. The second stage effectively solves the non-convex constraint by using alternating optimization techniques combined with a double-loop iterative algorithm for continuous convex approximation, thereby minimizing transmission energy consumption.

[0194] (3) Through comprehensive simulation verification, the present invention demonstrates a significant advantage in energy saving compared to the benchmark scheme. The simulation results further reveal the trade-off between flight time and energy consumption, indicating that optimizing the flight trajectory can effectively achieve higher energy efficiency.

[0195] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for minimizing energy consumption in UAV-assisted multi-cluster NOMA networks, characterized in that, Including the following steps: Construct an unmanned aerial vehicle (UAV) assisted multi-cluster NOMA network, where NOMA refers to Non-Orthogonal Multiple Access; the UAV assisted multi-cluster NOMA network includes unmanned aerial vehicles (UAVs) and is divided into... Clusters For each ground user, the drone's flight altitude is fixed at [missing information]. The drone starts from the starting position Starting from the designated hovering point, the drone sequentially visits the hovering points of each cluster to provide NOMA services to the clusters, and finally returns to the designated destination. ; With the objective of minimizing the total energy consumption of the UAV and the constraint of the UAV-assisted multi-cluster NOMA network, a joint optimization mechanism is constructed to optimize the UAV's hovering point access order, transmission power allocation P, transmission duration allocation T, and total duration. The first optimization problem; Solving the first optimization problem yields the UAV's hovering point access order, transmission power allocation P, transmission duration allocation T, and total duration. .

2. The energy consumption minimization method for UAV-assisted multi-cluster NOMA networks according to claim 1, characterized in that: The total energy consumption of the drone includes the drone's hovering energy consumption. Transmission energy consumption of drones and the propulsion energy consumption of drones .

3. The energy consumption minimization method for UAV-assisted multi-cluster NOMA networks according to claim 2, characterized in that: The constraints for UAV-assisted multi-cluster NOMA networks include the first to seventh constraints. The first constraint is that the set of hovering points of the UAV must include the centroid coordinates of each cluster. The second constraint is that the flight speed of the UAV is not less than the maximum speed. The third constraint is the given start and end positions of the UAV. The fourth constraint is that the throughput of each ground user is not less than a defined throughput threshold. The fifth constraint is that the decoded SINR of each ground user reaches at least a defined decoded SINR threshold. SINR refers to the signal-to-noise ratio. The sixth constraint is that the order of power allocation is consistent with the distance order between the UAV and the ground users. The seventh constraint is that the total transmission power of all users in each cluster does not exceed the power limit of the UAV. .

4. The energy consumption minimization method for UAV-assisted multi-cluster NOMA networks according to claim 3, characterized in that, Solving the first optimization problem yields the UAV's hovering point access order, transmission power allocation P, transmission duration allocation T, and total duration. The specific steps include: To minimize the flight propulsion energy consumption of drones The goal is to optimize the drone's flight speed and hovering point access order, which means optimizing the drone's flight duration and flight trajectory. Based on the determined access order of hovering points, to minimize the transmission energy consumption of the drone. and hovering energy consumption Optimize the transmission power allocation of the UAV with the sum of its components as the objective. and transmission duration allocation Allocation based on drone flight time and transmission time Obtain the total duration of the drone .

5. The energy consumption minimization method for UAV-assisted multi-cluster NOMA networks according to claim 4, characterized in that, To minimize the flight propulsion energy consumption of drones To achieve this, optimize the drone's flight speed and hovering point access sequence, specifically including the following steps: To minimize the flight propulsion energy consumption of drones With the objective as the objective and the first to third constraints as the constraints, the first optimization problem is transformed into a second optimization problem that optimizes the flight speed and hovering point access order of the UAV. Based on the speed range of the drone The optimal flight speed of the UAV was determined using the golden ratio search method. And determine the optimal flight trajectory It consists of line segments connecting the hovering points; Rearrange The order in which the hovering points are visited yields an ordered sequence of waypoints. ,make , Define the access order for flight energy consumption Represented as , express The propulsion energy consumption between them This represents finding the Euclidean distance, transforming the second optimization problem into minimizing... To achieve the goal, to satisfy To optimize only the hover point access order under constraints The third optimization problem; The flight path of the UAV is represented by a weighted graph, and virtual nodes are introduced that are zero distance from the start and end points but infinite distance from all other points. Improvements were made to the algorithm for the Traveling Salesman Problem; The third optimization problem is solved using an improved algorithm for the Traveling Salesman Problem.

6. The energy consumption minimization method for UAV-assisted multi-cluster NOMA networks according to claim 5, characterized in that: Constructed weighted graph , where the vertex set edge set , Represents any two distinct vertices and The edge between, For the weight function, ; The improved algorithm for the Traveling Salesman Problem includes the following steps: Construct a weighted graph ; Add virtual nodes arrive ; Set the edge weights to: , , , ; From virtual node To begin, execute the standard Traveling Salesman Problem algorithm to determine the initial order of visits. ; from Remove from and its related edges; The final access order is determined as follows .

7. The method for minimizing energy consumption in UAV-assisted multi-cluster NOMA networks according to claim 6, characterized in that, Based on the determined access order of hovering points, to minimize the transmission energy consumption of the drone. and hovering energy consumption Optimize the transmission power allocation of the UAV with the sum of its components as the objective. and transmission duration allocation The specific steps include: Based on the determined flight speed and hovering point access sequence of the drone, the goal is to minimize the drone's transmission energy consumption. and hovering energy consumption With the sum of the values ​​as the objective and the fourth to seventh constraints as conditions, the first optimization problem is transformed into optimizing the transmission power allocation of the UAV. and transmission duration allocation The fourth optimization problem; The fourth optimization problem is decomposed into optimizing transmission duration allocation. The fifth optimization problem and optimized transmission power allocation The sixth optimization problem; The fifth and sixth optimization problems are solved iteratively, alternating between them, to obtain the UAV's transmission power allocation. and transmission duration allocation .

8. The energy consumption minimization method for UAV-assisted multi-cluster NOMA networks according to claim 7, characterized in that, The objective of the fifth optimization problem is to minimize the transmission energy consumption of the UAV. and hovering energy consumption The sum of these constraints constitutes the fourth constraint. The solution to the fifth optimization problem is: , This represents the transmission duration allocated to the m-th cluster. This represents the k-th ground user in the m-th cluster. throughput threshold, express The downlink achievable rate, min indicates taking the minimum value.

9. The energy consumption minimization method for UAV-assisted multi-cluster NOMA networks according to claim 7, characterized in that: The optimization objective of the sixth optimization problem is to minimize the transmission energy consumption of the UAV. and hovering energy consumption The sum of these constraints is subject to the fourth to seventh constraints. Solving the sixth optimization problem includes the following steps: The fourth constraint Transformation into , It is about non-concave functions, It is a non-convex function; Will At a given local point Performing a first-order Taylor expansion at the given location yields its upper bound. ; The fourth constraint condition is rewritten as follows: ;when hour, ; Rewrite the fifth constraint as a linear constraint; Based on the sixth and seventh constraints, and the rewritten fourth and fifth constraints, the sixth optimization problem is transformed into the seventh optimization problem. The seventh optimization problem is solved using a convex optimization problem solver to obtain the UAV's transmission power allocation. .

10. An energy-saving system for UAV-assisted multi-cluster NOMA networks, wherein the system applies the energy-saving method for UAV-assisted multi-cluster NOMA networks as described in any one of claims 1 to 9, characterized in that: The system includes a network construction module, a problem construction module, and a problem solving module; the network construction module is used to construct an unmanned aerial vehicle-assisted multi-cluster NOMA network, the problem construction module is used to construct a first optimization problem, and the problem solving module is used to solve the first optimization problem.

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