Energy efficiency optimization method for multi-UAV relay system based on NOMA technology

Abstract

This disclosure proposes a method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology. The method comprises the following steps: establishing a system model for the multi-UAV relay system, which includes a base station, multiple ground users, and multiple UAVs; constructing a joint optimization problem for ground user grouping, UAV power allocation, and UAV trajectory planning based on the principles of NOMA technology, with the goal of optimizing the overall energy efficiency of the multi-UAV relay system within the same time period. This joint optimization problem is then divided into three sub-problems, each of which is optimized and solved separately; and repeating the three sub-problems to optimize the overall energy efficiency of the multi-UAV relay system for the next time period. The method proposed in this disclosure can optimize the energy efficiency performance of a multi-UAV relay system.

Description

Technical Field

[0001] The present disclosure relates to the technical field, and in particular to a method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology. Background Art

[0002] Unmanned aerial vehicles (UAVs) offer advantages such as rapid response, flexible deployment, and high cost-effectiveness. They can provide fast and flexible wireless coverage in areas lacking ground-based communication infrastructure, playing a vital role in emergency communications scenarios such as post-disaster rescue and battlefield communications. Due to the characteristics of ground-to-air channels, UAVs can establish line-of-sight (LoS) links between communication nodes, effectively acting as mobile relay systems. This offers significant advantages over traditional ground-based relay systems. UAV relay systems have a wide range of applications, improving communication quality and increasing wireless communication coverage.

[0003] The drone relay system based on Orthogonal Multiple Access (OMA) technology is difficult to provide services to a large number of users at the same time; while the Non-Orthogonal Multiple Access (NOMA) technology can provide services to more users by improving spectrum utilization.

[0004] Energy limitations have always been a key challenge facing drone relay system communications. Combining NOMA technology with a multi-drone relay system can effectively extend the wireless communication range while improving spectrum utilization, thereby providing services to more users. However, current research on multi-drone relay systems using NOMA technology mainly focuses on improving spectrum efficiency (SE), while less research has been conducted on how to improve energy efficiency (EE). Improving EE is crucial for drones to provide stable and reliable wireless connections as remote nodes. Therefore, it is necessary to provide a new technical solution to improve one or more of the problems existing in the above solutions.

[0005] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the Invention

[0006] The purpose of the embodiments of the present disclosure is to provide a method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology, which can effectively improve the energy efficiency performance of the UAV relay system. The method includes the following steps:

[0007] Establishing a system model of a multi-UAV relay system, wherein the system model includes a base station, multiple ground users, and multiple UAVs;

[0008] Based on the NOMA technology principle, with the goal of optimizing the overall energy efficiency of the multi-UAV relay system, a joint optimization problem of ground user grouping, UAV power allocation, and UAV trajectory planning is constructed. The joint optimization problem includes the following sub-problems:

[0009] During the same period,

[0010] The first sub-problem: Based on the communication distance between the UAV and the ground user and the rate requirement of the ground user, process the ground user grouping problem and obtain the optimal user grouping solution;

[0011] Second sub-problem: Based on the optimal user grouping scheme and the positions of the multiple drones, process the power allocation optimization problem of the multiple drones to obtain the optimal power allocation results of the multiple drones;

[0012] The third sub-problem: processing the trajectory planning problem of the multiple UAVs according to the optimal user grouping scheme and the optimal power allocation results of the multiple UAVs to obtain the optimal trajectory planning of the multiple UAVs;

[0013] The above three sub-problems are repeatedly processed iteratively to optimize the overall energy efficiency of the multi-UAV relay system in the next period.

[0014] In an exemplary embodiment of the present disclosure, in the step of establishing a system model of a multi-UAV relay system:

[0015] The plurality of ground users include high-rate demand users and low-rate demand users;

[0016] Each of the UAVs obtains the location information of the ground user once within a time period; each of the UAVs obtains the location information of the ground user through a synthetic aperture radar or optical imaging device equipped on the aircraft;

[0017] Each of said ground users is in a maneuverable state;

[0018] The communication channel between the UAV, the base station and the ground user is a line-of-sight communication link;

[0019] Among them, the set of multiple drones is U, U = {1, 2, 3, ..., N}; the set of multiple ground users is Ω, Ω = (Ω1, Ω2) = {1, 2, 3, ..., M}, Ω1 represents the set of high-rate demand users; Ω2 represents the set of low-rate demand users; N represents the total number of drones; M represents the total number of ground users.

[0020] In an exemplary embodiment of the present disclosure, the calculation formula for the total energy efficiency of the multi-UAV relay system includes:

[0021]

[0022] in, Indicates the total communication rate of the multi-UAV relay system in the same period, R m,n represents the communication rate between the nth UAV and the mth ground user, R m,n =B log2(1+S m ); B represents the communication bandwidth of the link between the UAV and the ground user; S m represents the signal-to-interference-and-noise ratio of the signal received by the mth ground user in time period t, P represents the maximum transmission power of the link between the UAV and the ground user; n0 represents the noise power spectrum density; θ m represents the power allocation factor of the mth ground user; θ k represents the power allocation factor of the kth ground user; h n,m represents the channel gain between the nth UAV and the mth ground user; μ m,k represents a binary variable, when θ m ≥θ k When μ m,k =1, otherwise μ m,k =0;G n Indicates the user group served by the nth drone; represents any value of n; λ n,m represents the scheduling factor for ground users, λ n,m ∈{0,1},λ n,m =1 means that the mth ground user is assigned to the nth UAV, λ n,m = 0 means the mth ground user is not in G n Inside; represents the propulsion power consumption of the multi-UAV relay system,

[0023] v represents the speed of the UAV; v0 represents the average rotor induced speed of the UAV when it is hovering; P0 represents the blade profile power of the UAV, ε is the drag coefficient; ρ is the air density; s is the volume of the rotor; A is the rotating area of ​​the rotor; Ω is the angular velocity of the blade; R m represents the radius of the rotor; f0 represents the drag ratio of the drone; U tip represents the speed of the outer tip of the rotor blade; P i represents the blade forward power, W represents the weight of the drone; k h Indicates the incremental correction factor for induction.

[0024] In an exemplary embodiment of the present disclosure, the total energy efficiency of optimizing the multi-UAV relay system is expressed as:

[0025] OP1: maxΞ (2)

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] Among them, R m,BS Indicates the communication rate between the ground user and the base station BS; represents the communication rate requirement of the mth ground user; K represents the maximum service capacity of the UAV; v max represents the maximum flight speed of the UAV; OP1 represents the total energy efficiency optimization problem; st represents “constrained by”; represents any value of m; represents the position of the nth UAV at time t; represents the position of the nth UAV at time t-1; represents the speed of the nth UAV at time t, and ΔT represents the flight time of the UAV.

[0035] In an exemplary embodiment of the present disclosure, the first sub-problem includes:

[0036] According to the maximum weight matching theory in graph theory, the distance matrix between the UAV and the high-rate demand users is initialized and represented by a weighted bipartite graph G = (V, E); wherein V = (U, Ω), Ω = (Ω1, Ω2), Ω1 represents the set of high-rate demand users; Ω2 represents the set of low-rate demand users; E represents the edge set, represents any value of m; the weight of the edge is the inverse of the distance between the drones, i.e. ω m,n =-||q m -q n||,q m represents the coordinates of the mth ground user; q n Indicates the coordinates of the nth drone;

[0037] Determine the maximum service capacity K of each UAV respectively; and use the Kuhn-Munkras algorithm to preferentially match the corresponding UAVs to users with high rate requirements;

[0038] Expand the drone set U, add multiple drone virtual nodes, and generate a new weighted bipartite graph G'=(V',E'); where V'=(U',Ω2), Determine a new distance matrix;

[0039] The weighted bipartite graphs G and G' are combined by the Kuhn-Munkras algorithm to obtain the optimal user grouping solution;

[0040] Wherein, each group of the optimal user grouping scheme includes a high-rate demand user and several low-rate demand users.

[0041] In an exemplary embodiment of the present disclosure, in the second sub-problem, the power allocation optimization problem of the plurality of drones is expressed as:

[0042]

[0043]

[0044]

[0045]

[0046] Where OP1.1 represents the power allocation optimization problem; st represents “constrained by”; represents auxiliary variables; θ m represents the power allocation factor of the mth ground user; P represents the maximum transmission power of the link between the UAV and the ground user; represents any value of m; G n Indicates the user group served by the nth drone; represents the communication rate requirement of the mth ground user; c m represents the power of interference and noise, n0 represents the noise power spectral density; B represents the communication bandwidth of the link between the UAV and the ground user; μ m,k represents the high-rate demand users in the group; θ k represents the power allocation factor of the kth ground user; R n,BS represents the communication rate between the nth UAV and the base station BS, W represents the communication bandwidth between the nth UAV and the base station BS; P BS represents the signal transmission power of the uplink between the base station BS and the nth UAV, β0 represents the channel gain when the reference distance is 1m; γ n,BS Indicates the signal-to-noise ratio of the base station signal received by the nth drone.

[0047] In an exemplary embodiment of the present disclosure, the problem OP1.1 is solved case by case based on the signal-to-interference-and-noise ratio of the received signal of the terrestrial user:

[0048] Case 1: In the multi-UAV relay system, if Then the formula (3a) is rewritten as: The left side of the inequality (3a') is a positive term, so the problem OP1.1 is a standard geometric programming problem, which is solved using the CVX toolbox;

[0049] Case 2: In other cases, the formula (3a) is rewritten as follows by shifting terms: Where G(θ)=c m +θ m Ph n,m ;because If it is not a standard positive term, the contraction method is used for iterative solution.

[0050] In an exemplary embodiment of the present disclosure, in the scenario 2, the process of iteratively solving using the condensation method includes:

[0051] Let θ (s) is the power allocation factor in the sth iteration of the condensation method. Based on the weighted-geometric arithmetic mean inequality, G(θ) is approximated as:

[0052]

[0053] Among them, u w represents the monomial in G(θ); w * represents the number of monomials in G(θ); At this point, the problem OP1.1 can be expressed as:

[0054]

[0055]

[0056] (3b), (3c), and (2b)

[0057] At this time, the problem OP1.1.1 is a standard geometric programming problem, which is solved using the CVX toolbox. After obtaining the solution to the problem OP1.1.1, it is used as the input for the next iteration. Through multiple iterative solutions, the optimal power allocation results of the multiple drones are obtained.

[0058] In an exemplary embodiment of the present disclosure, in the third sub-problem, the trajectory planning optimization problem of the plurality of drones is expressed as:

[0059]

[0060] In an exemplary embodiment of the present disclosure, the process of solving the problem OP1.2 includes:

[0061] According to the first-order Taylor expansion The forward power of the UAV can be approximated as Then the propulsion power of the UAV can be approximately expressed as:

[0062]

[0063] Formula (7) is a convex function, so the problem OP1.2 is a fractional programming problem, which can be solved using Bisection or Dinkelbach.

[0064] Introducing auxiliary variables Rewrite the question OP1.2 as follows:

[0065]

[0066]

[0067]

[0068]

[0069] (2d), (2g) and (2h);

[0070] Among them, ι m Represents auxiliary variables; v n Indicates the speed of the nth drone; represents the communication rate requirement of the mth ground user;

[0071] Introducing the Sigmoid function To approximate the variable {u m,k}, rewrite formula (8b) as:

[0072]

[0073] Among them, dn,m represents the distance between the nth UAV and the mth ground user; d n,k represents the distance between the nth UAV and the mth ground user; τ represents the auxiliary variable;

[0074] Introduce three more auxiliary variables: F m ,Q m,k ,D n,k , rewrite formula (8b') as:

[0075]

[0076]

[0077]

[0078]

[0079] At this point, the question OP1.2 becomes:

[0080]

[0081] st(2d), (2g), (2h), (8a), (8c), (8b'1), (8b'2), (8b'3) and (8b'4);

[0082] Using the SCA algorithm, let q (l) =(x R (l) ,y R (l) ,H) is the coordinate of the UAV in the first iteration of the SCA algorithm, q (l) -q (l-1) is the drone coordinate increment in the first iteration relative to the first-1 iteration; then in the first iteration, the BS-R communication rate The lower bound It can be approximated by a first-order Taylor expansion;

[0083] Then, the optimization problem OP1.2.2 is transformed into a standard convex optimization problem and solved using the CVX toolbox. After obtaining the optimal solution to the problem, λ is iteratively updated to

[0084] The technical solution provided by the present disclosure may have the following beneficial effects:

[0085] In the disclosed embodiments, a method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology is proposed. This method utilizes NOMA technology to improve the overall energy efficiency of the multi-UAV relay system. It constructs and solves a joint optimization problem of ground user grouping, UAV power allocation, and UAV trajectory planning, thereby effectively improving the energy efficiency performance of the multi-UAV relay system. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] The accompanying drawings are incorporated into and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification, serve to explain the principles of the present disclosure. Obviously, the drawings described below are only some embodiments of the present disclosure, and those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0087] Figure 1 A schematic diagram showing the steps of a method for optimizing energy efficiency of a multi-UAV relay system based on NOMA technology in an exemplary embodiment of the present disclosure;

[0088] Figure 2 A schematic diagram illustrating a system model of a multi-UAV relay system in an exemplary embodiment of the present disclosure;

[0089] Figure 3 A schematic diagram illustrating relative distances between multiple drones and multiple ground users in an exemplary embodiment of the present disclosure;

[0090] Figure 4 A schematic diagram showing a comparison of the running trajectories of drones under different design criteria when a single drone relay system is applied in a simulation experiment of an exemplary embodiment of the present disclosure;

[0091] Figure 5 A schematic diagram showing a comparison of the speed changes of a UAV under different design criteria when a single UAV relay system is applied in a simulation experiment of an exemplary embodiment of the present disclosure;

[0092] Figure 6 A schematic diagram showing a comparison of matching results between multiple ground users and multiple drones using different grouping schemes when a multi-drone relay system is applied in a simulation experiment of an exemplary embodiment of the present disclosure is shown;

[0093] Figure 7 A schematic diagram showing a comparison of rate requirements of ground users using different grouping schemes when a multi-UAV relay system is applied in a simulation experiment of an exemplary embodiment of the present disclosure is shown;

[0094] Figure 8 A schematic diagram showing a comparison of the operation trajectories of multiple UAVs under different numbers of ground users and distribution ranges when a multi-UAV relay system is applied in a simulation experiment of an exemplary embodiment of the present disclosure;

[0095] Figure 9 A schematic diagram illustrating how the energy efficiency of drones changes with the flight altitude of the drones when a multi-drone relay system is applied in a simulation experiment of an exemplary embodiment of the present disclosure;

[0096] Figure 10 A schematic diagram illustrating how the energy efficiency of drones varies with the maximum transmit power of drones when a multi-drone relay system is applied in a simulation experiment of an exemplary embodiment of the present disclosure;

[0097] Figure 11 A graph showing how the energy efficiency of drones changes with the maximum transmission power of drones when a multi-drone relay system is applied in a simulation experiment of an exemplary embodiment of the present disclosure. DETAILED DESCRIPTION

[0098] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0099] In addition, the accompanying drawings are merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0100] This example embodiment provides a method, such as Figure 1 As shown, the following steps may be included:

[0101] Step S101: Establishing a system model of a multi-UAV relay system, where the system model includes a base station, multiple ground users, and multiple UAVs;

[0102] Step S102: Based on the NOMA technology principle, with the goal of optimizing the overall energy efficiency of the multi-UAV relay system, a joint optimization problem of ground user grouping, UAV power allocation, and UAV trajectory planning is constructed. This joint optimization problem includes the following sub-problems:

[0103] During the same period,

[0104] The first sub-problem: Based on the communication distance between the UAV and the ground user and the rate requirements of the ground user, the ground user grouping problem is processed to obtain the optimal user grouping solution;

[0105] The second sub-problem is to solve the power allocation optimization problem of multiple UAVs based on the optimal user grouping scheme and the positions of multiple UAVs, and obtain the optimal power allocation results for multiple UAVs;

[0106] The third sub-problem is to solve the trajectory planning problem of multiple UAVs based on the optimal user grouping scheme and the optimal power allocation results of multiple UAVs, and obtain the optimal trajectory planning of multiple UAVs.

[0107] Step S103: Repeat the iterative processing of the above three sub-problems to optimize the overall energy efficiency of the multi-UAV relay system in the next period.

[0108] In the disclosed embodiments, a method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology is proposed. This method utilizes NOMA technology to improve the overall energy efficiency of the multi-UAV relay system. It constructs and solves a joint optimization problem of ground user grouping, UAV power allocation, and UAV trajectory planning, thereby effectively improving the energy efficiency performance of the multi-UAV relay system.

[0109] Below, each step of the above method in this exemplary embodiment will be described in more detail.

[0110] In step S101, Figure 2 As shown in the figure, a drone relay system provides services for ground-based mobile users (MUs). M randomly distributed remote MUs need to receive information from a base station (BS). Due to obstructions, the direct communication link between the BS and the MUs has poor channel quality and cannot provide reliable line-of-sight communication. MUs are divided into two categories based on their rate requirements: high-rate users and low-rate users. Given the limited service capabilities of a single drone, N drones are used as a relay system to assist in communication.

[0111] The set of multiple UAVs is U, where U = {1, 2, 3, ..., N}; the set of multiple ground users is Ω, where Ω = (Ω1, Ω2) = {1, 2, 3, ..., M}, where Ω1 represents the set of high-rate users; Ω2 represents the set of low-rate users; N represents the total number of UAVs; and M represents the total number of ground users. Each UAV acquires the location information of a ground user once per time period using its onboard synthetic aperture radar or optical imaging technology. The communication channels between the UAVs, the base station, and the MUs are primarily line-of-sight links, and each MU is in a maneuverable state.

[0112] In addition, it is assumed here that the Doppler effect caused by the maneuvering state of the MU can be fully compensated. The path loss model between the UAV and the ground user MU and the base station BS follows the free space path loss model, and the channel gain can be expressed as: Among them, X∈{U}, Y∈{Ω,BS}, β0 represents the channel gain when the reference distance is 1m, which is mainly determined by the carrier frequency and antenna gain, then d X,Y =||q X -q Y ||.

[0113] Assume that B is the downlink communication bandwidth between the UAV and the ground user; P is the maximum transmission power of the downlink between the UAV and the ground user, and set θ = {θ1, θ2, ..., θ M},(0≤θ m ≤1) is the power allocation factor of MU, and n0 is the noise power spectrum density. Here, the nth group of high-speed demand users is recorded as u, and drones are allocated to high-speed demand users first to ensure the communication rate requirements of ground users. According to the relative distance between MU and drone, the channel gain of low-speed demand users in the group is expressed in ascending order as ||h n,1 || 2 ≤||h n,2 || 2 ≤...≤||h n,u-1 || 2 ≤||h n,u+1 || 2 ...≤||h n,M || 2 .

[0114] According to the principle of power domain NOMA technology, the ground user with smaller channel gain obtains more power. Therefore, the corresponding power allocation factor should satisfy θ u ≥θ1≥θ2≥...≥θ M At the receiving end, MU uses SIC technology to eliminate interference from users with larger signal power and treats other low-power signals as noise. That is, the signal of the kth terrestrial user m needs to be subtracted before decoding (k<m, m≠u).

[0115] For the convenience of analysis, the binary variable μ is defined here m,k ∈{0,1}, when θ m ≥θ k When μ m,k =1; otherwise, μ m,k = 0. In a time period t, the calculation formula for the Signal to Interference plus Noise Ratio (SINR) of the signal received by the mth terrestrial user is:

[0116]

[0117] The communication rate between the nth UAV and the mth ground user is: R n,m =B log2(1+S m );

[0118] The communication rate between the nth UAV and the base station BS is:

[0119] Define λ n,m represents the scheduling factor for ground users, λ n,m ∈{0,1},λ n,m =1 means that the mth ground user is assigned to the nth UAV, λ n,m = 0 means the mth ground user is not in G n Within a period of time t, the total communication rate of the multi-UAV relay system is

[0120] Since the total power consumption of the UAV during the relay process is composed of propulsion power consumption and communication power consumption, in practical applications, the communication power consumption is much smaller than the propulsion power consumption, so the communication power consumption can be ignored. On this basis, the propulsion power consumption of the multi-UAV relay system can be approximately expressed as the propulsion power consumption of the multi-UAV relay system

[0121] Therefore, it can be concluded that the calculation formula for the total energy efficiency of the multi-UAV relay system is:

[0122]

[0123] in, Indicates the total communication rate of the multi-UAV relay system in the same period, R m,n represents the communication rate between the nth UAV and the mth ground user, R m,n =B log2(1+S m ); B represents the communication bandwidth of the link between the UAV and the ground user; S m represents the signal-to-interference-and-noise ratio of the signal received by the mth ground user in time period t, P represents the maximum transmission power of the link between the UAV and the ground user; n0 represents the noise power spectrum density; θ m represents the power allocation factor of the mth ground user; θ k represents the power allocation factor of the kth ground user; h n,m represents the channel gain between the nth UAV and the mth ground user; μ m,k represents a binary variable, when θ m ≥θk When μ m,k =1, otherwise μ m,k =0;G n Indicates the user group served by the nth drone; represents any value of n; λ n,m represents the scheduling factor for ground users, λ n,m ∈{0,1},λ n,m =1 means that the mth ground user is assigned to the nth UAV, λ n,m = 0 means the mth ground user is not in G n Inside; represents the propulsion power consumption of the multi-UAV relay system,

[0124] v represents the speed of the UAV; v0 represents the average rotor induced speed of the UAV when it is hovering; P0 represents the blade profile power of the UAV, ε is the drag coefficient; ρ is the air density; s is the volume of the rotor; A is the rotating area of ​​the rotor; Ω is the angular velocity of the blade; R m represents the radius of the rotor; f0 represents the drag ratio of the drone; U tip represents the speed of the outer tip of the rotor blade; P i represents the blade forward power, W represents the weight of the drone; k h Indicates the incremental correction factor for induction.

[0125] Under the constraints of information causality, the maximum number of users that can be served by the UAV, the rate requirement of the MU, the maximum transmit power of the UAV, and the maneuverability of the UAV, the following optimization problem is constructed with the goal of maximizing the total energy efficiency of the multi-UAV relay system:

[0126] The total energy efficiency of the multi-UAV relay system is expressed as:

[0127] OP1 maxΞ (2)

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136] Among them, R m,BS Indicates the communication rate between the ground user and the base station BS; represents the communication rate requirement of the mth ground user; K represents the maximum service capacity of the UAV; v max represents the maximum flight speed of the UAV; OP1 represents the total energy efficiency optimization problem; st represents “constrained by”; represents any value of m; represents the position of the nth UAV at time t; represents the position of the nth UAV at time t-1; represents the speed of the nth UAV at time t, and ΔT represents the flight time of the UAV.

[0137] Here, (2a) represents the information causal constraint of the multi-UAV relay system; (2b) θ m (2c) is the UAV speed constraint; (2d) is the UAV flight position constraint; (2e) is λ n,m (2f) ensures that each MU has a corresponding UAV relay to match it; (2g) is the UAV service capability constraint; (2h) ensures the minimum requirement of MU communication rate.

[0138] Problem OP1 is a highly coupled mixed-integer nonlinear programming problem. Obtaining the global optimal solution requires an exhaustive search, which is not suitable for communication scenarios with multiple ground users. To solve this problem more efficiently, we divide OP1 into three subproblems to obtain suboptimal solutions, thereby improving the energy efficiency of the multi-UAV relay system.

[0139] In step S102,

[0140] For the first sub-problem, since the communication link between the UAV and the MU and BS is mainly a line-of-sight link (i.e., LoS link), it is mainly affected by the communication distance. Therefore, the principle here is to reduce the sum of the relative distances between the MU and the UAV to ensure the communication rate requirements of the MU and avoid long-distance maneuvers of the UAV. The grouping problem of ground users is equivalent to a graph theory problem. Here, a low-complexity bottom user grouping algorithm based on the maximum weight matching theory in CAM is used, such as Figure 3 As shown,

[0141] According to the maximum weight matching theory in graph theory, the distance matrix between the UAV and the high-rate demand users is initialized and represented by a weighted bipartite graph G = (V, E); where V = (U, Ω), Ω = (Ω1, Ω2), Ω1 represents the set of high-rate demand users; Ω2 represents the set of low-rate demand users; E represents the edge set, represents any value of m; the weight of the edge is the inverse of the distance between the drones, i.e. ω m,n =-||q m -q n ||,q m represents the coordinates of the mth ground user; q n Indicates the coordinates of the nth drone;

[0142] Determine the maximum service capacity K of each drone. The maximum service capacity refers to the maximum number of ground users it can serve. Use the Kuhn-Munkras algorithm to prioritize matching drones with users with high-rate requirements.

[0143] Expand the drone set U, add multiple drone virtual nodes, and generate a new weighted bipartite graph G'=(V',E'); where V'=(U',Ω2), Determine the new distance matrix between drones and high-rate demand users; at this point, the grouping problem of drones and MUs with low-rate demands is equivalent to the maximum weight matching problem in graph theory.

[0144] And through the Kuhn-Munkras algorithm (KM algorithm), the weighted bipartite graphs G and G' are combined to obtain the optimal user grouping solution;

[0145] Each group of the optimal user grouping solution includes a high-rate demand user and several low-rate demand users.

[0146] Table 1 below records the grouping algorithm based on communication distance and user rate requirements

[0147] Table 1: Grouping algorithms based on communication distance and user rate requirements

[0148]

[0149] After executing the grouping algorithm, we perform intra-group optimization based on the grouping results. To address the coupling of the optimization problem, we further split the optimization problem into the second and third sub-problems based on the Alternating Iterative Optimization (AIO) algorithm framework.

[0150] For the second sub-problem, when the ground user grouping and the UAV position are fixed, the downlink power allocation of the UAV is optimized.

[0151] The power allocation optimization problem of multiple UAVs can be expressed as:

[0152]

[0153]

[0154]

[0155]

[0156] Where OP1.1 represents the power allocation optimization problem; st represents “constrained by”; represents auxiliary variables; θ m represents the power allocation factor of the mth ground user; P represents the maximum transmission power of the link between the UAV and the ground user; represents any value of m; G n Indicates the user group served by the nth drone; represents the communication rate requirement of the mth ground user; c m represents the power of interference and noise, n0 represents the noise power spectral density; B represents the communication bandwidth of the link between the UAV and the ground user; μ m,k represents the high-rate demand users in the group; θ k represents the power allocation factor of the kth ground user; R n,BS represents the communication rate between the nth UAV and the base station BS, W represents the communication bandwidth between the nth UAV and the base station BS; P BS represents the signal transmission power of the uplink between the base station BS and the nth UAV, β0 represents the channel gain when the reference distance is 1m; γ n,BS Indicates the signal-to-noise ratio of the base station signal received by the nth drone.

[0157] Furthermore, based on the signal-to-interference-and-noise ratio (SINR) of the ground user's received signal, problem OP1.1 is solved case by case:

[0158] Case 1: When there are multiple drone relay systems, Then formula (3a) can be rewritten as: The left side of inequality (3a') is a positive term, so problem OP1.1 is a standard geometric programming problem, which is solved using the CVX toolbox;

[0159] Case 2: In other cases, (3a) can be rewritten by transposing the terms as follows: Where G(θ)=c m +θ m Phn,m ;because If it is not a standard positive term, it is solved iteratively using the contraction method;

[0160] Furthermore, in the case 2, the process of iterative solution using the contraction method includes:

[0161] Let θ (s) is the power allocation factor in the sth iteration of the condensation method. Based on the weighted-geometric arithmetic mean inequality, G(θ) is approximated as:

[0162]

[0163] Among them, u w represents the monomial in G(θ); w * represents the number of monomials in G(θ); At this point, the problem OP1.1 can be expressed as:

[0164]

[0165]

[0166] (3b), (3c), and (2b)

[0167] At this time, the problem OP1.1.1 is a standard geometric programming problem, which is solved using the CVX toolbox. After obtaining the solution to the problem OP1.1.1, it is used as the input for the next iteration. Through multiple iterative solutions, the optimal power allocation results of the multiple drones are obtained.

[0168] Table 2 below records the power allocation algorithm of the drone

[0169] Table 2: UAV power allocation algorithm

[0170]

[0171]

[0172] For the third sub-problem, when the ground user grouping and the UAV power allocation are fixed, the trajectory planning optimization problem of multiple UAVs can be expressed as:

[0173]

[0174] The process of solving problem OP1.2 includes:

[0175] According to the first-order Taylor expansion The forward power of the UAV can be approximated as Then the propulsion power of the UAV can be approximately expressed as:

[0176]

[0177] Formula (7) is a convex function, so the problem OP1.2 is a fractional programming problem, which can be solved using Bisection or Dinkelbach.

[0178] Introducing auxiliary variables Rewrite the question OP1.2 as follows:

[0179]

[0180]

[0181]

[0182]

[0183] (2d), (2g) and (2h);

[0184] Among them, ι m Represents auxiliary variables; v n Indicates the speed of the nth drone; represents the communication rate requirement of the mth ground user;

[0185] Introducing the Sigmoid function To approximate the variable {u m,k}, rewrite formula (8b) as:

[0186]

[0187] Among them, d n,m represents the distance between the nth UAV and the mth ground user; d n,k represents the distance between the nth UAV and the mth ground user; τ represents the auxiliary variable;

[0188] Introduce three more auxiliary variables: F m ,Q m,k ,D n,k , rewrite formula (8b') as:

[0189]

[0190]

[0191]

[0192]

[0193] At this point, the question OP1.2 becomes:

[0194]

[0195] st(2d), (2g), (2h), (8a), (8c), (8b'1), (8b'2), (8b'3) and (8b'4);

[0196] Using the SCA algorithm, let q (l) =(x R (l) ,y R (l) ,H) is the coordinate of the UAV in the first iteration of the SCA algorithm, q (l) -q (l-1) is the drone coordinate increment in the first iteration relative to the first-1 iteration; then in the first iteration, the BS-R communication rate The lower bound It can be approximated by a first-order Taylor expansion;

[0197] Then, the optimization problem OP1.2.2 is transformed into a standard convex optimization problem and solved using the CVX toolbox. After obtaining the optimal solution to the problem, λ is iteratively updated to

[0198] Table 3 below records the trajectory planning algorithm of the drone

[0199] Table 3: UAV trajectory planning algorithm

[0200]

[0201] In summary, this embodiment proposes a method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology. In the first sub-problem, the complexity of the KM-based grouping algorithm is ο1(n 3 ). In the second and third subproblems, the algorithm complexity can be expressed as ο2(I(NK) 3 ), where I is the number of iterations and NK is the number of variables. At the same time, the objective function value is monotonically increasing during the iteration process. Therefore, the entire energy efficiency optimization algorithm can be solved through a finite number of iterations. See Table 4 below:

[0202] Table 4: Algorithms for trajectory planning optimization and power allocation optimization of multiple UAVs

[0203]

[0204] In order to verify the effectiveness of the method proposed in this embodiment, the following simulation experiments were carried out:

[0205] In the simulation process, in order to simulate the maneuvering situation of ground users, it is assumed that the ground users are in the L×L(m 2 ) are randomly distributed within the range of BS,cen represents the distance between the center of the circle and the base station. The distribution area of ​​ground users follows a specific trajectory. Each time the drone's position is updated, the position coordinates of the mobile users are randomly generated. M drones take off from the center of the ground users and the edge of the distribution area. Other parameters, unless otherwise specified, are shown in Table 5.

[0206] Table 5: Simulation experiment parameters

[0207]

[0208]

[0209] First, consider the case of a single UAV to illustrate the impact of different ground speed requirements on the UAV trajectory planning design, such as Figure 4 a and Figure 5 As shown in Figure a, when there is no minimum communication rate requirement for the MU, the UAV in the minimum energy consumption design (energy-min) flies in a straight line at a constant speed with minimal energy consumption. When spectral efficiency is maximized (SE-max), the UAV minimizes its distance from the MU to improve channel quality. When energy efficiency is maximized (EE-max), the distance between the UAV and the MU is greater than when SE-max is used. This is because, without a communication rate requirement, the UAV does not have to sacrifice excessive energy to achieve a smaller increase in throughput.

[0210] Figure 4 a is The trajectory of the drone; Figure 4 b is The trajectory of the drone;

[0211] Figure 5 a is The speed change of the drone; Figure 5 b is The speed change of the drone;

[0212] However, when the MU rate requirement is high, such as Figure 4 b and Figure 5 As shown in (b), the three trajectories under the EE-max, SE-max, and energy-min schemes are relatively close. In the EE-max design, the direction of the UAV's speed constantly changes due to the movement trend of the MU, but the speed magnitude does not change much and is close to the speed magnitude under the energy-min scheme.

[0213] In addition, by comparison Figure 4 a and Figure 4 As shown in Figure b, the trajectory of EE-max without a minimum communication rate requirement is smoother than the trajectory of EE-max with a higher rate requirement. This is expected, as to meet specific MU requirements, the drone needs to be relatively close to the MU with high rate requirements within the group. Conversely, when there is no communication rate requirement constraint, the drone will avoid this energy consumption.

[0214] Secondly, the situation of multi-UAV relay is analyzed. In order to cover the target area as much as possible, UAVs are deployed in different directions of the MU distribution area.

[0215] Figure 6 The matching results between MU and UAV when different grouping schemes are given. Figure 6 a is the grouping scheme proposed in this embodiment; Figure 6 b shows a grouping scheme based on communication distance. As can be seen, since each drone can only serve a limited number of users, there's no guarantee that each MU will be matched with the closest drone. Therefore, MUs with high-rate requirements are first matched with drone relays, and then MUs with low-rate requirements are grouped based on the drone's service capabilities. Figure 6 Figure (b) shows that a grouping strategy that does not consider the different rate requirements of MUs may result in multiple MUs with high rate requirements being grouped together. However, the limited transmit power of each UAV relay may result in some users with high rate requirements not always being satisfied.

[0216] Figure 7 The data rate that can be achieved by ground users under different grouping schemes is shown; Figure 7 a is the grouping scheme proposed in this embodiment; Figure 6 b is a grouping scheme based on communication distance.

[0217] Depend on Figure 7 It can be seen that under the grouping scheme proposed in this embodiment, the rate requirement of each MUd can be met. Figure 7 As shown in Figure 2, when only considering the fractional scheme of communication distance, some users with high rate requirements cannot be satisfied. Therefore, it can be proved that the grouping scheme proposed in this embodiment that combines communication distance and ground user rate requirements is more suitable for communication scenarios with different ground user rate requirements.

[0218] Figure 8 The figure shows the trajectory of multiple UAVs under different numbers of ground users and distribution ranges. Figure 8 When a is L = 400m and n = 2, the trajectories of multiple UAVs under different numbers of ground users and distribution ranges; Figure 8b is the trajectory of multiple UAVs under different numbers of ground users and distribution ranges when L = 700m and n = 3. Figure 8 As shown, the trajectory of each UAV aligns with the motion trend of the center of the ground user, but they do not overlap. This is because the trajectory of a UAV is related to the number of UAVs and the randomness of the MU's motion, especially the position changes of high-speed users. In this case, the method proposed in this embodiment is more suitable for wide-area communication coverage than the baseline trajectory design, because the baseline trajectory design cannot fully utilize the MU's location information and does not consider the communication rate requirements of different ground users.

[0219] Figure 9 Shown N = 10, P max = Changes in drone energy efficiency with flight altitude when Δm=35dBm; Figure 10 The figure shows the energy efficiency of the UAV changes with the maximum transmission power of the UAV when N=8 and H=100m.

[0220] To facilitate analysis, several benchmark scenarios were defined: Scheme 1: An OMA-based intra-group joint optimization algorithm. This algorithm uses the OMA mechanism within each group after ground users are grouped. Each ground user in the group is allocated the same bandwidth, while the SCA algorithm and the water filling theorem are used to optimize the bandwidth and power allocation of the UAV. Scheme 2: The UAV moves with the center of the MU. A fixed power allocation algorithm is used for the downlink between the UAV and the MU, namely: θ = {0.1, 0.9}, (N = 2), θ = {0.04, 0.06, 0.9}, (N = 3), θ = {0.02, 0.04, 0.06, 0.88}, (N = 4), and θ = {0.02, 0.04, 0.06, 0.08, 0.8}, (N = 5).

[0221] Figure 11 The energy efficiency of a drone changes with the maximum transmission power of the drone when it is a multi-drone relay system. Figure 11 Figure 2 shows a comparison of the EE of multiple drones with different numbers of MUs. When M = 12, the EE of each drone improves by approximately 6% compared to the case of M = 8. This demonstrates that the algorithm proposed in this embodiment is suitable for communication scenarios with multiple ground users. However, if a single drone serves too many ground users, it will be difficult to meet the drone's communication requirements, and the receiver design will become more complex. Furthermore, the complexity of the intra-group optimization algorithm increases with the number of MUs in the group. Therefore, it is necessary to limit the maximum number of MUs a drone can serve.

[0222] Simulation experiments show that in the NOMA-based multi-UAV relay system energy efficiency optimization method proposed in this embodiment, the total communication rate of the NOMA-based multi-UAV relay system is superior to that based on the OMA mechanism. Compared with the baseline solution, the effectiveness of the method proposed in this disclosure is demonstrated. In addition, as the number of ground users increases and the distribution range expands, the greater the distance between the non-coordinated trajectory of the UAV and the ground user center, the stronger the advantage of the trajectory planning algorithm disclosed in this disclosure. Through in-depth simulation analysis, the impact of different parameters on the performance of the NOMA-based multi-UAV relay system is demonstrated.

[0223] It should be noted that although several units of the system for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to the embodiment of the present disclosure, the features and functions of two or more units described above can be concretized in one unit. Conversely, the features and functions of a unit described above can be further divided into multiple units for concretization. Some or all of the units can be selected according to actual needs to achieve the purpose of the disclosed solution. Those of ordinary skill in the art can understand and implement it without paying creative work.

[0224] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the present disclosure being indicated by the appended claims.

Claims

1. A method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology, characterized in that: The following steps are involved: Establishing a system model of a multi-UAV relay system, wherein the system model includes a base station, multiple ground users, and multiple UAVs; Based on the NOMA technology principle, with the goal of optimizing the overall energy efficiency of the multi-UAV relay system, a joint optimization problem of ground user grouping, UAV power allocation, and UAV trajectory planning is constructed. The joint optimization problem includes the following sub-problems: During the same period, The first sub-problem: Based on the communication distance between the UAV and the ground user and the rate requirement of the ground user, process the ground user grouping problem and obtain the optimal user grouping solution; Second sub-problem: Based on the optimal user grouping scheme and the positions of the multiple drones, process the power allocation optimization problem of the multiple drones to obtain the optimal power allocation results of the multiple drones; The third sub-problem: processing the trajectory planning problem of the multiple UAVs according to the optimal user grouping scheme and the optimal power allocation results of the multiple UAVs to obtain the optimal trajectory planning of the multiple UAVs; Repeat the iterative processing of the above three sub-problems to optimize the overall energy efficiency of the multi-UAV relay system in the next period; In the steps of establishing the system model of the multi-UAV relay system: The plurality of ground users include high-rate demand users and low-rate demand users; Each of the UAVs obtains the location information of the ground user once within a time period; each of the UAVs obtains the location information of the ground user through a synthetic aperture radar or optical imaging device equipped on the aircraft; Each of said ground users is in a maneuverable state; The communication channel between the UAV, the base station and the ground user is a line-of-sight communication link; The set of multiple drones is U, ; The set of multiple ground users is , , Represents the set of users with high rate requirements; represents the set of users with low-rate requirements; N represents the total number of UAVs; M represents the total number of ground users.

2. The energy efficiency optimization method for a multi-UAV relay system based on NOMA technology according to claim 1 is characterized in that: The calculation formula for the total energy efficiency of the multi-UAV relay system includes: （1） in, Indicates the total communication rate of the multi-UAV relay system in the same period, ; Indicates the n The first drone and the m The communication rate between ground users, ; B Indicates the communication bandwidth of the link between the UAV and the ground user; Indicates the m terrestrial users in the period t The signal-to-interference-noise ratio of the received signal, ; P Indicates the maximum transmission power of the link between the UAV and the ground user; represents the noise power spectral density; Indicates the m Power allocation factor for each terrestrial user; Indicates the k Power allocation factor for each terrestrial user; Indicates the n drone and the m The channel gain between terrestrial users; represents a binary variable, when hour, ,on the contrary ; Indicates the n The user groups served by the drone; Indicates any n value; represents the scheduling factor for ground users, , When the m The terrestrial user is assigned to n drones, When m Ground users are not Inside; represents the propulsion power consumption of the multi-UAV relay system, ; Indicates the speed of the drone; Indicates the average rotor induced speed of the UAV when hovering; represents the blade profile power of the UAV, ; represents the drag coefficient; Indicates the air density; Indicates the volume of the rotor; represents the rotating area of ​​the rotor; represents the angular velocity of the blade; Indicates the radius of the rotor; It represents the drag ratio of the drone’s fuselage; represents the speed of the outer tip of the rotor blade; represents the blade forward power, ; Indicates the weight of the drone; Indicates the incremental correction factor for induction.

3. The energy efficiency optimization method of a multi-UAV relay system based on NOMA technology according to claim 2 is characterized in that: The total energy efficiency of optimizing the multi-UAV relay system is expressed as: (2) s.t. (2a) (2b) (2c) (2d) (2e) (2f) (2g) (2h) in, Represents ground users and base stations BS Communication rate between Indicates the m Communication rate requirements of ground users; K Indicates the maximum service capability of the drone; represents the maximum flight speed of the UAV; OP1 represents the total energy efficiency optimization problem; st represents "constrained on"; Indicates any m value; Indicates the n Drones at all times t location; Indicates the n Drones at all times t -1 position; Indicates the n Drones at all times t speed, Indicates the flight time of the drone.

4. The method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology according to claim 1 is characterized in that: The first sub-question includes: According to the maximum weight matching theory in graph theory, the distance matrix between the drone and the high-speed demand user is initialized and a weighted bipartite graph is used to calculate the distance matrix between the drone and the high-speed demand user. To express; among them, , , Represents the set of users with high rate requirements; represents the set of users with low rate requirements; E represents the edge set, ; Indicates any m The edge weight is the inverse of the distance between the UAVs. , Indicates the m The coordinates of the ground user; Indicates the n The coordinates of the drone; Determine the maximum service capability of each of the drones K ; and using the Kuhn-Munkras algorithm, prioritize matching the corresponding drones to users with high rate requirements; Expand the drone set U, add multiple drone virtual nodes, and generate a new weighted bipartite graph ;in, , ;Determine the new distance matrix; And through the Kuhn-Munkras algorithm, the weighted bipartite graph and Combining to obtain the optimal user grouping solution; Wherein, each group of the optimal user grouping scheme includes a high-rate demand user and several low-rate demand users.

5. The method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology according to claim 3 is characterized in that: In the second sub-problem, the power allocation optimization problem of multiple UAVs is expressed as: (3) s.t. (3a) (3b) (3c) Where OP1.1 represents the power allocation optimization problem; st represents "constrained on"; Represents auxiliary variables; Indicates the m Power allocation factor for each terrestrial user; P Indicates the maximum transmission power of the link between the UAV and the ground user; Indicates any m value; Indicates the n The user groups served by the drone; Indicates the m Communication rate requirements of ground users; represents the power of interference and noise, ; represents the noise power spectral density; B Indicates the communication bandwidth of the link between the UAV and the ground user; Indicates users with high-speed requirements in the group; Indicates the k Power allocation factor for each terrestrial user; Indicates the n Drones and base stations BS The communication rate between ; W Indicates the n Drones and base stations BS Communication bandwidth between Indicates base station BS With the n The signal transmission power of the uplink of the UAV is ; Indicates the channel gain when the reference distance is 1m; Indicates the n The signal-to-noise ratio of the base station signal received by the drone, represents the channel gain between the nth UAV and the mth ground user, Represents the distance between the nth UAV and the base station BS.

6. The method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology according to claim 5 is characterized in that: According to the signal-to-interference-and-noise ratio of the received signal of the ground user, the problem OP1.1 is solved case by case: Case 1: In the multi-UAV relay system, if , then the formula (3a) is rewritten as: (3a'); The left side of the inequality (3a') is a positive term, so the problem OP1.1 is a standard geometric programming problem, which is solved using the CVX toolbox; Case 2: In other cases, the formula (3a) is rewritten as follows by shifting terms: ,in, ;because If it is not a standard positive term, the contraction method is used for iterative solution.

7. The method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology according to claim 6 is characterized in that: In the case 2, the process of iteratively solving using the condensation method includes: make The condensation method s The power allocation factor during the round iteration is based on the weighted-geometric arithmetic mean inequality. Approximately: （4） in, express Monomials in ; express the number of monomials in ; ; At this time, the problem OP1.1 can be expressed as: (5) s.t. (5a) (3b), (3c), and (2b) At this point, the problem This is a standard geometric programming problem, which is solved using the CVX toolbox. After the solution is obtained, it is used as the input for the next iteration, and the optimal power allocation results of the multiple UAVs are obtained through multiple iterations.

8. The method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology according to claim 7 is characterized in that: In the third sub-problem, the trajectory planning optimization problem of multiple UAVs is expressed as: (6) st(2a), (2b), (2h).

9. The method for optimizing the energy efficiency of a multi-UAV relay system based on NOMA technology according to claim 8 is characterized in that: The process of solving the problem OP1.2 includes: when When, according to the first-order Taylor expansion , , the forward power of the UAV can be approximated as , then the propulsion power of the UAV can be approximately expressed as: （7） Formula (7) is a convex function, so the problem OP1.2 is a fractional programming problem, which can be solved using Bisection or Dinkelbach. Introducing auxiliary variables , rewrite the question OP1.2 as follows: (8) s.t. (8a) (8b) (8c) (2d), (2g) and (2h); in, Represents auxiliary variables; Indicates the n The speed of the drone; Indicates the m Communication rate requirements of ground users; Introducing the Sigmoid function To approximate the variable , rewrite formula (8b) as: （8b’） in, Indicates the n The first drone and the m The distance between ground users; Indicates the n The first drone and the m The distance between ground users; Represents auxiliary variables; Introduce three more auxiliary variables: , rewrite formula (8b') as: (8b’1) (8b’2) (8b’3) (8b’4) At this point, the question OP1.2 becomes: (9) st (2d), (2g), (2h), (8a), (8c), (8b'1), (8b'2), (8b'3) and (8b'4); Using the SCA algorithm, let The SCA algorithm The coordinates of the drone at the time of round iteration, For the Round iteration relative to the The coordinate increment of the drone in the first iteration; During the round iteration, the BS-R communication rate The lower bound It can be approximated by a first-order Taylor expansion; Then, the optimization problem OP1.2.2 is transformed into a standard convex optimization problem and solved using the CVX toolbox. After obtaining the optimal solution to the problem, Update the iteration to .

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