Energy efficiency maximization method for UAV relay system based on physical layer network coding

Abstract

The present invention discloses a method for maximizing the energy efficiency of a drone relay system based on physical layer network coding. The method comprises the following steps: mathematically modeling the energy efficiency maximization problem of the drone relay system, converting the energy efficiency maximization problem into a mixed-integer non-convex optimization problem, decoupling the non-convex optimization problem into subproblems for solving transmission scheduling and associated variables A, transmission power variables P for drones and UDs, and drone trajectory variables Q; and solving the subproblems by combining a block coordinate descent algorithm, a continuous convex optimization method, and a Dinkelbach algorithm. The energy efficiency maximization solution provided by the present invention can balance the throughput of the drone relay and the energy consumption caused by its flight, minimizing flight energy consumption while maximizing communication throughput.

Description

Technical Field

[0001] The present invention relates to the technical fields of wireless communications and mobile communications, and in particular provides a method for maximizing energy efficiency of an unmanned aerial vehicle relay system based on physical layer network coding. Background Art

[0002] In recent years, drones (UAVs) have garnered widespread attention from both academia and industry due to their unique characteristics. Compared to traditional wireless communication systems, UAV wireless communication systems offer numerous advantages. First, UAVs are highly flexible, can be rapidly deployed, and can be adjusted and reconfigured on demand. Second, UAVs typically have excellent line-of-sight links, resulting in superior link quality and more reliable signal transmission. Furthermore, their high maneuverability enables them to adapt to a variety of environments and application scenarios, enabling more flexible data communication services. With technological advancements, UAVs are becoming an integral part of modern life. They are used not only for scientific research and emergency rescue missions, but also in agriculture, environmental monitoring, urban planning, security surveillance, and other fields.

[0003] With the rapidly growing demand for data in 5G and beyond wireless communication systems, using drones as mobile relays is considered a promising technology for providing network coverage. However, previous research has largely focused on traditional static relays, treating drones as static relay devices. For example, studies have investigated drones acting as static relays, receiving information via free-space optical links and forwarding it via radio frequency links. To fully leverage the flexibility of drones in mobile networks and investigate the throughput maximization problem in drone-assisted mobile relay networks, drones are used as mobile relay platforms, responsible for transmitting information from one ground user device to another. Unlike the aforementioned scenarios, where only a single source ground user device transmits to a single destination ground user device, scenarios where drones collect information from multiple source ground user devices and transmit it to a single destination ground user device have also been investigated. Clearly, these existing studies primarily focus on drone-assisted information transmission between a single pair of ground user devices, which is inconsistent with the real-world scenario of multiple source ground user devices transmitting to multiple destination ground user devices. Furthermore, some studies have not fully exploited the flexibility and mobility of drones.

[0004] To make the scenario more realistic and to fully exploit the flexibility of drones, the energy efficiency maximization problem of multiple source ground user devices (UGDs) transmitting information to a base station via UAVs has been studied. Furthermore, in scenarios where UAVs act as mobile relays to facilitate information transmission between multiple UG pairs, the problem of maximizing the minimum average transmission rate for each UG pair, subject to power constraints on the source UGs and the UAV relay, has been studied. Furthermore, to ensure transmission security, the transmit power optimization problem of both the UAV relay and the sending UG has been studied. Separately, the joint optimization problem of the trajectory and schedule of a caching UAV relay has been studied to maximize the minimum average secure transmission rate. However, these studies have focused on unidirectional communication, where information is transmitted only from the sending UG to the receiving UG, and the sending UG does not need to receive messages from the receiving UG. In real-world scenarios, however, both communicating parties often need to exchange messages, something not considered in these studies.

[0005] In summary, current research on drone communication systems has only considered scenarios where a single source ground user device (GUE) sends information to a single destination ground user device (GUE). This differs from the typical scenario where multiple pairs of GUEs have communication needs. Furthermore, bidirectional communication between a pair of GUEs is rarely considered. Therefore, how to efficiently and energy-efficiently provide bidirectional communication between multiple pairs of GUEs using UAVs as relays is an urgent challenge. Summary of the Invention

[0006] The present invention provides a method for maximizing the energy efficiency of an unmanned aerial vehicle relay system based on physical layer network coding, which realizes high-energy-efficiency two-way information relay and transmits more data while saving system energy.

[0007] To achieve the above objectives, the present invention provides a method for maximizing energy efficiency of a UAV relay system based on physical layer network coding, comprising:

[0008] Mathematically model the energy efficiency maximization problem of the UAV relay system, transform the energy efficiency maximization problem into a mixed-integer non-convex optimization problem, and decouple the non-convex optimization problem into sub-problems of solving the transmission scheduling and associated variable A, the transmission power variable P of the UAV and UD, and the UAV trajectory variable Q.

[0009] Energy efficiency is defined as the ratio of the minimum downlink data volume transmitted by the UAV to all ground user devices during the mission time to the energy consumed by the UAV flight. The unit of the minimum downlink data volume is Mbit, and the unit of the energy consumed by the UAV flight is J.

[0010] The subproblems are solved by combining the block coordinate descent algorithm, the continuous convex optimization method and the Dinkelbach algorithm.

[0011] In particular, the mathematical modeling of the energy efficiency maximization problem of the UAV relay system includes:

[0012] A pair of ground user equipment adopts UD k,1 and UD k,2 denoted by , where UD represents a ground user equipment, k represents the group number of the ground user equipment pair, and “1” and “2” represent the sequence numbers of the ground user equipment in the ground user equipment pair, respectively;

[0013] in Represents the set of group numbers of ground user equipment pairs, K represents the maximum group number; UD k,j The horizontal coordinate of Indicates, where j represents the sequence number of the ground user equipment in the ground user equipment pair, x k,j and y k,j Represents UD k,j The horizontal and vertical coordinates of the drone are represented by the letter H.

[0014] By using the time discretization method, the task time T is divided into N time slots of equal size. The sequence number of each time slot is represented by n. in represents the set of time slot numbers, N represents the maximum time slot number; a time slot is recorded as The horizontal position of the UAV at the nth time slot is recorded as The starting and ending positions of the drone are determined by q I and q F Indicates that the maximum flight speed of the drone is represented by v max The flight distance of the UAV in each time slot is represented by Δ[n]=∥q[n]-q[n-1]∥; the UAV and UD k,j The transmission power is represented by p d [n] and p k,j [n] represents the transmission decision and association of each time slot, respectively, by two binary variables α u,k [n] and α d,k [n] indicates; when α u,k When [n] = 1, it means that the kth pair of UDs transmits data to the UAV; otherwise, α u,k [n]=0; when α d,k When [n] = 1, it means that the UAV forwards data to the kth pair of UDs; otherwise, α d,k [n] = 0; the channel power gain at the reference distance is represented by β0, the channel bandwidth is represented by B, and the noise power is represented by σ 2express; order According to Shannon's formula, from UD k,j The feasible uplink transmission rate to the UAV is expressed as in Represents the line of sight probability after regularization and homogeneous approximation; similarly, from drone to UD k,j The feasible downlink transmission rate is expressed as

[0015] Let m represent the total mass of the UAV, g represent the acceleration due to gravity, A represent the area of ​​the rotor disc, ρ represent the air density, and W = mg represent the weight of the UAV relay. represents the parameterized hovering power required; in the nth time slot, the power generated by horizontal flight is expressed as In the nth time slot, the power consumption of the blade profile is expressed as Among them C D0 is the drag coefficient of the shape that varies with the geometry of the rotor blades; the total propulsion power required for the UAV relay flight is expressed as a function of its horizontal flight speed in the nth time slot, that is, in Therefore, the total energy consumption of the UAV relay during flight is expressed as

[0016] Let A represent the transmission schedule and association P represents the transmission power of the UAV and UD Q represents the drone trajectory The energy efficiency maximization problem of the UAV-assisted mobile relay system that provides two-way communication for multiple UD pairs using physical layer network coding technology is formulated as:

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] q[0]=q I ,q[N]=q F (1h)

[0027] in, is the introduced slack variable;

[0028] Relaxing the binary variable A, problem (1) is transformed into:

[0029]

[0030]

[0031] (1a), (1c), (1d), (1e), (1f), (1g), (1h). (2b)

[0032] Specifically, by using the block coordinate descent algorithm, the transmission power variables P of the UAV and UD and the UAV trajectory variable Q are fixed, and the problem is transformed into a sub-problem of solving the transmission scheduling and the associated variable A:

[0033]

[0034] st(1a),(2a),(1c),(1d), (3a)

[0035] The objective function only contains the numerator of the objective function of problem (2). Problem (3) is a standard linear programming problem and is directly solved by convex optimization tools.

[0036] Specifically, by using the block coordinate descent algorithm, we fix the transmission scheduling and associated variables A and the UAV trajectory variables Q, and transform the problem into a sub-problem of solving the transmission power variable P of the UAV and UD:

[0037]

[0038] st(1c),(1d),(1e),(1f), (4a)

[0039] The objective function only contains the numerator of the objective function of problem (2). Since the left side of the constraint (1d) is non-convex with respect to pd[n], problem (4) is obviously non-convex. Problem (4) is reformulated as:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] (1e), (1f). (5d)

[0046] Problem (4) is a standard convex problem and is solved by the convex optimization tool CVX.

[0047] Specifically, by adopting the block coordinate descent algorithm, we fix the transmission schedule and association variables A and the transmission power variables P of the UAV and UD, and transform the problem into a subproblem of solving the UAV trajectory variable Q:

[0048]

[0049] st(5a),(5b),(5c),(1g),(1h). (6a)

[0050] Since the denominator of the objective function of problem (6) is non-convex with respect to q[n], problem (6) is a non-convex problem, and the right sides of constraints (5b) and (5c) are non-convex with respect to q[n];

[0051] Since the right side of (5b) is restricted to ||q[n]-w k,j′ || 2 Convex, so at the rth iteration, let represents a given drone trajectory;

[0052] Since the Taylor expansion of any convex function at any point is its lower bound, we can get R u,k,j [n] At a given point Q (r) The first-order Taylor expression for As R u,k,j [n] At a given point Q (r) The lower bound of ; among them, and is a constant, Similarly, obtain R d,k,j [n] At a given point Q (r) The first-order Taylor expression for As R d,k,j [n] At a given point Q (r) The lower bound of ; among them,

[0053] In order to deal with the non-convex terms in the expression of the total propulsion power required for the UAV relay flight Introducing slack variables in By transposing and squaring simultaneously, we get Therefore, the function of total propulsion power is reformulated as Thus, the expression of the new energy consumption function of the UAV relay is obtained: Problem (6) is reformulated as:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] (5a),(1g),(1h). (7e)

[0061] Obtain the first-order Taylor expansion of the right side of constraint (7c) as its lower bound:

[0062] Through the above transformation, a new optimization problem is obtained as follows:

[0063]

[0064]

[0065] (5a), (7a), (7b), (7d), (1g), (1h). (8b)

[0066] The constraints of problem (8) are all convex, and the objective function is a fraction with a concave numerator and a convex denominator. Problem (8) is solved by the Dinkelbach algorithm.

[0067] This invention provides a method for maximizing the energy efficiency of a drone relay system based on physical layer network coding. Using drones as mobile relays significantly improves communication performance. The mobile relays can flexibly adjust their positions as needed to meet coverage requirements in different areas. Mobile relays can expand coverage by moving, better meeting communication needs across a wide area. They can also adjust their positions as needed, reducing the risk of interruptions caused by natural disasters.

[0068] The physical layer network coding technology used in the present invention can help the relay receive information from a group of UD pairs at the same time, or forward information to a group of UD pairs at the same time, without being affected by interference; the physical layer network coding technology can accept the interference between transmission links and increase the amount of transmitted data.

[0069] The energy-efficiency-maximizing fair communication scheme considered in the present invention uses the minimum amount of downlink data among all UDs as the numerator of the objective function and the energy consumption of the drone flight as the denominator of the objective function, and maximizes the objective function. This ensures that the drone can relay a considerable amount of information for each UD while also minimizing the energy consumption caused by flight. The energy-efficiency-maximizing scheme considered in the present invention can take into account the throughput of drone relays and the energy consumption caused by their flight, while minimizing flight energy consumption and maximizing communication throughput. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0071] Figure 1 A schematic diagram of a UAV-assisted two-way relay system using physical layer network coding technology provided by the present invention;

[0072] Figure 2 Schematic diagram of the initial trajectory of UD distribution and UAV relay provided by the present invention;

[0073] Figure 3 Schematic diagram of the trajectory of the UAV relay under different mission times for the "EE max" solution provided by the present invention and the comparative solution;

[0074] Figure 4 The system energy efficiency performance of the "EE max" solution provided by the present invention and the comparative solution under different task times;

[0075] Figure 5 The throughput performance of the "EE max" solution provided by the present invention and the comparison solution under different task times;

[0076] Figure 6 This is the system energy consumption performance of the "EE max" solution provided by the present invention and the comparative solution under different task times. DETAILED DESCRIPTION

[0077] The present invention will be further explained below with reference to specific embodiments, but the present invention is not limited thereto.

[0078] Existing research on drone communication systems only considers scenarios where a single source ground user device sends information to a single destination ground user device. This differs from the typical scenario where multiple ground user devices need to communicate. Furthermore, bidirectional communication between a pair of ground user devices is rarely considered.

[0079] Physical-layer network coding techniques can be used to effectively address bidirectional communication issues between pairs of ground user devices. Although full-duplex communication can also be applied to bidirectional communication between pairs of ground user devices, the interference generated between the uplink and downlink will reduce the amount of transmitted data. Physical-layer network coding techniques can tolerate interference to improve throughput. By using physical-layer network coding techniques, the relay can convert the signals received simultaneously from the same pair of ground user devices into pre-processable output signals. After receiving the forwarded signal from the relay, the ground user device pair can extract the corresponding information from it.

[0080] Research has been conducted on UAV relay systems that utilize physical layer network coding techniques to facilitate bidirectional communication between a pair of ground user devices (UEs) and between two UEs within multiple UE pairs. However, these studies have not considered the energy consumption of these systems when maximizing the throughput of either system. Furthermore, the problem of maximizing the transmission rate of a UAV relay system using physical layer network coding, with multiple UE pairs, has been studied under a constant energy constraint. While UAVs face significant challenges in terms of energy consumption, energy conservation has not been considered in this study.

[0081] Transmitting more data while considering saving system energy is very necessary for UAV relay systems with multiple pairs of ground user equipment. Existing research has not provided a suitable solution to maximize the energy efficiency of UAV relay systems using physical layer network coding technology.

[0082] To this end, this embodiment provides a method for maximizing the energy efficiency of a UAV relay system based on physical layer network coding. Figure 1As shown. The system has multiple groups of ground user device pairs, each of which contains two ground user devices that need to communicate with each other. The drone acts as a mobile relay and uses physical layer network coding technology to provide two-way communication for two ground user devices belonging to a ground user device pair. In addition, the drone provides two-way communication fairly for each group of ground user device pairs throughout the mission time. To ensure fair communication for each group of ground user device pairs, we define energy efficiency as: the ratio of the minimum downlink data volume (unit: Mbit) among the data volume transmitted by the drone for all ground user devices during the mission time to the energy consumed by the drone flight (unit: J).

[0083] First, we mathematically modeled the energy efficiency maximization problem for the drone relay system. Since the formulated problem is a mixed-integer, non-convex optimization problem, we solved this challenging problem by combining the block coordinate descent algorithm, continuous convex optimization methods, and the Dinkelbach algorithm. The detailed process is as follows:

[0084] A pair of ground user equipment adopts UD k,1 and UD k,2 denoted by , wherein UD represents the ground user equipment, k represents the group number of the ground user equipment pair, and “1” and “2” represent the sequence numbers of the ground user equipment in the ground user equipment pair, respectively. in Represents the set of group numbers of ground user equipment pairs, K represents the maximum group number. k,j The horizontal coordinate of Indicates. Where j represents the sequence number of the ground user equipment in the ground user equipment pair, x k,j and y k,j Represents UD k,j The horizontal and vertical coordinates of the UAV are represented by the letter H. The mission time T is divided into N time slots of equal size by the time discretization method. The serial number of each time slot is represented by n. in represents the set of time slot numbers, and N represents the maximum time slot number. A time slot is recorded as The horizontal position of the UAV at the nth time slot is recorded as The starting and ending positions of the drone are determined by q I and q F The maximum flight speed of the UAV is represented by v max The flight distance of the UAV in each time slot is represented by Δ[n]=∥q[n]-q[n-1]∥. UAV and UD k,j The transmission power is represented by p d [n] and p k,j[n] represents the transmission decision and association of each time slot. u,k [n] and α d,k [n] represents. When α u,k When [n] = 1, it means that the kth pair of UDs transmits data to the UAV; otherwise, α u,k [n]=0. When α d,k When [n] = 1, it means that the UAV forwards data to the kth pair of UDs; otherwise, α d,k [n] = 0. The channel power gain at the reference distance is represented by β0, the channel bandwidth is represented by B, and the noise power is represented by σ 2 Indicates. According to Shannon's formula, from UD k,j The feasible uplink transmission rate to the UAV is expressed as in Represents the line of sight probability after regularization and homogeneous approximation. Similarly, from UAV to UD k,j The feasible downlink transmission rate is expressed as

[0085] Let m represent the total mass of the UAV, g represent the acceleration due to gravity, A represent the area of ​​the rotor disc, ρ represent the air density, and W = mg represent the weight of the UAV relay. represents the parameterized hovering power. In the nth time slot, the power generated by horizontal flight is expressed as In the nth time slot, the power consumption of the blade profile is expressed as Among them C D0 is the drag coefficient of the shape that varies with the geometry of the rotor blades. The total propulsion power required for the UAV relay flight is expressed as a function of its horizontal flight speed at the nth time slot, that is, in Therefore, the total energy consumption of the UAV relay during flight is expressed as

[0086] Let A represent the transmission schedule and association P represents the transmission power of the UAV and UD Q represents the trajectory of the drone The energy efficiency maximization problem of the UAV-assisted mobile relay system that provides two-way communication for multiple UD pairs using physical layer network coding technology is formulated as:

[0087]

[0088] q[0]=q I ,q[N]=q F (1h)

[0089] in, is the introduced slack variable.

[0090] In order to solve problem (1), relax the binary variable A, and problem (1) is transformed into

[0091]

[0092] (1a), (1c), (1d), (1e), (1f), (1g), (1h). (2b)

[0093] First, using the block coordinate descent algorithm, the transmission power variables P of the UAV and UD and the UAV trajectory variable Q are fixed, and the problem is transformed into a sub-problem of solving the transmission scheduling and the associated variable A:

[0094]

[0095] st(1a),(2a),(1c),(1d), (3a)

[0096] The objective function only contains the numerator of the objective function in problem (2). This is because the variables related to the drone's energy consumption in problem (3) are fixed, that is, treated as constants. Temporarily ignoring the denominator as a constant will not affect the final result of the overall fraction maximization. Problem (3) is a standard linear programming problem and can be directly solved by convex optimization tools.

[0097] Then, by using the block coordinate descent algorithm, the transmission schedule and associated variables A and the UAV trajectory variables Q are fixed, and the problem is transformed into a sub-problem of solving the transmission power variable P of the UAV and UD:

[0098]

[0099] st(1c),(1d),(1e),(1f), (4a)

[0100] The objective function only contains the numerator of the objective function of problem (2), which is the same as the treatment in problem (3). d [n] is non-convex, so problem (4) is obviously non-convex. Introducing slack variables Problem (4) is reformulated as:

[0101]

[0102] (1e),(1f). (5d)

[0103] Problem (4) is a standard convex problem and can be solved by the convex optimization tool CVX.

[0104] Then, by adopting the block coordinate descent algorithm, the transmission scheduling and association variables A and the transmission power variables P of the UAV and UD are fixed, and the problem is transformed into a sub-problem of solving the UAV trajectory variable Q:

[0105]

[0106] st(5a),(5b),(5c),(1g),(1h). (6a)

[0107] Since the denominator of the objective function of problem (6) is non-convex with respect to q[n], problem (6) is a non-convex problem. In addition, the right-hand sides of constraints (5b) and (5c) are non-convex with respect to q[n].

[0108] The above non-convex functions and non-convex constraints can be solved by continuous convex optimization methods. Since the right side of the constraint (5b) is about ||q[n]-w k,j′ || 2 Convex, so at the rth iteration, let Represents a given UAV trajectory. Since the Taylor expansion of any convex function at any point is its lower bound, we can obtain R u,k,j [n] At a given point Q (r) The first-order Taylor expression for As R u,k,j [n] At a given point Q (r) The lower bound of . Among them, and is a constant, Similarly, we can obtain R d,k,j [n] At a given point Q (r) The first-order Taylor expression for As R d,k,j [n] At a given point Q (r) The lower bound of . Among them,

[0109]

[0110] In order to deal with the non-convex terms in the expression of the total propulsion power required for the UAV relay flight Introducing slack variables in By transposing and squaring the terms simultaneously, we can get Therefore, the function of total propulsion power is reformulated as Thus, the expression of the new energy consumption function of the UAV relay can be obtained: Based on the above discussion, problem (6) is reformulated as:

[0111]

[0112] (5a),(1g),(1h). (7e)

[0113] Although the left side of the restriction (7c) is convex with respect to s2[n], the right side of the restriction (7c) is Regarding s2[n] being non-concave, About q[n] is non-concave. However, Regarding s2[n] convex, Convex about q[n]. The first-order Taylor expansion of the right side of the restriction (7c) can be obtained as its lower bound:

[0114] Through the above transformation, a new optimization problem can be obtained as follows:

[0115]

[0116]

[0117] (5a), (7a), (7b), (7d), (1g), (1h). (8b)

[0118] The constraints of problem (8) are all convex, and the objective function is a fraction with a concave numerator and a convex denominator, so problem (8) can be solved by the Dinkelbach algorithm.

[0119] After that, continue to iterate and solve subproblems (3), (5) and (8) in the order until the algorithm converges. The pseudo code of the algorithm is as follows:

[0120]

[0121]

[0122] Compared to traditional fixed relay solutions, using drones as mobile relays can significantly improve communication quality. First, traditional relays are typically deployed in specific locations, such as buildings or communication towers. Due to their fixed location, traditional relays cannot quickly adapt to changing network demands and can only serve specific areas. Furthermore, when natural disasters such as earthquakes and floods strike, traditional relays in fixed locations may be affected, causing equipment failure. Compared to traditional relays, mobile relays can be moved and deployed in different locations at any time. Therefore, mobile relays can be flexibly relocated as needed to meet coverage requirements in different areas. Furthermore, mobile relays can be moved to expand coverage, better meeting communication needs across a wide area. Furthermore, mobile relays can be relocated as needed, reducing the risk of interruptions caused by natural disasters.

[0123] Compared to traditional half-duplex relay solutions, physical layer network coding technology allows relays to simultaneously receive information from a group of UD pairs or forward information to a group of UD pairs without being affected by interference. In traditional half-duplex relay solutions, relays cannot transmit and receive simultaneously and must switch between the two. This significantly reduces the data volume transmitted by traditional half-duplex relay solutions compared to solutions using physical layer network coding technology. While full-duplex mode can also achieve simultaneous transmission on two links—uplink and downlink—interference between the uplink and downlink can affect the amount of data transmitted. Physical layer network coding technology, on the other hand, can mitigate the effects of interference between transmission links, increasing the amount of data transmitted.

[0124] In a mobile relay solution that prioritizes throughput maximization, a drone will always fly to the location closest to the UD, specifically directly above it, to relay information to the UD. This is because the location directly above the UD is closest to the UD. According to Shannon's equation, the shorter the communication distance, the greater the amount of data transmitted per unit time. Therefore, the drone can receive or transmit the most data from or to the UD directly above it. To maintain high-data-volume communications, the drone hovers at this location to maintain the shortest communication distance with the UD. However, the expression for the drone's total propulsion power shows that the propulsion power generated by the drone's flight reaches its maximum when the horizontal movement distance is zero. Furthermore, in the presence of multiple UDs, if the drone needs to fly above each UD to relay information, the drone's flight range will increase significantly, leading to increased propulsion energy consumption. Furthermore, factors such as the size, weight, and payload capacity of a drone limit the amount of energy it can carry for flight. Therefore, while hovering above each UD to relay information significantly increases the amount of data transmitted, it also increases the energy required for the drone's flight. This significant energy consumption is often a significant challenge for drones. In addition to energy consumption, traditional throughput maximization schemes often use the total or average throughput relayed by the drone for each UD as the objective function. This can result in the drone only providing communication for one or a few UDs close to it, while neglecting UDs farther away. This communication situation is clearly suboptimal for all UDs in the scenario. The fair communication scheme we are considering, which maximizes energy efficiency, uses the minimum downlink data volume among all UDs as the numerator of the objective function and the drone's flight energy consumption as the denominator, maximizing the objective function. This ensures that the drone can relay a significant amount of information for each UD while minimizing the energy consumption caused by flight.

[0125] In a mobile relay scheme that only considers energy minimization, the drone always flies along a straight path connecting the starting point to the end point at the most energy-efficient speed. However, according to Shannon's equation, this results in the drone relaying less information for UDs farther from this path. Compared to energy minimization schemes, the energy efficiency maximization scheme we are considering balances the throughput of the drone relay and the energy consumption caused by its flight, minimizing flight energy consumption while maximizing communication throughput.

[0126] Using the Python programming language and toolkits such as NumPy, Matplotlib, and CVXPY, simulation experiments were conducted on the proposed method for maximizing energy efficiency in a drone relay system based on physical layer network coding. Simulation experiments were also conducted on a throughput maximization scheme, an energy minimization scheme, an initial flight scheme, and an energy efficiency maximization scheme in half-duplex mode to demonstrate the superiority of the proposed solution.

[0127] First, the drone is designed to fly from the starting point at the maximum flight speed, along the line between the starting point and the destination point, and hover at the midpoint of the line, which is also the center of the entire area. Before the mission time is up, the drone ends its hovering flight and continues to fly from the center of the area along the line between the starting point and the destination point to the destination point at the maximum speed, and when the mission time is up, it just flies to the destination point. The hovering time of the drone is the total mission time minus the time it takes for the drone to fly from the starting point to the destination point at the maximum speed. The drone relays information for all UDs during the flight. When the mission duration is 200 seconds, the initial trajectory of the drone is as follows: Figure 2 shown.

[0128] Figure 3 The figure shows the trajectories of the drone relay under three different mission times of 160 seconds, 200 seconds and 240 seconds, and the different flight plans. The blue line represents the trajectory obtained by the energy efficiency maximization plan "EE max" proposed by this invention, the red line represents the trajectory obtained by the throughput maximization plan "Throughput max", the green line represents the trajectory obtained by the energy minimization plan "Energy min", and the purple line represents the trajectory obtained by the energy efficiency maximization plan "Half Duplex" in half-duplex mode. The trajectory obtained by the initial flight plan "Initial Flight" is the same as the trajectory obtained by the initial flight plan "Initial Flight". Figure 2 The trajectory is similar to that in Figure 3 The display is in order to avoid too many lines making it difficult to distinguish each solution. Figure 3As can be seen in (a), when the throughput maximization scheme is adopted, the drone tends to fly to the airspace near each UD to relay information to it. This is because the shorter the communication distance, the greater the amount of data transmitted per unit time in the communication. This conclusion can be easily obtained based on the Shannon formula. As the mission time increases, this rule becomes more obvious. Figure 3 (b) and Figure 3 In (c), we can see that the trajectory points of the UAV near each UD are very dense, which means that in order to increase the amount of relayed data under sufficient mission time, the UAV hovers in the dense trajectory points. Figure 3 It can be seen that no matter how the mission time changes, the drone trajectory points are evenly distributed on the straight line connecting the drone's take-off point to the destination point. This shows that when executing the energy minimization scheme, the drone flies at an energy-saving speed and uniform speed along the shortest path between the take-off point and the destination point, and relays information for each UD pair during the flight. In the initial flight plan, no matter how long the drone's mission is, the drone will fly from the starting point at the maximum speed to the center of the communication area to hover, and then fly to the destination point at the maximum speed after the hovering ends. Therefore, the trajectories generated by the drone flying at different mission times under the initial plan are the same. Figure 2 The trajectories of the medium mission with a duration of 200 seconds are very similar. Figure 3 The trajectory of the drone's flight under this solution is not shown. In the energy efficiency maximization solution in half-duplex mode and the energy efficiency maximization solution proposed in this invention using physical layer network coding technology, the drone's flight trajectory tends to approach the UD that deviates from the initial trajectory, but there are also some trajectories that are very close to the trajectory of the energy minimization solution. This is because the energy efficiency maximization solution must take into account both increasing the amount of relayed data and reducing the energy consumed by flight. Therefore, the drone cannot simply reduce the communication distance between itself and the UD in order to increase the amount of relayed data, fly over every UD, or only fly along the trajectory generated by the energy minimization solution.

[0129] Figure 4 The energy efficiency of each solution at different times is shown. The blue column represents the energy efficiency of the energy efficiency maximization solution "EE max" proposed by us, the red column represents the energy efficiency of the throughput maximization solution "Throughput max", the green column represents the energy efficiency of the energy minimization solution "Energy min", the yellow column represents the energy efficiency of the initial flight solution "Initial Flight", and the purple column represents the energy efficiency of the solution "Half Duplex" that maximizes energy efficiency in half-duplex mode. Figure 4As can be seen in the results, the energy efficiency maximization solution proposed by this invention outperforms other solutions in terms of energy efficiency, regardless of mission duration. Although the energy minimization solution also performs well in terms of energy efficiency, second only to the solution proposed by this invention, this solution achieves its goal of improving energy efficiency by reducing energy consumption. Under this solution, the amount of information relayed by the drone for the UD is not optimistic. Therefore, the energy minimization solution cannot be considered an ideal solution.

[0130] Figure 5 The data volume relayed by each scheme at different mission times is shown. The blue line represents the data volume relayed by our proposed energy efficiency maximization scheme "EE max," the red line represents the data volume relayed by the throughput maximization scheme "Throughputmax," the green line represents the data volume relayed by the energy minimization scheme "Energy min," the yellow line represents the data volume relayed by the initial flight scheme "Initial Flight," and the purple line represents the data volume relayed by the energy efficiency maximization scheme "Half Duplex" in half-duplex mode. It can be seen that the scheme proposed in this invention performs second only to the throughput maximization scheme in terms of the amount of data relayed, and outperforms the other three schemes.

[0131] Figure 6 The system energy consumed by each solution at different task times is shown. Among them, the blue line represents the energy consumption of the energy efficiency maximization solution "EE max" proposed by the present invention, the red line represents the energy consumption of the throughput maximization solution "Throughputmax", the green line represents the energy consumption of the energy minimization solution "Energy min", the yellow line represents the energy consumption of the initial flight solution "Initial Flight", and the purple line represents the energy consumption of the solution "HalfDuplex" that maximizes energy efficiency in half-duplex mode. It is not difficult to see that the energy consumption curve of the solution proposed by the present invention almost coincides with the energy consumption curve of the energy minimization solution, and is much lower than the energy consumption curve of the throughput maximization solution.

[0132] Combine Figure 5 and Figure 6 It can be seen that although the energy efficiency maximization solution proposed in the present invention is not the best in terms of both the amount of relayed data and system energy consumption, it is a suboptimal solution. When considering both the amount of relayed data and system energy consumption, the solution proposed in the present invention is the best solution.

[0133] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the scope of the present invention.

Claims

1. A method for maximizing energy efficiency of UAV relay system based on physical layer network coding, characterized by: include: Mathematically model the energy efficiency maximization problem of the UAV relay system, transform the energy efficiency maximization problem into a mixed-integer non-convex optimization problem, and decouple the non-convex optimization problem into sub-problems of solving the transmission scheduling and associated variable A, the transmission power variable P of the UAV and UD, and the UAV trajectory variable q. Energy efficiency is defined as the ratio of the minimum downlink data volume transmitted by the UAV to all ground user devices during the mission time to the energy consumed by the UAV flight. The unit of the minimum downlink data volume is Mbit, and the unit of the energy consumed by the UAV flight is J. The subproblems are solved by combining the block coordinate descent algorithm, the continuous convex optimization method and the Dinkelbach algorithm.

2. The method for maximizing energy efficiency of a UAV relay system based on physical layer network coding according to claim 1 is characterized in that: The mathematical modeling of the energy efficiency maximization problem of the UAV relay system includes: A pair of ground user equipment adopts UD k,1 and UD k,2 denoted by , where UD represents a ground user equipment, k represents a group number of a ground user equipment pair, and "1" and "2" represent the sequence numbers of the ground user equipment in the ground user equipment pair, respectively; in Represents the set of group numbers of ground user equipment pairs, K represents the maximum group number; UD k,j The horizontal coordinate of Indicates, where j represents the sequence number of the ground user equipment in the ground user equipment pair, x k,j and y k,j Represents UD k,j The horizontal and vertical coordinates of the drone are represented by the letter H. By using the time discretization method, the task time T is divided into N time slots of equal size. The sequence number of each time slot is represented by n. in represents the set of time slot numbers, N represents the maximum time slot number; a time slot is recorded as The horizontal position of the UAV at the nth time slot is recorded as The starting and ending positions of the drone are represented by q I and q F Indicates that the maximum flight speed of the drone is represented by v max The flight distance of the UAV in each time slot is represented by Δ[n]=||q[n]-q[n-1]||; the UAV and UD k,j The transmission power is represented by p d [n] and p k,j [n] represents the transmission decision and association of each time slot, respectively, by two binary variables α u,k [n] and α d,k [n] indicates; when α u,k When [n] = 1, it means that the kth pair of UDs transmits data to the UAV; otherwise, α u,k [n]=0; when α d,k When [n] = 1, it means that the UAV forwards data to the kth pair of UDs; otherwise, α d,k [n] = 0; the channel power gain at the reference distance is represented by β0, the channel bandwidth is represented by B, and the noise power is represented by σ 2 express; order According to Shannon's formula, from UD k,j The feasible uplink transmission rate to the UAV is expressed as in Represents the line of sight probability after regularization and homogeneous approximation; similarly, from drone to UD k,j The feasible downlink transmission rate is expressed as Let m represent the total mass of the UAV, g represent the acceleration due to gravity, A represent the area of ​​the rotor disc, ρ represent the air density, and W = mg represent the weight of the UAV relay. represents the parameterized hovering power required; in the nth time slot, the power generated by horizontal flight is expressed as In the nth time slot, the power consumption of the blade profile is expressed as Among them C D0 is the drag coefficient of the shape that varies with the geometry of the rotor blades; the total propulsion power required for the UAV relay flight is expressed as a function of its horizontal flight speed in the nth time slot, that is, in Therefore, the total energy consumption of the UAV relay during flight is expressed as Let A represent the transmission schedule and association P represents the transmission power of the UAV and UD Q represents the trajectory of the drone The energy efficiency maximization problem of the UAV-assisted mobile relay system that provides two-way communication for multiple UD pairs using physical layer network coding technology is formulated as: q[0]=q I ,q[N]=q F (1h) in, is the introduced slack variable; Relaxing the binary variable A, problem (1) is transformed into: (1a), (1c), (1d), (1e), (1f), (1g), (1h). (2b).

3. The method for maximizing energy efficiency of a UAV relay system based on physical layer network coding according to claim 2, characterized in that: By using the block coordinate descent algorithm, the transmission power variables P of the UAV and UD and the UAV trajectory variable Q are fixed, and the problem is transformed into a sub-problem of solving the transmission scheduling and the associated variable A: st(1a),(2a),(1c),(1d), (3a) The objective function only contains the numerator of the objective function of problem (2). Problem (3) is a standard linear programming problem and is directly solved by convex optimization tools.

4. The method for maximizing energy efficiency of a UAV relay system based on physical layer network coding according to claim 2, characterized in that: By using the block coordinate descent algorithm, we fix the transmission scheduling and associated variables A and the UAV trajectory variables Q, and transform the problem into a sub-problem of solving the transmission power variable P of the UAV and UD: st(1c),(1d),(1e),(1f), (4a) The objective function only contains the numerator of the objective function of problem (2). Since the left side of the constraint (1d) is about p d [n] Non-convex. Problem (4) is obviously non-convex; introduce slack variables Problem (4) is reformulated as: (1e),(1f). (5d) Problem (5) is a standard convex problem and is solved by the convex optimization tool CVX.

5. The method for maximizing energy efficiency of a UAV relay system based on physical layer network coding according to claim 2, characterized in that: By adopting the block coordinate descent algorithm, the transmission scheduling and association variables A and the transmission power variables P of the UAV and UD are fixed, and the problem is transformed into a sub-problem of solving the UAV trajectory variable Q: st(5a),(5b),(5c),(1g),(1h). (6a) Since the denominator of the objective function of problem (6) is non-convex with respect to q[n], problem (6) is a non-convex problem, and the right sides of constraints (5b) and (5c) are non-convex with respect to q[n]; Since the right side of (5b) is restricted to ||q[n]-w k,j′ || 2 Convex, so at the rth iteration, let represents a given drone trajectory; Since the Taylor expansion of any convex function at any point is its lower bound, we can get R u,k,j [n] At a given point Q (r) The first-order Taylor expression for As R u,k,j [n] At a given point Q (r) The lower bound of ; among them, and is a constant, Similarly, obtain R d,k,j [n] At a given point Q (r) The first-order Taylor expression for As R d,k,j [n] At a given point Q (r) The lower bound of ; among them, In order to deal with the non-convex terms in the expression of the total propulsion power required for the UAV relay flight Introducing slack variables in By transposing and squaring simultaneously, we get Therefore, the function of total propulsion power is reformulated as Thus, the expression of the new energy consumption function of the UAV relay is obtained: Problem (6) is reformulated as: (5a),(1g),(1h). (7e) Obtain the first-order Taylor expansion of the right side of constraint (7c) as its lower bound: Through the above transformation, a new optimization problem is obtained as follows: (5a),(7a),(7b),(7d),(1g),(1h). (8b) The constraints of problem (8) are all convex, and the objective function is a fraction with a concave numerator and a convex denominator. Problem (8) is solved by the Dinkelbach algorithm.

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