Joint trajectory optimization method for multi-UAV symbol-level precoding under interference communication

Abstract

The present invention relates to a joint trajectory optimization method for symbol-level precoding of multiple unmanned aerial vehicles under interference communication, including the steps of establishing a communication model composed of a jammer, a ground station and multiple unmanned aerial vehicles, estimating the position and interference power of the jammer, establishing a jammer obstacle area model formed by the influence of the ground station, and constructing a symbol-level precoding unmanned aerial vehicle trajectory optimization problem including the states of multiple unmanned aerial vehicles, the power of the ground station transmitted signal and non-strict phase constraints, thereby obtaining the optimized trajectories of multiple unmanned aerial vehicles. The present invention uses symbol-level precoding technology for space division multiplexing, performs precoding processing on the signals of different unmanned aerial vehicles according to channel state information, so that multiple unmanned aerial vehicles in the same time-frequency domain can make full use of legal interference signals, realize trajectory planning of multiple unmanned aerial vehicles, and significantly reduce the bit error rate of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicles, and in particular to a method for jointly optimizing symbol-level precoding and trajectories of unmanned aerial vehicles. Background Art

[0002] Drones have been widely used in many industries due to their advantages such as easy deployment, high flexibility and low maintenance cost, including road traffic monitoring, wireless coverage provision, remote sensing and precision agriculture. The path planning problem of drones has also become a key research object, and many path planning algorithms have been proposed, such as algorithm, Algorithm, genetic algorithm and Rapidly Exploring Random Tree (RRT) algorithm.

[0003] In the context of electronic warfare, many scholars have improved communication performance by optimizing drone trajectories. In secure communication scenarios, some scholars have maximized the confidentiality rate of the system by optimizing the trajectory of drones. Some scholars have focused on environments with malicious interference and geographical obstacles, and built a communication system consisting of base stations, relay drones, and multiple remote ground robots. They took the instantaneous average signal-to-interference ratio as the optimization target, and jointly optimized the drone position and the main lobe width of the drone antenna beam. Other scholars have studied the anti-interference communication scenario of installing RIS (Reconfigurable Intelligent Surface) on drones to resist malicious interference attacks, and proposed a passive beamforming optimization method combining drone trajectory and RIS.

[0004] However, existing research generally only considers the known information of the jammer, and does not consider modeling and analyzing the effective interference range of the jammer. In addition, for multi-UAV scenarios, only frequency division multiplexing is generally considered, ignoring the feasibility of interference between multiple UAVs. Summary of the invention

[0005] The purpose of the present invention is to avoid the shortcomings of the prior art and provide a method for estimating the jammer position and interference power through the received signal strength of multiple UAVs, and at the same time pre-code the signals of different UAVs according to channel state information, so that multiple UAVs in the same time and frequency domain can make full use of the legal interference signals between them, and complete the joint trajectory optimization method of symbol-level precoding of multiple UAVs under interference communication while improving the communication quality.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a joint trajectory optimization method for multi-UAV symbol-level precoding under interference communication, comprising the following steps:

[0007] Step 1: Establish a communication model consisting of a jammer, a ground station and multiple drones, and use the communication model to simulate the communication propagation between multiple drones and the ground station in an environment where the jammer interferes with the communication, wherein the multiple drones include at least four drones;

[0008] Step 2: In the communication propagation simulation using the communication model, the position and interference power of the jammer are estimated according to the signal power transmitted by the ground station and the signal strength received by any UAV relative to the signal transmitted by the ground station;

[0009] Step 3: Based on the communication requirements of the signal-to-interference-to-noise ratio thresholds of multiple UAVs, the interference coverage of the jammer in the communication model is determined according to the signal-to-interference-to-noise ratio and trajectory at any point in the communication model and the location of the jammer, and a jammer obstacle area model formed by the influence of the ground station is established;

[0010] Step 4. In the jammer obstacle area model, the flight length of the UAV and the interference power of the jammer are comprehensively considered to obtain the flight length cost function of multiple UAVs and the threat cost function in a given time slot. A UAV trajectory optimization problem including the status of multiple UAVs, the signal power transmitted by the ground station and symbol-level precoding with non-strict phase constraints is constructed to obtain the optimized trajectories of multiple UAVs.

[0011] Furthermore, the step 2 is specifically as follows:

[0012] Step 21: Consider the signal power transmitted by the ground station as According to the communication model, the signal strength received by the kth UAV relative to the signal transmitted by the ground station is It is expressed as:

[0013] ,

[0014] in It represents the channel power gain when the distance between any UAV and the ground station is 1m. represents the distance between the ground station and the kth UAV, k≧4;

[0015] Step 22: The strength of all signals received by the kth drone is expressed as , by Minus , calculate the signal strength received by the kth UAV relative to the signal transmitted by the jammer With noise intensity Added values , expressed as:

[0016] ,

[0017] Among them, the left formula is measured by the kth UAV, is calculated through the communication model, and is an unknown quantity, and considering the strong interference, it is assumed and equal;

[0018] Step 23: Express the interference power of the jammer's transmitted signal, which is still an unknown quantity, as According to the communication model, the signal strength received by the kth UAV relative to the signal transmitted by the jammer is Also expressed as:

[0019] ,

[0020] in represents the distance between the jammer and the kth UAV;

[0021] Therefore, we get the equations for the jammer position and jammer power. When the number of UAVs k is greater than or equal to 4, we can solve the distance between the jammer and the kth UAV. and interference power , that is, the jammer position and jammer power equation is:

[0022] ,

[0023] in, , , They represent the x-coordinate, y-coordinate and z-coordinate of the kth UAV respectively, , Respectively represent the x-coordinate and y-coordinate of the jammer;

[0024] Then, the equation group consisting of k drones is:

[0025] ,

[0026] In the system of equations there is , and For three unknown quantities, subtract every two adjacent equations to obtain a new set of equations:

[0027] ,

[0028] in,

[0029] ,

[0030] ,

[0031] ,

[0032] ,

[0033] Solve the equations to get the jammer's position and interference power .

[0034] Furthermore, in the jammer position and jamming power equation there is , and When there are three unknown quantities, and k is 1, 2, 3, and 4 respectively, then two adjacent equations in the equation consisting of k drones are subtracted to obtain a new set of equations:

[0035] ,

[0036] in,

[0037] ,

[0038] ,

[0039] ,

[0040] ,

[0041] Solve the equations to get the jammer's position and interference power .

[0042] Furthermore, step three is specifically as follows:

[0043] Step 31: Consider the communication model and assume that the position of any point in three-dimensional space is represented by , because the interference power is large, we temporarily ignore the influence of noise power, then The signal-to-interference-noise ratio of a point is expressed as:

[0044] ,

[0045] in, , They are Point to ground station and jammer Therefore, when determining the signal-to-interference-noise ratio threshold hour, Point to two fixed points and The ratio of the distances is a constant:

[0046] ,

[0047] In three-dimensional space, The trajectory of the points is a sphere with its center at a fixed point and On the straight line;

[0048] Step 32: Considering that the ground jammer is stationary and is jamming upward, the jamming angle is limited. Therefore, the jammer's jamming coverage is a partial sphere with the jammer as the center. The partial sphere is decomposed into a cone and a sphere top. The jammer is located at the top of the cone, and the radius of the bottom of the cone is The radius of the sphere and the length of the cone generatrix are ;

[0049] Step 33: Set the signal-to-interference-to-noise ratio threshold based on the need to ensure normal communication of the drone , in three-dimensional space, below the signal-to-interference-noise ratio threshold The area is spherical, and the area within the interference coverage is the jammer obstacle area.

[0050] Furthermore, step four is specifically as follows:

[0051] Step 41: Comprehensively consider the flight length cost of the UAV and the threat cost of the jammer obstacle area. The flight length cost refers to the flight length of k UAVs. Under the same flight mission, the longer the flight length, the more power the UAV consumes. Correspondingly, the shorter the flight length, the less power is consumed. The threat cost refers to the threat of the jammer obstacle area to the safe flight of the UAV. The closer the UAV is to the jammer obstacle area, the greater the threat it will bear. Conversely, the smaller the threat it will bear, so as to construct the UAV trajectory cost function F:

[0052] ,

[0053] In the formula, , and are the weights of the jammer’s flight length cost and threat cost, respectively. The UAV’s flight length cost is for:

[0054] ,

[0055] Where N is the number of UAV flight time slots, is the position of the kth UAV in time slot n, is the maximum flight length of a single UAV flight, then the threat cost of the jammer obstacle area for:

[0056] ,

[0057] In the formula, represents the threat cost of the jammer obstacle area of ​​the kth UAV in time slot n, The calculation formula is:

[0058] ,

[0059] In the formula, is the jammer's location;

[0060] Step 42: Construct the UAV trajectory optimization problem based on the UAV trajectory cost function F for:

[0061] ,

[0062] In the formula, represents the symbol-level precoding matrix of the ground station, represents the set of drone trajectories, represents the transmission symbol vector of the ground station; The operator symbol represents taking the modulus value of a complex number. The operator represents the 2-norm of the orientation quantity. and They represent the real part and imaginary part operators respectively;

[0063] C1 is the starting position constraint of the drone, represents the starting position of the kth UAV;

[0064] C2 is the end position constraint of the drone. represents the final position of the kth UAV;

[0065] C3 is the speed constraint of the drone, is the maximum flight speed of the drone, is the time length of each time slot;

[0066] C4 is a high degree of restriction on drones. represents the height of the k-th UAV in time slot n, Indicates the maximum altitude of the drone;

[0067] C5 is the steering angle constraint of the drone, represents the horizontal steering angle of the k-th UAV in time slot n, Indicates the maximum steering angle of the drone;

[0068] C6 is the pitch angle constraint of the drone. represents the pitch angle of the kth UAV in time slot n, Indicates the maximum pitch angle of the drone;

[0069] C7 is a multi-UAV collision avoidance constraint. is the safe distance between two drones;

[0070] C8 is the non-strict phase constraint of symbol-level precoding adopted by the ground station. represents the effective received signal of the kth UAV, represents the channel vector between the kth UAV and the ground station, represents the transmitted symbol vector of the ground station, express The element corresponding to the kth drone in , express The conjugate of Indicates that the ground station uses Phase decision threshold for constellation modulation;

[0071] C9 is the power constraint of the signal transmitted by the ground station. is the signal power transmitted by the ground station;

[0072] Step 43: Solve the drone trajectory optimization problem , calculate the equivalent signal-to-noise ratio of the effective received signals of multiple drones under the current iteration trajectory. If the absolute value of the difference between the equivalent signal-to-noise ratio of the current iteration trajectory and the previous iteration trajectory is less than the specified 10 -3 When the dB accuracy requirement is met or the maximum number of iterations of 50 to 100 is reached, the trajectory is optimized through the B-spline curve and the optimal UAV track is output, otherwise the iteration continues.

[0073] Furthermore, the UAV trajectory optimization problem Decompose it into two sub-optimization problems and solve them iteratively.

[0074] The first sub-optimization problem is given a UAV trajectory Optimizing the precoding matrix Sub-optimization problem for:

[0075] ,

[0076] In the formula, represents the equivalent signal-to-noise ratio of the effective received signal of the kth UAV, The expression is:

[0077] ,

[0078] In the formula, is the noise power received by the kth UAV;

[0079] The second sub-optimization problem is that given the precoding matrix Optimizing drone trajectories Sub-optimization problem for:

[0080] ,

[0081] Step 44: Optimize the sub-problem Introducing slack variables , then according to the convex relaxation optimization method, the optimization problem is for:

[0082] ,

[0083] In the formula, is the scale factor corresponding to the kth UAV introduced to simplify the expression of k Effective reception signal of drones ,

[0084] Solve to get the symbol level precoding matrix , calculate the equivalent signal to interference and noise ratio received by the UAV to model the interference obstacle area;

[0085] Step 45: Combine the artificial potential field method and the rapidly expanding random tree algorithm, introduce the target bias mechanism, and solve the sub-optimization problem Solve and obtain the trajectory of the UAV.

[0086] Furthermore, in step 44, the symbol-level precoding matrix is ​​obtained by solving Specifically:

[0087] Step 441: With The equivalent optimization problem is ,

[0088] ,

[0089] in, is the introduced Lagrange multiplier vector; Used to simplify expressions; By the identity matrix Construct, used to construct matrix form expression and simplify expression; definition represents the overall channel matrix formed by all drones and all users, To simplify the expression, and Respectively expressed as:

[0090] ,

[0091] ,

[0092] in, and denote the real part and imaginary part operators respectively, In order to transform the complex matrix Expand to the real number domain for operation;

[0093] S442: Due to optimization issues It is a simplex quadratic programming optimization problem, which can be effectively solved by optimization methods such as interior point method. , and obtain the final precoding matrix for:

[0094] ,

[0095] in, , , Indicates creating a diagonal matrix from a vector.

[0096] Furthermore, the target bias mechanism is introduced in step 45 to solve the sub-optimization problem Solve the UAV trajectory, including:

[0097] Step 451: Initialize algorithm parameters and determine the starting position of the drone trajectory and the end position ;

[0098] Step 452: Use the target bias mechanism to determine a target bias probability threshold, and then randomly generate a number between [0,1]. When the generated random number is less than the threshold, the end point is set as the random sampling point. , when the generated random number is greater than or equal to the threshold, the sampling point Random generation;

[0099] Step 453: Traverse all nodes in the tree and find the distance The nearest tree node ;

[0100] Step 454: Using the artificial potential field method, a new node is obtained based on the combined force of the attraction of the end point and the repulsion of the interference obstacle area and other drones. ;

[0101] Step 455: Detection through collision function and Whether there is an obstacle in the path between, if not, the path is feasible, otherwise, return to step 452;

[0102] Step 456: Determine the new node through the constraint function Whether the constraints are met, if so, List the tree node set, otherwise, return to step 452;

[0103] Step 457: Determine whether the random tree and the end point position reach the connection threshold. If the connection threshold is reached, it means that the drone trajectory is successfully generated. Otherwise, return to step 452.

[0104] Furthermore, the step 454 is specifically as follows:

[0105] Step 454-1: In view of the gravitational effect of the end point position on the node growth, the gravitational function pointing to the end point position is constructed as follows:

[0106] ,

[0107] in, is the gravitational gain coefficient;

[0108] Step 454-2: In view of the repulsive force of the interference obstacle area or other drones on the node growth, the repulsive force function pointing in the opposite direction of the obstacle is constructed as follows:

[0109] ,

[0110] ,

[0111] ,

[0112] Among them, the repulsion force of the interference obstacle area or other drones is composed of the repulsion component and composition, is the repulsion gain coefficient, d represents the effective radius of repulsion, To interfere with the coordinates of obstacle areas or other drones;

[0113] Step 454-3: Using the combined force of repulsion and attraction and sampling points Generate new node , as shown below:

[0114] ,

[0115] in is the weight coefficient of the sampling point direction.

[0116] The beneficial effects of the present invention are as follows: the present invention proposes a trajectory optimization method combining a multi-UAV interference model with symbol-level precoding, estimates the jammer position and interference power through the received signal strength of multiple UAVs, effectively models the interference obstacle area of ​​the jammer through the equivalent signal-to-noise ratio, and uses symbol-level precoding technology for space division multiplexing. The signals of different UAVs are precoded according to channel state information, so that multiple UAVs in the same time-frequency domain can make full use of the legal interference signals between them. Simulation verification is carried out, and the results prove that the method proposed by the present invention can complete multi-UAV trajectory planning while significantly reducing the bit error rate of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0117] Figure 1 It is a system model diagram of multi-UAV communication in the interference communication scenario of the present invention;

[0118] Figure 2 It is a flow chart of trajectory optimization of multiple UAVs in the interference communication scenario of the present invention;

[0119] Figure 3 is a flight trajectory diagram of a UAV in a simulation experiment of the present invention;

[0120] Figure 4 It is a diagram of the trajectory length of the UAV under different signal-to-interference-noise ratio thresholds of the algorithm proposed in the simulation experiment of the present invention;

[0121] Figure 5 It is a bit error rate diagram of different precoding methods under different signal to interference noise ratio thresholds in the simulation experiment of the present invention. DETAILED DESCRIPTION

[0122] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0123] In order to achieve the above object, the present invention provides the following specific implementation methods:

[0124] Example 1: Figure 1 , Figure 2 As shown, a joint trajectory optimization method for symbol-level precoding of multiple UAVs under interference communication includes the following steps:

[0125] S01. Establish a system consisting of jammers, ground stations and multiple drones. Figure 1 The communication model shown is used to simulate the communication propagation between multiple UAVs and a ground station in a jammer interference communication environment, wherein the multiple UAVs include at least four UAVs;

[0126] S02. In the communication propagation simulation using the communication model, the signal power transmitted by the ground station is considered to be According to the communication model, the signal strength received by the kth UAV relative to the signal transmitted by the ground station is It is expressed as:

[0127] ,

[0128] in It represents the channel power gain when the distance between any UAV and the ground station is 1m. represents the distance between the ground station and the kth UAV, k≧4;

[0129] S03. Express the strength of all signals received by the kth UAV as , by Minus , calculate the signal strength received by the kth UAV relative to the signal transmitted by the jammer With noise intensity Added values , expressed as:

[0130] ,

[0131] Among them, the left formula is measured by the kth UAV, is calculated through the communication model, and is an unknown quantity, and considering the strong interference, it is assumed and equal;

[0132] S04. The interference power of the jammer's transmitted signal, which is still an unknown quantity, is expressed as According to the communication model, the signal strength received by the kth UAV relative to the signal transmitted by the jammer is Also expressed as:

[0133] ,

[0134] in represents the distance between the jammer and the kth UAV;

[0135] Therefore, we get the equations for the jammer position and jammer power. When the number of UAVs k is greater than or equal to 4, we can solve the distance between the jammer and the kth UAV. and interference power , that is, the jammer position and jammer power equation is:

[0136] ,

[0137] in, , , They represent the x-coordinate, y-coordinate and z-coordinate of the kth UAV respectively, , Respectively represent the x-coordinate and y-coordinate of the jammer;

[0138] Then, the equation group consisting of k drones is:

[0139] ,

[0140] In the system of equations there is , and For three unknown quantities, subtract every two adjacent equations to obtain a new set of equations:

[0141] ,

[0142] in,

[0143] ,

[0144] ,

[0145] ,

[0146] ,

[0147] Solve the equations to get the jammer's position and interference power .

[0148] S05. Based on the communication requirements of multiple UAV signal-to-interference-to-noise ratio thresholds, consider the communication model and assume that the position of any point in three-dimensional space is represented by , because the interference power is large, we temporarily ignore the influence of noise power, then The signal-to-interference-noise ratio of a point is expressed as:

[0149] ,

[0150] in, , They are Point to ground station and jammer Therefore, when determining the signal-to-interference-noise ratio threshold hour, Point to two fixed points and The ratio of the distances is a constant:

[0151] ,

[0152] In three-dimensional space, The trajectory of the points is a sphere with its center at a fixed point and On the straight line;

[0153] S06. Considering that the ground jammer is stationary and is jamming upward, the jamming angle is limited. Therefore, the jammer's jamming coverage is a partial sphere with the jammer as the center. The partial sphere is decomposed into a cone and a sphere top. The jammer is located at the top of the cone, and the radius of the bottom of the cone is The radius of the sphere and the length of the cone generatrix are ;

[0154] S07. Set the signal-to-interference-to-noise ratio threshold according to the need to ensure normal communication of the drone , in three-dimensional space, below the signal-to-interference-to-noise ratio threshold The area is spherical, and the area within the interference coverage is the jammer obstacle area.

[0155] S08. In the jammer obstacle area model, the flight length cost of the UAV and the threat cost of the jammer obstacle area are comprehensively considered. The flight length cost refers to the flight length of k UAVs. Under the same flight mission, the longer the flight length, the more power the UAV consumes. Correspondingly, the shorter the flight length, the less power is consumed. The threat cost refers to the threat of the jammer obstacle area to the safe flight of the UAV. The closer the UAV is to the jammer obstacle area, the greater the threat it will bear, and vice versa. The UAV trajectory cost function F is constructed:

[0156] ,

[0157] In the formula, , and are the weights of the jammer’s flight length cost and threat cost, respectively. The UAV’s flight length cost is for:

[0158] ,

[0159] Where N is the number of UAV flight time slots, is the position of the kth UAV in time slot n, is the maximum flight length of a single UAV flight, then the threat cost of the jammer obstacle area for:

[0160] ,

[0161] In the formula, represents the threat cost of the jammer obstacle area of ​​the kth UAV in time slot n, The calculation formula is:

[0162] ,

[0163] In the formula, is the jammer's location;

[0164] S09. Based on the UAV trajectory cost function F, construct the UAV trajectory optimization problem for:

[0165] ,

[0166] In the formula, represents the symbol-level precoding matrix of the ground station, represents the set of drone trajectories, represents the transmission symbol vector of the ground station; The operator symbol represents taking the modulus value of a complex number. The operator represents the 2-norm of the orientation quantity. and They represent the real part and imaginary part operators respectively;

[0167] C1 is the starting position constraint of the drone, represents the starting position of the kth UAV;

[0168] C2 is the end position constraint of the drone. represents the final position of the kth UAV;

[0169] C3 is the speed constraint of the drone, is the maximum flight speed of the drone, is the time length of each time slot;

[0170] C4 is a high degree of restriction on drones. represents the height of the k-th UAV in time slot n, Indicates the maximum altitude of the drone;

[0171] C5 is the steering angle constraint of the drone, represents the horizontal steering angle of the k-th UAV in time slot n, Indicates the maximum steering angle of the drone;

[0172] C6 is the pitch angle constraint of the drone. represents the pitch angle of the kth UAV in time slot n, Indicates the maximum pitch angle of the drone;

[0173] C7 is a multi-UAV collision avoidance constraint. is the safe distance between two drones;

[0174] C8 is the non-strict phase constraint of symbol-level precoding adopted by the ground station. represents the effective received signal of the kth UAV, represents the channel vector between the kth UAV and the ground station, represents the transmitted symbol vector of the ground station, express The element corresponding to the kth drone in , express The conjugate of Indicates that the ground station uses Phase decision threshold for constellation modulation;

[0175] C9 is the power constraint of the signal transmitted by the ground station. is the signal power transmitted by the ground station;

[0176] S10, optimizing the trajectory of the UAV Decompose it into two sub-optimization problems and solve them iteratively.

[0177] The first sub-optimization problem is given a UAV trajectory Optimizing the precoding matrix Sub-optimization problem for:

[0178] ,

[0179] In the formula, represents the equivalent signal-to-noise ratio of the effective received signal of the kth UAV, The expression is:

[0180] ,

[0181] In the formula, is the noise power received by the kth UAV;

[0182] The second sub-optimization problem is that given the precoding matrix Optimizing drone trajectories Sub-optimization problem for:

[0183] ,

[0184] S11. For sub-optimization problems Introducing slack variables , then according to the convex relaxation optimization method, the optimization problem is for:

[0185] ,

[0186] In the formula, is the scale factor corresponding to the kth UAV introduced to simplify the expression of k Effective reception signal of drones ,

[0187] Solve to get the symbol level precoding matrix , calculate the equivalent signal to interference and noise ratio received by the UAV to model the interference obstacle area;

[0188] S12, and The equivalent optimization problem is ,

[0189] ,

[0190] in, is the introduced Lagrange multiplier vector; Used to simplify expressions; By the identity matrix Construct, used to construct matrix form expression and simplify expression; definition represents the overall channel matrix formed by all drones and all users, To simplify the expression, and Respectively expressed as:

[0191] ,

[0192] ,

[0193] in, and denote the real part and imaginary part operators respectively, In order to transform the complex matrix Expand to the real number domain for operation;

[0194] S13. Due to optimization issues It is a simplex quadratic programming optimization problem, which can be effectively solved by optimization methods such as interior point method. , and obtain the final precoding matrix for:

[0195] ,

[0196] in, , , Indicates creating a diagonal matrix from a vector.

[0197] S14, algorithm initialization parameters, determine the starting position of the drone trajectory and the end position ;

[0198] S15. Use the target bias mechanism to determine a target bias probability threshold, and then randomly generate a number between [0,1]. When the generated random number is less than the threshold, the end point is set as the random sampling point. , when the generated random number is greater than or equal to the threshold, the sampling point Random generation;

[0199] S16. Traverse all nodes in the tree and find the distance The nearest tree node ;

[0200] S17. In view of the gravitational effect of the end point position on the node growth, the gravitational function pointing to the end point position is constructed as follows:

[0201] ,

[0202] in, is the gravitational gain coefficient.

[0203] S18. In view of the repulsive force of the interference obstacle area or other drones on the node growth, the repulsive force function pointing in the opposite direction of the obstacle is constructed as follows:

[0204] ,

[0205] ,

[0206] ,

[0207] Among them, the repulsion force of the interference obstacle area or other drones is composed of the repulsion component and composition, is the repulsion gain coefficient, d represents the effective radius of repulsion, Coordinates of interference obstacles or other drones.

[0208] S19, using the combined force of repulsion and attraction and sampling points Generate new node , as shown below:

[0209] ,

[0210] in is the weight coefficient of the sampling point direction;

[0211] S20, detection through collision function and Whether there is an obstacle on the path between, if not, the path is feasible, otherwise, return to S15;

[0212] S21. Determine the new node through the constraint function Whether the constraints are met, if so, Add it to the tree node set, otherwise, return to S15;

[0213] S22, judging whether the random tree and the end point position are less than the maximum flight speed of the UAV, if so, it means that the UAV trajectory is generated successfully, otherwise, returning to S15.

[0214] S23, based on the obtained current iteration trajectory of the UAV, calculate the equivalent signal-to-noise ratio received by multiple UAVs, and the absolute value of the difference between the equivalent signal-to-noise ratio of the current iteration trajectory and the previous iteration trajectory is less than the specified 10 -3 When the dB accuracy requirement is met or the maximum number of iterations of 50 to 100 is reached, the trajectory is optimized through the B-spline curve and the optimal UAV track is output, otherwise the iteration continues.

[0215] Example 2: Figure 3-Figure 5 As shown in FIG. 1 , when there is malicious interference with unknown position and unknown interference power, four UAVs achieve anti-interference communication with the ground base station through symbol-level precoding and trajectory optimization, including the following steps:

[0216] S1: Establish a communication model consisting of four unmanned aerial vehicles (UAVs), a ground station (GCS) and a malicious jammer (Jammer) with unknown position and transmission power. According to the established model, three sub-problems of optimizing the trajectory of UAVs in the jamming environment are obtained, namely, estimating the position and power of the jammer, modeling the jammer obstacle area, and optimizing the trajectory of UAVs.

[0217] S2: Estimate the jammer's location and power, including:

[0218] S21: Consider the signal power transmitted by GCS as , the signal strength received by the kth UAV relative to the GCS transmission It is expressed as:

[0219] ,

[0220] in It represents the channel power gain when the distance between any UAV and the ground station is 1m. Represents the distance between GCS and the kth UAV.

[0221] S22: The strength of all signals received by the kth UAV is expressed as , by receiving signal strength from Minus The signal strength received by the kth UAV relative to the signal transmitted by the jammer can be calculated With noise intensity Added values , expressed as:

[0222] ,

[0223] Among them, the left formula It can be measured by drone. It can be calculated through the communication model. and is an unknown quantity, but considering the strong interference, assume and equal.

[0224] S23: The power of the jammer's transmitted signal is expressed as , which is still an unknown quantity. According to the signal propagation model, the signal strength received by the kth UAV relative to the signal transmitted by the jammer is It can also be expressed as:

[0225] ,

[0226] in represents the distance between the jammer and the kth UAV; therefore, the equation for the jammer position and jamming power can be obtained as follows:

[0227] ,

[0228] in, , , They represent the x-coordinate, y-coordinate and z-coordinate of the kth UAV respectively, , Represent the x-coordinate and y-coordinate of the jammer respectively; in this equation, , and Three unknown quantities. Subtract two adjacent equations from each other in the equation consisting of four drones to obtain a new set of equations:

[0229] ,

[0230] in,

[0231] ,

[0232] ,

[0233] ,

[0234] ,

[0235] Solve the equations to get the location of the interference source and interference power .

[0236] S3: Modeling jammer obstacle areas, including:

[0237] S31: Consider the communication model, assuming that the position of any point in three-dimensional space is represented by , because the interference power is large, we temporarily ignore the influence of noise power, then The signal-to-interference-noise ratio of a point can be expressed as:

[0238] ,

[0239] in, , They are Point to ground station and jammer Therefore, when determining the signal-to-interference-noise ratio threshold hour, Point to two fixed points and The ratio of the distances is a constant:

[0240] ,

[0241] In three-dimensional space, The trajectory of the points is a sphere with its center at a fixed point and On the straight line;

[0242] S32: Considering that the ground jammer is stationary and jamming upward, the jamming angle is limited. Therefore, the jammer's jamming coverage consists of a cone and a spherical top. The jammer is located at the top of the cone, and the radius of the bottom of the cone is The radius of the sphere and the length of the cone generatrix are ;

[0243] S33: Set the signal-to-interference-to-noise ratio threshold according to the need to ensure normal communication of the drone , in three-dimensional space, below the signal-to-interference-to-noise ratio threshold The area is spherical, and the area within the interference coverage is the jammer obstacle area.

[0244] S41: Considering the UAV flight length cost and the jammer obstacle area threat cost modeled in S3, the UAV trajectory cost function is constructed

[0245] ,

[0246] in, , and are the weights of the flight length cost and the jammer threat cost, respectively. The flight length cost of the UAV for:

[0247] ,

[0248] Where N is the number of UAV flight time slots, is the position of the kth UAV in time slot n, is the maximum flight length of a single UAV flight, then the threat cost of the jammer obstacle area for:

[0249] ,

[0250] in, It represents the threat cost of the jammer obstacle area of ​​the kth UAV in time slot n, and the calculation formula is as follows:

[0251] ,

[0252] In the formula, is the jammer's location;

[0253] S42: Constructing the UAV trajectory optimization problem based on the UAV trajectory cost function :

[0254] ,

[0255] in, represents the symbol-level precoding matrix of GCS, represents the set of drone trajectories, represents the transmission symbol vector of the ground station; The operator symbol represents taking the modulus value of a complex number. The operator represents the 2-norm of the orientation quantity. and They represent the real part and imaginary part operators respectively;

[0256] C1 is the starting position constraint of the drone, represents the starting position of the kth UAV;

[0257] C2 is the end position constraint of the drone. represents the final position of the kth UAV;

[0258] C3 is the speed constraint of the drone, is the maximum flight speed of the drone, is the time length of each time slot;

[0259] C4 is a high degree of restriction on drones. represents the height of the k-th UAV in time slot n, Indicates the maximum altitude of the drone;

[0260] C5 is the steering angle constraint of the drone, represents the horizontal steering angle of the k-th UAV in time slot n, Indicates the maximum steering angle of the drone;

[0261] C6 is the pitch angle constraint of the drone. represents the pitch angle of the kth UAV in time slot n, Indicates the maximum pitch angle of the drone;

[0262] C7 is a multi-UAV collision avoidance constraint. is the safe distance between two drones;

[0263] C8 is a non-strict phase constraint in GCS based on symbol-level precoding based on beneficial interference. represents the effective received signal of the kth UAV, represents the channel vector between the kth UAV and the GCS, represents the transmission symbol vector of GCS, express The element corresponding to the kth drone in , express The conjugate of Indicates that GCS adopts Phase decision threshold for constellation modulation;

[0264] C9 is the power constraint of the GCS transmission signal. is the signal power transmitted by the ground station.

[0265] S43: The optimization problem established in S42 Decompose it into two sub-optimization problems and solve them iteratively. Given the trajectory of the UAV Optimizing the precoding matrix Sub-optimization problem :

[0266] ,

[0267] in, represents the equivalent signal-to-noise ratio of the effective received signal of the kth UAV, The expression is:

[0268] ,

[0269] In the formula, is the noise power received by the kth UAV;

[0270] The second sub-optimization problem is that given the precoding matrix Optimizing drone trajectories Sub-optimization problem for:

[0271] ,

[0272] S44: For sub-optimization problems Introducing slack variables , then according to the convex relaxation optimization method, the optimization problem is The symbol-level precoding matrix is ​​obtained by solving , calculate the equivalent signal to noise ratio received by the drone to model the interference obstacle area,

[0273] ,

[0274] In the formula, is the scale factor corresponding to the kth UAV introduced to simplify the expression of k Effective reception signal of drones .

[0275] S441: Based on the research on constructive interference symbol-level precoding with non-strict phase rotation in the article "Interference exploitation precoding made practical: Optimal closed-form solutions for PSK modulations" by Li et al., we can get the same Equivalent optimization problem ,

[0276] ,

[0277] in, is the introduced Lagrange multiplier vector; Used to simplify expressions; By the identity matrix Construct, used to construct matrix form expression and simplify expression; definition represents the overall channel matrix formed by all drones and all users, To simplify the expression, and Respectively expressed as:

[0278] ,

[0279] ,

[0280] in, and denote the real part and imaginary part operators respectively, In order to transform the complex matrix Expand to the real number domain for operation;

[0281] S442: Optimization Problem It is a simplex quadratic programming (QP) optimization problem, which can be effectively solved by optimization methods such as interior point method. The final precoding matrix is:

[0282] ,

[0283] in, , , Indicates the creation of a diagonal matrix based on a vector;

[0284] S45: Combining the artificial potential field method with the Rapidly-Exploring Random Tree (RRT) algorithm, introducing a target bias mechanism, and solving sub-optimization problems Solve the UAV trajectory, including:

[0285] S451: Initialize algorithm parameters and determine the starting position of the drone trajectory and the end position ;

[0286] S452: Use the target bias mechanism to determine a target bias probability threshold, and then randomly generate a number between [0,1]. When the generated random number is less than the threshold, the end point is set as the random sampling point. , when the generated random number is greater than or equal to the threshold, the sampling point Randomly generated.

[0287] S453: Traverse all nodes in the tree and find the distance The nearest tree node ;

[0288] S454: Using the artificial potential field method, the new node is obtained according to the combined force of the attraction of the end point and the repulsion of the interference obstacle area and other drones. ; Specifically include:

[0289] S454-1: In view of the gravitational effect of the end point on the node growth, the gravitational function pointing to the end point is constructed as follows:

[0290] ,

[0291] in, is the gravitational gain coefficient.

[0292] S454-2: In view of the repulsive force of the interference obstacle area or other drones on the node growth, the repulsive force function pointing in the opposite direction of the obstacle is constructed as follows:

[0293] ,

[0294] ,

[0295] ,

[0296] Among them, the repulsion force of the interference obstacle area or other drones is composed of the repulsion component and composition, is the repulsion gain coefficient, d represents the effective radius of repulsion, Coordinates of interference obstacles or other drones.

[0297] S454-3: Using the combined force of repulsion and attraction and sampling points Generate new node , as shown below:

[0298] ,

[0299] in is the weight coefficient of the sampling point direction.

[0300] S455: Detection through collision function and Whether there is an obstacle in the path between, if not, the path is feasible, otherwise, return to step S452;

[0301] S456: Determine new nodes through constraint functions Whether the constraints are met, if so, List it in the tree node set, otherwise, return to step S452;

[0302] S457: Determine whether the random tree and the end point position reach a connection threshold. If so, it means that the drone trajectory is generated successfully. Otherwise, return to step S452.

[0303] S46: Calculate the equivalent signal to noise ratio of the received data based on the obtained UAV trajectory. If the absolute value of the difference between the equivalent signal to noise ratio of the current iteration trajectory and the previous iteration trajectory is less than the specified 10 -3When the dB accuracy requirement is met or the maximum number of iterations is 50, the trajectory is optimized through the B-spline curve and the optimal UAV track is output, otherwise the iteration continues.

[0304] The effect of the present invention can be achieved by Figure 3-5 The simulation results are further explained.

[0305] Figure 3 The 3D flight trajectory diagram of multiple drones in the simulation experiment is shown in Figure 1. The four drones successfully reached the destination under the constraints of height, speed, steering angle, and pitch angle, and successfully bypassed the obstacle range of the jammer, effectively achieving anti-interference communication while completing the flight mission.

[0306] Figure 4 The figure shows the drone trajectory length diagram of the proposed algorithm under different SINR thresholds. When the SINR threshold is lower than 6dB, the drone trajectory length remains basically unchanged. When the SINR threshold is higher than 6dB, the drone trajectory length gradually increases with the increase of the SINR threshold. The reason is that the jammer obstacle range modeled by different SINR thresholds is different. When the SINR threshold is less than 6dB, the jammer obstacle range is lower than the flight altitude of the drone, and the drone trajectory tends to fly straight to the end point at a fixed altitude, and the trajectory length is basically the same; when the SINR threshold is higher than 6dB, the higher the SINR threshold, the larger the jammer obstacle range modeled, and the longer the trajectory length when the drone successfully avoids it.

[0307] Figure 5 The bit error rate diagram of different precoding methods under different SINR thresholds is shown in Figure 2. When the SINR threshold is lower than 6dB, the bit error rate of the system remains unchanged. When the SINR threshold is higher than 6dB, the bit error rate gradually decreases as the SINR threshold increases. The reason is that the jammer obstacle ranges modeled by different SINR thresholds are different. When the SINR threshold is less than 6dB, the jammer obstacle range is lower than the flight altitude of the UAV, and the impact of different SINR thresholds on the UAV trajectory is basically the same; when the SINR threshold is higher than 6dB, the jammer obstacle ranges modeled by different SINR thresholds have significantly different impacts on the UAV trajectory. When the UAV successfully avoids the jammer obstacle range with a high SINR threshold, the communication performance is improved and the bit error rate is reduced. At the same time, compared with zero forcing coding (ZF) and singular value decomposition precoding (SVD), symbol level precoding (SLP) significantly reduces the bit error rate under the same SINR threshold, which shows the effectiveness of the proposed algorithm.

[0308] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A joint trajectory optimization method for symbol-level precoding of multiple UAVs under interference communication, characterized in that: The following steps are involved: Step 1: Establish a communication model consisting of a jammer, a ground station and multiple drones, and use the communication model to simulate the communication propagation between multiple drones and the ground station in an environment where the jammer interferes with the communication, wherein the multiple drones include at least four drones; Step 2: In the communication propagation simulation using the communication model, the position and interference power of the jammer are estimated according to the signal power transmitted by the ground station and the signal strength received by any UAV relative to the signal transmitted by the ground station; Step 3: Based on the communication requirements of the signal-to-noise ratio thresholds of multiple drones, the interference coverage of the jammer in the communication model is determined according to the signal-to-noise ratio and trajectory at any point in the communication model and the location of the jammer, and a jammer obstacle area model formed by the influence of the ground station is established, specifically: Step 31: Consider the communication model and assume that the position of any point in three-dimensional space is represented by , because the interference power is large, we temporarily ignore the influence of noise power, then The signal-to-interference-noise ratio of a point is expressed as: ， in, , They are Point to ground station and jammer Therefore, when determining the signal-to-interference-noise ratio threshold hour, Point to two fixed points and The ratio of the distances is a constant: ， In three-dimensional space, The trajectory of the points is a sphere with its center at a fixed point and On the straight line; Step 32: Considering that the ground jammer is stationary and is jamming upward, the jamming angle is limited. Therefore, the jammer's jamming coverage is a partial sphere with the jammer as the center. The partial sphere is decomposed into a cone and a sphere top. The jammer is located at the top of the cone, and the radius of the bottom of the cone is The radius of the sphere and the length of the cone generatrix are ; Step 33: Set the signal-to-interference-to-noise ratio threshold based on the need to ensure normal communication of the drone , in three-dimensional space, below the signal-to-interference-to-noise ratio threshold The area is spherical, and the area falling within the interference coverage is the jammer obstacle area; Step 4: In the jammer obstacle area model, the flight length of the UAV and the jammer's interference power are comprehensively considered to obtain the flight length cost function of multiple UAVs and the threat cost function in a given time slot. The trajectory optimization problem of the UAV including the states of multiple UAVs, the power of the ground station's transmitted signal and the symbol-level precoding with non-strict phase constraints is constructed to obtain the optimized trajectories of multiple UAVs, specifically: Step 41: Comprehensively consider the UAV's flight length cost and the jammer's obstacle area threat cost, where the flight length cost refers to k The flight length of the drone. Under the same flight mission, the longer the flight length, the more power the drone consumes. Correspondingly, the shorter the flight length, the less power is consumed. The threat cost refers to the threat of the jammer obstacle area to the safe flight of the drone. The closer the drone is to the jammer obstacle area, the greater the threat it will bear. Conversely, the smaller the threat it will bear, thus constructing the drone trajectory cost function. F : ， In the formula, , and are the weights of the jammer’s flight length cost and threat cost, respectively. The UAV’s flight length cost is for: ， Where N is the number of UAV flight time slots, It is k The position of the UAV in time slot n, is the maximum flight length of a single UAV flight, then the threat cost of the jammer obstacle area for: ， In the formula, Indicates k The threat cost of a UAV in the jammer obstacle area in time slot n is: The calculation formula is: ， In the formula, is the jammer's location; Step 42: Based on the cost function of the drone trajectory F , construct the UAV trajectory optimization problem for: ， In the formula, represents the symbol-level precoding matrix of the ground station, represents the set of drone trajectories, represents the transmission symbol vector of the ground station; The operator symbol represents taking the modulus value of a complex number. The operator represents the 2-norm of the orientation quantity. and They represent the real part and imaginary part operators respectively; C1 is the starting position constraint of the drone, Indicates k The starting position of the drone; C2 is the end position constraint of the drone. Indicates k The final location of the drone; C3 is the speed constraint of the drone, is the maximum flight speed of the drone, is the time length of each time slot; C4 is a high degree of restriction on drones. Indicates that in time slot n k The height of the drone, Indicates the maximum altitude of the drone; C5 is the steering angle constraint of the drone, Indicates that in time slot n k The horizontal steering angle of the drone, Indicates the maximum steering angle of the drone; C6 is the pitch angle constraint of the drone. Indicates that in time slot n k The pitch angle of the drone, Indicates the maximum pitch angle of the drone; C7 is a multi-UAV collision avoidance constraint. is the safe distance between two drones; C8 is the non-strict phase constraint of symbol-level precoding adopted by the ground station. Indicates k The effective reception signal of the UAV, Indicates k The channel vector between the UAV and the ground station, represents the transmitted symbol vector of the ground station, express The k The elements corresponding to the drone, express The conjugate of Indicates that the ground station uses Phase decision threshold for constellation modulation; C9 is the power constraint of the signal transmitted by the ground station. is the signal power transmitted by the ground station; Step 43: Solve the drone trajectory optimization problem , calculate the equivalent signal-to-noise ratio of the effective received signals of multiple drones under the current iteration trajectory. If the absolute value of the difference between the equivalent signal-to-noise ratio of the current iteration trajectory and the previous iteration trajectory is less than the specified 10 -3 When the dB accuracy requirement is met or the maximum number of iterations is 50 to 100, the trajectory is optimized through the B-spline curve and the optimal UAV track is output, otherwise the iteration continues; The UAV trajectory optimization problem Decompose it into two sub-optimization problems and solve them iteratively. The first sub-optimization problem is given a UAV trajectory Optimizing the precoding matrix Sub-optimization problem for: ， In the formula, Indicates k The equivalent signal-to-noise ratio of the effective received signal of the UAV, The expression is: ， In the formula, It is k The noise power received by the drone; The second sub-optimization problem is that given the precoding matrix Optimizing drone trajectories Sub-optimization problem for: ， Step 44: Optimize the sub-problem Introducing slack variables , then according to the convex relaxation optimization method, the optimization problem is for: ， In the formula, It is the first k The scale factor corresponding to the first UAV is used to simplify the expression of k Effective reception signal of drones , Solve to get the symbol level precoding matrix , calculate the equivalent signal to interference and noise ratio received by the UAV to model the jammer obstacle area; Among them, the symbol-level precoding matrix obtained is Specifically: Step 441: With The equivalent optimization problem is , ， in, is the introduced Lagrange multiplier vector; Used to simplify expressions; By the identity matrix Composition, used to form matrix form expression and simplify expression; definition represents the overall channel matrix formed by all drones and all users, To simplify the expression, and Respectively expressed as: ， ， in, and denote the real part and imaginary part operators respectively, In order to transform the complex matrix Expand to the real number domain for operation; S442: Due to optimization issues It is a simplex quadratic programming optimization problem, which is solved by the interior point optimization method. , and obtain the final precoding matrix for: ， in, , , Indicates creating a diagonal matrix based on a vector; Step 45: Combine the artificial potential field method and the rapidly expanding random tree algorithm, introduce the target bias mechanism, and solve the sub-optimization problem Solve to obtain the trajectory of the drone; The target bias mechanism is introduced to solve the sub-optimization problem Solve the UAV trajectory, including: Step 451: Initialize algorithm parameters and determine the starting position of the drone trajectory and the end position ; Step 452: Use the target bias mechanism to determine a target bias probability threshold, and then randomly generate a number between [0,1]. When the generated random number is less than the threshold, the end point is set as the random sampling point. , when the generated random number is greater than or equal to the threshold, the sampling point Random generation; Step 453: Traverse all nodes in the tree and find the distance The nearest tree node ; Step 454: Using the artificial potential field method, according to the attraction of the end position and the jammer obstacle area and the removal of the first K The combined repulsive force of multiple drones behind the drone is used to obtain the new node ; Step 455: Detection through collision function and Whether there is an obstacle in the path between, if not, the path is feasible, otherwise, return to step 452; Step 456: Determine the new node through the constraint function Whether the constraints are met, if so, List the tree node set, otherwise, return to step 452; Step 457: Determine whether the random tree and the end point position reach the connection threshold. If the connection threshold is reached, it means that the drone trajectory is successfully generated. Otherwise, return to step 452.

2. The joint trajectory optimization method for multi-UAV symbol-level precoding under interference communication as claimed in claim 1 is characterized in that: The step 2 is specifically as follows: Step 21: Consider the signal power transmitted by the ground station as , according to the communication model, then k The signal strength received by the drone relative to the signal transmitted by the ground station It is expressed as: ， in It represents the channel power gain when the distance between any UAV and the ground station is 1m. Indicates the ground station and k The distance of the drone, k ≥4; Step 22: k The strength of all signals received by the drone is expressed as , by Minus , calculate the k The signal strength received by the UAV relative to the jammer's transmission With noise intensity Added values , expressed as: ， Among them, the left formula By k The drone measured is calculated through the communication model, and is an unknown quantity, and considering the strong interference, it is assumed and equal; Step 23: Express the interference power of the jammer's transmitted signal, which is still an unknown quantity, as ,According to the communication model, the k The signal strength received by the UAV relative to the jammer's transmission Also expressed as: ， in Indicates the jammer and k The distance of the drone; Therefore, we get the equations about the jammer position and jammer power. When the number of UAVs is k When it is greater than or equal to 4, solve the jammer and the k The distance of the drone and interference power , that is, the jammer position and jammer power equation is: ， in, , , Respectively represent k The x-coordinate, y-coordinate and z-coordinate of the drone. , Respectively represent the x-coordinate and y-coordinate of the jammer; Then there is, k The equations for the drones are: ， In the system of equations there is , and For three unknown quantities, subtract every two adjacent equations to obtain a new set of equations: ， in, ， ， ， ， Solve the equations to get the jammer's position and interference power .

3. The joint trajectory optimization method for symbol-level precoding of multiple UAVs under interference communication as described in claim 2 is characterized in that: In the jammer position and jammer power equation there is , and Three unknown quantities, k When 1, 2, 3, and 4 are taken respectively, k In the equations consisting of the drones, two adjacent equations are subtracted to obtain a new set of equations: ， in, ， ， ， ， Solve the equations to get the jammer's position and interference power .

4. The joint trajectory optimization method for symbol-level precoding of multiple UAVs under interference communication as claimed in claim 1 is characterized in that: The step 454 is specifically as follows: Step 454-1: In view of the gravitational effect of the end point position on the node growth, the gravitational function pointing to the end point position is constructed as follows: ， in, is the gravitational gain coefficient; Step 454-2: Target the jammer obstacle area or remove the K The repulsive force of multiple drones behind the drone on the node growth, the repulsive force function pointing in the opposite direction of the obstacle is constructed as follows: ， ， ， Among them, the jammer obstacle area or remove the first K The repulsive force of multiple drones behind the drone is composed of the repulsive force component and composition, is the repulsion gain coefficient, d represents the effective radius of repulsion, For jammer obstacle area or remove the K The coordinates of multiple drones behind the drone; Step 454-3: Using the combined force of repulsion and attraction and sampling points Generate new node , as shown below: ， in is the weight coefficient of the sampling point direction.

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