Multi-dimensional resource scheduling algorithm for radar interference system based on PSO (Particle Swarm Optimization)

Abstract

The invention belongs to the field of resource management and control of a radar interference system, particularly relates to a multi-dimensional resource scheduling optimization problem of a system with a multi-beam, multi-channel and digital beam forming technology and an array plane division technology, and provides a multi-dimensional resource scheduling algorithm of a radar interference system based on PSO (Particle Swarm Optimization). According to the algorithm, time resources, frequency resources, airspace resources and array plane resources are considered at the same time, a PSO method is adopted to solve a multi-dimensional resource scheduling optimization problem, particles are used to represent a multi-dimensional resource scheduling strategy of a system, a target function of the system is used as particle fitness, and under the constraint of the multi-dimensional resources, a particle swarm is initialized and iteratively updated, so that the multi-dimensional resource scheduling optimization is realized. And finally determining a multi-dimensional resource scheduling strategy of the system.

Description

Technical Field

[0001] The present invention belongs to the field of resource management and control of radar jamming systems, and particularly relates to a multi-dimensional resource scheduling algorithm for a system with multi-beam, multi-channel, digital beamforming technology, and array division technology. Background Art

[0002] With the gradual increase in the number of tasks of radar jamming systems and the gradual development of electronic countermeasure technologies, radar jamming systems have become increasingly complex and diverse. To jam multiple targets simultaneously, advanced jamming devices use a multi-channel approach, and the array surface of each channel is divisible and can adopt digital beamforming (DBF) technology. Therefore, for such jamming systems, it is necessary not only to allocate time resources to each task but also to consider the scheduling of resources such as frequency domain, spatial domain, and array surface. However, while the system utilizes multi-dimensional resources to execute multiple tasks to obtain higher execution efficiency, it also means that the system needs to consider multi-dimensional resource constraints when executing tasks, that is, under multi-dimensional resource constraints, a multi-dimensional resource scheduling strategy is given for multiple radar jamming tasks. Therefore, how to establish an effective mathematical model and design an efficient resource scheduling algorithm for this problem is the key to solving this problem.

[0003] Regarding the establishment of a mathematical model for the interference system resource scheduling problem under multi-dimensional resource constraints, (Guo Xiaoyi, Yuan Weiwei, Huang Jincai. Radar interference resource one-to-many allocation method [J]. Fire Control & Command Control, 2008) simultaneously considered time resource constraints, frequency resource constraints, and airspace resource constraints. From the three-dimensional perspectives of time domain, airspace, and frequency domain, it judged the radar sets that could be interfered by a single jammer simultaneously, and grouped the target radars accordingly to achieve the simultaneous execution of multiple tasks. (X. Guangran, D. Zicheng, W. Wei and H. Lang. Multi-beam dwell adaptive scheduling algorithm for helicopter-borne radar. 2014 IEEE 7th Joint International Information Technology and Artificial Intelligence Conference, Chongqing, China, 2014) Simultaneously considered time resource constraints and array surface resource constraints, and achieved the purpose of simultaneously executing multiple tasks by simply dividing the entire array surface into multiple sub-arrays. (Wang Falong, Jiang Ning. Research on multi-objective fuzzy multi-stage interference resource scheduling [J]. Modern Defense Technology, 2015) While considering time resource constraints and array surface resource constraints, it further divided the array surface into 16 basic sub-arrays, and took 4 basic sub-arrays as a quadrant, considering the differences in task execution in different quadrants, effectively improving the interference performance of the system. However, the above models did not simultaneously consider the combined constraints of time resources, frequency resources, airspace resources, and array surface resources. (Xu Yuan, Wang Hongwei, Chen You, etc. Optimization allocation method of radar interference resources for multi-beam interference system [J]. Fire Control & Command Control, 2015) Simultaneously considering the combined constraints of these four-dimensional resources, a mathematical model for the resource scheduling problem was established, and a more effective interference resource allocation strategy was given. However, this model did not discuss the DBF technology and lacked the collaborative consideration of DBF and array division.

[0004] The interference resource scheduling problem is essentially a mathematical optimization problem. Since the objective function is often non-convex, under the combined constraints of multi-dimensional resources, the interference resource scheduling problem is a multi-dimensional, non-convex NP-hard problem. For the interference resource scheduling problem, swarm intelligence algorithms such as ant colony algorithm, genetic algorithm, particle swarm optimization (PSO), and artificial bee colony algorithm are mostly used for optimization and solution. (Sun Jun, Zhang Dalin, Yi Wei. Resource Scheduling Method for Multi-Radar Cooperative Jamming Network [J]. Radar Science and Technology, 2022) The particle swarm optimization algorithm is used to solve the joint optimization problem of interference beam and power with interference resource constraints. (Xing HX, Xing QH, Wang K. A Joint Allocation Method of Multi-Jammer Cooperative Jamming Resources Based on Suppression Effectiveness [J]. mathematics, 2023) The artificial bee colony algorithm is used to solve the joint optimization problem of interference beam and power with interference resource constraints to achieve reasonable allocation of interference resources.

[0005] Based on this, for a multi-beam multi-channel system that simultaneously adopts DBF and array division technology, the present invention comprehensively considers the constraints of time resources, frequency resources, spatial domain resources, and array resources to obtain a more reasonable resource scheduling strategy with higher interference efficiency. Based on the mathematical model of interference system resource scheduling, the present invention comprehensively considers the constraints of time resources, frequency resources, spatial domain resources, and array resources, and proposes a multi-dimensional resource scheduling algorithm for radar interference system based on PSO. Summary of the Invention

[0006] Assume that there are M channels in the system. Among them, the transmission power and transmission gain of channel m are P m and G m , m = 1, 2,..., M. The system has DBF technology and array division technology. The system time is discretized in units of Δt. At time k, the system receives N k interference task requests. The set composed of these N k task requests is denoted as T k . Among them, the threat degree of task n is denoted as ω n , ω n . The larger the value, the higher the threat level of task n. The application execution time is The application execution frequency range is At time k, the radial distance, azimuth angle, and elevation angle of the enemy radar relative to the own jammer are r k,n , θ k,n and αk,n , the transmitting power and antenna gain of the enemy radar are P k,n and G k,n , the combined loss of the transmitting feeder and atmospheric propagation of the enemy radar is The suppression coefficient of our jammer to the enemy radar is K k,n , the radar cross-section of our detected target relative to the enemy radar is RCS n , the combined loss of the transmitting feeder and atmospheric propagation of our jammer is Solve the resource scheduling optimization problem of the system at time k based on PSO. Denote the number of particles as NIND, and the position of particle i at time k as an Nk×M-dimensional matrix Xk,i. If X k,i (n,m) = 1, then task n is executed on channel m at time k; otherwise, X k,i (n,m) = 0, and task n is not executed on channel m at time k. The velocity of particle i is an N k ×M-dimensional matrix V k,i , w is the inertia weight, c1 is the individual learning factor, c2 is the swarm learning factor, r1 and r2 are random numbers in the interval [0,1], s is the current iteration number (initial value is 0), S is the maximum iteration number, δ is the fitness difference threshold, and E is the iteration end condition. When the absolute value of the fitness difference between the global optimal solutions of adjacent iterations is less than δ for E consecutive iterations, the iteration ends. The steps of the resource scheduling algorithm proposed in the present invention at time k are as follows:

[0007] Step 1: For the task application set T at time k k , select all tasks n that satisfy equation (1) from it to form a task set Equation (1) is as follows:

[0008]

[0009] Step 2: Initialize the resource scheduling strategies, particle positions and particle velocities For each particle:

[0010] Step 2.1: Select channel frequency bands. Quantize the application frequency ranges of each task in according to the unit frequency band B0, then the application frequency band of task n can be denoted as Count the application frequency bands of each task in to obtain the occurrence frequency of each unit frequency band, and use the occurrence frequency as the selection probability to randomly select M frequency bands as the channel frequency bands of particle i, denoted as a 2×M-dimensional matrix B k,i , B k,i (1,m) is the lower bound of the frequency band of channel m of particle i at time k, Bk,i (2,m) is the upper bound of the frequency band of channel m of particle i at time k.

[0011] Step 2.2: For each channel, select from the task set whose application interference frequency intersects with the frequency band of this channel

[0012] Step 2.3: For each channel, perform beam combining. Randomly select N tasks from m and denote the selected task set as Denote the remaining task set in as m where N is a random integer in the interval and DA is the maximum number of sub-arrays into which the entire array can be divided. For each task in in turn, select all the tasks that satisfy equation (2) with it from to form the task set where each task in can be executed by the same beam and there are no identical tasks in different

[0013]

[0014] where θ th and α th are the azimuth difference threshold and elevation difference threshold between tasks respectively when the system executes multiple tasks with the same beam. Denote as the beam to be realized and denote the beam set as

[0015] Step 2.4: For each channel, perform beam clustering. In turn, take each beam k,i,m in TC as the reference beam, and find the beams that satisfy equation (3) with it among the remaining beams in TC k,i,m . If the total number of the reference beam and the beams that meet the conditions exceeds the upper limit DB of the number of digital beams that can be generated by the system using the DBF technology at one time, then among the beams that meet the conditions, sort them according to the sum of the threat levels of the tasks executed by each beam, and select the DB - 1 beams with the largest sum of threat levels and the reference beam to form the beam set Each beam in can be realized by the DBF technology and there are no identical beams in different where Equation (3) is as follows:

[0016]

[0017] Among them, α th is the threshold of the elevation angle difference between beams when the system uses the DBF technology to implement multiple digital beams, and its value is the same as that in Equation (2). Denote Repeat the above beam clustering, and change the selection order of the reference beam in each clustering until all selection orders are traversed, and select the one with the smallest V value as the final beam clustering result BC k,i,m .

[0018] Step 2.5: For each channel, for BC k,i,m According to sort to obtain Among them,[[]] then The allocated array resources are successively 2 -1 , 2 -2 , …, 2 -(V-1) , The allocated array resources are Thus, the initialization of the resource scheduling strategy is completed.

[0019] Step 2.6: Initialize the particle position and the particle velocity For the m-th column of k,i,m , m = 1, 2, 3, …, M, set the elements corresponding to each task included in TC to 1, and the rest to 0. For k the N

[0020] × M elements of and the global optimal solution Take the initial position of each particle as its initial individual optimal solution According to the initial resource scheduling strategy corresponding to each particle, calculate the execution benefit f k,i as the particle fitness, and select the initial position of the particle with the maximum fitness as the initial global optimal solution f k,i The calculation method is as follows:

[0021]

[0022] Among them, I k,i represents the set of all tasks executed in particle i at time k, and AP k,i is an N k × M-dimensional matrix representing the occupancy of each task in particle i on each array resource at time k, and AP k,i(n, m) is the ratio of the number of array elements of the sub-array that executes task n on channel m in particle i at time k to the total number of array elements. If task n is not executed on channel m, then AP k,i (n, m) = 0.

[0023] Step 4: Iteratively update the resource scheduling strategies and particle positions corresponding to NIND particles For each particle:

[0024] Step 4.1: Initially update the particle position, and sequentially calculate Equations (5) and (6):

[0025]

[0026]

[0027] For all elements with a value of 1, first determine whether the corresponding task satisfies Equation (1). If not, modify the value to 0. Secondly, determine whether there is an intersection between the frequency band of the corresponding task and the corresponding channel. If there is no intersection, modify the value to 0.

[0028] Step 4.2: For each channel, perform beam combination. Randomly select N tasks from the tasks corresponding to the elements with a value of 1 in the corresponding column to form a task set m N N m is a random integer in the interval and form a task set for the tasks with a value of 1 in each column that have not been selected, and and for each task in successively select the tasks that satisfy Equation (2) from and to form a new task set Each task in can be executed with the same beam and there are no identical tasks in different

[0029] Step 4.3: For each channel, perform beam clustering. The specific method is the same as Step 2.4.

[0030] Step 4.4: For each channel, perform array surface resource partitioning. The specific method is the same as Step 2.5. Thus, the update of the resource scheduling strategy is completed.

[0031] Step 4.5: Update the particle position For the m-th column of k,i,mThe elements at the corresponding positions of the tasks included are denoted as 1, and the rest are 0, where m = 1, 2, …, M.

[0032] Step 5: Iteratively update the particle fitness and the individual optimal solution and the global optimal solution According to the resource scheduling strategies corresponding to each particle after update, calculate the execution benefit f according to Equation (4) k,i , and update the fitness of each particle. If the fitness of particle i after update is higher than the corresponding fitness, then Otherwise, it remains unchanged. Compare the maximum fitness of all the updated particles with the fitness of the global optimal solution. If the maximum fitness of all the updated particles is greater than the fitness of the global optimal solution, then update it to the position of the particle with the maximum current fitness.

[0033] Step 6: Iteratively update the particle velocity.

[0034]

[0035] Step 7: s = s + 1, calculate the difference in the fitness of the global optimal solution between adjacent iterations. If s = S or the absolute value of the difference in the fitness of the global optimal solution between adjacent iterations is less than δ for E consecutive iterations, then the algorithm ends. Otherwise, return to Step 4.

[0036] It should be noted that the above steps are for the self-defense radar jamming system, and this idea can also be used for the non-self-defense radar jamming system.

[0037] Principle of the invention

[0038] When the jamming system faces multiple task requests, it needs to resolve the conflicts of different tasks in the same single limited resource through the replacement of different single resources under multi-dimensional resource constraints according to the threat levels of each task and the requirements of each task for various resources, and finally generate a multi-dimensional resource scheduling strategy to effectively execute multiple tasks. The multi-dimensional resources of the jamming system mainly include time resources, frequency resources, airspace resources, and array surface resources. Discretize the system time in units of Δt, and the time resource at time k can be represented as kΔt; the frequency resource at time k can be represented as a 2×M-dimensional matrix B k , where M is the number of channels of the system, and B k (1, m) represents the lower bound of the frequency band of channel m at time k, and B k (2, m) represents the upper bound of the frequency band of channel m at time k; the airspace resource at time k can be represented as θ th , α th and DB; the array surface resource at time k can be represented as ap k = {apk,1 , ap k,2 , …, ap k,M} and DA, where apk,m represents the array surface resource amount of each sub-array on channel m at time k, and the sub-array surface resource amount is the ratio of the number of sub-array surface elements to the number of full-array surface elements.

[0039] Regarding multi-dimensional resource constraints, it specifically includes time resource constraints, frequency resource constraints, spatial domain resource constraints, and array surface resource constraints:

[0040] Time resource constraints: Assume that there are N k task applications at time k in the system, then the application interference time of the tasks to be executed should satisfy the following constraints:

[0041]

[0042] Among them, uk is an Nk-dimensional vector representing whether each task is executed at time k. If u k (n) = 1, then task n is executed at time k; otherwise, u k (n) = 0, and task n is not executed at time k.

[0043] Frequency resource constraints: Assume that there are N k task applications at time k in the system and the system has M channels. Then, there should be an intersection between the application interference frequency of the tasks to be executed in each channel and the corresponding channel frequency band. The frequency resource constraint can be expressed as:

[0044]

[0045] Among them, TB k is an N k ×M-dimensional matrix representing whether each task is executed on each channel at time k. If TB k (n, m) = 1, then task n is executed on channel m at time k; otherwise, TB k (n, m) = 0, and task n is not executed on channel m at time k.

[0046] Spatial domain resource constraints: Denote the beam set emitted on channel m of the system at time k as TC k,m , there is Among them represents the l-th beam, and the elements in are P l tasks executed by the same beam. Then, the spatial resource constraint can be expressed as:

[0047]

[0048] Denote the beam group set emitted on channel m of the system at time k as BC k,m , there is Among them If it represents the v-th beam group or single-beam beam group implemented by the DBF technology, the spatial resource constraint can be expressed as:

[0049]

[0050] Array surface resource constraint: For the beam group set BC emitted on channel m of the system at time k k,m , and each beam group in it needs to be implemented through a separate sub-array, then the array surface resource constraint can be expressed as:

[0051] |BC k,m | ≤ DA (12)

[0052] For the problem of resource scheduling optimization of an interference system facing multi-tasks and multi-dimensional resources, an execution revenue objective function is established to measure the advantages and disadvantages of the scheduling strategy and the scheduling algorithm. Assume that the system can obtain a certain execution revenue for each interference task executed. Obviously, the execution revenue of each interference task is related to its execution efficiency and threat level. Based on this, the execution revenue of the system at time k is defined as:

[0053]

[0054] Among them, eff k,n is the execution efficiency of task n at time k. Considering that the execution efficiency of the task is mainly related to the power and frequency band obtained by the task, it is defined as:

[0055]

[0056] Among them, and are respectively the effective interference power obtained by task n on channel m at time k and the interference power expected to be obtained by task n at time k. F k,n,m and are respectively the effective working frequency band occupied by task n on channel m at time k and the working frequency band applied for by task n. The specific calculation is as follows:

[0057]

[0058] Among them, AP k is an N k ×M-dimensional matrix representing the occupancy of each array surface resource by each task at time k. AP k (n, m) represents the actual occupancy of the array surface resource by task n on channel m at time k, and its value is the ratio of the number of array elements of the sub-array to which task n belongs on channel m at time k to the total number of array elements of the entire array, that is, the value at the corresponding position in ap k,m , and AP k(n, m) = 0 indicates that task n is not executed on channel m at time k, AP k (n, m) = 1 indicates that task n occupies all-array resources and is executed on channel m at time k, AP k If the value of (n, m) ranges from 0 to 1, it represents that task n utilizes a sub-array for execution on channel m at time k. represents the number of beams in the beam group to which task n on channel m belongs at time k.

[0059] Based on the above multi-dimensional resource constraint conditions and system objective function, for the system resource scheduling optimization problem of multi-tasks and multi-dimensional resources at time k, the following optimization model can be established:

[0060]

[0061] For the above optimization problem, the PSO method is used for solution. First, the particle swarm is initialized, as shown in steps 1 - 3 specifically. Subsequently, the particle swarm is iteratively updated, as shown in steps 4 - 7 specifically. Finally, the resource scheduling strategy corresponding to the global optimal solution at the end of the iteration is used as the system resource scheduling strategy, completing the optimization solution of the multi-dimensional resource scheduling problem for the radar jamming system. Description of the Drawings

[0062] Figure 1 is a schematic diagram of the time-domain resource scheduling strategy of the algorithm of the present invention;

[0063] Figure 2 is a schematic diagram of the frequency-domain resource scheduling strategy of the algorithm of the present invention;

[0064] Figure 3 is a schematic diagram of the spatial-domain resource and array-array resource scheduling strategy of the algorithm of the present invention;

[0065] Figure 4 is the comparison of the performance of the algorithm execution benefits. Detailed Implementation Manner

[0066] The system has 4 available channels, and the full-array radiation power P of each channel m is 100 W, the array antenna gain G of each channel m is 100, the frequency band width of each channel is B0, the system can adopt DBF technology and the azimuth threshold θ th , the elevation threshold α th , and the maximum number of digital beams DB that can be generated by DBF at one time are 5°, 5°, and 4 respectively. The system can adopt sub-array division technology and the maximum number of sub-arrays DA that the full array can be divided into is 4. Considering that there are 10 interference task applications in the scenario within [1, 50] s, the threat levels ω of these 10 interference tasks n , the application execution time application execution frequency Recorded in Table 1; the initial radial distance r of the enemy radar relative to the friendly jammer 1,n , azimuth angle θ 1,n and elevation angle α 1,n as well as the radial distance change rate dr k,n , azimuth angle change rate dθ k,n and elevation angle change rate dα k,n , recorded in Table 2; the suppression coefficient K of the friendly jammer on the enemy radar k,n , the transmission power P of the enemy radar k,n and antenna gain G k,n , the radar cross section RCS of the friendly detected target relative to the enemy radar n , the ratio of the combined loss between the friendly jammer and the enemy radar Recorded in Table 3, where K k,n , P k,n , G k,n do not change with time.

[0067] Table 1 Simulation scenario task parameters (1)

[0068]

[0069] Table 2 Simulation scenario task parameters (2)

[0070]

[0071] Table 2 (continued)

[0072]

[0073] Table 3 Simulation scenario task parameters (3)

[0074]

[0075] Adopt the multi-dimensional resource scheduling algorithm of the radar jamming system based on PSO proposed by the present invention for time-domain, frequency-domain, space-domain and array surface resource scheduling. The time-domain resource scheduling strategy at each moment is as Figure 1 shown, where the color of each colored block represents the execution situation of the corresponding task at the corresponding moment. The dark red colored block indicates that the task is executed, and the dark blue colored block indicates that the task is not executed. Comparing the task parameters with Figure 1 it can be seen that the algorithm of the present invention can adaptively determine the time-domain resource scheduling strategy according to the actual resource requirements; the frequency-domain resource scheduling strategy at each moment is as Figure 2 shown. Considering that different channels in the simulation scenario have the same frequency band width, the color of each colored block is used to represent the lower bound of the frequency band of the corresponding channel at the corresponding moment (unit: B0). From Figure 2It can be seen that the algorithm of the present invention can adaptively determine the frequency resource scheduling strategy of the system according to the resource requirements at each moment; taking the moment k = 2 as an example, the single-moment airspace resource and array surface resource scheduling strategy is as Figure 3 shown. Among them, the numbers of the tasks executed by each beam have been marked within the beam. Channels 1 and 4 use the sub-array division method to transmit multiple beams to execute multiple tasks. Channel 2 transmits a single beam with the entire array surface to execute multiple tasks. Channel 3 uses the DBF technology to transmit multiple beams to execute multiple tasks. It can be Figure 3 seen that the algorithm of the present invention simultaneously considers the DBF and sub-array division technologies and effectively schedules the airspace resources and array surface resources.

[0076] At the same time, in order to illustrate the advantages of this algorithm, its performance is compared with two commonly used resource scheduling algorithms, namely the combined beam priority method and the threat degree priority method. The combined beam priority method regards the tasks that can be executed by the same beam as tasks with higher priority and preferentially allocates resources. The threat degree priority method means that resources are allocated to tasks in the order of the threat degree of multiple tasks from high to low. In the above simulation scenario, the execution benefits of the three algorithms are compared as Figure 4 shown. The execution benefits obtained by the algorithm of the present invention at each moment are significantly higher than those of the other two algorithms, and the performance of the algorithm of the present invention is better. Combining the simulation results with the foregoing, it can be known that for the resource scheduling optimization problem of a multi-task-oriented interference system, the algorithm of the present invention can fully consider the DBF technology and the sub-array division technology, adaptively generate a multi-dimensional resource scheduling strategy, and has a higher execution benefit compared with other algorithms. The algorithm of the present invention has better multi-dimensional resource scheduling efficiency.

[0077] For a radar interference system with multiple beams, multiple channels, digital beamforming technology, and array surface division technology, the present invention can obtain a higher execution benefit compared with similar algorithms in a multi-task scenario with multi-dimensional resource requirements. In summary, the proposed multi-dimensional resource scheduling algorithm for a radar interference system based on PSO is an effective multi-dimensional resource scheduling algorithm for a radar interference system.

Claims

1. The multi-dimensional resource scheduling algorithm for radar jamming system based on PSO, the specific technical solution is as follows: Assume that there are M channels in the system, where, The transmit power and transmit gain of channel m are P m and G m , where m = 1, 2, …, M. The system has DBF technology and array division technology. The system time is discretized in units of Δt. At time k, the system receives N k interference task requests. The set composed of these N k task requests is denoted as T k . Among them, the threat degree of task n is denoted as ω n , and ω n . The larger the value, the higher the threat level of task n. The application execution time is The application execution frequency range is At time k, the radial distance, azimuth angle, and elevation angle of the enemy radar relative to our jammer are r k,n , θ k,n and α k,n . The transmit power and antenna gain of the enemy radar are P k,n and G k,n , and the combined loss of the enemy radar transmit feeder and atmospheric propagation is The suppression coefficient of our jammer on the enemy radar is K k,n . The radar cross-section (RCS) of our detected target relative to the enemy radar is RCS n . The combined loss of our jammer transmit feeder and atmospheric propagation is Based on PSO, solve the resource scheduling optimization problem of the system at time k. Denote the number of particles as NIND. The position of particle i at time k is an N k ×M-dimensional matrix X k,i . If X k,i (n, m) = 1, then at time k, task n is executed on channel m; otherwise, X k,i (n, m) = 0, and at time k, task n is not executed on channel m. The velocity of particle i is an N k ×M-dimensional matrix V k,i . w is the inertia weight, c1 is the individual learning factor, c2 is the swarm learning factor, r1 and r2 are random numbers in the interval [0, 1], s is the current iteration number (with an initial value of 0), S is the maximum iteration number, δ is the fitness difference threshold, and E is the iteration end condition. When the absolute value of the fitness difference between the global optimal solutions of adjacent iterations is less than δ for continuous E iterations, the iteration ends. The steps of the multi-dimensional resource scheduling algorithm for radar jamming system based on PSO at time k are as follows: Step 1: For the task application set T at time k k , select all tasks n that satisfy Equation (1) from it to form a task set Equation (1) is as follows: Step 2: Initialize the resource scheduling policies and particle positions corresponding to NIND particles and particle velocities For each particle: Step 2.1: Select channel frequency bands. Quantize the application frequency range of each task in according to the unit frequency band B0, then the application frequency band of task n can be denoted as Statistically analyze the application frequency bands of each task in to obtain the occurrence frequency of each unit frequency band, and use the occurrence frequency as the selection probability. Randomly select M frequency bands as the channel frequency bands of particle i and denote them as a 2×M-dimensional matrix B k,i , where B k,i (1, m) is the lower bound of the frequency band of channel m of particle i at time k, and B k,i (2, m) is the upper bound of the frequency band of channel m of particle i at time k. Step 2.2: For each channel, select from a task set whose application interference frequencies intersect with the frequency band of this channel Step 2.3: For each channel, perform beam combining. Randomly select N tasks from m , and denote the selected task set as . Denote the remaining task set in as . Among them, N m is a random integer in the interval . DA is the maximum number of sub-arrays that the full array can be divided into. For each task in in turn, all tasks that satisfy Equation (2) are selected from to form a task set . Among them, each task in can be executed with the same beam, and there are no identical tasks in different . Equation (2) is as follows: where, θ th and α th are respectively the azimuth difference threshold and the elevation difference threshold between tasks when the system executes multiple tasks using the same beam. Taking to represent the beam to be realized, and denoting the beam set as Step 2.4: For each channel, perform beam grouping. k,i,m Each beam in As a reference beam, in TC k,i,m The remaining beams are searched for beams that satisfy equation (3). If the total number of the reference beam and the beams that satisfy the condition exceeds the upper limit DB of the number of digital beams that can be generated by the system using DBF technology at a time, then among the beams that satisfy the condition, they are sorted according to the sum of the threat levels of the tasks performed by each beam, and the DB-1 beams with the largest sum of threat levels are selected together with the reference beam to form a beam set. Each The beams in the There are no identical beams in , where Formula (3) is as follows: Among them, α th is the elevation angle difference threshold between beams when the system uses the DBF technology to implement multiple digital beams, and its value is the same as that in Equation (2). Denote Repeat the above beam clustering, and change the selection order of the reference beam in each clustering until all selection orders are traversed, and select the one with the smallest V value as the final beam clustering result BC k,i,m . Step 2.5: For each channel, for BC k,i,m According to perform sorting to obtain wherein, then the allocated array surface resources are successively 2 -1 , 2 -2 , …, 2 -(V-1) , the allocated array surface resource is Thus, the initialization of the resource scheduling strategy is completed. Step 2.6: Initialize the particle positions and particle velocities For the m-th column of, m = 1, 2, 3, …, M, set the elements corresponding to each task included in TC k,i,m to 1 and the rest to 0. For the N k × M elements of, randomly assign values of -1, 0, or 1. Step 3: Initialize the individual optimal solution and the global optimal solution Take the initial position of each particle as its initial individual optimal solution According to the initial resource scheduling strategy corresponding to each particle, calculate the execution benefit f k,i As the particle fitness, and select the initial position of the particle with the maximum fitness as the initial global optimal solution f k,i The calculation method is as follows: Among them, I k,i represents the set of all tasks executed in particle i at time k, and AP k,i is an N k ×M dimensional matrix representing the occupation of each task in particle i at time k for each front array resource. AP k,i (n, m) takes the ratio of the number of array elements of the sub-array where task n is executed on channel m in particle i at time k to the total number of array elements. If task n is not executed on channel m, then AP k,i (n, m) = 0. Step 4: Iteratively update the resource scheduling policies and particle positions corresponding to NIND particles For each particle: Step 4.1: Initially update the particle positions, and calculate formula (5) and formula (6) in sequence: For For all elements with a value of 1, first determine whether the corresponding task satisfies Equation (1). If not, modify the value to 0. Secondly, determine whether there is an intersection between the frequency band of the corresponding task and the corresponding channel. If there is no intersection, modify the value to 0. Step 4.2: For each channel, perform beam combining. Randomly select N tasks from the tasks corresponding to the elements with a value of 1 in the corresponding column to form a task set m where N is a random integer in the interval m . For the tasks with an element value of 1 in each column that are not selected, form a task set and for each task in , successively select tasks from and that satisfy equation (2) with it to form a new task set . Each task in and can be executed with the same beam and there are no identical tasks in different . Each task in is still denoted as Step 4.3: For each channel, perform beam grouping. The specific method is the same as that in Step 2.

4. Step 4.4: For each channel, perform array surface resource partitioning. The specific method is the same as that in Step 2.

5. Thus, the update of the resource scheduling strategy is completed. Step 4.5: Update the particle positions For the m-th column, set the elements at the corresponding positions of the tasks included in TC k,i,m to 1 and the rest to 0, where m = 1, 2, …, M. Step 5: Iteratively update the particle fitness and the individual optimal solution and the global optimal solution According to the resource scheduling strategies corresponding to each particle after update, calculate the execution benefit f according to Equation (4) k,i , and update the fitness of each particle. If the fitness of particle i after update is higher than that corresponding, then otherwise, remain unchanged. Compare the maximum fitness of all updated particles with the fitness of the global optimal solution. If the maximum fitness of all updated particles is greater than the fitness of the global optimal solution, then update it to the position of the particle with the maximum current fitness. Step 6: Iteratively update the particle velocities. Step 7: s = s + 1, calculate the fitness difference of the global optimal solutions of adjacent iterations. If s = S or the absolute value of the fitness difference of the global optimal solutions of adjacent iterations is less than δ for E consecutive iterations, the algorithm ends; otherwise, return to Step 4.

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