Low-orbit satellite wireless resource scheduling method and device based on resource graph and adversarial learning

By adopting a method based on resource map and adversarial learning in the satellite Internet, the wireless resource map is constructed and optimized, and the problem of inefficient wireless resource scheduling in the satellite Internet is solved, and more efficient and accurate resource allocation is achieved.

CN115942460BActive Publication Date: 2025-02-07BEIJING UNIV OF POSTS & TELECOMM +1
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Patent Information

Application Number
CN202211356622.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-11-01
Publication Date
2025-02-07
Estimated Expiration
2042-11-01

AI Technical Summary

Technical Problem

The prior art is difficult to effectively dispatch low-orbit satellite wireless resources in the satellite Internet, especially in complex dynamic environments, and cannot fully utilize the prior information of user distribution and satellite periodic motion, resulting in low resource scheduling efficiency.

Method used

Using a method based on resource map and adversarial learning, an infinite resource map is constructed by constructing a three-dimensional bar chart and cutting it into two-dimensional pictures, and the images are optimized using a pre-trained generative adversarial network to achieve fine-grained resource allocation scheduling.

Benefits of technology

It improves the accuracy and efficiency of resource allocation strategies, can better adapt to the complex and dynamic wireless resource requirements in the satellite Internet, and improves system performance and resource utilization.

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Abstract

The present invention provides a low-orbit satellite wireless resource scheduling method and device based on resource map and adversarial learning. Based on the application scenario of beam hopping technology, the satellite network periodic prior information is first used to establish constraint conditions based on maximum throughput and priority requirements, and the number of time slots allocated to each spot beam is preliminarily solved; a three-dimensional bar graph of wireless network resource scheduling is established with time slots, spot beam numbers and spot beam frequencies as parameters, and an infinite resource map is constructed by cutting the time slots into two-dimensional pictures, and the overall time slot allocation scheduling is optimized for the two-dimensional pictures obtained by cutting through a pre-trained generative adversarial network, and the advantages of images in continuous and explicit color processing are used to achieve fine-grained optimization by processing the wireless resource map, thereby improving the accuracy of the resource allocation strategy.
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Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a method and device for scheduling wireless resources of a low-orbit satellite based on resource graph and adversarial learning. Background Art

[0002] With the commercial use of 5G networks, the communication problems of massive user access, large bandwidth and low latency in densely populated areas have been solved. However, due to the global expansion of human activities, production value, emergencies, etc., the high cost or inability to build ground networks in sparsely populated areas has led to a serious shortage of wireless resources, coverage and communication rates for information exchange under the global perspective. In recent years, satellite Internet based on large constellations, low orbits and high frequency bands has become one of the important solutions to the above problems at a low cost. At present, seamless space-ground communication integrating satellites, air-based platforms and ground networks has become an important topic of 6G research.

[0003] Different from the ground network and the existing satellite communication system, satellite Internet will focus on realizing high-concurrency mobile broadband access for users in global regions. To this end, the important innovative technical ideas of satellite Internet are to integrate the new air interface of ground 5GNR, introduce phased array beam hopping, and combine new technologies such as microservice core network to achieve more flexible, larger capacity and higher-speed communication support. At the same time, the communication service experience of satellite Internet has also been focused on. Operators plan to provide global ubiquitous users with mobile broadband services with a single-user peak rate of more than 100Mbps, real-time interactive services with a rate of less than 50ms, and IoT services with concurrent access of more than 1 million. The above services are very different, and have different requirements for service guarantees such as bandwidth, latency, and number of accesses, but there is a high probability that they are distributed under the same beam of satellite Internet, or the distribution changes dynamically with the region. In addition, the ground area covered by the same satellite changes rapidly, and the channel environment of ground users changes dramatically. Therefore, based on satellite Internet, the optimal wireless resource allocation and scheduling for different regions and different users in the same beam is the key to improving the flexibility and reliability of satellite Internet communications.

[0004] The core issues of satellite Internet wireless resource scheduling include two points. The first is to fine-grained modeling of satellite wireless communication resources such as frequency, time, space and timing of beams under beam hopping; the second is the optimal choice of multiple constraint relationships when multiple heterogeneous services coexist. First, the introduction of the new air interface of ground 5GNR enables user data in the same beam of satellite communication to be multiplexed using OFDM. Combined with the dynamic beamforming capability provided by the phased array, satellite communication can provide different frequencies, time slots and codes to different users in different regions at different times. In addition, due to the high-speed changes of satellites, the allocated wireless resources corresponding to each user at different times are also changing rapidly. At the same time, considering air-based platforms such as aircraft and airships, as well as space-based platforms such as remote sensing, meteorology, and space stations, the demand for wireless resources has expanded from two-dimensional ground to three-dimensional space and ground. The existing wireless communication resources are modeled using a single-point, fixed, and two-dimensional approach, which is difficult to adapt to the precise description requirements of the spatial multi-point, fine-grained changes, and three-dimensional distribution of wireless communication resources in the satellite Internet scenario. Second, in the satellite Internet scenario, there are demands for large-bandwidth, low-latency, and high-concurrency communication services in the same area. At the same time, due to the large relative distance between the satellite and the user, and the periodic coverage of the satellite, the service requests initiated by ground users do not obey a simple random distribution, but have more spatial and periodic regular distributions.

[0005] The existing wireless resource scheduling algorithm based on artificial intelligence focuses on link state perception to optimize and control wireless resources, emphasizes reliable connection, and does not make full use of the prior information brought by the relatively fixed user distribution and the periodic movement of satellites, and cannot further improve the efficiency of artificial intelligence algorithms in satellite Internet wireless resource scheduling. In view of the problem that the representation granularity of complex dynamic wireless resource scheduling in satellite Internet is insufficient and the artificial intelligence algorithm does not consider the periodic prior information of satellite networks, a new low-orbit satellite wireless resource scheduling method is urgently needed. Summary of the invention

[0006] In view of this, an embodiment of the present invention provides a low-orbit satellite wireless resource scheduling method and device based on resource graph and adversarial learning to eliminate or improve one or more defects existing in the prior art, and solve the problem of insufficient granularity in the representation of complex dynamic wireless resource scheduling of satellite Internet and insufficient utilization of the prior information brought about by the relatively fixed user distribution and the periodic motion of the satellite.

[0007] One aspect of the present invention provides a low-orbit satellite wireless resource scheduling method based on resource graph and adversarial learning, for a beam hopping access scenario of a low-orbit satellite wide beam combined with a dynamic spot beam, the method comprises the following steps:

[0008] A wide beam is used to cover multiple user cells, and each user cell is covered by a spot beam. Satellite resources are allocated according to a set time window as the granularity. The set time window is divided into a set number of time slots, and time slot resources are allocated to each spot beam. Users in each user cell obey a two-dimensional normal distribution, and the user traffic demand intensity is determined based on user distribution and service priority.

[0009] Based on full frequency reuse, the channel differences of multiple users served by each spot beam are averaged, and the channel capacity parameters provided by each user cell are approximately expressed by the idealized model of Shannon flux;

[0010] Setting a priority weight value for each user cell according to the service priority of each user cell;

[0011] According to the user traffic demand intensity, channel capacity parameters and priority weight value of each user cell, the service priority demand is introduced to establish constraints on the basis of maximizing throughput, and the number of time slots allocated to the corresponding point beam of each user cell is solved;

[0012] In a set time window, a three-dimensional bar graph is established with the time slot as the X-axis, the spot beam number as the Y-axis, and the spot beam frequency as the Z-axis, and the three-dimensional bar graph is cut into two-dimensional pictures according to each time slot, wherein the horizontal quantity of the two-dimensional picture represents the beam number, and the vertical quantity of the two-dimensional picture represents the spot beam frequency;

[0013] Converting beam-hopping satellite communication wireless resource constraints into graph constraints, and performing constraint adjustments on the two-dimensional image;

[0014] All two-dimensional images obtained by cutting a single three-dimensional histogram are input into the generator of the pre-trained generative adversarial network, and the optimized resource allocation map is output, and each resource allocation map is stacked according to the corresponding time slot to obtain a resource scheduling histogram, so as to schedule the time slot resources for each point beam according to the resource scheduling histogram. In some embodiments, based on full frequency reuse, the channel differences of multiple users served by each point beam are averaged, and the channel capacity parameters provided by each user cell are approximately expressed by the idealized model of Shannon flux, and the calculation formula is:

[0015]

[0016] in, is the actual amount of traffic allocated to the corresponding wave position of the nth spot beam, that is, the channel capacity parameter, N max is the number of spot beams working in each time slot in the beam hopping system; W is the total length of the set time window; N i is the number of time slots allocated to the i-th spot beam, B is the bandwidth of the beam-hopping system, log2(1+SINR ij) is the spectral efficiency of the i-th spot beam in the j-th time slot, SINR ij is the signal-to-noise ratio of the i-th spot beam in the j-th time slot.

[0017] In some embodiments, based on the user traffic demand intensity, channel capacity parameters and priority weight values ​​of each user cell, a service priority demand is introduced to establish constraints on the basis of maximizing throughput, including:

[0018] Establish the maximum throughput objective function, the expression is:

[0019]

[0020]

[0021] Establish the priority weight objective function, the expression is:

[0022]

[0023]

[0024] in, Indicates the user traffic demand intensity of the corresponding wave position of the nth spot beam, is the actual allocated traffic volume of the nth spot beam corresponding to the wave position, N max is the number of spot beams working in each time slot in the beam hopping system; W is the total length of the set time window; N i is the number of time slots allocated to the i-th spot beam, N * Represents a positive integer.

[0025] In some embodiments, the beam-hopping satellite communication wireless resource constraint condition expression is:

[0026]

[0027] Among them, N i represents the number of time slots allocated to the i-th spot beam, and W represents the set time window; represents the spatial interval between spot beams, r represents the radius of the spot beam, and B i represents the i-th spot beam, B j represents the jth spot beam; P i represents the power allocated to the i-th spot beam, P total Indicates total power; represents the spot beam frequency resource, p w Indicates the overall frequency resources of the system.

[0028] In some embodiments, the expression of the graph constraint is:

[0029]

[0030] Among them, L num Indicates the number of input images set in the GAN network, L vec-x Indicates the horizontal size of the input image, L vec-y represents the vertical size of the input image, W represents the set time window, B i represents the i-th spot beam, Represents the frequency parameter of the i-th spot beam.

[0031] In some embodiments, the pre-training step of generating an adversarial network includes:

[0032] Acquire a training sample set, wherein the training sample set includes a plurality of samples, each sample includes a plurality of two-dimensional images obtained by cutting a three-dimensional bar graph according to each time slot, the three-dimensional bar graph is established based on existing beam hopping wireless resource scheduling data with the time slot as the X-axis, the spot beam number as the Y-axis, and the spot beam frequency as the Z-axis, the horizontal amount of the two-dimensional image represents the beam number, and the vertical amount of the two-dimensional image represents the spot beam frequency;

[0033] Constructing and initializing a generator network and a discriminator network, and using the training sample set to train the generator network and the discriminator network;

[0034] The generator network is updated and iterated by minimizing the first loss function, and the expression of the first loss function is:

[0035]

[0036] Among them, z i represents the input of the generator network, G(z i ) represents the output of the generator network, D(G(z i )) represents the output of the discriminator network;

[0037] The discriminator network updates and iterates by maximizing the second loss function and minimizing the output. The expression of the second loss function is:

[0038]

[0039] Among them, x i represents the input of the discriminator network, represents the output of the generator network.

[0040] In some embodiments, the generator network and the discriminator network use gradient descent method to update parameters.

[0041] In some embodiments, the generator network and the discriminator network use an Adam optimizer to update parameters during pre-training.

[0042] On the other hand, the present invention also provides a low-orbit satellite wireless resource scheduling device based on resource graph and adversarial learning, including a processor and a memory, wherein the memory stores computer instructions, and the processor is used to execute the computer instructions stored in the memory. When the computer instructions are executed by the processor, the device implements the steps of the above method.

[0043] On the other hand, the present invention further provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the above method when executed by a processor.

[0044] The beneficial effects of the present invention include at least:

[0045] The method and device for scheduling wireless resources of low-orbit satellites based on resource graph and adversarial learning of the present invention are based on the application scenario of beam hopping technology. First, the constraint conditions are established based on the maximum throughput and priority requirements by using the periodic prior information of the satellite network, and the number of time slots allocated to each spot beam is preliminarily solved. A three-dimensional bar graph of wireless network resource scheduling is established with time slots, spot beam numbers and spot beam frequencies as parameters, and an infinite resource graph is constructed by cutting the time slots into two-dimensional images. The overall time slot allocation scheduling is optimized for the two-dimensional images obtained by cutting through a pre-trained generative adversarial network. The advantages of images in the continuous and explicit color processing process are utilized, and fine-grained optimization is achieved by processing the wireless resource graph, thereby improving the accuracy of the resource allocation strategy.

[0046] Additional advantages, purposes, and features of the present invention will be described in part in the following description, and will become apparent to those skilled in the art after studying the following, or may be learned from the practice of the present invention. The purposes and other advantages of the present invention may be achieved and obtained by the structures specifically indicated in the specification and the accompanying drawings.

[0047] Those skilled in the art will appreciate that the objectives and advantages that can be achieved with the present invention are not limited to the above specific description, and the above and other objectives that can be achieved by the present invention will be more clearly understood from the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of the present application, and do not constitute a limitation of the present invention. In the drawings:

[0049] Figure 1 The present invention is a flowchart of a method for scheduling wireless resources of low-orbit satellites based on resource graph and adversarial learning according to an embodiment of the present invention.

[0050] Figure 2 It is a schematic diagram of a three-dimensional bar chart constructed in a low-orbit satellite wireless resource scheduling method based on resource graph and adversarial learning according to an embodiment of the present invention.

[0051] Figure 3 To match the time slot Figure 2 Schematic diagram of cutting. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments and the accompanying drawings. Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0053] It should also be noted that, in order to avoid obscuring the present invention due to unnecessary details, only structures and / or processing steps closely related to the solutions according to the present invention are shown in the accompanying drawings, while other details that are not closely related to the present invention are omitted.

[0054] It should be emphasized that the term “include / comprises” when used herein refers to the presence of features, elements, steps or components, but does not exclude the presence or addition of one or more other features, elements, steps or components.

[0055] It should also be noted that, unless otherwise specified, the term “connection” herein may refer not only to a direct connection but also to an indirect connection involving an intermediate.

[0056] Beam-hopping satellite communication systems have great technical advantages in satellite Internet applications. In order to improve the utilization rate of on-board resources, the existing wireless resource management solutions are designed for a single service under certain constraints, which makes it difficult to adapt to the requirements of reliable communication services under the dynamic and changing satellite Internet environment. There is an urgent need to study wireless resource management under multiple services and multiple constraints. Therefore, the present invention mainly solves how to consider the multi-objective joint optimization scheduling of wireless resources from the perspective of time, space, frequency, and power under the premise of rapid changes in user demand, and how to continue to consider constraints such as fairness and service weights while taking maximum throughput as an indicator, so as to further improve satellite resource utilization and system performance. Its main problems include the following two points:

[0057] First, the difficulty of complex satellite Internet wireless resource models under high dynamics. Low-orbit satellites move quickly, and the coverage area is constantly changing. The allocated wireless resources corresponding to each user at different times are also changing rapidly. At the same time, considering air-based platforms such as aircraft and airships, as well as space-based platforms such as remote sensing, meteorology, and space stations, the demand for wireless resources has expanded from two-dimensional ground to three-dimensional space and ground. However, existing wireless communication resources are modeled with a single-point, fixed, and two-dimensional approach. Faced with the characteristics of multi-satellite collaborative work, joint networking, and different business requirements in medium and low-orbit satellite constellation systems, it is difficult to adapt to the precise description requirements of the spatial multi-point, fine-grained changes, and three-dimensional distribution of wireless communication resources in satellite Internet scenarios, and it is difficult to meet the needs of joint optimization and scheduling of multi-satellite resources.

[0058] Second, when the demand for service quality assurance varies greatly, it is difficult to efficiently schedule the global steady state and local rapid joint wireless resources. Under the guarantee of service quality, low-orbit satellite Internet has very different service scenarios. Artificial intelligence is introduced into the resource scheduling algorithm to realize the fuzzy and fine-grained wireless resource scheduling that cannot be solved by the deterministic model algorithm. However, artificial intelligence wireless resource scheduling algorithms, including deep learning, reinforcement learning, and transfer learning, focus on link state perception to optimize and control wireless resources, emphasize reliable connections, and do not make full use of the prior information brought by the relatively fixed user distribution and the periodic movement of satellites, thus failing to further improve the efficiency of artificial intelligence algorithms in satellite Internet wireless resource scheduling.

[0059] To this end, this application constructs a satellite resource model with multiple dimensions of time-space-frequency-machine, so that its resource division can more accurately meet the business needs of the cell, and uses a generative adversarial network for optimization, so that it can autonomously identify the current satellite service scenario and cell business needs, and make efficient resource scheduling. Furthermore, an intelligent resource scheduling algorithm based on adversarial learning is introduced, and the relativity of user distribution and the periodicity of satellite motion are used to construct a normal global scheduling. By converting the wireless resource model into an infinite resource map and processing it using an adversarial learning network (GAN network), it can adapt to the resource scheduling needs of medium and low orbit satellite constellations characterized by multi-satellite collaboration, joint networking, and massive users, and process them at a finer granularity.

[0060] Specifically, the present invention provides a low-orbit satellite wireless resource scheduling method based on resource graph and adversarial learning, targeting the beam hopping access scenario of low-orbit satellite wide beam combined with dynamic spot beam, such as Figure 1 As shown, the method includes the following steps S101 to S107:

[0061] Step S101: Use a wide beam to cover multiple user cells, each user cell is covered by a spot beam, satellite resources are allocated according to a set time window, the set time window is divided into a set number of time slots, and time slot resources are allocated to each spot beam; users in each user cell obey a two-dimensional normal distribution, and the user traffic demand intensity is determined based on user distribution and service priority.

[0062] Step S102: Based on full frequency reuse, the channel differences of multiple users served by each spot beam are averaged, and the channel capacity parameters provided by each user cell are approximately expressed by an idealized model of Shannon flux.

[0063] Step S103: setting a priority weight value for each user cell according to the service priority of each user cell.

[0064] Step S104: According to the user traffic demand intensity, channel capacity parameters and priority weight value of each user cell, a service priority demand is introduced to establish constraints on the basis of maximizing throughput, and the number of time slots allocated to the corresponding point beam of each user cell is solved.

[0065] Step S105: In a set time window, a three-dimensional bar graph is established with the time slot as the X-axis, the spot beam number as the Y-axis, and the spot beam frequency as the Z-axis. The three-dimensional bar graph is cut into two-dimensional images according to each time slot. The horizontal quantity of the two-dimensional image represents the beam number, and the vertical quantity of the two-dimensional image represents the spot beam frequency.

[0066] Step S106: converting the beam-hopping satellite communication wireless resource constraint condition into a spectrum constraint condition, and performing constraint adjustment on the two-dimensional image.

[0067] Step S107: All two-dimensional images obtained by cutting based on a single three-dimensional histogram are input into the generator of the pre-trained generative adversarial network, and the optimized resource allocation map is output, and each resource allocation map is stacked according to the corresponding time slot to obtain a resource scheduling histogram, so as to perform time slot resource scheduling for each point beam according to the resource scheduling histogram.

[0068] In steps S101 to S104, a system communication model of a beam-hopping access scheme combining a low-orbit satellite wide beam with a dynamic spot beam is established, and a technical scheme of beam-hopping switching under the guidance of wide beams and the cooperation of wide beams and spot beams is adopted. A system model is established based on the prior information of the access scheme, the operating frequency of the spot beam, and the user distribution characteristics. In the beam-hopping technology, the beam hopping period is in the second range. During the hopping period, the spatial distribution of service requests in the coverage area can be regarded as static and unchanged. Based on the above considerations, the present application mainly schedules on-board resources within a beam hopping period. Specifically, an adjustment period can be determined as a set time window, and multiple time slots can be further divided within the set time window as the maximum allocation unit for resource scheduling. The service block covered by the wide beam contains multiple user cells, and each user cell is covered by a spot beam for resource allocation. Within a time window, resources are allocated by allocating a corresponding number of time slots to each spot beam.

[0069] The communication model of the beam-hopping access scheme system is constructed based on prior information, the most important of which is the service demand in each user cell and the resources that each point beam can provide. In each service block, the location of the user is randomly distributed and obeys the characteristics of a two-dimensional normal distribution. The user service demand intensity of each user cell is related to the number of users. This application also simultaneously introduces service priority to determine the user service demand intensity. For a specified user cell, the service type involved can be predicted. According to the known service type, the corresponding service priority can be set for each user, and the user service demand intensity of each user cell is calculated.

[0070] In step S101, for the jth user served by the i-th spot beam, the number of users in each user cell is q i , then j = 1, 2, 3…q i , user u ij The position can be expressed as in, In contrast, their probability density function is:

[0071]

[0072] User ij Location It obeys a two-dimensional normal distribution with mean μ1 and μ2, variance σ1 and σ2, and ρ = 0. The variance describes the degree of dispersion of users in the cell. i In the case of , the user's service demand intensity can be expressed as:

[0073]

[0074] Further, in step S102, each spot beam adopts full frequency reuse, and in each time slot, the channel capacity provided by the satellite to each cell can be approximated by the ideal Shannon capacity. In some embodiments, based on full frequency reuse, the channel differences of multiple users served by each spot beam are averaged, and the channel capacity parameters provided by each user cell are approximated by the idealized model of Shannon flux, and the calculation formula is:

[0075]

[0076] in, is the actual amount of traffic allocated to the corresponding wave position of the nth spot beam, that is, the channel capacity parameter, N max is the number of spot beams working in each time slot in the beam hopping system; W is the total length of the set time window; N i is the number of time slots allocated to the i-th spot beam, B is the bandwidth of the beam-hopping system, log2(1+SINR ij ) is the spectral efficiency of the i-th spot beam in the j-th time slot, SINR ij is the signal-to-noise ratio of the i-th spot beam in the j-th time slot.

[0077] In step S104, based on the user traffic demand intensity, channel capacity parameters and priority weight values ​​of each user cell, a service priority demand is introduced to establish constraints on the basis of maximizing throughput, including:

[0078] Establish the maximum throughput objective function, the expression is:

[0079]

[0080]

[0081] Establish the priority weight objective function, the expression is:

[0082]

[0083]

[0084] in, Indicates the user traffic demand intensity of the corresponding wave position of the nth spot beam, is the actual allocated traffic volume of the nth spot beam corresponding to the wave position, N max is the number of spot beams working in each time slot in the beam hopping system; W is the total length of the set time window; N i is the number of time slots allocated to the i-th spot beam, N * Represents a positive integer.

[0085] Until step S104, the number of time slots allocated to each spot beam within the set time window has been preliminarily solved, but it presents the characteristics of coarse-grained discreteness. The solution based solely on prior information cannot meet the requirements of fine-grained continuous scheduling in complex communication environments. In steps S105 to S107, the scheduling strategy preliminarily solved is converted into an infinite resource map for optimization, and the advantages of images in continuous and explicit color processing are utilized to introduce a generative adversarial network for continuous fine-grained processing optimization.

[0086] First, in step S105, Figure 2 and Figure 3 Based on the preliminary resource allocation strategy, a three-dimensional bar graph is established with the time slot as the X-axis, the spot beam number as the Y-axis, and the spot beam frequency as the Z-axis. It is divided into multiple two-dimensional images according to the time slot. For example, for a set time window containing K time slots, the three-dimensional bar graph is divided into K two-dimensional images, each of which corresponds to a time slot. The horizontal quantity of the two-dimensional image represents the beam number, and the vertical quantity of the two-dimensional image represents the spot beam frequency.

[0087] In step S106, preliminary constraints are performed based on the beam-hopping satellite communication wireless resource constraints. First, the beam-hopping satellite communication wireless resource constraints are converted into graph constraints, and constraints are adjusted for each two-dimensional image.

[0088] In some embodiments, the beam-hopping satellite communication wireless resource constraint condition expression is:

[0089]

[0090] Among them, N i represents the number of time slots allocated to the i-th spot beam, and W represents the set time window; represents the spatial interval between spot beams, r represents the radius of the spot beam, and B i represents the i-th spot beam, B j represents the jth spot beam; P i represents the power allocated to the i-th spot beam, P total Indicates total power; represents the spot beam frequency resource, p w Indicates the overall frequency resources of the system.

[0091] Furthermore, the transformed graph constraint expression is:

[0092]

[0093] Among them, L num Indicates the number of input images set in the GAN network, L vec-x Indicates the horizontal size of the input image, Lvec-y represents the vertical size of the input image, W represents the set time window, B i represents the i-th spot beam, Represents the frequency parameter of the i-th spot beam.

[0094] In step S107, in order to achieve fine-grained continuous optimization and improve the overall generalization ability of the optimization process to adapt to the service requirements of various user cells, the generator of the pre-trained generative adversarial network of the overall input value of all two-dimensional images obtained by segmentation of the same three-dimensional histogram is optimized, the optimized resource allocation map is output, and the resource scheduling histogram is re-stacked, and the time slot resource scheduling of each point beam is performed according to the resource scheduling histogram to achieve fine-grained continuous optimization.

[0095] Specifically, in some embodiments, the pre-training step of generating an adversarial network includes steps S201 to S202:

[0096] Step S201: Obtain a training sample set, which includes multiple samples. Each sample includes multiple two-dimensional pictures obtained by cutting the three-dimensional bar chart according to each time slot. The three-dimensional bar chart is established based on the existing beam-hopping wireless resource scheduling data with the time slot as the X-axis, the point beam number as the Y-axis, and the point beam frequency as the Z-axis. The horizontal quantity of the two-dimensional picture represents the beam number, and the vertical quantity of the two-dimensional picture represents the point beam frequency.

[0097] Step S202: construct and initialize the generator network and the discriminator network, and use the training sample set to train the generator network and the discriminator network.

[0098] The generator network updates and iterates by minimizing the first loss function. The expression of the first loss function is:

[0099]

[0100] Among them, z i represents the input of the generator network, G(z i ) represents the output of the generator network, D(G(z i )) represents the output of the discriminator network.

[0101] The discriminator network updates and iterates by maximizing the second loss function and minimizing the output. The expression of the second loss function is:

[0102]

[0103] Among them, x i represents the input of the discriminator network, represents the output of the generator network.

[0104] In some embodiments, the generator network and the discriminator network use gradient descent method to update parameters.

[0105] In some embodiments, the generator network and the discriminator network use the Adam optimizer to update parameters during the pre-training process.

[0106] On the other hand, the present invention also provides a low-orbit satellite wireless resource scheduling device based on resource graph and adversarial learning, including a processor and a memory, wherein the memory stores computer instructions, and the processor is used to execute the computer instructions stored in the memory. When the computer instructions are executed by the processor, the device implements the steps of the above method.

[0107] On the other hand, the present invention further provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the above method when executed by a processor.

[0108] The present invention will be described below in conjunction with specific embodiments:

[0109] This embodiment performs architecture analysis and problem modeling on beam-hopping satellite wireless resources, and analyzes the characteristics of multi-dimensional resources changing with time slots. Then, multiple application scenarios and multiple objective functions are integrated, and resource allocation strategies based on indicators such as fairness and service weight are considered based on maximum throughput, and objective functions are solved and simulation results are analyzed. Finally, optimization is performed through generative adversarial networks to obtain fine-grained and accurate resource allocation strategies.

[0110] In this embodiment, Figure 1 As shown, the specific process is as follows:

[0111] Step 1: Construction of wireless resource model of “time-frequency-space-machine” satellite Internet beam-hopping system

[0112] A communication model of the beam-hopping access scheme system combining a wide beam of a low-orbit satellite with a dynamic spot beam is established. The satellite antenna transmits two types of beams, a wide beam and a spot beam. By adopting a scheme in which wide beams and spot beams cooperate with each other, that is, beam-hopping switching under the auxiliary guidance of wide beams, broadband communication in the low-orbit satellite coverage area is completed. The resource scheduling scenario of the satellite communication system is shown in the figure. The satellite communication system consists of M multi-beam communication satellites, which dynamically cover ground users, and there is a certain overlap between the coverage areas of different satellite beams. The area that the system can cover is divided into N ground areas, and the communication tasks are attributed to different ground areas according to the location of the initiating user.

[0113] When beam hopping technology is used, the beam hopping period is usually in the second range. Therefore, the spatial distribution of service requests in the coverage area can be regarded as static and unchanged during the beam hopping period. Based on the above considerations, the present invention mainly describes the on-board resource scheduling problem within a beam hopping period. Set the time window for satellite resource allocation to Tw i , the satellite communication resources are scheduled with the time window length as the granularity, and Tw1 represents the time window of the current beam resource allocation, Tw2 represents the time window of the next beam resource scheduling, and the start and end times of the time window are ST i and E.T. i The time window is further divided into N k A resource scheduling window is the maximum allocation unit of a task, and each resource scheduling window lasts for K time slots.

[0114] Taking a specific beam coverage cell as an example, a wide beam is composed of 9 user cells, while a spot beam allocates coverage resources to a single user cell. The space resources of the satellite system are beam resources, which are divided according to beams. Each beam contains time and frequency resources, that is, each beam contains RB (Resource Block, 12 consecutive subcarriers in frequency) within the system, and is allocated in units of time windows according to the allocation strategy based on the needs of ground users. In this way, multi-dimensional joint resource allocation of the satellite communication system is realized. Because resources are allocated in the time window Tw i In the example, time slots are used as time units to divide the time window, so each time window Tw i The total length is W, that is, each time window contains W time slots; N i is the i-th spot beam B f The number of allocated time slots, i.e. N i is the time slot resource in the resource model; p i represents the frequency parameter. Then the overall resource model E i The mathematical model is expressed as:

[0115] E i =f{(p i , B i , N i ), i≤i max};

[0116] According to the satellite coverage model, each wide beam C i It is divided into n areas corresponding to the coverage position (wave position) of the satellite spot beam, and each spot beam coverage area is defined as a user cell, denoted by B n Each user in the user cell uses u ijwhere i represents the number of wave numbers, j represents the user number, and the number of users in each user cell is q f , then j = 1, 2, 3...q f In each user cell, the user positions are randomly distributed. The users in the satellite coverage area follow a two-dimensional normal distribution. Suppose the ground cell B n In the ij Location by its location To express it, and In contrast, their probability density function is:

[0117]

[0118] Among them, user u ij Location It obeys a two-dimensional normal distribution with mean μ1 and μ2, variance σ1 and σ2, and ρ=0. The variance describes the degree of dispersion of users in the cell. For the service demand intensity of users in each user cell, this embodiment assumes that it is only related to the number of users, and the number of users obeys the user distribution, that is, the two-dimensional normal distribution. In addition, the user service demand intensity is also related to the service priority w i Therefore, the user traffic demand intensity can be expressed as:

[0119]

[0120] Step 2: Differentiated service assurance constraints based on multi-objective optimization functions - wireless resource scheduling

[0121] In the time window Tw i In the example, the number of spot beams for each satellite is S, and each spot beam is denoted by B. i Since full frequency reuse is adopted and the channel differences between different users in the beam are averaged, it is used as the channel capacity parameter of the corresponding wave position of the beam. In each time slot, for the convenience of modeling, the idealized model of Shannon flux is used to approximate the channel capacity resources provided by the satellite beam to each ground cell:

[0122]

[0123] in, is the actual amount of traffic allocated to the corresponding wave position of the nth spot beam, that is, the channel capacity parameter, N max is the number of spot beams working in each time slot in the beam hopping system; W is the total length of the set time window; N i is the number of time slots allocated to the i-th spot beam, B is the bandwidth of the beam-hopping system, log2(1+SINR ij) is the spectral efficiency of the i-th spot beam in the j-th time slot, SINR ij is the signal-to-noise ratio of the i-th spot beam in the j-th time slot.

[0124] The resource scheduling algorithm of this embodiment takes the maximum throughput of the system as the optimization goal and establishes the following maximum throughput objective function:

[0125]

[0126]

[0127] When the traffic volume of ground cell users is small but urgent, such as emergency communication, sudden business, etc., if the maximum system throughput is still used as the principle, fewer resources will be allocated and the business needs of the ground cell will not be met. Therefore, we introduce the weight objective function. On the basis of the maximum system throughput, the user services are compared to determine the priority of each service, and then different weight values ​​w are set. i (The setting of weight values ​​should be analyzed according to specific business scenarios) to meet the special needs of ground users. Therefore, it is necessary to list the corresponding priority weight objective function according to the system scenario and business needs, by combining the system and the above-mentioned constraints as follows:

[0128]

[0129]

[0130] in, Indicates the user traffic demand intensity of the corresponding wave position of the nth spot beam, is the actual allocated traffic volume of the nth spot beam corresponding to the wave position, N max is the number of spot beams working in each time slot in the beam hopping system; W is the total length of the set time window; N i is the number of time slots allocated to the i-th spot beam, N * Represents a positive integer.

[0131] Step 3: Establishing the wireless resource map of beam-hopping satellite communication

[0132] Located in Community B covered by 6G Internet satellite n In the example, the number of hopping beams of a single satellite is S. Each beam adopts full frequency multiplexing, and its frequency parameter P is i , in each time slot, for the convenience of modeling, the channel capacity provided by the satellite to each cell is approximated by the ideal Shannon capacity:

[0133]

[0134] Where B is the bandwidth of the beam-hopping system, log2(1+SINR ij ) is the spectrum efficiency, SINR ij is the signal-to-noise ratio of the ith cell in the jth time slot. The division of each beam is the division of spatial resources, so the beams are distinguished by the ground cell number covered by each beam, that is, beam C i It is the spatial resource in the resource model.

[0135] When the resource allocation problem focuses on a time window Tw i The center-to-point beam corresponds to the wave position B n In the scenario, the satellite obtains the service request volume of each cell and channel allocation capacity Allocate beam time slot N on the Y axis i The resource allocation problem in a time window can be graphically represented as follows: Figure 2 As shown, a three-dimensional bar graph w is established mod , each wave position B n Different columns are used to distinguish the time slot resources N of the wave position. i It is reflected as the width of the column, the frequency resource P i It is reflected in the height of the column, and the spatial resources are reflected between each beam.

[0136] Step 4: Mapping of beam-hopping satellite communication radio resource constraints and graph processing constraints

[0137] By graphing the satellite on-board resource model, a three-dimensional beam-hopping satellite communication wireless resource model w can be obtained. mod The beam hopping technology uses time slicing technology to optimize the on-board power and bandwidth resources in the time domain, and allocates the entire satellite on-board resources to each beam in units of time slots. Since the generative adversarial network uses images as input, it can be based on the unit time slot N. i 3D resource model mod Two-dimensional image cutting is performed as input, based on which there is a mapping relationship between the beam-hopping satellite communication wireless resource constraints and the spectrum processing constraints, and the two-dimensional image is constrained and adjusted based on the spectrum constraints obtained after mapping.

[0138] The beam-hopping satellite communication wireless resource constraint condition expression is:

[0139]

[0140] Among them, N i represents the number of time slots allocated to the i-th spot beam, and W represents the set time window; represents the spatial interval between spot beams, r represents the radius of the spot beam, and B i represents the i-th spot beam, B j represents the jth spot beam; P i represents the power allocated to the i-th spot beam, P total Indicates total power; represents the spot beam frequency resource, p w Indicates the overall frequency resources of the system.

[0141] The expression of the graph constraint condition is:

[0142]

[0143] Among them, L num Indicates the number of input images set in the GAN network, L vec-x Indicates the horizontal size of the input image, L vec-y represents the vertical size of the input image, W represents the set time window, B i represents the i-th spot beam, Indicates the frequency parameter of the i-th spot beam. In this embodiment, the time window W is set to 16 time slots, and the resource scheduling diagram is cut according to the unit time slot, so C4 indicates that the number of input picture sets is 16; the division of the spot beam is based on the coverage of the ground cell, and N = 16, so C5 indicates that the horizontal amount of the input picture is 16 units; and because full frequency reuse is adopted, the frequency resource P i It is divided into 16 frequency bands, so the image constraint is: C6 means that the vertical volume of the input image is 16 units.

[0144] Step 5: Optimal processing of wireless resource graph based on adversarial learning

[0145] By using the three-dimensional model mod According to time slot N i To perform two-dimensional image cutting, it means that in each unit time slot, each cell B n The resource scheduling algorithm is used to take the obtained two-dimensional image as the input of the GAN network. After the GAN network is optimized, the resource allocation diagram of the GAN network for each time slot can be obtained. Then, the two-dimensional images are stacked by Matlab to obtain an optimized time window Tw i Resource scheduling bar chart within.

[0146] Among them, the pre-training steps of the GAN network include:

[0147] Acquire a training sample set, wherein the training sample set includes a plurality of samples, each sample includes a plurality of two-dimensional images obtained by cutting a three-dimensional bar graph according to each time slot, the three-dimensional bar graph is established based on existing beam hopping wireless resource scheduling data with the time slot as the X-axis, the spot beam number as the Y-axis, and the spot beam frequency as the Z-axis, the horizontal amount of the two-dimensional image represents the beam number, and the vertical amount of the two-dimensional image represents the spot beam frequency;

[0148] Initialize the satellite beam hopping resource allocation scenario and initialize the discriminator network (D) parameters (θ d for D), initialize the generator network (G) parameters

[0149] Among them, the training of the discriminator network includes:

[0150] 1) Extract training sets from existing data. Specifically, according to the resource allocation diagram in a time window calculated by selecting the objective function and its constraints, perform two-dimensional image segmentation to obtain the training set. (1) , x (2) , x (3) …} as an intrinsic parameter indicator of the discriminator network.

[0151] 2) Take random noise of the same dimension as the input of the generator network, the image is in the form of {z (1) , z (2) , z (3) …}

[0152] 3) Get data from the output of the generator network Input to the D network.

[0153] 4) Update the parameters θ of the discriminator network d To maximize The bigger the better, and The smaller the better, using the loss function and gradient descent method for training, the expression is:

[0154]

[0155] The gradient descent method updates the discriminator network parameter expression as follows:

[0156]

[0157] The training of the generator network includes:

[0158] 1) Extract training sets from existing data. Specifically, according to the resource allocation graph within a time window calculated by selecting the objective function and its constraints, perform two-dimensional image cutting to obtain the training set as the input of the generator network. The image format is {z (1), z (2) , z (3) …}

[0159] 2) Update the parameters of the G network To minimize it, use the loss function and gradient descent method to train, the expression is:

[0160]

[0161] The gradient descent method updates the generator network parameter expression as follows:

[0162]

[0163] Combined solution to get N i That is, each wave position B n The number of allocated time slots, so N i That is the required optimization goal. By adjusting the parameters of the generative adversarial network, the generated probability distribution is as close as possible to the real data distribution. The loss function of the designed GAN network is:

[0164]

[0165] in, and Represents the probability of real data and generated data.

[0166] By adjusting the network parameters θ of the GAN network d and To make the value of the loss function L(G, D) smaller and smaller, the robustness of the entire algorithm is better, and then the prediction value of the generative adversarial network is calculated by the loss function formula and the actual value N i The difference between them is used to update all the parameters of the generated adversarial network θ through back propagation d and This can reduce the difference between the true value and the predicted value, making the predicted value generated by the GAN network The actual time slot allocation N i Get closer, thereby optimizing the overall resource allocation strategy.

[0167] Step 6: Conversion between optimal processing of wireless resource graph and wireless resource scheduling for beam-hopping satellite communication

[0168] Through the optimization of the GAN network, each time slot N i The optimal graph within each time slot N i The resource allocation diagram is used to stack two-dimensional images, and then a time window Tw is obtained after optimization by the GAN network. iThe resource scheduling histogram in the input graph is cut in two dimensions according to the unit time slot, so the optimal graph is cut in two dimensions according to the time slot N. i The optimal resource allocation diagram can be obtained by two-dimensional stacking. The optimal two-dimensional top view of resources and the top view before optimization are analyzed for time slots to determine the beam time slot N of each cell for the generative adversarial network. i The optimization degree is to set the time slot N i Combined with the wave position resource traffic formula, the optimized wave position B can be obtained n Actual allocated business volume This enables the generative adversarial network to transform from graph optimization to optimal resource scheduling optimization, which can solve the problems of ever-changing low-orbit 6G satellite Internet service scenarios and numerous business types.

[0169] This embodiment can significantly improve the utilization rate of satellite system resources within a time window, balance the user satisfaction of each cell, and thus adapt to the changing service scenarios of satellites.

[0170] In summary, the low-orbit satellite wireless resource scheduling method and device based on resource map and adversarial learning described in the present invention, based on the application scenario of beam hopping technology, first uses the periodic prior information of the satellite network to establish constraints based on the maximum throughput and priority requirements, and preliminarily solves the number of time slots allocated to each spot beam; a three-dimensional bar graph of wireless network resource scheduling is established with time slots, spot beam numbers and spot beam frequencies as parameters, and an infinite resource map is constructed by cutting the time slots into two-dimensional pictures, and the overall time slot allocation scheduling is optimized for the two-dimensional pictures obtained by cutting through a pre-trained generative adversarial network, and the advantages of the image in the continuous and explicit color processing process are utilized, and the processing of the wireless resource map is used to achieve fine-grained optimization, thereby improving the accuracy of the resource allocation strategy.

[0171] Corresponding to the above method, the present invention also provides an apparatus / system, which includes a computer device, the computer device includes a processor and a memory, the memory stores computer instructions, the processor is used to execute the computer instructions stored in the memory, and when the computer instructions are executed by the processor, the apparatus / system implements the steps of the method described above.

[0172] The embodiment of the present invention also provides a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the steps of the aforementioned edge computing server deployment method are implemented. The computer-readable storage medium can be a tangible storage medium, such as a random access memory (RAM), a memory, a read-only memory (ROM), an electrically programmable ROM, an electrically erasable programmable ROM, a register, a floppy disk, a hard disk, a removable storage disk, a CD-ROM, or any other form of storage medium known in the technical field.

[0173] It should be understood by those skilled in the art that the exemplary components, systems and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software or a combination of the two. Whether it is performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention. When implemented in hardware, it can be, for example, an electronic circuit, an application specific integrated circuit (ASIC), appropriate firmware, a plug-in, a function card, etc. When implemented in software, the elements of the present invention are programs or code segments used to perform the required tasks. The program or code segment can be stored in a machine-readable medium, or transmitted on a transmission medium or a communication link via a data signal carried in a carrier.

[0174] It should be clear that the present invention is not limited to the specific configuration and processing described above and shown in the figures. For the sake of simplicity, a detailed description of the known method is omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present invention is not limited to the specific steps described and shown, and those skilled in the art can make various changes, modifications and additions, or change the order between the steps after understanding the spirit of the present invention.

[0175] In the present invention, features described and / or illustrated for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with features of other embodiments or replace features of other embodiments.

[0176] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the embodiments of the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for scheduling low-orbit satellite wireless resources based on resource graph and adversarial learning, characterized in that: For the beam hopping access scenario of a low-orbit satellite wide beam combined with a dynamic spot beam, the method includes the following steps: A wide beam is used to cover multiple user cells, and each user cell is covered by a spot beam. Satellite resources are allocated according to a set time window as the granularity. The set time window is divided into a set number of time slots, and time slot resources are allocated to each spot beam. Users in each user cell obey a two-dimensional normal distribution, and the user traffic demand intensity is determined based on user distribution and service priority. Based on full frequency reuse, the channel differences of multiple users served by each spot beam are averaged, and the channel capacity parameters provided by each user cell are approximately expressed by the idealized model of Shannon flux. The calculation formula is: in, is the actual amount of traffic allocated to the corresponding wave position of the nth spot beam, that is, the channel capacity parameter, N max is the number of spot beams working in each time slot in the beam hopping system; W is the total length of the set time window; N i is the number of time slots allocated to the i-th spot beam, B is the bandwidth of the beam-hopping system, log2(1+SINR ij ) is the spectral efficiency of the i-th spot beam in the j-th time slot, SINR ij is the signal-to-noise ratio of the i-th spot beam in the j-th time slot; Setting a priority weight value for each user cell according to the service priority of each user cell; According to the user traffic demand intensity, channel capacity parameters and priority weight value of each user cell, the service priority demand is introduced to establish constraints on the basis of maximizing throughput, and the number of time slots allocated to the corresponding point beam of each user cell is solved; In a set time window, a three-dimensional bar graph is established with the time slot as the X-axis, the spot beam number as the Y-axis, and the spot beam frequency as the Z-axis, and the three-dimensional bar graph is cut into two-dimensional pictures according to each time slot, wherein the horizontal quantity of the two-dimensional picture represents the beam number, and the vertical quantity of the two-dimensional picture represents the spot beam frequency; Converting beam-hopping satellite communication wireless resource constraints into graph constraints, and performing constraint adjustments on the two-dimensional image; Input all two-dimensional images obtained by cutting a single three-dimensional histogram into the generator of a pre-trained generative adversarial network, output an optimized resource allocation map, and stack each resource allocation map according to the corresponding time slot to obtain a resource scheduling histogram, so as to perform time slot resource scheduling for each spot beam according to the resource scheduling histogram; Among them, according to the user traffic demand intensity, channel capacity parameters and priority weight value of each user cell, the service priority demand is introduced on the basis of maximizing the throughput to establish constraints, including: Establish the maximum throughput objective function, the expression is: Establish the priority weight objective function, the expression is: in, Indicates the user traffic demand intensity of the corresponding wave position of the nth spot beam, is the actual allocated traffic volume of the nth spot beam corresponding to the wave position, N max is the number of spot beams working in each time slot in the beam hopping system; W is the total length of the set time window; N i is the number of time slots allocated to the i-th spot beam, N * represents a positive integer; The beam-hopping satellite communication wireless resource constraint condition expression is: Among them, N i represents the number of time slots allocated to the i-th spot beam, and W represents the set time window; represents the spatial interval between spot beams, r represents the radius of the spot beam, and B i represents the i-th spot beam, B j represents the jth spot beam; P i represents the power allocated to the i-th spot beam, P total Indicates total power; represents the spot beam frequency resource, p w Indicates the overall frequency resources of the system; The expression of the graph constraint condition is: Among them, L num Indicates the number of input images set in the GAN network, L vec-x Indicates the horizontal size of the input image, L vec-y represents the vertical size of the input image, W represents the set time window, B i represents the i-th spot beam, represents the frequency parameter of the i-th spot beam; The pre-training step of the generative adversarial network includes: Acquire a training sample set, wherein the training sample set includes a plurality of samples, each sample includes a plurality of two-dimensional images obtained by cutting a three-dimensional bar graph according to each time slot, the three-dimensional bar graph is established based on existing beam hopping wireless resource scheduling data with the time slot as the X-axis, the spot beam number as the Y-axis, and the spot beam frequency as the Z-axis, the horizontal amount of the two-dimensional image represents the beam number, and the vertical amount of the two-dimensional image represents the spot beam frequency; Constructing and initializing a generator network and a discriminator network, and using the training sample set to train the generator network and the discriminator network; The generator network is updated and iterated by minimizing the first loss function, and the expression of the first loss function is: Among them, z i represents the input of the generator network, G(z i ) represents the output of the generator network, D(G(z i )) represents the output of the discriminator network; The discriminator network updates and iterates by maximizing the second loss function and minimizing the output. The expression of the second loss function is: Among them, x i represents the input of the discriminator network, represents the output of the generator network.

2. The method for scheduling low-orbit satellite wireless resources based on resource graph and adversarial learning according to claim 1 is characterized in that: The generator network and the discriminator network use the gradient descent method to update parameters.

3. According to claim 2, the method for scheduling low-orbit satellite wireless resources based on resource graph and adversarial learning is characterized in that: The generator network and the discriminator network use the Adam optimizer to update parameters during the pre-training process.

4. A low-orbit satellite wireless resource scheduling device based on resource map and adversarial learning, comprising a processor and a memory, characterized in that: The memory stores computer instructions, and the processor is used to execute the computer instructions stored in the memory. When the computer instructions are executed by the processor, the device implements the steps of the method as claimed in any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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