A routing method for large-scale LEO constellations
By adopting a location-aware distributed routing algorithm in the LEO constellation network and combining SVF and PVF for path convergence, the problems of poor robustness and high resource overhead of traditional routing algorithms in large-scale LEO constellations are solved, and efficient path selection and energy management are achieved.
Patent Information
- Application Number
- CN202111563390.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-12-20
- Publication Date
- 2025-09-30
- Estimated Expiration
- 2041-12-20
AI Technical Summary
Traditional LEO constellation network routing algorithms have problems such as poor robustness, high resource overhead, low routing efficiency in large-scale LEO constellations, and difficulty in determining the destination node of the reverse link.
A location-aware distributed routing algorithm is adopted to converge paths through a path preselection mechanism, state vector function (SVF), and propagation vector function (PVF). Two to three sending ports are preselected, and primary and backup paths are selected based on QoS requirements.
It reduces routing storage and overhead, improves throughput, reduces end-to-end delay, and enhances network robustness and energy efficiency.
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Figure CN116366120B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of satellite network routing and satellite communication technology, and in particular to a routing selection method applicable to large-scale LEO constellations. Background Art
[0002] With the rapid development of space information technology, low Earth orbit (LEO) satellite communication systems are playing an increasingly important role in global communications, navigation and positioning, weather forecasting, disaster monitoring, and military applications. As one of the key technologies of LEO satellite communication networks, inter-satellite routing algorithms are the core factor in improving the performance of the entire satellite communication network.
[0003] Currently, the common approach to topology partitioning for low-Earth orbit (LEO) satellite constellations is to leverage the periodicity and predictability of their operations to virtualize the constellation network topology temporally. This divides the constellation's operating cycle into several time segments, with the constellation system topology remaining unchanged within each time segment. Satellites employ static routing. Ground-based measurement and control systems pre-compute routing tables using known topology information and inject them into the measurement and control link. Satellites then switch routing paths based on system time and the time-sliced routing table. However, this topology partitioning approach, which decouples the constellation network from the ground network, presents the difficulty of determining the destination node for the reverse link (from user to gateway). Furthermore, due to the large number of ground gateways, the issue of gateway service area demarcation and satellite feeder link relaying between adjacent gateways, solely considering the topological changes of the satellite constellation network fails to truly reflect the overall network topology (inter-satellite and satellite-to-ground) and the actual connectivity of the links. Traditional constellation routing algorithms, when applied to large-scale LEO constellations, suffer from poor robustness, high resource overhead, and low routing efficiency. Therefore, designing a routing selection method suitable for large-scale LEO constellations has become increasingly important. Summary of the Invention
[0004] The present invention addresses the aforementioned shortcomings of the prior art and provides a routing method suitable for large-scale LEO constellations. Based on the predictable position of satellites during operation, a location-aware distributed routing algorithm is proposed. Taking into account the limited resources, numerous satellite nodes, and high dynamics of satellites, a location-aware path preselection mechanism is proposed to preliminarily determine the transmission path for data packets. Based on this, and taking into account service QoS requirements, a path convergence mechanism is proposed based on state and propagation vector functions to determine the primary and backup paths for data packet transmission without overlap.
[0005] The present invention is applicable to a technical solution for a routing method for a large-scale LEO constellation, and mainly includes the following two stages:
[0006] (1) Route preselection phase: Based on the predictability of satellite operating positions, each satellite preselects two to three sending ports when transmitting data packets. During this process, each satellite only needs to store the orbital parameters of surrounding satellites, and the storage space occupied is not affected by the size of the constellation.
[0007] (2) Path convergence stage: The pre-selected path is converged based on the State Vector Function (SVF) and the Propagation Vector Function (PVF).
[0008] SVF avoids network congestion and reduces queuing delays. PVF uses a path convergence process to select the better of two independent paths as the primary path and the backup path based on QoS requirements, improving routing robustness and throughput.
[0009] The present invention provides a routing method applicable to a large-scale LEO constellation, comprising the following steps:
[0010] S1 builds the LEO satellite network and updates the link status information database of the entire LEO satellite network, including the six orbital numbers i, Ω, e, ω, a, and M0;
[0011] S2 route preselection: Based on the predictability of satellite operating positions, each satellite preselects the sending port when transmitting data packets;
[0012] S2.1 Calculate satellite v i,j The surrounding satellites v x,y The position information at time t is expressed as follows:
[0013]
[0014] Where, P calc It is a function for calculating the longitude and latitude of the sub-satellite point with the six orbital numbers as parameters;
[0015] S2.2 Based on S2.1, the surrounding satellite v x,y The location information of the target satellite and the location information of the target satellite are used to calculate the location of each surrounding satellite v x,y The included angle with the target satellite is defined as the upper angle, lower angle, left angle and right angle according to the four directions of the surrounding satellites;
[0016] S2.3 takes all satellites with an angle less than 90° as next-hop objects and stores them in the set of candidate sending ports P, where P = [p, i], where p is the candidate sending port, p = U, D, L, R, and i is the angle.
[0017] S3 path convergence: The routing path is converged through the queuing factor SVF and the energy factor PVF.
[0018] S3.1 After receiving the routing request packet RREQ, the intermediate satellite calculates the next hop location information with the shortest queue time among the candidate sending ports p, writes it into the routing request packet RREQ, and sends the routing request packet RREQ to the port with the shortest queue time;
[0019] The S3.2 intermediate satellite iterative convergence process is performed until the destination satellite DST receives the routing request packets RREQ from two paths. During the S3.2 intermediate satellite iterative convergence process, if a convergence collision occurs, that is, when the routing request packet RREQ is transmitted to the same intermediate satellite, a main transmission path and a backup path are selected from the two colliding paths according to the energy factor PVF.
[0020] S3.3 converges the path from DST to SRC based on the energy factor PVF, that is, selects the path with the lowest residual energy and the highest value as the main path, and the other as the backup path, and replies the routing reply packet RREP along the two paths.
[0021] The queuing factor SVF is formulated as follows:
[0022]
[0023] Where, The satellite v is calculated by formula (7) x,y Queuing delay at ports U, D, L, and R; e u is a basis vector, which is orthogonal to the other four basis vectors; w x,y Satellite v x,y of the remaining energy.
[0024] The energy factor PVF is as follows:
[0025]
[0026] Where, Indicates satellite v x,y The propagation function of port C, where C represents any of the four ports of the satellite; f lh Represents the previous hop propagation vector function of the current satellite, f SRC represents the propagation vector function of the source satellite, . Equation (8) calculates the queuing delay at port C, w lh Indicates the remaining energy of the previous hop of the current satellite, e c , e are two mutually orthogonal bases.
[0027] Due to the adoption of the above technical solution, the present invention has the following beneficial effects compared with the prior art:
[0028] The routing selection method provided by the present invention is applicable to large-scale LEO constellations. Compared with traditional routing algorithms, it reduces routing storage and overhead, improves constellation throughput and reduces end-to-end delay as the interruption probability increases.
[0029] The queuing factor reduces the queuing delay and balances the network load, while the energy factor reduces the further consumption of satellites with relatively less energy and extends the operating time of the constellation.
[0030] The proposed path convergence strategy based on SVF and PVF, in addition to adopting queuing factor and energy factor, can also select factors such as end-to-end delay, routing hops, and link failure rate according to service QoS requirements. BRIEF DESCRIPTION OF THE DRAWINGS
[0031] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:
[0032] Figure 1 Schematic diagram of large-scale LEO constellation topology and satellite node definition of the present invention.
[0033] Figure 2 This is a schematic diagram of the data packet arrival time and data packet size of the present invention.
[0034] Figure 3 This is a positional relationship diagram of SRC and DST in the present invention.
[0035] Figure 4 This is a schematic diagram of SVF convergence without collision in the present invention.
[0036] Figure 5 This is a schematic diagram of SVF convergence collision in the present invention.
[0037] Figure 6 Processing SVF convergence collision process for satellite v2,2 of the present invention. DETAILED DESCRIPTION
[0038] The following is a detailed description of an embodiment of the present invention. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process. It should be noted that those skilled in the art may make various modifications and improvements without departing from the scope of the present invention, and these modifications and improvements fall within the scope of protection of the present invention.
[0039] The present invention adopts the polar orbit constellation (walker constellation) widely used in LEO constellations, and defines the constellation as an undirected graph G = (V, E), where V represents the satellite node, which is defined as V = {v 1,1 ,v 1,2 ,…,v 2,1 ,v 2,2 ,…,v n,m}, where n represents the orbit number and m represents the satellite number within the orbit. There are n*m satellites in the constellation, n orbits, and m satellites in each orbit. Each orbit is distributed at the same angular distance on the equator, and the phase difference of the satellites on each orbit is 2π / m. E represents the inter-satellite link in the constellation. Due to the reverse gap, the satellite in the first orbit and the satellite in the nth orbit cannot establish an inter-satellite link even though they are adjacent. The satellites in the first orbit and the nth orbit can only establish an inter-satellite link with the three adjacent satellites. Each of the remaining satellites can establish an inter-satellite link with the four surrounding satellites. Satellite v in the constellation n,m The intersatellite link representation is x represents v n,m The direction of the intersatellite link, x = {U, D, L, R} represents v n,m The intersatellite links in the four directions of up, down, left and right are shown in the constellation diagram. Figure 1 As shown in the figure, the satellite node v 2,2 Can communicate with satellite nodes in the same orbit 2,1 and v 2,3 Establish the upper and lower links, denoted as and , satellite node v 2,2 With satellite node v 1,2 and v 3,2 Establish the left and right links, denoted as and .
[0040] The traditional FIFO queuing model queues services in the order of arrival, with the first-in-first-out packets being the first-out packets, regardless of packet size. This invention improves the FIFO queuing rule, where the dequeuing rule is not only related to the time of entry, but also to the size of the packet and the transmission rate of the packet. The expression used for the dequeuing order is:
[0041] t e =t i +pkg / v (1)
[0042] Where, t i is the packet enqueuing time, v is the packet transmission rate, and pkg is the packet size. e Data packets with smaller values are dequeued first.
[0043] According to this rule, the calculation expression of the queuing delay of different data packets is as follows:
[0044]
[0045] In the formula, te i <te represents the t value of the data packet pkg calculated by formula (1) in the satellite, which is less than the t value of the data packet pkg. Δt represents the time that the data packet being transmitted has been transmitted when pkg joins the queue. For example, i the t e value, and the t e value of pkg2. As shown in Figure 1 the satellite node v 2,2 in, there are four data packets queuing at a sending port. The queueing times of the four data packets are as Figure 2 shown. It can be seen from formula (2) that the queuing delay of the data packet pkg3 is (pkg 1+ pkg 4+ pkg2) / v-(T1-T0), and the queuing delay of pkg2 is (pkg 1+ pkg4) / v.
[0046] The defined constellation throughput rate expression is:
[0047] <l
[0048] In the formula, Rcv ij is the amount of service data received by satellite v i,j as the destination node, T Rend is the moment when the data packet reception in the constellation ends, and T Rstart is the moment when there is a satellite receiving data in the constellation.
[0049] For a satellite network with limited resources, the routing overhead is another key indicator for evaluating routing algorithms. The routing overhead of this invention is defined as follows:
[0050]
[0051] [[ID=SB]]In the formula, P c represents the number of routing control packets in the constellation, and P d represents the total number of data packets received by the destination satellite.
[0052] The following further illustrates the technical solution provided by this invention in conjunction with a specific embodiment.
[0053] A routing selection method applicable to a large-scale LEO constellation is divided into the following stages:
[0054] Route preselection: Based on the predictability of satellite operating positions, each satellite preselects two to three sending ports when transmitting data packets. During this process, each satellite only needs to store the orbital parameters of surrounding satellites, and the storage space occupied is not affected by the size of the constellation.
[0055] During the operation of the satellite, the satellite can obtain its own position information through orbit prediction and real-time orbit determination. i,j The longitude and latitude corresponding to the subsatellite point at time t are recorded as Satellite v i,j The position information of surrounding satellites can be obtained in two ways: the first is to obtain it from the HELLO packets periodically sent by surrounding satellites; the second is to store the orbital parameters of surrounding satellites in v in advance based on the predictable characteristics of satellite movement positions. i,j In the formula (5), the latitude and longitude of the surrounding satellites are calculated in real time, where i, Ω, e, ω, a, and M0 are the six orbital numbers. v i,j The surrounding satellites v x,y The latitude and longitude at time t.
[0056]
[0057] Based on the latitude and longitude information of the source satellite (SRC) and the destination satellite (DST), combined with the real-time predictability of the satellite's operating position, a reliable transmission path can be established in real time when business data needs to be transmitted. Figure 3 As shown, at time t, if there is service data to be sent to DST, the longitude and latitude of SRC in the constellation are The longitude and latitude of DST are SRC is calculated by formula (5) Figure 3 The latitude and longitude of the SRC_U, SRC_D, SRC_L, and SRC_R satellites in the equation are: Figure 3 ∠α1 in .
[0058]
[0059] The same method is used to obtain the values of ∠β1, ∠η1, and ∠γ1. SRC selects the next hop based on the values of ∠α1, ∠β1, ∠η1, and ∠γ1. We use 90° as the threshold angle for selecting the next hop. Figure 3If ∠η1 and ∠γ1 are greater than 90°, SRC_L and SRC_D are not considered as the next-hop satellites for SRC. If ∠α1 and ∠β1 are less than 90°, SRC_U and SRC_R can be considered as the next-hop satellites for SRC. When selecting the next-hop satellite from SRC to DST, the intermediate node also selects a satellite with an angle less than 90° as the next-hop. The above process is iterated to transmit the routing request packet (RREQ) to DST. In the routing preselection mechanism, during the transmission of the RREQ from the source satellite to the destination satellite, each satellite will transmit the RREQ to one or two next-hop satellites, resulting in a large number of RREQs being transmitted in the constellation, wasting link resources and limited satellite energy. Therefore, a path convergence mechanism is proposed.
[0060] Select the satellite with an angle less than 90° as the next hop. Figure 3 It can be seen that SRC has two satellites that meet this condition. The next hop of the intermediate satellite may also have one or two satellites, such as Figure 3 Two satellites around SRC_R satisfy this condition. If there are many intermediate nodes, each intermediate satellite generates two branches, and establishing the path consumes a lot of satellite energy. Therefore, the present invention converges the path during establishment to reduce unnecessary RREQ replication. Two factors are used to converge the path: the first factor is based on the queue length at the satellite port, referred to as the queue factor; the second factor is based on the energy status of satellite nodes along different paths, referred to as the energy factor.
[0061] The queuing factor uses SVF, with a convergence path from SRC to DST. The energy factor uses PVF, with a convergence path from DST to SRC.
[0062] The expression of SVF is:
[0063]
[0064] Where, The satellite v is calculated by formula (7) x,y Queuing delay at ports U, D, L, and R; e u is a basis vector, which is orthogonal to the other four basis vectors in the formula; w x,y Satellite v x,y of the remaining energy.
[0065] The expression of PVF is:
[0066]
[0067] Where, Indicates satellite v x,y The propagation function of port C, where C represents any of the four ports of the satellite; flh Represents the previous hop propagation vector function of the current satellite, f SRC Represents the propagation vector function of the source satellite. Equation (8) calculates the queuing delay at port C, w lh Indicates the remaining energy of the previous hop of the current satellite, e c , e are two mutually orthogonal bases.
[0068] First, the path is preselected, and then the path is converged by the queuing factor and energy factor to finally determine the data packet transmission path. To prevent the SRC satellite from having only one path from the DST satellite after SVF convergence, the queuing factor affects the convergence of the path on the intermediate satellites. Figure 3 As shown, SRC uses path preselection and does not use SVF for convergence, while RREQ uses and The two intersatellite links are sent. After the intermediate satellite receives the RREQ, taking SRC_R as an example, after pre-selecting the path, SRC_R uses SVF convergence and selects the better link from the pre-selected links to send the RREQ. The intermediate node iterates the SRC_R processing process until the RREQ is transmitted to the DST. According to the above process, the DST will receive RREQs from both paths. DST uses PVF to achieve the final convergence of the paths, determining one path as the main path and the other path as the backup path. The RREQ sent by the SRC satellite is added with the SRC PVF. After receiving the RREQ, the intermediate node updates the PVF according to formula (8), and finally transmits the PVF of the two paths to the DST. The DST compares the minimum energy of the intermediate nodes of the two paths, selects the path with the larger minimum energy as the main transmission path, and the other path as the backup path, and replies the routing response packet along the two paths. When the main path is congested or other link problems occur, the SRC uses the backup path to transmit service data. When the intermediate satellite on the path senses that the position change range of the next hop exceeds the range of the path pre-selection, it will send a path update packet to the SRC. The SRC will rebuild the primary path and backup path according to the above process.
[0069] When using the SVF convergence path, there is a convergence collision problem. That is, before the RREQ is transmitted to the destination satellite, two satellites converge through SVF and transmit the RREQ to the same satellite, resulting in only one path for the RREQ to reach the destination satellite.
[0070] Using the SVF convergence path will produce two convergence results. The first is that from SRC to DST, the two paths will not converge to the same intermediate satellite. The second is that a convergence collision occurs during the SVF convergence process, and the two paths converge to the same intermediate satellite before reaching DST. The first SVF convergence result is as follows Figure 4 As shown. From the source satellite v 1,1To the destination satellite v 3,3 , no SVF convergence collision occurs, and two independent paths are generated from SRC to DST.
[0071] The second convergence result of SVF is as follows Figure 5 Satellite v 2,1 With satellite v 1,2 When selecting the next hop, satellite v 2,2 , according to the SVF convergence mechanism proposed above, v 2,2 There is only one path from the satellite to the destination satellite, which results in the failure of the PVF convergence mechanism. In response to the SVF convergence collision problem, the present invention proposes an SVF convergence collision processing mechanism. Figure 5 The following example illustrates the SVF convergence collision handling process. Figure 5 Medium v 2,2 Satellite and v 3,3 Satellite, due to v 3,3 The satellite is DST. When a collision occurs between DST satellites, PVF is used to select a main transmission path and a backup path from the two collision paths. 2,2 After the satellite preselects the path and then uses SVF to converge the path, it will result in only one path reaching the DST satellite. Therefore, for the convergence collision that occurs at the intermediate node, the satellite v 2,2 For example, the SVF convergence collision processing process is as follows Figure 6 shown.
[0072] Assume that the satellite v that has SVF convergence collision 2,2 , select v after PVF convergence 2,1 As the previous hop. Convergence collision is handled as follows:
[0073] 1) When the intermediate satellite transmits the RREQ packet, the next hop location information that is not selected after SVF convergence is added to the RREQ packet. For example, Figure 5 Medium v 1,2 To v 2,2 The RREQ packet sent contains v 1,3 location information.
[0074] 2) According to the assumption, v 2,2 After the convergence of PVF, select v 2,1 For the previous hop, v 2,1 In the RREQ package v 2,3 The location information of v is deleted and the 1,2 In the RREQ package v 1,3 The location information is written into v 2,2 In the RREQ package.
[0075] 3) Colliding satellite v 2,2 , after the path preselection mechanism, send the 1,3 RREQ packet of position information to satellite v 2,3 and v 3,2 , v 2,3 Receive the RREQ packet of the convergence collision satellite, calculate the possible location information of the previous hop, and compare it with v 1,3 Compare the location information to confirm v 1,3 It is v 2,3 The previous hop is v 2,3 Set the previous hop to v 1,3 .
[0076] 4) Satellite v 3,2 Receive the RREQ packet of the satellite that has a convergence collision, and communicate with v 2,3 Same operation, but v 1,3 Not v 2,3 The previous hop, v 2,3 The previous hop is confirmed to be v 2,2 .
[0077] The LADSR algorithm first performs path preselection through location sensing. It then uses SVF and PVF to converge the path. Finally, a process is presented to address collisions during SVF convergence. The pseudocode for the LADSR algorithm is shown in Algorithm 1.
[0078]
[0079]
[0080] Among them, numbers 1-7 are path preselection, and numbers 8-19 are the path convergence using queuing factors and energy factors.
[0081] Experiments have shown that the path preselection and convergence mechanism we proposed reduces routing overhead. Each time the route is updated, each satellite only needs to complete the position calculation of the surrounding satellites and the path convergence calculation. The satellite's routing storage overhead mainly includes the six orbital numbers of the surrounding satellites and is independent of the size of the constellation. The computational overhead mainly includes the calculation and numerical comparison of the positions of the surrounding satellites. The queuing factor reduces the queuing delay and balances the network load. The energy factor reduces the further consumption of satellites with relatively less energy and extends the operating time of the constellation. The path convergence strategy based on SVF and PVF proposed in this invention, in addition to adopting the queuing factor and energy factor, can also select factors such as end-to-end delay, number of routing hops, and link failure rate according to the service QoS requirements.
[0082] Matters not mentioned in the above embodiments of the present invention are well known in the art.
[0083] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various variations or modifications within the scope of the claims, which do not affect the essence of the present invention.
Claims
1. A routing method suitable for large-scale LEO constellations, characterized in that: The following steps are involved: S1 builds the LEO satellite network and updates the link status information database of the entire LEO satellite network, including the six orbital numbers i, Ω, e, ω, a, and M0; S2 route preselection: Based on the predictability of satellite operating positions, each satellite preselects the sending port when transmitting data packets; S3 path convergence: The routing path is converged using the queuing factor (SVF) and the energy factor (PVF). The specific steps are as follows: S3.1 After receiving the routing request packet RREQ, the intermediate satellite calculates the next hop location information with the shortest queue time among the candidate sending ports p, writes it into the routing request packet RREQ, and sends the routing request packet RREQ to the port with the shortest queue time; S3.2 intermediate satellite iterative convergence processing is performed until the destination satellite DST receives the route request packets RREQ from both paths. During S3.2 intermediate satellite iterative convergence processing, if a convergence collision occurs, that is, when the route request packet RREQ is transmitted to the same intermediate satellite, a primary transmission path and a backup path are selected from the two colliding paths based on the energy factor PVF. S3.3 converges the path from DST to SRC based on the energy factor PVF, that is, selects the path with the lowest residual energy and the highest value as the main path, and the other as the backup path, and replies the routing reply packet RREP along the two paths.
2. The routing method for large-scale LEO constellations according to claim 1, wherein: The S2 route preselection includes the following specific steps: S2.1 Calculate satellite v i,j The surrounding satellites v x,y The position information at time t is expressed as follows: (5) Where, P calc It is a function for calculating the longitude and latitude of the sub-satellite point with the six orbital numbers as parameters; S2.2 The surrounding satellite v obtained according to S2.1 x,y The location information of the target satellite and the location information of the target satellite are used to calculate the location of each surrounding satellite v x,y The included angle with the target satellite is defined as the upper angle, lower angle, left angle and right angle according to the four directions of the surrounding satellites; S2.3 All satellites with an angle less than 90° are selected as next-hop targets and stored in the candidate sending port set P, P = [p, phi].
3. The routing method applicable to large-scale LEO constellations according to claim 1 or 2, characterized in that: The queuing factor SVF is formulated as follows: (7) Where, 、 、 、 The satellite v is calculated by formula (7) x,y Queuing delay at ports U, D, L, and R; e u is a basis vector, which is orthogonal to the other four basis vectors; w x,y Satellite v x,y of the remaining energy.
4. The routing method applicable to large-scale LEO constellations according to claim 1 or 2, characterized in that: The energy factor PVF is as follows: (8) Where, Indicates satellite v x,y The propagation function of port C, where C represents any of the four ports of the satellite; f lh Represents the previous hop propagation vector function of the current satellite, f SRC represents the propagation vector function of the source satellite, Expression (8) calculates the queuing delay at port C, Indicates the remaining energy of the previous hop of the current satellite, e c , e are two mutually orthogonal bases.
5. The routing method applicable to large-scale LEO constellations according to claim 1 or 2, characterized in that: The S1 construction of the LEO satellite network refers to the LEO polar orbit constellation defined as G=(V, E), where V={v 1,1 , v 1,2 ,…, v 2,1 ,v 2,2 ,…, v n,m } represents the satellite node, n represents the orbit number, and m represents the satellite number in the orbit; there are n*m satellites in the constellation, n orbits, and m satellites in each orbit; E represents the inter-satellite link in the constellation, and the number of satellites in the constellation is n,m The intersatellite link representation is , x represents v n,m The direction of the intersatellite link, x={U,D,L,R} represents v n,m Intersatellite links in the four directions of up, down, left and right.