METHOD FOR PLANNING A VARIABLE NON-INTERFERENCE DISTANCE IN BEAM HIPPING AND BEAM FORMATION SYSTEM FOR PLANNING A VARIABLE NON-INTERFERENCE DISTANCE IN BEAM HIPPING

Abstract

NON-TRANSIENT COMPUTER-READABLE STORAGE MEDIA, BEAM FORMATION METHOD AND SYSTEM FOR PROGRAMMING A VARIABLE NON-INTERFERENCE DISTANCE IN BEAM HIPPING. This is a system and method for programming a variable non-interference distance in beam hopping, wherein the method includes providing an illumination area of ​​a satellite and candidate beam centers arranged in the illumination area; measuring a respective scan angle from an antenna view to a respective beam center of the candidate beam centers; and determining a reuse factor k for each of the candidate beam centers, based on a ratio of the respective scan angle to a maximum scan angle. Each candidate beam center can be processed sequentially.Before adding each candidate beam center to a set of candidate beam centers, verify that a candidate beam center meets the non-interference distance criteria of all beam centers that are already in the set of beam centers.

Description

1 / 19 METHOD FOR PLANNING A NON-INTERFERENCE DISTANCE Variable beam hopping and beamforming system for planning a variable non-interference distance in BEAM JUMP FIELD OF TECHNIQUE

[0001] The present invention relates to a planner that adapts its non-interference distance to accommodate reduced performance due to scan loss in a Very High Throughput Satellite (VHTS) system that uses beam hopping and antennas with high scan distortion towards the edges of a coverage area. BACKGROUND OF THE TECHNIQUE

[0002] Classic satellite systems use fixed beam delivery over time, typically implementing a fixed reuse pattern (e.g., 3-color reuse). Some systems have implemented “beam hopping,” a beam delivery that is not constant over time, with the concept of a “non-interference distance.” No two cells are ever allowed to be in the illuminated array if the distance between the cell centers is less than this non-interference distance. The non-interference distance is designed to limit interference between cells, for example, Coal Conveyor Interference (CCI). The use of a fixed non-interference distance is disadvantageous in systems where beam characteristics are not constant across the coverage area.

[0003] Beam hopping satellites require a beam hopping planning mechanism that needs to accommodate a temporally variable traffic pattern and Petition 870260052056, dated 05 / 29 / 2026, page 7 / 61 2 / 19 spatially. Previous beam hopping systems considered these factors, but not the reduced performance over the coverage area that is caused by changes in antenna performance over that coverage area.

[0004] A satellite antenna will typically produce the most compact beams towards the antenna's boresight distance and will produce degraded beams as the angle between the boresight distance and the beam center increases, an effect called loss of sweep. The area covered by beams at larger boresight distance angles (swept beams) is greater than the area covered by beams at the boresight distance. SUMMARY OF THE INVENTION

[0005] This summary is provided to introduce a selection of concepts in a simplified manner which is further described below in the Detailed Description. This Summary is not intended to identify fundamental or essential features of the claimed object, nor is it intended to be used to limit the scope of the claimed object.

[0006] These teachings enhance the design of VHTS. VHTS is an important building block for the consumer satellite, aeronautics, defense, government, enterprise, and international business areas. These teachings reveal a variable non-interference distance to accommodate beam performance loss as a function of scan angle.

[0007] A system of one or more computers can be configured to perform particular operations or actions by virtue of having software, firmware, hardware or a Petition 870260052056, dated 05 / 29 / 2026, page 8 / 61 3 / 19 combination of the same installed in the system that in operation leads or leads the system to perform the actions. One or more computer programs may be configured to perform particular operations or actions by virtue of the inclusion of instructions which, when executed by data processing equipment, lead the equipment to perform the actions. A general aspect includes a non-transient computer-readable storage medium that has instructions embedded therein to implement a method for planning a variable non-interference distance in beam hopping.The method includes providing a satellite illumination area and candidate beam centers arranged within the illumination area; measuring a respective scan angle from an antenna boresight distance to a respective beam center of the candidate beam centers; and determining a reuse factor k, for each of the candidate beam centers, based on a ratio of the respective scan angle to a maximum scan angle. Other embodiments of this aspect include computer systems, appliances, and computer programs recorded on one or more corresponding computer storage devices, each configured to perform the actions of the methods.

[0008] Hereafter, the terms non-interference distance and reuse factor will be used. As is well known from the field of cellular radio, for a fixed color reuse pattern, there is a relationship between a reuse factor k, a distance D between the centers of cells of the same color and a cell radius R, namely, =43kRr where k is the number of distinct sets of orthogonal features (colors). Petition 870260052056, dated 05 / 29 / 2026, page 9 / 61 4 / 19

[0009] Implementations may include one or more of the following features. The method in which the illumination area includes imaginary cells superimposed on the illumination area, each cell having a cell center and each of the candidate beam centers including one of the cell centers. The imaginary cells are substantially hexagonal in shape. The method in which the reuse factor k for each of the candidate beam centers is constrained by the hexagonal geometry. The method in which the centers of the imaginary cells are not constrained to a hexagonal grid. The method may include establishing the reuse factor k for each of the candidate beam centers by choosing either a next smaller reuse factor among all k1 or a next larger reuse factor among all k2, from a set of reuse factors based on a probability p.The method may involve generating a set of candidate beam centers by sequentially adding a respective candidate beam center from the candidate beam centers when the respective candidate beam center is outside a respective reuse distance D from each of the beam centers already in the set of candidate beam centers. The candidate beam centers are ordered by a traffic metric associated with each of the candidate beam centers. Implementations of the techniques described may include hardware, a method or process, or computer software on a computer-accessible medium.

[0010] A general aspect includes a beamforming system for planning that uses a variable non-interference distance in beam hopping. The system includes a satellite that covers an illumination area and beam centers. Petition 870260052056, dated 05 / 29 / 2026, p. 10 / 61 5 / 19 candidates positioned in the illumination area; and a non-interference planner to measure a respective sweep angle from an antenna boresight distance to a respective beam center of the candidate beam centers, and to determine a reuse factor k, for each of the candidate beam centers, based on a ratio of the respective sweep angle to a maximum sweep angle. Other embodiments of this aspect include computer systems, apparatus, and computer programs recorded on one or more corresponding computer storage devices, each configured to perform the actions of the methods.

[0011] Additional resources will be better set out in the following description, and will in part become apparent from the description or may be learned by practicing what is described. DESIGNS

[0012] In order to describe the manner in which the advantages and features mentioned above and others can be obtained, a more particular description is provided below and will be presented by way of reference to specific embodiments thereof which are illustrated in the attached drawings. It being understood that these drawings depict only typical embodiments and are therefore not limiting of their scope, the implementations will be described and explained with additional specificity and detail with the attached drawings.

[0013] Figure 1 illustrates a beamforming system for beam hopping planning using a variable non-interference distance according to various modes.

[0014] Figure 2 illustrates a method for planning Petition 870260052056, dated 05 / 29 / 2026, page 11 / 61 6 / 19 a variable non-interference distance in beam hopping according to various modes.

[0015] Figure 3 illustrates an exemplary hexagonal grid showing k=3 (i=1, j=1) cell reuse according to various modalities.

[0016] Figure 4 illustrates an exemplary hexagonal grid showing k=4 (i=0, j=2) cell reuse according to various modalities.

[0017] Throughout the drawings and detailed description, unless otherwise stated, the same reference numbers in the drawings will be understood to refer to the same elements, features, and structures. The relative size and representation of these elements may be exaggerated for the sake of clarity, illustration, and convenience. DETAILED DESCRIPTION

[0018] The present teachings may be a system, a method and / or a computer program product at any level of technical detail possible for integration. The computer program product may include a computer-readable storage medium (or media) that has computer-readable program instructions on it to direct a processor to perform aspects of the present invention.

[0019] Computer-readable storage media may be a tangible device that can retain and store instructions for use by an instruction-executing device. Computer-readable storage media may be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, a Petition 870260052056, dated 05 / 29 / 2026, page 12 / 61 7 / 19 electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof. A non-exhaustive list of more specific examples of computer-readable storage media includes the following: a portable computer floppy disk, a hard disk drive, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or Flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), a digital versatile disc (DVD), a memory card, a floppy disk, a mechanically coded device such as punched cards or raised structures in a groove that have instructions recorded on them, and any suitable combination thereof.A computer-readable storage medium, as used in this document, should not be interpreted as being transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., pulses of light traveling through a fiber-optic cable), or electrical signals transmitted through a wire.

[0020] Computer-readable program instructions described in this document can be downloaded to respective processing / computing devices from a computer-readable storage medium or to an external storage device or external computer via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network can Petition 870260052056, dated 05 / 29 / 2026, page 13 / 61 8 / 19 includes copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, communication gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer-readable program instructions from the network and forwards the computer-readable program instructions for storage on a computer-readable storage medium within the respective computing / processing device.

[0021] Computer-readable program instructions for performing operations of the present invention may be manufacturer instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state-establishing data, or source code or object code written in any combination of one or more programming languages, including an object-oriented programming language such as SMALLTALK, C++, or similar, and conventional procedural programming languages ​​such as the C programming language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on the remote computer or server.In the last scenario, the remote computer can be connected to the user's computer through any type of network, including a wireless one. Petition 870260052056, dated 05 / 29 / 2026, page 14 / 61 9 / 19 local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, via the Internet using an Internet Service Provider). In some embodiments, electronic circuits including, for example, programmable logic circuits, field programmable gate arrays (FPGAs), or programmable logic arrays (PLAs) can execute computer-readable program instructions using state information from the computer-readable program instructions to customize the electronic circuits in order to realize aspects of the present invention.

[0022] Aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0023] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing devices to produce a machine, so that the instructions, which are executed through the computer processor or other programmable data processing devices, create means to implement the functions / actions in the block or blocks of flowchart and / or block diagram. These computer-readable program instructions can also Petition 870260052056, dated 05 / 29 / 2026, page 15 / 61 10 / 19 be stored on a computer-readable storage medium that can direct a computer, a programmable data processing device and / or other devices to operate in a particular way, such that the computer-readable storage medium has instructions stored on it comprising an article of manufacture that includes instructions that implement aspects of the function / act specified in the block or blocks of the flowchart and / or block diagram.

[0024] Computer-readable instructions may also be loaded into a computer, other programmable data processing devices, or other device to conduct a series of operational steps to be performed on the computer, other programmable devices, or other device to produce a computer-implemented process, such that the instructions that are executed on the computer, other programmable device, or other device implement the functions / acts specified in the flowchart block or blocks and / or block diagram.

[0025] The flowchart or block diagram in the Figures illustrates the architecture, functionality, and operation of possible implementations of computer program systems, methods, and products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram may represent a module, segment, or portion of instructions, comprising one or more executable instructions to implement the specified logical function(s). In some alternative implementations, the functions indicated in the block may occur out of the order shown in the figures. For example, two blocks shown in succession. Petition 870260052056, dated 05 / 29 / 2026, page 16 / 61 11 / 19 can, in fact, be executed substantially simultaneously, or the blocks can sometimes be executed in reverse order, depending on the functionality involved. It will be noted that each block of the block diagram and / or flowchart illustrations, and combinations of blocks in the block diagram and / or flowchart illustrations, can be implemented by systems based on purpose-built hardware that perform the specified functions or perform combinations of purpose-built hardware and computer instructions.

[0026] Reference in the descriptive report to an (1) embodiment or an embodiment of the present invention, as well as other variations thereof, means that a feature, structure, characteristic, and so forth described in combination with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrase in an (1) embodiment or in an embodiment, as well as any other variations, appearing at various times throughout the descriptive report are not all necessarily referring to the same embodiment.

[0027] In the present teachings, a distance measurement refers to U, V coordinates. The U, V coordinates are angles, measured from a satellite antenna viewpoint (boresight distance). Thus, in the present teachings, the term distance is an angular distance. Furthermore, in the present teachings, the use of the well-known concept of reuse color is not advocated. The concept of reuse color is being used to find the set of possible distances between beam centers.

[0028] Classic satellite communication systems have typically implemented reuse Petition 870260052056, dated 05 / 29 / 2026, page 17 / 61 12 / 19 fixed cellular array to control intercell interference. Cells whose cell centers coincide with a beam center 120 are placed on the Earth's surface to provide an illumination area 110 from the satellite 106. Signal levels from a beam directed at a target cell are typically high enough to cause significant interference to a cell immediately adjacent to the target cell. Thus, the illumination of immediately adjacent cells can be chosen to use orthogonal features to limit interference. Orthogonal features could be frequency, timing, and / or polarization. For example, in a 3-color reuse design there might be 3 different (orthogonal) frequency bands. The cells are colored (e.g., R, G, B) and adjacent cells are assigned colors (frequency bands) so that two immediately adjacent cells have the same color.

[0029] Some newer satellite communication systems have implemented systems in which beam delivery is not constant, also called “beam hopping” systems without a concept of a variable non-interference distance. In this beam hopping system, the set of cells that share non-orthogonal resources (e.g., operating at the same time, frequency, and polarization) is not constant; however, the non-interference distance in this prior art system is constant.

[0030] The principle of having a variable non-interference distance between beam centers can be applied to a general beamforming system, for example, a beamforming system that targets beam centers at arbitrary points. In this case, the non-interference distance Petition 870260052056, dated 05 / 29 / 2026, page 18 / 61 13 / 19 D interference would not be restricted to distances corresponding to the distance between fixed beam centers in a hexagonal grid.

[0031] In some embodiments, the beamforming system can be simplified by using a set of potential beam centers that are not arbitrary points, but are restricted to a particular set of potential points. In some systems, a hexagonal grid arranges the plane side-by-side, and the centers of this grid are the set of possible beam centers. The lines of the hexagonal grid are used in radio communication systems, such as cellular systems (with or without beamforming), satellite systems, or similar systems. By restricting the distance between active beam centers in this grid to be greater than some minimum value, the distances between potential beam centers can only assume certain discrete values.

[0032] When beam centers are restricted to cell centers of a predefined grid (e.g., the hexagonal grids of Figure 3 and Figure 4), an average non-interference distance can be approximately achieved. Arbitrary non-interference distances are not always achievable and are therefore approximated with a discrete set of distances and with a “coin toss”. When implementing an average non-interference, for each beam center, the process decides between the next largest non-interference among all (compared to the desired average non-interference) and the next smallest non-interference among all (compared to the desired average non-interference), choosing between them with some probability. An obvious extension would be the use of three or more non-interference distances. Petition 870260052056, dated 05 / 29 / 2026, page 19 / 61 14 / 19

[0033] Figure 1 illustrates a beamforming system for beam hopping planning using a variable non-interference distance according to various modes.

[0034] Figure 1 shows an example of a beamforming system 100 for planning that uses a variable non-interference distance in beam hopping. In Figure 1, a beam center 120 is marked with an X, and a beam definition 122 is illustrated as a grayed-out region centered on beam center 120. It is observed that beams near the boresight distance (near the center of the coverage area, i.e., at the origin 0.0) have better beam definition (less diffuse) than beams farther from the boresight distance (near the corners of the coverage area, i.e., at -1, 3). The better-defined beams near the center cover smaller areas (within and around the target cell) compared to beams farther from the boresight distance. Therefore, beams at the large scan angle are more subject to interference from adjacent beams.It would be advantageous for overall system performance to employ a larger non-interference distance for beams with a large scan angle and a smaller non-interference distance for beams with a small scan angle. A 122 non-interference planner plans beam hopping using a variable non-interference distance.

[0035] A useful guide for determining variable non-interference is to employ a reuse factor k1, corresponding to the scan angle S1 (see Figure 1) near the boresight distance, and a reuse factor k2, corresponding to a maximum scan angle S2. For a beam at a scan angle S, the reuse factor k Petition 870260052056, dated 05 / 29 / 2026, page 20 / 61 15 / 19 can be defined as k=F(S) for some function F. The function F could be any function chosen to vary the non-interference distance according to the scanning angle. For example, assuming that the minimum k is kmin, the maximum k is kmax, and the maximum scanning angle is Smax, the reuse factor k can be calculated as follows: k = F(S) = kmin x (1 — f 1 Ί + kmax x ( ) \ XSpnnA / 7 (.Sinai· /

[0036] The exponent α must be set to 2 for example.

[0037] In the example system, after determining or choosing the variable reuse factor ka, variable reuse can be implemented. One way to implement variable reuse is to find the corresponding reuse distance D by applying the previous formula that relates D to k. This approach would be ideal for systems where cell centers are not restricted to being in a hexagonal grid, in which case the reuse distance D is applied directly as the non-interference distance associated with that cell center. For systems where the locations of the possible beam centers form a hexagonal grid, the distances between the beam centers cannot assume all possible values. Therefore, for an arbitrary non-interference distance D, a minimum interbeam distance will be some other D', where D' corresponds to the next possible reuse distance greater than D.Therefore, a better approach to determining the non-interference distance can be implemented through coin tossing. Petition 870260052056, dated 05 / 29 / 2026, p. 21 / 61 16 / 19

[0038] Assuming that we implement a system in which the interbeam distances correspond to a reuse factor that has an average value of k. As is well known, not all values ​​of the reuse factor k are possible; only *= 1+ ij + J for integers 1, j are possible.

[0039] Coin toss can choose the next shortest reuse distance among all kl<k e a próxima k2> k is the largest among all. Therefore, for any potential beam, a non-interference distance can be chosen by flipping a partial coin and choosing a distance that corresponds to k² with probability p, or choosing a distance that corresponds to k¹ with probability 1-p, where an exemplary p can be chosen by k - k¹p ​​= 1 / 2 - k¹.

[0040] Using this scheme, the average reuse factor for the system will be k as is easily verified. Combining the variable reuse described above to choose the reuse factor as a function of a cell sweep angle with the coin toss scheme to implement variable reuse results in a design where the average reuse factor varies as a function of the sweep angle and the reuse chooses locations corresponding to the cell centers in the hexagonal grid.

[0041] Figure 2 illustrates a method for planning a variable non-interference distance in beam hopping according to various modalities.

[0042] In one modality, a jumping system of Petition 870260052056, dated 05 / 29 / 2026, page 22 / 61 17 / 19 beam can implement a method 200 to plan a variable non-interference distance in beam hopping. Candidate beam centers can be provided to the system by operation 202. Beam centers included as candidate beam centers can be changed and / or reordered at each time step (epoch). In some embodiments, the set of beam centers at each time step may be different and determined, for example, by traffic demand, which dissipates in the cell. Sweep angles from an antenna boresight distance to candidate beam centers can be measured by operation 204. Here, measuring a sweep angle includes obtaining the sweep angle from a table and the like.Each candidate beam center can be processed sequentially to determine a reuse factor k for each of the candidate beam centers, based on a ratio of the respective sweep angle up to a maximum sweep angle per operation 206. The candidate beam centers can be ordered by a traffic metric per operation 210, for example, by highest to lowest traffic demand, traffic age, traffic priority, traffic Quality of Service assurance, or similar. Per operation 212, when generating a set of candidate beam centers by adding each candidate beam center, operation 212 checks if a candidate beam center meets a respective reuse distance D from each of the candidate beam centers that are already in the set of candidate beam centers.

[0043] In some modes, each beam center may have an associated non-interference distance. In some modes, the non-interference distance Petition 870260052056, dated 05 / 29 / 2026, page 23 / 61 18 / 19 is recomputed at each epoch, for example, to account for coin toss variations. In other embodiments, by adding a beam center to the set of beam centers, the process can generate non-interference distance criteria for that beam center through a (pseudo) random process, so that, overall, a desired non-interference distance value is produced. For example, process 200 can establish the reuse factor k for each of the candidate beam centers by choosing either a next smaller reuse factor among all k1 or a next larger reuse factor among all k2 based on a probability p per operation 208.

[0044] Figure 3 illustrates an exemplary hexagonal grid showing k=3 (i=l, j=l) cell reuse, according to various modalities.

[0045] Figure 4 illustrates an exemplary hexagonal grid showing k=4 (i=0, j=2) cell reuse, according to various modalities.

[0046] In the case of reuse 3 (Figure 3), 3 colors illuminate the grid. A k=3 can be provided by setting i=l and j=l (* =1+ U + J ). In the case of reuse 4 (Figure 4), there are 4 colors. A k=4 can be provided by setting i=0 and j=2. The closest cell centers that can be illuminated simultaneously (same time / frequency / polarization) are those shown with the same color. In the case of k=3, the closest cell centers of the same color are at a distance of 3R, while for k=4 the distance is 2^ / 3 R, where is the radius of the hexagon.

[0047] As an example, a simulation of Petition 870260052056, dated 05 / 29 / 2026, p. 24 / 61 A 19 / 19 computer system-level simulation was conducted to illustrate the benefit of the variable non-interference concept. This simulation was for a satellite system covering a larger number of users across the continental US. In this example, a hexagonal grid was used for the potential beam centers, as described in this document. Two cases are compared with the only difference between them being that in one case there is a fixed reuse factor = 3, while in the other there is a variable reuse factor in the range ^ = [3...5]_ q. The fixed reuse system delivers 3.73 units of throughput, while the variable reuse delivers 3.84 units.

[0048] Having described preferred embodiments of a system and method (which are intended to be illustrative and not limiting), it is noted that modifications and variations may be made by persons skilled in the art taking into account the above teachings. Therefore, it should be understood that changes may be made to the disclosed embodiments that are within the scope of the invention as described in the appended claims. Thus, having described the aspects of the invention, with the details and particulars required by patent law, what is claimed and sought to be protected by the Patent Letters is set forth in the appended claims. Petition 870260052056, dated 05 / 29 / 2026, page 25 / 61

Claims

1 / 4 CLAIMS 1. METHOD FOR PLANNING A VARIABLE NON-INTERFERENCE DISTANCE IN BEAM HIPPING, wherein the method comprises: providing an illumination area (110) of a satellite and candidate beam centers (120) arranged in the illumination area (110); measuring (204) a respective scan angle from an antenna boresight direction to a respective beam center of the candidate beam centers (120); determining (206) a reuse factor k, for each of the candidate beam centers (120), based on a mathematical ratio of the respective scan angle to a maximum scan angle; establish the reuse factor k for each of the candidate beam centers (120) by choosing either the next smallest reuse factor kl among all or the next largest reuse factor k2 among all from a set of reuse factors based on a probability p, where the probability p is calculated as k — kl P = k2-kl;and determine, for each of the candidate beam centers (120), a reuse distance D based on the chosen reuse factor.; 2. METHOD, according to claim 1, characterized in that the illumination area (110) comprises imaginary cells superimposed on the illumination area, wherein each cell has a cell center, and wherein each of the candidate beam centers (120) comprises one of the cell centers.

3. METHOD, according to claim 2, characterized in that the centers of the imaginary cells are restricted to a hexagonal grid.

4. METHOD, according to claim 1, characterized in that the imaginary cells are hexagonal in shape.

5. METHOD, according to claim 1, characterized by the reuse factor k for each of the candidate beam centers (120) being calculated as k = = kmm x (1 — ( *. 1 Ί + kmax x ( $ 1 where α is 2 .

6. METHOD, according to claim 1, characterized by further comprising generating a set of candidate beam centers by sequentially adding a respective candidate beam center from the candidate beam centers (120) when the respective candidate beam center is outside a respective reuse distance D from each of the candidate beam centers (120) that are already in the set of candidate beam centers.

7. METHOD, according to claim 6, characterized by the candidate beam centers being ordered (210) by a traffic metric associated with each of the candidate beam centers.

8. BEAM FORMATION SYSTEM (100) FOR PLANNING A VARIABLE NON-INTERFERENCE DISTANCE IN BEAM HIPPING, wherein the system (100) is characterized by comprising: a satellite (106) covering an illumination area Petition 870260052056, dated 05 / 29 / 2026, page 27 / 61 3 / 4 (110) and candidate beam centers (120) disposed in the illumination area;and a non-interference planner (122) to measure a respective sweep angle from an antenna view to a respective beam center of the candidate beam centers, and to determine a reuse factor k, for each of the candidate beam centers, based on a mathematical ratio of the respective sweep angle to a maximum sweep angle, wherein the non-interference planner (122) establishes the reuse factor k for each of the candidate beam centers by choosing either a next smaller reuse factor kl among all or a next larger reuse factor k2 among all, from a set of non-interference distances based on a probability k — kl p =------ p, wherein the probability p is calculated as k2 — kl, and determine, for each of the candidate beam centers, a reuse distance D based on the chosen reuse factor.; 9. SYSTEM (100), according to claim 8, characterized in that the illumination area (110) comprises imaginary cells superimposed on the illumination area (110), wherein each cell has a cell center, and wherein each of the candidate beam centers (120) comprises one of the cell centers.

10. SYSTEM (100), according to claim 9, characterized in that the centers of the imaginary cells are restricted to a hexagonal grid.

11. SYSTEM (100), according to claim 9, Petition 870260052056, dated 05 / 29 / 2026, page 28 / 61 4 / 4 characterized by the imaginary cells being hexagonal in shape.

12. SYSTEM (100), according to claim 8, characterized in that the reuse factor k for each of the candidate beam centers (120) is calculated as k = F(S) — kmtn x (1 — ( 1 Ί + kmax xf S 1 where α is 2 .

13. SYSTEM (100), according to claim 8, characterized by the non-interference planner (122) generating a set of candidate beam centers by sequentially adding a respective candidate beam center from the candidate beam centers (120) when the respective candidate beam center is outside a respective reuse distance D from each of the candidate beam centers (120) that are already in the set of candidate beam centers.

14. SYSTEM (100), according to claim 13, characterized by candidate beam centers (120) being ordered by a traffic metric associated with each of the candidate beam centers (120). Petition 870260052056, dated 29 / 05 / 2026, p. 29 / 61

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