Satellite routing methods and systems

Abstract

A method, carried out by one or more processing devices, is used for mapping cells on Earth that contain communications terminals to communications spacecraft or aircraft, as appropriate, referred to as satellite routing. The method comprises: grouping the cells into groups or clusters by applying clustering techniques; mapping the groups of cells to spacecraft or aircraft; and outputting parameters usable to control at least one spacecraft or aircraft to provide service to the assigned cells. The invention also relates to a system, computer program products, and a method and system for simulating a satellite routing.

Description

Attorney Docket No. MIT-25388WO01 SATELLITE ROUTING METHODS AND SYSTEMS CROSS-REFERENCE TO RELATED APPLICATION(S)

[0001] This application claims the priority benefit, under 35 U.S.C. 119(e), of U.S. Application No. 63 / 631,587, filed April 9, 2024, which is incorporated herein by reference in its entirety. BACKGROUND

[0002] Modern communications satellites have directional antennas or antenna arrays that transmit and receive radio-frequency (RF) signals or optical signals to and from different points on Earth. Some communications satellites are in geosynchronous orbit (GEO) above the equator and so appear to be fixed in the sky. Other communications satellites form constellations in non-geostationary orbit (NGSO) and move across the sky. A communications satellite may relay signals from a terminal at one point on Earth to another terminal at a different point on Earth, possibly via one or more other communications satellites or other repeaters.

[0003] The terminals can be distributed across the surface of the Earth, which can be divided into regions or cells, each of which can contain one or more terminals. Dividing the world into cells is usually done by gridding the surface of the Earth into hexagons. Other ways of defining cells are also possible. These cells are illuminated by beams from the directional antennae or antenna arrays on communications satellites orbiting the Earth. Each beam, also called a coverage beam or, when relatively small, a spot beam, covers a region on Earth, also called a coverage area or beam footprint.

[0004] A terminal located in a given coverage area can communicate with other terminals via the communications satellite. These other terminals can be in the same coverage area or in other coverage areas covered by other beams from the same communications satellite or different communications satellite, in which case the communications satellites may communicate with each other.

[0005] Each beam results from a radiation pattern emitted by the directional antenna or antenna array. A radiation pattern typically comprises a main lobe plus various sidelobes. The coverage area or beam footprint for a beam directed towards Earth may be represented on Earth’s surface by a disk, ellipse, or similar shape where the antenna’s gainAttorney Docket No. MIT-25388WO01 remains within a predetermined value of its peak gain, for example, 3 dB, 6 dB, 10 dB, 15 dB, 20 dB, 25 dB, etc. That is, the antenna gain at the edge of the coverage area is a predetermined value (e.g., 3 dB) below the peak antenna gain, which is typically at or near the center of the coverage area.

[0006] A communications satellite can host a single directional antenna or antenna array or multiple directional antennas and / or antenna arrays. Likewise, a communications satellite can form a single beam or multiple beams, e.g., from a few beams to tens, hundreds, or even thousands of beams, depending on the number(s) and type(s) of directional antennas and / or antenna arrays on the communications satellite. SUMMARY

[0007] For mapping terminals to satellites, the cells on Earth that contain the terminals are chosen so that a beam from a communications satellite is large enough to cover a single cell and addresses terminals in only one cell at a time. If, geographically, a terminal can be assigned to two or more different cells—for example, because it is on the border between the cells—the terminal’s operator should assign the terminal to only one cell.

[0008] The beam from a communications satellite in geosynchronous orbit covers a large, fixed coverage area, so mapping cells to satellites in geosynchronous orbit can be accomplished trivially. Similarly, conventional constellations of communications satellites usually have relatively small numbers of beams and coverage areas (e.g., dozens), with only a single communications satellite visible from a given spot on Earth at a time, again leading to a trivial mapping or allocation of communications satellites to cells (and the terminals in those cells). But as the number of communications satellites grows, so do the number of beams and the number of coverage areas, making it more challenging to allocate or map satellites to different cells.

[0009] In a modern satellite constellation, or constellation for short, there may be tens or hundreds of satellites visible from each cell, so operators must decide which communications satellites serve which cells. Allocating communications satellites in a modern constellation to cells using traditional techniques, such as choosing the closest communications satellite or the communications satellite with the highest elevation angle, may turn out to be inefficient under the new configurations because the terminals are not equally distributed across the globe. In dense areas, this leads to the over-saturation ofAttorney Docket No. MIT-25388WO01 individual communications satellites, while other communications satellites in the constellation may be under-utilized.

[0010] Brute-force methods to find a more efficient mapping may be used for constellations with small numbers of spacecraft and terminals, where the number of decisions is low. Nevertheless, with the current proposals using thousands of satellites and serving hundreds of thousands of terminals, brute-force methods generally cannot provide solutions in practical time. In view of this growth in both constellation size and number of terminals, there is a need for solutions to assist in efficiently mapping the cells to satellites to provide service to many terminals on Earth, especially in scenarios with thousands of spacecraft, which are representative of current constellations.

[0011] The present satellite routing technology relates to methods and systems for assisting in providing connectivity to terminals located within the Earth’s atmosphere. The present technology may be used to, though is not limited to, assist in providing broadband communications, such as internet connectivity to a plurality of terminals. For instance, the present technology can be implemented as a method of mapping communications satellites in non-geostationary orbit to cells on Earth. This method can include aggregating the cells into groups of cells such that each of the cells belongs to only one cell group, assigning each of the communications satellites to a corresponding cell group, and, for each of the cell groups, aggregating the communications satellites assigned to that cell group into a corresponding set of communications satellites. Each cell in that cell group can then be mapped to a corresponding communications satellite in the corresponding set of communications satellites for that cell group.

[0012] Mapping each cell to a corresponding communications satellite can be based on satellite elevation angle, distance between that cell and the corresponding communications satellite, power consumption, visibility conditions, weather conditions, interference level, available bandwidth, available carrier frequencies, and / or satellite battery status.

[0013] If desired, a different pool of resources can be allocated to each cell group. For example, this may include allocating a different set of satellites to each cell group. Allocating different sets of satellites to different groups of cells may include selecting the satellites to avoid interference between communications signals in adjacent cells.Attorney Docket No. MIT-25388WO01

[0014] The assignments can be updated for each of a sequence of time steps based at least in part on changes in positions of the communications satellites over the sequence of time steps. The assignments can be updated without changing frequency channel allocations for the cell groups.

[0015] Alternatively, communications satellites in non-geostationary orbit can be assigned to cells on Earth by clustering the cells into cell groups such that each cell belongs to only one cell group, then identifying which of the cells coincide on each of the communications satellites and which of the cells are likely to produce interference if assigned to the same frequency channel. Based on this information, it is possible to generate assignments of the cell groups to respective communications satellites. The assignments are transmitted to the communications satellites, which communicate with terminals located in the cell groups specified by the assignments.

[0016] Identifying which of the cells are likely to produce interference if assigned to the same frequency channel can be based at least in part on geographical separation of the cells.

[0017] Generating the assignments may comprise load balancing across the communications satellites.

[0018] If desired, frequency channel assignments for the cell groups can be generated and transmitted to the communications satellites.

[0019] The assignments can be updated for each of a sequence of time steps based at least in part on changes in positions of the communications satellites over the sequence of time steps. Updating the assignments can include mapping each of the cells to only one of the communications satellites for each time step in the sequence of time steps, to one of the communications satellites that is visible from that cell at that time step in the sequence of time steps, and / or identifying, for each of the cells, which of the communications satellites can connect to terminals in that cell. This identification step can be performed at a ground station and / or onboard the communications satellites. The assignments can be updated without changing frequency channel allocations for the cell groups.

[0020] In some aspects, the present technology includes ground terminals configured to communicate with communications satellites configured according to the inventive method(s).Attorney Docket No. MIT-25388WO01

[0021] All combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the inventive subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the inventive subject matter disclosed herein. The terminology explicitly employed herein that also may appear in any disclosure incorporated by reference should be accorded a meaning most consistent with the particular concepts disclosed herein. BRIEF DESCRIPTIONS OF THE DRAWINGS

[0022] The skilled artisan will understand that the drawings primarily are for illustrative purposes and are not intended to limit the scope of the inventive subject matter described herein. The drawings are not necessarily to scale; in some instances, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate an understanding of different features. In the drawings, like reference characters generally refer to like features (e.g., functionally and / or structurally similar elements).

[0023] FIG.1A illustrates different cells on Earth arranged in groups and served by beams from different communications satellites.

[0024] FIG. 1B illustrates an inventive process for routing satellite signals among different cells on Earth.

[0025] FIG.2A is a plot of the time evolution of the cells that are close enough to each other to produce interfering signals (^^^^, left axis) and throughput (right axis) for the SpaceX Starlink satellite constellation.

[0026] FIG.2B illustrates one instance of cells (grey circles) mapped to satellites (black satellite icons). Each connection is represented by a line. The value inside each circle represents the elevation angle of the assigned satellite with respect to the center of the corresponding cell.

[0027] FIG. 3 shows plots of throughput versus power consumption for different combinations of interference-aware satellite routing implementations (square, triangle, circle) and frequency assignment (shading) for the O3b mPower, Telesat Lightspeed, and SpaceX Starlink satellite constellations.Attorney Docket No. MIT-25388WO01

[0028] FIG. 4A is a plot of throughput (left axis) and power consumption (right axis) versus time for a satellite with seven changes in group-to-satellite mapping during operation (each dashed line represents a change in the group-to-satellite mapping).

[0029] FIG. 4B is a plot of throughput (left axis) and power consumption (right axis) versus time for a satellite with thirty-nine changes in group-to-satellite mapping during operation. DETAILED DESCRIPTION

[0030] To provide connectivity services to ground terminals using airborne or spaceborne beam sources, operators map each ground terminal to at least one beam source (e.g., a communications satellite). A beam source can be mapped to a particular terminal if the beam source is visible to that terminal, that is, if the elevation angle between the beam source and the terminal is above a predefined threshold and there is path between the terminal and the beam source that is not obstructed. If multiple beam sources are visible to a given terminal, operators choose how to map beam sources to terminals. This mapping problem is called the satellite routing problem, satellite scheduling (problem), or user association (problem). The present technology addresses the satellite routing problem with the objective of enhancing the system capacity over existing methods.

[0031] The satellite routing problem involves determining the mapping between cells containing terminals and satellites as shown in FIG.1A at each of several time steps. A solution to this problem should achieve load balancing among satellites while reducing or minimizing potential interference between terminals in different cells. Each cell is smaller than the beam footprints / coverage areas for the beams from the satellites. As explained below, the cells are aggregated into clusters or groups, which are mapped to different sets of satellites.

[0032] Additionally, any solution to the satellite routing problem should ensure that the satellite assigned to each cell on the ground remains visible to all of the users (terminals) in that cell. The cell-to-satellite (user-to-beam) mapping should be established in a way that guarantees user coverage within a given cell on Earth, irrespective of the satellite’s position, as long as the satellite is above a predefined minimum elevation angle.

[0033] Formally, we denote B as the set of cells on Earth that should be mapped to a constellation of satellites S over a specified duration T. Each cell is characterized by itsAttorney Docket No. MIT-25388WO01 center ^^^^and an associated expected demand ^^^^. Optionally, B can include information specifying a subset of satellites ^^^^that are responsible for covering a particular cell b. If this subset is defined, only satellites within ^^^^are eligible for covering cell b. In theabsence of this specification, we assume that ^^^^ = ^^. The set S provides informationregarding the orbital characteristics of each satellite, with the assumption that orbital elements, except for the mean anomaly, remain fixed during operations.

[0034] To tackle the satellite routing problem, we introduce the binary variable ^^^^,^^(^^), representing the mapping between cell b and satellite s at time t. We enforce the constraint that each cell can only be mapped to a single satellite at any given time: C1:∑s∈^^^^ xb,s(t) = 1. (Other settings might map cells to more than one satellite, e.g., bypicking C1 to be greater than 1.) Additionally, we ensure that the mapping is restricted tovalid and visible satellites for each cell: C2: xb,s(t) ≤ 1s∈^^^^ 1s∈LoS(b,t), where^^^^^^(^^, ^^) denotes the set of points within the line of sight of cell b at time t. To balancecells across satellites, we introduce the auxiliary binary variable ybA1,b2, indicating whether cell ^^1and cell ^^2are active on the same satellite at any point during T. Based on the valuesexpressed as:

[0035] To address interference between cells, we introduce another auxiliary binary variable, ^^^^^^1,^^2, indicating whether cell ^^1and cell ^^2lack sufficient geographical separation at any point during T. This can be determined using the binary parameter (^^), which indicates if the relative gain between ^^1connected to ^^1and ^^2connected to ^^2exceeds ^^^^ℎ^^^^^^. Using ^^^^,^^(^^)and ^^^^ℎ^^^^^^, we can define ^^^^^^1,^^2as:

[0036] We introduce weighting factors ^^^^and ^^^^to balance the load and reduce interference, respectively. The complete formulation of the problem is as follows:This formulation represents an integer-linear formulation of the satellite routing problem in non-geostationary orbit (NGSO) constellations, with the objective to achieve load balancing across satellites while minimizing potential interference.Attorney Docket No. MIT-25388WO01

[0037] Once a solution is obtained, we define ^^^^as the set of cells that coincide on (i.e., are addressed or served by) the same satellite at some point in time and ^^^^as the set of cells comprising pairs of cells that lack sufficient geographical separation (i.e., that are likely to produce interference if assigned to the same frequency channel). These sets can be derived from the variablescan be represented as a matrix of zeros and ones, where a one (1) indicates that a pair of cells are in the same group or cluster and can see the same satellite and a zero (0) indicates that a pair of cells are in different groups or clusters. Similarly, ^^^^can be represented as a matrix of ones and zeros, where a one (1) indicates that two cells are close enough to generate interfering communications and a zero (0) indicates little to no potential for interference. To use the same resources (e.g., frequency channels or polarizations), a pair of channels should have zeros in both the matrices. Addressing the Satellite Routing Problem

[0038] FIG.1B illustrates a method for tackling the satellite routing problem. Given the computational complexity of achieving an optimal solution (e.g., a solution that minimizes an objective function) in practical time, we divide the satellite routing problem into two sub-problems, enabling us to obtain a close-to-optimal solution within a reasonable timeframe.

[0039] Given the computational complexity of the problem formulation, an off-the-shelf mathematical solver becomes infeasible for real-world operational scenarios with tens of thousands of cells and thousands of satellites. To address this challenge, we use a two- layer decomposition approach that trades optimality for computational efficiency. First, we address the time duration issue by solving the problem incrementally, one time-step at a time. Second, we employ clustering techniques to group cells (lower and center left, FIG. 1B) and assign these groups of cells to (sets of) satellites (lower right, FIG. 1B), reducing the combinatorial complexity. The subsequent subsections elaborate on the implementation details of each step.

[0040] One of the principal complexities of the prior formulation is the exponential growth of possible solutions with the time horizon, which can be indefinite. To mitigate this challenge, we use a time-step-based approach where the problem is solved iteratively, focusing on one time-step at a time. However, this introduces the challenge of varying values for ^^^^^^1,^^2andbetween different time-steps, which affects the sets ^^^^andAttorney Docket No. MIT-25388WO01 ^^^^. To address this, we use an iterative method that aims to identify the smallest sets ^^^^and ^^^^without a solution for all time-steps. This is achieved by modifying the constraints C3 and C4 to consider only the pairs of cells not already belonging to ^^^^and ^^^^during the computation:

[0041] Another challenge of the original formulation lies in the significant size of the space segment, particularly for modern constellations where the number of visible satellites per cell can range from tens to hundreds. Even when addressing a single time- step, the extensive search space and NP-Hardness may hinder the efficient discovery of high-quality solutions. To mitigate this complexity, we introduce the concept of cell groups or clusters. The cells in a cluster or group of cells share the resources of a subset of satellites. Cells within the same cluster or group may be mapped to the same group of satellites, while cells in different clusters or groups may be mapped to different groups of satellites. Grouping or clustering partitions the resource pool, originally comprising the entire constellation, into multiple sub-pools, where satellite routing determines how to distribute the load across cells, satellites, and groups / clusters. The original satellite routing problem is then decomposed into two sub-problems: cell clustering (lower left and lower middle, FIG.1B) and cell-cluster-to-satellite mapping (lower right, FIG.1B). Assuming that the dimensionality of the cell groups or clusters is relatively low, we transform a problem involving the mapping of cells (high dimensional, HD) to satellites (HD) into two sub-problems: mapping cells (HD) to clusters (low dimensional, LD), and mapping cell clusters (LD) to satellites (HD), thereby reducing complexity. Satellite routing does not necessarily aim to optimize resource allocation within individual clusters.

[0042] To group or cluster cells, we use hierarchical clustering as shown at lower left in FIG. 1B. A group or cluster is formed by cells that exhibit the property that any pair of cells within the cluster can communicate with at least one common valid and visible satellite at some point in time is in ^^^^. Based on the geometry of the satellite constellation, each cell should always see at least a minimum number of satellites in a satellite constellation. This number may vary with latitude and longitude, so adjacent cells mayAttorney Docket No. MIT-25388WO01 see different numbers of satellites (e.g., 8 satellites, whereas the other cell sees 10 satellite). (If a cell can communicate with only one satellite, then the cell is assigned to that satellite.) Each cell is associated with a single cell group, with the number of available groups for each cell determined by the minimum number of visible and valid satellites across all time steps. To capture nearby cells with varying satellite visibility, a hierarchy is established among the groups of cells. This hierarchy is depicted as shaded branches A–G at different levels 1–4 in the lower left corner of FIG. 1B. Consequently, the constraint of a single cell group is extended to all cell groups within the same branch of the hierarchy.

[0043] In this example, terminals in every cell in branch A of the hierarchy in FIG. 1B can communicate with the same satellite and possibly, though not necessarily, other satellites as well. Terminals in every cell in branches B and C can communicate with at least two satellites, one of which is the same satellite visible to every cell in branch A. Terminals in every cell in branches D and E can communicate with at least three satellites, including the two satellites visible to every cell in branch C (this includes the same satellite visible to every cell in branch A). Similarly, terminals in each cell in branches F and G can communicate with at least four satellites, including the two satellites visible to every cell in branch B (again, this includes the same satellite visible to every cell in branch A).

[0044] A cell’s branch in the hierarchy determines which cells it may pair with for clustering. For instance, a cell in branch B may form pairs with cells in branches A, B, F, or G if they share overlapping satellites, but not with cells in branches C, D, or E. The set^^^^ denotes pairs ^^1, ^^2 belonging to the same branch of the hierarchy, implying potentialinclusion in ^^^^. When assigning groups of cells to satellites, a cell should connect only to satellites assigned to the same group of cell or groups of cells downstream within the same branch. Hence, a cell in branch B can associate with a satellite assigned to branches B, F, or G, but not branches A, C, D, or E. This arrangement guarantees that only cells adhering to the appropriate constraints are assigned to the same satellite. The set ^^^^comprises pairs ^^1, ^^2 where the groups of cells are on the same branch, with ^^2 eitherequal to or further downstream than ^^1. Grouping or Clustering CellsAttorney Docket No. MIT-25388WO01

[0045] To assign cells to groups of cells (lower middle, FIG.1B), we introduce a binary variable ^^^^,^^, representing whether cell b is assigned to group c. Each cell can only be assigned to a group or cluster of cells contingent upon the minimum number of visible and valid satellites for that cell at any given time. A cell should be allocated to exactlyone valid group, as expressed by constraint= 1. The determination ofpairs of cells belonging to ^^^^is achieved by verifying if both cells share a satellite that is both valid and visible for both cells simultaneously at any time:

[0046] The variable ^^^^1,^^2depends on the geometric characteristics of the problem and can be computed in advance. This equation allows us to determine which pairs of cells will share the same satellite at some point, without explicitly specifying the cell-to- satellite mapping. However, computing potential interference involves precise knowledge of the cell-to-satellite mapping, as it is highly sensitive to these assignments. Nevertheless, we can utilize the distance between cells to estimate when two cells might be assigned to the same or neighboring satellites. In practice, this may be the distance between the centers of the cells. To incorporate this information, we introduce the distance factor ^^^^1,^^2, defined as follows:

[0047] By definition, if ^^^^1 = ^^^^2, ^^^^1,^^2 = 1, and if ^^^^1,^^2 = 0, ^^^^1,^^2 = 0. Thecomputation of ^^^^1,^^2can be incorporated into the geometric analysis of the problem. With this, the objective is to distribute the demand of nearby cells among different groups, thereby achieving load balancing across satellites while reducing or minimizing potential interference. The comprehensive formulation for the cell grouping or clustering problem is presented below:Attorney Docket No. MIT-25388WO01 Unlike the time-dependent nature of the original formulation, the cell grouping or clustering formulation is not time-dependent and may have only one solution. By utilizing this formulation, the complete set ^^^^can be computed without simulating all time-steps. Mapping Groups of Cells to Satellites

[0048] Once the cell grouping or clustering is established, the subsequent step involves the time-dependent cell-cluster / group-to-satellite mapping (lower right, FIG. 1B). To address this efficiently, we can solve for a single time-step. For a given time t, we introduce the binary variable ^^^^,^^, representing the assignment of satellite s to group c. Ensuring that each satellite is assigned to only one group can be formulated as constraint

[0049] For each time-step, every cell maintains a list of potential satellite connections, sequenced by preference as… , ^^^^, where the cell may prefer connecting to^^1over ^^2, ^^2over ^^3, and so on. This ordering parameter, customizable by the operator, could, for instance, be based on visible satellites sorted by highest elevation angle to lowest. However, for a cell b with group ^^^^and satellite s with group ^^^^, the cell can onlybe assigned to satellite s if it has a matching cluster ({^^^^, ^^^^}Notably, a cell bshould be assigned to satellite s if it shares a matching cluster and if no other satellite in ^^^∗^ has such a cluster. This assignment criterion can be efficiently modeled using the binary variable ^^^^,^^^^:

[0050] In this equation, ^^^^,^^^^might assume values less than 1, but we consider cell bmatched with satellite ^^^^ only when ^^^^,^^^^ = 1. Furthermore, each cell should have at leastone valid and visible satellite with a matching cluster:Utilizing the variable ^^^^,^^, we can formulate the group-to-satellite mapping sub-problem as:

[0051] This refined formulation allows us to address the group-to-satellite mapping sub- problem as an integer-linear problem, similar to the original formulation. Notably, the variables and constraints concerning load balancing (^^^^^1^,^^2, C4') do not appear, as theyAttorney Docket No. MIT-25388WO01 were already accounted for during the cell grouping / clustering phase. Integrating the outcomes of both the cell grouping / clustering and group-to-satellite mapping phases provides a comprehensive solution for the satellite routing problem. Nonetheless, in certain scenarios, the feasibility of the prior formulation may be affected by geometric properties of the problem. Complete Satellite Routing Process

[0052] The inventive approach involves the following sequential steps (shown in the middle row of FIG.1B): 1. Resolve the cell clustering problem using the formulation presented above; 2. Compute ^^^^, initialize ^^^^ = ∅, and set t to the initial time-step;3. Simulate time t, calculating relevant geometrical parameters; 4. Resolve the cluster-to-satellite mapping using the formulation presented above; 5. Add any new pairs of cells with ^^^^^^1,^^2 = 1 to ^^^^; and6. Upon convergence, finish, otherwise set t to the next time-step and return to step 3.

[0053] We check for convergence by verifying if there have been ^^^^^^^^^^iterations without adding new cell pairs to ^^^^or ^^^^. For the resolution of the formulations (step 1 and 4), we employ commercial mathematical solvers.

[0054] For the cell grouping / clustering sub-problem, any suitable grouping or clustering technique can be used to organize the cells into groups. For the group-to-satellite sub- problem, any matching or coloring technique can be used to associate each group of cells (cell group) with a satellite. Frequency Assignment

[0055] Frequency assignment involves assigning a frequency channel to each cell and can be used in conjunction with satellite routing to increase performance. Conceptually, satellite routing attempts to distribute the demand across satellites, while frequency assignment attempts to optimize the allocation of the frequency spectrum, reuse factor, and transmission polarizations of individual satellites. Frequency assignment is described here in part to illustrate the benefits of satellite routing with respect to and combined with other resource allocation techniques.Attorney Docket No. MIT-25388WO01

[0056] The objective of frequency assignment is to assign an initial frequency, bandwidth, and reuse factor to each cell considering constraints derived from ^^^^or ^^^^as defined above. The frequency assignment remains fixed for an indefinite duration. Although it could be possible to adjust the spectrum each time a cell changes satellite, potentially enhancing efficiency, the complexity of addressing such a problem for high- dimensional scenarios is currently intractable, with uncertain benefits. This formulation reduces or minimizes a set of objectives, such as power consumption or bandwidth, while mitigating potential interference between the beams. Here, we focus on minimizing power consumption.

[0057] To assign the initial frequency, bandwidth, and reuse factor for each cell, we define ^^^^,^^,^^,^^as a binary variable indicating if beam ^^ is mapped to initial frequency ^^, bandwidth ^^, and reuse factor ^^. We define ^^^^,^^,^^,^^as a utility function representing the expected power consumption of beam ^^ when using frequency ^^, bandwidth ^^, and reuse factor ^^. We also introduce ^^^^1,^^1,^^2,^^2as a binary parameter determining if the spectrumboundedoverlaps with ^^2 and ^^2: ^^10: ^^^^1,^^1,^^2,^^2 = ^^^^1≤^^2+^^2^^^^2≤^^1+^^1.

[0058] We enforce constraints to ensure that beams sharing a satellite (i.e., a pair in ^^^^)do not share overlapping resources: ^^11:+ ^^^^2,^^2,^^2,^^2) ≤1∀{^^1, ^^2} ∈ ^^^^. Furthermore, cells susceptible to potential interference (i.e., a pair in^^^^) should not share overlapping spectrum: ^^12: ^^^^1,^^1,^^2,^^2(^^^^1,^^1,^^1,^^1 + ^^^^2,^^2,^^2,^^2) ≤1∀{^^1, ^^2} ∈ ^^^^. Finally, each cell should only be assigned, at most, once:^^13: ∑^^,^^,^^ (^^^^,^^,^^,^^1. The problem then reduces to finding the set of^^^^,^^,^^,^^that maximize the utility function:

[0059] Here,serves as a large number aimed at maximizing the number of activecells, defined as= max ^^^^,^^,^^,^^,^^ ^^^^,^^,^^,^^,^^|ℬ|. To perform frequency assignment, weinitially obtain a warm start. Subsequently, we iteratively optimize a subset of cells until no superior solution is found for a certain number of iterations. During each iteration only the most promising set of options is considered for each cell, using a ranking approach based on the utility function above. Combining satellite routing and frequency assignment achieves the desired outcome: satellite routing divides beams into resource pools (frequency channels, etc.), while frequency assignment optimizes the utilization of eachAttorney Docket No. MIT-25388WO01 pool. Frequency assignment remains agnostic to the cluster-like representation employed in satellite routing, as the information is encoded in the overlapping and interference sets. General Applicability of Satellite Routing Technology

[0060] The inventive satellite routing methods can be applied to large constellations of communications satellite. They can also be extended to applications that involve transferring data between multiple satellites and multiple ground terminals, including satellite imaging and Earth observation, as well to applications that involve communicating with devices other than satellites, such as aircraft, balloons, high altitude stations, etc. These devices may include high-altitude platform stations (HAPS), high- altitude long-endurance (HALE) aircraft, aerostats, balloons, airships, airplanes, unmanned aerial vehicles, and so on. In all these applications, the receiver stations can be fixed, if the antenna is located on an unchanging position on the Earth, or mobile, if the antenna is located in a moving entity, such as aircraft, ship, truck, hand-held device, etc. Advantages and Improvements over Existing Methods of Satellite Routing

[0061] This section discloses simulated results obtained with inventive satellite routing processes. It includes a demonstration of the validation and convergence analysis of the inventive satellite routing. A performance analysis on contemporary constellations evaluates the effectiveness of the inventive framework and its impact.TABLE 1: Summary of the orbit characteristics of the O3b mPower, ViaSat LEO, Telesat Lightspeed, and SpaceX Starlink constellations. Values extracted from public filings and may be altered at the discretion of the operator.Attorney Docket No. MIT-25388WO01TABLE 2: Summary of the link characteristics of the O3b mPower, ViaSat LEO, Telesat Lightspeed, and SpaceX Starlink constellations. Characteristics marked with * are extracted from public filings or public information.

[0062] To assess the inventive processes under realistic operational conditions, we adopt representative space and user segments from modern environments. Four different constellations, the O3b mPower, ViaSat LEO, Telesat Lightspeed, and SpaceX Starlink constellations, are utilized for the space segment, with their orbital characteristics provided in TABLE 1. A user distribution based on the global population distributionsimulates the user segment. This involves creating a grid with a resolution of 0.1∘ × 0.1∘and generating ^^^^^^^^locations, where the selection probability of each location corresponds to the percentage of population residing in that cell. At each location, we assume ^^^^^^ / ^^^^^^users, each with a 100 Mbps connection. The specific values of ^^^^^^^^and ^^^^^^ / ^^^^^^vary depending on the experiment. For the O3b mPower constellation, only users within the ±50° latitude range are considered valid. The users are then organized into cells. For example, the world can be divided into cells (e.g., hexagonal cells) and each user can be assigned to the cell that contains or is closest to their location.

[0063] TABLE 2 gives the payload configuration for each satellite. TABLE 3 summarizes the parameters for each experiment. In all simulations, ^^^^ℎ^^^^^^and ^^^^^^^^^^are set to –30 dB and 10 iterations, respectively. To address the different formulations, we execute the commercial solver Gurobi (version 9.1.2) in an Intel(R) Xeon(R) Platinum 8160 CPU @ 2.10GHz, allowing up to 16 simultaneous threads.Attorney Docket No. MIT-25388WO01TABLE 3: Summary of simulations

[0064] We assess the performance of the inventive methods by performing satellite routing and frequency assignment, followed by simulating each constellation downlink for ^^^^^^time-steps, with ^^^^seconds between time-steps. Results are evaluated on two primary metrics: throughput and power consumption, computed as the sum of the individual values for each satellite across the entire constellation, and averaged over all time-steps. As secondary metrics, the number of active satellites represents the average count of satellites with non-zero throughput, and the spectrum represents the total bandwidth assigned for all cells. Convergence and Validation Analysis

[0065] This simulation serves a dual purpose: first, to investigate the validity of the proposed convergence criteria, and second, to assess the effectiveness of the satellite routing method. For this evaluation, we simulate the SpaceX Starlink constellation withparameters ^^^^^^^^ = 10,000 and ^^^^^^ / ^^^^^^ = 1.

[0066] FIG. 2A illustrates the evolution of the interference set ^^^^and throughput until convergence is achieved. The cell grouping / clustering phase, aimed at determining a complete overlapping set (^^^^) representing pairs of cells that will share a satellite at some point in time, is performed only once. This phase spans the initial 10,000 seconds of the evolution. Subsequently, during the group / cluster-to-satellite phase, we observe the dynamic evolution of the interference set (^^^^), representing pairs of cells that may experience potential interference at some time. This phase is iterative, leading to gradual changes in the size of the ^^^^set. Notably, during the final iterations, the growth in the size of ^^^^stabilizes, confirming the validity of the convergence criteria. The convergence is achieved after approximately 120,000 seconds, affirming the effectiveness of the criteria. Furthermore, both phases exhibit a comparable computation time.Attorney Docket No. MIT-25388WO01

[0067] FIG.2B provides a snapshot of the constellation state over the Iberian Peninsula, displaying the elevation angles of the cells and the respective connected satellites. This visualization confirms the feasibility of the proposed solution, as no elevation angle falls below the operator-defined minimum (here, 25°). Furthermore, the distribution of cells across satellites demonstrates successful load balancing, optimizing resource utilization. Notably, the assignment of nearby cells to different satellites aligns with the objectives of the formulation: achieving load balance across satellites and reducing or minimizing potential interference, thereby enhancing overall performance and service quality. Hence, this validation confirms the feasibility of the solution and its alignment with the intended objectives. Performance Analysis

[0068] Consider three different implementations for the satellite routing problem: (1) mapping each cell to the satellite with the highest elevation angle, commonly used in practice; (2) utilizing a particle swarm optimization (PSO) process (applicable to the O3b mPower constellation); and (3) the inventive satellite routing approach. For the frequency assignment problem, we consider two implementations: one heuristic method and one optimized approach. This comparative analysis evaluates the impact of the inventive satellite routing methodology compared to other approaches and sheds light on the performance benefits and efficiency of the inventive approach.

[0069] FIG.3 illustrates simulation results for throughput and power consumption when providing fixed satellite service (FSS) using the O3b mPower, Telesat Lightspeed, and SpaceX Starlink constellations, along with mobile satellite service (MSS) using the SpaceX Starlink constellation. Additionally, TABLE 4 provides further details on key performance metrics for each scenario, in addition to results on the ViaSat LEO and OneWeb constellations.

[0070] The proposed cooperative framework, represented by the circles in FIG.4 and as the IO-IO combination in TABLE 4, consistently achieves the highest throughput, except for the O3b mPower constellation. This discrepancy is influenced by two factors. First, the low number of visible satellites in line of sight at any given point over the Earth surface (typically between one and two for O3b mPower) limits flexibility during satellite routing resolution, resulting in reduced benefits compared to larger systems. Second, utilizing complicated satellite routing increases power consumption compared to theAttorney Docket No. MIT-25388WO01 maximum elevation angle heuristic, due to greater distances between antennas and consequently higher free-space loss, leading to reduced throughput.

[0071] Increasing the number of visible satellites enhances flexibility in satellite routing, compensating for higher path loss and enabling significant throughput gains. Compared to heuristics, the inventive satellite routing boosts FSS service throughput by approximately 67% in ViaSat LEO, 68% in Telesat Lightspeed, 138% in SpaceX Starlink, and 83% in OneWeb. Throughput improvements are more pronounced with larger constellations, although not directly proportional. However, due to increased path loss, the inventive satellite routing raises power consumption by 143% in ViaSat LEO, 228% in Telesat Lightspeed, 395% in SpaceX Starlink, and 104% in OneWeb.

[0072] When employing individual optimization processes independently, higher throughput is observed compared to heuristics but is reduced compared to the coordinated method. In systems with more than 1,000 satellites, utilizing only the optimized satellite routing provides most of the benefits of the coordinated approach, resulting in throughput increases ranging between 39% and 95%. However, it also increases power consumption by between 106% and 347%. In these large systems, the impact of frequency assignment on throughput diminishes, contributing to throughput gains of 14% to 27% but with a comparatively modest increase in power consumption, ranging from 16% to 26%. Conversely, in smaller systems with up to 1,000 satellites where the flexibility of satellite routing is constrained, frequency assignment drives throughput improvements.

[0073] While counter-intuitive, in medium to large constellations (>100 satellites), adopting the inventive satellite routing enables greater spectrum utilization compared to employing optimized frequency assignment. This outcome is attributed to the ability of the proposed method to distribute demand more effectively, resulting in a higher number of active satellites and consequently increasing the available spectrum pool. With the coordinated approach, spectrum utilization can be enhanced by up to a factor of 3.3 when compared to heuristic techniques.

[0074] In the context of the SpaceX Starlink constellation, the throughput increase is 52% for MSS and 138% for FSS. This discrepancy arises due to the use of less directive antennas in MSS, which leads to two primary issues: (1) increased interference, thereby reducing the effectiveness of frequency reuse, and (2) higher power consumption, resulting in diminished throughput when power constraints cannot be met.Attorney Docket No. MIT-25388WO01Swcroeean nllitrthrmymtat eiOs:o coesiMn s nmp timE i stu i -s e lzM rellaatap t iotioanxirmeion sensso;Wun.mte Edaftc hhe F- WEleincO3 vaomb aateti robmrowinPo F n ill A,waw inntigghoele enr,;reo VIO †f s iaS- inIndat atti ecll LEeaite Ogetes ro,rthuTee tinlegsatAttorney Docket No. MIT-25388WO01

[0075] Consequently, the utilization of optimized satellite routing and frequency assignment results in a diminished benefit. Nonetheless, employing the coordinated approach still yields a notable throughput increase. Due to heightened interference among signals, computation time for MSS services extends to weeks due to the extra simulations. Operational Implementation

[0076] The inventive techniques address the allocation of cells on Earth to satellites for each time-step. In this approach, operators compute the solution in a centralized manner iteratively, considering all satellites simultaneously. Satellite routing assignments (and frequency assignments) can be determined and updated, for example, using a multi-core central processing unit (CPU) with sufficient random access memory (RAM), e.g., 16 cores of a 96-core CPU with 200 GB of RAM. The time for each iteration should be shorter than the interval between iterations to maintain smooth operations.

[0077] Upon computing the solution, e.g., with one or more suitable processors on the ground, the operators transmit relevant satellite routing information to the satellites. In particular, the operators transmit three blocks of information to the satellites: (1) the group of satellites assigned to each cell, which remains constant over time and can be transmitted once before the satellites begin operations; (2) the list of satellites that each cell can connect to at each time-step, denoted as ^^^∗^ (if ^^^∗^ is structured as a complete list of satellites ordered by elevation angle, this list can be computed through onboard computation (i.e., computation on the corresponding satellite)—alternative preference structures may involve additional telemetry); and (3) the group of cells assigned to each satellite, which is subject to change over time and may be updated regularly.

[0078] Nevertheless, operators do not need to transmit the full mapping of satellites to cell groups at every time-step. Instead, they may transmit only the sequence of cell groups for each satellite and the times when the cell groups change. This approach optimizes telemetry usage as consecutive time-steps usually have similar solutions. Additionally, the formulation can be optimized to reduce or minimize changes at each iteration, further reducing telemetry.Attorney Docket No. MIT-25388WO01

[0079] The operators on the ground can also perform frequency assignment, that is, assign the available frequency channels to the different cells, and transmit the frequency assignments to the satellites. More specifically, the operators can use one or more suitable processors on the ground to determine the central frequency, bandwidth, polarization, and frequency reuse for each cell. Unlike the cell-to-satellite mapping determined using satellite routing, frequency assignments remain fixed over time. As a result, the operators can compute frequency assignments in a centralized manner once, prior to the start of satellite operations. Since the frequency assignments remain fixed during operation of the satellite constellation, the operators can transmit the frequency assignments to the satellites once, before operations begin.

[0080] Once the satellites in the constellation have received the cell assignments and frequency assignments, they can because communicating with the ground terminals in those cells. Each satellite communicates with terminals in its assigned cells on the assigned frequency channels for those cells. For each time step, each satellite either updates its cell assignments or receives updates to its cell assignments from one or more of the ground terminal(s). The frequency assignments for the cells are fixed, so each satellite communicates with the updated cells at the previously assigned frequency channels for those cells.

[0081] Satellite routing does not constrain the frequency assignment to be fixed; rather, the fixed frequency assignments are a consequence of current frequency assignment methods. In addition, satellite routing still allows for other optimization or resource allocations techniques to be applied to different terminals within each cell. For instance, an operator could use multi-frequency time-division multiple access (MF-TDMA) or another suitable technique to allocate time and frequency / spectrum resources among terminals within the same cell. Similarly, beam hopping and similar techniques can be used to allocate resources among cells communicating with the same satellite. In summary, satellite routing does not necessarily constrain the use of other resource allocation techniques. Operations SimulationTABLE 5: Summary of parameters and results in the operations simulationAttorney Docket No. MIT-25388WO01

[0082] FIGS. 4A and 4B illustrate the evolution of throughput and power consumptionfor two distinct satellites in the SpaceX Starlink constellation with ^^^^^^^^ = 10,000locations and ^^^^^^ / ^^^^^^ = 10 users per location, along with the time placement of clusterto satellite changes. As depicted, a group / cluster change leads to significant fluctuations in both throughput and power consumption.

[0083] TABLE 5 presents results of the simulation. Notably, it shows a total of 20,114 cluster changes during the 1,000 seconds of simulation. This translates to an average of approximately 20 changes per second or an average time of 219 seconds before each satellite changes clusters. For the satellite with the highest number of changes, a cluster change occurred roughly every 25.6 seconds on average. Assuming clusters can be encoded using 2 Bytes of information and the time at which a cluster changes can be encoded using 8 Bytes, this implies a total of 1,609 bps to transmit the changes to the whole satellite constellation.

[0084] The total number of handovers are on the same order of magnitude as those made with simpler methods like the maximum elevation angle heuristic, meaning that the inventive satellite routing does not introduce unfeasible overhead. In this simulation, the computation time (950 seconds) is lower than the total simulated time (1,000 seconds), indicating that the satellite constellation can operate continuously without interruptions. To ensure feasibility, the computation for each time-step does not have to be lower than the time between time-steps, as the computation can be performed in advance. Continuous operations can be maintained so long as the average time-step computation is shorter than the time between time-steps. This indicates the feasibility and practicality of the proposed methodology for real-world applications, ensuring efficient use of resources and maintaining optimized performance over time. Commercial Applications

[0085] Satellite communications operators, e.g., for video streaming services or in-flight or in-cruise connectivity, can use the inventive technology to increase substantially the capacity offered by their constellations, without any hardware modification and only minor impacts on operations. In constellations like SpaceX, using the inventive methodology can lead to up to 75% increase in total throughput. Similar gains are expected in constellations with more than 1,000 LEO satellites (e.g., Telesat, OneWeb, SpaceX, Amazon, and Boeing constellations), or more than 100 MEO satellites (ViaSat,Attorney Docket No. MIT-25388WO01 SES, and Boeing constellations). Constellations with fewer satellites, like O3b mPower, observe enhanced capacity.

[0086] For the SpaceX constellation, using conventional satellite routing techniques leads to a total throughput of 7.31 Tbps, whereas using the inventive methodology leads to a total throughput of 12.8 Tbps. Currently, SpaceX offers residential products to most countries at a speed of around 100 Mbps. For the purpose of this lower bound estimate, assume that all customers are residential. This implies that SpaceX could serve 73,100 simultaneous customers using conventional satellite routing methods versus 128,000 simultaneous customers using the inventive satellite routing methods. Similar to terrestrial services, Internet connectivity tends to be oversubscribed, since the probability of all customers requiring Internet simultaneously is low. For this exercise, assume an oversubscription factor of 10:1. While this is relatively low compared to terrestrial factors (100:1), satellite contracts tend to be more limiting in the outage time allowed. This means that SpaceX could potentially have 731,000 subscribed customers using conventional satellite routing methods versus 1,280,000 subscribed customers using the inventive satellite routing methods. Conclusion

[0087] While various inventive embodiments have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and / or structures for performing the function and / or obtaining the results and / or one or more of the advantages described herein, and each of such variations and / or modifications is deemed to be within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and / or configurations will depend upon the specific application or applications for which the inventive teachings is / are used. Those skilled in the art will recognize or be able to ascertain, using no more than routine experimentation, many equivalents to the specific inventive embodiments described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed. Inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and / or method described herein. InAttorney Docket No. MIT-25388WO01 addition, any combination of two or more such features, systems, articles, materials, kits, and / or methods, if such features, systems, articles, materials, kits, and / or methods are not mutually inconsistent, is included within the inventive scope of the present disclosure.

[0088] Also, various inventive concepts may be embodied as one or more methods, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.

[0089] All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and / or ordinary meanings of the defined terms.

[0090] The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”

[0091] The phrase “and / or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the components so conjoined, i.e., components that are conjunctively present in some cases and disjunctively present in other cases. Multiple components listed with “and / or” should be construed in the same fashion, i.e., “one or more” of the components so conjoined. Other components may optionally be present other than the components specifically identified by the “and / or” clause, whether related or unrelated to those components specifically identified. Thus, as a non-limiting example, a reference to “A and / or B”, when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including components other than B); in another embodiment, to B only (optionally including components other than A); in yet another embodiment, to both A and B (optionally including other components); etc.

[0092] As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and / or” as defined above. For example, when separating items in a list, “or” or “and / or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of components, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of” or “exactly one of,” or, when used in the claims, “consisting of,” will referAttorney Docket No. MIT-25388WO01 to the inclusion of exactly one component of a number or list of components. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e., “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of.” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law.

[0093] As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more components, should be understood to mean at least one component selected from any one or more of the components in the list of components, but not necessarily including at least one of each and every component specifically listed within the list of components and not excluding any combinations of components in the list of components. This definition also allows that components may optionally be present other than the components specifically identified within the list of components to which the phrase “at least one” refers, whether related or unrelated to those components specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and / or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including components other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including components other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other components); etc.

[0094] In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.

Claims

Attorney Docket No. MIT-25388WO01 CLAIMS 1. A method of assigning communications satellites in non-geostationary orbit to cells on Earth, each of the cells containing at least one terminal for communicating with at least one of the communications satellites, the method comprising: aggregating the cells into cell groups such that each cell belongs to only one cell group; assigning each of the communications satellites to a corresponding cell group; for each of the cell groups, aggregating the communications satellites assigned to that cell group into a corresponding set of communications satellites; generating an assignment of each cell in each cell group to a corresponding communications satellite in the corresponding set of communications satellites for that cell group; transmitting the assignments to the communications satellites; and communicating, by the communications satellites, with terminals located in the cell groups to which the communications satellites are assigned.

2. The method of claim 1, wherein assigning each cell to a corresponding communications satellite is based on at least one of satellite elevation angle, distance between that cell and the corresponding communications satellite, power consumption, visibility conditions, weather conditions, interference level, available bandwidth, available carrier frequencies, or satellite battery status.

3. The method of claim 1, further comprising: allocating a different pool of resources to each of the cell groups.

4. The method of claim 3, wherein allocating a different pool of resources to each of the cell groups comprises allocating a different frequency channel to each of the cell groups.

5. The method of claim 4, wherein allocating a different frequency channel to each of the cell groups comprises selecting the different frequency channels to avoid interference between communications signals in adjacent cells.

6. The method of claim 1, further comprising:Attorney Docket No. MIT-25388WO01 updating the assignments for each of a sequence of time steps based at least in part on changes in positions of the communications satellites over the sequence of time steps.

7. The method of claim 6, further comprising: updating the assignments without changing frequency channel allocations for the cell groups.

8. A ground terminal configured to communicate with communications satellites configured according to the method of claim 1.

9. A method of assigning communications satellites in non-geostationary orbit to cells on Earth, each of the cells containing at least one terminal for communicating with at least one of the communications satellites, the method comprising: clustering the cells into cell groups such that each cell belongs to only one cell group; identifying which of the cells coincide on each of the communications satellites and which of the cells are likely to produce interference if assigned to the same frequency channel; generating assignments of the cell groups to respective communications satellites based on which of the cells coincide on each of the communications satellites and which of the cells are likely to produce interference if assigned to the same frequency channel; transmitting the assignments to the communications satellites; and communicating, by the communications satellites, with terminals located in the cell groups specified by the assignments.

10. The method of claim 9, wherein identifying which of the cells are likely to produce interference if assigned to the same frequency channel is based at least in part on geographical separation of the cells.

11. The method of claim 9, wherein generating the assignments comprises load balancing across the communications satellites.

12. The method of claim 9, further comprising: generating frequency channel assignments for the cell groups; andAttorney Docket No. MIT-25388WO01 transmitting the frequency channel assignments to the communications satellites.

13. The method of claim 9, further comprising: updating the assignments for each of a sequence of time steps based at least in part on changes in positions of the communications satellites over the sequence of time steps.

14. The method of claim 13, wherein updating the assignments comprises mapping each of the cells to only one of the communications satellites for each time step in the sequence of time steps.

15. The method of claim 13, wherein updating the assignments comprises mapping each of the cells to one of the communications satellites that is visible from that cell at that time step in the sequence of time steps.

16. The method of claim 13, wherein updating the assignments comprises identifying, for each of the cells, which of the communications satellites can connect to terminals in that cell.

17. The method of claim 16, wherein identifying, for each of the cells, which of the communications satellites can connect to the terminals in that cell is performed at a ground station.

18. The method of claim 16, wherein identifying, for each of the cells, which of the communications satellites can connect to the terminals in that cell is performed onboard the communications satellites.

19. The method of claim 9, further comprising: updating the assignments without changing frequency channel allocations for the cell groups.

20. A terminal on Earth configured to communicate with communications satellites configured according to the method of claim 9.

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