Method for determining radius of user cluster of low-orbit satellite, electronic equipment and program product

Abstract

The invention provides a low-orbit satellite user cluster radius determination method, electronic equipment and a computer program product. The method comprises the following steps: determining a cluster center of a target user cluster corresponding to a to-be-researched area and a deviation angle of the cluster center relative to a satellite nadir point; obtaining a user space distribution model based on the Poisson cluster process model; constructing a Doppler frequency shift function, a differential Doppler frequency shift function and a differential Doppler frequency shift cumulative distribution function; determining a first maximum cluster radius corresponding to the target user cluster through a differential Doppler frequency shift function based on the satellite parameters and the deviation angle of the satellite; based on the satellite parameters, the deviation angle and a user space distribution model, determining a second maximum cluster radius corresponding to the target user cluster through a differential Doppler frequency shift cumulative distribution function; an allowable maximum cluster radius is determined based on the first maximum cluster radius and the second maximum cluster radius.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of satellite communication, in particular to a low earth orbit satellite user cluster radius determination method, an electronic device and a program product. BACKGROUND

[0002] With the rapid development of low earth orbit (LEO) satellite communication systems, it has shown significant advantages in providing global coverage, low latency communication and supporting massive terminal access, and has become an important part of future space-earth integrated networks. In low earth orbit satellite communication systems, users are usually distributed in clusters. Especially in urban hotspots or specific application scenarios (such as Internet of Vehicles, Internet of Things, emergency communication, etc.), users show obvious spatial aggregation characteristics. In order to improve system resource utilization efficiency, optimize beamforming design, reduce multi-user interference and guarantee communication service quality, it is crucial to accurately model the spatial distribution of user clusters and reasonably determine the effective radius of user clusters. SUMMARY

[0003] The present disclosure provides a low earth orbit satellite user cluster radius determination method, an electronic device and a program product.

[0004] According to one aspect of the present disclosure, a low earth orbit satellite user cluster radius determination method is provided, comprising: determining a cluster center of a target user cluster corresponding to a to-be-studied region based on the to-be-studied region; determining an offset angle of the cluster center relative to a satellite nadir point based on the cluster center and a position of the satellite; generating random user positions around the cluster center based on a Poisson cluster process model to obtain a user spatial distribution model; constructing a Doppler shift function, the Doppler shift function being used to calculate Doppler shifts of each user in the user cluster relative to the satellite; constructing a differential Doppler shift function based on the Doppler shift function, the differential Doppler shift function being used to calculate a difference between Doppler shifts of any two users in the target user cluster; constructing a differential Doppler shift cumulative distribution function based on the differential Doppler shift function, the differential Doppler shift cumulative distribution function being used to represent a probability that a differential Doppler shift between any two users in the target user cluster does not exceed a given differential Doppler shift value; determining a first maximum cluster radius corresponding to the target user cluster by the differential Doppler shift function based on satellite parameters of the satellite and the offset angle; determining a second maximum cluster radius corresponding to the target user cluster by the differential Doppler shift cumulative distribution function based on the satellite parameters, the offset angle and the user spatial distribution model; and determining an allowed maximum cluster radius based on the first maximum cluster radius and the second maximum cluster radius.

[0005] According to the technical solution of the aspect, by constructing a unified analysis framework of fusing spherical random geometry and Poisson cluster process, the dependence on the deterministic user position is broken. Starting from the random user distribution, the analytical expression and the cumulative distribution function of the single-user Doppler shift and the differential Doppler shift between users in the same cluster are established, so as to quantify the OFDM subcarrier orthogonality destruction and the same frequency interference risk in the probabilistic sense. By determining the first maximum cluster radius and the second maximum cluster radius which take into account the worst case and the statistical confidence, and then determining the allowed maximum cluster radius, the user cluster size can be scientifically and adaptively constrained in the low-orbit satellite high-speed dynamic scene, and the negative influence of the differential Doppler shift on synchronization and demodulation performance can be effectively suppressed. At the same time, the single-cluster coverage efficiency is maximized under the premise of ensuring communication reliability, significantly reducing the beam management complexity and system signaling overhead, and providing a user clustering solution with robustness, scalability and deployment flexibility for non-terrestrial networks.

[0006] According to at least one embodiment of the present disclosure, the satellite parameters include an orbital height and a carrier frequency of the satellite.

[0007] According to the technical solution of the present embodiment, the physical nature of the Doppler effect in low-orbit satellite communication can be accurately reflected.

[0008] According to at least one embodiment of the present disclosure, based on the satellite parameters and the offset angle of the satellite, the first maximum cluster radius corresponding to the target user cluster is determined by the differential Doppler shift function, including: determining a differential Doppler shift threshold based on the 3GPP standard; constructing a maximum differential Doppler shift function, the maximum differential Doppler shift function is used to determine the maximum value of the difference between the Doppler shifts of any two users in the target user cluster; based on the orbital height and the offset angle, the maximum differential Doppler shift under different cluster radii is determined by the maximum differential Doppler shift function; and the cluster radius when the maximum differential Doppler shift is equal to the differential Doppler shift threshold is taken as the first maximum cluster radius corresponding to the target user cluster.

[0009] According to the technical solution of the present embodiment, by accurately solving the first maximum cluster radius satisfying the frequency synchronization tolerance under the worst geometric configuration, a strict cluster size upper limit constraint can be provided for the low-orbit satellite communication system. The inter-OFDM subcarrier interference and demodulation performance degradation caused by too large Doppler difference between users in the cluster are effectively avoided, and the link robustness and system reliability in the high-speed dynamic scene are significantly improved.

[0010] According to at least one embodiment of the present disclosure, based on the 3GPP standard, the differential Doppler shift threshold is determined, comprising: based on the 3GPP standard, determining an end-to-end residual frequency error tolerance; and converting the end-to-end residual frequency error tolerance into the differential Doppler shift threshold according to the carrier frequency.

[0011] According to the technical solution of the present embodiment, the standardized frequency synchronization performance requirement can be directly mapped to a quantifiable Doppler dynamic constraint. Thus, an engineering threshold basis conforming to the 3GPP specification is provided for user clustering in a high-speed mobile scenario such as a low-orbit satellite.

[0012] According to at least one embodiment of the present disclosure, the maximum differential Doppler shift function is a segmented function, wherein: in the case that the offset angle is greater than or equal to the cluster radius, the output of the maximum differential Doppler shift function is the difference between the Doppler shifts of the two users farthest and closest to the satellite nadir point located at the edge of the target user cluster; in the case that the offset angle is less than the cluster radius, the output of the maximum differential Doppler shift function is the Doppler shift of the user farthest to the satellite nadir point.

[0013] According to the technical solution of the present embodiment, the geometric accuracy and robustness of the first maximum cluster radius calculation are significantly improved, and overestimation or underestimation of the traditional unified model in the cross-nadir point scenario is avoided.

[0014] According to at least one embodiment of the present disclosure, based on the satellite parameters, the offset angle and the user spatial distribution model, the second maximum cluster radius corresponding to the target user cluster is determined through the differential Doppler shift cumulative distribution function, comprising: based on the 3GPP standard, determining a differential Doppler shift threshold; based on the orbital height, the offset angle and the user spatial distribution model, determining the probability that the differential Doppler shift between any two users in the target user cluster does not exceed the differential Doppler shift threshold under different cluster radii through the differential Doppler shift cumulative distribution function; and taking the cluster radius when the probability is equal to the target confidence as the second maximum cluster radius corresponding to the target user cluster.

[0015] According to the technical solution of the present embodiment, the random distribution characteristics of users and the reliability requirements of the system can be considered in the sense of probability, breaking through the conservative limit of worst-case design. While ensuring high-confidence synchronization performance, the user cluster coverage radius and spectrum resource utilization efficiency are significantly improved.

[0016] According to at least one embodiment of the present disclosure, based on the first maximum cluster radius and the second maximum cluster radius, determining an allowed maximum cluster radius comprises: extracting a minimum value in the first maximum cluster radius and the second maximum cluster radius; and dividing the minimum value by a safety factor to obtain the allowed maximum cluster radius.

[0017] According to the technical solution of the present embodiment, the design margin for coping with non-ideal factors can be effectively reserved under the premise of simultaneously meeting the deterministic performance boundary and the probabilistic reliability requirement, thereby significantly improving the synchronization stability, link robustness and deployment fault tolerance capability of the low-orbit satellite communication system in a dynamic complex environment, and avoiding performance degradation or connection interruption caused by boundary condition fluctuation.

[0018] According to at least one embodiment of the present disclosure, after determining the allowed maximum cluster radius, further comprising: based on the allowed maximum cluster radius, setting a target user cluster corresponding to the to-be-studied area, so that the cluster radius of the target user cluster does not exceed the allowed maximum cluster radius.

[0019] According to the technical solution of the present embodiment, the differential Doppler frequency shift between different users in the user cluster can be effectively controlled within the tolerance range specified in the 3GPP standard.

[0020] According to at least one embodiment of the present disclosure, based on the allowed maximum cluster radius, setting a target user cluster corresponding to the to-be-studied area comprises: in the case that the actual cluster radius corresponding to the current user cluster is greater than the allowed maximum cluster radius, dividing the current user cluster into multiple sub-clusters, so that the cluster radius of each sub-cluster does not exceed the allowed maximum cluster radius; and taking the multiple sub-clusters as the target user cluster corresponding to the to-be-studied area.

[0021] According to the technical solution of the present embodiment, the differential Doppler frequency shift between users in the user cluster can be avoided to exceed the compensation capability of the receiver, and the frequency error within each sub-cluster is ensured to be always within the system tolerable range.

[0022] According to at least one embodiment of the present disclosure, in the step of dividing the current user cluster into multiple sub-clusters, comprising: determining the number of sub-clusters; and based on the number, dividing the current user cluster into a corresponding number of sub-clusters, wherein in the step of determining the number of sub-clusters: dividing the cluster radius of the current user cluster by the allowed maximum cluster radius to obtain a radius ratio; multiplying the square of the radius ratio by a hexagonal dense packing optimal surface density constant to obtain a product; and rounding up the product to obtain the number of sub-clusters.

[0023] According to the technical solution of the embodiment, the number of sub-clusters can be minimized in a close-to-theoretical optimal coverage efficiency under the premise that each sub-cluster strictly satisfies the differential Doppler frequency shift constraint, scheduling complexity and signaling overhead increase caused by excessive segmentation are avoided, the area utilization advantage of the hexagonal cell model in plane coverage is fully utilized, and a user cluster division that is geometrically reasonable, resource-efficient and implementable in engineering is realized.

[0024] According to another aspect of the present disclosure, an electronic device is provided, comprising a memory storing execution instructions, and a processor executing the execution instructions stored in the memory, so that the processor executes the low-orbit satellite user cluster radius determination method of any embodiment of the present disclosure.

[0025] According to still another aspect of the present disclosure, a readable storage medium is provided, in which execution instructions are stored, the execution instructions being executed by a processor to implement the low-orbit satellite user cluster radius determination method of any embodiment of the present disclosure.

[0026] According to still another aspect of the present disclosure, a computer program product is provided, comprising a computer program, which, when executed by a processor, implements the low-orbit satellite user cluster radius determination method of any embodiment of the present disclosure. BRIEF DESCRIPTION OF DRAWINGS

[0027] The accompanying drawings illustrate exemplary embodiments of the present disclosure and together with the description, explain the principles of the present disclosure, in which the drawings are included to provide further understanding of the present disclosure and constitute a part of the description.

[0028] Figure 1 is a flowchart of the low-orbit satellite user cluster radius determination method according to one embodiment of the present disclosure.

[0029] Figure 2 is a schematic diagram of the geometric relationship between a satellite and a user according to one embodiment of the present disclosure.

[0030] Figure 3 is a flowchart of the method corresponding to step S170 according to one embodiment of the present disclosure.

[0031] Figure 4 is a flowchart of the method corresponding to step S180 according to another embodiment of the present disclosure.

[0032] Figure 5 is a structural schematic block diagram of the low-orbit satellite user cluster radius determination device according to one embodiment of the present disclosure.

[0033] Figure 6This is a schematic structural block diagram of an electronic device employing a processor-based hardware implementation according to one embodiment of the present disclosure. Detailed Implementation

[0034] The present disclosure will now be described in further detail with reference to the accompanying drawings and examples. It should be understood that the specific examples described herein are for illustrative purposes only and are not intended to limit the scope of the disclosure. Furthermore, it should be noted that, for ease of description, only the parts relevant to the present disclosure are shown in the accompanying drawings.

[0035] It should be noted that, where there is no conflict, the embodiments and features described in this disclosure can be combined with each other. The technical solutions of this disclosure will now be described in detail with reference to the accompanying drawings and embodiments.

[0036] In traditional terrestrial cellular networks, the user cluster radius is typically set based on static indicators such as geographical coverage, user density, or channel correlation. However, low-Earth orbit (LEO) satellites are characterized by high-speed motion, low orbital altitude, and dynamically changing coverage areas, causing the link characteristics between users and satellites (such as propagation distance, angle of incidence, and Doppler shift) to change rapidly over time. Doppler shift is a key physical effect in LEO satellite communication, affecting not only carrier synchronization and signal demodulation but also introducing significant frequency offset differences within user clusters. When the Doppler shift difference between different users within a cluster relative to the satellite is too large, it becomes difficult for the receiver to employ a unified frequency offset compensation strategy, leading to inter-symbol interference, increased bit error rate, and even communication interruptions.

[0037] In existing technologies, some studies attempt to limit the user cluster radius based on the maximum Doppler frequency shift or geometric coverage, but these often neglect the randomness of user spatial distribution and the statistical characteristics of Doppler differences between any two users within the cluster. Furthermore, most methods do not adequately consider the impact of the relative position (i.e., offset angle) between the satellite nadir and the user cluster center on the Doppler gradient, and lack quantitative analysis of the coupling relationship between the user distribution model and Doppler performance. Therefore, existing methods for determining the user cluster radius struggle to balance the frequency offset tolerance of the communication system with the actual situation of user spatial distribution, exhibiting problems such as poor adaptability, high conservatism, or insufficient performance guarantees.

[0038] To address this, this disclosure proposes the following technical solution, which involves modeling the random distribution of user space using a Poisson cluster process. Combining satellite geometry and Doppler frequency shift characteristics, a differential Doppler frequency shift and its cumulative distribution function are constructed. This allows for the simultaneous quantification of the impact of user cluster radius on Doppler frequency shift compatibility from both a deterministic dimension (i.e., the maximum differential Doppler frequency shift) and a statistical dimension (i.e., the cumulative distribution function of the differential Doppler frequency shift). Based on this, the maximum allowable cluster radius is determined by combining the first maximum cluster radius (based on the worst-case scenario) and the second maximum cluster radius (based on probabilistic constraints). This avoids the drawbacks of overly conservative or aggressive traditional methods while effectively ensuring the frequency offset tolerance and communication reliability of users within the cluster in high-speed moving satellite scenarios, significantly improving the resource scheduling efficiency and service quality of low-Earth orbit satellite systems in densely populated user areas.

[0039] To facilitate description and make the technical solutions of this disclosure easier to understand, the terminology of this disclosure will be explained before describing the technical solutions of this disclosure.

[0040] Doppler shift refers to the change in phase and frequency caused by the difference in propagation path when a mobile station moves at a constant speed in a certain direction. This change is usually called Doppler shift.

[0041] The Poisson Cluster Process (PCP) is an extension of the Poisson process in multidimensional space, used to describe the distribution of random points with clustering properties. The Poisson process is a type of stochastic process, a counting process with independent, stationary increments.

[0042] 3GPP is a standardization body established by multiple telecommunications standards organizations worldwide, with the aim of developing and maintaining technical specifications for mobile communication systems.

[0043] The cumulative distribution function (CDF) is a function that describes the probability that a random variable takes a value less than or equal to a certain specific value.

[0044] This disclosure can be widely applied to 5G or 6G non-terrestrial network systems based on low-Earth orbit satellites, and is particularly suitable for high-speed, dynamic, and wide-area coverage scenarios, such as satellite internet services (e.g., Starlink systems), broadband access in remote areas, maritime and aviation communications, emergency disaster relief communications, and wide-area collaborative sensing in vehicle-to-everything (V2X) networks. In these scenarios, the system needs to efficiently cluster ground users to support beamforming, resource scheduling, and synchronization management. The cluster radius determination method provided in this disclosure can adaptively calculate the maximum allowable user cluster radius that meets Doppler performance constraints based on satellite parameters, user spatial distribution models, and 3GPP standard frequency tolerances, and guide the intelligent partitioning of user clusters. This improves spectrum efficiency and network scalability while ensuring link reliability, providing key technical support for the standardized deployment and commercial operation of low-Earth orbit satellite communication systems.

[0045] Figure 1 A schematic flowchart illustrating the overall process of a method for determining the radius of a low-Earth orbit satellite user cluster according to one embodiment of this disclosure is shown. Figure 1 The method shown includes steps S110 to S190.

[0046] In step S110, based on the region to be studied, the cluster center of the target user cluster corresponding to the region to be studied is determined.

[0047] The area to be studied can be a region with obvious user clustering characteristics, such as a city, industrial park, or port. In this disclosure, the area to be studied needs to be determined in advance.

[0048] In low Earth orbit satellite communication systems, a user cluster refers to a group of ground users that are grouped together within a specific geographical area (such as the coverage area of ​​a single satellite beam) due to geographical proximity, service needs, or network scheduling strategies. These users typically exhibit spatial clustering characteristics and may be concentrated in hotspot areas such as cities, ports, and industrial parks.

[0049] The cluster center refers to a representative location point of a user cluster in geospatial space, used to characterize the overall spatial location and aggregation core of the user cluster. In subsequent steps, the cluster center serves as the parent point of the Poisson cluster process, acting as a benchmark reference for generating random user locations within the user cluster, directly affecting the geometric relationships and differential Doppler statistical characteristics of Doppler frequency shift modeling.

[0050] As one possible implementation, in determining the cluster center of the target user cluster corresponding to the region under study, the geometric center of the region under study can be used as the cluster center. This implementation is suitable for scenarios where user location information is unknown, sparse, or dynamically changing.

[0051] As another possible implementation, considering that in most terrestrial communication scenarios, the distribution of user terminals (such as mobile phones and IoT devices) is highly positively correlated with population density, the statistical center of the area under study can be used as the cluster center when determining the cluster center of the target user cluster corresponding to the area under study. For example, the statistical center can be the population density center. By using the population density center as the cluster center of the target user cluster, the spatial aggregation pattern of human activities and communication needs can be effectively reflected.

[0052] In step S120, the offset angle of the cluster center relative to the satellite nadir is determined based on the cluster center and the location of the satellite.

[0053] The satellite nadir point refers to the point where, when a satellite is in orbit, the line connecting its center of mass (or antenna phase center) to the center of the Earth intersects with the Earth's surface (usually the reference ellipsoid or mean sea level).

[0054] The offset angle reflects the degree to which the cluster center deviates from the position directly below the satellite (i.e., the satellite nadir point), and is a key geometric parameter affecting the magnitude and direction of the Doppler shift.

[0055] Figure 2 The geometric relationship between the satellite and the user is shown. Figure 2 In the diagram, O represents the Earth's center (i.e., the center of the planet), and C represents the cluster center. r Here, s represents the satellite's nadir, u represents the user, h represents the satellite's altitude above mean sea level, and R represents the Earth's radius. Indicates the cluster radius, Θ represents the geocentric angle of the user relative to the satellite nadir point, and Θ represents the geocentric angle of the user relative to the cluster center. This represents the offset angle of the cluster center relative to the satellite's nadir point.

[0056] In determining the offset angle of the cluster center relative to the satellite nadir, the central angle formed by the cluster center and the satellite nadir with respect to the Earth's center can be calculated using spherical trigonometric formulas, based on the cluster center (e.g., the coordinates of the cluster center) and the satellite's position (e.g., the three-dimensional coordinates of the satellite). This central angle is the offset angle of the cluster center relative to the satellite nadir.

[0057] In step S130, based on the Poisson cluster process model, random user locations are generated around the cluster center to obtain the user spatial distribution model.

[0058] As one possible implementation, based on the Poisson cluster process model, a user spatial distribution model is obtained by generating random user locations around the cluster center. First, the cluster center is set as the parent point (representing the core of the user cluster). Then, around the cluster center, several "sub-points" are randomly generated according to a certain probability distribution (such as a two-dimensional Gaussian distribution or a uniform disk distribution), with each sub-point corresponding to the location of a ground user. Finally, the initial cluster radius of the user cluster is determined. This method yields a user spatial distribution model with the cluster center as its core, exhibiting randomness and spatial correlation. This model not only preserves the macroscopic characteristics of user clustering but also introduces the uncertainty of microscopic locations, overcoming the limitations of traditional deterministic assumptions (such as all users being located at fixed grid points).

[0059] In step S140, the Doppler frequency shift function is constructed.

[0060] The Doppler shift function is used to calculate the Doppler shift of each user within a user cluster relative to the satellite.

[0061] As one possible implementation method, the Doppler frequency shift function Represented as: in, Indicates the angular velocity of the satellite; The carrier frequency of the satellite is represented by 'c'; the speed of light is represented by 'a'; and the orbital radius of the satellite is represented by 'a' (i.e., the distance from the Earth's center to the satellite, a = R + h).

[0062] In step S150, a differential Doppler frequency shift function is constructed based on the Doppler frequency shift function.

[0063] The differential Doppler frequency shift function is used to calculate the difference in Doppler frequency shift between any two users within a target user cluster. As one possible implementation, the differential Doppler frequency shift function is expressed as: in, This represents the differential Doppler frequency shift between user A and user B; This indicates the Doppler frequency shift of user A; This indicates the Doppler frequency shift of user B.

[0064] In step S160, a differential Doppler frequency shift cumulative distribution function is constructed based on the differential Doppler frequency shift function.

[0065] The differential Doppler shift cumulative distribution function (DDoSFC) represents the probability that, for any given DDoS shift value, the DDoS shift between any two users within a target user cluster does not exceed that value. As one possible implementation, the DDoSFC cumulative distribution function... Represented as: in, This represents the differential Doppler frequency shift threshold. This is the normalization constant. This indicates the maximum geocentric angle corresponding to the coverage area of ​​the satellite beam. It is a normalized joint probability density kernel function. I (.) is a surface integral function of a sphere, where the parameter in the function is Time is represented as . As a parameter of a function, it can take the value of or . Indicates that under given parameters and Under the condition that |X( )-X( )∣≤ The minimum geocentric angle. Indicates that under given parameters and Under the condition that |X( )-X( )∣≤ The maximum geocentric angle X( ) indicates the geocentric angle is The user's Doppler frequency shift. In |X( )-X( ) | in, Given the known reference user's geocentric angle, Let be the geocentric angle of another user, which is the variable to be solved. Denotes the integration field, by Control, its explicit integration domain is . The parameter is The integration domain at time, and They belong to the same integration domain. Let be an indicator function, representing the pairwise geocentric angles between three known points on a sphere, ... , When and Θ, and The included angle between the two sides (spherical angle).

[0066] In step S170, based on the satellite parameters and offset angle, the first maximum cluster radius corresponding to the target user cluster is determined by the differential Doppler frequency shift function.

[0067] As one possible implementation, satellite parameters include the satellite's orbital altitude and carrier frequency.

[0068] Regarding step S170, in some embodiments of this disclosure, it may include, for example... Figure 3 Steps S1701 to S1704 are shown.

[0069] In step S1701, the differential Doppler frequency shift threshold is determined based on the 3GPP standard.

[0070] As one possible implementation, determining the differential Doppler frequency shift threshold based on the 3GPP standard includes: determining the end-to-end remaining frequency error tolerance based on the 3GPP standard; and converting the end-to-end remaining frequency error tolerance into a differential Doppler frequency shift threshold based on the carrier frequency.

[0071] In wireless communication systems, frequency errors mainly originate from frequency deviations, Doppler shifts, and network synchronization errors in the local oscillators of user equipment (UE) and base stations (gNB). End-to-end residual frequency error refers to the frequency offset remaining at the receiver after frequency correction mechanisms (such as initial synchronization, tracking loop, and reference signal-assisted correction) have been implemented. 3GPP defines a frequency error tolerance, stipulating that the single-end error should be within 0.1 ppm; therefore, the end-to-end residual frequency error tolerance can be set to 0.2 ppm.

[0072] In one example, if the end-to-end residual frequency error tolerance is 0.2 ppm, then the converted differential Doppler frequency shift threshold is 0.2 ppm × =2×10 -7 × .

[0073] In step S1702, the maximum differential Doppler frequency shift function is constructed.

[0074] The maximum differential Doppler shift function (MDF) is used to determine the maximum difference between the Doppler shifts of any two users within a target user cluster. As one possible implementation, the MDF is a piecewise function, where: when the offset angle is greater than or equal to the cluster radius, the output of the MDF is the difference between the Doppler shifts of the two users located at the edge of the target user cluster and furthest and closest to the satellite nadir. When the offset angle is less than the cluster radius, the output of the MDF is the Doppler shift of the user furthest from the satellite nadir. Exemplarily, the MDF... Represented as: in, This is the proportionality coefficient.

[0075] This maximum difference Doppler shift function can accurately distinguish different geometric positions of user clusters relative to the satellite nadir. When the user cluster as a whole is located on one side of the satellite nadir (offset angle ≥ cluster radius), it accurately captures the difference in Doppler shift between the farthest and nearest users within the cluster. When the user cluster covers the satellite nadir (offset angle < cluster radius), the Doppler shift of the farthest user on one side is used as the dominant error source. Therefore, it can estimate the worst-case difference Doppler shift with high fidelity under different coverage configurations, avoiding overestimation or underestimation in cross-nadir scenarios using traditional unified models.

[0076] In step S1703, based on the orbital altitude and offset angle, the maximum differential Doppler frequency shift under different cluster radii is determined using the maximum differential Doppler frequency shift function.

[0077] In step S1704, the cluster radius at which the maximum differential Doppler frequency shift equals the differential Doppler frequency shift threshold is taken as the first maximum cluster radius corresponding to the target user cluster.

[0078] In scenarios where the satellite position and cluster center position are fixed, all parameters in the maximum differential Doppler shift function (MDF) except for the cluster radius (such as orbital altitude, carrier frequency, relative geometric angle, etc.) are known constants. Therefore, the MDF can be considered a single-variable function of the cluster radius, and it monotonically increases within a physically reasonable range. When the target MDF is given (e.g., equal to the MDF threshold), the corresponding cluster radius, i.e., the first maximum cluster radius, can be uniquely determined by solving the inverse function of this function.

[0079] In steps S1701 to S1704, by combining the differential Doppler frequency shift threshold specified in the 3GPP standard with the maximum differential Doppler frequency shift function constructed based on parameters such as satellite orbital altitude and offset angle, the first maximum cluster radius that satisfies the frequency synchronization tolerance constraint is accurately calculated. This implementation method can maximize the service coverage of a single beam or single cluster while ensuring receiver demodulation performance and system synchronization reliability, effectively balancing spectral efficiency, link robustness, and user scheduling complexity, and providing a basis for user clustering in high-speed mobile scenarios.

[0080] In step S180, based on satellite parameters, offset angle, and user space distribution model, the second maximum cluster radius corresponding to the target user cluster is determined by the differential Doppler frequency shift cumulative distribution function.

[0081] Regarding step S180, in some embodiments of this disclosure, it may include, for example...Figure 4 Steps S1801 to S1803 are shown.

[0082] In step S1801, the differential Doppler frequency shift threshold is determined based on the 3GPP standard. The implementation process of step S1801 is the same as that of step S1701, and will not be described again here.

[0083] In step S1802, based on the orbital altitude, offset angle, and user space distribution model, the probability that the differential Doppler frequency shift between any two users in the target user cluster does not exceed the differential Doppler frequency shift threshold is determined using the differential Doppler frequency shift cumulative distribution function under different cluster radii.

[0084] In scenarios where the satellite position and cluster center position are fixed, the statistical characteristics of differential Doppler shift can be fully characterized by its cumulative distribution function, taking into account orbital altitude, offset angle, and user spatial distribution model. The differential Doppler shift cumulative distribution function describes the probability that, given a cluster radius, the differential Doppler shift between any two users within the target user cluster does not exceed a certain threshold.

[0085] In step S1803, the cluster radius when the probability equals the target confidence level is taken as the second maximum cluster radius corresponding to the target user cluster.

[0086] Since parameters such as orbital altitude, carrier frequency, satellite velocity, and offset angle are all known, and the user space distribution model is fixed, the differential Doppler frequency shift cumulative distribution function only changes with the cluster radius; that is, it can be regarded as a univariate function of the cluster radius.

[0087] As the cluster radius increases, the maximum spatial distance between users increases, leading to an expansion of the differential Doppler shift range. Consequently, the cumulative distribution function of this function monotonically decreases at a fixed differential Doppler shift threshold. Therefore, when a target confidence level is set—that is, the probability that the differential Doppler shift between any two users within a cluster does not exceed this threshold is not lower than this target confidence level—there exists a unique cluster radius such that this probability is exactly equal to the target confidence level, provided that the user spatial distribution is continuous and the geometric relationship is reasonable. This cluster radius can be determined by solving for the inverse function (or numerical inverse solution) of the differential Doppler shift cumulative distribution function; this is the second maximum cluster radius corresponding to the target user cluster. The second maximum cluster radius, while ensuring statistical robustness, is more flexible and resource-efficient than the first maximum cluster radius obtained based on the worst-case scenario.

[0088] In step S190, the maximum allowable cluster radius is determined based on the first maximum cluster radius and the second maximum cluster radius.

[0089] As one possible implementation, determining the maximum allowable cluster radius based on a first maximum cluster radius and a second maximum cluster radius includes: extracting the minimum value between the first maximum cluster radius and the second maximum cluster radius; dividing the minimum value by a safety factor to obtain the maximum allowable cluster radius. For example, the safety factor can be set to a value between 1.1 and 1.25. By setting a safety factor, a design margin can be effectively reserved while considering robustness and actual deployment uncertainties, thereby significantly improving the stability of non-terrestrial networks in high-speed dynamic scenarios and avoiding performance drops or connection interruptions caused by sudden changes in boundary conditions.

[0090] As a further implementation, after determining the maximum allowable cluster radius, the method further includes: setting the target user cluster corresponding to the area under study based on the maximum allowable cluster radius, such that the cluster radius of the target user cluster does not exceed the maximum allowable cluster radius. This implementation can effectively control the differential Doppler frequency shift between different users within a user cluster to be within the tolerance range specified by the 3GPP standard.

[0091] As one possible implementation, based on the maximum allowable cluster radius, the target user cluster corresponding to the area under study is configured, including: if the actual cluster radius of the current user cluster is greater than the maximum allowable cluster radius, the current user cluster is divided into multiple sub-clusters, such that the cluster radius of each sub-cluster does not exceed the maximum allowable cluster radius. These multiple sub-clusters are then used as the target user clusters corresponding to the area under study. This implementation can prevent the inter-user differential Doppler frequency shift within a user cluster from exceeding the receiver's compensation capability, ensuring that the frequency error within each sub-cluster remains within the system's tolerable range.

[0092] For example, within a low-Earth orbit satellite beam service area covering a suburban city, the initial user cluster (i.e., the current user cluster) has an actual cluster radius of 25 kilometers, while the maximum allowable cluster radius calculated using the aforementioned method is 15 kilometers. Since 25 kilometers > 15 kilometers, the current user cluster cannot meet the frequency synchronization performance requirements, and therefore needs to be divided into multiple sub-clusters. In the sub-cluster division, starting from the cluster center of the current user cluster, a spatial clustering algorithm (such as K-means or grid partitioning) is used to reorganize the users into multiple sub-regions, ensuring that the geometric radius of each sub-cluster does not exceed 15 kilometers (e.g., it can be divided into two closely spaced sub-clusters with radii of 12 kilometers and 13 kilometers, respectively). These newly generated sub-clusters serve as the target user cluster for the area under study. The target user cluster obtained through this implementation satisfies both the 3GPP constraints on differential Doppler frequency shift and ensures the reliability of downlink synchronization and data demodulation.

[0093] As one possible implementation, dividing the current user cluster into multiple subclusters includes: determining the number of subclusters; and dividing the current user cluster into a corresponding number of subclusters based on the number of subclusters. Specifically, in determining the number of subclusters: the cluster radius of the current user cluster is divided by the maximum allowed cluster radius to obtain a radius ratio. The square of the radius ratio is multiplied by the optimal surface density constant of the hexagonal tessellation to obtain a product. The product is then rounded up to obtain the number of subclusters.

[0094] For example, in the above example, the current user cluster's cluster radius is 25 kilometers, and the maximum allowed cluster radius is 15 kilometers. The radius ratio is 25 / 15 ≈ 1.667. The product is 1.667. 2 ×1.1547 (optimal surface density constant for hexagonal tessellation) ≈ 3.21. Rounding up 3.21 gives 4 subclusters.

[0095] This implementation method can minimize the number of subclusters with near-theoretical optimal coverage efficiency while ensuring that each subcluster strictly satisfies the differential Doppler frequency shift constraint. It avoids increased scheduling complexity and signaling overhead caused by excessive segmentation, and fully utilizes the area utilization advantage of the hexagonal cellular model in planar coverage to achieve geometrically reasonable, resource-efficient and engineering-feasible user cluster partitioning.

[0096] The following example illustrates the process of finding the maximum allowed cluster radius.

[0097] Set the satellite's orbital altitude Earth's radius R = 6378 km, speed of light c = m / s, standard gravitational parameter = carrier frequency =2.0GHz, offset angle Target confidence =99%, with a safety factor of 1.1.

[0098] The differential Doppler frequency shift threshold determined based on the 3GPP standard is: =2×10 -7 × =400hz.

[0099] Substituting the above satellite parameters and offset angle into the maximum differential Doppler frequency shift function Then, it is inversely solved to output 400Hz (i.e., The first maximum cluster radius is obtained as .

[0100] Substituting the aforementioned satellite parameters, offset angle, and target confidence level into the differential Doppler frequency shift cumulative distribution function, and performing an inverse solution to obtain the target confidence level, the second maximum cluster radius is obtained. .

[0101] The first maximum cluster radius is less than the second maximum cluster radius. Therefore, the minimum value (i.e., the first maximum cluster radius) is divided by the safety factor to obtain the maximum allowable cluster radius: / 1.1= The equivalent arc length is 23.81 km. Therefore, the maximum allowable cluster radius achievable in this case is 23.81 km.

[0102] According to any of the above embodiments, this disclosure also provides a low-orbit satellite user cluster radius determination device 200. Figure 5 This is a schematic block diagram of a low-Earth orbit satellite user cluster radius determination device 200 according to one embodiment of this disclosure. Figure 5 As shown, the low-Earth orbit satellite user cluster radius determination device 200 includes a cluster center determination module 210, an offset angle determination module 220, a user spatial distribution model construction module 230, a Doppler frequency shift function construction module 240, a differential Doppler frequency shift function construction module 250, a cumulative distribution function construction module 260, a first maximum cluster radius determination module 270, a second maximum cluster radius determination module 280, and an allowable maximum cluster radius determination module 290. Specifically, the cluster center determination module 210 determines the cluster center of the target user cluster corresponding to the region under study. The offset angle determination module 220 determines the offset angle of the cluster center relative to the satellite's nadir point based on the cluster center and the satellite's location. The user spatial distribution model construction module 230 generates random user locations around the cluster center based on a Poisson cluster process model to obtain a user spatial distribution model. The Doppler frequency shift function construction module 240 constructs the Doppler frequency shift function. The differential Doppler frequency shift function construction module 250 is used to construct a differential Doppler frequency shift function based on the differential Doppler frequency shift function. The cumulative distribution function construction module 260 is used to construct a differential Doppler frequency shift cumulative distribution function based on the differential Doppler frequency shift function. The first maximum cluster radius determination module 270 is used to determine the first maximum cluster radius corresponding to the target user cluster based on the satellite parameters and offset angle, using the differential Doppler frequency shift function. The second maximum cluster radius determination module 280 is used to determine the second maximum cluster radius corresponding to the target user cluster based on the satellite parameters, offset angle, and user space distribution model, using the differential Doppler frequency shift cumulative distribution function. The allowable maximum cluster radius determination module 290 is used to determine the allowable maximum cluster radius based on the first and second maximum cluster radii.

[0103] According to further embodiments of this disclosure, an electronic device is also provided. Figure 6This diagram illustrates a schematic block diagram of an electronic device employing a processor-based hardware implementation according to an embodiment of the present disclosure. The hardware structure of the electronic device of the present disclosure can be implemented using a bus architecture. The bus architecture can include any number of interconnect buses and bridges, depending on the specific application and overall design constraints of the hardware. Bus 1100 connects various circuits including one or more processors 1200, memory 1300, and / or hardware modules. Bus 1100 can also connect various other circuits 1400 such as peripheral devices, voltage regulators, power management circuits, external antennas, etc. Bus 1100 can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Component (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, only one connecting line is used in this figure, but this does not imply that there is only one bus or one type of bus. Memory 1300 stores a computer program, and when processor 1200 executes the computer program, processor 1200 is able to perform the following processes. Based on the region under study, the cluster center of the target user cluster corresponding to the region is determined. Based on the cluster center and the satellite's location, the offset angle of the cluster center relative to the satellite's nadir is determined. Based on the Poisson cluster process model, random user locations are generated around the cluster center to obtain a user spatial distribution model. A Doppler frequency shift function is constructed to calculate the Doppler frequency shift of each user within the user cluster relative to the satellite. Based on the Doppler frequency shift function, a differential Doppler frequency shift function is constructed to calculate the difference between the Doppler frequency shifts of any two users within the target user cluster. Based on the differential Doppler frequency shift function, a differential Doppler frequency shift cumulative distribution function is constructed to represent the probability that, for any given differential Doppler frequency shift value, the differential Doppler frequency shift between any two users within the target user cluster does not exceed that value. Based on the satellite parameters and offset angle, the first maximum cluster radius corresponding to the target user cluster is determined using the differential Doppler frequency shift function. Based on satellite parameters, offset angle, and user space distribution model, the second maximum cluster radius corresponding to the target user cluster is determined using the differential Doppler frequency shift cumulative distribution function. Based on the first and second maximum cluster radii, the allowable maximum cluster radius is then determined.

[0104] This disclosure also provides a readable storage medium storing a computer program that, when executed by a processor, is used to implement the methods described above. A "readable storage medium" can be any means capable of containing, storing, communicating, propagating, or transmitting a program for use by or in conjunction with an instruction execution system, apparatus, or device. More specific examples of a readable storage medium include: an electrical connection with one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and portable read-only memory (CDROM), etc.

[0105] This disclosure also provides a computer program product, the methods of which can be implemented wholly or partially through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented wholly or partially as a computer program product. The computer program product includes one or more computer programs or instructions. When the computer program or instructions are loaded and executed, all or part of the processes or functions of this disclosure are performed.

[0106] Computer programs or instructions can be stored in a readable storage medium or transferred from one readable storage medium to another. For example, the computer program or instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The readable storage medium can be any available medium capable of access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, such as a floppy disk, hard disk, or magnetic tape; an optical medium, such as a digital video optical disc; or a semiconductor medium, such as a solid-state drive. The computer-readable storage medium can be a volatile or non-volatile storage medium, or it can include both volatile and non-volatile types of storage media.

[0107] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0108] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0109] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0110] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0111] In the description of this specification, the references to terms such as "one embodiment / mode," "some embodiments / modes," "example," "specific example," or "some examples," etc., refer to specific features, structures, or characteristics described in connection with that embodiment / mode or example, which are included in at least one embodiment / mode or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment / mode or example. Moreover, the specific features, structures, or characteristics described may be combined in any suitable manner in one or more embodiments / modes or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments / modes or examples described in this specification, as well as the features of different embodiments / modes or examples.

[0112] Those skilled in the art should understand that the above embodiments are merely for illustrating the present disclosure and are not intended to limit the scope of the disclosure. Those skilled in the art can make other changes or modifications based on the above disclosure, and these changes or modifications still fall within the scope of the present disclosure.

Claims

1. A method for determining the radius of a low-Earth orbit satellite user cluster, characterized in that, include: Based on the region to be studied, determine the cluster center of the target user cluster corresponding to the region to be studied; Based on the location of the cluster center and the satellite, determine the offset angle of the cluster center relative to the satellite's nadir point; Based on the Poisson cluster process model, random user locations are generated around the cluster center to obtain a user spatial distribution model. Construct a Doppler frequency shift function, which is used to calculate the Doppler frequency shift of each user in the user cluster relative to the satellite; Based on the Doppler frequency shift function, a differential Doppler frequency shift function is constructed. The differential Doppler frequency shift function is used to calculate the difference between the Doppler frequency shifts of any two users within the target user cluster. Based on the differential Doppler frequency shift function, a differential Doppler frequency shift cumulative distribution function is constructed. The differential Doppler frequency shift cumulative distribution function is used to represent the probability that, for any given differential Doppler frequency shift value, the differential Doppler frequency shift between any two users in the target user cluster does not exceed that value. Based on the satellite parameters and the offset angle, the first maximum cluster radius corresponding to the target user cluster is determined using the differential Doppler frequency shift function; Based on the satellite parameters, the offset angle, and the user space distribution model, the second maximum cluster radius corresponding to the target user cluster is determined using the differential Doppler frequency shift cumulative distribution function. as well as Based on the first maximum cluster radius and the second maximum cluster radius, the maximum allowable cluster radius is determined.

2. The method as described in claim 1, characterized in that, The satellite parameters include the satellite's orbital altitude and carrier frequency.

3. The method as described in claim 2, characterized in that, Based on the satellite parameters and the offset angle, the first maximum cluster radius corresponding to the target user cluster is determined using the differential Doppler frequency shift function, including: Based on the 3GPP standard, the differential Doppler frequency shift threshold is determined; A maximum differential Doppler frequency shift function is constructed, which is used to determine the maximum value of the difference between the Doppler frequency shifts of any two users within the target user cluster; Based on the orbital altitude and the offset angle, the maximum differential Doppler frequency shift (MDF) is determined using the MDF function for different cluster radii; and The cluster radius at which the maximum differential Doppler frequency shift equals the differential Doppler frequency shift threshold is taken as the first maximum cluster radius corresponding to the target user cluster.

4. The method as described in claim 3, characterized in that, Based on the 3GPP standard, the differential Doppler frequency shift threshold is determined, including: Based on the aforementioned 3GPP standard, determine the end-to-end remaining frequency error tolerance; and Based on the carrier frequency, the end-to-end residual frequency error tolerance is converted into the differential Doppler frequency shift threshold.

5. The method as described in claim 3, characterized in that, The maximum differential Doppler frequency shift function is a piecewise function, where: When the offset angle is greater than or equal to the cluster radius, the output of the maximum differential Doppler frequency shift function is the difference in Doppler frequency shift between the two users located at the edge of the target user cluster and the two users farthest and closest to the satellite nadir point; When the offset angle is less than the cluster radius, the output of the maximum differential Doppler shift function is the Doppler shift of the user farthest from the satellite nadir.

6. The method as described in claim 2, characterized in that, Based on the satellite parameters, the offset angle, and the user space distribution model, the second maximum cluster radius corresponding to the target user cluster is determined using the differential Doppler frequency shift cumulative distribution function, including: Based on the 3GPP standard, the differential Doppler frequency shift threshold is determined; Based on the orbital altitude, the offset angle, and the user spatial distribution model, the probability that the differential Doppler frequency shift between any two users within the target user cluster does not exceed the differential Doppler frequency shift threshold is determined using the differential Doppler frequency shift cumulative distribution function, under different cluster radii; and The cluster radius at which the probability equals the target confidence level is taken as the second maximum cluster radius corresponding to the target user cluster.

7. The method as described in claim 1, characterized in that, After determining the maximum allowable cluster radius, the following is also included: Based on the maximum allowed cluster radius, the target user cluster corresponding to the region under study is set such that the cluster radius of the target user cluster does not exceed the maximum allowed cluster radius.

8. The method as described in claim 7, characterized in that, Based on the maximum allowed cluster radius, the target user clusters corresponding to the region under study are set, including: If the actual cluster radius of the current user cluster is greater than the maximum allowed cluster radius, the current user cluster is divided into multiple sub-clusters, such that the cluster radius of each sub-cluster does not exceed the maximum allowed cluster radius; and The multiple subclusters are used as target user clusters corresponding to the region under study.

9. An electronic device, characterized in that, include: The memory stores execution instructions; as well as A processor that executes the execution instructions stored in the memory, causing the processor to perform the method for determining the radius of a low-orbit satellite user cluster as described in any one of claims 1 to 8.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for determining the low-orbit satellite user cluster radius as described in any one of claims 1 to 8.

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