A user-base station-LEO satellite uplink transmission model based on DF protocol and a coverage performance analysis method

Abstract

The application discloses a user-base station-LEO satellite uplink transmission model based on a DF protocol and a coverage performance analysis method, the transmission model comprising: a plurality of ground base stations; a plurality of user equipment which is distributed in a cluster around the ground base stations; the spatial positions of the user equipment and the ground base stations are modeled by using a Matern cluster process; a plurality of satellites which are modeled by using a homogeneous Poisson point process on the surface of the earth shell of a given orbit; wherein the large-scale fading channel between the satellites and the ground base stations is modeled by using a spatial loss model; and the small-scale fading channel between the satellites and the ground base stations is modeled by using a shadowed Rician fading model.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and specifically relates to a user-base station-LEO satellite uplink transmission model and coverage performance analysis method based on the DF protocol. Background Technology

[0002] The evolution of 6G is accelerating the construction of an integrated space-air-ground network system. As a crucial component, low-Earth orbit (LEO) satellite constellations can provide wide-area coverage, but the availability and reliability of direct satellite-to-ground links are limited under conditions such as urban obstruction and signal attenuation due to rain and snow. Relay cooperation technology, by introducing relay nodes to forward signals, solves problems of signal attenuation, interference, and capacity, thereby improving system coverage, spectrum efficiency, and network capacity.

[0003] In large-scale network scenarios, the spatial distribution of ground base stations, equipment terminals, and satellite nodes is often random and irregular, and is affected by factors such as geographical environment, constellation configuration, and access strategy. Traditional regular topology models are difficult to accurately characterize the spatial statistical features of the network.

[0004] Currently, to address some of the aforementioned challenges, there are BPP modeling methods commonly used for modeling finite-area networks with a defined number of nodes, and AF-based relay transmission models. However, each has its own limitations.

[0005] The deployment of low-Earth orbit satellite constellations is modeled as a binomial process (BPP) at a fixed altitude on the Earth's surface.

[0006] A binomial point process (BPP) is a discrete stochastic point process that describes the number of points within a given region that follows a binomial distribution. It is typically used to describe the number of successful events from a fixed number of independent trials within a finite region.

[0007] In d-dimensional Euclidean space In a subset B, there exist N independent points that follow a uniform distribution, where N is a fixed non-negative integer. These points are superimposed to form BPP. For any compact set C contained in B, the number of points in it is a binomial random variable, and the number of points in disjoint sets are independent.

[0008] BPP is often used to model finite-area networks with a defined number of nodes. Scenarios such as device-to-device (D2D) networks within a limited area on the ground, drone networks within a limited area in the air, and satellite networks in space with a limited number of nodes can all be accurately characterized using BPP, allowing for in-depth analysis of network performance, communication mechanisms, and other related issues.

[0009] The shortcomings of the BPP model include:

[0010] (1) It is extremely difficult to perform rigorous mathematical analysis on networks based on the BPP model, and it is usually difficult to obtain analytical solutions.

[0011] (2) The implementation process of BPP is relatively complex and the amount of computation is large.

[0012] (3) BPP is determined by two parameters, which is not flexible enough.

[0013] A dual-hop FSO communication system based on the AF relay protocol deploys a drone as a relay in the end-to-end FSO link. The drone is equipped with signal processing equipment compatible with the AF protocol. In the system, the transmission of the FSO signal from the source to the destination involves two processes. First, the laser diode (LD) of the source sends the FSO signal to the hovering drone. Then, the drone relay, using the AF protocol, amplifies the FSO signal with a fixed gain. Finally, the LD at the drone relay sends the amplified FSO signal to the destination.

[0014] Amplify-and-Forward (AF) is a widely used physical layer protocol in cooperative relay transmission. Its basic mechanism is that the relay node linearly amplifies the received signal and forwards it directly to the destination without demodulation and decoding.

[0015] The main drawback of the two-hop FSO communication system based on the AF relay protocol is that while forwarding useful signals, AF amplifies the noise in the relay segment. The end-to-end performance is not only constrained by the quality of the two-hop links, but also affected by the noise accumulation effect, especially when the signal-to-noise ratio of the first hop is low. Summary of the Invention

[0016] One of the objectives of this invention is to overcome the shortcomings of the prior art and provide a user-base station-LEO satellite uplink transmission model based on the DF protocol, which can significantly suppress noise accumulation effects under reliable decoding conditions.

[0017] Another objective of this invention is to provide a coverage performance analysis method for a user-base station-LEO satellite uplink transmission model based on the DF protocol, which can simplify the calculation of the model's coverage performance and provide calculation results with good accuracy.

[0018] The technical solution provided by this invention is as follows:

[0019] A user-base station-LEO satellite uplink transmission model based on the DF protocol includes:

[0020] Multiple ground base stations;

[0021] Multiple user equipments are clustered around the ground base station; the spatial positions of the user equipments and the ground base station are modeled using the Matrn clustering process.

[0022] Multiple satellites are modeled using a homogeneous Poisson point process on the Earth's crust surface in a given orbit;

[0023] Specifically, the large-scale fading channel between the satellite and the ground base station is modeled using a spatial loss model; the small-scale fading channel between the satellite and the ground base station is modeled using a shadowed Rice fading model; and information uplink transmission between the user equipment, the ground base station, and the satellite is based on the DF protocol.

[0024] Preferably, in a cluster consisting of a ground base station and user equipment, the base station is taken as the parent point and the center point of the cluster, and the user equipment is taken as the child point.

[0025] The spatial location of the ground base station follows a Poisson point process.

[0026] Preferably, the density of the satellites is set as follows:

[0027] ;

[0028] in, Indicates satellite density, Indicates the number of satellites. Represents the Earth's radius. This indicates the satellite's altitude above Earth.

[0029] Preferably, the wireless channel between the ground base station and the user equipment is modeled using Rayleigh fading.

[0030] Preferably, the shortest distance between the satellite and the ground base station is:

[0031] The service distance between the satellite and the ground base station is:

[0032] ;

[0033] The furthest distance between the satellite and the ground base station is:

[0034] ;

[0035] in, Indicates the satellite's orbital radius. Represents the Earth's radius. Let be a random variable with polar angle. This indicates the maximum polar angle.

[0036] Preferably, the maximum polar angle is calculated using the following formula:

[0037] ;

[0038] in, Indicates the satellite beamwidth.

[0039] A method for coverage performance analysis of a user-base station-LEO satellite uplink transmission model based on the DF protocol includes:

[0040] Determine the coverage probability from user equipment to ground base station in the uplink. ;

[0041] Determine the coverage probability between terrestrial base stations and satellites ;

[0042] When the instantaneous signal-to-interference-plus-noise ratio (SIR) of the first hop exceeds the decoding threshold, the overall coverage probability of the transmission model is calculated based on the DF protocol. ;

[0043] Among them, the overall coverage probability The mathematical expression is:

[0044] .

[0045] Preferably, the coverage performance analysis method for the user-base station-LEO satellite uplink transmission model based on the DF protocol also includes:

[0046] Calculate the traversal capacity of the terrestrial access link :

[0047] ;

[0048] And calculate the capacity of over-the-air link traversal :

[0049] ;

[0050] in, The signal-to-interference-plus-noise ratio (SIR) of the terrestrial access link. This represents the signal-to-interference-plus-noise ratio (SIR) of the air link.

[0051] Preferably, the formula for calculating the coverage probability from the user equipment to the ground base station in the uplink is:

[0052] ;

[0053] in, This is the threshold for the received signal-to-interference-plus-noise ratio (SIR) from the user equipment to the ground base station. The cluster radius of the Matérn cluster process. Where α is the fixed transmit power of the user equipment, and α is the path loss exponent. For typical users to their associated service base stations (such as Figure 2 As shown in the figure, the associated serving base station of a typical user is the typical base station distance. This is aggregate interference at a typical base station;

[0054] Preferably, the formula for calculating the coverage probability between the ground base station and the satellite is:

[0055] ;

[0056] In the formula, The signal-to-interference-plus-noise ratio (SIR) of the air link. The threshold for the signal-to-interference-plus-noise ratio at the satellite receiver. This represents the visible probability.

[0057] The beneficial effects of this invention are:

[0058] The user-base station-LEO satellite uplink transmission model based on the DF protocol provided by this invention adopts the decode-forward (DF) relay protocol, which can significantly suppress the noise accumulation effect under the condition of reliable decoding.

[0059] The user-base station-LEO satellite uplink transmission model based on the DF protocol provided by this invention adopts homogeneous Poisson point process, Matérn cluster process, Rayleigh fading, and shadowed Rice fading model, which can realize quantitative analysis of the system's bit error rate performance, coverage capability, and reliability, and provide important support for communication scheme design.

[0060] The coverage performance analysis method of the user-base station-LEO satellite uplink transmission model based on the DF protocol provided by this invention systematically characterizes the visibility probability, contact angle / contact distance and critical link distance distribution, aggregation interference and SINR expressions under unified spatial statistical modeling, and further gives the calculable forms of core indicators such as end-to-end coverage probability and traversal capacity. The analysis results obtained are consistent with the simulation results. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of two-hop relay cooperative transmission based on the DF protocol as described in this invention.

[0062] Figure 2 This is a schematic diagram of the terrestrial network link transmission of the user-base station-LEO satellite uplink transmission model based on the DF protocol described in this invention.

[0063] Figure 3 This is a spatial relationship model diagram of the low-Earth orbit satellite constellation and ground base stations described in this invention.

[0064] Figure 4This is a comparison chart of the probability density function of normalized power gain under shadow Ricean fading as described in this invention.

[0065] Figure 5 This is a comparison chart of the coverage probability with SINR threshold at different cluster radii obtained using the performance coverage analysis method described in this invention, and the simulation results.

[0066] Figure 6 This is a comparison chart of the coverage probability as a function of cluster radius under different satellite surface densities obtained by the performance coverage analysis method described in this invention, and the simulation results.

[0067] Figure 7 This is a comparison chart of the coverage probability under different satellite surface densities as a function of SINR threshold, obtained using the performance coverage analysis method described in this invention, and the simulation results.

[0068] Figure 8 This is a comparison chart of the end-to-end coverage probability under different satellite surface densities obtained by the performance coverage analysis method described in this invention with the beam half-angle variation and simulation results.

[0069] Figure 9(a) shows the satellite surface density obtained using the performance coverage analysis method described in this invention. =1.000e-12 Heatmap of bottom-to-end coverage probability as a function of beam half-angle and threshold.

[0070] Figure 9(b) shows the satellite surface density obtained using the performance coverage analysis method described in this invention. =3.000e-13 Heatmap of bottom-to-end coverage probability as a function of beam half-angle and threshold.

[0071] Figure 9(c) shows the satellite surface density obtained using the performance coverage analysis method described in this invention. =1.080e-13 Heatmap of bottom-to-end coverage probability as a function of beam half-angle and threshold.

[0072] Figure 10(a) is a graph showing the traversal capacity variation of the terrestrial access link obtained by the performance coverage analysis method described in this invention.

[0073] Figure 10(b) is a graph showing the change in traversal capacity of the air link obtained by the performance coverage analysis method described in this invention. Detailed Implementation

[0074] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0075] like Figure 1As shown, this invention provides a user-base station-LEO satellite uplink transmission model based on the DF protocol. Based on the two-hop relay cooperation mechanism of the DF protocol, within a stochastic geometric framework, in the ground link, the Matérn Cluster Process (MCP) is used to characterize the cluster distribution of users around the base station, and uplink aggregation interference is analyzed under the condition of "single active user per cell and no co-channel interference within the cluster". In the air link, the satellite is modeled as a homogeneous Poisson point process (HPPP) on the surface of a given orbital spherical shell, and a channel model closer to engineering practice is established by combining the ITU-R S.465 ground station radiation pattern and the ITU-R S.1528 non-geostationary satellite radiation pattern, free-space path loss, and Shadowed-Rician small-scale fading.

[0076] Matrn cluster process (MCP): The child point lies within a cluster centered on the parent point with a radius of... Evenly distributed within the disk:

[0077] ;

[0078] For terrestrial links, the Matrn Cluster Process (MCP) is used for modeling, where the base station is the parent and the user equipment is the child. The base station follows a density... The Poisson point process (PPP) is used as the center point of the cluster. For a radius of... In each cluster, a limited number of user equipment are evenly distributed around the base station, assuming no intra-cluster interference. Interference is... This is expressed as follows. Slivnyak's theorem concludes that, under the assumption that each base station has only one active uplink device in a resource block randomly selected from all devices in its cluster, the density of interfering devices is... Equal to the density of base stations A schematic diagram of terrestrial network link transmission is shown below. Figure 2 As shown.

[0079] Slivnyak's Theorem is a fundamental conclusion in stochastic geometry and Poisson point process theory, holding a central position in the performance analysis of wireless communication networks. This theorem provides a rigorous theoretical basis for the analysis of "typical users" or "typical links," making the statistical performance evaluation of complex networks mathematically feasible and consistent.

[0080] The Poisson point process (PPP) is one of the most commonly used spatial point processes in stochastic geometry. It is used to probabilistically characterize the random distribution of nodes (such as base stations, users, gateways, satellite projection points, etc.) in space. Its core idea is that the number of points appearing within a given region follows a Poisson distribution, and the number of points in different regions is independent of each other, thus providing an analytical mathematical basis for the interference and performance analysis of complex networks. (The text then repeats the definition of a point process.) Let the set of nodes in space be defined such that for any bounded measurable set... ,random variable satisfy k = 0, 1, 2... and for any disjoint sets If they are mutually independent, then they are called This is a Poisson point process. Here, Λ(A) is called the intensity measure. If the average density at any point in space is the same, the intensity measure is... ,in The intensity is a constant (average number of points per unit area). If the area is the region, then It is a homogeneous PPP (HPPP).

[0081] The positions of satellite nodes follow a density function. Homogeneous Poisson point process (HPPP) Low Earth orbit (LEO) satellites operate at altitudes ranging from 500km to 2000km. The base station connects to the nearest satellite, and the satellite from which it can successfully receive signals becomes the service satellite. Assume the satellite is placed at a radius of... On the surface of a sphere, and the number of satellites is This is not without generality; a typical satellite is located at (0, 0, ...). Satellite density for:

[0082] ;

[0083] Satellite establishes spherical coordinate system , This represents the radial distance. The Earth's radius is approximately 6371 km. This represents the satellite's altitude above the ground. A diagram illustrating the spatial relationship between a low-Earth orbit satellite constellation and ground stations is shown below. Figure 3 As shown, For the height of the ball crown, Polar angle, This is the azimuth angle.

[0084] The user equipment is equipped with a single omnidirectional antenna. The base station transmit antenna gain adopts the reference pattern in ITU-R Recommendation S.465, and the base station transmit antenna gain is:

[0085] ;

[0086] in, It is the off-axis angle. Antenna equivalent aperture related.

[0087] For the air link, the satellite receiving antenna gain adopts the reference pattern model given in ITU-R Recommendation S.1528, and the satellite receiving antenna gain is:

[0088] ;

[0089] , ;

[0090] in, This is half the 3dB beamwidth (in degrees). The maximum gain of the main lobe. This represents the level of the side lobes near the main lobe. This represents the level of the farthest sidelobe.

[0091] The satellite-to-ground channel model considered in this invention consists of two parts: 1) the channel between the satellite and the ground base station; and 2) the channel between the ground base station and the user equipment. For a satellite-to-base station link, its channel gain consists of two parts: large-scale fading and small-scale fading. Large-scale fading mainly includes path loss and shadowing fading, while small-scale fading is used to characterize multipath effects. In satellite communication scenarios, links are mostly line-of-sight (LoS) propagation, and commonly used path loss models include free-space path loss models and power-law / logarithmic distance path loss models. Given that this invention focuses on the LoS transmission characteristics of satellite-to-ground links, a free-space path loss model is used to model the large-scale fading of the satellite-to-base station link. Its mathematical expression is:

[0092] ;

[0093] in, It is the speed of light , It is the carrier frequency. It is a random variable from satellite to ground base station.

[0094] Small-scale fading channels use the shadowed Ricean fading model (SR) to represent the line-of-sight (LOS) and scattering components. Shadowed Ricean fading channel gain. The cumulative distribution function (CDF) is as follows:

[0095] ;

[0096] in, , and These are the parameters for shadow Rice decay. Represents the Gamma function. This represents an incomplete Gamma function. For the Pochhammer symbol.

[0097] Shadow Rice fading channel gain The probability density function (PDF) is as follows:

[0098] ;

[0099] Among them, it means Average power of the line-of-sight component, This represents the average power of the multipath components, where m is the Nakagami parameter. It is a confluence hypergeometric function.

[0100] However, the above formula is too complex and cannot be calculated. Therefore, it is approximated as a gamma random variable. Approaching That is, its cumulative distribution function (CDF) is approximated as:

[0101] ;

[0102] Its PDF is approximately:

[0103] ;

[0104] in, It is the gamma function. These are shape parameters. It is a scale parameter. and The expression is as follows:

[0105] ;

[0106] ;

[0107] Figure 4 The normalized power gain is given. The probability density function, For a single power gain, The average value was used to compare the consistency between the exact shading Rice (SR) results and the Gamma approximation under light, medium, and heavy shading scenarios. It can be seen that the Gamma approximation curve generally closely matches the exact SR curve, indicating that the moment-matching approximation can accurately characterize the statistical properties of SR fading. Meanwhile, the PDF peak value decreases and its distribution broadens significantly as shading increases from light to heavy, indicating stronger gain fluctuations and a higher likelihood of low-gain events under heavy shading.

[0108] The wireless channel between the base station and user equipment is modeled using Rayleigh fading. As one of the most typical small-scale fading models, the Rayleigh distribution is often used to characterize propagation patterns in environments with dense obstacles. In such environments, there is usually no direct line-of-sight component between the source and destination; electromagnetic waves mainly rely on multiple paths formed by reflection, scattering, and diffraction to reach the receiver. Therefore, multipath fading is dominant. Accordingly, the probability density function of the received signal envelope r can be expressed as:

[0109] , ;

[0110] Where r represents the amplitude of the received signal, It is the variance of the normal distributions X and Y, also known as half the power of the multipath component.

[0111] Distance distribution function:

[0112] I. Distance distribution function of air links and ground access links

[0113] Assume the satellite's classical position is (0, 0, ...). The base station is located at (0, 0, ...). (This means that the satellite is at the very top of the base station, and the distance between the satellite and the base station is the service distance.)

[0114] The service distance between the satellite and the ground base station is:

[0115] ;

[0116] in, The random variable with polar angle follows a uniform distribution. The CDF and PDF of the typical distance between a base station and a serving satellite are given by the following formula:

[0117] ;

[0118] ;

[0119] in, For the Earth's radius, where is the satellite's orbital radius and h is the satellite's orbital altitude. The value is determined by the satellite beamwidth. It is determined together with the geometry between the Earth and the planet.

[0120] Specifically, the farthest distance between the base station and the satellite , The value of is also related to the satellite's beamwidth angle:

[0121] .

[0122] II. Free Space Loss Distribution Function

[0123] In the stochastic geometric model of this invention, the service distance of the air link (base station to satellite) Since it is a random variable, its corresponding free-space propagation gain is also random. To more accurately characterize the large-scale propagation effect in subsequent SINR and coverage probability analyses, based on service distance... The distribution of the distance-related propagation gain is further derived. The probability distribution.

[0124] The service distance between a typical user facility and a serving satellite is a random variable. Its PDF is The domain is According to the free-space path loss model, the distance-dependent path loss (link gain) of a link can be written as:

[0125] , ;

[0126] Where c is the speed of light. For carrier frequency.

[0127] therefore, It is itself a random variable. Therefore, its PDF can be derived using the random variable transformation method (RVtransformation method). Because... about It is a monotonic function, and its inverse function is... According to the CDF relationship,

[0128] ;

[0129] Taking the derivative of the equation further, we can obtain the probability density function of L0 as follows:

[0130] ;

[0131] in, c is the speed of light. For carrier frequency, , This refers to the service distance between a typical user facility and a serving satellite.

[0132] This invention also provides a method for coverage performance analysis of a user-base station-LEO satellite uplink transmission model based on the DF protocol, specifically including:

[0133] 1. Visible probability

[0134] Geometrically, the spherical cap area corresponds to the visible coverage area of ​​a typical base station location on the Earth's surface, given a satellite altitude and beamwidth. A larger spherical cap area indicates a larger visible area of ​​the Earth's surface under the illumination of that satellite beam. Under the same satellite spatial density, the average number of satellites falling within this area is also greater, thus increasing the probability of visible satellites. Therefore, the spherical cap area not only reflects the spatial scale of satellite beam coverage but also serves as a key factor in deriving the visibility probability P. vis And an important geometric basis for analyzing satellite-to-ground coverage performance.

[0135] Let D be the visible spherical cap region corresponding to a typical base station. vis In order to calculate the visible probability P vis First, we need to calculate the area S(D) of the spherical cap. vis Based on the definition of the area of ​​a spherical cap:

[0136] ;

[0137] in, It is the satellite orbital radius, h l It refers to the height of the ball's crown.

[0138] ;

[0139] in, The radial distance is the sum of the Earth's radius and the satellite's altitude, and θ is the polar angle (0 < θ < θ). c ), θ c Let be the maximum central angle corresponding to the visible spherical cap. The final expression for the area of ​​the spherical cap is: .

[0140] (1) When the serving satellite is located at D vis In addition, no satellite is in D. vis In this context, the probability P is that all satellites are unable to establish a connection with a typical relay and all satellites are invisible. invis for:

[0141] ;

[0142] In the visible region D vis The probability that at least one satellite exists in the middle. Then it is:

[0143] .

[0144] 2. Interference Characteristics Analysis and SINR

[0145] A challenging aspect of uplink performance analysis is the characterization of interference. In this invention, total interference—the total amount of interference from all active jammers—is represented using I0. agg Symbol. In other words, I agg It is the sum of received power from all other active wireless transmitters besides the typical wireless transmitter, and represents the interference power at the typical receiver. The Laplace transform of air link aggregation interference is defined as:

[0146] .

[0147] The specific derivation process is as follows:

[0148] ;

[0149] (a) The product of transmit antenna gain and receive antenna gain is obtained by utilizing the independence of point processes, the independent and identically distributed characteristics of channel fading, and the linearity of the expectation operator; (b) The independent and identically distributed characteristics of channel fading are derived by accumulating the exp function into a cumulative product; (c) The path loss expression L is... i Expand; (d) The SR fading distribution approximates the Gamma distribution. (e) is the moment generating function MGF of the Gamma distribution.

[0150] Aggregate interference at a typical base station can be expressed as:

[0151] ;

[0152] (a) is obtained by utilizing the independence of point processes (PP), the independent and identically distributed (iid) characteristics of channel fading, and the linearity of the expectation operator; (b) originates from the density λ. bs The probabilistic generating functional (PGFL) of the Poisson point process (PPP) is defined and the integral over R² is calculated using polar coordinates; finally, (c) uses the moment generating function (MGF) of an exponential random variable with a mean of 1.

[0153] To simplify the analysis, this invention assumes that each base station and user transmits at a constant power. and emission.

[0154] 1) The typical receiving power of an air link satellite is:

[0155] ;

[0156] in, This refers to the base station's transmission power. For the base station transmit antenna gain, Satellite receiving antenna gain For path loss, This represents the power gain of the shaded Rice channel.

[0157] The signal-to-interference-plus-noise ratio can be expressed as:

[0158] ;

[0159] in, , Aggregation interference at typical service satellite locations.

[0160] 2) For terrestrial links, Rayleigh fading is employed. The power received from typical and interfering user equipment at the serving base station is modeled as follows:

[0161] ;

[0162] ;

[0163] in, This is the fixed transmit power of all devices, and α is the path loss exponent. and This is the small-scale fading gain. Under the Rayleigh fading model, and They are assumed to be independent and identically distributed exponential random variables, and satisfy the following conditions: .

[0164] The instantaneous signal-to-interference-plus-noise ratio (SIR) of the first-hop ground access link can be expressed as:

[0165] ;

[0166] in, The useful signal power for a typical user, For receiver noise power, Aggregated interference generated by users on the same frequency.

[0167] 3. Coverage probability

[0168] The uplink user coverage probability to the base station is: under a given threshold τ1, the received signal-to-interference-plus-noise ratio (SINNR) from a typical user to its serving base station is denoted as . Then the coverage probability Defined as:

[0169] ;

[0170] In this context, term (a) is derived from the Rayleigh fading hypothesis, g∼exp(1), and term (b) is obtained based on the definition of the Laplace transform (LT). The derivation process is as follows:

[0171] ;

[0172] In equation (a), the following variable substitution was applied.

[0173] Coverage probability between base station and satellite The probability of satisfying the following conditions: (1) A typical base station is within the coverage of at least one LEO satellite. (2) The SINR at the receiver is higher than a certain threshold τ. Base station and satellite coverage probability. The mathematical expression is:

[0174] ;

[0175] in, The proof is as follows:

[0176]

[0177] Where (a) is represented as (b) Obtained by the shaded Rice approximation gamma function (c) The proof is... Definition of CDF , (d) is , .

[0178] To find the expression for the overall coverage probability, the system modeling phase assumes: no interference within the cluster, and that the geometric location, interference distribution, and small-scale fading of the ground subnet (user-base station) and the satellite-ground subnet (base station-satellite) are independent of each other. Under this assumption, the overall coverage probability is discussed in different cases.

[0179] When the instantaneous signal-to-interference-plus-noise ratio (SINR1) of the first hop exceeds the decoding threshold, the relay node can achieve reliable decoding. Under this condition, the system switches to the DF protocol, and the end-to-end coverage probability can be written as the product of the two-hop coverage probabilities, that is, the mathematical expression for the overall coverage probability is:

[0180] .

[0181] 4. Traverse capacity

[0182] After deriving the analytical expression for the end-to-end coverage probability, this invention further introduces ergodic capacity as an evaluation metric to provide a more detailed performance characterization of the constructed satellite-ground integrated relay uplink from a rate perspective. Ergodic capacity characterizes the long-term average transmission rate per unit bandwidth achievable based on Shannon's formula under given system parameters and random channel conditions; essentially, it is a function of the instantaneous signal-to-noise-interference ratio (SINR) log2(1+SINR). bs-s Take the expected value. Therefore, once the distribution characteristics of the end-to-end SINR or its coverage probability function are obtained... The average rate can then be obtained through integration, providing a basis for system design such as bandwidth configuration, power control, and relay deployment. Based on the coverage probability expression derived above, the traversal capacity of the ground access link in the system considered in this invention can be expressed as:

[0183]

[0184]

[0185]

[0186]

[0187] Step (a) utilizes And the tail integral formula for nonnegative random variables Step (b) involves variable substitution. At this time, Substitute step (c) The result, .

[0188] The over-the-air link traversal capacity of the system considered in this invention can be expressed as:

[0189]

[0190] In step (a), the expected identity is used. as well as The integral representation of the traversal capacity is written as an integral form of the coverage probability function; step (b) transforms the integral variable from the rate domain to the SINR threshold domain through variable substitution; step (c) further substitutes the variables into the formula. Thus, we obtain the expression for the capacity of the air link traversal.

[0191] Simulation analysis:

[0192] Table 1 Simulation Parameter Table

[0193]

[0194] like Figure 5 As shown, the simulation results of coverage probability varying with SINR threshold under different cluster radii are compared with the calculation results (theoretical curves) using the coverage analysis method provided in this invention. The coverage probability decreases monotonically as the SINR threshold increases, and the Monte Carlo simulation curves for the three cluster radii almost coincide with the theoretical curves, verifying the accuracy of the stochastic geometric analysis model. Meanwhile, the smaller the cluster radius (e.g., 50 m), the higher the curve generally appears, indicating that dense deployment can significantly improve coverage performance in low / medium threshold areas by shortening the service distance and enhancing the received signal. However, coverage still decays rapidly at high SINR thresholds. The fundamental reason is that aggregation interference gradually becomes the dominant limiting factor. Therefore, network planning should combine moderate densification with interference suppression and resource coordination strategies to meet high reliability requirements. The results show that in areas with medium SINR thresholds, reducing the cluster radius can effectively improve network coverage.

[0195] The coverage probability under different satellite surface densities is varied with the cluster radius R. c A comparison of the theory of change with Monte Carlo simulations is shown in the following results. Figure 6 As shown, at different satellite densities λ s Below this, end-to-end coverage monotonically decreases with increasing cluster radius, and this decreases further at small cluster radii R. c The interval decreases faster, then gradually slows down; meanwhile, the theoretical curve matches the Monte Carlo simulation points well. This trend mainly stems from the assumption of "no disturbance within the cluster," which increases the cluster radius R. c This will lengthen the service distance from typical users to the base station, causing signal power to attenuate rapidly due to path loss, while external cluster interference remains approximately constant, making the terrestrial link the end-to-end performance bottleneck; increasing density λ s The coverage curve can be improved overall by increasing visibility probability / shortening service distance, but when the cluster radius R... c When the gain is large, it will be partially offset by strong path loss on the ground. The results show that when improving the end-to-end coverage performance of the network, prioritizing the reduction of cluster radius and shortening the ground access distance is usually more effective; in contrast, for scenarios with large cluster radii, the performance improvement brought about by simply increasing the satellite surface density is relatively limited.

[0196] The theoretical variation of coverage probability with SINR threshold under different satellite surface densities is compared with Monte Carlo simulations, such as... Figure 7 As shown, with a satellite altitude h = 600 km, a beam half-angle of 10 degrees, and a cluster radius R... c At a depth of 200m, the end-to-end DF coverage monotonically decreases with increasing SINR threshold; simultaneously, the satellite surface density λ sThe larger the density λ, the higher the overall coverage curve, and at the same coverage level, it represents a larger "tolerable range" for the threshold; the theoretical curve basically coincides with the Monte Carlo simulation points. This is because increasing the density λ... s This will increase visible coverage and the number of available service satellites, thereby shortening the typical link service distance, increasing effective received power, and significantly improving coverage in low-threshold areas. However, when the threshold enters the mid-to-high range, two-hop links must simultaneously meet stricter SINR conditions, and the accumulation of interference and noise accelerates the decay of coverage probability. The results show that if higher coverage is desired near 0dB in engineering practice, it should be achieved by prioritizing increased satellite density or link gain (such as main lobe gain / beam optimization). Under high SINR threshold requirements, interference suppression measures (such as reducing co-frequency reuse intensity or enhancing interference coordination) can be used to avoid a rapid decline in coverage performance.

[0197] End-to-end coverage probability with different satellite surface densities varies with beam half-angle. A comparison of the theory of change with Monte Carlo simulation, such as... Figure 8 As shown, with other parameters of the ground network and air link fixed, different satellite surface densities The theoretical coverage probability varies with beam half-angle. The increase shows a trend of "first monotonically rising, then gradually saturating"; at the same time, satellite density... The higher the value, the higher the overall curve and the earlier it enters the plateau region. Increase... This is equivalent to expanding the visible satellite canopy area, increasing visibility probability and the chance of serviceable satellites being present, thereby significantly improving coverage in small corner regions; and when After increasing to a certain extent, visibility is no longer the primary bottleneck; the system becomes limited by interference and link quality (SINR constraints), leading to a decrease in the curve slope and the appearance of a plateau. Results indicate that high-density constellations... When the value is small, the coverage probability can approach the saturation value, and the marginal benefit of further widening the beam decreases rapidly; low- and medium-density constellations are more sensitive to beam spread and require larger beams. Only then can we gradually approach its plateau value; therefore, engineering should combine... By selecting the half-angle of the beam, a compromise optimization between "coverage benefits and interference costs" can be achieved.

[0198] End-to-end coverage probability with different satellite surface densities varies with beam half-angle. With threshold The heatmaps showing the changes are shown in Figures 9(a)-9(c). Under different satellite surface density conditions, the end-to-end coverage probability increases with the SINR threshold. It decreases significantly with increasing beam half-angle, and decreases significantly with increasing beam half-angle. It gradually increases as it increases, but when After increasing to a certain range, the increase in coverage probability gradually decreases and eventually tends to saturate, as shown in Figure 9(a). Approaching -20, The coverage probability reaches its maximum value of 0.864 when it approaches 20, as shown in Figure 9(b). Approaching -20, The coverage probability reaches its maximum value of 0.864 when it approaches 25, as shown in Figure 9(c). Approaching -20, The coverage probability reaches its maximum of 0.813 when the satellite density approaches 25. Further comparison shows that as satellite density increases... The increase in [value] improves the overall coverage probability, and high coverage performance can be achieved under more parameter combinations. This is because the smaller [value]... The relatively low requirements for link reception quality make it easier for two-hop links to simultaneously meet the coverage decision conditions; while increasing the beam half-angle... This helps to expand the visible spherical cap range, increase the visibility probability of visible satellites, and increase the number of candidate service satellites, thereby improving the service distance statistics of the air link and enhancing overall coverage performance. With the beam half-angle... As the density increases further, the improvement in coverage probability gradually decreases, and coverage performance becomes more limited by link quality, interference, and noise levels. On the other hand, increasing satellite surface density... This approach can further increase the number of visible satellites and shorten service distance, thereby improving end-to-end coverage performance overall. Results show that reducing the SINR threshold, increasing the beam half-angle, and increasing satellite surface density all improve end-to-end coverage probability. However, once the beam half-angle increases to a certain extent, further increases in its value will gradually weaken the improvement in coverage probability. In contrast, increasing satellite surface density provides a more sustained improvement in coverage performance. Improving network coverage performance requires a combined consideration of threshold settings, beam parameters, and satellite deployment density.

[0199] Figures 10(a) and 10(b) show the curves of the traversal capacity of the first-hop ground access link and the second-hop air link as a function of different parameters. As can be seen from the figures, in Figure 10(a), the traversal capacity of the first-hop ground access link varies with the cluster radius. The ergonomic capacity decreases continuously with increasing cluster radius, and the theoretical curve basically matches the Monte Carlo simulation results, indicating that the established model and theoretical derivation can accurately characterize the average transmission performance of the ground access link. This is because, as the cluster radius increases, the average access distance from a typical user to the serving base station increases, the path loss increases accordingly, leading to a decrease in the received useful signal power, thereby reducing the signal-to-interference-plus-noise ratio of the link and ultimately resulting in a decrease in ergonomic capacity. In Figure 10(b), the ergonomic capacity of the second-hop air link decreases with increasing satellite surface density. The increase in density exhibits a trend of first rising, then leveling off, and slightly decreasing in high-density regions. This is because, under conditions of lower satellite surface density, the increase... This can increase the satellite's visibility probability and improve service distance statistics, thereby increasing the average transmission rate of the air link; and when With further increases, the increase in traversal capacity gradually decreases, while the impact of co-channel interference intensifies, suppressing its growth trend and causing a slight decline in high-density areas. The results indicate that reducing the cluster radius on the ground helps improve first-hop access capability, while moderately increasing satellite surface density can improve the transmission performance of the second-hop air link.

[0200] This invention addresses the issue of unstable coverage caused by obstruction and fading in direct uplink links of satellite-ground integrated networks. It establishes a two-hop DF relay uplink transmission model of "user-base station-LEO satellite" and systematically characterizes coverage and rate performance within a unified stochastic geometric framework. On the ground side, the Matérn Cluster Process (MCP) is used to describe user clustering access characteristics. Combined with the resource occupancy assumption of "single active uplink user per cluster / cell, no co-channel interference within the cluster," uplink aggregation interference is equated to spatial superposition interference caused by users activated from external clusters. On the airside, the satellite constellation is modeled as HPPP on the spherical surface, and the visibility probability is derived based on the visible spherical cap geometry to obtain the contact angle / contact distance distribution of the serving satellites. Regarding channel and engineering constraints, Rayleigh fading is used for the ground link, while free-space path loss and shadowed Rice small-scale fading are used for the satellite-ground backhaul link. Furthermore, the ITU-R S.465 ground station antenna pattern and the ITU-R S.1528 satellite receiving antenna pattern are introduced to enhance engineering consistency.

[0201] Based on the above modeling, calculable expressions for two-hop coverage probability and end-to-end DF coverage probability are derived using PGFL / LT, and the integral form of air link ergonomic capacity is further given. The Matlab Monte Carlo results are in high agreement with the theoretical curves, verifying the correctness and reproducibility of the derivation. Parameter sensitivity analysis reveals that the coverage probability monotonically decreases as the SINR threshold increases; reducing the cluster radius can significantly improve coverage (shortening the service distance and enhancing the expected signal power); increasing satellite surface density and beam half-angle can improve visibility and coverage, but the beam half-angle has a significant plateau area and diminishing marginal returns. Therefore, a key conclusion for engineering deployment is that the beam half-angle should be selected at the "platform front" to obtain the main visibility benefits, while further improving coverage depends more on constellation density / link gain improvement or service threshold adjustment, and needs to be optimized in conjunction with interference constraints.

[0202] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A user-base station-LEO satellite uplink transmission model based on the DF protocol, characterized in that, include: Multiple ground base stations; Multiple user equipment units are clustered around the ground base station; The spatial location of the user equipment and the ground base station is modeled using a Matrn cluster process. Multiple satellites are modeled using a homogeneous Poisson point process on the Earth's crust surface in a given orbit; Specifically, the large-scale fading channel between the satellite and the ground base station is modeled using a spatial loss model; the small-scale fading channel between the satellite and the ground base station is modeled using a shadowed Rice fading model; and information uplink transmission between the user equipment, the ground base station, and the satellite is based on the DF protocol.

2. The user-base station-LEO satellite uplink transmission model based on the DF protocol according to claim 1, characterized in that, In a cluster consisting of ground base stations and user equipment, the base station is taken as the parent point and the center point of the cluster, and the user equipment is taken as the child point. The spatial location of the ground base station follows a Poisson point process.

3. The user-base station-LEO satellite uplink transmission model based on the DF protocol according to claim 2, characterized in that, The density of the satellites is set as follows: ； in, Indicates satellite density, Indicates the number of satellites. Represents the Earth's radius. This indicates the satellite's altitude above Earth.

4. The user-base station-LEO satellite uplink transmission model based on the DF protocol according to any one of claims 1-3, characterized in that, The wireless channel between the ground base station and the user equipment is modeled using Rayleigh fading.

5. The user-base station-LEO satellite uplink transmission model based on the DF protocol according to claim 4, characterized in that, The shortest distance between the satellite and the ground base station is: The service distance between the satellite and the ground base station is: ； The furthest distance between the satellite and the ground base station is: ； in, Indicates the satellite's orbital radius. Represents the Earth's radius. Let be a random variable with polar angle. This indicates the maximum polar angle.

6. The user-base station-LEO satellite uplink transmission model based on the DF protocol according to claim 5, characterized in that, The maximum polar angle is calculated using the following formula: ； in, Indicates the satellite beamwidth.

7. A method for coverage performance analysis of a user-base station-LEO satellite uplink transmission model based on the DF protocol, characterized in that, include: Determine the coverage probability from user equipment to ground base station in the uplink. ; Determine the coverage probability between terrestrial base stations and satellites ; When the instantaneous signal-to-interference-plus-noise ratio (SIR) of the first hop exceeds the decoding threshold, the overall coverage probability of the transmission model is calculated based on the DF protocol. ; Among them, the overall coverage probability The mathematical expression is: 。 8. The coverage performance analysis method for the user-base station-LEO satellite uplink transmission model based on the DF protocol according to claim 7, characterized in that, Also includes: Calculate the traversal capacity of the terrestrial access link : ； And calculate the capacity of over-the-air link traversal : ； in, The signal-to-interference-plus-noise ratio (SIR / NDR) of the terrestrial access link. This represents the signal-to-interference-plus-noise ratio (SIR) of the air link.

9. The coverage performance analysis method for the user-base station-LEO satellite uplink transmission model based on the DF protocol according to claim 8, characterized in that, The formula for calculating the coverage probability from user equipment to ground base station in the uplink is: ； in, This is the threshold for the received signal-to-interference-plus-noise ratio (SIR) from the user equipment to the ground base station. The cluster radius of the Matérn cluster process. Where α is the fixed transmit power of the user equipment, and α is the path loss exponent. The distance from a typical user to its associated service base station. This is aggregated interference at a typical base station.

10. The coverage performance analysis method for the user-base station-LEO satellite uplink transmission model based on the DF protocol according to claim 9, characterized in that, The formula for calculating the coverage probability between terrestrial base stations and satellites is: ； In the formula, The signal-to-interference-plus-noise ratio (SIR) of the air link. The threshold for the signal-to-interference-plus-noise ratio at the satellite receiver. This represents the visible probability.

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