Method for determining number of optimal cooperative satellites for communication of multiple low-orbit satellites

Abstract

The invention discloses a method for determining the number of optimal cooperative satellites for communication of multiple low-orbit satellites, and the method comprises the following steps: constructing a spatial distribution model of a low-orbit satellite constellation, so as to determine the position relation between the low-orbit satellites; constructing a satellite-ground wireless channel model for cooperative communication of multiple low-orbit satellites; constructing signal-to-noise ratio models of an uplink and a downlink; establishing a multi-low orbit satellite cooperative communication strategy; establishing an association relationship between the signal-to-noise ratio models of the uplink and the downlink and key performance indexes; deriving an analytical expression of the overall successful transmission probability of the network and the overall time delay of the network; establishing an optimal cooperative satellite number optimization scheme; and obtaining the optimal value of the network effectiveness and the number of cooperative communication satellites enabling the network effectiveness to be optimal according to the solving result. According to the method, the network overall successful transmission probability and the network overall time delay of the cooperative communication of the multiple low-orbit satellites can be efficiently analyzed, the performance gain of the cooperative communication of the multiple low-orbit satellites is effectively quantified, the complexity of performance evaluation is greatly reduced, reasonable distribution of low-orbit satellite communication network resources is facilitated, and the performance evaluation efficiency is improved. And further, the deployment planning of future large-scale low-orbit satellite constellations is guided.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite communication, and in particular to a method for determining the optimal number of cooperative satellites for multi-low-earth-orbit satellite communication. Background Art

[0002] In recent years, low-earth-orbit communication satellites (referred to as low-orbit satellites for short) can extend communication services into space by virtue of their advantages such as wide coverage, strong anti-destruction ability, and being not restricted by geographical environment. A low-orbit satellite communication network composed of multiple low-orbit satellites can make up for the deficiencies of traditional terrestrial cellular networks and provide seamless network services for remote areas such as deserts, oceans, and rural areas. At present, international companies such as SpaceX Starlink, OneWeb, Telesat, and Amazon Kuiper have successfully launched a series of low-orbit satellites. At the same time, China has also actively made arrangements and caught up, successively carrying out projects such as Qianfan Constellation, Hongyan Constellation, and Hongyun Project, and promoting the development of various emerging communication services such as inter-satellite communication services and mobile phone direct satellite communication services. However, considering that the cost of satellite communication is relatively high compared to that of traditional terrestrial cellular networks, in the existing research on low-orbit satellite communication networks, most mobile users, vehicles, Internet of Things devices, and other terrestrial users are provided with data transmission services by a certain satellite in the low-orbit satellite communication network. However, due to the characteristics of long propagation distance and strong scattering of the satellite-ground link, relying solely on a single satellite to provide communication services will face challenges such as limited signal strength and low data rate, and it is often difficult to meet the data transmission requirements of terrestrial users. In addition, there are harsh environmental factors such as high-energy particles, electromagnetic radiation, and solar wind in the cosmic space, which can cause satellite functions to be damaged or even completely fail, thereby reducing the reliability of single-satellite communication. Summary of the Invention

[0003] The present invention provides a method for determining the optimal number of cooperative satellites for multi-low-earth-orbit satellite communication to overcome the technical problems that relying solely on a single satellite to provide communication services will face challenges such as limited signal strength and low data rate, and it is often difficult to meet the data transmission requirements of terrestrial users.

[0004] To achieve the above object, the technical solution of the present invention is as follows:

[0005] A method for determining the optimal number of cooperative satellites for multi-low-earth-orbit satellite communication, the specific steps include:

[0006] S1: Construct a spatial distribution model of the low-orbit satellite constellation in the low-orbit satellite communication network to determine the positional relationship between each low-orbit satellite;

[0007] S2: According to the spatial distribution model of the low-orbit satellite constellation, construct a satellite-ground radio channel model for multi-low-orbit satellite cooperative communication;

[0008] S3: Construct the signal-to-noise ratio (SNR) models for the uplink and downlink based on the spatial distribution model of the LEO satellite constellation and the satellite-ground wireless channel model for multi-LEO satellite cooperative communication. The uplink is the link for ground users to transmit signals to LEO satellites, and the downlink is the link for LEO satellites to transmit signals to ground users.

[0009] S4: Establish a multi-LEO satellite cooperative communication strategy in the LEO satellite communication network according to the SNR models of the uplink and downlink to determine the LEO satellites used by ground users for end-to-end signal transmission.

[0010] S5: Establish the correlation between the SNR models of the uplink and downlink and the key performance indicators, where the key performance indicators include the end-to-end successful transmission probability and the end-to-end delay.

[0011] S6: Derive the analytical expressions for the overall network successful transmission probability and the overall network delay according to the multi-LEO satellite cooperative communication strategy and the correlation between the SNR models of the uplink and downlink and the key performance indicators.

[0012] S7: Establish an optimal cooperative satellite number optimization scheme based on the derived analytical expressions for the overall network successful transmission probability and the overall network delay.

[0013] S8: Solve based on the optimal cooperative satellite number optimization scheme to obtain the optimal value of the network effectiveness and the number of cooperative communication satellites that maximize the network effectiveness.

[0014] Furthermore, in S7, the optimal cooperative satellite number optimization scheme established based on the derived analytical expressions for the overall network successful transmission probability and the overall network delay includes:

[0015] Define the network effectiveness η as the ratio of the overall network successful transmission probability to the overall network delay, expressed as:

[0016]

[0017] Establish an optimal cooperative satellite number optimization scheme to maximize the network effectiveness η by optimizing the number of cooperative satellites. The optimal cooperative satellite number optimization scheme is expressed as:

[0018]

[0019] s.t. Φ vis , Φ s ≠ φ, (1a)

[0020]

[0021] 500km ≤ r min≤1500km, (1c)

[0022] P s (τ), P k (τ), q ∈ [0, 1], (1d)

[0023] Among them, constraint (1a) is used to ensure that both the set of visible satellites and the set of LEO satellites for cooperative communication are non-empty sets; constraint (1b) is used to stipulate that the number of LEO satellites in the LEO satellite constellation and the number of LEO satellites for cooperative communication must be positive integers, and it is required that the number of cooperative satellites does not exceed the total number of satellites in the LEO satellite constellation; constraint (1c) is used to define the altitude range of the LEO satellite constellation; constraint (1d) is used to ensure that both the overall successful transmission probability of the network and the end-to-end successful transmission probability of communication through the k-th LEO satellite are within the range of 0 to 1.

[0024] Furthermore, in S1, the steps of constructing the spatial distribution model of the LEO satellite constellation include:

[0025] S11: Set the communication nodes in the LEO satellite communication network, and the communication nodes include an LEO satellite constellation and a ground user;

[0026] S12: Take the center of the earth as the origin to establish a three-dimensional Cartesian coordinate system. In this three-dimensional Cartesian coordinate system, the x-axis points from the origin to an arbitrary point on the equator, the y-axis lies in the plane of the equator and is perpendicular to the x-axis, and the z-axis points from the origin to the geographic north pole;

[0027] S13: Set the position of the ground user on the earth's surface as (0, 0, r e ), r e is the radius of the earth, and the ground user can directly communicate with the LEO satellite;

[0028] S14: Set that in the LEO satellite constellation, N LEO satellites are distributed on the sphere with a radius of r a to form a binomial point process distribution, where r a = r e + r min , r min is the constellation altitude;

[0029] S15: Sort all the LEO satellites in the LEO satellite constellation according to the distance between the LEO satellite and the ground user, including:

[0030] Define each LEO satellite as the first, the second,..., the k-th LEO satellite in order from the nearest to the farthest from the ground user, 1 ≤ k ≤ N, where N is the total number of LEO satellites; among them, the distance from the k-th LEO satellite to the ground user is R k ;

[0031] S16: Set the visible satellite set to be represented as Φ vis ={s1, s2,..., s M}, where M is the number of visible satellites, M ≤ N and M is a positive integer; set the low Earth orbit satellite set for cooperative communication, and the low Earth orbit satellite set for cooperative communication is a subset of the visible satellite set, represented as Φ s ={s1, s2,..., s K}, where K is the total number of low Earth orbit satellites for cooperative communication, K ≤ M and K is a positive integer.

[0032] Furthermore, in S2, according to the space distribution model of the low Earth orbit satellite constellation, the satellite - to - ground wireless channel model for multi - low Earth orbit satellite cooperative communication constructed includes:

[0033] Path loss model: In both the uplink and downlink, the power - law path loss model is used to represent the path loss between a ground user and the k - th low Earth orbit satellite, expressed as:

[0034]

[0035] where R k is the distance from the k - th low Earth orbit satellite to the ground user, c is the speed of light, f c is the carrier frequency of the signal, and α is the power - law path loss factor;

[0036] Small - scale fading model: The shadowed Rician fading model is used to characterize the channel fading between a ground user and the k - th low Earth orbit satellite. The cumulative distribution function of the channel gain |H| 2 in the satellite - to - ground link is expressed as:

[0037]

[0038] where Ω, m, and b are respectively the average power of the line - of - sight component, the Nakagami parameter, and half of the average power of the scattered component, and (x) n is the Pochhammer symbol;

[0039] The probability density function of the channel gain |H| 2 in the satellite - to - ground link is expressed as:

[0040]

[0041] Furthermore, in S3, according to the space distribution model of the low Earth orbit satellite constellation and the satellite - to - ground wireless channel model for multi - low Earth orbit satellite cooperative communication, the signal - to - noise ratio models for the uplink and downlink constructed include:

[0042] In the multi - low - earth - orbit satellite cooperative communication of a low - earth - orbit satellite communication network, a total of K orthogonal channels in the Ka band are set;

[0043] It is assumed that each low - earth - orbit satellite is equipped with a directional antenna with its main - lobe beam pointing to the center of the earth. Ground users are within the beam of the directional antenna of each low - earth - orbit satellite and have omnidirectional antennas capable of communicating with each low - earth - orbit satellite;

[0044] For the uplink where a ground user transmits a signal to the k - th low - earth - orbit satellite, the signal - to - noise ratio received by the k - th low - earth - orbit satellite is expressed as:

[0045]

[0046] In the formula, p GU is the transmission power of the ground user; is the antenna gain from the ground user to the k - th low - earth - orbit satellite; is the noise power of the k - th channel, is the channel gain from the ground user to the k - th low - earth - orbit satellite; is the transmitting antenna gain of the ground user, is the receiving antenna gain of the k - th low - earth - orbit satellite;

[0047] For the downlink where the k - th low - earth - orbit satellite transmits a signal to the ground user, the signal - to - noise ratio received at the ground user is:

[0048]

[0049] In the formula, p LEO is the transmission power of each low - earth - orbit satellite, is the antenna gain from the k - th low - earth - orbit satellite to the ground user, is the transmitting antenna gain of the k - th low - earth - orbit satellite, is the receiving antenna gain of the ground user, represents the channel gain from the k - th low - earth - orbit satellite to the ground user.

[0050] Furthermore, in S4, according to the signal - to - noise ratio models of the uplink and downlink, a multi - low - earth - orbit satellite cooperative communication strategy in the low - earth - orbit satellite communication network is established, including:

[0051] S41: The ground user sends a pilot signal to the first low - earth - orbit satellite through the first channel;

[0052] S42: The first low - earth - orbit satellite measures the signal - to - noise ratio of the received pilot signal;

[0053] S43: Judge whether the measured signal - to - noise ratio exceeds the predefined signal - to - noise ratio threshold τ. If it exceeds, execute S431 - S433; otherwise, execute S44;

[0054] S431: The first low-earth orbit satellite sends a feedback pilot signal to the ground user on the same channel;

[0055] S432: The ground user evaluates the signal-to-noise ratio of the feedback pilot signal;

[0056] S433: Determine whether the signal-to-noise ratio at the ground user exceeds the predefined signal-to-noise ratio threshold τ. If it exceeds, it means that the first low-earth orbit satellite is a qualified low-earth orbit satellite, and execute S45; otherwise, execute S44;

[0057] S44: Switch the first low-earth orbit satellite to the second low-earth orbit satellite and re-execute according to the rules of S41 until the switching of K satellites is completed, then terminate the pilot signal transmission process;

[0058] S45: The ground user selects the qualified low-earth orbit satellite to transmit the message signal.

[0059] Furthermore, in S5, the correlation relationship between the established signal-to-noise ratio models of the uplink and downlink and the key performance indicators includes:

[0060] Express the probability that the signal-to-noise ratios received at the low-earth orbit satellite and the ground user simultaneously meet the predefined signal-to-noise ratio threshold τ as the end-to-end successful transmission probability of communicating through the kth low-earth orbit satellite, so as to construct the correlation relationship between the signal-to-noise ratio models of the uplink and downlink and the end-to-end successful transmission probability, expressed as:

[0061]

[0062] In the formula, and respectively represent the signal-to-noise ratios received at the kth low-earth orbit satellite and the ground user when the ground user communicates with the kth low-earth orbit satellite, is the probability measure;

[0063] The end-to-end delay of the ground user communicating through the kth low-earth orbit satellite includes the transmission delay and the handover delay, expressed as:

[0064]

[0065] In the formula, represents the uplink delay of end-to-end communication through the kth satellite, represents the downlink delay of end-to-end communication through the kth satellite, is the transmission delay; B is the channel bandwidth; (k - 1)T ho represents the cumulative handover delay generated when switching from the first low-earth orbit satellite to the kth low-earth orbit satellite, T hois the handover delay for each handover, and T ho is a constant.

[0066] Furthermore, in S6, according to the multi-low-earth-orbit satellite cooperative communication strategy and the correlation between the signal-to-noise ratio models and key performance indicators of the uplink and downlink, the analytical expressions for the overall network successful transmission probability and the overall network delay are derived as follows:

[0067] 1) Based on the multi-low-earth-orbit satellite cooperative communication strategy, the analytical expression for the overall network successful transmission probability of K low-earth-orbit satellites in cooperative communication is:

[0068]

[0069] where q is the failure probability of each low-earth-orbit satellite;

[0070] P k (τ) is the end-to-end successful transmission probability for communication through the k-th low-earth-orbit satellite, expressed as:

[0071]

[0072] where is the probability density function of the distance between the k-th low-earth-orbit satellite and the ground user, expressed as:

[0073]

[0074] where r min ≤r k ≤r max , k ∈ {1, 2, 3,..., K}, r min is the constellation altitude, r max is the maximum visible distance, and the maximum visible distance is the distance between the ground user and any point on the horizon at its location, r e is the radius of the earth; j is the summation variable;

[0075] 2) Based on the multi-low-earth-orbit satellite cooperative communication strategy, the analytical expression for the overall network delay of K low-earth-orbit satellites in cooperative communication is:

[0076]

[0077] where T k represents the end-to-end delay for communication through the k-th low-earth-orbit satellite;

[0078] T k is expressed as:

[0079]

[0080] where ω is the length of the data packet, is the indicator function.

[0081] Beneficial effects: By establishing a multi-low-Earth-orbit satellite cooperative communication strategy in a low-Earth-orbit satellite communication network, this invention determines the low-Earth-orbit satellites used by ground users for end-to-end signal transmission, and establishes the correlation relationships between the signal-to-noise ratio models of the uplink and downlink, the end-to-end successful transmission probability, and the end-to-end delay, thereby deriving the analytical expressions for the overall network successful transmission probability and the overall network delay; Based on the derived analytical expressions for the overall network successful transmission probability and the overall network delay, an optimal cooperative satellite number optimization scheme is established, and finally the optimal value of the network effectiveness and the number of cooperative communication satellites that optimize the network effectiveness are obtained. This invention can efficiently analyze the overall network successful transmission probability and the overall network delay of multi-low-Earth-orbit satellite cooperative communication, effectively quantify the performance gain of multi-low-Earth-orbit satellite cooperative communication, greatly reduce the complexity of performance evaluation, facilitate the reasonable allocation of low-Earth-orbit satellite communication network resources, and further guide the deployment planning of future large-scale low-Earth-orbit satellite constellations. In addition, this method can effectively improve the reliability of communication between low-Earth-orbit satellites and ground users, providing technical support and useful references for the development of low-Earth-orbit satellite cooperative communication technology. Description of the Drawings

[0082] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0083] Figure 1 is a flowchart of a method for determining the optimal number of cooperative satellites for multi-low-Earth-orbit satellite communication in the present invention;

[0084] Figure 2 is a schematic diagram of multi-low-Earth-orbit satellite cooperative communication in a low-Earth-orbit satellite communication network in an embodiment of the present invention;

[0085] Figure 3 is a graph showing the relationship between the overall network successful transmission probability and the predefined signal-to-noise ratio threshold in an embodiment of the present invention;

[0086] Figure 4 is a graph showing the relationship between the overall network delay and the constellation altitude in an embodiment of the present invention;

[0087] Figure 5 is a comparison graph of the maximized network effectiveness for different constellation altitudes in an embodiment of the present invention;

[0088] Figure 6This is a comparison chart of the optimal number of cooperative satellites at different constellation altitudes in the embodiments of the present invention. Specific embodiments

[0089] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0090] This embodiment provides a method for determining the optimal number of cooperative satellites for multi-Low Earth Orbit (LEO) satellite communication, as Figure 1 shown, the specific steps include:

[0091] S1: Construct a spatial distribution model of the LEO satellite constellation in the LEO satellite communication network to determine the positional relationship between each LEO satellite;

[0092] S2: Construct a space-ground radio channel model for multi-LEO satellite cooperative communication according to the spatial distribution model of the LEO satellite constellation;

[0093] S3: Construct signal-to-noise ratio (SNR) models for the uplink and downlink according to the spatial distribution model of the LEO satellite constellation and the space-ground radio channel model for multi-LEO satellite cooperative communication; the uplink is the link for ground users to transmit signals to LEO satellites, and the downlink is the link for LEO satellites to transmit signals to ground users;

[0094] S4: Establish a multi-LEO satellite cooperative communication strategy in the LEO satellite communication network according to the SNR models of the uplink and downlink to determine the LEO satellites used by ground users for end-to-end signal transmission;

[0095] S5: Establish the correlation between the SNR models of the uplink and downlink and key performance indicators, where the key performance indicators include end-to-end successful transmission probability and end-to-end delay;

[0096] S6: Derive the analytical expressions of the overall network successful transmission probability and the overall network delay according to the multi-LEO satellite cooperative communication strategy and the correlation between the SNR models of the uplink and downlink and the key performance indicators;

[0097] S7: Establish an optimal cooperative satellite number optimization scheme based on the derived analytical expressions of the overall network successful transmission probability and the overall network delay;

[0098] S8: Solve the optimal value of network effectiveness and the number of cooperative communication satellites that optimize network effectiveness based on the obtained optimal cooperative satellite number optimization scheme.

[0099] In a specific embodiment, in S1, the steps of constructing the spatial distribution model of the LEO satellite constellation include:

[0100] S11: Set the communication nodes in the LEO satellite communication network, where the communication nodes include a LEO satellite constellation and a ground user;

[0101] S12: Take the center of the earth as the origin to establish a three-dimensional Cartesian coordinate system. In the three-dimensional Cartesian coordinate system, the x-axis points from the origin to an arbitrary point on the equator, the y-axis lies in the plane of the equator and is perpendicular to the x-axis, and the z-axis points from the origin to the geographic north pole;

[0102] S13: Set the position of the ground user on the earth's surface as (0, 0, r e ), where r e is the radius of the earth, and the ground user can directly communicate with the LEO satellite;

[0103] S14: Set that in the LEO satellite constellation, N LEO satellites are distributed on the sphere with a radius of r a to form a Binomial Point Process (BPP) distribution, where r a = r e + r min , r min is the constellation altitude;

[0104] S15: Sort all the LEO satellites in the LEO satellite constellation according to the distance between the LEO satellite and the ground user, including:

[0105] As Figure 2 shown, each LEO satellite is sequentially defined as the first, the second,..., the kth LEO satellite in the order of the distance from the ground user from near to far, 1 ≤ k ≤ N, where N is the total number of LEO satellites; among them, the distance from the kth LEO satellite to the ground user is R k ;

[0106] S16: Set the visible satellite set as Φ vis = {s1, s2,..., s M}, where M is the number of visible satellites, M ≤ N and M is a positive integer. The visible satellites are the LEO satellites located above the horizon of the ground user, and the horizon is the intersection line of the horizontal tangent plane at the point where the ground user is located and the sphere where the LEO satellites are located; set the set of LEO satellites for cooperative communication, and the set of LEO satellites for cooperative communication is a subset of the visible satellite set, denoted as Φs = {s1, s2,..., s K}, where K is the total number of LEO satellites for cooperative communication, K ≤ M and K is a positive integer.

[0107] In a specific embodiment, in S2, according to the spatial distribution model of the LEO satellite constellation, the space-ground wireless channel model for multi-LEO satellite cooperative communication constructed includes:

[0108] Path loss model: In both the uplink and downlink, the power-law path loss model is used to represent the path loss between the ground user and the k-th LEO satellite, expressed as:

[0109]

[0110] where R k is the distance from the k-th LEO satellite to the ground user, c is the speed of light, f c is the carrier frequency of the signal, and α is the power-law path loss factor;

[0111] Small-scale fading model: The shadow Rice fading model is used to characterize the channel fading between the ground user and the k-th LEO satellite. The cumulative distribution function of the channel gain |H| 2 in the space-ground link is expressed as:

[0112]

[0113] where Ω, m, and b are the average power of the line-of-sight component, the Nakagami parameter, and half of the average power of the scattered component respectively, and (x) n is the Pochhammer symbol;

[0114] The probability density function of the channel gain |H| 2 in the space-ground link is expressed as:

[0115]

[0116] In a specific embodiment, in S3, according to the spatial distribution model of the LEO satellite constellation and the space-ground wireless channel model for multi-LEO satellite cooperative communication, the signal-to-noise ratio models for the uplink and downlink constructed include:

[0117] In the multi-LEO satellite cooperative communication of the LEO satellite communication network, a total of K orthogonal channels in the Ka band are set;

[0118] It is set that each LEO satellite is equipped with a directional antenna with the main lobe beam pointing to the center of the earth. The ground user is within the beam of the directional antenna of each LEO satellite and has an omnidirectional antenna capable of communicating with each LEO satellite;

[0119] For the uplink where a ground user transmits a signal to the k-th low-earth orbit (LEO) satellite, the signal-to-noise ratio (SNR) received by the k-th LEO satellite is expressed as:

[0120]

[0121] In the formula, p GU is the transmit power of the ground user; is the antenna gain from the ground user to the k-th LEO satellite; is the noise power of the k-th channel, is the channel gain from the ground user to the k-th LEO satellite, characterized by the shadowed Rice fading model; is the transmit antenna gain of the ground user, is the receive antenna gain of the k-th LEO satellite;

[0122] For the downlink where the k-th LEO satellite transmits a signal to the ground user, the SNR received at the ground user is:

[0123]

[0124] In the formula, p LEO is the transmit power of each LEO satellite, is the antenna gain from the k-th LEO satellite to the ground user, is the transmit antenna gain of the k-th LEO satellite, is the receive antenna gain of the ground user, represents the channel gain from the k-th LEO satellite to the ground user.

[0125] Specifically, in the multi-LEO satellite cooperative communication network, this embodiment uses the decode-and-forward protocol to provide signal forwarding services for the end-to-end communication between the ground user and the LEO satellite.

[0126] In a specific embodiment, in S4, according to the SNR models of the uplink and downlink, a multi-LEO satellite cooperative communication strategy in the multi-LEO satellite communication network is established, including:

[0127] S41: The ground user sends a pilot signal to the first LEO satellite through the first channel;

[0128] S42: The first LEO satellite measures the SNR of the received pilot signal;

[0129] S43: Determine whether the measured SNR exceeds a predefined SNR threshold τ. If it exceeds, execute S431 - S433; otherwise, execute S44;

[0130] S431: The first LEO satellite sends a feedback pilot signal to the ground user on the same channel;

[0131] S432: Signal-to-noise ratio of the pilot signal evaluated and fed back by the ground user;

[0132] S433: Determine whether the signal-to-noise ratio at the ground user exceeds a predefined signal-to-noise ratio threshold τ. If it exceeds, it indicates that the first low-earth orbit satellite is a qualified low-earth orbit satellite, and execute S45; otherwise, execute S44;

[0133] S44: Switch the first low-earth orbit satellite to the second low-earth orbit satellite and re-execute according to the rules of S41 until the switching of K satellites is completed, then terminate the pilot signal transmission process;

[0134] S45: The ground user selects the qualified low-earth orbit satellite to transmit the message signal.

[0135] Specifically, in this embodiment, when the signal-to-noise ratios of the pilot signal received by a certain low-earth orbit satellite and the earth user both exceed the predefined signal-to-noise ratio threshold τ, it indicates that the low-earth orbit satellite is a qualified low-earth orbit satellite.

[0136] In a specific embodiment, in S5, the correlation relationship between the signal-to-noise ratio models of the established uplink and downlink and the key performance indicators includes:

[0137] Express the probability that the signal-to-noise ratios received at the low-earth orbit satellite and the ground user both meet the predefined signal-to-noise ratio threshold τ as the end-to-end successful transmission probability of communicating through the kth low-earth orbit satellite, so as to construct the correlation relationship between the signal-to-noise ratio models of the uplink and downlink and the end-to-end successful transmission probability, expressed as:

[0138]

[0139] In the formula, and respectively represent the signal-to-noise ratios received at the kth low-earth orbit satellite and the ground user when the ground user communicates with the kth low-earth orbit satellite, is the probability measure;

[0140] The end-to-end delay of the ground user communicating through the kth low-earth orbit satellite includes the transmission delay and the handover delay, expressed as:

[0141]

[0142] In the formula, represents the uplink delay of end-to-end communication through the kth satellite, represents the downlink delay of end-to-end communication through the kth satellite, is the transmission delay; B is the channel bandwidth; due to the use of the multi-low-earth orbit satellite cooperative communication strategy, when the ground user switches satellites, a handover delay will be generated, (k - 1)Tho Denote the cumulative handover delay generated when switching from the first low-earth orbit satellite to the k-th low-earth orbit satellite as T ho The handover delay for each handover, and T ho is a constant.

[0143] In a specific embodiment, in S6, according to the multi-low-earth orbit satellite cooperative communication strategy and the correlation relationship between the signal-to-noise ratio model and key performance indicators of the uplink and downlink, the derivation of the analytical expressions for the overall network successful transmission probability and the overall network delay includes:

[0144] 1) Based on the multi-low-earth orbit satellite cooperative communication strategy, the analytical expression for the overall network successful transmission probability of K low-earth orbit satellites in cooperative communication is:

[0145]

[0146] In the formula, q is the failure probability of each low-earth orbit satellite;

[0147] Specifically, in order to better characterize the operating state of low-earth orbit satellites, the present invention introduces the failure probability q to quantify the possibility of low-earth orbit satellite failures caused by potential threats such as solar storms, high-speed collisions, and other space hazards.

[0148] P k (τ) is the end-to-end successful transmission probability for communication through the k-th low-earth orbit satellite. According to the definition of the end-to-end successful transmission probability, it can be obtained that:

[0149]

[0150] In the formula, Since the uplink and downlink do not affect each other, formula (a) can be obtained; the cumulative distribution function of shadow Rice fading is adopted in formula (b), that is, formula (2); formula (d) is obtained by substituting the probability density function of shadow Rice fading, that is, formula (3), into formula (c).

[0151] In formula (c), is the probability density function of the distance between the k-th low-earth orbit satellite and the ground user, expressed as:

[0152]

[0153] where r min ≤r k ≤r max , k ∈ {1, 2, 3,..., K}, r min is the constellation altitude, r max is the maximum visible distance, and the maximum visible distance is the distance between the ground user and any point on its local horizon. r e is the radius of the Earth; j is the summation variable;

[0154] 2) Based on the multi - low - earth - orbit satellite cooperative communication strategy, the analytical expression for the overall network delay of K low - earth - orbit satellites in cooperative communication is:

[0155]

[0156] where, T k represents the end - to - end delay of communication through the k - th low - earth - orbit satellite;

[0157] T k is expressed as:

[0158]

[0159] where, ω is the length of the data packet, is the indicator function.

[0160] In a specific embodiment, in S7, the optimal cooperative satellite number optimization scheme established based on the derived analytical expressions of the overall network successful transmission probability and the overall network delay includes:

[0161] In a multi - low - earth - orbit satellite cooperative communication network, although the cooperative communication of multi - low - earth - orbit satellites can improve the overall network successful transmission probability, the ground users will introduce additional handover delays during each handover of low - earth - orbit satellites, resulting in a sharp increase in the overall network delay. To improve the performance of the multi - low - earth - orbit satellite cooperative communication network, this embodiment defines the network efficiency η as the ratio of the overall network successful transmission probability to the overall network delay, expressed as:

[0162]

[0163] Establish an optimal cooperative satellite number optimization scheme to maximize the network efficiency η by optimizing the number of cooperative satellites. The optimal cooperative satellite number optimization scheme is expressed as:

[0164]

[0165] s.t. Φ vis , Φ s ≠φ,(12a)

[0166]

[0167] 500km ≤ r min ≤ 1500km,(12c)

[0168] P s (τ), P k (τ), q ∈ [0,1],(12d)

[0169] Among them, constraint (12a) is used to ensure that both the set of visible satellites and the set of LEO satellites for cooperative communication are non-empty sets; constraint (12b) is used to stipulate that the number of LEO satellites in the LEO satellite constellation and the number of LEO satellites for cooperative communication must be positive integers, and it is required that the number of cooperative satellites does not exceed the total number of satellites in the LEO satellite constellation. Constraint (12c) is used to define the altitude range of the LEO satellite constellation, which varies from 500 km to 1500 km; constraint (12d) is used to ensure that both the overall network successful transmission probability and the end-to-end successful transmission probability of communication through the k-th LEO satellite are within the range of 0 to 1.

[0170] To verify the correctness of the proposed method for determining the optimal number of cooperative satellites in multi-LEO satellite communication, in this embodiment, the Monte Carlo simulation method is used in the Matlab simulation platform to obtain the simulation results of the overall network successful transmission probability and the overall network delay, and the simulation results are compared with the theoretical results obtained by solving the relevant analytical expressions using the Mathematica scientific computing platform. Subsequently, by adjusting the design parameters of the multi-LEO satellite cooperative communication network, such as the predefined signal-to-noise ratio threshold, the altitude of the LEO satellite constellation, the satellite failure probability, etc., the changing trends of the key performance indicators are analyzed. In addition, by constructing an optimization problem for maximizing the network effectiveness, the optimal value of the network effectiveness and the number of cooperative communication satellites that optimize the network effectiveness are solved. The parameter settings in the theoretical solution and simulation verification process are shown in Table 1 specifically.

[0171] Table 1 Parameter Settings

[0172]

[0173]

[0174] Figure 3 It shows the variation of the overall network transmission success rate with the predefined signal-to-noise ratio threshold when the number of cooperative satellites K takes values of 1, 2, and 3 respectively, and the satellite failure probability q is 0.1. It can be seen from the figure that the theoretical results match the simulation results, verifying the accuracy of the derived analytical expressions. In addition, as the number of cooperative satellites increases, the overall network successful transmission probability gradually increases. This is because when the overall network successful transmission probability is relatively low due to factors such as channel fading for the first LEO satellite, the cooperative communication scheme given in this embodiment can enable other LEO satellites to provide additional signal coverage for ground users, thereby reducing the possibility of signal interruption. This shows that compared with the communication service provided by a single satellite, multi-LEO satellite cooperative communication can effectively improve the performance of end-to-end signal transmission.

[0175] Figure 4It presents the influence of the constellation altitude on the overall network delay when the data packet length is 1 megabit (Mbit). It can be analyzed that as the constellation altitude increases, the overall network delay shows an upward trend. This is because a higher constellation altitude increases the distance between the low-earth orbit satellite and the ground user, and the signal transmission path becomes longer, resulting in an increase in the transmission delay. In addition, when multiple low-earth orbit satellites adopt a cooperative communication method, due to the introduction of additional handover delay, the overall network delay will increase with the increase in the number of cooperative low-earth orbit satellites.

[0176] As Figure 5 and Figure 6 shown, they are the maximum network efficiency η and the optimal number of cooperative satellites at different constellation altitudes. It can be seen from the figure that when the constellation altitude is relatively high, the successful transmission probability of a single satellite decreases, and more low-earth orbit satellites are required for cooperative communication to improve the overall network performance. On the contrary, at a lower constellation altitude, a single satellite can provide sufficient signal coverage. Therefore, it is advisable to reduce the number of cooperative satellites to reduce the overall network delay. For large data packet transmission, the overall network delay is mainly determined by the transmission delay, and the handover delay can be ignored. Therefore, at this time, the cooperation of low-earth orbit satellites should be increased to improve the reliability of the network. In contrast, for small data packet transmission, not too much satellite cooperative communication is required. Because frequent handovers, although increasing the overall network successful transmission probability, will reduce the network efficiency.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining the optimal number of cooperative satellites for multi-low-orbit satellite communications, characterized in that: The specific steps include: S1: Construct a spatial distribution model of low-orbit satellite constellations in the low-orbit satellite communication network to determine the positional relationship between each low-orbit satellite; S2: constructing a satellite-to-ground wireless channel model for cooperative communication between multiple low-orbit satellites according to the spatial distribution model of the low-orbit satellite constellation; S3: constructing a signal-to-noise ratio model of an uplink and a downlink according to the spatial distribution model of the low-orbit satellite constellation and the satellite-to-ground wireless channel model for cooperative communication of multiple low-orbit satellites; the uplink is a link for ground users to transmit signals to low-orbit satellites, and the downlink is a link for low-orbit satellites to transmit signals to ground users; S4: establishing a multi-low-orbit satellite cooperative communication strategy in a low-orbit satellite communication network according to the signal-to-noise ratio model of the uplink and the downlink, so as to determine the low-orbit satellite used by the ground user for end-to-end signal transmission; S5: Establishing an association relationship between the uplink and downlink signal-to-noise ratio models and key performance indicators, where the key performance indicators include end-to-end successful transmission probability and end-to-end delay; S6: deriving analytical expressions of the overall network successful transmission probability and the overall network delay according to the multi-LEO satellite cooperative communication strategy and the correlation between the uplink and downlink signal-to-noise ratio models and key performance indicators; S7: Establish an optimization scheme for the optimal number of cooperative satellites based on the derived analytical expressions of the overall network successful transmission probability and the overall network delay; S8: Based on the optimal cooperative satellite number optimization scheme, the optimal network effectiveness value and the number of cooperative communication satellites that optimizes the network effectiveness are obtained.

2. The method for determining the optimal number of cooperative satellites for multi-low-orbit satellite communications according to claim 1, characterized in that: In S7, the optimal number of cooperative satellites optimization scheme established based on the derived analytical expressions of the overall network successful transmission probability and the overall network delay includes: The network effectiveness η is defined as the ratio of the overall network successful transmission probability to the overall network delay, expressed as: An optimal cooperative satellite number optimization scheme is established to maximize the network effectiveness η by optimizing the number of cooperative satellites. The optimal cooperative satellite number optimization scheme is expressed as: stΦ vis ,F s ≠φ,(1a) 500km≤r min ≤1500km, (1c) P s (t),P k (τ),q∈[0,1], (1d) Among them, constraint (1a) is used to ensure that the visible satellite set and the low-orbit satellite set used for cooperative communication are both non-empty sets; constraint (1b) is used to stipulate that the number of low-orbit satellites in the low-orbit satellite constellation and the number of low-orbit satellites used for cooperative communication must be positive integers, and require that the number of cooperative satellites does not exceed the total number of satellites in the low-orbit satellite constellation; constraint (1c) is used to define the altitude range of the low-orbit satellite constellation; constraint (1d) is used to ensure that the overall network successful transmission probability and the end-to-end successful transmission probability of communication through the kth low-orbit satellite are both in the range of 0 to 1.

3. The method for determining the optimal number of cooperative satellites for multi-low-orbit satellite communications according to claim 2, characterized in that: In S1, the step of constructing the spatial distribution model of the low-orbit satellite constellation includes: S11: Setting a communication node in a low-orbit satellite communication network, wherein the communication node includes a low-orbit satellite constellation and a ground user; S12: Establish a three-dimensional Cartesian coordinate system with the center of the earth as the origin, in which the x-axis points from the origin to any point on the equator, the y-axis is in the plane where the equator is located and is perpendicular to the x-axis, and the z-axis points from the origin to the geographic North Pole; S13: Set the position of the ground user on the earth's surface to (0,0,r e ), r e is the radius of the earth, and ground users can communicate directly with low-orbit satellites; S14: In the low-orbit satellite constellation, N low-orbit satellites are distributed in a radius of r. a On the sphere of , a binomial point process distribution is formed, where r a =r e +r min , r min is the constellation altitude; S15: Sort all low-orbit satellites in the low-orbit satellite constellation according to the distance between the low-orbit satellites and ground users, including: Each low-orbit satellite is defined as the first, second, ..., kth low-orbit satellite in the order of distance from the ground user from near to far, 1≤k≤N, N is the total number of low-orbit satellites; the distance from the kth low-orbit satellite to the ground user is R k ; S16: Set the visible satellite set to Φ vis ={s1,s2,...,s M }, M is the number of visible satellites, M≤N and M is a positive integer; set a low-orbit satellite set for cooperative communication, the low-orbit satellite set for cooperative communication is a subset of the visible satellite set, expressed as Φ s ={s1,s2,...,s K }, K is the total number of low-orbit satellites used for cooperative communication, K≤M and K is a positive integer.

4. The method for determining the optimal number of cooperative satellites for multi-low-orbit satellite communications according to claim 3, characterized in that: In S2, based on the spatial distribution model of the low-orbit satellite constellation, the satellite-to-ground wireless channel model for multi-low-orbit satellite cooperative communication is constructed including: Path loss model: In both the uplink and downlink, the power path loss model is used to represent the path loss between the ground user and the kth low-orbit satellite, which is expressed as: Among them, R k is the distance from the kth low-orbit satellite to the ground user, c is the speed of light, f c is the carrier frequency of the signal, α is the power path loss factor; Small-scale fading model: The shadow Rice fading model is used to characterize the channel fading between the ground user and the kth low-orbit satellite. The channel gain |H| in the satellite-to-ground link 2 The cumulative distribution function of is expressed as: in, Ω, m, and b are the average power of the line-of-sight component, the Nakagami parameter, and half of the average power of the scattered component, respectively. (x) n It is the Pochhammer symbol; Channel gain in satellite-to-ground link |H| 2 The probability density function of is expressed as:

5. The method for determining the optimal number of cooperative satellites for multi-low-orbit satellite communications according to claim 4, characterized in that: In S3, based on the spatial distribution model of the low-orbit satellite constellation and the satellite-to-ground wireless channel model for multi-low-orbit satellite cooperative communication, the uplink and downlink signal-to-noise ratio models constructed include: In the cooperative communication of multiple low-orbit satellites in the low-orbit satellite communication network, a total of K orthogonal channels located in the Ka frequency band are set; It is assumed that each low-orbit satellite is equipped with a directional antenna with a main lobe beam pointing to the center of the earth, and the ground user is located in the beam of the directional antenna of each low-orbit satellite and has an omnidirectional antenna capable of communicating with each low-orbit satellite; For the uplink of the ground user transmitting signals to the k-th low-orbit satellite, the signal-to-noise ratio received by the k-th low-orbit satellite is expressed as: In the formula, p GU The transmission power for ground users; is the antenna gain from the ground user to the kth low-orbit satellite; is the noise power of the kth channel, is the channel gain from the ground user to the kth low-orbit satellite; is the transmitting antenna gain of the ground user, is the receiving antenna gain of the kth low-orbit satellite; For the downlink signal transmission from the kth low-orbit satellite to the ground user, the signal-to-noise ratio received by the ground user is: In the formula, p LEO is the transmission power of each low-orbit satellite, is the antenna gain from the kth low-orbit satellite to the ground user, is the transmitting antenna gain of the kth low-orbit satellite, is the receiving antenna gain of the ground user, represents the channel gain from the kth low-orbit satellite to the ground user.

6. The method for determining the optimal number of cooperative satellites for multi-low-orbit satellite communications according to claim 5, characterized in that: In S4, a multi-low-orbit satellite cooperative communication strategy in a low-orbit satellite communication network is established according to the signal-to-noise ratio model of the uplink and the downlink, including: S41: The ground user sends a pilot signal to the first low-orbit satellite through the first channel; S42: the first low-orbit satellite measures the signal-to-noise ratio of the received pilot signal; S43: Determine whether the measured signal-to-noise ratio exceeds a predefined signal-to-noise ratio threshold τ. If so, execute S431-S433; otherwise, execute S44; S431: The first low-orbit satellite sends a feedback pilot signal to ground users on the same channel; S432: The ground user evaluates the signal-to-noise ratio of the pilot signal fed back; S433: Determine whether the signal-to-noise ratio at the ground user exceeds a predefined signal-to-noise ratio threshold τ. If so, it indicates that the first low-orbit satellite is a qualified low-orbit satellite, and execute S45; otherwise, execute S44; S44: Switch the first low-orbit satellite to the second low-orbit satellite, and re-execute according to the rules of S41 until K satellites are switched, then terminate the pilot signal transmission process; S45: The ground user selects the qualified low-orbit satellite to transmit a message signal.

7. The method for determining the optimal number of cooperative satellites for multi-low-orbit satellite communications according to claim 6, characterized in that: In S5, the established association relationship between the uplink and downlink signal-to-noise ratio models and key performance indicators includes: The probability that the signal-to-noise ratio received at the low-orbit satellite and the ground user simultaneously meets the predefined signal-to-noise ratio threshold τ is expressed as the end-to-end successful transmission probability of communication through the k-th low-orbit satellite, so as to construct the correlation relationship between the signal-to-noise ratio model of the uplink and downlink and the end-to-end successful transmission probability, which is expressed as: In the formula, and They represent the signal-to-noise ratios received at the kth low-orbit satellite and the ground user when the ground user communicates with the kth low-orbit satellite, is a probability measure; The end-to-end delay of ground users communicating through the kth low-orbit satellite includes transmission delay and switching delay, which can be expressed as: In the formula, represents the uplink delay of end-to-end communication through the kth satellite, represents the downlink delay of end-to-end communication through the kth satellite, is the transmission delay; B is the channel bandwidth; (k-1)T ho represents the cumulative switching delay generated when switching from the first low-orbit satellite to the kth low-orbit satellite, T ho is the switching delay of each switching, and T ho is a constant.

8. The method for determining the optimal number of cooperative satellites for multi-low-orbit satellite communications according to claim 7, characterized in that: In S6, according to the multi-low-orbit satellite cooperative communication strategy and the correlation between the uplink and downlink signal-to-noise ratio models and key performance indicators, the analytical expressions for deriving the overall network successful transmission probability and the overall network delay include: 1) Based on the multi-LEO satellite cooperative communication strategy, the analytical expression of the overall successful transmission probability of the network of K LEO satellite cooperative communication is: Where q is the failure probability of each low-orbit satellite; P k (τ) is the probability of end-to-end successful transmission through the kth low-orbit satellite, expressed as: In the formula, is the probability density function of the distance between the kth low-orbit satellite and the ground user, expressed as: Among them, r min ≤r k ≤r max , k∈{1,2,3,...,K}, r min is the constellation height, r max is the maximum visible distance, which is the distance between the ground user and any point on the horizon where the user is located. r e is the radius of the earth; j is the summation variable; 2) Based on the multi-LEO satellite cooperative communication strategy, the analytical expression of the overall network delay of K LEO satellite cooperative communication is: Among them, T k represents the end-to-end delay of communication through the kth low-orbit satellite; T k It is expressed as: Where ω is the length of the packet, is the indicator function.

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