A method for determining optimal number of cooperating satellites for multi-low earth orbit satellite communication

Abstract

The application discloses a kind of optimal cooperation satellite quantity determination methods for multiple low-orbit satellite communication, comprising the following steps: constructing the spatial distribution model of low-orbit satellite constellation, to determine the positional relationship between each low-orbit satellite;Construct the space wireless channel model for multiple low-orbit satellite cooperation communication;Construct the signal-to-noise ratio model of uplink and downlink;Establish multiple low-orbit satellite cooperation communication strategy;Establish the association between the signal-to-noise ratio model of uplink and downlink and key performance indicators;Deduce the analytical expression of network overall success transmission probability and network overall delay;Establish optimal cooperation satellite quantity optimization scheme;According to the result obtained by solving, network efficiency optimal value and the cooperation communication satellite quantity that make network efficiency optimal.The application can efficiently analyze the network overall success transmission probability and network overall delay of multiple low-orbit satellite cooperation communication, effectively quantify the performance gain of multiple low-orbit satellite cooperation communication, greatly reduce the complexity of performance evaluation, which is conducive to the rational allocation of low-orbit satellite communication network resources, and then guide the deployment planning of future large-scale low-orbit satellite constellation.

Description

TECHNICAL FIELD

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

[0002] In recent years, low earth orbit communication satellites (hereinafter referred to as low earth orbit satellites) can extend communication services to space due to their wide coverage, strong anti-destruction ability and freedom from geographical constraints. A low earth orbit satellite communication network composed of multiple low earth orbit satellites can make up for the shortcomings of traditional ground cellular networks and provide seamless network services to 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 earth orbit satellites. At the same time, China has also actively laid out and caught up, successively carried out projects such as Qianfanchuan constellation, Hongyan constellation, Hongyun project, and promoted the development of various emerging communication services such as inter-satellite communication services and satellite communication services directly connected to mobile phones. However, considering that the cost of satellite communication is higher than that of traditional ground cellular networks, in the existing research on low earth orbit satellite communication networks, mobile users, vehicles, Internet of Things devices and other ground users are mostly provided with data transmission services by a satellite in the low earth orbit satellite communication network. However, due to the long propagation distance and strong scattering of the satellite-ground link, relying 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 needs of ground users. In addition, there are harsh environmental factors such as high-energy particles, electromagnetic radiation and solar wind in space, which will cause the satellite to be damaged or even completely disabled, thereby reducing the reliability of single-satellite communication. SUMMARY

[0003] The present application provides a method for determining the optimal number of cooperating satellites for multi-low earth orbit satellite communication to overcome the technical problem that relying 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 needs of ground users.

[0004] In order to achieve the above-mentioned purpose, the technical scheme of the present application is as follows:

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

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

[0007] S2: constructing a satellite-ground wireless channel model for multi-low earth orbit satellite cooperative communication according to the spatial distribution model of the low earth orbit satellite constellation;

[0008] S3: constructing a signal-to-noise ratio model of uplink and downlink according to the spatial distribution model of the low earth orbit satellite constellation and the satellite-ground wireless channel model for multi-low earth orbit satellite cooperative communication; the uplink is a link for a ground user to transmit a signal to a low earth orbit satellite, and the downlink is a link for a low earth orbit satellite to transmit a signal to a ground user;

[0009] S4: establishing a multi-low earth orbit satellite cooperative communication strategy in a low earth orbit satellite communication network according to the signal-to-noise ratio model of the uplink and the downlink, to determine a low earth orbit satellite used by a ground user for end-to-end signal transmission;

[0010] S5: establishing an association between the signal-to-noise ratio model of the uplink and the downlink and key performance indicators, the key performance indicators including an end-to-end successful transmission probability and an end-to-end delay;

[0011] S6: deriving an analytical expression of a network overall successful transmission probability and a network overall delay according to the multi-low earth orbit satellite cooperative communication strategy and the association between the signal-to-noise ratio model of the uplink and the downlink and the key performance indicators;

[0012] S7: establishing an optimal cooperative satellite number optimization scheme based on the derived analytical expression of the network overall successful transmission probability and the network overall delay;

[0013] S8: obtaining a network effectiveness optimal value and a cooperative communication satellite number that optimizes the network effectiveness based on the optimal cooperative satellite number optimization scheme.

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

[0015] Defining a network effectiveness η as a ratio of the network overall successful transmission probability to the network overall delay, and representing as:

[0016]

[0017] Establishing an optimal cooperative satellite number optimization scheme to maximize the network effectiveness η by optimizing the cooperative satellite number, and representing the optimal cooperative satellite number optimization scheme 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 low-Earth orbit satellites used for cooperative communication are non-empty sets; constraint (1b) is used to stipulate that the number of low-Earth orbit satellites in the low-Earth orbit satellite constellation and the number of low-Earth orbit satellites used for cooperative communication must be positive integers, and requires that the number of cooperative satellites does not exceed the total number of satellites in the low-Earth orbit satellite constellation; constraint (1c) is used to define the altitude range of the low-Earth orbit satellite constellation; constraint (1d) is used to ensure that the overall network success transmission probability and the end-to-end success transmission probability through the k-th low-Earth orbit satellite are both within the range of 0 to 1.

[0024] Furthermore, in S1, the step of constructing the spatial distribution model of the low-Earth orbit satellite constellation includes:

[0025] S11: Configure a communication node in a low-Earth orbit satellite communication network, wherein the communication node includes a low-Earth orbit satellite constellation and a ground user;

[0026] S12: Establish a three-dimensional Cartesian coordinate system with the Earth's center as the origin. In the three-dimensional Cartesian coordinate system, the x-axis points from the origin to any 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 location of the ground user on the Earth's surface to (0,0,r). e ), r e It is the Earth's radius, and ground users can communicate directly with low-Earth orbit satellites;

[0028] S14: In a low-Earth orbit satellite constellation, N low-Earth orbit satellites are distributed over a radius of r. a On the surface of a sphere, a binomial point process distribution is formed, where r a =r e +r min r min Constellation altitude;

[0029] S15: Based on the distance between the low-Earth orbit (LEO) satellites and the ground user, sort all LEO satellites in the constellation, including:

[0030] Each low-Earth orbit (LEO) satellite is designated as LEO satellite 1, 2, ..., k, in ascending order of distance from the ground user, where 1 ≤ k ≤ N, and N is the total number of LEO satellites. The distance from the k-th LEO satellite to the ground user is R. k ;

[0031] S16: Define the set of visible satellites as Φ vis ={s1,s2,...,s M}, where M is the number of visible satellites, M≤N and M is a positive integer; define a set of low-Earth orbit (LEO) satellites used for cooperative communication, which is a subset of the set of visible satellites, denoted as Φ. s ={s1,s2,...,s K}, where K is the total number of low-Earth orbit satellites used for cooperative communication, K≤M and K is a positive integer.

[0032] Furthermore, in S2, the satellite-to-ground wireless channel model for multi-Low Earth orbit satellite cooperative communication, constructed based on the spatial distribution model of the aforementioned LEO satellite constellation, includes:

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

[0034]

[0035] Among them, R k Let f be the distance from the k-th low-Earth orbit satellite to the ground user, c be the speed of light, and f be the distance from the k-th low-Earth orbit satellite to the ground user. c Let α be the carrier frequency of the signal, and α be the power loss factor.

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

[0037]

[0038] in, Ω, m, and b represent the average power of the line-of-sight component, the Nakagami parameter, and half the average power of the scattering component, respectively. (x) n It is the Pochhammer symbol;

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

[0040]

[0041] Furthermore, in S3, based on the spatial 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 uplink and downlink signal-to-noise ratio models constructed include:

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

[0043] Each low earth orbit satellite is equipped with a directional antenna with a main lobe pointing to the center of the earth, and the ground user is located in the beam of the directional antenna of each low earth orbit satellite and has an omnidirectional antenna capable of communicating with each low earth orbit satellite;

[0044] For uplink of signal transmission from the ground user to the kth low earth orbit satellite, the signal-to-noise ratio received by the kth low earth orbit satellite is represented as:

[0045]

[0046] In the formula, p GU is the transmission power of the ground user; is the antenna gain of the ground user to the kth low earth orbit satellite; is the noise power of the kth channel, is the channel gain from the ground user to the kth low earth orbit satellite; is the transmission antenna gain of the ground user, is the reception antenna gain of the kth low earth orbit satellite;

[0047] For downlink of signal transmission from the kth low earth orbit satellite 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 of the kth low earth orbit satellite to the ground user, is the transmission antenna gain of the kth low earth orbit satellite, is the reception antenna gain of the ground user, is the channel gain from the kth low earth orbit satellite to the ground user.

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

[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: it is judged whether the measured signal-to-noise ratio exceeds a predefined signal-to-noise ratio threshold τ, if yes, S431-S433 are executed; otherwise, S44 is executed;

[0054] S431: the first LEO 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: it is judged whether the signal-to-noise ratio at the ground user exceeds a predefined signal-to-noise ratio threshold τ, if yes, it means that the first LEO satellite is a qualified LEO satellite, and S45 is executed; otherwise, S44 is executed;

[0057] S44: the first LEO satellite is switched to the second LEO satellite, and the process is re-executed according to the rule of S41 until K satellites are switched, and then the pilot signal transmission process is terminated;

[0058] S45: the ground user selects the qualified LEO satellite to transmit a message signal.

[0059] Further, in S5, the association between the signal-to-noise ratio model of the uplink and downlink and the key performance indicators includes:

[0060] The probability that the signal-to-noise ratios received at the LEO satellite and the ground user both satisfy the predefined signal-to-noise ratio threshold τ is represented as an end-to-end successful transmission probability through the kth LEO satellite, to construct the association between the signal-to-noise ratio model of the uplink and downlink and the end-to-end successful transmission probability, represented as:

[0061]

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

[0063] The end-to-end delay of the ground user communicating through the kth LEO satellite includes a transmission delay and a switching delay, represented 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 switching delay generated when switching from the first LEO satellite to the kth LEO satellite, T hois the switching delay for each handover, and T ho is a constant.

[0066] Further, in S6, according to the multi-low earth orbit satellite cooperative communication strategy and the association relationship between the signal-to-noise ratio model of the uplink and downlink and the key performance indicators, the analytical expressions of the network overall successful transmission probability and the network overall delay are derived, including:

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

[0068]

[0069] In the formula, q is the failure probability of each low earth orbit satellite;

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

[0071]

[0072] In the formula, is the probability density function of the distance between the kth low earth orbit satellite and the ground user, which is expressed as:

[0073]

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

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

[0076]

[0077] wherein, T k represents the end-to-end delay of communication through the kth low earth orbit satellite;

[0078] T k is expressed as:

[0079]

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

[0081] Beneficial effects: the present application establishes a multi-low earth orbit satellite cooperative communication strategy in a low earth orbit satellite communication network, determines a low earth orbit satellite for end-to-end signal transmission of a ground user, and establishes an association between a signal-to-noise ratio model of an uplink and a downlink and an end-to-end successful transmission probability and an end-to-end delay, thereby deducing an analytical expression of a network overall successful transmission probability and a network overall delay; based on the deduced analytical expression of the network overall successful transmission probability and the network overall delay, an optimal cooperative satellite number optimization scheme is established, and finally the network efficiency optimal value and the cooperative communication satellite number that optimizes the network efficiency are solved. The present application can efficiently analyze the network overall successful transmission probability and the network overall 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, and be beneficial to the rational allocation of low earth orbit satellite communication network resources, thereby guiding the deployment planning of future large-scale low earth orbit satellite constellation. In addition, the present method can effectively improve the reliability of low earth orbit satellite and ground user communication, and provide technical support and beneficial reference for the development of low earth orbit satellite cooperative communication technology. BRIEF DESCRIPTION OF DRAWINGS

[0082] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0083] Figure 1 is a flow chart of an optimal cooperative satellite number determination method for multi-low earth orbit satellite communication in the present application;

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

[0085] Figure 3 is a network overall successful transmission probability change relationship graph with a predefined signal-to-noise ratio threshold in the embodiment of the present application;

[0086] Figure 4 is a network overall delay change relationship graph with constellation altitude in the embodiment of the present application;

[0087] Figure 5 is a maximum network efficiency comparison graph of different constellation altitudes in the embodiment of the present application;

[0088] Figure 6A comparison chart of optimal satellite numbers for different star elevation angles in the embodiments of the present application. DETAILED DESCRIPTION

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

[0090] The embodiments provide a method for determining optimal satellite numbers for multi-low earth orbit satellite communication, as shown in the following formula (1). Figure 1 The specific steps include:

[0091] S1: constructing a spatial distribution model of a low earth orbit satellite constellation in a low earth orbit satellite communication network to determine the positional relationship between each low earth orbit satellite;

[0092] S2: constructing a satellite-ground wireless channel model for multi-low earth orbit satellite cooperative communication according to the spatial distribution model of the low earth orbit satellite constellation;

[0093] S3: constructing a signal-to-noise ratio model of an uplink and a downlink according to the spatial distribution model of the low earth orbit satellite constellation and the satellite-ground wireless channel model for multi-low earth orbit satellite cooperative communication; the uplink is a link for a ground user to transmit a signal to a low earth orbit satellite, and the downlink is a link for a low earth orbit satellite to transmit a signal to a ground user;

[0094] S4: establishing a multi-low earth orbit satellite cooperative communication strategy in the low earth orbit satellite communication network according to the signal-to-noise ratio model of the uplink and the downlink to determine a low earth orbit satellite used by a ground user for end-to-end signal transmission;

[0095] S5: establishing an association between the signal-to-noise ratio model of the uplink and the downlink and key performance indicators, the key performance indicators including an end-to-end successful transmission probability and an end-to-end delay;

[0096] S6: deriving an analytical expression of a network overall successful transmission probability and a network overall delay according to the multi-low earth orbit satellite cooperative communication strategy and the association between the signal-to-noise ratio model of the uplink and the downlink and the key performance indicators;

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

[0098] S8: Based on the optimization scheme for the optimal number of cooperative satellites, the optimal value of network efficiency and the number of cooperative communication satellites that maximizes network efficiency are obtained.

[0099] In a specific embodiment, step S1, constructing the spatial distribution model of the low-Earth orbit satellite constellation, includes:

[0100] S11: Configure a communication node in a low-Earth orbit satellite communication network, wherein the communication node includes a low-Earth orbit satellite constellation and a ground user;

[0101] S12: Establish a three-dimensional Cartesian coordinate system with the Earth's center as the origin. In the three-dimensional Cartesian coordinate system, the x-axis points from the origin to any 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 location of the ground user on the Earth's surface to (0,0,r). e ), r e It is the Earth's radius, and ground users can communicate directly with low-Earth orbit satellites;

[0103] S14: In a low-Earth orbit satellite constellation, N low-Earth orbit satellites are distributed over a radius of r. a On the surface of the sphere, a binomial point process (BPP) distribution is formed, where r a =r e +r min r min The altitude of the constellation;

[0104] S15: Based on the distance between the low-Earth orbit (LEO) satellites and the ground user, sort all LEO satellites in the constellation, including:

[0105] like Figure 2 As shown, each low-Earth orbit (LEO) satellite is sequentially defined as the first, second, ..., kth LEO satellite, in order of increasing distance from the ground user, where 1 ≤ k ≤ N, and N is the total number of LEO satellites. The distance from the kth LEO satellite to the ground user is R. k ;

[0106] S16: Define the set of visible satellites as Φ vis ={s1,s2,...,s M Let M be the number of visible satellites, M ≤ N and M is a positive integer. The visible satellites are low-Earth orbit (LEO) satellites located above the horizon of the ground user. The horizon is the intersection of the horizontal tangent plane at the ground user's location and the sphere containing the LEO satellites. A set of LEO satellites for cooperative communication is defined, which is a subset of the visible satellite set, denoted as Φ.s = {s1, s2,..., sK}, K is the total number of low earth orbit satellites for cooperative communication, K≤M and K is a positive integer. K}, K is the total number of low earth orbit satellites for cooperative communication, K≤M and K is a positive integer.

[0107] In specific embodiments, in S2, according to the spatial distribution model of the low earth orbit satellite constellation, a satellite-to-ground wireless channel model for multi-low earth orbit satellite cooperative communication is constructed, which includes:

[0108] Path loss model: in the uplink and downlink, the path loss between the ground user and the kth low earth orbit satellite is represented by a power path loss model, which is expressed as:

[0109]

[0110] wherein Rkis the distance from the kth low earth orbit satellite to the ground user, c is the speed of light, f is the carrier frequency of the signal, and a is the power path loss factor. k c

[0111] Small-scale fading model: a shadowed-Rician fading model is used to represent the channel fading between the ground user and the kth low earth orbit satellite, and the cumulative distribution function of the channel gain |H| in the satellite-to-ground link is expressed as: 2

[0112]

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

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

[0115]

[0116] In specific embodiments, in S3, according to the spatial 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 of the uplink and the downlink are constructed, which include:

[0117] In the multi-low earth orbit satellite cooperative communication of the low earth orbit satellite communication network, K orthogonal channels in the Ka frequency band are set;

[0118] Each low earth orbit satellite is equipped with a directional antenna with a main lobe pointing to the center of the Earth, and the ground user is located within the beam of the directional antenna of each low earth orbit satellite and has an omnidirectional antenna capable of communicating with each low earth orbit satellite.

[0119] ​​​​For the uplink of the signal transmission from the ground user to the kth LEO satellite, the signal-to-noise ratio received by the kth LEO satellite is expressed as:

[0120]

[0121] wherein p is the transmission power of the ground user; GU is the transmission power of each LEO satellite, is the antenna gain of the ground user to the kth LEO satellite, is the noise power of the kth channel, is the channel gain from the ground user to the kth LEO satellite, which is characterized by a shadowed Rician fading model, is the transmission antenna gain of the ground user, is the reception antenna gain of the kth LEO satellite,

[0122] For the downlink of the signal transmission from the kth LEO satellite to the ground user, the signal-to-noise ratio received at the ground user is:

[0123]

[0124] wherein p is the transmission power of each LEO satellite, LEO is the transmission power of each LEO satellite, is the antenna gain of the kth LEO satellite to the ground user, is the transmission antenna gain of the kth LEO satellite, is the reception antenna gain of the ground user, is the channel gain from the kth LEO satellite to the ground user.

[0125] Specifically, in the multi-LEO satellite cooperative communication network, the embodiment adopts a 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, the multi-LEO satellite cooperative communication strategy in the multi-LEO satellite communication network is established according to the signal-to-noise ratio models of the uplink and the downlink, comprising:

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

[0128] S42: the first LEO satellite measures the signal-to-noise ratio of the received pilot signal;

[0129] S43: it is judged whether the measured signal-to-noise ratio exceeds a predefined signal-to-noise ratio threshold τ, if yes, S431-S433 are executed; otherwise, S44 is executed;

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

[0131] S432: the ground user evaluates the signal-to-noise ratio of the feedback pilot signal;

[0132] S433: it is judged whether the signal-to-noise ratio at the ground user exceeds a predefined signal-to-noise ratio threshold τ, if yes, it is indicated that the first low earth orbit satellite is a qualified low earth orbit satellite, and S45 is executed; otherwise, S44 is executed;

[0133] S44: the first low earth orbit satellite is switched to a second low earth orbit satellite, and the re-execution is performed according to the rule of S41 until K satellites are switched, and then the pilot signal transmission process is terminated;

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

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

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

[0137] The probability that the signal-to-noise ratios received at the low earth orbit satellite and the ground user both satisfy the predefined signal-to-noise ratio threshold τ is represented as an end-to-end successful transmission probability of communication through the kth low earth orbit satellite, to construct an association relationship between the signal-to-noise ratio model of the uplink and the downlink and the end-to-end successful transmission probability, represented 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 a probability measure;

[0140] The end-to-end delay of the ground user communicating through the kth low earth orbit satellite includes a transmission delay and a switching delay, represented 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 a transmission delay; B is a channel bandwidth; since a multi-low earth orbit satellite cooperative communication strategy is adopted, the ground user will generate a switching delay when switching satellites, (k-1)Tho denotes the accumulated switching delay generated when switching from the first low earth orbit satellite to the kth low earth orbit satellite, T ho is the switching delay for each switching, and T ho is a constant.

[0143] In specific embodiments, in S6, the analytical expressions of the network overall successful transmission probability and the network overall delay are derived according to the multi-low earth orbit satellite cooperative communication strategy and the association between the signal-to-noise ratio model of the uplink and the downlink and the key performance indicators, comprising:

[0144] 1) Based on the multi-low earth orbit satellite cooperative communication strategy, the analytical expression of the network overall successful transmission probability of K low earth orbit satellite 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 represent the running state of the low earth orbit satellite, the failure probability q is introduced to quantify the possibility of low earth orbit satellite failure caused by solar storm, high-speed collision and other potential threats such as space hazards.

[0148] P k (τ) is the end-to-end successful transmission probability of communication through the kth 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 the downlink do not affect each other, formula (a) can be obtained; formula (b) adopts the cumulative distribution function of shadowed Rician fading, that is, formula (2); formula (d) is obtained by bringing the probability density function of shadowed Rician fading, that is, formula (3), into formula (c).

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

[0152]

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

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

[0155]

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

[0157] T k represents:

[0158]

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

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

[0161] In the multi-low earth orbit satellite cooperative communication network, although the cooperative communication of multiple low earth orbit satellites can improve the network overall successful transmission probability, the ground user will introduce additional switching delay in the process of switching the low earth orbit satellite each time, thereby causing the network overall delay to surge. In order to improve the performance of the multi-low earth orbit satellite cooperative communication network, the embodiment defines the network effectiveness η as the ratio of the network overall successful transmission probability to the network overall delay, which is expressed as:

[0162]

[0163] An optimal cooperative satellite number optimization scheme is established to maximize the network effectiveness η by optimizing the number of cooperative satellites, and 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 the set of visible satellites and the set of low-orbit satellites for cooperative communication are both non-empty sets; constraint (12b) is used to stipulate that the number of low-orbit satellites in the low-orbit satellite constellation and the number of low-orbit satellites for cooperative communication must be positive integers, and requires that the number of cooperative satellites does not exceed the total number of satellites in the low-orbit satellite constellation, constraint (12c) is used to define the height range of the low-orbit satellite constellation, which is from 500 km to 1500 km; constraint (12d) is used to ensure that the overall network successful transmission probability and the end-to-end successful transmission probability through the kth low-orbit satellite are both in the range of 0 to 1.

[0170] In order to verify the correctness of the constructed optimal cooperative satellite number determination method of multi-low-orbit satellite communication, in this embodiment, the simulation results of the overall network successful transmission probability and the overall network delay are obtained by using the Monte Carlo simulation method in the Matlab simulation platform, and the simulation results are compared with the theoretical results obtained by solving the related analytical expressions by using the Mathematica scientific calculation platform. Subsequently, by adjusting the design parameters of the multi-low-orbit satellite cooperative communication network, such as the pre-defined signal-to-noise ratio threshold, the low-orbit satellite constellation height, the satellite failure probability, etc., the change trend of the key performance indicators is analyzed. In addition, by constructing the network effectiveness maximization optimization problem, the optimal value of the network effectiveness and the cooperative communication satellite number that makes the network effectiveness optimal are solved. The parameter settings in the process of theoretical solving and simulation verification are shown in Table 1.

[0171] Table 1 Parameter settings

[0172]

[0173]

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

[0175] Figure 4The impact of constellation altitude on overall network latency is presented when the data packet length is 1 megabit (Mbit). Analysis shows that overall network latency increases with increasing constellation altitude. This is because higher constellation altitudes increase the distance between low-Earth orbit (LEO) satellites and ground users, lengthening the signal transmission path and thus increasing transmission latency. Furthermore, when multiple LEO satellites use cooperative communication, the introduced handover latency further increases the overall network latency as the number of cooperating LEO satellites increases.

[0176] like Figure 5 and Figure 6 The figure shows the maximum network efficiency η and the optimal number of cooperating satellites at different constellation altitudes. As can be seen from the figure, at higher constellation altitudes, the success probability of a single satellite's transmission decreases, requiring more low-Earth orbit (LEO) satellites for cooperative communication to improve overall network performance. Conversely, at lower constellation altitudes, a single satellite can provide sufficient signal coverage. Therefore, reducing the number of cooperating satellites is advisable to lower overall network latency. For large data packet transmissions, the overall network latency is mainly determined by transmission latency, while handover latency is negligible. Therefore, in this case, increasing the cooperation of LEO satellites is crucial to improve network reliability. In contrast, for small data packet transmissions, excessive satellite cooperation is unnecessary. While frequent handovers increase the overall probability of successful transmission, they reduce network efficiency.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to 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 cooperating satellites for multi-low-Earth orbit satellite communication, characterized in that, The specific steps include: S1: Construct a spatial distribution model of a low-Earth orbit satellite constellation in a low-Earth orbit satellite communication network to determine the positional relationships between various low-Earth orbit satellites; S2: Based on the spatial distribution model of the low-Earth orbit satellite constellation, construct a satellite-to-ground wireless channel model for multi-low-Earth orbit satellite cooperative communication; S3: Based on the spatial 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, construct the signal-to-noise ratio models for the uplink and downlink; the uplink is the link for ground users to transmit signals to low-Earth orbit satellites, and the downlink is the link for low-Earth orbit satellites to transmit signals to ground users. S4: Establish a multi-low-Earth orbit satellite cooperative communication strategy in the low-Earth orbit satellite communication network based on the signal-to-noise ratio model of the uplink and downlink, so as to determine the low-Earth orbit satellites used by ground users for end-to-end signal transmission; S5: Establish the correlation between the signal-to-noise ratio model and key performance indicators of the uplink and downlink, wherein the key performance indicators include the end-to-end successful transmission probability and the end-to-end latency; S6: Based on 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, derive analytical expressions for the overall network successful transmission probability and the overall network latency. S7: Based on the derived analytical expressions for the overall network successful transmission probability and overall network latency, establish an optimal scheme for the number of cooperative satellites; The optimal cooperative satellite number optimization scheme, established based on the derived analytical expressions for the overall network successful transmission probability and overall network latency, includes: Define network effectiveness The ratio of the overall network success probability to the overall network latency is expressed as: ， Establish an optimal scheme for the number of cooperating satellites to maximize network effectiveness by optimizing the number of cooperating satellites. η The optimal scheme for the number of cooperating satellites is expressed as: Among them, constraint (1a) ensures that both the visible satellite set and the low-Earth orbit (LEO) satellite set used for cooperative communication are non-empty sets; constraint (1b) stipulates that the number of LEO satellites in the LEO satellite constellation and the number of LEO satellites used for cooperative communication must be positive integers, and requires that the number of cooperative satellites does not exceed the total number of satellites in the LEO satellite constellation; constraint (1c) defines the altitude range of the LEO satellite constellation; constraint (1d) ensures the overall network success rate and the probability of successful transmission. k The probability of successful end-to-end transmission for communication between low-Earth orbit satellites is in the range of 0 to 1. S8: Based on the optimization scheme for the optimal number of cooperative satellites, the optimal value of network efficiency and the number of cooperative communication satellites that maximizes network efficiency are obtained.

2. The method for determining the optimal number of cooperating satellites for multi-low-Earth orbit satellite communication according to claim 1, characterized in that, In S1, the steps for constructing the spatial distribution model of the low-Earth orbit satellite constellation include: S11: Configure a communication node in a low-Earth orbit satellite communication network, wherein the communication node includes a low-Earth orbit satellite constellation and a ground user; S12: Establish a three-dimensional Cartesian coordinate system with the Earth's center as the origin. In this three-dimensional Cartesian coordinate system, x The axis points from the origin to any point on the equator. y The axis lies in the plane of the equator and is perpendicular to it. x axis, z The axis points from the origin to the geographic North Pole; S13: Set the location of the ground user on the Earth's surface as follows , r e It is the Earth's radius, and ground users can communicate directly with low-Earth orbit satellites; S14: Set within a low-Earth orbit satellite constellation. N Low-orbit satellites are distributed in a radius of r a On the surface of the sphere, a binomial point process distribution is formed, where, r a = r e + r min , r min Constellation altitude; S15: Based on the distance between the low-Earth orbit (LEO) satellites and the ground user, sort all LEO satellites in the constellation, including: Each low-Earth orbit satellite is designated as the first, second, ..., the third, in order of increasing distance from the ground user. k 1 low-orbit satellite, 1≤ k ≤ N , N This represents the total number of low-Earth orbit satellites; among them, the [number]th... k The distance from a low-orbit satellite to a ground user is ; S16: Define the visible satellite set as... , M The number of visible satellites, M ≤ N and M Let be a positive integer; define a set of low-Earth orbit (LEO) satellites used for cooperative communication, which is a subset of the set of visible satellites, denoted as . , K The total number of low-Earth orbit satellites used for cooperative communication. K ≤ M and K It is a positive integer.

3. The method for determining the optimal number of cooperating satellites for multi-low-Earth orbit satellite communication according to claim 2, characterized in that, In S2, the satellite-to-ground wireless channel model for multi-Low Earth orbit satellite cooperative communication, constructed based on the spatial distribution model of the aforementioned low-Earth orbit satellite constellation, includes: Path loss model: In both uplink and downlink, a power-law loss model is used to represent the path loss between the ground user and the first... k The path loss between low-Earth orbit satellites is expressed as: ,(2) in, For the first k The distance from a low-orbit satellite to a ground user, c At the speed of light, f c The carrier frequency of the signal. α The power-law loss factor; Small-scale fading model: The shadowed Ricean fading model is used to characterize the relationship between ground users and the first... k Channel fading between low-Earth orbit satellites, channel gain in satellite-to-ground links The cumulative distribution function is expressed as: ,(3) in, , , Ω、 m , b These are the average power of the line-of-sight component, the Nakagami parameter, and half the average power of the scattering component, respectively. It is the Pochhammer symbol; Channel gain in satellite-to-ground links The probability density function is expressed as: (4)。 4. The method for determining the optimal number of cooperating satellites for multi-low-Earth orbit satellite communication according to claim 3, characterized in that, In S3, based on the spatial 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 are constructed as follows: In multi-Low Earth orbit satellite cooperative communication within a low Earth orbit satellite communication network, a shared... K A pair of orthogonal channels located in the Ka band; Each low-Earth orbit satellite is equipped with a directional antenna whose main lobe beam points to the center of the Earth. Ground users are located within the beam of the directional antenna of each low-Earth orbit satellite and have an omnidirectional antenna that can communicate with each low-Earth orbit satellite. For ground users to the first k The uplink for signal transmission between low-Earth orbit satellites, the first k The signal-to-noise ratio received by a low-Earth orbit satellite is expressed as: ,(5) , In the formula, For ground users' transmission power; For ground users to the first k Antenna gain of a low-Earth orbit satellite; For the first k Noise power of each channel, For from ground users to the first k Channel gain of a low-Earth orbit satellite; For the transmit antenna gain of ground users, For the first k The receiving antenna gain of a low-Earth orbit satellite; For the k The downlink signal transmission from a low-Earth orbit satellite to a ground user results in the following signal-to-noise ratio at the ground user: (6) , In the formula, The launch power for each low-Earth orbit satellite, For the first k Antenna gain from a low-Earth orbit satellite to a ground user For the first k The transmit antenna gain of a low-Earth orbit satellite For the receiving antenna gain of ground users, Indicates from the first k Channel gain from a low-Earth orbit satellite to ground users.

5. The method for determining the optimal number of cooperating satellites for multi-low-Earth orbit satellite communication according to claim 4, characterized in that, In S4, a multi-Low Earth orbit satellite cooperative communication strategy is established in the low Earth orbit satellite communication network based on the signal-to-noise ratio models of the uplink and downlink, including: S41: Ground users send pilot signals to the first low-Earth orbit satellite through the first channel; S42: Signal-to-noise ratio of the pilot signal received by the first low-Earth orbit satellite; S43: Determine whether the measured signal-to-noise ratio exceeds the predefined signal-to-noise ratio threshold. τ If the number of cases exceeds the limit, execute S431-S433; otherwise, execute S44. S431: The first low-Earth orbit satellite sends a feedback pilot signal to ground users on the same channel; S432: Signal-to-noise ratio of the pilot signal in the ground user assessment feedback; S433: Determine whether the signal-to-noise ratio at the ground user location exceeds a predefined signal-to-noise ratio threshold. τ If the number of satellites exceeds the limit, it indicates that the first low-Earth orbit satellite is a qualified low-Earth orbit satellite, and S45 is executed; otherwise, S44 is executed. S44: Switch the first LEO satellite to the second LEO satellite, and repeat the process according to the rules of S41 until... K Once the switching of satellites is complete, the pilot signal transmission process will terminate. S45: Ground users select the eligible low-orbit satellite to transmit message signals.

6. The method for determining the optimal number of cooperating satellites for multi-low-Earth orbit satellite communication according to claim 5, characterized in that, In S5, the established correlation between the signal-to-noise ratio models of the uplink and downlink and key performance indicators includes: The signal-to-noise ratio (SNR) received by both low-Earth orbit satellites and ground users must simultaneously meet a predefined SNR threshold. τ The probability is expressed as passing the first k The end-to-end successful transmission probability of communication between two low-Earth orbit satellites is used to construct the correlation between the signal-to-noise ratio model of the uplink and downlink and the end-to-end successful transmission probability, expressed as: (7) In the formula, and Representing ground users and the first k When communicating with a low-Earth orbit satellite, in the first k The signal-to-noise ratio received by low-Earth orbit satellites and ground users. It is a probability measure; Ground users through the first k The end-to-end latency for communication between two low-Earth orbit satellites includes transmission latency and handover latency, and is expressed as: (8) In the formula, Indicates passing through the first k The uplink latency for end-to-end communication between satellites. Indicates passing through the first k Downlink latency for end-to-end communication between satellites For transmission delay; B Channel bandwidth; This indicates a switch from the first low-Earth orbit satellite to the second. k The cumulative switching delay generated when using low-orbit satellites Let be the switching delay for each switch, and ω is a constant; ω is the length of the data packet.

7. The method for determining the optimal number of cooperating satellites for multi-low-Earth orbit satellite communication according to claim 6, characterized in that, In S6, based on the multi-low-Earth 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 the overall network successful transmission probability and the overall network latency are derived, including: 1) Based on a multi-low-Earth orbit satellite cooperative communication strategy, K The analytical expression for the overall successful transmission probability of a network of low-Earth orbit satellites in cooperative communication is: (9) In the formula, q The failure probability of each low-Earth orbit satellite; To pass the first k The probability of successful end-to-end transmission in communication between low-Earth orbit satellites; 2) Based on a multi-low-Earth orbit satellite cooperative communication strategy, K The analytical expression for the overall network latency of low-Earth orbit satellite cooperative communication is: (10) in, T k Indicates passing through the first k End-to-end latency for communication between low-orbit satellites.

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