Low earth orbit satellite multi-group multicast beam forming method for realizing user full coverage

Abstract

The invention particularly relates to a low earth orbit satellite multi-group multicast beam forming method for realizing user full coverage. The method comprises the following steps: establishing an LEO satellite communication downlink propagation model under a planar antenna array structure; establishing a receiving signal model of the ground user terminal; deducing a transmission rate which can be realized by each multicast group in a multi-group multicast scene; establishing an optimization problem of multi-group multicast beam forming under the guarantee of the UTs coverage rate; uTs grouping is carried out on the ground based on channel correlation, each beam center is determined based on UTs position distribution and beam capacity, and UTs grouping is further adjusted; convex difference planning problem conversion and convex-concave process-based optimization problem solving are carried out. The beam radius is adjusted by introducing the beam area factor, the matching degree of the resource of each beam and the actual demand of the ground user is improved, and the utilization rate of the beam resource is improved.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication, and particularly to a method for multi-group multicast beamforming of low-orbit satellites for achieving full user coverage. Background Art

[0002] The rapid development of Low Earth Orbit (LEO) satellite networks provides a more efficient solution for global communication. Especially in the application of multi-beam antenna technology, it greatly improves the coverage ability and resource utilization rate of satellite systems. Currently, in LEO satellite communication systems, the traditional single-beam coverage method can no longer meet the growing user needs, especially when facing complex ground user distributions and changing communication environments. For this reason, multi-beam technology has emerged. It configures an antenna array at the satellite end and uses multiple beams to cover different ground areas simultaneously, optimizing the use of spectrum resources.

[0003] Currently, most studies assume that the coverage radius of each beam is the same, which makes the beamforming design relatively simple, but ignores the diversity of ground user distributions and the differences in beam coverage requirements in different regions. Therefore, existing solutions cannot fully optimize the utilization rate of beams and the throughput of the system.

[0004] In addition, existing multi-beam LEO satellite communication systems use time-division multiplexing-based user grouping. For example, considering grouping users according to geographical location in each time slot, and jointly optimizing user grouping and beam width through a heuristic iterative algorithm to maximize the average transmission rate of all groups within the entire time slot. Or minimizing interference by scheduling users with low channel correlation in each time slot. Or considering serving some users selected from known user groups in each time slot, and proposing a sum-rate maximization user grouping algorithm in combination with zero-forcing beamforming. Although the method of serving each group using time-division multiplexing can avoid interference between beams, it does not fully utilize beam resources and can only serve some users within a certain time slot.

[0005] It should be noted that the information disclosed in the above background art section is only used to enhance the understanding of the background of the present invention, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0006] The present invention provides a method for multi-group multicast beamforming of low-orbit satellites for achieving full user coverage, which is used to solve the following problems of the prior art:

[0007] 1. The assumption that the beam coverage radius is the same does not meet the actual requirements: Existing technologies usually assume that the coverage radius of all beams is the same. However, the distribution of ground users is usually non-uniform, and the requirements for beam coverage in dense areas and sparse areas are different. This assumption leads to the unreasonable allocation of beam resources according to the actual needs.

[0008] 2. The user grouping efficiency and beam resource utilization rate are relatively low: Existing technical solutions use time-division multiplexing to serve each group. Although this method can avoid interference between beams, only some users can be served in a certain time slot, and all ground users cannot be served simultaneously, without making full use of beam resources. Especially in the case of tight beam resources, it may affect the overall communication performance.

[0009] Other features and advantages of the present invention will become apparent from the following detailed description or be learned in part through the practice of the present invention.

[0010] According to a first aspect of the present invention, there is provided a low-earth orbit satellite multi-group multicast beamforming method for achieving full user coverage, and the method includes:

[0011] Step 1: Establish a propagation model for the LEO satellite communication downlink in a planar antenna array structure;

[0012] Step 2: Establish a received signal model for ground user terminals;

[0013] Step 3: Deduce the achievable transmission rate of each multicast group in a multi-group multicast scenario according to the received signal model of ground user terminals;

[0014] Step 4: Establish an optimization problem for multi-group multicast beamforming under the guarantee of user coverage;

[0015] Step 5: Group UTs on the ground based on channel correlation, determine the center of each beam based on the UTs position distribution and beam capacity, and further adjust the UTs grouping;

[0016] Step 6: Transform the convex difference programming problem and solve the optimization problem based on the concave-convex process.

[0017] In some exemplary embodiments, the LEO satellite communication downlink propagation model is specifically:

[0018]

[0019] In the formula, C L is the free space loss, P n is the received end noise power, G R is the ground terminal receiving antenna gain, G s (α) is the satellite antenna gain, ξ nLet \(R\) be the rain attenuation, \(v(\varphi,\theta)\) be the response vector generated by the UPA antenna equipped on the satellite, and \(h\) be the geometric-based three-dimensional downlink channel vector between the LEO satellite and the ground UTs.

[0020] In some exemplary embodiments, the received signal model of the ground user terminal is specifically:

[0021]

[0022] where represents the channel vector from the LEO satellite to the \(l\)th UT in the \(m\)th multicast group; \(f\) m (t) is the Doppler shift caused by the movement of the LEO satellite; more specifically, the first term in the formula represents the desired received signal of the UT, the second term is the inter-group interference caused by the transmission of signals from other multicast groups, and \(n\) m,l (t) is the circularly symmetric complex Gaussian white noise with mean 0 and variance \(N_0\) for the \(i\)th user in the multicast group \(m\), that is \(y\) m,l (t) is the received signal of the \(l\)th UT in the \(m\)th multicast group at time \(t\), is the multi-beam weight, is the transmitted signal.

[0023] In some exemplary embodiments, the step 3 is specifically:

[0024] According to the UTs received signal model described in step 2, the received signal-to-interference-plus-noise ratio \(\gamma\) of the \(l\)th UT in the \(m\)th multicast group m,l is:

[0025]

[0026] Therefore, the achievable transmission rate of the \(l\)th UT in the \(m\)th multicast group is

[0027] In the multi-group multicast transmission scenario, all UTs within the same multicast group receive the same signal. Therefore, the UT with the lowest rate within this multicast group determines the achievable transmission rate of the group, that is

[0028]

[0029] The UPA equipped on the LEO satellite can generate multiple beams to cover different ground areas. In the same area, that is, all UTs within the same group are served simultaneously; therefore, the geographical location constraint on the UTs in the multicast group can be expressed as

[0030] \(\|\mathbf{u}\) m,l -\mathbf{c}\) m \(\|\leq r\) m

[0031] In the formula, and respectively represent the coordinates of the l-th UT and the m-th beam center in the m-th multicast group; is the coverage radius of the beam corresponding to the m-th multicast group, d is the distance from the satellite to the ground, and k m is the beam area factor.

[0032] In some exemplary embodiments, step 4 is specifically as follows:

[0033] The problem of maximizing the system sum rate under the UTs full coverage constraint is described as

[0034]

[0035] In the formula, η m is the weight factor, which is determined by the number of UTs simultaneously served in multicast group m; C1 is the position constraint of UTs in all multicast groups; C2 and C3 are the grouping constraints of all UTs; C4 is the QoS requirement for maintaining the link connection of UTs within the multicast group, where R0 is the minimum transmission rate requirement for each multicast group; C5 is the total satellite load power constraint.

[0036] In some exemplary embodiments, step 5 is specifically as follows:

[0037] In the UTs grouping process, first, select the user with the maximum channel gain among all UTs as the first candidate grouping center, that is

[0038]

[0039] Then, calculate the channel correlation between the candidate grouping center and the remaining users; select the UTs with weak correlation less than the predetermined threshold as the candidate grouping centers v′ for other groups; the set Λ of candidate grouping centers for other groups can be obtained by the following formula:

[0040]

[0041] When the number of UTs in the set Λ is less than M - 1, that is, when the candidate grouping centers selected according to the initial threshold are insufficient, update the threshold by the following formula, that is:

[0042]

[0043] In the formula, is the updated threshold; after obtaining all candidate grouping centers Ω = Λ ∪ v1, divide the remaining UTs into their respective groups according to the channel correlation coefficient, that is:

[0044]

[0045] In the beam center determination step, the maximum distance between any two UTs in the m-th multicast group can be expressed as

[0046]

[0047] If it indicates that the beam can cover all UTs in the group. At this time, the distribution center of all UTs in the group is used as the center of the beam, that is:

[0048]

[0049] Otherwise, it is considered that the number of users in the multicast group exceeds the beam capacity, and the group is invalid. At this time, the threshold and the beam region factor k m are adjusted and the UTs are regrouped until all beam centers are determined.

[0050] In some exemplary embodiments, step 6 is specifically as follows:

[0051] Based on the user grouping and beam center results, beamforming design is performed for each multicast group. First, by introducing slack variables for each group, the original problem is transformed into a DC programming problem; then, based on the iterative algorithm of CPP, a feasible solution to the optimization problem in step 4 is obtained while ensuring convergence.

[0052] According to the second aspect of the present invention, there is provided a storage medium having stored thereon a computer program, which when executed by a processor implements the method for low-earth orbit satellite multi-group multicast beamforming for achieving user full coverage described in the first aspect above.

[0053] According to the third aspect of the present invention, there is provided a computer program product having stored thereon a computer program, which when executed by a processor implements the method for low-earth orbit satellite multi-group multicast beamforming for achieving user full coverage described in the first aspect above.

[0054] According to the fourth aspect of the present invention, there is provided an electronic device, including:

[0055] a processor; and

[0056] a memory for storing executable instructions of the processor;

[0057] wherein the processor is configured to implement the method for low-earth orbit satellite multi-group multicast beamforming for achieving user full coverage described in the first aspect above when executing the executable instructions.

[0058] The method for multi - group multicast beamforming of low - earth - orbit satellites to achieve full user coverage provided by the embodiments of the present invention has the following beneficial effects compared with the prior art:

[0059] 1. Differentiated beam radius design: The prior art assumes that the coverage radii of all beams are the same and cannot be optimized according to the user requirements in different regions, resulting in low resource utilization efficiency. According to the distribution of ground users and the user requirements in different ground regions, the present invention adjusts the coverage radius of the beam by introducing a beam region factor, which is more suitable for actual applications, can meet the communication requirements in different scenarios, improves the utilization rate of beam resources, and enhances the actual performance of low - earth - orbit satellite communication.

[0060] 2. Beam capacity and user grouping optimization: The traditional user grouping scheme fails to consider the differences in beam capacity, resulting in waste of some beam resources. The present invention reasonably groups ground users based on the beam radius adjusted according to the beam capacity, ensuring that each beam can serve an appropriate number of user groups, avoiding the waste or under - utilization of beam resources in the traditional method.

[0061] 3. Two - stage multi - group multicast beamforming strategy: The prior art mainly uses a time - division multiplexing service method to avoid interference between beams, but this method fails to fully utilize beam resources in actual applications and can only serve some users in a certain time slot. Through the first stage of "user grouping and beam center determination" and the second stage of "beamforming design", the present invention ensures that, on the premise of mitigating interference between beams and achieving full coverage of ground users, beamforming design is carried out for multiple beams, achieving full coverage of users by multiple beams, maximizing the throughput and resource utilization rate of the entire system, and avoiding waste of beam resources.

[0062] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present invention. Brief Description of the Drawings

[0063] The drawings here are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present invention, and are used together with the specification to explain the principles of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings without creative efforts based on these drawings.

[0064] Figure 1 It is a multi - user multi - beam satellite forward - link communication network system;

[0065] Figure 2 It is a schematic diagram of the low - earth - orbit satellite multi - group multicast beamforming process under the guarantee of user coverage rate of the exemplary embodiment of the present invention. Detailed Implementation Modes

[0066] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The features, structures, or characteristics described may be combined in any suitable manner in one or more embodiments.

[0067] In addition, the accompanying drawings are only schematic illustrations of the present invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus repeated descriptions thereof will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in the form of software, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0068] The present invention is applicable to LEO satellites equipped with a Uniform Planar Array (UPA). In a multi-user multi-beam satellite forward link communication network system as shown in Figure 1 the UPA of the LEO satellite consists of N = N x N y antennas, with N x and N y antennas deployed on the x-axis and y-axis respectively. The gateway station sends information data to the satellite through a high-capacity feedback link, and uses this information data to obtain the channel state information (CSI) between the satellite and the ground user terminals (UTs), and assumes that the feedback link between the gateway and the satellite is ideal. To improve the spectral efficiency and throughput of the multi-beam LEO satellite communication system, the present invention considers the full frequency reuse (FFR) transmission strategy for all beams. Define to represent the index set of all UTs, and the UTs are randomly distributed within the satellite coverage area. The UPA at the satellite end uses the CSI to generate N s beams to serve K fixed single-antenna ground UTs. Define to represent the index set of all multicast groups, and consider that one beam serves one multicast group, i.e., M = N s . Define the binary variable x k,m to describe the UT grouping result. If the k-th UT belongs to group m, then x k,m = 1, otherwise x k,m= 0. Denote the set of UTs included in the m-th group as In addition, each UT belongs to only one group, which can be expressed as:

[0069]

[0070] The present invention aims to achieve low-earth-orbit satellite multi-group multicast beamforming under user coverage guarantee, define that each beam has a different coverage radius, so that the beam capacity can better match the actual ground user distribution and user requirements, and improve the utilization rate of beam resources; use multiple spot beams to fully cover ground users, so that all UTs can receive signals sent by the satellite end within a short time interval, and improve the service efficiency of multi-beams.

[0071] Its process is as Figure 2 shown, and each step will be elaborated in detail below.

[0072] Step 1: Establish a propagation model for the downlink of LEO satellite communication under the UPA structure.

[0073] Considering the line-of-sight (LoS) link model between the satellite and the ground receiving end, the three-dimensional downlink channel vector based on geometry between the LEO satellite and the ground UTs can be expressed as:

[0074]

[0075] In the formula, C L is the free space loss, P n is the receiving end noise power, G R is the receiving antenna gain of the ground terminal, G s (α) is the satellite antenna gain, ξ n is the rain fade, and v(φ,θ) is the response vector generated by the UPA antenna equipped on the satellite. These components will be described in detail below:

[0076] (1) Free space loss Since the UTs are distributed at different positions in the satellite coverage area, the distances between each UT and the satellite are different. The free space loss of the LEO satellite communication downlink can be expressed as

[0077]

[0078] In the formula, c is the speed of light; f represents the carrier frequency; represents the distance between the satellite and the ground receiving device; d u represents the distance between the ground receiving device and the center point of the satellite coverage area; d h is the operating orbit altitude of the LEO satellite.

[0079] (2) Receiver noise power The received noise power of the ground terminal user can be expressed as

[0080] P n = κBT(4)

[0081] where κ is the Boltzmann constant; B represents the downlink bandwidth; T represents the noise temperature at the receiving terminal.

[0082] (3) Satellite antenna gain The gain of the on-board transmitting antenna depends on the radiation pattern of the beam and the position of the ground terminal user. The gain of the radiation pattern of the LEO satellite antenna can be expressed as

[0083]

[0084] where G max and respectively represent the maximum antenna gain at the satellite end and the 3dB angle; α is the angle between the line-of-sight axis of the beam and the direction of the ground terminal; L s is the intersection point where the main beam and the near sidelobe mask are lower than the peak gain; L F represents the far sidelobe value.

[0085] (4) Rain fade In a satellite communication system, rain fade can be regarded as a slow fading process. It is assumed that the rain fade of the ground receiving terminals within the multicast group served by the same beam is the same. The power gain of rain fade in dB can be expressed as ξ dB = 20log 10 (ξ n ), and ξ dB satisfies a lognormal distribution with a mean of μ and a standard deviation of σ 2 , that is

[0086] (5) UPA antenna response vector Define The UPA antenna response vector can be expressed as:

[0087]

[0088] where φ and θ are the azimuth angle and elevation angle formed by the signal and the x-axis and z-axis respectively. As shown in the network model in Figure 1 ,

[0089] Then, the antenna response vector with respect to the x-axis or y-axis can be expressed as:

[0090]

[0091] Where λ is the wavelength of the transmission signal; d represents the spacing between any adjacent antenna units of the UPA. Generally, the spacing between adjacent antennas is half a wavelength, that is, d = λ / 2. Combining formula (6) and formula (7), the final antenna response vector can be obtained.

[0092] Step 2: Establish a receiving signal model for the ground user terminal.

[0093] Let x m (t) is the multicast group of the downlink at time t The original transmission signal with unit power in is The signal relayed by the satellite can be expressed as:

[0094]

[0095] In the formula, is the beamforming vector designed for the mth multicast group.

[0096] The satellite broadcasts x(t) to all UTs in the multicast group m through the downlink channel. The Doppler shift caused by the satellite motion can be expressed as

[0097] f m (t) = f[v(t) / c]cosψ(t) (9)

[0098] Where f, v(t), c and ψ(t) represent the carrier frequency, the speed of light, the orbital velocity of the satellite, and the angle between the satellite's direction of travel and the line-of-sight axis from the satellite to the ground receiving terminal, respectively.

[0099] Therefore, the received signal of the lth UT in the mth multicast group at time t can be expressed as

[0100]

[0101] In the formula, represents the channel vector from the LEO satellite to the lth UT in the mth multicast group; f m (t) is the Doppler frequency shift caused by the motion of the LEO satellite. More specifically, the first term in the equation represents the desired received signal of the UT, and the second term is the inter-group interference caused by the transmission of other multicast group signals. m,l (t) is a circularly symmetric complex Gaussian white noise with mean 0 and variance N0 for the i-th user in multicast group m, that is, is the multi-beam weight, To transmit the signal.

[0102] In addition, by utilizing the Doppler characteristics of LEO operation and downlink channel propagation, Doppler compensation can be performed on the signals received by ground terminal devices. Therefore, the present invention assumes that the time and frequency of LEO satellites and UTs are completely synchronized. At the same time, considering that the position distribution of UTs on the ground is fixed and the relative positions of LEO satellites and UTs do not change significantly within a short time interval, it is assumed that the physical parameters in the channel model, including free space loss, rain fade, Doppler frequency shift, and array response vector, remain unchanged during this period. For the sake of convenience in representation, the time symbol t is omitted in the subsequent writing.

[0103] Step 3: Deduce the achievable transmission rates of each multicast group in multiple multicast scenarios. According to the UTs received signal model described by formula (10), the received signal-to-interference-plus-noise ratio γ of the l-th UT in the m-th multicast group m,l is:

[0104]

[0105] Therefore, the achievable transmission rate of the l-th UT in the m-th multicast group is

[0106] In a multiple multicast transmission scenario, all UTs within the same multicast group receive the same signal. Therefore, the UT with the lowest rate within this multicast group determines the achievable transmission rate of the group, that is,

[0107]

[0108] The UPA equipped on the LEO satellite can generate multiple beams to cover different ground areas. In the same area, that is, all UTs within the same group are served simultaneously. Therefore, the geographical location constraint of UTs in the multicast group can be expressed as

[0109] ||u m,l -c m ||≤r m (13)

[0110] In the formula, and represent the coordinates of the l-th UT and the center of the m-th beam in the m-th multicast group respectively; is the coverage radius of the beam corresponding to the m-th multicast group, d is the distance from the satellite to the ground, and k m is the beam area factor, which can be adjusted according to different regional conditions. For example, the radius of the beam can be optimized according to the density of ground users or a specific area covered by the satellite, so as to realize the differential design of beam radii in different regions.

[0111] Step 4: Establish the optimization problem of multi-group multicast beamforming under the guarantee of UTs coverage. The present invention aims to achieve full coverage of ground UTs using multiple point beams and design beamformers for each multicast group to maximize the sum rate of the entire system. Therefore, the problem of maximizing the system sum rate under the UTs full coverage constraint can be described as

[0112]

[0113] where η m is the weight factor, which is determined by the number of UTs simultaneously served in multicast group m; C1 is the location constraint of UTs in all multicast groups; C2 and C3 are the grouping constraints of all UTs; C4 is the QoS requirement to maintain the link connection of UTs within the multicast group, where R0 is the minimum transmission rate requirement of each multicast group; C5 is the total power constraint of the satellite load.

[0114] For the UPA antenna equipped on the LEO satellite, the beamforming design determines the coverage of the beam to the ground area, and the beamforming design depends on the grouping result of ground UTs. Therefore, the present invention proposes a two-stage multi-group multicast beamforming method. In the first stage, the ground UTs are grouped, and the center positions of each beam are determined to ensure full coverage of the UTs. In the second stage, the beamforming design of each multicast group is carried out according to the grouping result.

[0115] Step 5: Group the ground UTs based on channel correlation, determine the center of each beam based on the UTs position distribution and beam capacity, and further adjust the UTs grouping. In the UTs grouping link, first, select the user with the maximum channel gain among all UTs as the first candidate grouping center, that is

[0116]

[0117] Then, calculate the channel correlation between the candidate grouping center and the remaining users. Select the UTs with weak correlation less than the predetermined threshold as the candidate grouping centers ν′ of other groups. The set Λ of candidate grouping centers of other groups can be obtained by the following formula:

[0118]

[0119] When the number of UTs in the set Λ is less than M - 1, that is, when the candidate grouping centers selected according to the initial threshold are insufficient, update the threshold by the following formula, that is:

[0120]

[0121] where is the updated threshold. After obtaining all candidate group centers Ω = Λ ∪ ν1, the remaining UTs are partitioned into their respective groups according to the channel correlation coefficient, i.e.:

[0122]

[0123] In the beam center determination step, the maximum distance between any two UTs in the m-th multicast group can be expressed as

[0124]

[0125] If it indicates that the beam can cover all UTs in this group. At this time, the distribution center of all UTs in this group is used as the center of the beam, i.e.:

[0126]

[0127] Otherwise, it is considered that the number of users in this multicast group exceeds the beam capacity, and this group is invalid. At this time, the threshold and the beam region factor k m (equivalent to the beam radius) are adjusted and the UTs are grouped again, that is, starting from formula (16) again until all beam centers are determined.

[0128] Step 6: Transformation of the Difference of Convex (DC) programming problem and solution of the optimization problem based on the Convex Concave Procedure (CCP). According to the user grouping and beam center results, beamforming design is performed for each multicast group. First, by introducing slack variables for each group, the original problem is transformed into a DC programming problem. Then, based on the iterative algorithm of CPP, a feasible solution of the original optimization problem is obtained while ensuring convergence. Specifically,

[0129] Based on the user grouping and beam center results in Step 5, problem (14) can be transformed into

[0130]

[0131] wherein,

[0132] Due to the non-convex objective function and non-convex constraint C6 of problem (21), this problem is still difficult to solve directly. A new slack variable is introduced for each group m and is set. With the help of the variables and γ0, problem (21) is transformed into

[0133]

[0134] Furthermore, the non-convex constraint C7 in problem (22) can be transformed into a DC function. By re-representing the constraint C7, problem (22) can be transformed into a concave objective maximization problem with DC and convex constraints:

[0135]

[0136] wherein, a convex function with respect to W, is a jointly convex function with respect to W and .

[0137] When using the CCP algorithm to solve the above DC programming problem (23), it is first necessary to determine a feasible initial point (FIP): obtain the initial value W 0 of W through a complex Gaussian distribution, and satisfy the constraint condition Based on W 0 and the UTs grouping result calculate the minimum received SINR of the UTs in each multicast group to obtain the initialization value

[0138] Then, based on the CCP algorithm, convexification and optimization are iteratively executed. In each iteration, the non-convex term in the DC programming problem is introduced until convergence. Let be the estimated values of W and at the (t - 1)-th iteration, and be the objective function of problem (23) at the t-th iteration.

[0139] The convexification in the t-th iteration replaces the concave part of the constraint C9 in the problem with its first-order Taylor approximation of the estimated value near , that is

[0140]

[0141] wherein,

[0142]

[0143] The optimization in the t-th iteration uses formula (24) to replace the concave part of the constraint C9 in the problem to obtain a sub-convex problem, and the updated result is obtained by solving this sub-convex problem, that is

[0144]

[0145] In addition, the above-mentioned drawings are only schematic illustrations of the processes included in the method according to the exemplary embodiments of the present invention, rather than for limiting purposes. It is easy to understand that the processes shown in the above-mentioned drawings do not indicate or limit the chronological order of these processes. Additionally, it is also easy to understand that these processes can be executed, for example, synchronously or asynchronously in multiple modules.

[0146] Other embodiments of the present invention will be readily apparent to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the present invention and include known common general knowledge or conventional technical means in the technical field not disclosed by the present invention. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the present invention are pointed out by the claims.

[0147] It should be understood that the present invention is not limited to the exact structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present invention is only defined by the appended claims.

Claims

1. A method for multi - group multicast beamforming of low - earth orbit satellites to achieve full user coverage, characterized in that, The method includes: Step 1, establish a propagation model for the LEO satellite communication downlink in a planar antenna array structure; Step 2, establish a received signal model for the ground user terminal; Step 3, derive the achievable transmission rates of each multicast group in multiple multicast scenarios according to the received signal model of the ground user terminal; Step 4, establish an optimization problem for multi-group multicast beamforming under the guarantee of user coverage; Step 5, group the UTs on the ground based on channel correlation, determine the center of each beam based on the position distribution and beam capacity of the UTs, and further adjust the UT grouping; Step 6, transform the convex difference programming problem and solve the optimization problem based on the concave-convex procedure.

2. The method according to claim 1, wherein The LEO satellite communication downlink propagation model is specifically: Where C L is the free space loss, P n is the received - end noise power, G R is the receiving - antenna gain of the ground terminal, G s (α) is the satellite - antenna gain, ξ n is the rain fade, v(φ,θ) is the response vector generated by the UPA antenna equipped on the satellite, and h is the geometric - based three - dimensional downlink channel vector between the LEO satellite and the ground UTs.

3. The method according to claim 2, characterized in that The received signal model of the ground user terminal is specifically: wherein, represents the channel vector from the LEO satellite to the l-th UT in the m-th multicast group; f m (t) is the Doppler frequency shift caused by the movement of the LEO satellite; more specifically, the first term in the formula represents the desired received signal of the UT, the second term is the inter-group interference caused by the transmission of signals in other multicast groups, and n m,l (t) is the circularly symmetric complex Gaussian white noise with a mean of 0 and a variance of N0 for the i-th user in the multicast group m, that is y m,l (t) is the received signal of the l-th UT in the m-th multicast group at time t, w l is the multi-beam weight, and x m (t), x l (t) are the transmitted signals.

4. The method according to claim 3, wherein The specific content of Step 3 is: According to the received signal model of UTs described in step 2, the received signal-to-interference-plus-noise ratio γ of the l-th UT in the m-th multicast group m,l is as follows: Therefore, the achievable transmission rate of the l-th UT in the m-th multicast group is In multiple multicast transmission scenarios, all UTs in the same multicast group receive the same signal. Therefore, the UT with the lowest rate in this multicast group determines the achievable transmission rate of the group, that is Multiple beams can be generated by the UPA equipped on the LEO satellite to cover different ground areas. In the same area, that is, all UTs in the same group are served simultaneously; therefore, the geographical location constraint of UTs in the multicast group can be expressed as ||u m,l -c m || ≤ r m In the formula, and respectively represent the coordinates of the l-th UT and the m-th beam center in the m-th multicast group; is the coverage radius of the beam corresponding to the m-th multicast group, d is the distance from the satellite to the ground, and k m is the beam area factor.

5. The method according to claim 4, characterized in that The specific content of Step 4 is: The problem of maximizing the system sum rate under the full coverage constraint of UTs is described as s.t.C1: C2: C3: C4: C5: where η m is the weight factor, determined by the number of UTs served simultaneously in multicast group m; C1 is the location constraint of UTs in all multicast groups; C2 and C3 are the grouping constraints of all UTs; C4 is the QoS requirement for maintaining the link connection of UTs within the multicast group, where R0 is the minimum transmission rate requirement for each multicast group; C5 is the total satellite load power constraint.

6. The method according to claim 5, characterized in that The specific content of Step 5 is: In the UT grouping step, first, select the user with the maximum channel gain among all UTs as the first candidate grouping center, that is Then, calculate the channel correlation between the candidate group centers and the remaining users; select the UTs with weak correlation less than a predetermined threshold as the candidate group centers v' of other groups; the set Λ of candidate group centers of other groups can be obtained by the following formula: When the number of UTs in the set Λ is less than M - 1, that is, when the number of candidate grouping centers selected according to the initial threshold is insufficient, update the threshold by the following formula, that is: In the formula, is the updated threshold value; After obtaining all candidate grouping centers Ω = Λ ∪ v1, divide the remaining UTs into their respective groups according to the channel correlation coefficient, that is: In the beam center determination step, the maximum distance between any two UTs in the m-th multicast group can be expressed as If it indicates that the beam can cover all UTs in the group. At this time, the distribution center of all UTs in the group is used as the center of the beam, that is: Otherwise, it is considered that the number of multicast group users exceeds the beam capacity, and the packet is invalid. At this time, the threshold is adjusted and the beam area factor k m and the UTs are grouped again until all beam centers are determined.

7. The method according to claim 6, wherein The specific content of Step 6 is: According to the user grouping and beam center results, perform beamforming design for each multicast group. First, introduce a slack variable for each group to transform the original problem into a DC programming problem; then, based on the iterative algorithm of CPP, obtain a feasible solution to the optimization problem in Step 4 while ensuring convergence.

8. A storage medium, on which a computer program is stored, characterized in that, When the computer program is executed by a processor, it implements the method for multi-group multicast beamforming of LEO satellites to achieve full user coverage as described in any one of claims 1 to 7.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method for multi-group multicast beamforming of LEO satellites to achieve full user coverage as described in any one of claims 1 to 7.

10. An electronic device, characterized in that, It includes: A processor; And A memory for storing executable instructions of the processor; Wherein, the processor is configured to execute the method for multi-group multicast beamforming of LEO satellites to achieve full user coverage as described in any one of claims 1 to 7 by executing the executable instructions.

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