Low-orbit multi-satellite collaborative beamforming method and system based on asynchronous interference elimination

Abstract

The present invention relates to the field of wireless communication technology, and is a low-orbit multi-satellite collaborative beamforming method and system based on asynchronous interference elimination. The method includes: establishing a low-orbit satellite multi-satellite multi-beam downlink transmission system; setting a transmission mechanism; estimating the propagation delay between multiple satellites and multiple users, timing advance the desired signal link, and calculating the asynchronous factors corresponding to different interference links; constructing a beamforming optimization model, establishing an asynchronous transmission rate maximization model under the constraints of multi-satellite transmission power, and converting it into a per-user signal-to-interference-noise ratio maximization problem, and solving the beamforming weights under asynchronous transmission based on the minimum mean square error algorithm. The present invention adopts a timing advance mechanism to achieve coherent alignment of multi-satellite transmission signals, and utilizes the time asynchronism caused by the difference in multi-satellite propagation delays to naturally eliminate part of the inter-satellite interference, thereby improving the spectrum efficiency and service quality of the communication system.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a low-orbit multi-satellite collaborative beamforming method and system based on asynchronous interference elimination. Background Art

[0002] The next generation of mobile communication systems will realize the integration of satellite communication systems and ground mobile communication systems to meet the vision of seamless global coverage of mobile broadband services. Among them, the ultra-dense low-orbit satellite constellation is the infrastructure of the future mobile communication network, and the low-orbit satellite network will become an important part of the space-ground integrated network.

[0003] However, due to the dynamic changes in the node topology of low-orbit satellites and a series of problems caused by large-scale space, the deep integration of LEO satellite networks and ground networks requires new planning and deployment designs from the network layer, access layer to the physical layer. Unlike the collaborative transmission of multiple base stations on the ground, the spatial scale of the multi-satellite collaborative transmission mode is extremely large, and the difference in propagation delays from different satellites to different users is much greater than that on the ground. This difference in propagation delay leads to misalignment of signal transmission, and a timing advance mechanism is required to ensure the time slot alignment of user signals. In contrast, interference signals cannot be aligned through any timing method, and the existing multi-beam transmission method is not designed for the asynchrony of interference time, which can easily lead to a decrease in the system's spectrum efficiency performance. Summary of the invention

[0004] In order to overcome the defects of the prior art, the present invention provides a multi-satellite cooperative beamforming method and system based on asynchronous interference elimination, which can realize the time slot alignment of the desired signal and the elimination of asynchronous interference signals through the timing advance mechanism combined with the multi-satellite cooperative beamforming method. The scheme can naturally eliminate part of the inter-satellite interference by utilizing the time asynchronism caused by the multi-satellite propagation delay difference, thereby saving transmission power and improving the spectrum efficiency performance of the multi-satellite cooperative network.

[0005] In a first aspect, an embodiment of the present invention provides a low-orbit multi-satellite collaborative beamforming method based on asynchronous interference elimination, comprising the following steps:

[0006] Establishing a multi-satellite multi-beam cooperative transmission system for low-orbit satellites, wherein satellites in the multi-satellite multi-beam system share channel state information and user data through inter-satellite links;

[0007] The transmission mechanism is set up, and the pulse shaping at the transmitting end and the matched filtering at the receiving end are both root raised cosine filters; coherent cooperative transmission is carried out between multiple satellites to provide signal diversity for users;

[0008] Estimate the propagation delay from different satellites to different users, and set the corresponding timing advance for the desired signal based on the estimated delay;

[0009] According to the estimated propagation delay and filter parameters, the asynchronous factors and user spectrum efficiencies corresponding to different interference links are calculated, wherein the asynchronous factor is the interference power degradation coefficient caused by the deviation between the arrival time of the inter-satellite interference signal and the sampling peak value;

[0010] Construct a beamforming optimization model and establish a spectrum efficiency maximization model under multi-satellite transmission power constraints;

[0011] Transform the beamforming model to transform the spectrum efficiency maximization model under asynchronous interference arrival into the signal-to-interference-to-noise ratio maximization problem for each user, which is equivalent to the mean square error minimization problem.

[0012] Solve the collaborative beamforming weights. Based on the minimum mean square error algorithm, combine the asynchronous factor and the channel state information matrix to calculate the beamforming weights set by each satellite for each user.

[0013] In a second aspect, an embodiment of the present invention provides a low-orbit multi-satellite collaborative beamforming system based on asynchronous interference elimination, comprising the following modules:

[0014] The low-orbit satellite multi-satellite multi-beam system establishment module is used to establish a low-orbit satellite multi-satellite multi-beam system including a satellite cluster composed of adjacent satellites and ground users in the satellite cluster coverage area; and is used to set up a transmission mechanism, with root raised cosine filters used for pulse shaping at the transmitter and matched filtering at the receiver; coherent cooperative transmission is performed between multiple satellites to provide signal diversity for users;

[0015] The timing advance estimation module is used to estimate the propagation delay between multiple satellites and multiple users; set the timing advance of the desired signal to ensure the synchronous arrival of the desired signal; calculate the interference power degradation asynchronous factor caused by the deviation between the arrival time of the inter-satellite interference signal and the sampling peak value;

[0016] A beamforming optimization model building module is used to build a beamforming optimization model and establish a spectrum efficiency maximization model under the condition of multi-satellite transmission power constraints; the transmission power constraint means that the transmission power of each satellite must not exceed a given threshold; the spectrum efficiency is the maximum transmission rate achieved by each satellite user when inter-satellite interference does not arrive at the same time;

[0017] The beamforming weight calculation module is used to solve the beamforming weight. According to the model transformation result of the spectrum efficiency maximization problem, based on the mean square error algorithm, combined with the asynchronous factor and the channel state information matrix, the beamforming weight vector solution set by each satellite for each user is obtained.

[0018] Compared with the prior art, the present invention has the following beneficial effects:

[0019] Most of the existing low-orbit satellite network transmissions use multi-color frequency multiplexing technology or traditional space division multiplexing technology to suppress inter-satellite interference, without considering the asynchronous characteristics of interference arrival in the satellite network, and without making full use of channel resource blocks. The present invention is based on the form of asynchronous interference elimination, and can reduce the interference between different satellites in the ultra-dense low-orbit satellite network by quantitatively calculating the interference power degradation caused by the deviation between the arrival time of the inter-satellite interference signal and the sampling peak value, and further improve the spectrum efficiency by using the inherent delay characteristics of the satellite network, and realize more efficient beam power allocation, thereby improving the overall spectrum efficiency performance of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic flow chart of a low-orbit multi-satellite collaborative beamforming method based on asynchronous interference elimination provided in an embodiment of the present invention;

[0021] Figure 2 It is a structural schematic diagram of a low-orbit satellite multi-satellite multi-beam transmission system established in an embodiment of the present invention;

[0022] Figure 3 This is a schematic diagram comparing the average spectrum efficiency of different users with the traditional MMSE algorithm after adopting the multi-satellite cooperative beamforming method provided by an embodiment of the present invention;

[0023] Figure 4 A schematic diagram showing how the total spectrum efficiency varies with the number of satellites and the number of users after the multi-satellite collaborative beamforming method provided by an embodiment of the present invention is adopted;

[0024] Figure 5 A schematic diagram of average spectrum efficiency of users under different system layouts after adopting the multi-satellite cooperative beamforming method provided by an embodiment of the present invention;

[0025] Figure 6 The figure is a schematic diagram of the total spectrum efficiency of the system when different bandwidths and different array sizes are used after adopting the multi-satellite cooperative beamforming method provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0026] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention; it is obvious that the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0027] It should be noted that the step numbers in the text are only for the convenience of explaining the specific embodiment and do not limit the order in which the steps are executed. The method provided in this embodiment can be executed by a related server, and the following description will be given by taking the edge server as the execution subject as an example.

[0028] Example 1

[0029] like Figure 1 As shown, this embodiment provides a low-orbit multi-satellite collaborative beamforming method based on asynchronous interference elimination, which specifically includes the following steps:

[0030] S1. Establish a multi-satellite multi-beam coherent collaborative transmission system for low-orbit satellites; in the multi-satellite multi-beam system, satellites share channel state information and user data through inter-satellite links.

[0031] In this embodiment, the multi-satellite multi-beam system includes C adjacent LEO satellites and K single-antenna user terminals. The user is located in the service area of ​​the satellites and is provided with services by these satellites. User's subscript collection Each satellite is equipped with a uniform planar array antenna, and the array has and An array element. Indicates the total number of antenna elements.

[0032] like Figure 2 As shown, in this embodiment, the multi-satellite multi-beam system includes three LEO satellites, and the satellite transmitter uses a phased array antenna including 1024 transmitting array elements to provide access for 48 ground satellite users.

[0033] Specifically, in the LEO satellite multi-satellite multi-beam system of this step, the channel vector between the satellite c transmitting antenna and the user k receiving antenna is denoted as h c,k , the beamforming vector set by satellite c for user k is denoted as w c,k , the length of the data packet received by each user is M; represents the transmission symbol of user k, that is, the original signal.

[0034] S2. Set up the transmission mechanism. Root raised cosine filters are used for pulse shaping at the transmitter and matched filtering at the receiver. Phased array antennas are used for coherent collaborative transmission between multiple satellites to provide signal diversity for users. Ground users use omnidirectional antennas for reception.

[0035] In this embodiment, both the pulse shaping at the transmitting end and the matched filtering at the receiving end adopt a root raised cosine filter with a roll-off factor of β, which is expressed as:

[0036]

[0037] Among them, T s is the sampling period of the signal.

[0038] Coherent cooperative transmission is adopted between multiple satellites to provide signal diversity for users. The baseband transmission waveform from satellite c to user k is expressed as:

[0039]

[0040] Where m is the time slot, s k (m) represents the signal of the mth time slot of user k, δ c,k is the timing advance set by satellite c for user k signal transmission; after beamforming weighting, the transmission waveform of satellite c is expressed as:

[0041]

[0042] The ground user uses an omnidirectional antenna for reception, and the receiving waveform of user k is expressed as:

[0043]

[0044] Where n k is the additive Gaussian noise at the receiver, The beamforming vector set by satellite c for user l is denoted as w c,l ;s l (m) represents the signal of the mth time slot of user l; δ c,l is the timing advance set by satellite c for user l signal transmission; τ c,k is the normalized delay.

[0045] S3. Estimate the propagation delays from different satellites to different users, and set corresponding timing advances for the desired signals according to the estimated propagation delays.

[0046] This step estimates the propagation delay and adjusts the timing advance. c,k Set to the estimated propagation delay between satellite c and user k, that is, δ c,k =τ c,k T s , the user end is in nT s After sampling at time instant, the obtained discrete data value is expressed as:

[0047]

[0048] where Δτ c,kl =τ c,k -τ c,l represents the normalized delay difference between satellite c and user k and between satellite c and user l, g(τ)=∫p(t)p(t-τ)dt is the raised cosine pulse function; s k (n) represents the signal of the nth time slot of user k, n k (n) represents the noise of the nth time slot, ik (n) represents the interference of the nth time slot.

[0049] S4. Calculate the asynchronous factors and user spectrum efficiency corresponding to different interference links according to the estimated propagation delay and filter parameters. The asynchronous factor is the interference power degradation coefficient caused by the deviation between the arrival time of the inter-satellite interference signal and the sampling peak value.

[0050] This step calculates the interference link asynchronous factor and user spectrum efficiency. For the interference link, the interference power degradation asynchronous factor caused by the deviation between the arrival time of the intersatellite interference signal and the sampling peak value needs to be calculated based on the estimated propagation delay and the roll-off coefficient of the root raised cosine pulse filter; and then the user spectrum efficiency is further calculated, as described below:

[0051] S41. For user k, the interference coefficient of satellite c1 and satellite c2 to user k when transmitting the signal of user l is calculated as:

[0052] For user k, the interference coefficient is a function of the filter roll-off factor and the propagation delay difference; the function Ξ(τ1, τ2) represents the relationship between the sampling time offset and the obtained sampling signal power, and the expression used can be:

[0053]

[0054] Among them, τ2 and τ1 are the two independent variables of the function Ξ(τ1,τ2).

[0055] S42. According to the interference coefficient of user k calculated in step S41, the spectrum efficiency of user k is calculated as follows:

[0056]

[0057] where γ k is the signal to interference and noise ratio of user k, which is calculated as follows:

[0058]

[0059] In the above formula, represents the transpose of the beamforming vector set by satellite c1 for user k, represents the beamforming vector set by satellite c2 for user k, represents the channel vector between the satellite c1 transmitting antenna and the user k receiving antenna, represents the transpose of the channel vector between the satellite c2 transmitting antenna and the user k receiving antenna, represents the transpose of the beamforming vector set by satellite c1 for user l, represents the beamforming vector set by satellite c2 for user l, represents the noise variance; The coefficient representing the power loss is caused by the misalignment between the arrival time of the interference and the sampling time. The coefficient of the power loss is also called the asynchronous factor.

[0060] S5. Construct a beamforming optimization model and establish a spectrum efficiency maximization model under the constraints of multi-satellite transmission power.

[0061] In this embodiment, the spectrum efficiency maximization model established under the multi-satellite transmission power constraint can be specifically expressed as the following problem:

[0062]

[0063] in is the precoding vector of user k, P c represents the power budget of satellite c.

[0064] S6. Transform the beamforming model to transform the spectrum efficiency maximization model under asynchronous interference arrival into the signal-to-interference-noise ratio maximization problem for each user, which is equivalent to the mean square error minimization problem.

[0065] Among them, the mean square error minimization problem is specifically expressed as:

[0066]

[0067]

[0068] In order to find a closed-form solution, the satellite power constraint is replaced by the user power constraint and problem P2 is transformed into the following problem:

[0069]

[0070]

[0071] y k represents the signal received by user k, s k represents the original signal; P k Represents the threshold for constraining user power. The received power of user k does not exceed the threshold P k .

[0072] S7. Solve the collaborative beamforming weights. Based on the minimum mean square error algorithm, combine the asynchronous factor and the channel state information matrix to calculate the beamforming weights set by each satellite for each user.

[0073] In this embodiment, the Lagrange multiplier method is used to solve the Lagrange function and the corresponding first-order derivative function of the optimization problem of the user power constraint, and then the first-order derivative function is set to zero to obtain the beamforming vector. The specific decomposition is as follows:

[0074] S71. Solve the Lagrangian function and its derivatives. Use e k Representation problem The objective function in Further expanded to:

[0075]

[0076] Among them, i k represents the interference received by user k, n k represents the noise received by user k.

[0077] To solve the problem in closed form Minimize the following Lagrangian objective function:

[0078]

[0079] where v k is the Lagrangian multiplier for the power constraint of user k, and the derivative of the Lagrangian function is:

[0080]

[0081] S72, solving the beamforming vector. Let the first-order derivative of the above Lagrangian function be equal to 0 and express it in matrix form, then:

[0082] H k w k +υ k w k =h k

[0083] where w k represents the beamforming vector set by all the satellites for user k; h k represents the aggregate channel vector of user k, H k is the second-order statistical channel state information matrix of user k, which is used to characterize the channel covariance and spatial signal asynchrony. The expression of this matrix can be:

[0084]

[0085] And there is Therefore, the beamforming vector of user k is obtained as:

[0086] w k =(H k +υk I) -1 h k

[0087] Where I is the identity matrix and the optimal Lagrange multiplier is

[0088] In this embodiment, the system is mathematically modeled and simulated using the Matlab 2023a satellite communication toolbox, and the proposed forming method is numerically simulated based on the NTN-CDL channel model defined in the 3GPP standard. Figure 3-Figure 6 shown.

[0089] from Figure 3 It can be seen from the comparison that the spectrum efficiency of the beamforming method proposed in this embodiment is higher than that of the traditional synchronous interference elimination solution, and the performance gap increases with the improvement of the signal-to-noise ratio.

[0090] from Figure 4 It can be seen from the comparison that the total spectrum efficiency of the system increases almost exponentially with the increase in the number of satellites. For the dual-satellite system, the shaping method proposed in this embodiment improves 17.64% when there are 36 users and 23.8% when there are 48 users compared to the traditional synchronous interference elimination scheme.

[0091] from Figure 5 It can be seen from the comparison that with the increase in the number of users, the average spectrum efficiency of users decreases almost linearly, and the increase in the number of users and satellites will cause further interference.

[0092] from Figure 6 It can be seen from the comparison that the system spectrum efficiency performance increases with the increase in the number of antenna elements. Since the traditional synchronous interference elimination scheme cannot accurately eliminate interference, the performance is poor at a smaller array scale; in contrast, this embodiment uses time asynchrony to eliminate part of the interference and improve the spectrum efficiency performance.

[0093] Example 2

[0094] This embodiment is based on the same inventive concept as Embodiment 1, and provides a low-orbit multi-satellite cooperative beamforming system based on asynchronous interference elimination, including:

[0095] The low-orbit satellite multi-satellite multi-beam system establishment module is used to establish a low-orbit satellite multi-satellite multi-beam system including a satellite cluster composed of adjacent satellites and ground users in the satellite cluster coverage area; and is used to set up a transmission mechanism, with root raised cosine filters used for pulse shaping at the transmitter and matched filtering at the receiver; coherent cooperative transmission is performed between multiple satellites to provide signal diversity for users;

[0096] The timing advance estimation module is used to estimate the propagation delay between multiple satellites and multiple users; set the timing advance of the desired signal to ensure the synchronous arrival of the desired signal; calculate the interference power degradation asynchronous factor caused by the deviation between the arrival time of the inter-satellite interference signal and the sampling peak value;

[0097] A beamforming optimization model building module is used to build a beamforming optimization model and establish a spectrum efficiency maximization model under the condition of multi-satellite transmission power constraints; the transmission power constraint means that the transmission power of each satellite must not exceed a given threshold; the spectrum efficiency is the maximum transmission rate achieved by each satellite user when inter-satellite interference does not arrive at the same time;

[0098] The beamforming weight calculation module is used to solve the beamforming weight. According to the model transformation result of the spectrum efficiency maximization problem, based on the mean square error algorithm, combined with the asynchronous factor and the channel state information matrix, the beamforming weight vector solution set by each satellite for each user is obtained.

[0099] In this embodiment, when calculating the asynchronous factors and user spectrum efficiencies corresponding to different interference links, the asynchronous factor of interference power degradation caused by the deviation between the arrival time of the inter-satellite interference signal and the sampling peak value is first calculated based on the estimated propagation delay and the roll-off coefficient of the root raised cosine pulse filter, and then the user spectrum efficiency is further calculated.

[0100] In addition, the problem of solving the spectrum efficiency maximization model under asynchronous arrival of interference is transformed into the problem of maximizing the signal-to-interference-and-noise ratio of each user, which is equivalent to the problem of minimizing the mean square error; further, the satellite power constraint is replaced by the user power constraint to obtain a closed-form solution.

[0101] The modules of this embodiment are respectively used to implement the steps of Embodiment 1. Please refer to Embodiment 1 for the detailed implementation process, which will not be described in detail.

[0102] It can be seen from the detailed technical solutions described in the above embodiments that the technical solutions of the present invention have the following beneficial effects:

[0103] The low-orbit multi-satellite collaborative beamforming scheme based on asynchronous interference elimination of the present invention can reduce the interference between different satellites in the ultra-dense low-orbit satellite network, and further improve the spectrum efficiency by utilizing the inherent delay characteristics of the satellite network. Most of the existing low-orbit satellite network transmissions use multi-color frequency multiplexing technology or traditional space division multiplexing technology to suppress inter-satellite interference, and do not consider the asynchronous characteristics of interference arrival in the satellite network, and do not fully utilize the channel resource blocks. This form based on asynchronous interference elimination achieves more efficient beam power allocation by quantitatively calculating the interference power degradation caused by the deviation between the arrival time of the inter-satellite interference signal and the sampling peak, thereby improving the overall spectrum efficiency performance of the system.

[0104] The above is a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements and modifications without departing from the principle of the present invention. These improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A low-orbit multi-satellite collaborative beamforming method based on asynchronous interference elimination, characterized in that: The following steps are involved: Establishing a multi-satellite multi-beam cooperative transmission system for low-orbit satellites, wherein satellites in the multi-satellite multi-beam system share channel state information and user data through inter-satellite links; The transmission mechanism is set up, and the pulse shaping at the transmitting end and the matched filtering at the receiving end are both root raised cosine filters; coherent cooperative transmission is carried out between multiple satellites to provide signal diversity for users; Estimate the propagation delay from different satellites to different users, and set the corresponding timing advance for the desired signal based on the estimated delay; According to the estimated propagation delay and filter parameters, the asynchronous factors and user spectrum efficiencies corresponding to different interference links are calculated, wherein the asynchronous factor is the interference power degradation coefficient caused by the deviation between the arrival time of the inter-satellite interference signal and the sampling peak value; Construct a beamforming optimization model and establish a spectrum efficiency maximization model under multi-satellite transmission power constraints; Transform the beamforming model to transform the spectrum efficiency maximization model under asynchronous interference arrival into the signal-to-interference-to-noise ratio maximization problem for each user, which is equivalent to the mean square error minimization problem. Solve the collaborative beamforming weights. Based on the minimum mean square error algorithm, combine the asynchronous factor and the channel state information matrix to calculate the beamforming weights set by each satellite for each user.

2. The multi-satellite collaborative beamforming method according to claim 1, wherein: Multiple satellites provide signal diversity for users, where the baseband transmission waveform from satellite c to user k is expressed as: Where m is the time slot, s k (m) represents the signal of the mth time slot of user k, δ c，k is the timing advance set by satellite c for user k’s signal transmission, T s is the sampling period of the signal, and p represents a root raised cosine filter.

3. The multi-satellite collaborative beamforming method according to claim 2, wherein: The timing advance δ c，k Set to the estimated propagation delay between satellite c and user k, that is, δ c，k =τ c，k T s , τ c，k is the normalized delay; The user end is in nT s After sampling at time instant, the obtained discrete data value is expressed as: in represents the transpose of the channel vector between the satellite c transmitting antenna and the user k receiving antenna; w c，k represents the beamforming vector set by satellite c for user k; s k (n) represents the signal of the nth time slot of user k; q c，l represents the beamforming vector set by satellite c for user l; s l (m) represents the signal of the mth time slot of user l; Δτ c，kl =τ c，k -τ c，l represents the normalized delay difference from satellite c to user k and user l, g(τ) = ∫ p (t) p (t-τ)dt is the raised cosine pulse function; n k (n) represents the noise of the nth time slot, i k (n) represents the interference of the nth time slot.

4. The multi-satellite collaborative beamforming method according to claim 1, wherein: When calculating the asynchronous factors and user spectrum efficiency corresponding to different interference links, the asynchronous factor of interference power degradation caused by the deviation between the arrival time of the intersatellite interference signal and the sampling peak value is first calculated based on the estimated propagation delay and the roll-off coefficient of the root raised cosine pulse filter, and then the user spectrum efficiency is further calculated; The steps to calculate user spectrum efficiency include: The interference coefficient of satellite c1 and satellite c2 to user k when transmitting the signal of user l is calculated by the function that characterizes the relationship between the sampling time offset and the obtained sampling signal power. According to the calculated interference coefficient for user k, the spectrum efficiency of user k is calculated as: where γ k is the signal to interference and noise ratio of user k, which is calculated as follows: represents the transpose of the beamforming vector set by satellite c1 for user k, represents the beamforming vector set by satellite c2 for user k, represents the channel vector between the satellite c1 transmitting antenna and the user k receiving antenna, represents the transpose of the channel vector between the satellite c2 transmitting antenna and the user k receiving antenna, represents the transpose of the beamforming vector set by satellite c1 for user l, represents the beamforming vector set by satellite c2 for user l, represents the noise variance; A coefficient representing the power loss caused by the misalignment between the arrival time of interference and the sampling time.

5. The multi-satellite collaborative beamforming method according to claim 4, wherein: The interference coefficient is a function of the filter roll-off coefficient and the propagation delay difference; the normalized delay difference from satellite c to user k and user l is expressed as: Dt c，kl =t c，k -t c，l where τ c，k For satellite c to user k about sampling period T s The normalized propagation delay, τ c，l For the satellite c to user l about the sampling period T s The normalized propagation delay of .

6. The multi-satellite collaborative beamforming method according to claim 1, wherein: The problem of solving the spectrum efficiency maximization model under asynchronous arrival of interference is transformed into the problem of maximizing the signal-to-interference-and-noise ratio of each user, which is equivalent to the problem of minimizing the mean square error. The satellite power constraint is further replaced by the user power constraint to obtain a closed-form solution.

7. The multi-satellite collaborative beamforming method according to claim 6, wherein: The closed-form solution is obtained by using the Lagrange multiplier method to obtain the Lagrange function and the corresponding first-order derivative function of the optimization problem of the user power constraint, and then setting the first-order derivative function to zero to obtain the beamforming vector.

8. The multi-satellite collaborative beamforming method according to claim 7, wherein: The closed-form solution consists of the following steps: Solve the Lagrangian function and its derivatives; use e k represents the objective function of the user power constraint optimization problem, Further expanded to: where i k represents the interference received by user k, n k represents the noise received by user k; Minimize the following Lagrangian objective function: where υ k is the Lagrange multiplier for the power constraint of user k, P k Indicates the threshold for constraining user power; Derivative the Lagrangian function to obtain the first-order derivative of the Lagrangian function; Solve the beamforming vector, set the first-order derivative of the Lagrangian function equal to 0, and express it in matrix form: H k w k +υ k w k =h k where w k represents the beamforming vector set by all the satellites for user k; h k represents the aggregate channel vector of user k, H k is the second-order statistical channel state information matrix of user k, which is used to characterize the channel covariance and spatial signal asynchrony; The beamforming vector of user k is obtained as: w k =(H k +υ k I) -1 h k Where I is the identity matrix and the optimal Lagrange multiplier is 9. A low-orbit multi-satellite collaborative beamforming system based on asynchronous interference elimination, characterized in that: Includes the following modules: The low-orbit satellite multi-satellite multi-beam system establishment module is used to establish a low-orbit satellite multi-satellite multi-beam system including a satellite cluster composed of adjacent satellites and ground users in the satellite cluster coverage area; and is used to set up the transmission mechanism, and the pulse shaping at the transmitter and the matched filtering at the receiver both use root raised cosine filters; Coherent collaborative transmission between multiple satellites provides signal diversity for users; The timing advance estimation module is used to estimate the propagation delay between multiple satellites and multiple users; set the timing advance of the expected signal to ensure that the expected signal arrives synchronously; Calculate the interference power degradation asynchronous factor caused by the deviation between the arrival time of the inter-satellite interference signal and the sampling peak value; A beamforming optimization model building module is used to build a beamforming optimization model and establish a spectrum efficiency maximization model under the condition of multi-satellite transmission power constraints; the transmission power constraint means that the transmission power of each satellite must not exceed a given threshold; the spectrum efficiency is the maximum transmission rate achieved by each satellite user when inter-satellite interference does not arrive at the same time; The beamforming weight calculation module is used to solve the beamforming weight. According to the model transformation result of the spectrum efficiency maximization problem, based on the mean square error algorithm, combined with the asynchronous factor and the channel state information matrix, the beamforming weight vector solution set by each satellite for each user is obtained.

10. The multi-satellite collaborative beamforming system according to claim 9, characterized in that: When calculating the asynchronous factors and user spectrum efficiency corresponding to different interference links, the asynchronous factor of interference power degradation caused by the deviation between the arrival time of the intersatellite interference signal and the sampling peak value is first calculated based on the estimated propagation delay and the roll-off coefficient of the root raised cosine pulse filter, and then the user spectrum efficiency is further calculated; The problem of solving the spectrum efficiency maximization model under asynchronous arrival of interference is transformed into the problem of maximizing the signal-to-interference-and-noise ratio of each user, which is equivalent to the problem of minimizing the mean square error. The satellite power constraint is further replaced by the user power constraint to obtain a closed-form solution.

Images