Large-scale MIMO low-orbit satellite-ground communication perception integrated cooperative precoding method

Abstract

The invention discloses a large-scale MIMO (Multiple Input Multiple Output) low-orbit satellite-ground communication sensing integrated cooperative precoding method, which is characterized in that a base station and a low-orbit satellite use the same spectrum resource to cooperatively serve ground communication users and sensing targets. According to the method, a system traversal and rate maximization problem constrained by perceptual performance and limited by energy consumption is established. The method comprises the following steps: firstly, respectively solving precoders which only consider communication performance and perception performance; a communication precoder is solved by using methods such as quadratic transformation and alternate optimization. And the optimal perception precoder can be directly obtained under the condition that only perception performance is considered. And then, a weighting factor is introduced to convert an original problem into weighted Euclidean distance minimization between the precoder and the optimal communication precoder as well as between the precoder and the optimal sensing precoder, so that a final precoder is solved. According to the method, the complexity of solving the optimization problem is remarkably reduced, and the communication performance and the sensing performance are successfully balanced, so that the overall performance of the system is improved.

Description

Technical Field

[0001] The present invention relates to the field of satellite and ground collaborative communication and perception, and in particular to a large-scale MIMO low-orbit satellite-to-ground communication and perception integrated collaborative precoding method that takes into account the realization of communication and perception integration within the system and the use of statistical channel state information by the low-orbit satellite end. Background Art

[0002] In the future, sixth-generation (6G) wireless networks will enable ubiquitous global connectivity. Traditional terrestrial networks are limited by geographical barriers and high deployment costs, preventing them from providing global connectivity. However, low-Earth orbit (LEO) satellite networks, with their global coverage, are an effective solution, significantly expanding network coverage. Furthermore, 6G networks are expected to integrate sensing capabilities, providing diversified sensing services to user terminals. With the rapid development of wireless communication technology, spectrum resources are becoming increasingly scarce. The overlap of sensing and communication bands makes spectrum sharing a key challenge. Against this backdrop, integrated communication and sensing (ISAC) technology has emerged. Massive multiple-input, multiple-output (MIMO) technology provides numerous degrees of freedom in the spatial domain. Its application in ISAC systems can simultaneously improve the performance of both communication and sensing modules. By integrating the complementary advantages of satellite and terrestrial networks, building a satellite-ground integrated network (STN) is considered an effective approach to achieving global coverage. Due to the significant Doppler shift and non-negligible propagation delay in LEO satellite channels, accurately acquiring instantaneous channel state information (CSI) is extremely challenging. In contrast, statistical channel state information (sCSI) has a slowly varying characteristic and is easier to obtain in practice. Low-orbit satellites can design precoders based on sCSI. To improve spectral efficiency, satellite and terrestrial networks share spectrum resources, which can lead to interference between the two networks. Therefore, collaborative precoding design should be considered to mitigate this interference. Furthermore, the overlap of perception and communication frequency bands and the sharing of hardware resources can lead to coupling between communication and perception metrics, and conflicts between communication and perception performance. Therefore, a trade-off between communication and perception performance is necessary in the precoding design of ISAC systems. Summary of the Invention

[0003] Purpose of the invention: In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a large-scale MIMO low-orbit satellite-to-ground communication and perception integrated collaborative precoding method that takes into account the use of satellite channel statistical channel state information and the simultaneous existence of both communication and perception functional requirements in the system. It can achieve a balance between the system communication requirements and perception requirements, and reduce the complexity of implementing this optimization process, making it easier to implement.

[0004] Technical solution: To achieve the purpose of the above invention, the present invention is a large-scale MIMO low-orbit satellite-to-ground communication perception integrated collaborative precoding method, wherein both the low-orbit satellite end and the ground base station end are equipped with a large-scale MIMO antenna array, and the two share the same spectrum resources to improve the system spectrum efficiency; within the coverage of the base station, there are single-antenna base station users who need communication services and targets to be detected; outside the coverage of the base station, the satellite provides communication services for single-antenna satellite users and detects multiple targets at the same time; the signals sent by the low-orbit satellite and the base station are dual-function waveforms, which can be used for both communication and perception; considering that it is difficult for the low-orbit satellite side to obtain accurate instantaneous channel state information of the user, the designed precoding scheme is a collaborative precoding scheme based on the statistical channel state information of the low-orbit satellite and the instantaneous channel state information of the base station; specifically comprising the following steps:

[0005] A system traversal and rate maximization problem subject to perceptual performance constraints and energy consumption limits is established. Based on the statistical channel state information of the satellite and the instantaneous channel state information of the base station, and taking into account the interference of the satellite to the base station users, the satellite and base station precoders are collaboratively designed.

[0006] Decomposing the original problem into a first optimization problem of designing a communication precoder considering only communication indicators and a second optimization problem of designing a perceptual precoder considering only perceptual indicators;

[0007] For the case where only communication indicators are considered, the optimization problem is rewritten using rate approximation and quadratic transformation, and the communication precoder is solved using the alternating optimization method;

[0008] For the case where only perceptual indicators are considered, the optimal perceptual precoder is directly solved;

[0009] The original optimization problem is transformed into a third optimization problem of minimizing the weighted Euclidean distance between the precoder and the optimal communication precoder and the optimal perceptual precoder, and the final precoder is solved using an alternating optimization method.

[0010] As a preferred method, communication users and sensing targets outside the coverage of low-orbit satellite service base stations are introduced, and ground communication users and sensing targets are divided into satellite users, satellite targets and base station users, and base station targets; the signal-to-interference-and-noise ratios of satellite users and base station users are expressed as:

[0011]

[0012] Among them, g j and g k are the channel from the low-orbit satellite to the jth satellite user and the channel from the kth base station user, respectively. k is the channel from the base station to the kth base station user, N0 is the noise variance, and They are low-orbit satellites and base stations for their respective The precoding vector of each user, K su and K cu are the number of satellite users and base station users respectively.

[0013] As a preference, the ergodic rate of the j-th satellite user adopts the following upper bound function:

[0014]

[0015] Among them, α is the energy mean of satellite channel gain, a j and b j are the uniform plane array response vector and precoding vector of the satellite to the jth satellite user,

[0016] The ergodic rate of the k-th base station user is:

[0017]

[0018] in,

[0019] As a preference, for low-orbit satellites, T s The optimal perceptual precoder is is a diagonal vector, representing the M corresponding to the uniform plane array response from the low-orbit satellite to its i-th target t / T s elements; for the base station T b objectives, the optimal perceptual precoder is is a diagonal vector, representing the N corresponding to the uniform planar array response from the base station to its i-th target t / T b elements, M t and N t are the number of satellite and base station antennas respectively; when satellite precoder B=Q s U s and base station precoder W = Q b U b When , the system obtains the optimal perception beam pattern, and is the auxiliary unitary matrix.

[0020] As a preferred option, the original optimization problem is formulated as:

[0021]

[0022] Among them, P B,max and P S,maxare the maximum transmission power of the base station and the satellite respectively. ε1 and ε2 represent the permissible deviation of the Euclidean distance between the precoder and the optimal perceptual precoder. and is the identity matrix.

[0023] As a preference, for the communication precoder design considering only the communication index, only the energy constraint and optimization target in the original problem are focused on, the quadratic transformation method is used to process the non-convex objective function, and the auxiliary variable is introduced. and Rewrite the problem as:

[0024]

[0025] in:

[0026]

[0027] As a preferred approach, an alternating optimization framework is used to solve the rewritten problem: First, W and B are fixed to optimize λ and μ, and the derivative of μ and λ with respect to the objective function is taken and set to zero, resulting in the following solution:

[0028]

[0029] After that, fix λ and μ to solve W and B. When μ and λ are fixed, The problem is simplified to a standard convex optimization problem. After the objective function converges, the communication precoder B is obtained. com and W com .

[0030] As an optimal solution, for perceptual precoder design considering only perceptual indicators, the following two independent sub-problems are solved:

[0031]

[0032] from Start solving when When , the optimal B is Q s U s ; Otherwise, scale B to meet the energy constraint; Optimal perceptual precoder B for LEO satellites sen =Q s U s ; Similarly, the optimal perceptual precoder of the base station is W sen =Q b U b .

[0033] Preferably, the third optimization problem is expressed as:

[0034]

[0035] Where η is the weight factor, The subscripts com and sen are used to mark the communication and perception precoders; first, fix B and W and solve the problem Translates to:

[0036]

[0037] Obtain analytical solution through singular value decomposition; update unitary matrix U s The formula is as follows:

[0038]

[0039] Among them, U 1s and U 2s yes The singular value decomposition result of the auxiliary unitary matrix U b Update in the same way;

[0040] After that, fix U s ,U b and will Translates to:

[0041]

[0042] The analytical solution is:

[0043] B * =ηB com +(1-η)B sen ,

[0044] W * =ηW com +(1-η)W sen .

[0045] Among them, B sen =Q s U s , W sen =Q b U b ; When the iteration converges, the optimal precoding matrix B is obtained opt and W opt .

[0046] The present invention also provides a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of the large-scale MIMO low-orbit satellite-to-ground communication perception integrated collaborative precoding method.

[0047] Beneficial Effects: This paper models a massive MIMO low-orbit satellite-ground communication and perception integrated collaborative system. It derives the signal-to-interference-and-noise ratio (SINR) of received signals for satellite and base station users, as well as the optimal sensing beam patterns for satellite and base station sensing targets. Based on this, a system traversal and rate maximization problem, subject to sensing performance and energy consumption constraints, is established. First, precoder designs focusing solely on communication and sensing metrics are considered. When considering only communication metrics, the optimization problem is recast using rate approximation and quadratic transformation. The communication precoder is then designed using an alternating optimization algorithm. When considering only sensing metrics, the sensing precoder can be directly solved. After obtaining the communication and sensing precoders, the original problem is transformed into minimizing the weighted Euclidean distance between the precoder and the optimal communication and sensing precoders. Furthermore, the final low-orbit satellite and base station precoders are solved using an alternating optimization method. This method significantly reduces the complexity of solving the optimization problem and successfully balances communication and sensing performance, thereby improving overall system performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of the scene of the present invention.

[0049] Figure 2 4 is a flow chart of the overall method of an embodiment of the present invention. DETAILED DESCRIPTION

[0050] To more clearly illustrate the purpose, technical solutions and advantages of the present invention, the following is a clear and complete description of the technical solutions in conjunction with the accompanying drawings in the embodiments of the present invention. It should be noted that the embodiments are only examples of some of the present invention, not all of the embodiments. Based on these embodiments, all other implementation methods obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0051] The present invention provides a large-scale MIMO low-orbit satellite-to-ground communication perception integrated collaborative precoding method, such as Figure 1As shown, considering that there are users who need communication services and targets to be perceived in the system, some users and targets are located outside the coverage of the base station, and low-orbit satellites are introduced to serve these users and perceive these targets; this method is equipped with large-scale MIMO antenna arrays on both the low-orbit satellite and the base station, and the low-orbit satellite and the ground base station use the same spectrum resources; it is difficult for the low-orbit satellite to obtain accurate instantaneous channel state information, and the statistical channel state information of the low-orbit satellite is used, while the ground base station can obtain accurate instantaneous channel state information; based on this, the ground gateway manages the downlink transmission of the low-orbit satellite and the base station, so that the low-orbit satellite and the ground base station send the precoded information to each user; the communication and perception integrated collaborative precoding method is a precoding scheme based on the statistical channel state information of the low-orbit satellite, which balances communication performance and perception performance; each antenna unit of the antenna array of the low-orbit satellite and the base station sends a signal independently, and the precoding of the low-orbit satellite and the ground base station is updated as the position of the satellite and each user terminal changes.

[0052] like Figure 2 As shown, an embodiment of the present invention discloses a large-scale MIMO low-orbit satellite-to-ground communication perception integrated collaborative precoding method. First, a system traversal and rate maximization problem subject to perception performance constraints and energy consumption restrictions is established; wherein the satellite and base station precoders are collaboratively designed based on the statistical channel state information of the satellite and the instantaneous channel state information of the base station, and considering the interference of the satellite to the base station users; then, the original problem is decomposed into a first optimization problem of designing a communication precoder considering only communication indicators and a second optimization problem of designing a perception precoder considering only perception indicators; for the case where only communication indicators are considered, the optimization problem is rewritten using rate approximation and quadratic transformation, and the communication precoder is solved using an alternating optimization method; for the case where only perception indicators are considered, the optimal perception precoder is directly solved; finally, the original optimization problem is converted into a third optimization problem of minimizing the weighted Euclidean distance between the precoder and the optimal communication precoder and the optimal perception precoder, and the final precoder is solved using an alternating optimization method.

[0053] The method of this embodiment is described in more detail below with reference to a specific scenario.

[0054] Part 1: Constructing low-orbit satellite channel models and ground base station channel models

[0055] Specifically, consider a low-orbit satellite equipped with a massive MIMO uniform planar array with M antennas. t =M x M y , where M x and M y Denote the number of antennas uniformly distributed along the x-axis and y-axis respectively. Then the uniform plane array response vector from the low-orbit satellite to the j-th satellite user is:

[0056]

[0057] Where θ s,j and Represents the user's angle relative to the x-axis and y-axis respectively. and a y (θ s,j ) are the response vectors related to the x-axis and y-axis respectively, and their expressions are as follows:

[0058]

[0059] The downlink channel from the low-orbit satellite to the j-th satellite user can be expressed as:

[0060]

[0061] Where, α j Denotes the channel gain and assumes it follows the Rice factor κ m and energy The Rice distribution.

[0062] The ground base station is also equipped with large-scale MIMO antennas with a number of N t =N x N y , where N x and N y Denotes the number of antennas uniformly distributed along the x-axis and y-axis respectively. The channel from the base station to the k-th base station user can be modeled as:

[0063]

[0064] Where, L k is the number of multipaths, and the gain of each path is β k,l Independent and identically distributed θ b,k,l and are the angles of the lth path along the x-axis and y-axis respectively. and are the response vectors in two directions, respectively expressed as:

[0065]

[0066] Part II: Building Communication Signal Model and Perception Signal Model

[0067] The signal sent by the low-orbit satellite can be expressed as:

[0068] x su =Bs su , (8)

[0069] in, is the satellite precoder, K su is the number of satellite users. The signal sent satisfy Similarly, the signal sent by the base station is represented as follows:

[0070] x cu =Ws cu , (9)

[0071] Where, is the precoder at the base station, K cu is the number of base station users. Since satellite users are outside the base station coverage, the base station-to-base station channel can be ignored. Therefore, the received signal of the kth base station user and the jth satellite user can be expressed as:

[0072]

[0073] In the formula, noise is the noise variance. κ=1.38×10 -23 is the Boltzmann constant, B is the bandwidth, and T is the equivalent noise temperature. g k represents the channel from the low-orbit satellite to the k-th base station user. Then the signal-to-interference-and-noise ratio between the j-th satellite user and the k-th base station user is:

[0074]

[0075] Since it is difficult to obtain accurate instantaneous channel state information on low-orbit satellites, the present invention utilizes the statistical state information of the satellite channel including the channel gain α j and uniform planar array response vector a j The ergodic rate of the jth satellite user and the kth base station user can be expressed as:

[0076]

[0077] Where,

[0078]

[0079] The expectation is to traverse the gain of the satellite channel. In order to reduce the complexity of the traversal rate calculation, the following upper bound function is used:

[0080]

[0081] Here, the perception beam pattern is introduced to measure the perception performance of the target. The transmission beam pattern of the low-orbit satellite can be expressed as:

[0082]

[0083] Where, is the covariance matrix. is a space angle pair that satisfies Similarly, the transmit beam pattern of the base station can be obtained.

[0084] For low-orbit satellites, T s For this objective, the optimal perceptual precoder is as follows:

[0085]

[0086] Where, is a diagonal vector, representing the M corresponding to the uniform plane array response from the low-orbit satellite to its i-th target t / T s elements.

[0087] Similarly, for the base station's T b For this goal, the optimal perceptual precoder of the base station can be expressed as:

[0088]

[0089] Where, is a diagonal vector, representing the N corresponding to the uniform planar array response from the base station to its i-th target t / T b elements.

[0090] When B=Q s U s and W = Q b U b When , the system obtains the optimal perception beam pattern. Here, and are auxiliary unitary matrices, which are related to Q s and Q b It does not affect the perceptual beam pattern, but only adjusts the matrix dimension to adapt the precoder.

[0091] Part III: Constructing the Optimization Problem

[0092] The goal is to design a cooperative precoding scheme that maximizes the system traversal and rate while ensuring perceptual performance. Therefore, the entire optimization problem can be expressed as:

[0093]

[0094] Where, P B,max and P S,max are the maximum transmit powers of the base station and satellite, respectively. ε1 and ε2 represent the permissible Euclidean distance deviations between the precoder and the optimal sensing precoder. A decrease in the Euclidean distance indicates that both the LEO satellite and the base station are approaching their respective optimal sensing beam patterns.

[0095] Part 4: Design of Communication-Aware Integrated Collaborative Precoder

[0096] because The non-convexity of makes it very difficult to solve it directly. To solve this problem, a communication precoder that only considers communication indicators and a perceptual precoder that only focuses on perceptual indicators are derived respectively.

[0097] When only the communication index is considered, we only need to focus on the energy constraint and optimization objective in the original problem. Here, the quadratic transformation method is used to deal with non-convex objective functions. Auxiliary variables are introduced. and Convert the fraction in the ergodic rate into the following form:

[0098]

[0099] Therefore, the original optimization problem can be rewritten as:

[0100]

[0101] To address this problem, an alternating optimization architecture is employed. First, W and B are fixed to optimize λ and μ. By taking the derivative of the objective function with respect to μ and λ and setting them to zero, the following solution is obtained:

[0102]

[0103] Then, fix λ and μ to solve for W and B. In this case, and Respectively with w k and b j In addition, About w k and b j is convex, and About b j is also convex. Therefore, when μ and λ are fixed, The problem can be simplified to a standard convex optimization problem that can be solved efficiently. After the objective function converges, the communication precoder B is obtained. com and W com .

[0104] When designing the perceptual precoder, the original problem This is transformed into two independent sub-problems as follows:

[0105]

[0106] from Start solving when When , the optimal B is Q s Us Otherwise, B should be scaled to satisfy the energy constraint. Here, because Considering that the transmission power exceeds 1W, the optimal perceptual precoder B for low-orbit satellites is sen =Q s U s Similarly, the optimal perceptual precoder of the base station is W sen =Q b U b .

[0107] Part 5: Design of Communication-Aware Integrated Collaborative Precoder

[0108] The communication precoder and perception precoder have been obtained above. Here, the weight factor η is introduced to achieve a trade-off between communication performance and perception performance. The original optimization problem is can be rewritten as:

[0109]

[0110] Where, This problem can be solved by alternating optimization.

[0111] First, fix B, W and solve the problem Translates to:

[0112]

[0113] This problem can be solved analytically by singular value decomposition. Update the unitary matrix U s The formula is as follows:

[0114]

[0115] Where U 1s and U 2s yes The singular value decomposition result of and Auxiliary unitary matrix U b Can be updated in the same way.

[0116] After that, fix U s ,U b and will Translates to:

[0117]

[0118] Let G(F,U) be differentiated with respect to F, and the result is as follows:

[0119]

[0120] Therefore, the question It can be solved analytically into the following form:

[0121] B * =ηB com +(1-η)B sen , (35)

[0122] W * =ηW com +(1-η)W sen . (36)

[0123] The proposed alternating optimization scheme converges to the optimal precoding matrix B within a relatively small number of iterations. opt and W opt , and ultimately the desired performance trade-off can be achieved.

[0124] An embodiment of the present invention also discloses a computer program product, including a computer program, which, when executed by a processor, implements the steps of the large-scale MIMO low-orbit satellite-to-ground communication perception integrated collaborative precoding method.

[0125] Anything not described in detail in the present invention is well known to those skilled in the art.

[0126] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A massive MIMO low-orbit satellite-to-ground communication perception integrated collaborative precoding method, characterized in that: The base station and the low-orbit satellite use the same spectrum resources to collaboratively serve users on the ground who need to communicate and targets that need to be sensed. The method includes: A system traversal and rate maximization problem subject to perceptual performance constraints and energy consumption limits is established. Based on the statistical channel state information of the satellite and the instantaneous channel state information of the base station, and taking into account the interference of the satellite to the base station users, the satellite and base station precoders are collaboratively designed. Decomposing the original problem into a first optimization problem of designing a communication precoder considering only communication indicators and a second optimization problem of designing a perceptual precoder considering only perceptual indicators; For the case where only communication indicators are considered, the optimization problem is rewritten using rate approximation and quadratic transformation, and the communication precoder is solved using the alternating optimization method; For the case where only perceptual indicators are considered, the optimal perceptual precoder is directly solved; The original optimization problem is transformed into a third optimization problem of minimizing the weighted Euclidean distance between the precoder and the optimal communication precoder and the optimal perceptual precoder, and the final precoder is solved using an alternating optimization method.

2. The method for integrated collaborative precoding of massive MIMO low-orbit satellite-to-ground communication perception according to claim 1, characterized in that: Introducing communication users and sensing targets outside the coverage of low-orbit satellite service base stations, the communication users and sensing targets on the ground are divided into satellite users, satellite targets and base station users, and base station targets. The signal-to-interference-and-noise ratios of satellite users and base station users are expressed as: Among them, g j and g k are the channel from the low-orbit satellite to the jth satellite user and the channel from the kth base station user, respectively. k is the channel from the base station to the kth base station user, N0 is the noise variance, b l and w l are the precoding vectors of the low-orbit satellite and the base station for their respective l-th users, K su and K cu are the number of satellite users and base station users respectively.

3. The method for integrated collaborative precoding of massive MIMO low-orbit satellite-to-ground communication perception according to claim 2, characterized in that: The ergodic rate of the jth satellite user uses the following upper bound function: Among them, α is the energy mean of satellite channel gain, a j and b j are the uniform plane array response vector and precoding vector of the satellite to the jth satellite user, The ergodic rate of the k-th base station user is: in, 4. The method for integrated collaborative precoding of massive MIMO low-orbit satellite-to-ground communication perception according to claim 1, characterized in that: For low-orbit satellites, T s The optimal perceptual precoder is is a diagonal vector, representing the M corresponding to the uniform plane array response from the low-orbit satellite to its i-th target t / T s elements; for the base station T b objectives, the optimal perceptual precoder is is a diagonal vector, representing the N corresponding to the uniform planar array response from the base station to its i-th target t / T b elements, M t and N t are the number of satellite and base station antennas, respectively; When satellite precoder B = Q s U s and base station precoder W = Q b U b When , the system obtains the optimal perception beam pattern, and is the auxiliary unitary matrix, K su and K cu are the number of satellite users and base station users respectively.

5. The method for integrated collaborative precoding for massive MIMO low-orbit satellite-to-ground communication perception according to claim 4, characterized in that: The original optimization problem is formulated as: in, is the ergodic rate of the k-th base station user, is the upper bound of the ergodic rate of the jth satellite user, K su and K cu are the number of satellite users and base station users, P B,max and P S,max are the maximum transmission powers of the base station and satellite respectively. ε1 and ε2 represent the permissible deviation of the Euclidean distance between the precoder and the optimal perceptual precoder. and is the identity matrix.

6. The method for integrated collaborative precoding of massive MIMO low-orbit satellite-to-ground communication perception according to claim 1, characterized in that: For the communication precoder design considering only communication indicators, we only focus on the energy constraints and optimization objectives in the original problem, use the quadratic transformation method to deal with non-convex objective functions, and introduce auxiliary variables. and Rewrite the problem as: in: Where W and B are the precoders of the base station and satellite respectively, h k is the channel from the base station to the kth base station user, w k is the precoding vector of the base station for each k-th user, α is the energy mean of the satellite channel gain, a j and b j are the uniform plane array response vector and precoding vector of the satellite to the jth satellite user, N0 is the noise variance, K su and K cu are the number of satellite users and base station users, P B,max and P S,max are the maximum transmission powers of the base station and satellite respectively.

7. The method for integrated collaborative precoding for massive MIMO low-orbit satellite-to-ground communication perception according to claim 6, characterized in that: The rewritten problem is solved using an alternating optimization architecture: First, W and B are fixed to optimize λ and μ. The following solution is obtained by taking the derivative of the objective function with respect to μ and λ and setting them to zero: After that, fix λ and μ to solve W and B. When μ and λ are fixed, The problem is simplified to a standard convex optimization problem. After the objective function converges, the communication precoder B is obtained. com and W com .

8. The method for integrated collaborative precoding for massive MIMO low-orbit satellite-to-ground communication perception according to claim 4, characterized in that: For the perceptual precoder design considering only perceptual indicators, the following two independent sub-problems are solved: from Start solving when When , the optimal B is Q s U s ; Otherwise, scale B to meet the energy constraint; Optimal perceptual precoder B for LEO satellites sen =Q s U s ; Similarly, the optimal perceptual precoder of the base station is W sen =Q b U b .

9. The method for integrated collaborative precoding for massive MIMO low-orbit satellite-to-ground communication perception according to claim 8, characterized in that: The third optimization problem is expressed as: Where η is the weight factor, The subscripts com and sen are used to mark the communication and perception precoders; first, fix B and W and solve the problem Translates to: Obtain analytical solution through singular value decomposition; update unitary matrix U s The formula is as follows: Among them, U 1s and U 2s yes The singular value decomposition result of the auxiliary unitary matrix U b Update in the same way; After that, fix U s ,U b and will Translates to: The analytical solution is: B * =ηB com +(1-n)B sen , W * =ηW com +(1-n)W sen . Among them, B sen =Q s U s , W sen =Q b U b ; When the iteration converges, the optimal precoding matrix B is obtained opt and W opt .

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the large-scale MIMO low-orbit satellite-to-ground communication perception integrated collaborative precoding method according to any one of claims 1 to 9 are implemented.

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