A method for optimizing energy efficiency of low-orbit satellite communication systems based on imperfect CSI

Abstract

The present invention belongs to the field of satellite communication technology, and specifically relates to a low-orbit satellite communication system energy efficiency optimization method based on imperfect CSI. The method comprises: establishing a multi-user multi-beam low-orbit satellite downlink transmission system; constructing a maximization minimum system user energy efficiency optimization model based on the multi-user multi-beam low-orbit satellite downlink transmission system; constructing a Gaussian channel uncertainty model according to the imperfect CSI; constructing a robust resource allocation model based on maximization minimum system user energy efficiency according to the maximization minimum system user energy efficiency optimization model and the Gaussian channel uncertainty model; solving the robust resource allocation model to obtain a robust resource allocation scheme; and the system performing resource allocation according to the robust resource allocation scheme to obtain optimal system energy efficiency. The present invention improves the energy efficiency and robustness of users of the low-orbit satellite communication system and reduces the interruption probability of system users.

Description

Technical Field

[0001] The present invention belongs to the field of satellite communication technology, and in particular relates to a method for optimizing energy efficiency of a low-orbit satellite communication system based on imperfect CSI. Background Art

[0002] With the development of modern aerospace and communications technologies, satellite communications have gained widespread application in navigation, broadcasting, rescue, and disaster relief due to their ability to overcome long distances and harsh terrain, wide coverage, and high data rates. Compared to high-orbit satellites, low-orbit satellites offer relatively low latency, minimal path loss, and lower production and launch costs, garnering greater attention. Beamforming is a key technology for satellite resource allocation. In satellite communication systems, beamforming adaptively adjusts the excitation weights of array antenna elements based on specific criteria and algorithms, ensuring that the weighted summation of the array's received signals produces an optimal output signal under the chosen criteria. This technology also enables interference suppression, further increasing the capacity of satellite communication links.

[0003] Many existing methods have studied resource allocation in low-Earth orbit satellite communication systems, but most have only considered resource optimization under ideal channel conditions. In actual low-Earth orbit satellite communication systems, due to fluctuations in the satellite feeder link and the influence of weather factors, it is difficult to obtain true channel information. Therefore, assuming perfect channel state information is unfeasible, and imperfect channel state information can lead to performance degradation in resource allocation methods.

[0004] In summary, in order to facilitate practical engineering applications, there is an urgent need for an energy efficiency optimization method for low-orbit satellite communication systems based on imperfect CSI to improve the minimum energy efficiency of users. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the present invention proposes a method for optimizing the energy efficiency of a low-orbit satellite communication system based on imperfect CSI, which includes:

[0006] S1: Establish a multi-user multi-beam low-orbit satellite downlink transmission system;

[0007] S2: Constructing an optimization model for maximizing the minimum system user energy efficiency based on a multi-user multi-beam low-orbit satellite downlink transmission system;

[0008] S3: Construct a Gaussian channel uncertainty model based on imperfect CSI;

[0009] S4: Based on the maximization of minimum system user energy efficiency optimization model and Gaussian channel uncertainty model, a robust resource allocation model based on maximization of minimum system user energy efficiency is constructed;

[0010] S5: Solve the robust resource allocation model and obtain a robust resource allocation plan; the system allocates resources according to the robust resource allocation plan to obtain optimal system energy efficiency.

[0011] Preferably, the multi-user multi-beam low-orbit satellite downlink transmission system specifically includes: a multi-beam low-orbit earth satellite, M beams, each beam serving N system users and K earth stations in the network.

[0012] Preferably, the process of constructing a maximum minimum system user energy efficiency optimization model includes:

[0013] Calculate the instantaneous reachable rate of the user and the instantaneous reachable rate of the earth station; establish an interruption rate constraint based on the instantaneous reachable rate of the user and the instantaneous reachable rate of the earth station;

[0014] Construct power allocation coefficient constraints and maximum transmit power constraints;

[0015] Calculate the user's power consumption and construct the minimum user energy efficiency optimization function based on the user's instantaneous achievable rate and power consumption;

[0016] According to the minimum user energy efficiency optimization function, a maximum minimum system user energy efficiency optimization model is constructed with the interruption rate constraint, power allocation coefficient constraint and maximum transmission power constraint as constraints.

[0017] Furthermore, the formula for calculating the instantaneous reachable rate of a user is:

[0018]

[0019] Among them, h m,n represents the downlink channel vector from the satellite to the nth user in the mth beam, α m,n represents the power allocation coefficient of the nth user in the mth beam, α m,j represents the power allocation coefficient of the jth user in the mth beam, α i,n represents the power allocation coefficient of the nth user in the i-th beam, M represents the number of beams, N represents the number of users, and w i represents the weight vector assigned by the satellite to the i-th beam, represents the noise power of the additive white Gaussian noise at the nth user receiving end in the mth beam.

[0020] Furthermore, the formula for calculating the user's power consumption is:

[0021]

[0022] Among them, P m,n represents the power consumption of the nth user in the mth beam, ζ represents the power amplification factor, α m,nrepresents the power allocation coefficient of the nth user in the mth beam, w m represents the weight vector assigned by the satellite to the mth beam, Indicates the power consumption of the user circuit.

[0023] Preferably, the Gaussian channel uncertainty model is expressed as:

[0024]

[0025]

[0026] Among them, h m,n represents the actual channel vector from the satellite to the nth user in the mth beam, h k represents the actual channel vector between the satellite and the kth earth station, represents the channel gain estimate of the actual channel vector from the satellite to the nth user in the mth beam, Denotes the estimated channel gain of the actual channel vector between the satellite and the kth earth station, Δh m,n Denotes the channel gain estimation error of the actual channel vector from the satellite to the nth user in the mth beam, Δh k represents the channel gain estimation error of the actual channel vector between the satellite and the kth earth station, E m,n Denotes Δh m,n The covariance matrix, E k represents Δh k The covariance matrix of .

[0027] Preferably, the robust resource allocation model based on maximizing the minimum system user energy efficiency is expressed as:

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] C5:rank(W m )=1

[0034] Among them, R m,n represents the instantaneous achievable rate of the nth user in the mth beam, P m,n represents the power consumption of the nth user in the mth beam, R k represents the instantaneous achievable rate of the kth earth station, W m represents the intermediate parameter, αm,n represents the power allocation coefficient of the nth user in the mth beam, P max is the total power transmitted by the satellite, represents the minimum rate threshold of the nth user in the mth beam, represents the minimum rate threshold of the kth earth station, M represents the number of beams, N represents the number of users, Tr(·) represents the trace of the matrix, Pr(·) represents the probability, ε m,n represents the interruption probability of the maximum allowed communication rate of the nth user in the mth beam, ε k represents the interruption probability of the maximum allowed communication rate of the kth earth station, and rank(·) represents the rank of the matrix.

[0035] Preferably, the process of solving the robust resource allocation model includes:

[0036] S41: The nonlinear objective function, i.e., the function that maximizes the minimum system user energy efficiency, is converted into an equivalent subtraction form using the Dinkelbach method. Variables are introduced to transform the objective function into a tractable form, resulting in a rewritten robust resource allocation problem.

[0037] S42: The outage probability constraint is transformed into a deterministic constraint using the Bernstein approximation inequality. Equivalent substitution, semi-positive relaxation, and alternating optimization are used to transform the robust resource allocation problem into a standard convex optimization subproblem.

[0038] S43: Use convex optimization tools to solve the convex optimization subproblem and obtain the optimal satellite beamforming vector and power allocation factor, that is, the robust resource allocation solution.

[0039] The beneficial effects of the present invention are as follows: the present invention addresses the resource allocation problem of traditional satellite communication networks, introduces beamforming technology into a multi-user multi-beam low-orbit satellite communication system, considers the interruption rate constraint, power allocation coefficient constraint and maximum transmit power constraint of each user, and constructs a robust resource allocation model based on the Gaussian channel uncertainty model to jointly optimize the satellite beamforming vector and the power allocation factor. In addition, the present invention takes into account the imperfect channel state information of the satellite transmission channel, avoiding the degradation of resource allocation performance. Unlike traditional resource allocation methods that only guarantee transmit power or meet service quality, the present invention studies the fairness transmission of system users and the energy-rate balance problem, and takes it into more comprehensive consideration. In addition, compared with existing methods, the present invention improves the energy efficiency and robustness of users of low-orbit satellite communication systems, and reduces the interruption probability of system users. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of the method for optimizing energy efficiency of a low-orbit satellite communication system based on imperfect CSI in the present invention;

[0041] Figure 2 Schematic diagram of the multi-user multi-beam low-orbit satellite downlink transmission system model in the present invention;

[0042] Figure 3 The graphs are of user energy efficiency under different channel error variances for the present invention and the comparative method;

[0043] Figure 4 The graph is a graph showing the user interruption probability under different channel error variances for the present invention and the comparative method. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, 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 making creative efforts are within the scope of protection of the present invention.

[0045] The present invention proposes a method for optimizing the energy efficiency of a low-orbit satellite communication system based on imperfect CSI. Figure 1 As shown, the method includes the following contents:

[0046] S1: Establish a multi-user multi-beam low-orbit satellite downlink transmission system.

[0047] like Figure 2 As shown, the low-orbit satellite downlink transmission system of the present invention considers a multi-user multi-beam satellite system downlink transmission scenario. In this scenario, each coverage area is served by a multi-beam low-orbit earth satellite. The satellite is equipped with multiple feed sources to form M beams, each of which serves N system users. The multi-beam satellite sends information to users based on non-orthogonal multiple access. K in-network earth stations located in the coverage area will simultaneously receive signals from the satellite. Definition and are the sets of satellite beams, system users and earth stations respectively.

[0048] S2: Construct an optimization model to maximize the minimum system user energy efficiency based on a multi-user multi-beam low-orbit satellite downlink transmission system.

[0049] Calculate the instantaneous achievable rate of the user and the instantaneous achievable rate of the earth station; specifically, this system is a downlink transmission scenario of a multi-beam satellite system. The satellite transmits multiple signals, and the instantaneous achievable rate of the nth user in the mth beam of the satellite is:

[0050]

[0051] Among them, h m,nrepresents the downlink channel vector from the satellite to the nth user in the mth beam, α m,n represents the power allocation coefficient of the nth user in the mth beam, α m,j represents the power allocation coefficient of the jth user in the mth beam, α i,n represents the power allocation coefficient of the nth user in the i-th beam, w i represents the weight vector assigned by the satellite to the i-th beam, represents the noise power of the additive white Gaussian noise at the nth user receiving end in the mth beam.

[0052] The instantaneous achievable rate of the kth earth station is:

[0053]

[0054] Among them, h k represents the channel vector between the satellite and the kth earth station, represents the noise power of the additive white Gaussian noise at the receiving end of the kth earth station.

[0055] An interruption rate constraint is constructed based on the user's instantaneous achievable rate and the earth station's instantaneous achievable rate; a power allocation coefficient constraint and a maximum transmission power constraint are constructed; the user's power consumption is calculated, and a minimum user energy efficiency optimization function is constructed based on the user's instantaneous achievable rate and power consumption.

[0056] The power consumption P of the nth user in the mth beam m,n for:

[0057]

[0058] Where ζ represents the power amplification factor, w m represents the weight vector assigned by the satellite to the mth beam, Indicates the power consumption of the user circuit.

[0059] The minimum user energy efficiency optimization function is expressed as:

[0060]

[0061] Among them, η m,n represents the energy efficiency of the nth user in the mth beam.

[0062] According to the minimum user energy efficiency optimization function, a maximum minimum system user energy efficiency optimization model is constructed with the interruption rate constraint, power allocation coefficient constraint, and maximum transmission power constraint as constraints. The maximum minimum system user energy efficiency optimization model is expressed as:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] Among them, P max is the total power transmitted by the satellite, represents the minimum rate threshold of the nth user in the mth beam, represents the minimum rate threshold of the kth earth station, Tr(·) represents the trace of the matrix, Pr(·) represents the probability, ε m,n represents the interruption probability of the maximum allowed communication rate of the nth user in the mth beam, ε k represents the interruption probability of the maximum allowed communication rate of the kth earth station, and rank(·) represents the rank of the matrix. C1 is the interruption rate constraint of the nth user in the mth beam, C2 is the interruption rate constraint of the kth earth station, C3 is the maximum transmit power constraint of the satellite beam, and C4 is the power allocation coefficient constraint for users within the beam.

[0069] S3: Construct a Gaussian channel uncertainty model based on the imperfect CSI.

[0070] The present invention considers the resource optimization problem under imperfect CSI state and constructs a Gaussian channel uncertainty model based on imperfect CSI. The Gaussian channel uncertainty model is expressed as:

[0071] h m,n represents the actual channel vector (actual downlink channel vector) from the satellite to the nth user in the mth beam, h k represents the actual channel vector between the satellite and the kth earth station, represents the channel gain estimate of the actual channel vector from the satellite to the nth user in the mth beam, Denotes the estimated channel gain of the actual channel vector between the satellite and the kth earth station, Δh m,n Denotes the channel gain estimation error of the actual channel vector from the satellite to the nth user in the mth beam, Δh k represents the channel gain estimation error of the actual channel vector between the satellite and the kth earth station; E m,n represents Δh m,n The covariance matrix, E k represents Δh k The covariance matrix of and

[0072] S4: Based on the maximization of minimum system user energy efficiency optimization model and Gaussian channel uncertainty model, a robust resource allocation model based on maximization of minimum system user energy efficiency is constructed.

[0073] The robust resource allocation model based on maximizing the minimum system user energy efficiency is a robust resource allocation model that jointly optimizes the satellite beamforming vector and the power allocation factor, and its expression is:

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] C5:rank(W m )=1

[0080] Among them, W m represents the intermediate parameters, C1 is the interruption rate constraint of the nth user in the mth beam, C2 is the interruption rate constraint of the kth earth station, C3 is the maximum transmit power constraint of the satellite beam, C4 is the power allocation coefficient constraint of the users in the beam, and C5 is the rank-one constraint.

[0081] S5: Solve the robust resource allocation model and obtain a robust resource allocation plan; the system allocates resources according to the robust resource allocation plan to obtain optimal system energy efficiency.

[0082] The process of solving the robust resource allocation problem includes:

[0083] S41: The nonlinear objective function, i.e., maximizing the minimum system user energy efficiency function, is transformed into an equivalent subtraction form using the Dinkelbach method. Variables are introduced to transform the objective function into a tractable form, resulting in a rewritten robust resource allocation problem.

[0084] Based on Dinkelbach theory, the fractional objective function can be transformed into a subtraction form and then defined and are the optimal energy efficiency, beamforming matrix, and power allocation coefficient respectively. Then the objective function can be converted into the following form:

[0085]

[0086] To obtain the optimal solution and Required if and only if:

[0087]

[0088] However, is an unknown quantity, so we need to define the function f(η m,n ):

[0089]

[0090] When the function f(η m,n )=0, the optimal solution can be obtained Therefore, we can use the bisection method to solve f(η m,n )=0 and obtain For a given η m,n , the original optimization problem can be solved by equivalent changes, and the problem can be written as follows:

[0091]

[0092] stC1,C2,C3,C4,C5

[0093] At this point, the objective function is still difficult to handle. To this end, we introduce variables and define Then R m,n (W m ,α m,n ) can be transformed into:

[0094]

[0095]

[0096] η m,n P m,n (W m ,α m,n ) can be transformed into:

[0097]

[0098] The nonlinear objective function, namely the function of maximizing the minimum system user energy efficiency, can be transformed into:

[0099]

[0100] Reintroduce the auxiliary variable τ m,n , whose expression is:

[0101]

[0102] At this point, the original non-smooth objective function is transformed into a smooth optimization problem, and the robust resource allocation problem can be rewritten as:

[0103]

[0104] stC1-C5

[0105]

[0106] S42: The outage probability constraint is transformed into a deterministic constraint using the Bernstein approximation inequality. Equivalent substitution, semi-positive relaxation method and alternating optimization are used to transform the robust resource allocation problem into a standard convex optimization subproblem.

[0107] In order to obtain the deterministic form of the probability constraints C1 and C2, we first perform some transformations and can write them as follows:

[0108]

[0109] in, Substituting the Gaussian channel uncertainty model, we can obtain:

[0110]

[0111] in,

[0112] Rewrite the CSI random error as in Then the outage probability constraint can be expressed as:

[0113]

[0114] in,

[0115] To this end, the Bernstein inequality is used to convert the probabilistic form into a deterministic form. The equivalent deterministic form of the above interruption probability constraint is as follows:

[0116]

[0117]

[0118]

[0119] Among them, μ m,n =-ln(ε m,n ), vec(Ω m,n ) represents Ω m,n The straightening matrix, β m,n and ν m,n is an auxiliary variable.

[0120] Similarly, the probability constraint C2 can be equivalently converted into the following form:

[0121]

[0122]

[0123]

[0124] in, μ k =-ln(ε k ), β k and ν k is an auxiliary variable.

[0125] Constraint C6 can be written as:

[0126]

[0127] Then introduce the auxiliary variable A(W m ,α m,n ) and B(W m ,α m,n ),in

[0128]

[0129]

[0130] Constraint C6 can be rewritten as follows:

[0131]

[0132] Therefore, the robust resource allocation problem is transformed into a standard convex optimization subproblem, which can be expressed as:

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140] C3-C6

[0141] S43: Use convex optimization tools to solve the convex optimization subproblem and obtain the optimal satellite beamforming vector and power allocation factor, that is, the robust resource allocation solution.

[0142] For the optimization variable coupling constraint C6, the Block Coordinate Descent (BCD) method can be used to solve it. Specifically, the problem is divided into two sub-problems. When the power allocation coefficient α is given m.n When , the optimization problem becomes to optimize the detection matrix W m and τ m,n This subproblem is a convex optimization problem, which can be further solved by the corresponding convex optimization theory. Similarly, the optimal value W m and τ m,n Bringing it into the original problem, another sub-problem is to give the beam-forming vector W m , optimize the power allocation coefficient α m.n and τ m,n The sub-problem of is also a convex optimization problem. Finally, by using the convex optimization toolkit to alternately optimize the two sub-problems, we can get the original problem and Furthermore, if the solution satisfies the rank-one constraint, then the optimal This can be obtained using the eigenvalue decomposition method. Otherwise, the Gaussian random method is used to obtain an approximate solution, namely the robust resource allocation scheme. The system allocates resources according to the resource allocation scheme to achieve optimal system energy efficiency.

[0143] Evaluation of the present invention:

[0144] The application effect of the present invention is described in detail with reference to simulation:

[0145] 1) Simulation conditions

[0146] The present invention sets the number of users in each beam to 3, the number of earth stations to 2, and the accuracy error to 10 -3 and 10 -3 , the power amplification factor is set to 2, and the autocorrelation matrix of the CSI random error is set to E m,n =ρ m,n ×I m,n , where ρ m,n >0 indicates channel error variance. Other specific simulation parameters are given in Table 1.

[0147] Table 1 Specific simulation parameters

[0148]

[0149] 2) Simulation results

[0150] from Figure 3It can be seen that as the channel error variance increases, the user energy efficiency of different methods decreases. However, the user energy efficiency of the method of the present invention is higher than that of other methods, because increasing channel uncertainty will make the signal more susceptible to influence during channel transmission, while the method of the present invention takes channel uncertainty into consideration in advance, thus relatively reducing these influences. Figure 4 As can be seen, as the variance of the channel error increases, the outage probability of different methods increases accordingly, but the outage probability of the method of the present invention is always lower than that of other methods. Therefore, the method of the present invention can provide better robustness. Compared with the traditional method, the average outage probability of the method of the present invention is reduced by 5.59%, indicating that the performance of the present invention is better than the comparison method.

[0151] The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation plans of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing energy efficiency of a low-orbit satellite communication system based on imperfect CSI, characterized in that: include: S1: Establish a multi-user multi-beam low-orbit satellite downlink transmission system; S2: Constructing an optimization model for maximizing the minimum system user energy efficiency based on a multi-user multi-beam low-orbit satellite downlink transmission system; The process of building an optimization model to maximize the energy efficiency of minimum system users includes: Calculate the instantaneous reachable rate of the user and the instantaneous reachable rate of the earth station; establish an interruption rate constraint based on the instantaneous reachable rate of the user and the instantaneous reachable rate of the earth station; Construct power allocation coefficient constraints and maximum transmit power constraints; Calculate the user's power consumption and construct the minimum user energy efficiency optimization function based on the user's instantaneous achievable rate and power consumption; According to the minimum user energy efficiency optimization function, a model for maximizing the minimum system user energy efficiency is constructed with the interruption rate constraint, power allocation coefficient constraint and maximum transmission power constraint as constraints. S3: Construct a Gaussian channel uncertainty model based on the imperfect CSI. The Gaussian channel uncertainty model is expressed as: Among them, h m,n represents the actual channel vector from the satellite to the nth user in the mth beam, h k represents the actual channel vector between the satellite and the kth earth station, represents the channel gain estimate of the actual channel vector from the satellite to the nth user in the mth beam, Denotes the estimated channel gain of the actual channel vector between the satellite and the kth earth station, Δh m,n Denotes the channel gain estimation error of the actual channel vector from the satellite to the nth user in the mth beam, Δh k represents the channel gain estimation error of the actual channel vector between the satellite and the kth earth station, E m,n Denotes Δh m,n The covariance matrix, E k Denotes Δh k The covariance matrix of S4: Based on the maximization of minimum system user energy efficiency optimization model and the Gaussian channel uncertainty model, a robust resource allocation model based on maximization of minimum system user energy efficiency is constructed; the robust resource allocation model based on maximization of minimum system user energy efficiency is expressed as: C5:rank(W m )=1 Among them, R m,n represents the instantaneous achievable rate of the nth user in the mth beam, P m,n represents the power consumption of the nth user in the mth beam, R k represents the instantaneous achievable rate of the kth earth station, W m represents the intermediate parameter, α m,n represents the power allocation coefficient of the nth user in the mth beam, P max is the total power transmitted by the satellite, represents the minimum rate threshold of the nth user in the mth beam, represents the minimum rate threshold of the kth earth station, M represents the number of beams, N represents the number of users, Tr(·) represents the trace of the matrix, Pr(·) represents the probability, ε m,n represents the interruption probability of the maximum allowed communication rate of the nth user in the mth beam, ε k represents the interruption probability of the maximum allowed communication rate of the kth earth station, and rank(·) represents the rank of the matrix; S5: Solve the robust resource allocation model and obtain a robust resource allocation plan; the system allocates resources according to the robust resource allocation plan to obtain optimal system energy efficiency.

2. The method for optimizing energy efficiency of a low-orbit satellite communication system based on imperfect CSI according to claim 1, wherein: The multi-user multi-beam low-orbit satellite downlink transmission system specifically includes: a multi-beam low-orbit earth satellite, M beams, each beam serving N system users and K earth stations in the network.

3. The method for optimizing energy efficiency of a low-orbit satellite communication system based on imperfect CSI according to claim 1, wherein: The formula for calculating the instantaneous reachable rate of a user is: Among them, h m,n represents the downlink channel vector from the satellite to the nth user in the mth beam, α m,n represents the power allocation coefficient of the nth user in the mth beam, α m,j represents the power allocation coefficient of the jth user in the mth beam, α i,n represents the power allocation coefficient of the nth user in the i-th beam, M represents the number of beams, N represents the number of users, and w i represents the weight vector assigned by the satellite to the i-th beam, represents the noise power of the additive white Gaussian noise at the nth user receiving end in the mth beam.

4. The method for optimizing energy efficiency of a low-orbit satellite communication system based on imperfect CSI according to claim 1, wherein: The formula for calculating the power consumption of a user is: Among them, P m,n represents the power consumption of the nth user in the mth beam, ζ represents the power amplification factor, α m,n represents the power allocation coefficient of the nth user in the mth beam, w m represents the weight vector assigned by the satellite to the mth beam, Indicates the power consumption of the user circuit.

5. The method for optimizing energy efficiency of a low-orbit satellite communication system based on imperfect CSI according to claim 1, wherein: The process of solving the robust resource allocation model includes: S41: The nonlinear objective function, i.e., the function that maximizes the minimum system user energy efficiency, is converted into an equivalent subtraction form using the Dinkelbach method. Variables are introduced to transform the objective function into a tractable form, resulting in a rewritten robust resource allocation problem. S42: The outage probability constraint is transformed into a deterministic constraint using the Bernstein approximation inequality. Equivalent substitution, semi-positive relaxation, and alternating optimization are used to transform the robust resource allocation problem into a standard convex optimization subproblem. S43: Use convex optimization tools to solve the convex optimization subproblem and obtain the optimal satellite beamforming vector and power allocation factor, that is, the robust resource allocation solution.

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