A robust energy efficiency optimization method for IRS-assisted multi-antenna communication systems

Abstract

This invention belongs to the field of information security, specifically relating to a robust energy efficiency optimization method for IRS-assisted multi-antenna communication systems. The method includes: constructing a secure transmission model for an IRS-assisted cellular communication system; establishing a non-convex, multi-variable coupled robust resource allocation problem with the goal of maximizing system energy efficiency; transforming the non-convex objective function and robust constraints with parameter perturbations into convex functions and deterministic constraints respectively using continuous convex approximation, the S-Procedure method, Schur's complement lemma, and first-order Taylor expansion; and solving the original problem as a base station active beam optimization subproblem and an IRS passive beam optimization subproblem to obtain a resource allocation scheme. This invention considers the uncertainties of all transmission link channels and the influence of multiple eavesdroppers, establishing a multi-antenna communication system that maximizes the communication quality of legitimate users and maximizes the system's energy efficiency, exhibiting strong robustness and security.

Description

Technical Field

[0001] This invention belongs to the field of information security, specifically relating to a robust energy efficiency optimization method for a multi-antenna communication system based on IRS assistance. Background Technology

[0002] With the development of 5G technology, the system capacity and transmission performance of current cellular communication systems have been significantly improved. However, the transmission link from the base station to the receiver can be blocked by obstacles, resulting in poor transmission quality. In recent years, Intelligent Reflecting Surface (IRS) has been proposed as a novel technology to address these problems. Unlike traditional reflective surface communication, IRS can reflect signals by adjusting the phase shift or amplitude of the reflective element. This reflected signal can both enhance the signal strength of the target user and cancel out the signal of an eavesdropper, thereby improving system security. Therefore, research on IRS is of great significance.

[0003] Energy efficiency is a crucial performance indicator for communications, as improved energy efficiency translates to increased transmission rates and reduced power consumption. Furthermore, cellular communication systems suffer from low security due to eavesdropping, leading to extensive research on the security and energy efficiency optimization of IRS-assisted multi-antenna cellular communication systems. However, existing work assumes ideal channel conditions. In reality, due to complex electromagnetic environments and channel delays, base stations struggle to accurately obtain channel gain.

[0004] In summary, the problem with existing technologies is that, under the influence of channel uncertainty and eavesdroppers, the communication quality of legitimate users and the energy efficiency of multi-antenna cellular systems cannot be guaranteed. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a robust energy efficiency optimization method for multi-antenna communication systems based on IRS assistance, comprising:

[0006] S1: Establish an IRS-assisted secure transmission model for a multi-input single-output cellular communication system;

[0007] S2: Considering the uncertainties of all transmission link channels and the impact of multiple eavesdroppers, we establish a non-convex, multivariable coupled robust resource allocation problem with the goal of maximizing model energy efficiency, while simultaneously satisfying the security rate, maximum transmit power and continuous phase shift constraints of legitimate users.

[0008] S3: Using the continuous convex approximation method, the S-Procedure method, Schur's supplementary lemma, and the first-order Taylor expansion, the non-convex objective function and the robust constraints with parameter perturbations in the non-convex, multivariable coupled robust resource allocation problem with the goal of maximizing the energy efficiency of the system model are transformed into convex functions and deterministic constraints, respectively.

[0009] S4: The transformed problem is converted into a base station active beam optimization subproblem and an IRS passive beam optimization subproblem using an alternating iterative algorithm, and the resource allocation scheme is obtained.

[0010] Preferably, the IRS-assisted multiple-input single-output cellular communication system secure transmission model includes: a base station equipped with L antennas, an IRS containing N reflective elements, M legitimate users with single antennas, and K eavesdroppers with single antennas;

[0011] Using downlink transmission, a base station equipped with L antennas sends information to a legitimate user with M single antennas via a direct transmission link and an IRS containing N reflective elements. K eavesdroppers with single antennas eavesdrop on the user's information and use the IRS to reflect the signal back to the eavesdropper's location to interfere with their eavesdropping behavior.

[0012] Preferably, the uncertainty of all transmission link channels includes:

[0013]

[0014]

[0015] in, and Let f represent the first and second uncertainty sets, respectively; k This represents the direct channel gain from the base station to the k-th eavesdropper; F represents the estimated direct channel gain from the base station to the k-th eavesdropper; k This represents the cascaded channel gain from the base station to the k-th eavesdropper; Δf represents the estimated cascaded channel gain from the base station to the k-th eavesdropper. k ΔF represents the direct channel gain estimation error from the base station to the k-th eavesdropper. k This represents the cascaded channel gain estimation error from the base station to the kth eavesdropper. This represents the upper bound of the direct channel gain estimation error from the base station to the k-th eavesdropper. The upper bound of the cascaded channel gain estimation from the base station to the k-th eavesdropper is shown; g m This represents the direct channel gain from the base station to the legitimate user m; G represents the direct channel gain estimate from the base station to the m-th user; mThis represents the cascaded channel gain from the base station to the m-th legitimate user; Δg represents the estimated cascaded channel gain from the base station to the m-th legal user; m ΔG represents the direct channel gain estimation error from the base station to the m-th legitimate user; m This represents the cascaded channel gain estimation error from the base station to the m-th legitimate user; This represents the upper bound of the direct channel gain estimation error from the base station to the m-th legitimate user; This represents the upper bound of the cascaded channel gain estimation error from the base station to the m-th legitimate user.

[0016] Preferably, a non-convex, multivariable coupled robust resource allocation problem with the goal of maximizing system energy efficiency is established, including:

[0017]

[0018] stC1:R sec,m ≥R min,m

[0019]

[0020]

[0021]

[0022] Where w = [w1, ..., w M [] represents the base station beamforming matrix, and M represents the number of legitimate users; Let T denote the IRS phase shift vector, and T denote the transpose of the vector. α represents the parameter of the nth reflecting element of the IRS. n ∈[0,1] and θ n ∈[0,2π) represents the amplitude coefficient and phase shift of the nth reflecting element of the IRS, respectively; set α n =1, to obtain the maximum reflection gain, where j represents the imaginary unit. Represents any nth IRS reflective element; This represents the signal-to-interference-plus-noise ratio (SIR) of a legitimate user m. This represents the conjugate transpose of the direct channel gain from the base station to the legitimate user m. This represents the conjugate transpose of the IRS phase shift vector, w m This represents the beamforming vector sent by the base station to the legitimate user m. This represents the cascaded channel gain from the base station to the m-th legitimate user. This represents the conjugate transpose of the channel gain from the IRS to the m-th legitimate user, where H represents the channel gain from the base station to the IRS, and w -mThis represents the beamforming matrix excluding the m-th beam. P represents the noise variance at the m-th user; μ represents the power amplification factor; P c This represents the fixed circuit power consumption of the entire system; ||w m || 2 Represents the beamforming vector w m 2-norm; R sec,m This represents the safe rate for the m-th legitimate user. R U,m This represents the reachable rate of the m-th legitimate user. R m,k This represents the achievable rate at which eavesdropper k can eavesdrop on the m-th message. F represents the conjugate transpose of the direct channel gain from the base station to the eavesdropper k. k This represents the cascaded channel gain from the base station to the k-th eavesdropper. This represents the conjugate transpose of the channel gain from the IRS to the k-th eavesdropper; This represents the noise variance at the k-th eavesdropper. Represents arbitrary eavesdropping k; R min,m P represents the minimum security rate threshold required by user m; max Δg represents the maximum transmit power threshold of the base station. m ΔG represents the direct channel gain estimation error from the base station to the m-th legitimate user; m This represents the cascaded channel gain estimation error from the base station to the m-th legitimate user; Denotes the second set of uncertainties; Δf k ΔF represents the direct channel gain estimation error from the base station to the k-th eavesdropper. k This represents the cascaded channel gain estimation error from the base station to the kth eavesdropper. Let represent the first set of uncertainties.

[0023] Preferably, the non-convex objective function and the robust constraint with parameter perturbation are transformed into a convex function and a deterministic constraint, respectively, using the continuous convex approximation method, the S-Procedure method, Schur's complement lemma, and the first-order Taylor expansion, including:

[0024] S31: Introduce non-negative auxiliary variables η, κ and υ, and use the continuous convex approximation method to transform the non-convex objective function optimization problem into a convex function optimization problem;

[0025] S32: First, using the first-order Taylor inequality and matrix transformation Tr(AB)=vec H (A)vec(B) and We obtain the linear lower bound of the non-convex constraint; then we use the S-Procedure method and Schur's complement lemma to transform the robust constraint with parametric perturbation into a deterministic constraint.

[0026] S33: Apply the first-order Taylor expansion to obtain the approximate convex upper limit of the non-convex constraint, thus transforming the deterministic constraint into a convex constraint.

[0027] Preferably, the original problem is transformed into a base station active beamforming optimization subproblem and an IRS passive beamforming optimization subproblem using an alternating iterative algorithm, including:

[0028] S41: Fixed IRS phase shift The active beam optimization subproblem of the base station is transformed into a convex semi-positive definite programming problem.

[0029] S42: With the active beam w fixed, the IRS passive beam optimization subproblem is transformed into a convex semi-positive definite programming problem;

[0030] S43: Use the CVX toolbox to solve the two convex semi-positive definite programming problems mentioned above, and obtain the optimal w. * and Value, i.e., resource allocation scheme.

[0031] The beneficial effects of this invention are:

[0032] This invention considers the uncertainty of transmission link channels and the impact of multiple eavesdroppers to establish a multi-antenna communication system, which can maximize the communication quality of legitimate users and maximize the energy efficiency of the system. Compared with multi-antenna communication systems that consider ideal channel state information and do not have IRS assistance, this system has stronger robustness and security. Attached Figure Description

[0033] Figure 1 This is a flowchart of a robust energy efficiency optimization method for a multi-antenna communication system based on IRS assistance, according to the present invention.

[0034] Figure 2 This is a schematic diagram of the system model of the present invention;

[0035] Figure 3 A graph showing the relationship between the probability of security interruption and the upper bound of the user's direct channel error under different algorithms. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] In this invention, the following representation is used: (a) T This indicates the transpose of vector a or matrix a; (a) H This indicates the conjugate transpose of a complex vector a or a complex matrix a; (a) * This indicates the conjugation operation on vector a or matrix a; Let represent the mean of the random variable 'a'; |·| represents the modulus of the complex number; ||·||1 represents the 1-norm of the vector; ||·||2 represents the 2-norm of the vector; ||·|| F Denotes the Frobenius norm of a matrix; Represents an N×M dimensional complex matrix; Represents an N×M dimensional real matrix; diag(·) denotes vector diagonalization; tr(·) denotes the trace of a matrix; vec(·) denotes matrix vectorization; Indicates the Kronecker product; I N Represents an N×N dimensional identity matrix; O N This represents an N×N dimensional zero matrix.

[0038] A robust energy efficiency optimization method for IRS-assisted multi-antenna communication systems, such as Figure 1 As shown, it includes:

[0039] S1: Establish an IRS-assisted secure transmission model for a multi-input single-output cellular communication system;

[0040] S2: Considering the uncertainties of all transmission link channels and the impact of multiple eavesdroppers, we establish a non-convex, multivariable coupled robust resource allocation problem with the goal of maximizing model energy efficiency, while simultaneously satisfying the security rate, maximum transmit power and continuous phase shift constraints of legitimate users.

[0041] S3: Using the continuous convex approximation method, the S-Procedure method, Schur's supplementary lemma, and the first-order Taylor expansion, the non-convex objective function and the robust constraints with parameter perturbations in the non-convex, multivariable coupled robust resource allocation problem with the goal of maximizing the energy efficiency of the system model are transformed into convex functions and deterministic constraints, respectively.

[0042] S4: The transformed problem is converted into a base station active beam optimization subproblem and an IRS passive beam optimization subproblem using an alternating iterative algorithm, and the resource allocation scheme is obtained.

[0043] Construct an IRS-assisted secure transmission model for a multiple-input single-output cellular communication system: such as Figure 2As shown, a base station equipped with L antennas sends information to a legitimate user with M single antennas via a direct transmission link and an IRS containing N reflective elements. At the same time, K single-antenna eavesdroppers attempt to eavesdrop on the user's information. To prevent the user's information from being eavesdropped on, the IRS is used to reflect the signal back to the eavesdroppers' location, interfering with their eavesdropping behavior.

[0044] Assume that all channel gains follow a block fading model, meaning that the channel gains of the base station and users remain essentially constant over a certain period, and consecutive symbols suffer the same fading during this time. Define the user set as... The eavesdroppers are assembled as The set of reflection array sources is

[0045] Define the information s sent by the base station to M legitimate users as: Among them, s m This represents the information sent by the base station to the legitimate user m, and satisfies... The transmitted signal x can be represented as x = ws, where w is the beamforming matrix. This represents the beamforming vector sent by the base station to legitimate user m, and the received signal of the m-th legitimate user is represented as...

[0046]

[0047] in, This represents the cascaded channel gain from the base station to the m-th legitimate user; This represents the channel gain from the IRS to the m-th legitimate user; This represents the channel gain from the base station to the IRS; This represents the direct channel gain from the base station to the legitimate user m; For IRS phase shift vector, α represents the parameter of the nth reflecting element of the IRS. n ∈[0,1] and θ n ∈[0,2π) represents the amplitude coefficient and phase shift of the nth reflecting element of the IRS, respectively; set α n =1, to obtain the maximum reflection gain; The mean is 0 and the variance is at the m-th user. The noise; then the signal-to-interference-plus-noise ratio of the legitimate user m can be expressed as

[0048]

[0049] Among them, w -m w represents the beamforming matrix excluding the m-th beam. -m =[w1,…,w m-1 ,w m+1 ,…,wM Then, the reachable rate of user m is expressed as: In step S1, the received signal of the k-th eavesdropper is represented as

[0050]

[0051] in, This represents the cascaded channel gain from the base station to the k-th eavesdropper; This represents the channel gain from the IRS to the k-th eavesdropper; This represents the direct channel gain from the base station to the eavesdropper k; The mean is 0 and the variance is at the k-th eavesdropper. The noise; the signal-to-interference-plus-noise ratio when an eavesdropper k eavesdrops on user m's information is expressed as

[0052]

[0053] The achievable rate at which the eavesdropper at point k receives the m-th message is represented by R. m,k =log2(1+γ) m,k ).

[0054] Therefore, the safe rate R that the m-th legitimate user can obtain is sec,m (That is, the security rate) can be expressed as Among them, (a) + =max(a,0).

[0055] Considering channel uncertainty, a non-convex, multivariable coupled robust resource allocation problem is established with the goal of maximizing system energy efficiency, while simultaneously satisfying the security rate, maximum transmit power, and continuous phase shift constraints for legitimate users; specifically, a bounded channel error model is considered, namely...

[0056]

[0057]

[0058] in, and Represents a set of uncertainties; This represents the estimated direct channel gain from the base station to the k-th eavesdropper. Δf represents the estimated cascaded channel gain from the base station to the k-th eavesdropper. k ΔF represents the direct channel gain estimation error from the base station to the k-th eavesdropper. k This represents the cascaded channel gain estimation error from the base station to the kth eavesdropper. This represents the upper bound of the direct channel gain estimation error from the base station to the k-th eavesdropper. The upper bound of the cascaded channel gain estimation from the base station to the k-th eavesdropper is shown. This represents the direct channel gain estimate from the base station to the m-th user; Δg represents the estimated cascaded channel gain from the base station to the m-th legal user; m ΔG represents the direct channel gain estimation error from the base station to the m-th legitimate user; m This represents the cascaded channel gain estimation error from the base station to the m-th legitimate user; This represents the upper bound of the direct channel gain estimation error from the base station to the m-th legitimate user; This represents the upper bound of the cascaded channel gain estimation error from the base station to the m-th legitimate user.

[0059] Based on the above analysis, the robust resource allocation problem for maximizing system energy efficiency can be described as follows:

[0060]

[0061] stC1:R sec,m ≥R min,m

[0062]

[0063]

[0064]

[0065] Where μ represents the power amplification factor; P c Represents the fixed circuit power consumption of the entire system; C1 is the safe rate constraint for each user, R min,m C1 is the minimum security rate threshold required by user m; C2 is the maximum transmit power constraint of the base station; P max C1 is the maximum transmit power threshold of the base station; C2 is the phase shift constraint of the IRS reflector; C3 is the set of uncertainty parameters.

[0066] Using the continuous convex approximation method, the S-Procedure method, Schur's complement lemma, and the first-order Taylor expansion, non-convex objective functions and robust constraints with parameter perturbations are transformed into convex functions and deterministic constraints, respectively.

[0067] By introducing nonnegative auxiliary variables η, κ, and υ, and based on the continuous convex approximation method, the optimization problem can be reformulated as follows:

[0068]

[0069] stC1-C4

[0070]

[0071] C6:κ / v≥η

[0072]

[0073] For the non-convex constraints in P2, firstly, a slack variable r is introduced. m If C5 is processed, then constraint C5 becomes and Similarly, we introduce a slack variable φ m If constraint C1 is processed by ≥1, then constraint C1 becomes R. U,m (Δg m ,ΔG m )-log2φ m ≥R min,m and R m,k (Δf k ,ΔF k )≤log2φ m , where log2φ m Let R represent the maximum rate at which the eavesdropper eavesdrops on user m; according to the transformed form of constraint C5, then constraint R... U,m (Δg m ,ΔG m )-log2φ m ≥R min,m It can become

[0074] log2(1+r m )-log2φ m ≥R min,m

[0075] To handle constraints and R m,k (Δf k ,ΔF k )≤log2φ m Introducing auxiliary variable λ U,m ≥0 and λ m,k If ≥0, it can be transformed into the following expression.

[0076]

[0077]

[0078]

[0079]

[0080] set up and If the optimal solution is obtained in the i-th iteration, then according to the first-order Taylor inequality and according to Tr(AB) = vec H (A)vec(B) and but exist The lower linear bound at is

[0081]

[0082] The specific parameters are as follows:

[0083]

[0084] β m =c 1,m +c 2,m -q m ,β m =2Re{c m}-q m ,

[0085]

[0086]

[0087]

[0088]

[0089] Introducing slack variables and Then, according to the S-Procedure method, Transform into the following equivalent linear matrix inequalities

[0090]

[0091] in,

[0092] Similarly, introduce slack variables and Furthermore, through matrix transformation and the application of the S-Procedure method, then Can be converted into

[0093]

[0094] The specific parameters are as follows:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] Introducing slack variables and And based on Schur's complement lemma and the semidefinite relaxation method, It can be transformed into the following semidefinite constraint form

[0102]

[0103] in, and Similarly, introduce slack variables and And based on Schur's complement lemma and the semidefinite relaxation method, Can be converted

[0104]

[0105] in, and

[0106] To convexify constraint C6, this paper applies a first-order Taylor expansion to transform it, i.e. Here, the superscript i indicates the approximate value in the i-th iteration, and f(τ,ρ) is the value of τ / ρ around the point (τ). (i) ,ρ (i) The first-order Taylor expansion of ).

[0107] Based on the above analysis, It is denoted as the following formula

[0108]

[0109] Similarly, It is denoted as the following formula:

[0110]

[0111] The original problem is transformed into a base station active beamforming optimization subproblem and an IRS passive beamforming optimization subproblem using an alternating iterative algorithm, which are then solved to obtain the resource allocation scheme:

[0112] BS active beamforming optimization subproblem: fixed IRS phase shift Solve the active beam problem to obtain the optimal w * value.

[0113] At a given IRS phase shift In the case of [the specific condition], the optimization subproblem of the active beam w can be expressed as:

[0114]

[0115]

[0116]

[0117]

[0118]

[0119] C10:φ m ≥1

[0120] in, and In the constraints of problem P3 of and constraints d m This makes it non-convex, so applying the first-order Taylor expansion yields its approximate convex upper bound, i.e. and Problem P3 is a convex positive semidefinite programming problem. Using the CVX toolbox, the optimal value w can be obtained. * value.

[0121] IRS Passive Beam Optimization Subproblem: With the active beam w fixed, solve the IRS passive beam subproblem to obtain the optimal v. * value;

[0122] Based on the obtained w * Introduce slack variables z = [z1, ..., z 2N ] T Based on the framework of the first-order Taylor expansion and the penalty concavity / convexity process, passive beaming... The optimization subproblem can be expressed as:

[0123]

[0124]

[0125]

[0126]

[0127] C13:z≥0

[0128] Where, χ (i) It is a regularization factor that measures the impact of the penalty term ||z||1, and controls the feasibility of the constraint. of and d mBy employing the method of the BS active beamforming problem to obtain a convex approximate upper bound, problem P4 becomes a convex positive semi-definite programming problem. Solving this problem using the CVX toolbox yields the optimal solution. Value; the above solution to the two subproblems yields the optimal w. * and Value, i.e., resource allocation scheme.

[0129] The application effects of this invention are described in detail using simulation:

[0130] 1) Simulation conditions

[0131] Assume the channel model includes large-scale fading and small-scale fading, with the large-scale fading model being PL = -PL0 - 10αlog 10 (x)dB, where PL0 = -40dB is the path loss at a distance of 1m, x is the distance between a given user and its connected base station, α is the path loss factor, and small-scale fading follows Rayleigh fading. Assume the base station and IRS are located at (0m, 0m) and (50m, 10m) respectively. All users and eavesdroppers are randomly distributed in circles centered at (70m, 0m) and (40m, 0m) with radii of 5m. The path loss factor from the base station to the user / eavesdropper is 4, the path loss factor from the base station to the IRS is 2.2, and the path loss factor from the IRS to the user / eavesdropper is 2. Define the channel gain. and The upper bounds of the normalized error are respectively and for example: Other important simulation parameters are: P c =10dBm,P max =30dBm, μ=1, maximum number of iterations T max =10 5 ,R min,m =1.5 bits / Hz / s, convergence accuracy θ = 10 -5 .

[0132] 2) Simulation Results

[0133] Figure 3 The relationship between different methods and the probability of security interruption is presented. As can be seen from the figure, the probability of security interruption for different methods increases with the upper bound of the user channel error. Furthermore, the probability of security interruption for the method of this invention is significantly lower than that of other methods. This is because, under the same channel environment, the method of this invention considers the robustness of the system in advance, thus overcoming the influence of a certain range of channel errors.

[0134] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A robust energy efficiency optimization method for a multi-antenna communication system based on IRS assistance, characterized in that, include: S1: Establish an IRS-assisted secure transmission model for a multi-input single-output cellular communication system; The secure transmission model of an IRS-assisted multiple-input single-output cellular communication system includes: a base station equipped with L antennas, an IRS containing N reflective elements, M legitimate users with single antennas, and K eavesdroppers with single antennas. Using downlink transmission, a base station equipped with L antennas sends information to M legitimate users with a single antenna through a direct transmission link and an IRS containing N reflective elements. K eavesdroppers with single antennas eavesdrop on the user's information. The IRS is used to reflect the signal back to the eavesdropper's location to interfere with their eavesdropping behavior. S2: Considering the uncertainties of all transmission link channels and the impact of multiple eavesdroppers, establish a non-convex, multivariable coupled robust resource allocation problem with the goal of maximizing system energy efficiency, while satisfying the security rate, maximum transmit power and continuous phase shift constraints of legitimate users; All transmission link channel uncertainties include: in, and Let f represent the first and second uncertainty sets, respectively; k This represents the direct channel gain from the base station to the k-th eavesdropper; F represents the estimated direct channel gain from the base station to the k-th eavesdropper; k This represents the cascaded channel gain from the base station to the k-th eavesdropper; Δf represents the estimated cascaded channel gain from the base station to the k-th eavesdropper. k ΔF represents the direct channel gain estimation error from the base station to the k-th eavesdropper. k This represents the cascaded channel gain estimation error from the base station to the kth eavesdropper. This represents the upper bound of the direct channel gain estimation error from the base station to the k-th eavesdropper. The upper bound of the cascaded channel gain estimation from the base station to the k-th eavesdropper is shown; g m This represents the direct channel gain from the base station to the legitimate user m; G represents the direct channel gain estimate from the base station to the m-th user; m This represents the cascaded channel gain from the base station to the m-th legitimate user; Δg represents the estimated cascaded channel gain from the base station to the m-th legal user; m ΔG represents the direct channel gain estimation error from the base station to the m-th legitimate user; m This represents the cascaded channel gain estimation error from the base station to the m-th legitimate user; This represents the upper bound of the direct channel gain estimation error from the base station to the m-th legitimate user; This represents the upper bound of the cascaded channel gain estimation error from the base station to the m-th legitimate user; S3: Using the continuous convex approximation method, the S-Procedure method, Schur's supplementary lemma, and the first-order Taylor expansion, the non-convex objective function and the robust constraints with parameter perturbations in the non-convex, multivariable coupled robust resource allocation problem with the goal of maximizing the energy efficiency of the system model are transformed into convex functions and deterministic constraints, respectively. S4: The transformed problem is converted into a base station active beam optimization subproblem and an IRS passive beam optimization subproblem using an alternating iterative algorithm, and the resource allocation scheme is obtained.

2. The robust energy efficiency optimization method for a multi-antenna communication system based on IRS assistance according to claim 1, characterized in that, Establish a non-convex, multivariable coupled robust resource allocation problem with the goal of maximizing system energy efficiency, including: Where w = [w1, ..., w M [] represents the base station beamforming matrix, and M represents the number of legitimate users; Let T denote the IRS phase shift vector, and T denote the transpose of the vector. α represents the parameter of the nth reflecting element of the IRS. n ∈[0,1] and θ n ∈[0,2π) represents the amplitude coefficient and phase shift of the nth reflecting element of the IRS, respectively; set α n =1, to obtain the maximum reflection gain, where j represents the imaginary unit. Represents any nth IRS reflective element; This represents the signal-to-interference-plus-noise ratio (SIR) of a legitimate user m. This represents the conjugate transpose of the direct channel gain from the base station to the legitimate user m. This represents the conjugate transpose of the IRS phase shift vector, w m This represents the beamforming vector sent by the base station to the legitimate user m. This represents the cascaded channel gain from the base station to the m-th legitimate user. This represents the conjugate transpose of the channel gain from the IRS to the m-th legitimate user, where H represents the channel gain from the base station to the IRS, and w -m This represents the beamforming matrix excluding the m-th beam. P represents the noise variance at the m-th user; μ represents the power amplification factor; P c This represents the fixed circuit power consumption of the entire system; ||w m || 2 Represents the beamforming vector w m 2-norm; R sec,m This represents the safe rate for the m-th legitimate user. R U,m This represents the reachable rate of the m-th legitimate user. R m,k This represents the achievable rate at which eavesdropper k can eavesdrop on the m-th message. F represents the conjugate transpose of the direct channel gain from the base station to the eavesdropper k. k This represents the cascaded channel gain from the base station to the k-th eavesdropper. This represents the conjugate transpose of the channel gain from the IRS to the k-th eavesdropper; This represents the noise variance at the k-th eavesdropper. Represents arbitrary eavesdropping k; R min,m P represents the minimum security rate threshold required by user m; max Indicates the maximum transmit power threshold of the base station; Δg m ΔG represents the direct channel gain estimation error from the base station to the m-th legitimate user; m This represents the cascaded channel gain estimation error from the base station to the m-th legitimate user; Denotes the second set of uncertainties; Δf k ΔF represents the direct channel gain estimation error from the base station to the k-th eavesdropper. k This represents the cascaded channel gain estimation error from the base station to the kth eavesdropper. Let represent the first set of uncertainties.

3. The robust energy efficiency optimization method for a multi-antenna communication system based on IRS assistance according to claim 1, characterized in that, Using continuous convex approximation methods, the S-Procedure method, Schur's complement lemma, and first-order Taylor expansion, non-convex objective functions and robust constraints with parameter perturbations are transformed into convex functions and deterministic constraints, respectively, including: S31: Introduce non-negative auxiliary variables η, κ and v, and use the continuous convex approximation method to transform the non-convex objective function optimization problem into a convex function optimization problem; S32: First, using the first-order Taylor inequality and matrix transformation Tr(AB)=vec H (A)vec(B) and We obtain the linear lower bound of the non-convex constraint; then we use the S-Procedure method and Schur's complement lemma to transform the robust constraint with parametric perturbation into a deterministic constraint. S33: Apply the first-order Taylor expansion to obtain the approximate convex upper limit of the non-convex constraint, thus transforming the deterministic constraint into a convex constraint.

4. The robust energy efficiency optimization method for a multi-antenna communication system based on IRS assistance according to claim 1, characterized in that, The original problem is transformed into a base station active beamforming optimization subproblem and an IRS passive beamforming optimization subproblem using an alternating iterative algorithm, which are then solved as follows: S41: Fixed IRS phase shift The active beam optimization subproblem of the base station is transformed into a convex semi-positive definite programming problem. S42: With the active beam w fixed, the IRS passive beam optimization subproblem is transformed into a convex semi-positive definite programming problem; S43: Use the CVX toolbox to solve the two convex semi-positive definite programming problems mentioned above, and obtain the optimal w. * and Value, i.e., resource allocation scheme.

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