IRS-assisted NOMA network security rate maximization method under imperfect CSI

Abstract

The present invention claims a method for optimizing the security rate of NOMA network assisted by IRS under imperfect CSI. The method takes into account the situation that multiple eavesdroppers exist and the eavesdropping channel is imperfect CSI, and maximizes the security rate of NOMA network under the constraints of maximum base station transmission power, IRS phase shift, and SIC decoding. The present invention is based on the maximum security rate model of NOMA network assisted by IRS under imperfect CSI. First, the SIC decoding order is determined based on the combined channel gain of legitimate users. Based on slack variables, penalty functions, S-procedure and other methods, the objective function and constraints are converted into convex optimization problems, and then an alternating iterative algorithm is used to maximize the security rate of legitimate users. Compared with the resource allocation scheme of centralized deployment of IRS, random phase shift, and no IRS, the method provided by the invention can effectively improve the security rate of the system, and enhance the robustness of the NOMA network, and has strong practicality and feasibility.

Description

Technical Field

[0001] The present invention belongs to the field of resource allocation in NOMA networks, and specifically, relates to an IRS-assisted NOMA network security rate maximization method under imperfect CSI. Background Art

[0002] With the development of the fifth generation of mobile communication technology, the requirements for transmission rate for mobile communication devices and users are increasing day by day. In this context, how to achieve secure and reliable transmission while meeting large-scale connections and high spectrum efficiency has become an urgent problem to be solved. Non-Orthogonal Multiple Access (NOMA) has the advantages of improving spectrum efficiency and supporting large-scale connections, and is considered to be one of the promising technologies to solve these challenges. Specifically, NOMA allows the same time or frequency resources to serve multiple users at the same time, transmits information to users by superposition coding, and uses Successive Interference Cancellation (SIC) to decode at the receiving end to distinguish different signals. In addition, as an emerging technology, Intelligent Reflecting Surface (IRS) has attracted widespread attention from industry and academia due to its low cost, low power consumption, and the ability to reconfigure the wireless propagation environment by compensating for long-distance power loss to improve throughput. Combining it with NOMA can further improve the spectrum utilization of the network and the reliability of information transmission.

[0003] At present, in the IRS-assisted communication network resource allocation method, Yunpeng Feng et al. published an article entitled "Max-Min FairBeamforming for IRS-Aided Secure NOMA Systems" in IEEE Communications Letters, 2022, 26(2): 234-238. They only considered the communication scenario of two legitimate users and a single eavesdropper, and the eavesdropping channel has perfect channel state information (CSI). This scenario design is too simple and is not suitable for actual network application scenarios. Zheng Zhang et al. published an article entitled "Robust and Secure Communications in Intelligent Reflecting Surface Assisted NOMA Networks" in IEEE Communications Letters, 2021, 25(3): 739-743. They considered the eavesdropping channel as imperfect CSI, but also had only two legitimate users and a single eavesdropper, and minimized the base station transmit power by jointly optimizing the beamforming vector and IRS phase shift. The patent "A method for maximizing the security rate of an IRS-assisted NOMA drone network [P]. CN115002802A, 2022-05-10." publicly invented by Wang Zhengqiang et al. discloses a resource allocation method based on security rate maximization for a NOMA network. However, the method in this patent is aimed at the security rate in a communication scenario with a single eavesdropper and the eavesdropping channel with perfect CSI. It does not optimize the security rate of the NOMA network where multiple eavesdroppers exist and the base station cannot fully obtain the CSI of the eavesdropping channel. The proposed method cannot solve the situation where there are multiple eavesdroppers and the eavesdropping channel has non-perfect CSI.

[0004] From the above results, we can see that most scholars have studied the resource allocation in IRS-assisted NOMA networks, only considering the communication scenario where a single eavesdropper exists and the eavesdropping channel is an ideal CSI, or only considering minimizing the base station transmission power. Therefore, for communication scenarios with multiple legitimate users and multiple eavesdroppers, and considering the eavesdropping channel as an imperfect CSI, studying the IRS-assisted NOMA network security rate maximization method has important practical significance and application value. Summary of the invention

[0005] The present invention aims to solve the above problems of the prior art. A method for maximizing the security rate of NOMA network assisted by IRS under imperfect CSI is proposed. The technical solution of the present invention is as follows:

[0006] An IRS-assisted NOMA network security rate maximization method under imperfect CSI includes the following steps:

[0007] 101. Considering the existence of multiple eavesdroppers and the imperfect CSI of the eavesdropping channel, an IRS-assisted NOMA network security rate maximization model under imperfect CSI is established;

[0008] 102. Initialize the relevant parameters of the target problem, including the beamforming vector w k , IRS phase shift Θ, safe rate decision threshold ξ and rank-one accuracy ρ n ;

[0009] 103. Determine a SIC decoding order according to the combined channel gains of the legal users;

[0010] 104. According to the determined SIC decoding order and given IRS phase shift, a beamforming vector is solved and updated;

[0011] 105. According to the determined SIC decoding order, given the beamforming vector, the IRS phase shift is solved and updated;

[0012] 106. Inner iterative safety rate update convergence judgment: If the absolute value of the difference between the two safety rates is not greater than the safety rate decision threshold, and the positive penalty term ρ is less than the rank-one accuracy ρ n , the safe rate converges and gives the maximum safe rate of the inner layer; if the absolute value of the difference between the two safe rates is greater than the safe rate decision threshold, or the positive penalty term ρ is greater than or equal to the rank-one accuracy ρ n , then the safety rate at this time is saved, and the process jumps to step 105, until the safety rate meets the condition, and the maximum safety rate of the inner iteration is given;

[0013] 107. Outer layer iterative safety rate update convergence judgment: If the absolute value of the difference between the two safety rates and the ratio of the current safety rate are not greater than the safety rate decision threshold, the safety rate converges, the maximum safety rate of the outer layer is given, and the method ends; if the absolute value of the difference between the two safety rates and the ratio of the current safety rate are greater than the safety rate decision threshold, the safety rate at this time is saved and jumps to step 104 until the safety rate meets the conditions and the maximum safety rate is given.

[0014] Further, the step 101 is specifically as follows: considering the existence of multiple eavesdroppers and the imperfect CSI of the eavesdropping channel, the IRS-assisted NOMA network security rate maximization objective optimization problem under imperfect CSI is established:

[0015]

[0016] stC1:α n ∈[0,2π),1≤n≤N

[0017]

[0018] C3:R k ≤R j→k ,s(k)≤s(j)

[0019] C4:s(k)∈Ω

[0020] In the formula, R S,k For legitimate users U k The achievable safe speed, From the base station to the eavesdropper E l , IRS to eavesdropper E l The channel gain estimation error is, k is the legal user index value, K is the number of legal users; constraint C1 is the IRS phase shift constraint, α n is the phase shift of the nth reflective element of the IRS, N is the number of reflective elements of the IRS; constraint C2 is the maximum transmit power constraint of the base station, P max is the maximum transmission power of the base station; constraint C3 is to ensure the success of SIC decoding and achieve fairness among legitimate users, R k For U k The rate, R j→k For U k Decode the legitimate user U j The rate of s(k) and s(j) is U k , U j The decoding order of ; in constraint C4, Ω is the SIC decoding order set.

[0021] Further, the step 103 specifically includes: determining the SIC decoding order according to the combined channel gains of the legal users, and the optimization problem of maximizing the sum of the combined channel gains of all legal users is:

[0022]

[0023] U n,n =1, 1≤n≤N+1

[0024] U≥0

[0025] In the formula, is the introduced auxiliary channel gain matrix, From base station to legitimate user U k The channel gain, For IRS to legal users k The combined channel gain, For the Tth IRS to the legitimate user U kThe channel gain, G = [G1, ..., G T ] T is the combined channel gain from the base station to the IRS, G T is the channel gain from the base station to the Tth IRS, is the auxiliary phase shift matrix and vector introduced, is the IRS phase shift vector, α n is the phase shift of the nth reflective element of the IRS, and ≥ is a positive semi-definite sign.

[0026] Furthermore, in step 104, according to the determined SIC decoding order, given the IRS phase shift θ, the beamforming vector w is solved. k , specifically:

[0027] Fixed Θ, optimize the beamforming vector w k , the optimization problem is

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] In the formula, Is a legitimate user U k The lower bound of the rate SCA obtains is, For U k The combined channel gain, is the phase shift vector composed of the diagonal of the IRS phase shift matrix Θ, is the introduced auxiliary channel gain matrix, For IRS to U k The channel gain from the base station to the IRS is G, Base station to U k The channel gain, u t is the value of u in the tth iteration, s(j) and s(k) are legitimate users U k , U j The decoding order is For U k Gaussian noise, is w in the tth iteration jThe value of constraint C1 and constraint C2 are obtained by converting the eavesdropping rate containing uncertain parameters into finite linear matrix inequalities based on slack variables and S-procedure method. γ l,k , is the auxiliary variable introduced, for Using the first-order Taylor expansion, the feasible point is given in the tth iteration The upper bound of B,l >0,ε r,l >0 indicates that the base station is connected to the eavesdropper E l and IRS to E l The range of channel gain estimation error, is the auxiliary variable introduced, 0 represents the zero matrix, I represents the unit matrix, N represents the number of reflective elements of the IRS, and M represents the number of antennas of the base station; in constraint C2 is the joint beamforming matrix, For eavesdropper E l The denominator of the eavesdropping rate score is the feasible point at the tth iteration The lower bound obtained by the first-order Taylor expansion is (x) * represents the conjugate of x, is the auxiliary variable introduced, For E l The estimated channel matrix is For IRS to eavesdropper E l and base station to E l Estimated channel, For E l Gaussian noise; constrain C3 in P max is the maximum transmission power of the base station; constraint C4 is obtained by re-converting constraint C3 in problem P2 after determining the SIC decoding order, and the right side is At the feasible point of the tth iteration is a first-order Taylor expansion; constraint C5 is an introduced auxiliary variable constraint.

[0035] Furthermore, in step 105, according to the determined SIC decoding order, a beamforming vector w is given. k , solve for the IRS phase shift Θ, specifically:

[0036] Fixed beamforming vector w k , optimize the IRS phase shift Θ, the optimization problem is

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] In the formula, Is a legitimate user U k The lower bound of the rate SCA obtains is, For U k The combined channel gain, For IRS to U k The channel gain from the base station to the IRS is G, Base station to U k The channel gain, u t is the value of u in the tth iteration, For U k Gaussian noise, is w in the tth iteration j The value of ζ>0 indicates the constant proportional factor of the penalty term, and ρ is the positive penalty term; the constraint C1 is to Relaxed to convex LMI form and guaranteed rank-one constraint transformation, α n is the phase shift of the nth reflector element of the IRS, and the left side of the second equation is At the feasible point of the tth iteration is a first-order Taylor expansion; constraint C2 is obtained by re-transforming constraint C3 in problem P2 after determining the SIC decoding order. The right side is At the feasible point of the tth iteration is a first-order Taylor expansion; in constraint C3 γ l,k , is the auxiliary variable introduced, for Using the first-order Taylor expansion, the feasible point is given in the tth iteration The upper bound of B,l >0,ε r,l >0 indicates that the base station is connected to the eavesdropper E l and IRS to E l The range of channel gain estimation error, is the auxiliary variable introduced, 0 represents the zero matrix, I represents the unit matrix, N represents the number of reflective elements of the IRS, and M represents the number of antennas of the base station; in constraint C4 S i =[diag(s i ),0],V i =[diag(v i ), 0], s i 、v i for The singular value decomposition is performed, Indicates taking The first N values ​​of is the auxiliary variable introduced, For eavesdropper E l The estimated channel matrix is For E l Gaussian noise; constraint C5 is the introduced auxiliary variable constraint.

[0045] Furthermore, the step 106 specifically includes: comparing and the size of the safe rate decision threshold ξ, where is the safe rate of the nth inner iteration, is the safe rate of the n-1th inner iteration; if Not greater than ξ, and ρ<ρ n , ρ represents a positive penalty term, ρn represents rank-one accuracy, then the safe rate converges, giving the maximum safe rate of the inner iteration; if Greater than ξ or ρ ≥ ρ n , then the safety rate at this time is saved and the process jumps to step 105 until the safety rate meets the condition and the maximum safety rate of the inner iteration is given.

[0046] Furthermore, the step 107 specifically includes: comparing and the size of the safe rate decision threshold ξ, where is the safe rate of the tth outer iteration, is the safe rate of the t-1th outer iteration; if If is not greater than ξ, the safe rate converges and gives the maximum safe rate; if If it is greater than ξ, the safety rate at this time is saved and the process jumps to step 104 until the safety rate meets the condition and the maximum safety rate is given.

[0047] The advantages and beneficial effects of the present invention are as follows:

[0048] The present invention first determines the SIC decoding order based on the combined channel gain of the legitimate user under the constraints of the maximum transmission power of the base station, the IRS phase shift, and the SIC decoding. The objective function and the constraints are converted into a convex optimization problem by introducing slack variables, penalty functions, S-procedure, and the like, and then an alternating iterative algorithm is used to solve the maximum security rate of the legitimate user. The innovation of the present invention is that, in order to ensure that the IRS provides services to each legitimate user nearby, an IRS-assisted NOMA network under imperfect CSI is adopted. In addition, compared with the traditional simple scenario of only considering the existence of one eavesdropper, the existence of multiple eavesdroppers is considered in step 101, which is extended to a more practical communication scenario. In addition, since the eavesdropper usually eavesdrops on the information of the legitimate user in silence, the base station cannot fully obtain the ideal CSI of the eavesdropping channel. In step 101, the eavesdropping channel is considered to be imperfect CSI, which has the advantage of strong channel adaptability. In step 103, the SIC decoding order of the legitimate user is not directly set, but the SIC decoding order is determined based on the combined channel gain of the legitimate user. The present invention improves the system security rate compared with the centralized deployment of IRS, random phase shift and IRS-free schemes. It is particularly suitable for IRS-assisted NOMA networks where multiple eavesdroppers exist and the base station cannot fully obtain the CSI of the eavesdropping channel. It has good practical significance and application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 The system model of the IRS-assisted NOMA network under imperfect CSI in the preferred embodiment provided by the present invention;

[0050] Figure 2 It is an iterative convergence diagram of the present invention under different base station transmission powers and antenna numbers;

[0051] Figure 3 The maximum safe rate of the system under different base station transmission powers for the present invention and the comparison method;

[0052] Figure 4 The maximum safe rate of the system under different numbers of reflective elements for the present invention and the comparative method;

[0053] Figure 5 The maximum safe rate of the system of the present invention under different numbers of reflective elements and base station antennas and upper bounds of eavesdropping channel estimation errors;

[0054] Figure 6 A flowchart of a method for maximizing the security rate of NOMA networks assisted by IRS under imperfect CSI is provided for a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0055] The following will describe the technical solutions in the embodiments of the present invention in detail in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention.

[0056] The technical solution of the present invention to solve the above technical problems is:

[0057] Figure 6 A method for maximizing the security rate of NOMA network with IRS assistance under imperfect CSI is disclosed. The method comprises the following steps:

[0058] Step 1: Considering the existence of multiple eavesdroppers and the imperfect CSI of the eavesdropping channel, an IRS-assisted NOMA network security rate maximization model is established;

[0059] Step 2: Initialize the relevant parameters of the target problem, the beamforming vector w k , IRS phase shift Θ, safe rate decision threshold ξ, rank-one accuracy ρ n ;

[0060] Step 3: Determine the SIC decoding order based on the combined channel gain of the legitimate users;

[0061] Step 4: According to the determined SIC decoding order, given the IRS phase shift, the beamforming vector is solved and updated;

[0062] Step 5: According to the determined SIC decoding order, given the beamforming vector, solve the IRS phase shift and update it;

[0063] Step 6: Inner iterative safety rate update convergence judgment: If the absolute value of the difference between the two safety rates is not greater than the safety rate decision threshold, and the positive penalty term ρ is less than the rank-one precision, the safety rate converges and the maximum safety rate of the inner layer is given; if the absolute value of the difference between the two safety rates is not greater than the safety rate decision threshold, or the positive penalty term ρ is not less than the rank-one precision, the safety rate at this time is saved and jumps to step 105 until the safety rate meets the conditions, and the maximum safety rate of the inner iteration is given;

[0064] Step 7: Outer layer iterative safety rate update convergence judgment: If the absolute value of the difference between the two safety rates and the ratio of the current safety rate are not greater than the safety rate decision threshold, the safety rate converges, the maximum safety rate of the outer layer is given, and the method ends; if the absolute value of the difference between the two safety rates and the ratio of the current safety rate are not greater than the safety rate decision threshold, the safety rate at this time is saved and jumps to step 104 until the safety rate meets the conditions and the maximum safety rate is given.

[0065] Furthermore, the optimization problem of the IRS-assisted NOMA network security rate maximization objective under imperfect CSI established in the first step is:

[0066]

[0067] stC1:α n ∈[0,2π),1≤n≤N

[0068]

[0069] C3:R k ≤R j→k ,s(k)≤s(j)

[0070] C4:s(k)∈Ω

[0071] In the formula, R S,k For legitimate users U k The achievable safe speed, From the base station to the eavesdropper E l , IRS to eavesdropper E l The channel gain estimation error is, k is the legal user index value, K is the number of legal users; constraint C1 is the IRS phase shift constraint, α n is the phase shift of the nth reflective element of the IRS, N is the number of reflective elements of the IRS; constraint C2 is the maximum transmit power constraint of the base station, P max is the maximum transmission power of the base station; constraint C3 is to ensure the success of SIC decoding and achieve fairness among legitimate users, R k For U k The rate, R j→k For U k Decode the legitimate user U j The rate of s(k) and s(j) is U k , U j The decoding order of ; in constraint C4, Ω is the SIC decoding order set.

[0072] Furthermore, the second step initializes the relevant parameters of the target problem, the beamforming vector w k , IRS phase shift Θ, safe rate decision threshold ξ, rank-one accuracy ρ n .

[0073] Furthermore, the third step determines the SIC decoding order according to the combined channel gains of the legal users, and the optimization problem of maximizing the sum of the combined channel gains of all legal users is:

[0074]

[0075] Us n,n =1, 1≤n≤N+1

[0076] U≥0

[0077] In the formula, is the introduced auxiliary channel gain matrix, From base station to legitimate user U k The channel gain, For IRS to legal users k The combined channel gain, For the Tth IRS to the legitimate user U k The channel gain, G = [G1, ..., G T ] T is the combined channel gain from the base station to the IRS, G T is the channel gain from the base station to the Tth IRS, is the auxiliary phase shift matrix and vector introduced, is the IRS phase shift vector, α n is the phase shift of the nth reflective element of the IRS, and ≥ is a positive semi-definite sign.

[0078] Furthermore, the fourth step is to solve the beamforming vector according to the determined SIC decoding order and given the IRS phase shift θ, which is specifically:

[0079] Fixed Θ, optimize the beamforming vector w k , the optimization problem is

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] In the formula, Is a legitimate user U k The lower bound of the rate SCA obtains is, For U k The combined channel gain, is the phase shift vector composed of the diagonal of the IRS phase shift matrix Θ, is the introduced auxiliary channel gain matrix, For IRS to U k The channel gain from the base station to the IRS is G, Base station to U k The channel gain, u t is the value of u in the tth iteration, s(j) and s(k) are legitimate users U k , U j The decoding order is For U k Gaussian noise, is w in the tth iteration j The value of constraint C1 and constraint C2 are obtained by converting the eavesdropping rate containing uncertain parameters into finite linear matrix inequalities based on slack variables and S-procedure method. γ l,k , is the auxiliary variable introduced, for Using the first-order Taylor expansion, the feasible point is given in the tth iteration The upper bound of B,l >0,ε r,l >0 indicates that the base station is connected to the eavesdropper E l and IRS to E l The range of channel gain estimation error, is the auxiliary variable introduced, 0 represents the zero matrix, I represents the unit matrix, N represents the number of reflective elements of the IRS, and M represents the number of antennas of the base station; in constraint C2 is the joint beamforming matrix, For eavesdropper E l The denominator of the eavesdropping rate score is the feasible point at the tth iteration The lower bound obtained by the first-order Taylor expansion is (x) * represents the conjugate of x, is the auxiliary variable introduced, For E l The estimated channel matrix is For IRS to eavesdropper E l and base station to E l Estimated channel, For E l Gaussian noise; constrain C3 in P max is the maximum transmission power of the base station; constraint C4 is obtained by re-converting constraint C3 in problem P2 after determining the SIC decoding order, and the right side is At the feasible point of the tth iteration is a first-order Taylor expansion; constraint C5 is an introduced auxiliary variable constraint.

[0087] Furthermore, the fifth step is to solve the IRS phase shift according to the determined SIC decoding order and given beamforming vector, specifically:

[0088] Fixed beamforming vector wk , optimize the IRS phase shift Θ, the optimization problem is

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] In the formula, Is a legitimate user U k The lower bound of the rate SCA is obtained, ζ>0 represents the constant proportional factor of the penalty term, and ρ is the positive penalty term; constraint C1 is to Relaxed to convex LMI form and guaranteed rank-one constraint transformation, α n is the phase shift of the nth reflector element of the IRS, and the left side of the second equation is At the feasible point of the tth iteration is a first-order Taylor expansion; constraint C2 is obtained by re-transforming constraint C3 in problem P2 after determining the SIC decoding order. The right side is At the feasible point of the tth iteration is a first-order Taylor expansion; in constraint C3 γ l,k , is the auxiliary variable introduced, for Using the first-order Taylor expansion, the feasible point is given in the tth iteration The upper bound of B,l >0,ε r,l >0 indicates that the base station is connected to the eavesdropper E l and IRS to E l The range of channel gain estimation error, is the auxiliary variable introduced, 0 represents the zero matrix, I represents the unit matrix, N represents the number of reflective elements of the IRS, and M represents the number of antennas of the base station; in constraint C4 S i =[diag(s i ),0],V i =[diag(v i ), 0], si 、v i for The singular value decomposition is performed, Indicates taking The first N values ​​of is the auxiliary variable introduced, For eavesdropper E l The estimated channel matrix is For E l Gaussian noise; constraint C5 is the introduced auxiliary variable constraint.

[0097] Furthermore, the sixth step compares and the size of the safe rate decision threshold ξ, where is the safe rate of the nth inner iteration, is the safe rate of the n-1th inner iteration; if Not greater than ξ, and ρ<ρ n , ρ represents the positive penalty term, ρ n represents rank-one accuracy, then the safe rate converges and gives the maximum safe rate of the inner iteration; if Greater than ξ or ρ ≥ ρ n , then the safety rate at this time is saved and the process jumps to step 105 until the safety rate meets the condition and the maximum safety rate of the inner iteration is given.

[0098] Furthermore, the seventh step compares and the size of the safe rate decision threshold ξ, where is the safe rate of the tth outer iteration, is the safe rate of the t-1th outer iteration; if If is not greater than ξ, the safe rate converges and gives the maximum safe rate; if If it is greater than ξ, the safety rate at this time is saved and the process jumps to step 104 until the safety rate meets the condition and the maximum safety rate is given.

[0099] Under the constraints of the maximum transmission power of the base station, IRS phase shift, and SIC decoding, the present invention first determines the SIC decoding order based on the combined channel gain of the legitimate user, and transforms the objective function and constraints into a convex optimization problem by introducing slack variables, penalty functions, S-procedure, and other methods, and then uses an alternating iterative algorithm to solve the maximum security rate of the legitimate user. The innovation of the present invention is that, in order to ensure that the IRS provides services to each legitimate user nearby, an IRS-assisted NOMA network under imperfect CSI is adopted. In addition, compared with the traditional simple scenario that only considers the existence of one eavesdropper, the present invention considers the existence of multiple eavesdroppers and expands to a more practical communication scenario. In addition, since the eavesdropper usually eavesdrops on the information of the legitimate user in silence, the base station cannot fully obtain the ideal CSI of the eavesdropping channel. The present invention considers that the eavesdropping channel is imperfect CSI and has the advantage of strong channel adaptability. The present invention improves the system security rate compared with the centralized deployment of IRS, random phase shift, and IRS-free schemes, and is particularly suitable for IRS-assisted NOMA networks in actual eavesdropping scenarios, and has good practical significance and application value.

[0100] This embodiment is a method for maximizing the security rate of an IRS-assisted NOMA network under imperfect CSI. In an IRS-assisted NOMA network under imperfect CSI, the coordinates of the base station are (20, 0) m, equipped with M = 4 antennas. The coordinates of the first IRS are (5, 50) m, the coordinates of the second IRS are (35, 50) m, and the total number of IRS reflective elements is N = 10. Under imperfect CSI, two equivalent IRS deployments are considered for IRS, namely: The number of legitimate users is K = 4, randomly distributed in a circular area with a radius of 10m and a center at (20,50)m. The number of eavesdroppers is L = 2, randomly distributed in a circular area with a radius of 5m and a center at (20,70)m. The maximum transmission power of the base station is P max =30dBm, the noise power is The error range of the eavesdropping channel estimation is ε B,l =0.1,ε r,l = 0.1. The channels from the base station to the legitimate user and the eavesdropper are modeled as Rayleigh fading, the channel from the base station to the t-th IRS is modeled as a Ricean channel, and similarly the channel from the t-th IRS to the legitimate user and the eavesdropper is modeled as a Ricean channel.

[0101] In this example, Figure 1 This is a system model of an IRS-assisted NOMA network under non-perfect CSI in a preferred embodiment of the present invention. In the figure, a base station is equipped with M antennas to transmit information to a legitimate user through a direct link and an IRS with N reflective elements; Figure 2 It is an iterative convergence diagram of the present invention under different base station transmission powers and antenna numbers; Figure 3The maximum safe rate curve of the system of the present invention and the comparison method (perfect CSI, centralized IRS deployment, random phase shift, no IRS) under different base station transmission powers; Figure 4 The maximum safe rate curves of the systems of the present invention and the comparative method under different IRS reflective element conditions; Figure 5 The maximum safe rate of the system of the present invention under different numbers of reflective elements, base station antennas and upper bounds of eavesdropping channel estimation errors. Figure 2 It can be seen that the method proposed in this invention converges with the increase of the number of iterations. Figure 3 It can be seen that the proposed method is better than the comparison methods (centrally deployed IRS, random phase shift, and no IRS), and the gap with the ideal safety rate can be seen. Moreover, the maximum safety rate of the system of all methods increases with the increase of base station transmission power; Figure 4 It can be seen that the system safety rate increases with the increase in the number of IRS reflective elements, and the maximum safety rate of the proposed algorithm is higher than that of the comparison methods (centrally deployed IRS, random phase shift, and no IRS); Figure 5 It can be seen that under different numbers of reflective elements and base station antennas and upper bounds of eavesdropping channel estimation errors, the system security rate of the present invention increases with the increase in the number of base station antennas or the number of IRS reflective elements. It can also be seen that the system security rate decreases with the increase in the upper bound of the eavesdropping channel estimation error.

[0102] The systems, devices, modules or units described in the above embodiments may be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, the computer may be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0103] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0104] The above embodiments should be understood to be only used to illustrate the present invention and not to limit the protection scope of the present invention. After reading the contents of the present invention, technicians can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for maximizing the security rate of NOMA network with IRS assistance under imperfect CSI, characterized in that: The following steps are involved:

101. Considering the existence of multiple eavesdroppers and the imperfect CSI of the eavesdropping channel, an IRS-assisted NOMA network security rate maximization model under imperfect CSI is established; 102. Initialize the relevant parameters of the target problem, including the beamforming vector w k , IRS phase shift Θ, safe rate decision threshold ξ and rank-one accuracy ρ n ; 103. Determine a SIC decoding order according to the combined channel gains of the legal users; 104. According to the determined SIC decoding order and given IRS phase shift, a beamforming vector is solved and updated; 105. According to the determined SIC decoding order, given the beamforming vector, the IRS phase shift is solved and updated; 106. Inner iterative safety rate update convergence judgment: If the absolute value of the difference between the two safety rates is not greater than the safety rate decision threshold, and the positive penalty term ρ is less than the rank-one accuracy ρ n , the safe rate converges and gives the maximum safe rate of the inner layer; if the absolute value of the difference between the two safe rates is greater than the safe rate decision threshold, or the positive penalty term ρ is greater than or equal to the rank-one accuracy ρ n , then the safety rate at this time is saved, and the process jumps to step 105, until the safety rate meets the condition, and the maximum safety rate of the inner iteration is given; 107. Outer iterative safety rate update convergence judgment: If the absolute value of the difference between the two safety rates and the ratio of the current safety rate are not greater than the safety rate decision threshold, the safety rate converges, the maximum safety rate of the outer layer is given, and the method ends; if the absolute value of the difference between the two safety rates and the ratio of the current safety rate are greater than the safety rate decision threshold, the safety rate at this time is saved, and jump to step 104 until the safety rate meets the conditions and the maximum safety rate is given; The step 101 is specifically as follows: considering the existence of multiple eavesdroppers and the imperfect CSI of the eavesdropping channel, the IRS-assisted NOMA network security rate maximization objective optimization problem under imperfect CSI is established: In the formula, R S,k For legitimate users U k The achievable safe speed, From the base station to the eavesdropper E l , IRS to eavesdropper E l The channel gain estimation error is, k is the legal user index value, K is the number of legal users; Constraint C1 is the IRS phase shift constraint, α n is the phase shift of the nth reflective element of the IRS, and N is the number of reflective elements of the IRS; Constraint C2 is the maximum transmission power constraint of the base station, P max is the maximum transmission power of the base station; constraint C3 is to ensure the success of SIC decoding and achieve fairness among legitimate users, R k For U k The rate, R j→k For U k Decode the legitimate user U j The rate of s(k) and s(j) is U k , U j The decoding order of In constraint C4, Ω is the set of SIC decoding orders; The step 103 specifically includes: determining the SIC decoding order according to the combined channel gains of the legal users, and the optimization problem of maximizing the sum of the combined channel gains of all legal users is: In the formula, is the introduced auxiliary channel gain matrix, From base station to legitimate user U k The channel gain, For IRS to legal users k The combined channel gain, For the Tth IRS to the legitimate user U k The channel gain, G = [G1, ..., G T ] T is the combined channel gain from the base station to the IRS, G T is the channel gain from the base station to the Tth IRS, is the auxiliary phase shift matrix and vector introduced, is the IRS phase shift vector, α n is the phase shift of the nth reflector element of the IRS, ≥ is a semi-positive definite sign; In step 104, according to the determined SIC decoding order, given the IRS phase shift θ, the beamforming vector w is solved k , specifically: Fixed Θ, optimize the beamforming vector w k , the optimization problem is In the formula, Is a legitimate user U k The lower bound of the rate SCA obtains is, For U k The combined channel gain, is the phase shift vector composed of the diagonal of the IRS phase shift matrix Θ, is the introduced auxiliary channel gain matrix, For IRS to U k The channel gain from the base station to the IRS is G, For base station to U k The channel gain, u t is the value of u in the tth iteration, s(j) and s(k) are legitimate users U k , U j The decoding order is For U k Gaussian noise, is w in the tth iteration j The value of constraint C1 and constraint C2 are obtained by converting the eavesdropping rate containing uncertain parameters into finite linear matrix inequalities based on slack variables and S-procedure method. γ l,k , is the auxiliary variable introduced, for Using the first-order Taylor expansion, the feasible point is given in the tth iteration The upper bound of ε B,l >0,ε r,l >0 indicates that the base station is connected to the eavesdropper E l and IRS to E l The range of channel gain estimation error, is the auxiliary variable introduced, 0 represents the zero matrix, I represents the unit matrix, N represents the number of reflective elements of the IRS, and M represents the number of antennas of the base station; in constraint C2 is the joint beamforming matrix, For eavesdropper E l The denominator of the eavesdropping rate score is the feasible point at the tth iteration The lower bound obtained by the first-order Taylor expansion is (x) * represents the conjugate of x, is the auxiliary variable introduced, For E l The estimated channel matrix is For IRS to eavesdropper E l and base station to E l Estimated channel, For E l Gaussian noise; constrain C3 in P max is the maximum transmission power of the base station; constraint C4 is obtained by re-converting constraint C3 in problem P2 after determining the SIC decoding order, and the right side is At the feasible point of the tth iteration is a first-order Taylor expansion; constraint C5 is an auxiliary variable constraint introduced; In step 105, according to the determined SIC decoding order, a beamforming vector w is given k , solve for the IRS phase shift Θ, specifically: Fixed beamforming vector w k , optimize the IRS phase shift Θ, the optimization problem is In the formula, Is a legitimate user U k The lower bound of the rate SCA obtains is, For U k The combined channel gain, For IRS to U k The channel gain from the base station to the IRS is G, For base station to U k The channel gain, u t is the value of u in the tth iteration, For U k Gaussian noise, w t is the value of w in the tth iteration, ζ>0 represents the constant proportional factor of the penalty term, and ρ is the positive penalty term; constraint C1 is to set Relaxed to convex LMI form and guaranteed rank-one constraint transformation, α n is the phase shift of the nth reflector element of the IRS, and the left side of the second equation is At the feasible point of the tth iteration is a first-order Taylor expansion; constraint C2 is obtained by re-transforming constraint C3 in problem P2 after determining the SIC decoding order. The right side is At the feasible point of the tth iteration is a first-order Taylor expansion; in constraint C3 γ l,k , is the auxiliary variable introduced, for Using the first-order Taylor expansion, the feasible point is given in the tth iteration The upper bound of ε B,l >0,ε r,l >0 indicates that the base station is connected to the eavesdropper E l and IRS to E l The range of channel gain estimation error, is the auxiliary variable introduced, 0 represents the zero matrix, I represents the unit matrix, N represents the number of reflective elements of the IRS, and M represents the number of antennas of the base station; in constraint C4 S i =[diag(s i ),0],V i =[diag(v i ), 0], s i 、v i for The singular value decomposition is performed, Indicates taking The first N values ​​of is the auxiliary variable introduced, For eavesdropper E l The estimated channel matrix is For E l Gaussian noise; constraint C5 is the introduced auxiliary variable constraint.

2. The IRS-assisted NOMA network security rate maximization method under imperfect CSI according to claim 1 is characterized in that: The step 106 specifically includes: comparing and the size of the safe rate decision threshold ξ, where is the safe rate of the nth inner iteration, is the safe rate of the n-1th inner iteration; if Not greater than ξ, and ρ<ρ n , ρ represents the positive penalty term, ρ n represents rank-one accuracy, then the safe rate converges and gives the maximum safe rate of the inner iteration; if Greater than ξ or ρ ≥ ρ n , then the safety rate at this time is saved and the process jumps to step 105 until the safety rate meets the condition and the maximum safety rate of the inner iteration is given.

3. The IRS-assisted NOMA network security rate maximization method under imperfect CSI according to claim 2 is characterized in that: The step 107 specifically includes: comparing and the size of the safe rate decision threshold ξ, where is the safe rate of the tth outer iteration, is the safe rate of the t-1th outer iteration; if If is not greater than ξ, the safe rate converges and gives the maximum safe rate; if If it is greater than ξ, the safety rate at this time is saved and the process jumps to step 104 until the safety rate meets the condition and the maximum safety rate is given.

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