Uplink Security Energy Efficiency Maximization Design Method Based on Distributed Intelligent Reflecting Surface

Abstract

The present invention belongs to the technical field of uplink communication security energy efficiency optimization based on intelligent reflecting surfaces, and relates to a design method for maximizing uplink security energy efficiency based on distributed intelligent reflecting surfaces. The present invention gives the exact positions of the distributed IRS and the base station, as well as the estimated positions of the users and eavesdroppers. By reasonably designing the discretized reflection phase shift matrix set of the IRS, the transmission power of the user transmitter, and the switching states of the distributed IRS, a deployment scheme for maximizing the security energy efficiency of the communication system is achieved. The present invention provides a reference value method for maximizing the security energy efficiency of the distributed IRS-assisted uplink communication system.

Description

Technical Field

[0001] The present invention belongs to the technical field of uplink communication security energy efficiency optimization based on intelligent reflecting surfaces, and relates to a method for maximizing uplink security energy efficiency based on distributed intelligent reflecting surfaces. Background Art

[0002] With the 5G communication network entering the commercial era, the exploration of next-generation communication technologies is also underway to achieve faster and more reliable data transmission. Among these technologies, intelligent reflecting surfaces (IRSs) have attracted particular attention. The broad prospects of IRSs in future wireless networks have inspired extensive research on them by scholars. Among them, the most worthy of attention is communication security. Due to the increasingly complex communication environment, the security of private information urgently needs to be maintained and improved. Therefore, secure communication is crucial in the 6G communication network.

[0003] The biggest advantage of IRSs actually lies in being "passive", because each reflecting element of an IRS reflects signals passively, so compared with traditional active technologies, the hardware cost required by it is greatly reduced. Therefore, in an IRS-assisted communication system, in order to improve the security performance of the communication system, it often comes at the cost of increasing the number of passive reflecting elements of the IRS. However, when the legitimate user receiver is far from the IRS, even if the number of IRS reflecting elements is increased, the improvement in the security rate (SR) is not significant. In the simulated centralized IRS-assisted communication system, it is indeed possible to effectively improve the security performance by adjusting the deployment position of the IRS and increasing the number of IRS reflecting elements. However, considering the actual application, both the legitimate user receiver and the eavesdropping interference terminal are mobile, while the IRS is fixedly installed on the outer surface of some buildings, so it cannot be ensured that the position of the IRS is beneficial to all secure communication scenarios. If the total number of IRS elements is continuously increased, the security rate is likely not to be significantly improved, and energy will also be wasted.

[0004] It should be noted that although the secure communication problem based on IRSs has been studied under various system and channel settings, the existing work on IRS-assisted communication mainly focuses on a single IRS, and the work on multi-IRS scenarios is relatively limited. Moreover, the design of distributed IRS beamforming rarely takes into account practical limitations such as CSI defects. In fact, deploying a large number of IRSs in a wireless network is a more practical solution. On the one hand, IRSs have the advantages of limited cost, easy integration, and easy installation; on the other hand, distributed IRSs can provide multiple paths for received signals. Since the base station (BS)-IRS channel is expected to be low-rank in many practical cases, using distributed IRSs can generate a high-rank BS-IRS channel matrix, thereby enhancing the strength of received signals and the robustness of data transmission. Summary of the Invention

[0005] In view of the above-mentioned deficiencies in the prior art, this invention studies the security energy efficiency based on the scenario of distributed IRS. When the IRS is not properly deployed, a large number of IRS elements are required to improve the security performance, but too many IRS elements will reduce the energy efficiency, and the transmission energy of the uplink device (user side) is limited. Therefore, if there are multiple IRSs in the considered scenario, the most suitable IRS for assisting secure transmission can be selected to activate for auxiliary communication, and at this time, the improvement effect of the communication performance is the most significant. Based on this, this invention studies for the first time the security energy efficiency problem of a multi-IRS-assisted uplink communication system, optimizes the switching state, and selects and deploys a suitable IRS to further improve the security energy efficiency.

[0006] The purpose of this invention is to solve the security energy efficiency problem in a distributed IRS communication system. For the designed uplink single-input single-output (SISO) communication system, a method of flexibly selecting the IRS operation to maximize the security energy efficiency is proposed. The specific solution is as Figure 1 shown. By jointly optimizing the discrete phase shift matrix set Θ of the IRS, the transmit power P of the uplink device (user side), and the switching states x of multiple IRSs, only the most suitable IRS for assisting secure communication is selected and activated each time, reducing the redundant energy consumption, reasonably weighing the security rate and the total energy consumption, and achieving the purpose of maximizing the security energy efficiency of the communication system.

[0007] The technical solution adopted by this invention to solve the technical problem is as follows:

[0008] A design method for maximizing the uplink security energy efficiency based on a distributed intelligent reflecting surface is as follows:

[0009] The first step is to construct a system model:

[0010] In an uplink single-input single-output communication system, a single-antenna user sends a signal to a single-antenna base station (BS). During the signal transmission, an eavesdropper (Eve) will try to steal its information. Considering the introduction of L IRSs, each IRS has N adjustable reflection elements. By controlling the reflection coefficient of each reflection element, not only can the signal strength at the BS receiving end be enhanced, but also the signal strength of Eve can be weakened, thereby improving the security rate. For the convenience of expression, and are respectively defined as the sets of the number of reflection elements of the IRS and a single IRS, that is,

[0011] 1) First, construct a security rate model. In this model, the signals received at the BS / Eve ends can be expressed as:

[0012]

[0013] where \(x\) l \(\in \{0, 1\}\), and \(x\) l \(= 1\) indicates that the \(l\)-th IRS (IRS l ) is turned on, otherwise the \(l\)-th IRS is turned off; denotes the channel from IRS l to the BS / Eve side; denotes the channel from the User to IRS l ; is a diagonal matrix, which represents the phase shift matrix corresponding to IRS l , and \(\varphi\) li represents the phase shift change caused by the \(i\)-th element of IRS l ; \(h\) uk represents the direct link channel from the User to the BS / Eve side; \(s\) represents the information symbol at the User transmitter, and \(P\) is the transmission power at the User side; \(n\) i follows a normal distribution with an expectation of 0 and a variance of \(\sigma\) 2 , which represents the additive white Gaussian noise (AWGN) at the BS / Eve side.

[0014] The direct link model of this system can be expressed as:

[0015]

[0016] where \(L\) 0 represents the path loss constant in meters, \(d\) uk represents the distance from the User to the BS / Eve, and \(\alpha\) 1 represents the path attenuation exponent of the channel from the User to the BS / Eve. The indirect link model can be expressed as:

[0017]

[0018] where \(\beta\) j represents the Rice factor of the corresponding channel, and represent the line-of-sight (LoS) and Rayleigh fading components of the corresponding channel, respectively.

[0019] For the convenience of implementation in practical applications, the phase shift of the IRS is discretized here. The number of phase shift levels of each element of the IRS is represented by \(2\) b , and \(b\) represents the number of bits of the phase shift. Therefore, the set of discrete phase shift values at each element can be expressed as where \(\Delta\varphi = 2\pi / 2\) b .

[0020] ​​​​​​​Based on formula (1), the transmission rate expression at the BS / Eve side is:

[0021]

[0022] Therefore, the secrecy rate can be expressed as R s =[R b -R e + , where [x] + denotes taking the maximum value between x and 0.

[0023] 2) Construct an energy consumption model. The energy consumption of the communication system assisted by the distributed IRS is mainly divided into three parts: the transmission power P of the user, the total circuit power consumption P g of the base station, the user, and the eavesdropper, and the total power consumption of the L IRSs. Therefore, the total energy consumption of the system can be expressed as follows:

[0024]

[0025] where P n (b) represents the energy consumption of the nth reflection element of the IRS l , which is related to the number of discrete phase shift bits b.

[0026] The second step is to simplify the objective function and list the optimization problem:

[0027] According to the system settings, a secure energy efficiency maximization scheme for the distributed IRS-assisted uplink communication system is proposed. The specific optimization problem can be expressed as:

[0028]

[0029] s.t.P≤P max , (6b)

[0030]

[0031]

[0032] where Θ={Θ 1 ,…,Θ l ,…,Θ L}, represents the set of multiple IRS phase shift matrices, P max represents the maximum transmit power available at the user side, ​Obviously, problem (6) is a mixed-integer non-linear programming problem (MINLP), and it is usually difficult to find the global optimal solution for such problems. Accordingly, an iterative algorithm based on alternating optimization (AO) is proposed to solve this problem in three steps, and a near-optimal solution is obtained using a low-complexity solution method. The step flow is as Figure 2 shown.

[0033] In the third step, design an algorithm to solve the optimization problem:

[0034] Step S1: Fix the switch state set x and transmission power P of the L IRSs, and solve the phase shift matrix Θ.

[0035] First, let where Accordingly, the target problem (6) can be rewritten as:

[0036]

[0037] s.t. |v n | = 1, n = 1, 2, 3,..., Q, (7b)

[0038] where ρ = P / σ 2 , v n = e jφli , Q is the sum of the reflection elements of the L IRSs, i.e., L × N = Q. The solution steps are as follows:

[0039] S101: Obtain the optimal solution v * (μ) of v with respect to the parameter μ.

[0040] Adopt the Dinkelbach and MM algorithms, introduce the non-negative parameter μ, and obtain the upper bound of the original objective function where c is a constant, specifically expressed as X = λ max (H D )I Q , is the result of the previous iteration of v. Accordingly, rewrite problem (7) according to the upper bound:

[0041]

[0042] s.t. |v n | = 1, n = 1, 2, 3,..., Q. (8b)

[0043] The minimum value can only be obtained when v n and β n take the equality. Therefore, given μ, the optimal solution of v can be expressed as v *(μ) = (exp(jarg(β))) T , after obtaining this solution, compare the phase shift closest to v in

[0044] S102: Obtain the optimal solution of v (i.e., the phase shift matrix) through multiple iterations. The specific process is as Figure 2 shown in step 1 of

[0045] Step S2: Optimize the transmission power P and the switch state variable x. The specific steps are as follows:

[0046] S201: Fix the switch state set x and the phase shift matrix Θ, and obtain the optimal solution P * (λ) of P with respect to λ. First, define t 1 = |v H g B + h ub | 2 , t 2 = |v H g E + h ue | 2 , introduce a non - negative parameter λ, and problem (6) is simplified to:

[0047]

[0048] s.t. P ≤ P max . (9b)

[0049] By taking the second - order derivative of H(λ), it can be obtained that: when t 1 - t 2 > 0, H(λ) is a strictly concave function; otherwise, R s ≤ 0, and the secure energy efficiency is 0. Therefore, the root of

[0050] Case 1: If t 1 - t 2 > 0, then the expression for the optimal solution of problem (9) when λ is given is:

[0051]

[0052] If this solution expression is less than 0, it indicates that the channel condition is extremely poor or the gap between the legitimate channel and the eavesdropping channel is small, which is not conducive to energy - efficient secure transmission. At this time, set P * (λ) = 0.

[0053] Case 2: If t 1 - t 2≤ 0, then R s ≤ 0, the safety energy efficiency is directly 0 and there is no need to optimize P.

[0054] S202: Fix the set of phase shift matrices Θ and the transmission power P at the user side, and optimize the set of switching states x. The problem model is as follows:

[0055]

[0056]

[0057] S2021: Convert problem (11) into a convex function. The specific steps are as follows:

[0058] S20211: To handle the non-convex problem (11), first introduce two auxiliary variables s, q and a non-negative parameter λ, and problem (11) can be rewritten in the following form:

[0059]

[0060]

[0061]

[0062]

[0063] S20212: To solve the non-convexity of the constraint conditions (12b)(12c). It can be rewritten in the following form:

[0064]

[0065] where,

[0066]

[0067]

[0068]

[0069]

[0070]

[0071] In addition, to handle the coupling term x l x m , introduce a new variable z lm = x l x m , since x l ∈ {0, 1}, so z lm is equivalent to:

[0072] zlm ≥ x l + x m -1, 0 ≤ z lm ≤ 1, z lm ≤ x l , z lm ≤ x m (15)

[0073] where

[0074] Substituting (13) into problem (12), the constraint conditions (12b) and (12c) can be rewritten as:

[0075]

[0076]

[0077] Since (16b) is still non - convex. Therefore, write e q as the first - order Taylor expansion of q at :

[0078]

[0079] S20213: Relax (12d) to 0 ≤ x l ≤ 1.

[0080] According to S2021, the optimization problem model (12) can be rewritten as (18), and (18) is a standard convex optimization problem.

[0081]

[0082] s.t. ρD(x, z)+1 ≥ e s , (18b)

[0083]

[0084] z lm ≥ x l + x m -1, z lm ≤ x l , z lm ≤ x m , (18d)

[0085]

[0086]

[0087] S2022: The convex optimization problem (18) can be solved by the dual Lagrangian method. Its Lagrangian expression is:

[0088]

[0089] where γ = {γ 1lm , γ 2lm , γ 3lm} l＝2,…,L,m＝1,…,L-1 , and both α and β are non - negative Lagrange multipliers. Therefore, the dual Lagrangian form of problem (18) can be written as:

[0090]

[0091]

[0092]

[0093] S2023: Obtain the update expressions for the variables (x, z, γ, α, β, s, q) with respect to the dual problem (20).

[0094] S20231: Obtain the update expressions for the variables x l and z lm . It is observed that formula (19) is a linear function of the variables x l and z lm . Therefore, to maximize (19), the positive coefficients corresponding to x l and z lm must be 1. The positive coefficients can be obtained by taking the partial derivatives of (19), and when D l > C l it can also ensure the safety performance. Therefore, the optimal solutions for x l and z lm can be written as:

[0095]

[0096]

[0097] where:

[0098]

[0099] S20232: Obtain the update formula for the Lagrange multiplier γ. First, take γ 1lm (k) as an example. If z lm (k) ≥ x l + x m - 1, then γ 1lm (k) = 0; otherwise, use the bisection method according to (27) to find the one that satisfies z lm (k) ≥ x l + xm γ of -1 1lm (k) 。γ 2lm (k) and γ 3lm (k) can be updated respectively based on x m ≥ z lm (k) and x m ≥ z lm (k) using a similar method.

[0100] S20233: Obtain the updated formula of (α, β, s, q). According to formula (24), the optimal solution of variable s can be derived from the following formula:

[0101]

[0102] From formula (24), it can be seen that the update of variable s is also related to the Lagrange multiplier α. Therefore, s and α can be updated here by judging the constraint condition (18b). If s (k-1) satisfies the constraint condition (18b), then update Otherwise, update s (k) forcing it to satisfy the constraint condition, s (k) = ln(ρD(x, z)+1),

[0103] In addition, (19) is a linear function of variable q. Therefore, variable q can be updated using the subgradient method:

[0104]

[0105] β can also be updated using the subgradient method, where, φ i > 0 represents the step size.

[0106] S20234: Adopt the Dinkelbach method to jointly optimize the transmission power P and the switch state x. The specific process is as Figure 2 shown in step 2 of

[0107] Step S3: Jointly optimize step S1 and step S2 until the objective function converges.

[0108] The present invention proposes a double-loop algorithm to maximize the secure energy efficiency. In the outer loop, the original problem is divided into two algorithmic blocks for solution using alternating optimization. In each iteration, the two algorithmic blocks are alternately optimized. In each algorithmic block, the corresponding sub-problem is transformed into a convex problem, and each algorithmic block is optimized and solved through multiple iterations.

[0109] The beneficial effects of the present invention are as follows:

[0110] The present invention provides the exact positions of the distributed IRS and the base station, as well as the estimated positions of the users and eavesdroppers, and realizes a deployment scheme for maximizing the secure energy efficiency of the communication system by reasonably designing the discretized reflection phase shift matrix set of the IRS, the transmission power of the user transmitter, and the switching states of the distributed IRS. The present invention provides a reference value method for maximizing the secure energy efficiency of the distributed IRS-assisted uplink communication system. Description of the Drawings

[0111] Appendix Figure 1 is a schematic diagram of a secure uplink system based on a distributed IRS.

[0112] Appendix Figure 2 is a flowchart of the algorithm.

[0113] Appendix Figure 3 is a graph showing the variation of the secure rate and secure energy efficiency performance with P max under three different switching state operations.

[0114] Appendix Figure 4 shows the influence of the number of reflection elements of a single IRS on the secure energy efficiency performance of the distributed IRS and the centralized IRS.

[0115] Appendix Figure 5 is a graph of the ratio of the secure energy efficiency of the distributed IRS and the centralized IRS under two scenarios. Detailed Implementation Manner

[0116] To better understand the above technical solution, the following provides a specific analysis in combination with the drawings and specific implementation manners. First, the fixed parameters are given: IRS reflection element spacing = λ / 4, b = 3, L = 3, P n (b) = 1.5 mW, the circuit power consumptions of the user and the eavesdropper are 10 mW respectively, P g = 220 mW, σ 2 = -110 dBm, L 0 = -30 dBm, α 1 = 3.6, α 2 = 2.2, β j = 3 dB.

[0117] Example 1

[0118] Assume the user location is = [8, 0, 0], the legitimate base station receiver location is = [8, 100, 0], and the interfering eavesdropper location is = [5, 80, 0]; the positions of the three distributed IRSs are: IRS1 = [5, 0, 5], IRS2 = [5, 100, 5], IRS3 = [2, 150, 5]; the number of reflection elements of a single IRS is set to N = 16.

[0119] Figure 3 Shows the relationship between the maximum transmission power P max and the secure energy efficiency and the secure rate, considering three cases: optimizing the switch state, not optimizing the switch state, and randomizing the switch state. From Figure 3 it can be seen that the secure energy efficiency performance after optimizing the switch state is much better than that without optimizing the switch state and the random switch state. In terms of the comparison of the secure energy efficiency performance, the performance of the random switch state is also the worst. In addition, the secrecy rate of the optimized switch state is slightly lower than that of the non-optimized switch state and basically coincides at high P max values. This indicates that when the IRS position is not reasonably deployed (IRS3 = [2, 150, 5]), turning on this IRS cannot significantly improve the secure rate but will instead waste energy. Therefore, optimizing the switch state of the IRS is crucial for improving the secure energy efficiency of the distributed IRS, and the design of optimizing the switch state in this invention is reasonable.

[0120] Embodiment 2

[0121] mainly considers two distribution scenarios of d ub <d ue and d ub >d ue When d ub <d ue the coordinates of the user, the base station, and the eavesdropper are set to: [8, 40, 0], [8, 100, 0], [5, 140, 0]; when d ub <d ue the coordinates of the eavesdropper are changed to [5, 60, 0]. In both scenarios, the 3 IRSs are placed near the user, the base station, and the eavesdropper respectively, and the coordinates of the centralized IRS are set to: [5, 90, 0].

[0122] Figure 4 Shows the relationship between the secure energy efficiency performance of the distributed IRS and the centralized IRS and the number of reflection elements of a single IRS. The total number of elements of the distributed IRS is the same as the number of elements of the centralized IRS. From Figure 4 it can be seen that in both cases, the secure energy efficiency performance of the distributed IRS is always better than that of the centralized IRS. Specifically, when d ub <d ueWhen the number of individual IRS elements increases, the secure energy efficiency of both the distributed IRS and the centralized IRS first increases and then decreases, indicating that an excessive number of IRS elements may not be conducive to improving the secure energy efficiency. By recording the ratio of the secure energy efficiency of the distributed IRS to that of the centralized IRS, the specific table can be found in Figure 5 , the following conclusion can be drawn: as the number of individual IRS elements increases, due to the stronger reflection channels of the centralized IRS, the performance gap between the distributed IRS and the centralized IRS becomes smaller; d ub >d ue The ratio of the secure energy efficiency in the scenario is much larger than that in d ub <d ue . This shows that in a more challenging scenario with a stronger eavesdropping channel, the secure energy efficiency performance of using a distributed IRS is more superior than that of the traditional centralized IRS. Therefore, in the case where the eavesdropper is closer to the transmitter or the number of IRS elements is small, compared with the traditional centralized IRS, the present invention can effectively improve the secure rate by optimizing the switching state of the distributed IRS.

Claims

1. An uplink security energy efficiency maximization design method based on a distributed intelligent reflecting surface, characterized in that, it includes the following steps: The first step is to construct a system model: In an uplink single-input single-output communication system, a single-antenna user User sends a signal to a single-antenna base station BS. During the signal transmission, an eavesdropper Eve will try to steal its information; Consider introducing L IRSs, each of which has N tunable reflection elements. By controlling the reflection coefficients of each reflection element, not only can the signal strength at the BS receiver be enhanced, but also the signal strength at Eve can be weakened, thereby improving the security rate. For the sake of easy expression, we respectively define and as the sets of the number-of-reflection-element indicators of IRSs and a single IRS, that is 1) First, construct a security rate model; in this security rate model, the signals received at the BS / Eve ends are expressed as: where \(x\) l \(\in\{0,1\}\), \(x\) l \( = 1\) indicates that the \(l\)-th IRS (IRS l ) is turned on, otherwise the \(l\)-th IRS is turned off; denotes the channel from the IRS l to the BS / Eve side; denotes the channel from the User to the IRS l ; is a diagonal matrix, which represents the phase shift matrix corresponding to the IRS l , \(\varphi\) li represents the phase shift change caused by the \(i\)-th element of the IRS l ; \(h\) uk denotes the direct link channel from the User to the BS / Eve side; \(s\) represents the information symbol at the User transmitter, and \(P\) is the transmission power at the User side; \(n\) i follows a normal distribution with an expected value of 0 and a variance of \(\sigma\) 2 , which represents the additive white Gaussian noise AWGN at the BS / Eve side; The direct link model of this system is expressed as: Among them, L 0 represents the path loss constant in meters, d uk represents the distance from the User to the BS / Eve, α 1 represents the path attenuation exponent of the channel from the User to the BS / Eve, and the indirect link model is expressed as: Among them, β j represents the Rice factor of the corresponding channel, and respectively represent the line-of-sight propagation component and the Rayleigh fading component of the corresponding channel; Discretize the IRS phase shift. The number of phase shift levels of each element of the IRS is represented by 2 b denoted as, b represents the number of bits of the phase shift. Therefore, the set of discrete phase shift values at each element is expressed as where Δφ = 2π / 2 b ; Based on formula (1), the transmission rate expressions at the BS / Eve ends are: Therefore, the secrecy rate is expressed as R s = [R b - R e + , where [x] + denotes the maximum of x and 0;​ 2) Construct an energy consumption model; the energy consumption of the distributed IRS-assisted communication system is mainly divided into three parts: the transmission power \(P\) of the user, the total circuit power consumption \(P\) of the base station, the user, and the eavesdropper g and the total power consumption of \(L\) IRSs; therefore, the total energy consumption of this system is expressed as follows: Among them, P n (b) represents the energy consumption of the nth reflection element of the IRS l which is related to the number of bits b of the discrete phase shift; The second step is to simplify the objective function and list the optimization problem: According to the system settings, a security energy efficiency maximization scheme for a distributed IRS-assisted uplink communication system is proposed. The specific optimization problem is expressed as: s.t.P≤P max , (6b) where, Θ = {Θ 1 , …, Θ l , …, Θ L}, representing a set of multiple IRS phase shift matrices, P max represents the maximum transmit power available at the user terminal, Obviously, equations (6a) to (6d) form a mixed-integer non-linear programming problem MINLP, and it is usually difficult to find the global optimal solution for such problems. Accordingly, an iterative algorithm based on alternating optimization AO is proposed to solve this problem in three steps, and a near-optimal solution is obtained using a low-complexity solution method. The third step is to design an algorithm to solve the optimization problem: Step S1: Fix the switch state set x of L IRSs and the transmission power P, and solve the phase shift matrix Θ; Step S2: Optimize the transmission power P and the switch state variable x; Step S3: Jointly optimize Step S1 and Step S2 until the objective function converges.

2. The uplink security energy efficiency maximization design method based on a distributed intelligent reflecting surface as described in claim 1, characterized in that, for the said Step S1: Fix the switch state set x of L IRSs and the transmission power P, and solve the phase shift matrix Θ. The specific operations are as follows: First, let wherein Accordingly, formulas (6a) to (6d) are rewritten as: s.t. |v n | = 1, n = 1, 2, 3, ..., Q, (7b) where ρ = P / σ 2 , Q is the sum of the reflection elements of L IRSs, that is, L×N = Q; the solution steps are as follows: S101: Obtain the optimal solution v of v with respect to the parameter μ, v * (μ);​ Using the Dinkelbach and MM algorithms and introducing the non - negative parameter μ, an upper bound of the original objective function is obtained where c is a constant, specifically expressed as X = λ max (H D )I Q , which is the result of the previous iteration of v; accordingly, rewrite equations (7a) - (7b) according to the upper bound: s.t. |v n | = 1, n = 1, 2, 3,..., Q, (8b) Only when v n and β n take equal values can the minimum value be obtained; therefore, given μ, the optimal solution of v is expressed as v * (μ) = (exp(jarg(β))) T . After obtaining this solution, compare the phase shift closest to v in to discretize v; S102: Obtain the optimal solution of v through multiple iterations.

3. The uplink security energy efficiency maximization design method based on a distributed intelligent reflecting surface as described in claim 1 or 2, characterized in that, for the said Step S2: Optimize the transmission power P and the switch state variable x. The specific steps are as follows: S201: Fix the set of switch states \(x\) and the phase shift matrix \(\Theta\) to obtain the optimal solution \(P(\lambda)\) of \(P\) with respect to \(\lambda\); first, define \(t = |v_{g}+h|\), \(t = |v_{g}+h|\), introduce a non - negative parameter \(\lambda\), and Eqs. (6a) - (6d) are simplified as follows: * (\lambda); First, define \(t\) 1 = |v H g B + h ub | 2 , \(t\) 2 = |v H g E + h ue | 2 , introduce a non - negative parameter \(\lambda\), and Eqs. (6a) - (6d) are simplified as follows: s.t. P ≤ P max , (9b) By taking the second derivative of H(λ), we can obtain: when t 1 -t 2 > 0, H(λ) is a strictly concave function; otherwise, R s ≤ 0 and the safety energy efficiency is 0; therefore, the root of is the optimal solution of formulas (9a) to (9b); Therefore, the optimal solution of P with respect to λ can be obtained in the following two cases; Case 1: If t 1 -t 2 > 0, then when given λ, the optimal solution expressions of formulas (9a) to (9b) are as follows: If the solution expression is less than 0, it indicates that the channel condition is extremely poor or the gap between the legitimate channel and the eavesdropping channel is small, which is not conducive to energy-efficient secure transmission. At this time, set P * (λ) = 0; Case 2: If t 1 -t 2 ≤ 0, then R s ≤ 0, and the safety energy efficiency is directly 0 without the need to optimize P; S202: Fix the phase shift matrix set Θ and the transmission power P of the user side, and optimize the switch state set x; the problem model is as follows: S2021: Convert formulas (11a) - (11b) into convex functions; the specific steps are as follows: S20211: To process formulas (11a) - (11b), first introduce two auxiliary variables s, q and a non-negative parameter λ, and rewrite formulas (11a) - (11b) in the following form: S20212: To solve the non-convexity of formulas (12b) and (12c); rewrite them in the following form: where, In addition, to handle the coupling term x l x m , a new variable z is introduced lm = x l x m , since x l ∈{0,1}, then z lm is equivalent to: z lm ≥x l +x m -1.0 ≤ z lm ≤ 1, z lm ≤ x l , z lm ≤ x m , (15) wherein, l = 2, …, L, m = 1, …, L - 1; Substitute formula (13) into formulas (12a) - (12d), and rewrite the constraint conditions formulas (12b) and (12c) as: Since formula (16b) is still non-convex; thus, rewrite e q as the first-order Taylor expansion of q at : S20213: Relax the formula (12d) to 0 ≤ x l ≤ 1; According to S2021, optimize formulas (12a) - (12d) and rewrite them as formulas (18a) - (18f), which is a standard convex optimization problem; such that ρD(x, z) + 1 ≥ e s , (18b) z lm ≥x l +x m -1,z lm ≤x l ,z lm ≤x m ,(18d) S2022: Use the dual Lagrangian method to solve formulas (18a) - (18f); its Lagrangian expression is: where γ = {γ 1lm , γ 2lm , γ 3lm}, l = 2, …, L, m = 1, …, L - 1, and both α and β are non - negative Lagrange multipliers; thus, the dual Lagrangian form of equations (18a) to (18f) is written as: S2023: Obtain the update expressions of variables (x, z, γ, α, β, s, q) with respect to formula (20).

4. The uplink security energy efficiency maximization design method based on a distributed intelligent reflecting surface as described in claim 3, characterized in that, S2023: Obtain the update expressions of variables \((x, z, \gamma, \alpha, \beta, s, q)\) with respect to formula (20), and the specific operations are as follows: S20231: Obtain the update expressions for variables x l and z lm ; It is observed that formula (19) is a linear function of variables x l and z lm . Therefore, to maximize formula (19), the positive coefficients corresponding to x l and z lm must be 1. The positive coefficients can be obtained by taking the partial derivative of formula (19), and when D l > C l , the safety performance can also be guaranteed; thus, the optimal solutions of x l and z lm are written as follows: Where: S20232: Get the updated formula of Lagrange multiplier γ; first use γ 1lm (k) For example, if z lm (k) ≥x l +x m -1, then γ 1lm (n) = 0; otherwise, use the binary search method to find the value that satisfies z lm (k) ≥x l +x m -1 gamma 1lm (k) ; γ 2lm (n) and γ 3lm (n) Based on x m ≥z lm (k) and x m ≥z lm (k) Update with similar method; S20233: Obtain the update expressions of \((\alpha, \beta, s, q)\); according to formula (24), the optimal solution of variable \(s\) is derived from the following formula: According to formula (24), the update of variable s is also related to the Lagrange multiplier α. Therefore, s and α can be updated here by judging the constraint formula (18b); if s (k-1) satisfies formula (18b), then update Otherwise, update s ( k ) Force it to satisfy formula (18b), s (k) = ln(ρD(x,z)+1), In addition, formula (19) is a linear function of variable \(q\); therefore, variable \(q\) is updated using the subgradient method: β can also be updated by the subgradient method, wherein, φ i > 0 represents the step size; S20234: Use the Dinkelbach method to jointly optimize the transmission power \(P\) and the switch state \(x\).

5. The uplink secure energy efficiency maximization design method based on a distributed intelligent reflecting surface as described in claim 3, characterized in that S2023: Obtain the update expressions of variables \((x, z, \gamma, \alpha, \beta, s, q)\) with respect to formula (20), and the specific operations are as follows: S20231: Obtain the update expressions for variables x l and z lm ; It is observed that formula (19) is a linear function of variables x l and z lm . Therefore, to maximize formula (19), the positive coefficients corresponding to x l and z lm must be 1. The positive coefficients can be obtained by taking the partial derivative of formula (19), and when D l > C l , the safety performance can also be guaranteed. Therefore, the optimal solutions of x l and z lm are written as follows: Where: S20232: Get the updated formula of Lagrange multiplier γ; first use γ 1lm (k) For example, if z lm (k) ≥x l +x m -1, then γ 1lm (n) = 0; otherwise, use the binary search method to find the value that satisfies z lm (k) ≥x l +x m -1 gamma 1lm (k) ; γ 2lm (n) and γ 3lm (n) Based on x m ≥z lm (k) and x m ≥z lm (k) Update with similar method; S20233: Obtain the update expressions of \((\alpha, \beta, s, q)\); according to formula (24), the optimal solution of variable \(s\) is derived from the following formula: According to formula (24), the update of variable s is also related to the Lagrange multiplier α. Therefore, s and α can be updated by judging formula (18b) here; if s (k-1) satisfies formula (18b), then update Otherwise, update s ( k ) Force it to satisfy formula (18b), s (k) = ln(ρD(x,z)+1), In addition, formula (19) is a linear function of variable \(q\); therefore, variable \(q\) is updated using the subgradient method: β can also be updated using the subgradient method, wherein, φ i > 0 represents the step size; S20234: Use the Dinkelbach method to jointly optimize the transmission power \(P\) and the switch state \(x\).

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