A Safety Rate Maximization Design Method Assisted by IRS under Interruption Probability Constraints

Abstract

This invention discloses an IRS-assisted secure rate maximization design method under interruption probability constraints, belonging to the field of wireless communication technology. In a communication system model involving a transmitter, smart reflector, desired receiver, and eavesdropper, this invention introduces a probabilistic constraint to ensure the interruption probability of the secure transmission system remains within a tolerable range, proposing a secure rate maximization problem with this constraint: since phase shift, power allocation, and transmission rate are coupled in the objective function and the probabilistic constraint. This paper first utilizes the exponential distribution of received signal power to transform the difficult-to-handle probabilistic constraint into a deterministic constraint. Then, using the Alternating Optimization (AO) method to fix the beamforming matrix of the transmitter and the phase shift matrix of the smart reflector respectively, and through inequality transformations and solving the Rayleigh quotient problem, it effectively solves the problem of optimal phase shift, power allocation, and transmission rate design for secure transmission under uncertain channel conditions, where the probabilistic constraints of coupled variables are difficult to handle.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to an IRS-assisted method for maximizing the safe rate under interruption probability constraints. Background Technology

[0002] The massive data transmissions in the Internet of Things (IoT) era have raised serious concerns about security, making physical layer security a key consideration in future wireless network design. In recent years, to improve physical layer security, Intelligent Reflectors (IRS) have been introduced. IRS typically consist of a number of low-cost reflective elements, each capable of reflecting reconfigurable phase shifts and amplitudes of incident electromagnetic waves. IRS-based communication offers significant advantages in improving spectral efficiency and enhancing physical layer security. Specifically, when a legitimate receiver and an eavesdropper are aligned with the base station (BS), the channel response of the legitimate user will be highly correlated with the eavesdropper's. This makes traditional beamforming, which directs energy to the legitimate receiver, also advantageous to the eavesdropper. Therefore, using beamforming solely on the transceiver is insufficient to guarantee security. Since deploying IRS provides greater freedom for the legitimate receiver's additional transmission links while eliminating the directionality towards the eavesdropper, it can significantly improve the quality of service for legitimate users, reduce information leakage, and thus enhance secure transmission performance.

[0003] Due to its numerous advantages, IRS is widely considered for physical layer security to improve secure rate performance. This paper assumes that the eavesdropper's channel has perfect Channel State Information (CSI) and that the eavesdropper is considered an unscheduled active user in the network. Under this assumption, secure transmission using IRS can achieve higher secure rates compared to transmissions with random or fixed phase shift matrices. However, even if the eavesdropper is an unplanned active user in the network, CSI estimation and acquisition are more challenging than in traditional communication systems due to the cascading channels introduced by IRS. Although channel estimation schemes for IRS systems have recently been proposed, assuming perfect CSI for the eavesdropper remains unrealistic. Because of the uncertainty in the eavesdropper's CSI, the possibility of security transmission disruptions needs to be considered.

[0004] Therefore, to ensure that the outage probability of the secure transmission system remains within a tolerable range, the secure transmission system design of this invention introduces a probabilistic constraint, which poses a challenge for further analysis. Furthermore, phase shift, power allocation, and transmission rate are coupled within the objective function and the probabilistic constraint. To address these challenges, this paper first utilizes the exponential distribution of the received signal power to transform the cumbersome probabilistic constraint into a deterministic constraint. An optimization problem based on the receiver security rate and eavesdropper redundancy rate is constructed under the constraints of SOP and transmission power budget. Then, an alternating iterative optimization algorithm is used to optimize the variables, thereby obtaining a reasonably optimal solution. Summary of the Invention

[0005] The purpose of this invention is to design an optimal secure transmission that maximizes the achievable secure rate under SOP constraints and transmission power budget.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A safety rate maximization design method assisted by IRS under interruption probability constraints, specifically including the following steps:

[0008] S1. Construct a communication system model: Select the transmitter (Alice), intelligent reflector (IRS), eavesdropper (Eve), and receiver (Bob) as the entities to be studied in the communication system model;

[0009] S2. Derive the probability of security interruption of receiver (Bob) due to eavesdropper (Eve): Calculate the signal-to-noise ratio distribution function based on the statistical channel information of eavesdropper (Eve) and construct a redundancy rate characterization of the security interruption probability; transform the difficult-to-handle probabilistic constraints into deterministic constraints based on the exponential distribution of received signal power.

[0010] S3. Constructing an optimization problem: Under the constraints of security outage probability and transmission power budget, construct a problem to maximize the achievable secure rate;

[0011] S4. Simplify the optimization problem: Analyze and simplify the optimization problem constructed in S3, and simplify the problem of maximizing the safe rate under the constraint of safe interruption probability into an optimization problem that only depends on two scalars;

[0012] S5. Alternating Optimization Variables: Based on the simplified optimization problem in S4, the AO algorithm is used to further simplify the optimization problem. The phase shift matrix and beamforming matrix are fixed respectively. First, the beamforming matrix is ​​fixed and the optimal phase shift matrix is ​​obtained. Then, the obtained phase shift matrix is ​​fixed and the optimal beamforming matrix is ​​obtained. The iteration is continued until the objective function value converges. Then, the optimal phase shift matrix and beamforming matrix of the objective function are derived and determined.

[0013] S6. Simulation Experiment: Design a simulation experiment and conduct simulations based on the method proposed in S5 to verify the effectiveness of the proposed secure rate maximization transmission design method.

[0014] Preferably, S1 specifically includes the following:

[0015] Assuming the transmitter has multiple antennas, and both the receiver and the eavesdropper are expected to have single antennas (one in each case); using smart reflectors to improve secure transmission performance, ignoring signals reflected twice or more by the smart reflectors; considering the impact of quasi-static flat fading on all channels in the system, the baseband equivalent channels of Alice-IRS, Alice-Bob, and IRS-Bob are expressed as follows: Due to the passive and unauthorized nature of the eavesdropping, Alice only knows the statistical channel state information of the IRS-Eve channel and the Alice-Eve channel, respectively.

[0016] Let χ ij This represents large-scale path loss. Where β0 represents the channel power gain at a reference distance of 1m; d ij α represents the distance between node i and node j; ij This represents the corresponding path loss exponent, where ij∈{ar,ab,ae,rb,re} corresponds to different channels, and and This represents the corresponding small-scale fading coefficient;

[0017] Assuming the phase of the smart reflector elements changes continuously and the signal suffers no power loss from each reflector element, the diagonal reflection matrix of the smart reflector phase shift coefficient can be expressed as:

[0018]

[0019] Assuming the amplitude of each element is equal to 1, θ n Let ∈ [0, 2π) represent the phase shift of the nth element of the merged incident signal, where n = 1, ..., N. Therefore, the transmitted signal of the transmitter can be represented as:

[0020] x=ws (1)

[0021] Where s:CN(0,1) represents an independent information signal. Indicates the beamforming vector;

[0022] Assume the transmitter has a maximum transmit power budget P max Then w H w≤P max ;

[0023] The received signal y from the receiver b Represented as:

[0024]

[0025] The eavesdropper's received signal y eRepresented as:

[0026]

[0027] in, This represents the channel vector between the transmitter and the desired receiver. H represents the channel vector from the smart reflector to the desired receiver. ar This represents the channel vector from the transmitter to the smart reflector; n b The Gaussian white noise of the receiver follows an n-order property. b : That is, the circle with zero mean is symmetric, and the variance is The noise vector.

[0028] Preferably, S2 specifically includes the following:

[0029] The channel capacity of the eavesdropper is expressed as:

[0030]

[0031] in, This represents the channel vector between the transmitter and the eavesdropper. This represents the channel vector from the smart reflector to the desired receiver; n e The Gaussian white noise of the receiver follows an n-order property. e : That is, the circle with zero mean is symmetric, and the variance is The noise vector.

[0032] When the channel capacity of the eavesdropper is C e Redundancy R exceeding the user's e When a security breach occurs at the transmitter, the probability that a security breach will occur at the receiver due to an eavesdropper is:

[0033]

[0034] Here, SOP represents the probability of an interruption caused by Rayleigh fading. Using the exponential distribution of received signal power under Rayleigh fading conditions, a closed-form expression for SOP is derived. The specific derivation process is as follows:

[0035] First, define for:

[0036]

[0037] in, and (H) ar w) n They represent and H ar The nth element of w It follows a complex Gaussian distribution with a mean of 0 and a variance of δ.

[0038] in,

[0039] Following an exponential distribution, we obtain:

[0040]

[0041] In summary, the expression for SOP is:

[0042]

[0043] Where, χ ae and χ re These represent the large-scale path loss from the receiver to the eavesdropper and the large-scale path loss from the smart reflector to the eavesdropper, respectively.

[0044] Preferably, S3 specifically includes the following:

[0045] Based on the communication model constructed in S1, the channel capacity at the receiver is given by the following formula:

[0046]

[0047] Therefore, the safe rate maximization problem is formulated as follows:

[0048]

[0049] Where ε∈(0,1) is a predefined upper bound, representing the maximum tolerable SOP; P max This indicates the maximum transmit power at the receiver.

[0050] Preferably, S4 specifically includes the following:

[0051] A1. According to equation (8), constrain the interruption probability p so ≤ε is equivalent to:

[0052]

[0053] A2. Simplify the optimization problem by using the properties of functions. In problem (10), R e Decreasing the value of the objective function increases the value of the objective function. When the C1 inequality is equal, we obtain R. e The optimal value is represented by the following function:

[0054]

[0055] Substituting equation (12) into the optimization problem (10), we get:

[0056]

[0057] Preferably, S5 specifically includes the following:

[0058] B1. The optimization problem is solved using the AO algorithm, with a fixed transmitted beamforming w, and the phase shift matrix Θ is optimized; by applying variables... The optimization problem can be represented as:

[0059]

[0060] Where v = [v1,...,v] N ] T ;

[0061] Based on the properties of inequalities, the objective function (14) satisfies the following inequality:

[0062]

[0063] Among them, if and only if The equation holds; arg(·) represents the component direction phase of the complex vector; then the optimal θ in the optimal problem of formula (14) is:

[0064]

[0065] B2. Finding the beamforming matrix w with a fixed phase shift matrix Θ, the optimization problem is expressed as:

[0066]

[0067] Among them, let The beamforming vector of the transmitter is designed and written as... in, P represents the transmitter's unit beamforming carrier; w This represents the corresponding power allocation factor;

[0068] Will Substituting into formula (17), the original optimization problem is transformed into the following form:

[0069]

[0070] The safe rate must be greater than or equal to 0, that is, the objective function in formula (18) must be greater than or equal to 1, thus yielding the inequality:

[0071]

[0072] When the inequality in formula (19) holds, for any given beamforming vector The objective function in optimization problem (17) with respect to P w Monotonically increasing; consider P w ≤P max Under the constraints, the optimal power allocation factor is obtained as follows:

[0073]

[0074] Then, in order to determine the optimal unit beamforming vector The original optimization problem is transformed into the following form:

[0075]

[0076] The optimization problem (21) is a standard Rayleigh quotient problem, and its optimal unit beamforming vector is... The eigenvectors corresponding to the largest eigenvalue of the matrix given in the following formula are:

[0077]

[0078] The optimal w is obtained as

[0079] Finally, the w obtained in B2 is used... * Given w in B1, calculate Θ by iterating cyclically until the objective function value converges, in order to obtain the optimal w and Θ.

[0080] Compared with existing technologies, this invention provides an IRS-assisted safe rate maximization design method under interruption probability constraints, which has the following beneficial effects:

[0081] (1) The present invention fully considers the uncertainty of the eavesdropper's CSI, and improves the maximum secure transmission rate while ensuring that the interruption probability of the secure transmission system is within a tolerable range.

[0082] (2) This invention solves the problem of coupling phase shift, beamforming matrix and transmission rate in objective function and probability constraint through mathematical properties.

[0083] (3) The present invention can make full use of the alternating iterative optimization algorithm to solve the variables in turn, which greatly reduces the difficulty of solving the problem. Attached Figure Description

[0084] Figure 1 This is a system schematic diagram of an IRS-assisted safe rate maximization design method under interruption probability constraints proposed in Embodiment 1 of the present invention;

[0085] Figure 2 This is a schematic diagram of the algorithm flow for an IRS-assisted safe rate maximization design method under interruption probability constraints proposed in Embodiment 1 of the present invention;

[0086] Figure 3 This is a schematic diagram of the change curve of the safe rate as a function of the number of transmitter antennas in the IRS-assisted safe rate maximization design method under interruption probability constraints proposed in Embodiment 2 of the present invention.

[0087] Figure 4 This is a schematic diagram of the curve showing the change of the safety rate with the horizontal position of the smart reflector in the IRS-assisted safety rate maximization design method under interruption probability constraints proposed in Embodiment 2 of the present invention. Detailed Implementation

[0088] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0089] Example 1:

[0090] Please see Figure 1-2 This invention proposes an IRS-assisted safe rate maximization design method under interruption probability constraints, which specifically includes the following steps:

[0091] Step 1: Construct a communication system model: Select the transmitter (Alice), intelligent reflector (IRS), eavesdropper (Eve), and receiver (Bob) as the entities to be studied in the communication system model, specifically including the following:

[0092] Assuming the transmitter has multiple antennas, and both the receiver and the eavesdropper are expected to have single antennas (one in each case); using smart reflectors to improve secure transmission performance, ignoring signals reflected twice or more by the smart reflectors; considering the impact of quasi-static flat fading on all channels in the system, the baseband equivalent channels of Alice-IRS, Alice-Bob, and IRS-Bob are expressed as follows: Due to the passive and unauthorized nature of the eavesdropping, Alice only knows the statistical channel state information of the IRS-Eve channel and the Alice-Eve channel, respectively.

[0093] Let χ ij This represents large-scale path loss. Where β0 represents the channel power gain at a reference distance of 1m; d ij α represents the distance between node i and node j; ij This represents the corresponding path loss exponent, where ij∈{ar,ab,ae,rb,re} corresponds to different channels, and and This represents the corresponding small-scale fading coefficient;

[0094] Assuming the phase of the smart reflector elements changes continuously and the signal suffers no power loss from each reflector element, the diagonal reflection matrix of the smart reflector phase shift coefficient can be expressed as:

[0095]

[0096] Assuming the amplitude of each element is equal to 1, θ n Let ∈ [0, 2π) represent the phase shift of the nth element of the merged incident signal, where n = 1, ..., N. Therefore, the transmitted signal of the transmitter can be represented as:

[0097] x=ws (1)

[0098] Where s:CN(0,1) represents an independent information signal. Indicates the beamforming vector;

[0099] Assume the transmitter has a maximum transmit power budget P max Then w H w≤P max ;

[0100] The received signal y from the receiver b Represented as:

[0101]

[0102] The eavesdropper's received signal y e Represented as:

[0103]

[0104] in, This represents the channel vector between the transmitter and the desired receiver. H represents the channel vector from the smart reflector to the desired receiver. ar This represents the channel vector from the transmitter to the smart reflector; n b The Gaussian white noise of the receiver follows an n-order property. b : That is, the circle with zero mean is symmetric, and the variance is The noise vector.

[0105] Step 2: Derive the probability of a security breach at the receiver (Bob) due to an eavesdropper (Eve): Calculate the signal-to-noise ratio distribution function based on the eavesdropper's (Eve's) statistical channel information, and construct a redundancy rate characterization of the security breach probability; based on the exponential distribution of the received signal power, transform the difficult-to-handle probabilistic constraints into deterministic constraints, specifically including the following:

[0106] The channel capacity of the eavesdropper is expressed as:

[0107]

[0108] in, This represents the channel vector between the transmitter and the eavesdropper. This represents the channel vector from the smart reflector to the desired receiver; n e The Gaussian white noise of the receiver follows an n-order property. e : That is, the circle with zero mean is symmetric, and the variance is The noise vector.

[0109] When the channel capacity of the eavesdropper is C e Redundancy R exceeding the user's e When a security breach occurs at the transmitter, the probability that a security breach will occur at the receiver due to an eavesdropper is:

[0110]

[0111] Here, SOP represents the probability of an interruption caused by Rayleigh fading. Using the exponential distribution of received signal power under Rayleigh fading conditions, a closed-form expression for SOP is derived. The specific derivation process is as follows:

[0112] First, define for:

[0113]

[0114] in, and (H) ar w) n They represent and H ar The nth element of w It follows a complex Gaussian distribution with a mean of 0 and a variance of δ.

[0115] in,

[0116] Following an exponential distribution, we obtain:

[0117]

[0118] In summary, the expression for SOP is:

[0119]

[0120] Where, χ ae and χ re These represent the large-scale path loss from the receiver to the eavesdropper and the large-scale path loss from the smart reflector to the eavesdropper, respectively.

[0121] Step 3: Construct the optimization problem: Given the security outage probability constraint and transmission power budget in Step 2, construct the problem of maximizing the achievable secure rate, which includes the following:

[0122] The objective of this invention is to design an optimal secure transmission that maximizes the achievable secure rate within SOP constraints and transmission power budget.

[0123] Based on the communication model constructed in S1, the channel capacity at the receiver is given by the following formula:

[0124]

[0125] Therefore, the safe rate maximization problem is formulated as follows:

[0126]

[0127] Where ε∈(0,1) is a predefined upper bound, representing the maximum tolerable SOP; P max This indicates the maximum transmit power at the receiver.

[0128] Step 4: Simplify the optimization problem: Analyze and simplify the optimization problem constructed in Step 3, reducing the problem of maximizing the safe rate under the constraint of safe interruption probability to an optimization problem that only involves two scalars, specifically including the following:

[0129] Step 4.1: According to equation (8), the probability of security interruption can be constrained to p. so The equivalent representation of ≤ε is:

[0130]

[0131] Step 4.2: Simplify the optimization problem using the properties of the function, and note that R should be reduced in (10). e This will cause the value of the objective function to increase. Therefore, when the C1 inequality reaches equality, we obtain R. e The optimal value is expressed as:

[0132]

[0133] Substituting equation (12) into the optimization problem (10), we can obtain:

[0134]

[0135] Step 5: Alternating Iterative Optimization of Variables: Based on the simplified optimization problem in Step 4, the AO algorithm is proposed to further simplify the optimization problem. The phase shift matrix and beamforming matrix are fixed respectively. First, the beamforming matrix is ​​fixed, and the optimal phase shift matrix is ​​found. Then, the obtained phase shift matrix is ​​fixed to obtain the optimal beamforming matrix. This process is iterated until the objective function value converges. Finally, the optimal phase shift matrix and beamforming matrix of the objective function are derived and determined, specifically including the following:

[0136] Step 5.1: The AO algorithm is used to solve the optimization problem. First, the transmitted beamforming w is fixed to optimize the phase shift matrix Θ. This is achieved by applying variables... The optimization problem can be represented as:

[0137]

[0138] Where v = [v1,...,v] N ] T ;

[0139] Based on the properties of inequalities, the objective function (14) satisfies the following inequality:

[0140]

[0141] Among them, if and only if The equation holds; arg(·) represents the component direction phase of the complex vector; then the optimal θ in the optimal problem of formula (14) is:

[0142]

[0143] Step 5.2: Calculate the beamforming matrix w with the phase shift matrix Θ fixed. The optimization problem is expressed as:

[0144]

[0145] Among them, let The beamforming vector of the transmitter is designed and written as... in, P represents the transmitter's unit beamforming carrier; w This represents the corresponding power allocation factor;

[0146] Will Substituting into formula (17), the original optimization problem is transformed into the following form:

[0147]

[0148] The safe rate must be greater than or equal to 0, that is, the objective function in formula (18) must be greater than or equal to 1, thus yielding the inequality:

[0149]

[0150] When the inequality in formula (19) holds, for any given beamforming vector The objective function in optimization problem (17) with respect to P w Monotonically increasing; consider P w ≤P max Under the constraints, the optimal power allocation factor is obtained as follows:

[0151]

[0152] Then, in order to determine the optimal unit beamforming vector The original optimization problem can be transformed into the following form:

[0153]

[0154] The optimization problem (21) is a standard Rayleigh quotient problem, and its optimal unit beamforming vector is... The eigenvectors corresponding to the largest eigenvalue of the matrix given in the following formula are:

[0155]

[0156] The optimal w is obtained as

[0157] Finally, the w obtained in B2 is used... * Given w in B1, calculate Θ by iterating cyclically until the objective function value converges, in order to obtain the optimal w and Θ.

[0158] Example 2:

[0159] Based on Example 1, but with a difference: to demonstrate the correctness and effectiveness of the above derivation results, the advantages of the proposed security performance optimization algorithm for security interruption probability protection are further verified through simulation. For practicality, the specific simulation parameters are set as follows: a three-dimensional coordinate system is considered. Alice, Bob, Eve, and IRS are located at (0, 0, 0), (70, 10, 0), (70, -10, 0), and (70, 0, 5), respectively. The path loss index from Alice to IRS is set to 2.4, the path loss index from Alice to Bob and Alice to Willie is set to 3.6, and the path loss index from IRS to Eve and IRS to Bob is 3.0. Unless otherwise specified, the values ​​of the remaining parameters are as follows:

[0160] IRS element count N = 50, transmitter antenna count M = 8, desired noise levels at the receiver (Bob) and the eavesdropper (Eve) are equal (i.e. The upper bound of the interruption probability is ε = 0.05. The algorithm's iteration termination condition is a target difference of 0.0001, and the achievable safe rate is obtained by averaging the safe rates corresponding to 500 random channels.

[0161] Please see Figure 3 ,like Figure 3 The figure shows the curves of the system's average secure rate as a function of the number of intelligent reflective surface units (IRS) under different upper bounds of the security outage probability ε. This reflects the relationship between the average secure rate performance and the tolerable security outage probability (SOP). Simulation results show that, all other things being equal, a smaller ε leads to a decrease in the achievable secure rate performance. In fact, this result is completely consistent with actual communication conditions, because the magnitude of ε measures the security level, and a smaller value forces a larger redundancy rate R to avoid security outage events, thus reducing the achievable secure rate performance. Furthermore, when the upper bound of the security outage probability ε is constant, it can be observed that the system's average secure rate increases with the increase of the number of IRS. This is because, as the number of IRS reflective units increases, the reflected signal strength also continuously increases, thus better interfering with eavesdroppers. This demonstrates that IRS can effectively improve the security of wireless communication systems.

[0162] Please see Figure 4 , Figure 4The figure shows the curves of the system's average security rate as a function of the horizontal position of the IRS under different upper bounds of the security outage probability ε. It can be observed that the system security rate reaches its peak when the IRS is at a horizontal position of 70. To explain this phenomenon, we need to review the horizontal coordinates of each node and find that the horizontal coordinates of both the eavesdropper Eve and the legitimate receiver Bob are at 70. The principle behind the IRS's ability to improve wireless system security lies in its ability to weaken the eavesdropper Eve's signal while simultaneously strengthening the legitimate receiver's signal. When the IRS is also at a horizontal position of 70, it is closest to both the eavesdropper Eve and the legitimate receiver Bob. Therefore, at this point, the path loss of the IRS reflected signal is minimized, the signal weakening effect on the eavesdropper and the signal strengthening effect on the legitimate receiver are maximized, the superposition of various system gains reaches its maximum, and the security rate naturally reaches its peak. It can be seen that after reaching the peak, the farther the horizontal position of the IRS is from the transmitter Alice, the smaller its gain effect on the security rate of the wireless communication system. This is because as the IRS moves further away from the transmitter, the received signal weakens due to path attenuation and other environmental factors. Consequently, the reflected signal from the IRS also weakens, reducing its weakening effect on the eavesdropper's signal and its enhancement effect on the legitimate receiver. This explains why the secure rate decreases with a horizontal distance greater than 70 units. It's conceivable that as the distance between the IRS and the transmitter further increases, its gain on the overall secure rate of the wireless communication system will decrease until it approaches the secure rate and transmission power achievable by a wireless communication system without an IRS. Therefore, the optimal horizontal location for IRS deployment should be a compromise that accommodates both the eavesdropper Eve and the legitimate receiver Bob, and should avoid being placed too far from the transmitter Alice. Finally, it can be directly observed that, at various locations shown in the diagram, the wireless communication system with IRS assistance achieves a higher secure rate while meeting security interruption and power constraints compared to the wireless communication system without IRS, proving that the IRS can effectively improve the system's security performance.

[0163] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for maximizing safe rate with IRS assistance under interruption probability constraints, characterized in that, Specifically, the following steps are included: S1. Construct a communication system model: Select the transmitter, intelligent reflector, eavesdropper, and receiver as the entity research objects of the communication system model; S2. Derive the probability of security interruption of the receiver due to eavesdroppers: Calculate the signal-to-noise ratio distribution function based on the statistical channel information of the eavesdropper, and construct a redundancy rate characterization of the security interruption probability; transform the difficult-to-handle probabilistic constraints into deterministic constraints based on the exponential distribution of the received signal power. S3. Constructing an optimization problem: Under the constraints of security outage probability and transmission power budget, constructing a problem to maximize the achievable secure rate; S4. Simplify the optimization problem: Analyze and simplify the optimization problem constructed in S3, and simplify the problem of maximizing the safe rate under the constraint of safe interruption probability into an optimization problem that only depends on two scalars; S5. Alternating Optimization Variables: Based on the simplified optimization problem in S4, the AO algorithm is used to further simplify the optimization problem. The phase shift matrix and beamforming matrix are fixed respectively. First, the beamforming matrix is ​​fixed and the optimal phase shift matrix is ​​obtained. Then, the obtained phase shift matrix is ​​fixed and the optimal beamforming matrix is ​​obtained. The iteration is continued until the objective function value converges. Then, the optimal phase shift matrix and beamforming matrix of the objective function are derived and determined. S6. Simulation Experiment: Design a simulation experiment and conduct simulations based on the method proposed in S5 to verify the effectiveness of the proposed secure rate maximization transmission design method.

2. The IRS-assisted safe rate maximization design method under interruption probability constraints according to claim 1, characterized in that, S1 specifically includes the following: Assuming the transmitter has multiple antennas, and both the receiver and the eavesdropper are expected to have single antennas (one in each case); using smart reflectors to improve secure transmission performance, ignoring signals reflected twice or more by the smart reflectors; considering the impact of quasi-static flat fading on all channels in the system, the baseband equivalent channels of Alice-IRS, Alice-Bob, and IRS-Bob are expressed as follows: , , Based on the passive and unauthorized nature of the eavesdropping, Alice only knows the statistical channel state information of the IRS-Eve channel and the Alice-Eve channel, respectively. , ; make This represents large-scale path loss. ,in, This represents the channel power gain at a reference distance of 1 m. Represents a node With nodes The distance between them; This represents the corresponding path loss index. Corresponding to different channels, and , , , and This represents the corresponding small-scale fading coefficient; Assuming the phase of the smart reflector elements changes continuously and the signal suffers no power loss from each reflector element, the diagonal reflection matrix of the smart reflector phase shift coefficient can be expressed as: Assuming the amplitude of each element is equal to 1, The first incident signal after merging Phase shift of each element, Therefore, the transmitter's transmitted signal can be represented as: （1） in, Indicates independent information signals, Indicates the beamforming vector; Assume the transmitter has a maximum transmit power budget. ,but ; The received signal of the receiver Represented as: （2） The signal received by the eavesdropper Represented as: （3） in, This represents the channel vector between the transmitter and the desired receiver. This represents the channel vector from the smart reflector to the desired receiver. This represents the channel vector from the transmitter to the smart reflector; The white Gaussian noise of the receiver is represented by the following expression: That is, the circle with zero mean is symmetric and the variance is The noise vector; n e The white Gaussian noise of the receiver is represented by the following expression: n e ~CN(0, That is, the zero-mean circle is symmetric, and the variance is The noise vector.

3. The IRS-assisted safe rate maximization design method under interruption probability constraints according to claim 2, characterized in that, S2 specifically includes the following: The channel capacity of the eavesdropper is expressed as: （4） in, This represents the channel vector between the transmitter and the eavesdropper. This represents the channel vector from the smart reflector to the desired receiver; When the channel capacity of the eavesdropper Exceeding the user's redundancy rate When a security breach occurs at the transmitter, the probability that a security breach will occur at the receiver due to an eavesdropper is: （5） Here, SOP represents the probability of an interruption caused by Rayleigh fading. Using the exponential distribution of received signal power under Rayleigh fading conditions, a closed-form expression for SOP is derived. The specific derivation process is as follows: First, define for: （6） in, and They represent and The nth element, It follows a complex Gaussian distribution with a mean of 0 and a variance of . δ ; in, ; Following an exponential distribution, we obtain: （7） In summary, the expression for SOP is: （8） in, and These represent the large-scale path loss from the receiver to the eavesdropper and the large-scale path loss from the smart reflector to the eavesdropper, respectively.

4. The IRS-assisted safe rate maximization design method under interruption probability constraints according to claim 3, characterized in that, S3 specifically includes the following: Based on the communication model constructed in S1, the channel capacity at the receiver is given by the following formula: （9） Therefore, the safe rate maximization problem is formulated as follows: （10） in, This is a predefined upper bound, representing the maximum tolerable SOP; This indicates the maximum transmit power at the receiver.

5. The IRS-assisted safe rate maximization design method under interruption probability constraints according to claim 4, characterized in that, S4 specifically includes the following: A1. Constrain the interruption probability according to equation (8) The equivalent representation is: （11） A2. By simplifying the optimization problem using the properties of functions, in problem (10), Decreasing the value of the objective function increases the value of the objective function. When the C1 inequality becomes equal, we obtain... The optimal value is represented by the following function: （12） Substituting equation (12) into the optimization problem (10), we get: （13）。 6. The IRS-assisted safe rate maximization design method under interruption probability constraints according to claim 5, characterized in that, S5 specifically includes the following: B1. Solve the optimization problem using the AO algorithm, with a fixed transmit beamforming. Optimize the phase shift matrix By applying variables The optimization problem can be expressed as: （14） in ; ; , ; Based on the properties of inequalities, the objective function (14) satisfies the following inequality: （15） Among them, if and only if The equation holds true; The component direction phase represents the complex vector; then the optimal solution in equation (14) is optimal. for: （16） B2, Fixed Phase Shift Matrix Find the beamforming matrix The optimization problem is expressed as: （17） Among them, let , The beamforming vector of the transmitter is designed and written as follows: ,in, , Indicates the transmitter's unit beamforming carrier; This represents the corresponding power allocation factor; Will Substituting into formula (17), the original optimization problem is transformed into the following form: （18） The safe rate must be greater than or equal to 0, that is, the objective function in formula (18) must be greater than or equal to 1, thus yielding the inequality: （19） When the inequality in formula (19) holds, for any given beamforming vector The objective function in optimization problem (18) is about Monotonically increasing; consider Under the constraints, the optimal power allocation factor is obtained as follows: （20） Then, in order to determine the optimal unit beamforming vector The original optimization problem can be transformed into the following form: （21） The optimization problem (21) is a standard Rayleigh quotient problem, and its optimal unit beamforming vector is... The eigenvectors corresponding to the largest eigenvalue of the matrix given in the following formula are: （22） To obtain the optimal for ; Finally, the result obtained in B2 As given in B1 In order to The process is iterated until the objective function value converges, in order to obtain the optimal value. and .

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