Multi-Objective Secure Massive MIMO Resource Allocation Method Based on Intelligent Reflecting Surface

Abstract

The present invention provides a multi-objective secure Massive MIMO resource allocation method based on intelligent reflecting surface. By combining the wild horse herd intelligence with the dominance relationship, a multi-objective wild horse optimization algorithm for solving multi-objective continuous optimization problems is designed. The position update formulas for the wild horse herd intelligence to execute grazing behavior and mating behavior are improved, and the mode of grouped optimization of the wild horse herd intelligence is abandoned, breaking through the application limitation that the existing wild horse optimization algorithms can only solve single-objective optimization problems. For the secure Massive MIMO communication system based on intelligent reflecting surface, the phase shift control angle of each reflecting element and the base station power transmission matrix are optimized by using multi-objective wild horse herd intelligence with the goals of maximizing the information transmission rate at the legitimate users and minimizing the information transmission rate at the illegitimate users. The present invention simultaneously optimizes the phase shift control angle of each reflecting element in the intelligent reflecting surface and the base station power transmission matrix, improving the resource utilization rate of the system.

Description

Technical Field

[0001] The present invention relates to a resource allocation scheme for a Massive MIMO communication system with illegal users, and particularly to a multi-objective resource allocation method based on multi-objective wild horse herd intelligence, belonging to the technical field of Massive MIMO secure communication. Background Art

[0002] Intelligent Reflecting Surface (IRS) technology, as a low-power and low-cost technology, can reconfigure the propagation environment and enhance the performance of existing communication links, and has attracted much attention since its proposal. The intelligent reflecting surface technology is significantly different from technologies such as amplify-and-forward relay technology and backscatter communication technology, mainly reflected in that it does not require additional signal transmission and processing modules, supports operation in full-duplex mode, and both the direct-path signal and the reflected-path signal carry useful information in practical applications. Aiming at the problem of excessive energy loss in the current communication system, since the intelligent reflecting surface does not require an additional signal transmission module, it can play an energy-saving role. The intelligent reflecting surface is thin and light in appearance, so it is applicable to a wide range of environments and can be easily installed in different environments, such as aerial platforms and tall buildings. The reflection link constructed by it can bypass many obstacles on the direct link, thus effectively alleviating signal fading and avoiding the problem that the signal at the legal user decays too much or even falls into a signal blind area, and improving the signal quality of the receiving ends of many users and the Internet access experience of edge users. Compared with the fourth-generation mobile communication technology, the Massive MIMO technology has significantly improved the information transmission rate of the communication system. However, in practical applications, the Massive MIMO technology still has problems such as the need to obtain continuously changing channel state information to perform optimal beamforming and the difficulty in determining the optimal placement method of a large-scale antenna array.

[0003] By deploying intelligent reflecting surfaces in different environments, it helps to achieve information sensing, analog computing, and wireless communication. Currently, there are many literatures on the application of intelligent reflecting surfaces in various fields, such as capacity and rate enhancement analysis, energy efficiency optimization, communication reliability, physical layer security, wireless power transfer communication, etc. For the scenario of intelligent reflecting surface assisting wireless communication systems, Qingqing Wu et al. published "IRS-Aided WPCNs: A New Optimization Framework for Dynamic IRS Beamforming" in 《IEEE Transactions on Wireless Communications》, which studied three special cases of dynamic intelligent reflecting surface beamforming, proposed a general optimization framework for dynamic intelligent reflecting surface beamforming, optimized the phase shift vector of the intelligent reflecting surface to improve the efficiency of downlink wireless power transfer and the efficiency of uplink wireless information transfer, and improved the throughput of the wireless power transfer communication network, but did not consider the situation of the existence of illegal devices. Lu Weidang et al. published "Security Communication Method for UAV Relay System Based on Intelligent Reflecting Surface Assistance" in 《Journal of Electronics & Information Technology》(2022, vol.44, no.7, pp.2273-2280), which proposed a security communication method for UAV relay system based on intelligent reflecting surface assistance. With the goal of maximizing the minimum secrecy rate of users and subject to the constraints of limited base station transmission power and the phase shift control of reflecting elements of the intelligent reflecting surface within a certain range, the original problem was decomposed into several sub-problems for alternating optimization to seek the optimal solution. However, it only considered the case where the reflecting elements in the intelligent reflecting surface were arranged in a uniform linear array and did not consider the case where the reflecting elements were arranged in a planar array.

[0004] By consulting the literature, it is found that for the resource allocation problem of Massive MIMO communication systems with illegal users, most of the literature optimizes the resource allocation scheme with the goal of maximizing the secrecy rate, that is, the difference between the information transmission rate at the legitimate user and the information transmission rate at the illegal user. No literature has been found that uses multi-objective swarm intelligence to solve the multi-objective resource allocation problem of secure Massive MIMO systems based on intelligent reflecting surfaces. Summary of the Invention

[0005] To solve the conflicting problem of maximizing the information transmission rate at legitimate users and minimizing the information transmission rate at illegal users in a Massive MIMO system with illegal users, the present invention first combines the single-objective wild horse optimization algorithm with the dominance relationship, proposes a multi-objective wild horse swarm intelligence based on the dominance relationship, and designs a resource allocation method for a secure Massive MIMO system based on multi-objective wild horse swarm intelligence and intelligent reflecting surfaces, obtaining a variety of resource allocation schemes for decision-makers to choose from.

[0006] The object of the present invention is achieved as follows: The steps are as follows:

[0007] Step 1: Establish a Massive MIMO communication system model with non-legitimate users;

[0008] Step 2: Initialize the multi-objective wild horse herd and put the non-dominated solutions into the repository;

[0009] Step 3: Calculate the crowding distance of all non-dominated solutions in the repository and select non-dominated solutions in the repository by means of roulette wheel selection;

[0010] Step 4: Update the position of each wild horse by performing grazing behavior or mating behavior;

[0011] Step 5: Calculate all objective function values corresponding to each wild horse, determine the position of each wild horse according to the selection mechanism, and update the non-dominated solutions in the repository;

[0012] Step 6: If the number of iterations has reached the set maximum number of iterations, terminate the iteration, output all non-dominated solutions in the repository, and correspondingly obtain multiple resource allocation schemes for decision-makers to choose; otherwise, let x = x + 1 and continue to execute Step 3.

[0013] Further, Step 1 specifically includes: In a Massive MIMO system with non-legitimate users, there are non-legitimate users with Q antennas, legitimate users with W antennas, a base station with E antennas, and an intelligent reflecting surface with R reflecting elements, and the antenna arrays at the base station, legitimate users, and non-legitimate users are all uniform linear arrays; Let be a matrix composed of the transmission power of the base station, where diag{.} represents a diagonal matrix, that is, all elements except the diagonal elements in the matrix are 0, and a e represents the transmission power of the e-th base station antenna, e = 1, 2,..., E; Let O Bs-User ∈C W×E be the channel state information matrix from the base station to the legitimate users; For the reflected signal, let O Bs-Irs ∈C R×E be the channel state information matrix from the base station to the intelligent reflecting surface, and O Irs-User ∈C W×R be the channel state information matrix from the intelligent reflecting surface to the legitimate users, then the information transmission rate at the legitimate users is expressed as:

[0014]

[0015] where, D W is a W-dimensional identity matrix, that is, the diagonal elements in the matrix are 1 and the rest of the elements are all 0, (.) Hdenotes the conjugate and then transpose of a matrix, and det(.) represents the value of the determinant of a matrix. χ is the reflection coefficient, and β r is the phase shift control angle of the r-th reflecting element, where r = 1, 2,..., R. f1 is the noise power at the IRS, and f2 is the noise power at the legitimate user.

[0016] The signal received by the non-legitimate user also includes the direct signal and the reflected signal, and let O Bs-Evae ∈C Q×E and O Irs-Evae ∈C Q×R be the channel state information matrices from the base station to the non-legitimate user and from the IRS to the non-legitimate user respectively. Then the information transmission rate at the non-legitimate user is expressed as:

[0017]

[0018] where D Q is the Q-dimensional identity matrix. f3 is the noise power at the non-legitimate user.

[0019] Furthermore, in step two, assume that the multi-objective wild horse herd consists of L wild horses. The dimension of the search space of each wild horse is Z. The maximum and minimum values that each wild horse can take in the z-th dimensional search space are The position of the l-th wild horse at the x-th generation is represented as where l = 1, 2,..., L, z = 1, 2,..., Z; the initial position of each wild horse in the z-th dimension is randomly generated within the z-th dimensional search space; the position of the l-th wild horse at the x-th generation is substituted into the two objective functions to calculate the corresponding two objective function values. If for the m-th and n-th wild horses, both are satisfied and at least one strict inequality holds, then it is said that the m-th wild horse dominates the n-th wild horse at the x-th generation; if initially none of the other wild horses can dominate the φ-th wild horse, then the position of the φ-th wild horse is put into the repository for storing non-dominated solutions, and the size of the repository is L max , that is, the repository can store at most L max non-dominated solutions.

[0020] Furthermore, in step three, when calculating the crowding distance, first sort all the non-dominated solutions in the repository in ascending order according to the size of each objective function value; for the y-th objective function, the crowding distance of the solution corresponding to the maximum or minimum value of the objective function is 1, and the crowding distance of the remaining solutions is: where DIS y (v ψ) is the crowding distance of the ψ-th non-dominated solution in the y-th objective function, h y (v ψ+1 ) and h y (v ψ-1 ) represent the values of the (ψ + 1)-th and (ψ - 1)-th non-dominated solutions corresponding to the y-th objective function respectively, and are the maximum and minimum values of the y-th objective function respectively; calculate the crowding distance of each non-dominated solution corresponding to each objective function, and add up the crowding distances of each non-dominated solution corresponding to each objective function to obtain the crowding distance of each non-dominated solution; for the l-th wild horse, select a non-dominated solution according to the crowding distance of each non-dominated solution in the repository using the roulette wheel selection method to assist the l-th wild horse in performing grazing behavior or mating behavior.

[0021] Furthermore, in step four, for the l-th wild horse, generate a random number uniformly distributed between 0 and 1 If then the l-th wild horse performs grazing behavior; otherwise, it performs mating behavior, where η1, η2, and λ are all constants, and X is the maximum number of iterations; when the l-th wild horse performs grazing behavior, the update of the z-th dimension position is: where represents a random number obeying a normal distribution with a mean of 0 and a variance of 1, is a random number uniformly distributed between -2 and 2, represents the z-th dimension position of the non-dominated solution selected according to the roulette wheel selection method from the repository of the x-th generation; when the l-th wild horse performs mating behavior, for its z-th dimension position, first generate a random number uniformly distributed between 0 and 1 The update of the z-th dimension position is: where ρ is a constant.

[0022] Furthermore, in step five, after the multi-objective wild horse group updates its position, calculate the values of all objective functions corresponding to the position of each wild horse; if the position of the l-th wild horse after completing grazing behavior or mating behavior and the position before update If then remains unchanged, where η3 is a constant between 0 and 1; otherwise, let If dominates then remains unchanged, if dominates then let If Then, it is compared with each non-dominated solution in the repository; if it can dominate at least one non-dominated solution originally in the repository, it is put into the repository and the solutions it can dominate are deleted from the repository; if the number of non-dominated solutions in the repository exceeds its storage scale L after update max , then the crowding distance of all non-dominated solutions is calculated and sorted in descending order according to the crowding distance, and the first L max non-dominated solutions are selected and put into the repository of the (x + 1)-th generation, and the remaining non-dominated solutions are deleted from the repository.

[0023] Compared with the prior art, the beneficial effects of the present invention are: (1) The present invention combines wild horse herd intelligence with the dominance relationship, designs a multi-objective wild horse optimization algorithm for solving multi-objective continuous optimization problems, improves the position update formula for the wild horse herd intelligence to execute grazing behavior and mating behavior, and abandons the pattern of grouped optimization of wild horse herd intelligence, simplifies the implementation structure, and breaks through the application limitation that the existing wild horse optimization algorithms can only solve single-objective optimization problems.

[0024] (2) For the secure Massive MIMO communication system based on intelligent reflecting surface, aiming at maximizing the information transmission rate at the legitimate users and minimizing the information transmission rate at the non-legitimate users, the multi-objective wild horse herd intelligence is used to optimize the phase shift control angle of each reflecting element and the base station power transmission matrix. Compared with most of the current related literature that alternately optimizes the phase shift of the reflecting element and the base station power transmission matrix by using convex optimization algorithms, it can optimize the phase shift control angle of each reflecting element in the intelligent reflecting surface and the base station power transmission matrix simultaneously, and improve the resource utilization rate of the system.

[0025] (3) For the Massive MIMO communication system with non-legitimate users, the present invention uses the multi-objective wild horse herd intelligence to optimize the resource allocation method for the secure Massive MIMO based on intelligent reflecting surface, and obtains a Pareto solution set containing different resource allocation schemes for the decision maker to choose. The decision maker can select the optimal resource allocation scheme from the Pareto solution set according to the specific decision method. For example, when the Massive MIMO communication system requires that the information transmission rate at the non-legitimate users is not higher than a certain limit value, the decision maker can select the resource allocation scheme corresponding to the maximum information transmission rate at the legitimate users while meeting the above requirements, or when the Massive MIMO communication system requires that the information transmission rate at the legitimate users is not lower than a certain limit value, the decision maker can select the resource allocation scheme corresponding to the minimum information transmission rate at the non-legitimate users while meeting the above requirements. Description of the Drawings

[0026] Figure 1Schematic diagram of a resource allocation method for a Massive MIMO communication system with illegal users using multi-objective wild horse herd intelligence optimization.

[0027] Figure 2 Comparison graph of Pareto optimal fronts obtained by a resource allocation method for a Massive MIMO communication system with illegal users optimized by multi-objective wild horse herd intelligence and multi-objective particle swarm algorithm.

[0028] Figure 3 Comparison graph of the Pareto optimal front obtained by optimizing the resource allocation scheme using multi-objective wild horse herd intelligence and the optimal resource allocation schemes corresponding to the two objective function values obtained by optimizing the two objective functions using the butterfly algorithm respectively. Detailed implementation manners

[0029] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0030] As Figure 1 shown, the resource allocation method for a Massive MIMO communication system with illegal users designed by the multi-objective wild horse optimization algorithm of the present invention includes the following steps:

[0031] Step 1, establish a Massive MIMO communication system model with illegal users

[0032] In a Massive MIMO system with illegal users, there are illegal users with Q antennas, legal users with W antennas, a base station with E antennas, and an intelligent reflecting surface with R reflecting elements. And the antenna arrays at the base station, legal users, and illegal users are all uniform linear arrays. Let be the matrix composed of the transmission power of the base station, where diag{.} represents a diagonal matrix, that is, all elements except the diagonal elements in the matrix are 0, and a e represents the transmission power of the e-th base station antenna, e = 1, 2,..., E. The signal received by the legal user includes the direct signal from the base station to the legal user and the reflected signal transmitted to the legal user after being reflected by the intelligent reflecting surface. For the direct signal, let O Bs-User ∈C W×E be the channel state information matrix from the base station to the legal user; for the reflected signal, let O Bs-Irs ∈C R×E be the channel state information matrix from the base station to the intelligent reflecting surface, and O Irs-User ∈C W×R be the channel state information matrix from the intelligent reflecting surface to the legal user. Then the information transmission rate at the legal user can be expressed as:

[0033]

[0034] Among them, D W is a W-dimensional identity matrix, that is, the diagonal elements of the matrix are 1 and the rest of the elements are all 0, (.) H represents taking the conjugate of the matrix and then transposing it, and det(.) represents the value of the matrix determinant. χ is the reflection coefficient, and β r is the phase shift control angle of the r-th reflecting element, where r = 1, 2,..., R. f1 is the noise power at the intelligent reflecting surface, and f2 is the noise power at the legitimate user.

[0035] The signal received by the non-legitimate user also includes the direct signal and the reflected signal. Let O Bs-Evae ∈C Q×E and O Irs-Evae ∈C Q×R be the channel state information matrices from the base station to the non-legitimate user and from the intelligent reflecting surface to the non-legitimate user respectively. Then the information transmission rate at the non-legitimate user can be expressed as:

[0036]

[0037] Among them, D Q is a Q-dimensional identity matrix. f3 is the noise power at the non-legitimate user.

[0038] For a Massive MIMO communication system with non-legitimate users, there are two objectives for optimizing the resource allocation scheme: the first is to maximize the information transmission rate at the legitimate user, that is, maxG(A, α) = maxS User ; the second is to minimize the information transmission rate at the non-legitimate user, that is, minH(A, α) = minS Evae . For convenience, the optimization objective is transformed into: max[G(A, α), J(A, α)], where J(A, α) = K - H(A, α), and K is a constant. The constraint conditions are: represents the maximum transmit power allowed for each base station antenna, where e = 1, 2,..., E, 0 ≤ β r < 2π, r = 1, 2,..., R.

[0039] Step 2: Initialize the multi-objective wild horse herd and put the non-dominated solutions into the repository.

[0040] Suppose the multi-objective wild horse herd consists of L wild horses. The dimension of the search space for each wild horse is Z. The maximum and minimum values that each wild horse can take in the z-th dimensional search space are respectively Represent the position of the l-th wild horse at the x-th generation as where \(l = 1, 2, \cdots, L\), and \(z = 1, 2, \cdots, Z\). The initial position of the \(z\)-th dimension of each wild horse is randomly generated within the range of the \(z\)-th dimension search space. Substitute the position of the \(l\)-th wild horse in the \(x\)-th generation into the two objective functions to calculate the corresponding two objective function values. If for the \(m\)-th and \(n\)-th wild horses, the following conditions are simultaneously satisfied: and at least one strict inequality holds, then it is said that the \(m\)-th wild horse dominates the \(n\)-th wild horse in the \(x\)-th generation. If initially none of the other wild horses can dominate the \(\varphi\)-th wild horse, then put the position of the \(\varphi\)-th wild horse into the repository for storing non-dominated solutions, and the size of the repository is \(L\) max , that is, the repository can store at most \(L\) max non-dominated solutions.

[0041] Step 3: Calculate the crowding distance of all non-dominated solutions in the repository, and select non-dominated solutions in the repository using the roulette wheel selection method

[0042] When calculating the crowding distance, first sort all non-dominated solutions in the repository in ascending order according to the magnitude of each objective function value. For the \(y\)-th objective function, the crowding distance of the solution corresponding to the maximum or minimum value of the objective function is 1, and the crowding distance of the remaining solutions is: where \(DIS\) y \((v\) ψ ) is the crowding distance of the \(\psi\)-th non-dominated solution in the \(y\)-th objective function, \(h\) y \((v\) ψ+1 ) and \(h\) y \((v\) ψ-1 ) represent the values of the \((\psi + 1)\)-th and \((\psi - 1)\)-th non-dominated solutions corresponding to the \(y\)-th objective function respectively, and are the maximum and minimum values of the \(y\)-th objective function respectively. Calculate the crowding distance of each non-dominated solution corresponding to each objective function, and add the crowding distances of each non-dominated solution corresponding to each objective function to obtain the crowding distance of each non-dominated solution. For the \(l\)-th wild horse, select a non-dominated solution using the roulette wheel selection method according to the crowding distance of each non-dominated solution in the repository to assist the \(l\)-th wild horse in performing grazing behavior or mating behavior.

[0043] Step 4: Update the position of each wild horse by performing grazing behavior or mating behavior

[0044] For the \(l\)-th wild horse, generate a random number uniformly distributed between 0 and 1 If then the \(l\)-th wild horse performs grazing behavior; otherwise, it performs mating behavior, where η1, η2, and λ are all constants, and X is the maximum number of iterations. When the l-th wild horse performs the grazing behavior, the update of the z-th dimension position is as follows: where represents a random number obeying the normal distribution with a mean of 0 and a variance of 1, is a random number obeying the uniform distribution between -2 and 2, represents the z-th dimension position of the non-dominated solution selected according to the roulette wheel selection method from the x-th generation repository. When the l-th wild horse performs the mating behavior, for its z-th dimension position, a random number obeying the uniform distribution between 0 and 1 is first generated The update of the z-th dimension position is as follows: where ρ is a constant.

[0045] Step Five, calculate all the objective function values corresponding to each wild horse, determine the position of each wild horse according to the selection mechanism, and update the non-dominated solutions in the repository

[0046] After the positions of the multi-objective wild horse herd are updated, calculate all the objective function values corresponding to the position of each wild horse. If the position of the l-th wild horse after completing the grazing behavior or mating behavior and the position before the update do not dominate each other, then a random number obeying the uniform distribution between 0 and 1 is generated. If then remains unchanged, where η3 is a constant between 0 and 1; otherwise, let If dominates then remains unchanged. If dominates then let If can dominate at least one of the original non-dominated solutions in the repository, then is put into the repository and the solutions it can dominate are deleted from the repository. If the number of non-dominated solutions in the repository exceeds its storage scale L max , then calculate the crowding distance of all non-dominated solutions and sort them in descending order according to the crowding distance, and select the first L max non-dominated solutions and put them into the (x + 1)-th generation repository, and the remaining non-dominated solutions are deleted from the repository.

[0047] Step Six, if the number of iterations has reached the set maximum number of iterations, then terminate the iteration, output all the non-dominated solutions in the repository, and correspondingly obtain multiple resource allocation schemes for the decision maker to choose; otherwise, let x = x + 1 and continue to execute Step Three.

[0048] Next, the beneficial effects of the present invention are further illustrated through simulation experiments:

[0049] For a Massive MIMO communication system with illegal users, assume that the illegal user and the legitimate user are located at (190, 30, 0) m and (200, 0, 0) m respectively. The number of antennas of the illegal user and the legitimate user are Q = 1 and W = 10 respectively. The noise powers at the illegal user and the legitimate user are f3 = f2 = -80 dBm. The intelligent reflecting surface is located at (100, 100, 50) m, the reflection coefficient χ = 1, the number of reflecting elements R = 50, and the noise power at the intelligent reflecting surface is f1 = -80 dBm. The base station coordinates are located at (0, 0, 50) m, the number of base station antennas E = 40, and the maximum power allowed for each base station antenna The channels between the illegal user, the legitimate user, the base station and the intelligent reflecting surface are considered as Rice channels with a Rice factor of 1 and a channel fading coefficient of 2.2. The channels between the illegal user, the legitimate user and the base station are considered as Rayleigh channels with a channel fading coefficient of 3.5. The parameter settings of the multi-objective wild horse herd intelligent optimization resource allocation scheme are as follows: the search space dimension Z = 90, the population size L = 50, the storage size of the repository L max = 50, the maximum number of iterations X = 500, K = 100, λ = 0.25, η1 = 0.2, η2 = 0.8, η3 = 0.5, ρ = 2. The superiority of the designed multi-objective wild horse herd intelligence is reflected by optimizing the resource allocation scheme using the multi-objective particle swarm algorithm and the single-objective butterfly algorithm. The population sizes of the multi-objective particle swarm algorithm and the butterfly algorithm are 50, and the maximum number of iterations is 500. The other parameter settings of the multi-objective particle swarm algorithm and the butterfly algorithm refer to "Handling Multiple Objectives with Particle Swarm Optimization" published by Coello C et al. in 《IEEE Transactions on Evolutionary Computation》(2004, 8(3): 256-279) and "Butterfly optimization algorithm: a novel approach for global optimization" published by S. Arora et al. in 《Soft Computing》(2019, vol. 23, pp. 715-734). At Figure 2 、 Figure 3Among them, the intelligent reflecting surface security Massive MIMO resource allocation method based on multi-objective wild horse herd intelligence is denoted as "MOWHO", the intelligent reflecting surface security Massive MIMO resource allocation method based on multi-objective particle swarm optimization algorithm is denoted as "MOPSO", the resource allocation method obtained by maximizing the information transmission rate at the legitimate user using the butterfly algorithm is denoted as "BOA-1", and the resource allocation method obtained by minimizing the information transmission rate at the illegitimate user using the butterfly algorithm is denoted as "BOA-2".

[0050] Figure 2 It is a comparison graph of the Pareto optimal frontiers obtained by applying multi-objective wild horse herd intelligence and multi-objective particle swarm optimization algorithm to optimize the intelligent reflecting surface-based security Massive MIMO resource allocation method. From Figure 2 it can be seen that the range of the Pareto optimal solution set corresponding to the information transmission rates of legitimate users and illegitimate users obtained by the multi-objective particle swarm optimization algorithm is smaller than that of the Pareto optimal solution set corresponding to the information transmission rates of legitimate users and illegitimate users obtained by applying the multi-objective wild horse optimization algorithm. And for any Pareto optimal solution obtained by the multi-objective particle swarm optimization algorithm, at least one Pareto optimal solution can be found in the Pareto optimal solution set obtained by the multi-objective wild horse herd intelligence to dominate the Pareto optimal solution obtained by the multi-objective particle swarm optimization algorithm. The designed multi-objective wild horse herd intelligence obtains a resource allocation scheme with better performance and more diversification.

[0051] Figure 3 It is a comparison graph of the Pareto optimal frontiers obtained by applying multi-objective wild horse herd intelligence to optimize the resource allocation scheme and the optimal resource allocation schemes obtained by applying the butterfly algorithm to maximize the information transmission rate at the legitimate user and minimize the information transmission rate at the illegitimate user corresponding to the two objective function values. From Figure 3 it can be seen that the two optimal solutions obtained by the butterfly algorithm are both dominated by some Pareto optimal solutions obtained by the multi-objective wild horse herd intelligence, which reflects the superiority of the designed multi-objective wild horse herd intelligence.

Claims

1. A multi-objective secure Massive MIMO resource allocation method based on intelligent reflecting surface, characterized in that The steps are as follows: Step 1: Establish a Massive MIMO communication system model with illegal users; In a Massive MIMO system with illegal users, there are illegal users with Q antennas, legitimate users with W antennas, a base station with E antennas, and an intelligent reflecting surface with R reflecting elements. Moreover, the antenna arrays at the base station, legitimate users, and illegal users are all uniform linear arrays. Let be the matrix composed of the transmission power of the base station, where diag{.} represents a diagonal matrix, that is, all elements except the diagonal elements in the matrix are 0, and a e represents the transmission power of the e-th base station antenna, e = 1, 2,..., E; let be the channel state information matrix from the base station to the legitimate users; for the reflected signal, let be the channel state information matrix from the base station to the intelligent reflecting surface, be the channel state information matrix from the intelligent reflecting surface to the legitimate users. Then the information transmission rate at the legitimate users is expressed as: Among them, D W is a W-dimensional identity matrix, that is, the diagonal elements of the matrix are 1 and the rest of the elements are all 0. (.) H denotes taking the conjugate of the matrix and then transposing it, and det(.) represents the value of the matrix determinant. χ is the reflection coefficient, and β r is the phase shift control angle of the r-th reflecting element, where r = 1, 2,..., R. f1 is the noise power at the intelligent reflecting surface, and f2 is the noise power at the legitimate user. The signals received by illegal users also include direct signals and reflected signals. Let be the channel state information matrices from the base station to the illegal user and from the intelligent reflecting surface to the illegal user respectively. Then the information transmission rate at the illegal user is expressed as: Among them, D Q is a Q-dimensional identity matrix, and f3 is the noise power at an illegal user; Step 2: Initialize the multi-objective wild horse herd and put the non-dominated solutions into the repository; Suppose the multi-objective wild horse group consists of L wild horses, the dimension of the search space of each wild horse is Z, and the maximum and minimum values that each wild horse can take in the z-th dimensional search space are respectively The position of the l-th wild horse in the x-th generation is represented as where l = 1, 2,..., L, z = 1, 2,..., Z; the initial position of each wild horse in the z-th dimension is randomly generated within the range of the z-th dimensional search space; the position of the l-th wild horse in the x-th generation is brought into two objective functions The corresponding two objective function values are calculated; if for the m-th and n-th wild horses, both of the following are satisfied simultaneously: and at least one strict inequality holds, then it is said that the m-th wild horse dominates the n-th wild horse in the x-th generation; if initially none of the other wild horses can dominate the φ-th wild horse, then the position of the φ-th wild horse is put into the repository storing non-dominated solutions, and the scale of the repository is L max , that is, at most L max non-dominated solutions are stored in the repository; Among them, the objective function K is a constant; Step 3: Calculate the crowding distance of all non-dominated solutions in the repository and select non-dominated solutions from the repository using the roulette wheel selection method; Step 4: Update the position of each wild horse by performing grazing behavior or mating behavior; For the lth wild horse, generate a random number uniformly distributed between 0 and 1 like Then the lth wild horse performs grazing behavior; otherwise, it performs mating behavior, where η1, η2 and λ are all constants, X is the maximum number of iterations; when the lth wild horse performs grazing behavior, the z-th dimension position is updated as: in represents a random number that follows a normal distribution with a mean of 0 and a variance of 1. is a random number uniformly distributed between -2 and 2. represents the z-th dimension position of the non-dominated solution selected from the x-th generation repository according to the roulette wheel selection method; when the l-th wild horse performs mating behavior, a random number uniformly distributed between 0 and 1 is first generated for its z-th dimension position The z-th dimension position is updated as: in ρ is a constant; Step 5: Calculate all objective function values corresponding to each wild horse, determine the position of each wild horse according to the selection mechanism and update the non-dominated solutions in the repository; After the multi-objective wild horse herd updates its positions, calculate all the objective function values corresponding to the positions of each wild horse; if the position of the l-th wild horse after the grazing behavior or mating behavior and the position before the update do not dominate each other, then generate a random number uniformly distributed between 0 and 1 If then remain unchanged, where η3 is a constant between 0 and 1; otherwise, let If dominates then remain unchanged, if dominates then let If then compare with each non-dominated solution in the repository; if can dominate at least one of the original non-dominated solutions in the repository, put into the repository and delete the solutions it can dominate from the repository; if the number of non-dominated solutions in the repository exceeds its storage scale L after the update max , then calculate the crowding distance of all non-dominated solutions and sort them in descending order according to the crowding distance, and select the first L max non-dominated solutions and put them into the repository of the (x + 1)-th generation, and delete the remaining non-dominated solutions from the repository; Step 6: If the number of iterations has reached the set maximum number of iterations, terminate the iteration, output all non-dominated solutions in the repository, and correspondingly obtain multiple resource allocation schemes for decision-makers to choose from; otherwise, let x = x + 1 and continue to execute Step 3.

2. The multi-objective secure Massive MIMO resource allocation method based on intelligent reflecting surface according to claim 1, wherein In Step 3, when calculating the crowding distance, first sort all non-dominated solutions in the repository in ascending order according to the magnitude of each objective function value; for the y-th objective function, the crowding distance of the solution corresponding to the maximum or minimum value of the objective function is 1, and the crowding distance of the remaining solutions is: where DIS y (v ψ ) is the crowding distance of the ψ-th non-dominated solution for the y-th objective function, h y (v ψ+1 ) and h y (v ψ-1 ) represent the values of the ψ + 1-th and ψ - 1-th non-dominated solutions for the y-th objective function respectively, and are the maximum and minimum values of the y-th objective function respectively; calculate the crowding distance of each non-dominated solution corresponding to each objective function, and add the crowding distances of each non-dominated solution corresponding to each objective function to obtain the crowding distance of each non-dominated solution; for the l-th wild horse, select a non-dominated solution using the roulette wheel selection method according to the crowding distance of each non-dominated solution in the repository to assist the l-th wild horse in performing grazing behavior or mating behavior.

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