A MA-SR system weighted energy efficiency optimization method for near-field secure transmission

Abstract

The application discloses a MA-SR system weighted energy efficiency optimization method for near-field safe transmission, and when a base station broadcasts the same data stream to multiple communication users, secondary information is parasitically loaded on the main signal by a passive RIS and transmitted to secondary equipment, and the threat of eavesdropping on the broadcast communication signal by an eavesdropper is considered. Firstly, a joint optimization problem with the maximum weighted energy efficiency of the communication users and the secondary equipment as the target is constructed, and then a design method based on alternating optimization (AO) iteration is proposed, and the beam vector, RIS matrix and MA position are optimized respectively. The application can solve the problems of near-field safe broadcast transmission, secondary information transmission, beamforming design, RIS passive reflection design and antenna position optimization in the system, and the suboptimal solution of the system weighted energy efficiency is obtained through iterative updating, and the system energy efficiency and safe transmission performance can be effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of network technology in mobile communication systems, and particularly relates to a weighted energy efficiency optimization method for MA-SR systems oriented towards near-field secure transmission. Background Technology

[0002] Movable antenna (MA) technology allows base station antennas to move freely in one-dimensional, two-dimensional, and three-dimensional space under certain constraints, thus making fuller use of spatial degrees of freedom and improving spatial resolution. This enables more effective adaptation to the current wireless environment and enhances system communication performance. Parasitic radio (SR) technology reduces power consumption by carrying secondary signals onto the main signal. As communication frequencies increase, signal loss becomes greater. Near-field communication improves signal quality by bringing the base station and terminal closer together. Currently, no literature has researched MA-SR systems for near-field secure transmission. Therefore, this invention constructs a corresponding optimization problem for this scheme and proposes an AO algorithm to solve it. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by providing a weighted energy efficiency optimization method for MA-SR systems with near-field secure transmission. This method obtains the lower bound of the original problem by introducing auxiliary variables, solves the subproblems of beam vector and RIS reflection matrix using CVX, and then solves the antenna position subproblem using the PSO algorithm, which can converge in a finite time.

[0004] To achieve the above-mentioned objectives, the technical solution adopted by the present invention includes the following steps: A weighted energy efficiency optimization method for a near-field secure multi-user broadcast downlink MA-SR system includes the following steps: Step 1: Establish the primal optimization problem P1 for the MA-SR system for near-field secure transmission, with the goal of maximizing the system's weighted energy efficiency. The constraints include base station transmit power constraints, RIS reflector modulus constraints, eavesdropper decoding main signal rate constraints, user decoding main signal rate constraints, secondary device decoding main signal rate constraints, secondary device decoding secondary signal rate constraints, antenna movement range constraints, and minimum spacing between antennas constraints. Step 2: Iteratively solve the original optimization problem P1 using an alternating optimization framework. By fixing some variables, iteratively optimize the beam vector, RIS reflection matrix, and antenna position until the result converges.

[0005] Furthermore, the alternating optimization iteration process in step 2 specifically includes the following steps: Step a: Initialize system parameters and optimize variables; Step b: Update the beam vector based on the stored RIS reflection matrix and antenna position. Specifically, this includes introducing auxiliary variables to transform the original optimization problem P1, replacing the original objective function by optimizing the lower bound of the original objective function, transforming the objective fraction using the Dinkelbach method to obtain the transformed problem P1.1, and then solving it with the help of the CVX toolbox. Step c: Update the RIS reflection matrix based on the beam vector updated in step b and the stored antenna position. Specifically, this includes introducing auxiliary variables to transform the original optimization problem P1, replacing the original objective function by optimizing the lower bound of the original objective function, and introducing a penalty factor to penalize the equality constraint on the objective function. Then, by introducing new optimization variables, we obtain problem P2.1, and then solve it using CVX. Step d: Using the updated RIS reflection matrix from step c and the stored beam vector, the original optimization problem is first transformed into P3, and then the particle swarm optimization algorithm (PSO) is used to solve the antenna position subproblem to update the antenna position variables. Step e: Calculate the weighted energy efficiency of the current system. If its relative change is less than the threshold and the maximum number of iterations has not been reached, return to step b; otherwise, output the optimization result.

[0006] Furthermore, the original optimization problem P1 in step b above is: in, and These are the weighting coefficients for each communication user and secondary device, respectively, and their sum is 1; Beam vector; To control circuit power consumption; This refers to static power consumption. This refers to the base station power threshold. The coefficient of the i-th reflecting unit; This is the RIS reflection matrix; These are the local coordinates of the i-th and j-th cells of the base station, respectively. Let x be the x-coordinate of the i-th cell of the base station. Let be the ordinate of the i-th cell of the base station; It is the maximum lateral movement distance of the antenna. is the maximum longitudinal movement distance of the antenna; N is the number of RIS reflector elements; It is the minimum spacing between antennas; The threshold for decoding the main signal for the eavesdropper; The threshold for decoding the main signal for communication users; The threshold for decoding the main signal for secondary devices; The threshold for decoding secondary signals for secondary devices; Let be the rate at which the i-th user decodes the main signal; The rate at which secondary devices decode secondary signals; The rate at which the eavesdropper decodes the main signal; The rate at which the secondary device decodes the main signal; , , The definition is as follows: It is the symbol length; It is the channel vector from the base station to the secondary device. It is the channel matrix from the base station to the RIS. It is the channel vector from the base station to the eavesdropper. It is the channel vector from the base station to the i-th user. It is the channel vector from RIS to the i-th user. It is the channel vector from RIS to the eavesdropper; Indicates conjugate transpose; It is the noise power at the i-th user. It is the noise power at the eavesdropper's location. This refers to the noise power at the secondary equipment; the specific definitions of each channel vector and matrix are as follows: ,in, Where M is the subcarrier wavelength, M is the number of antennas, and e represents the natural exponent. It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution. The nth element in this vector L is the distance from the base station to the i-th user, and L is the number of paths. These are the global coordinates of the m-th antenna; Let be the local coordinates of the i-th antenna; It is the location of the i-th communication user. It is the location of the m-th scatterer near the i-th communication user; ,in, It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution, i.e. It is the distance from RIS to the i-th user; Let be the local coordinates of the i-th unit in RIS.

[0007] ,in, It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution, i.e. It is the distance from the base station to the i-th eavesdropper; That's the location of the eavesdropper. These are the coordinates of the m-th scattering object near the eavesdropper; ,in, It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution, i.e. It's the distance from RIS to the eavesdropper; ,in, It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution, i.e. It is the distance from the base station to the SU; It is the location of the secondary equipment. It is the location of the m-th scatterer near the secondary device; ,in, It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution, i.e. It is the distance from RIS to the i-th eavesdropper; ,in, It is the distance between the base station and the RIS. Indicates a complex Gaussian distribution; The auxiliary variables introduced in step b include Using Dinkelbach's transformation on the target fraction, we obtain the following P1.1: in, These represent weighting coefficients, which are positive numbers between 0 and 1, and their sum is 1. Represents the square of the modulus; Indicates the length of the secondary symbol; Let represent the value of × in the t-th iteration, and y be the auxiliary variable that the Dinkelbach method needs to introduce. The channel matrices are defined as follows, taking the real part: Solving P1.1 involves the following steps: Step 1.1: Initialize parameters; Step 1.2: Solve for P1.1 using the CVX optimization tool; Step 1.3: Update y for round t+1 based on the parameter values ​​from round t. : Step 1.4: Repeat steps 1.2 and 1.3 until the objective function value converges; Furthermore, after introducing auxiliary variables and penalty factors in step c above, and performing variable substitution... ,in This means taking the diagonal elements to form a column vector, resulting in problem P2.1 as follows: Where C is the penalty factor. yes The parameters of the i-th element are defined as follows: Solve problem P2.1 using the CVX tool.

[0008] Furthermore, by fixing all variables except the antenna position in step d above, the original optimization problem transforms into P3: Where A is the antenna movement region, the specific steps involved in solving this problem using PSO are as follows: Step 2.1: For problem P3, use PSO to optimize the position of the movable antenna; set the number of particles to... The maximum number of iterations is The current iteration number is The inertia weight is , The learning factor is The initial annealing temperature is The cooling coefficient is The convergence threshold is The maximum speed proportionality coefficient is The penalty factor is ; Step 2.2: Randomly generate S particle positions within the movable area. , where the s-th particle The candidate antenna positions are: If not satisfied Then the particle is regenerated, where, This represents the initial local coordinates of the i-th antenna in the s-th particle; Step 2.3: Randomly initialize the velocity of each particle. , in each direction The maximum speed is set to the corresponding movement range. , This indicates a uniform distribution; the channel response is recalculated based on the initial position, and the rates are obtained. ; Step 2.4: Calculate the fitness of each particle using the penalized fitness function. in These are the local coordinates of the i-th antenna in the s-th particle. ; Step 2.5: Initialize the optimal position of the s-th particle as follows: And select the particle with the highest fitness from the particles as the initial guiding particle. At the same time, the historical best solution is initialized as ,in This indicates finding the variable that maximizes the inner function; Step 2.6: In the t-th iteration, the inertia weight is updated in a linear decreasing manner: Step 2.7: For the s-th particle, generate... , This indicates a uniform distribution. The velocity and position of all particles are then updated. And cut into ,in It is the velocity of the s-th particle in the t-th iteration. It is the maximum speed of the s-th particle. Then update the position of the s-th particle. If the boundary is exceeded, the image will be projected back to the movable area. in, Let x and y be the x and y coordinates of the i-th antenna in the s-th particle, respectively. These represent taking the minimum and maximum values ​​within the parentheses, respectively.

[0009] Step 2.8: Recalculate based on the new position , , and and calculate .like Then let Otherwise, ; Step 2.9: Select the current optimal particle from the particles obtained in the (t+1)th iteration: ;like Then update Otherwise, calculate the simulated annealing acceptance probability: Randomly generated ,like Then let Otherwise, ; Step 2.10: Update annealing temperature ;like or If yes, then stop; otherwise, let Then return to step 2.6 to continue iterating; the algorithm outputs the following after termination: .

[0010] This invention presents a weighted energy efficiency optimization method for MA-SR systems oriented towards near-field secure transmission, which solves the weighted energy efficiency maximization problem of MA-SR systems oriented towards near-field security, and proposes an AO iterative algorithm. It has been verified that this algorithm can converge in a finite time.

[0011] 1. This invention is the first to solve the weighted energy efficiency optimization problem of MA-SR systems for near-field safety scenarios. In existing technologies, the safety issues of MA-SR systems are mainly studied in the far-field context. No literature has addressed research in near-field safety scenarios. This invention, for the first time, constructs the weighted energy efficiency maximization problem for this complex system and provides a complete solution, filling a technological gap.

[0012] 2. To address the difficulty of directly solving the original non-convex optimization problem (P1), this invention innovatively designs an iterative algorithm based on alternating optimization. This algorithm decomposes the complex problem into a series of solvable sub-problems by fixing other variables and iteratively optimizing the beam vector, RIS reflection matrix, and antenna position, significantly reducing computational complexity.

[0013] 3. By jointly optimizing the beam vector, RIS reflection matrix, and antenna position, this invention fully utilizes the spatial degrees of freedom provided by the MA to improve the system performance of the SR system in near-field safety scenarios. Simulation results show that this scheme can effectively maximize the system's weighted energy efficiency and outperforms traditional fixed antenna schemes.

[0014] 4. The alternating optimization algorithm proposed in this invention has a clear structure, ensuring that the entire iterative process can converge to a high-quality suboptimal solution, thus meeting the performance requirements of practical communication systems. Attached Figure Description

[0015] Figure 1 This is a network architecture diagram of a near-field safe movable antenna-parasitic radio (MA-SR) system. Detailed Implementation

[0016] The technical solution of the present invention will be described in detail below, but the scope of protection of the present invention is not limited to the embodiments described.

[0017] This invention proposes a weighted energy efficiency optimization method for near-field safety MA-SR systems.

[0018] The following is an example. Figure 1 System Implementation Examples: This embodiment considers a MA-SR communication system for near-field security. A single base station at (0m, 0m) simultaneously communicates with near-field... In broadcast communication among multiple users, each user receives the same information stream. Secondary devices, eavesdroppers, and the users and their nearby scattering objects are distributed across... Within the area. The base station is equipped with... A movable antenna, the antenna can be... Within the designated area, they can move freely, and the spacing between adjacent antennas must be no less than [amount missing]. =0.5 In addition, a reconfigurable smart surface is placed at (0m, 5m), which has... One reflecting unit. The carrier frequency for communication is f=2.4GHz, corresponding to a wavelength of... Maximum transmission power of the base station Noise power is set to In addition, the number of transmit paths and the number of receive paths. And the elevation angle of each signal propagation path is Uniformly distributed within.

[0019] The method includes the following steps: Step 1: Establish the primal optimization problem P1 for the MA-SR system for near-field secure transmission, with the goal of maximizing the system's weighted energy efficiency. The constraints include base station transmit power constraints, RIS reflector modulus constraints, eavesdropper decoding main signal rate constraints, user decoding main signal rate constraints, secondary device decoding main signal rate constraints, secondary device decoding secondary signal rate constraints, antenna movement range constraints, and minimum spacing between antennas constraints. Step 2: Iteratively solve the original optimization problem P1 using an alternating optimization framework. By fixing some variables, iteratively optimize the beam vector, RIS reflection matrix, and antenna position until the result converges.

[0020] Step one includes: This invention considers a downlink multi-user communication system, wherein the base station is equipped with One antenna, and each antenna can be used in the area. Intra-field movement, base station simultaneously with near-field User communication, antenna and user set are respectively and A third eavesdropper was also present in the near field, attempting to intercept the main signal. Meanwhile, a reconfigurable smart surface (RIS) was placed away from the base station; the RIS contained… There are 10 reflector units, each capable of independently adjusting the phase of the incident signal. A secondary device exists in the near field; the secondary signal required by this device is transmitted to the secondary device via a RIS (Reflector System) mounted on the main signal.

[0021] The original problem (P1) corresponding to the proposed system is: in, and These are the weighting coefficients for each communication user and secondary device, respectively, and their sum is 1; Beam vector; To control circuit power consumption; This refers to static power consumption. This refers to the base station power threshold. The coefficient of the i-th reflecting unit; This is the RIS reflection matrix; Let be the local coordinates of the i-th cell of the base station; Let x be the x-coordinate of the i-th cell of the base station. Let be the ordinate of the i-th cell of the base station; The threshold for decoding the main signal for the eavesdropper; The threshold for decoding the main signal for communication users; The threshold for decoding the main signal for secondary devices; The threshold for decoding secondary signals for secondary devices; Let be the rate at which the i-th user decodes the main signal; The rate at which secondary devices decode secondary signals; The rate at which the eavesdropper decodes the main signal; This refers to the rate at which the secondary device decodes the main signal. The rate is defined as follows: It is the symbol length It is the channel vector from the base station to the secondary device. It is the channel matrix from the base station to the RIS. It is the channel vector from the base station to the eavesdropper. It is the channel vector from the base station to the i-th user. It is the channel vector from RIS to the i-th user. It is the channel vector from RIS to the eavesdropper. It is the noise power at the i-th user. It is the noise power at the eavesdropper's location. It is the noise power at the secondary equipment location.

[0022] Step two includes: First, the sub-problems related to the beam vector and their solution schemes are given: the auxiliary variables introduced in step (b) include Using Dinkelbach's transformation of the target fraction, we obtain the following (P1.1): in, Let represent the value of × in the t-th iteration, and y be the auxiliary variable introduced by the Dinkelbach method. The channel matrices are defined as follows: (P1.1) The solution involves the following steps: Initialize parameters; Solve using optimization tools such as CVX (P1.1); Update the value of y: Repeat steps (b) and (c) until the objective function value converges; The following presents the subproblems related to the RIS reflection matrix and their solution schemes: After introducing auxiliary variables and penalty factors, and performing variable substitutions... The question (P2.1) is as follows: Where C is the penalty factor, which is a large positive number, and the parameters are defined as follows: Problem (P2.1) can be solved using tools such as CVX.

[0023] The antenna position update scheme is as follows: (1) For problem P3, PSO is used to optimize the position of the movable antenna. The number of particles is set to... The maximum number of iterations is The current iteration number is The inertia weight is , The learning factor is The initial annealing temperature is The cooling coefficient is The convergence threshold is The maximum speed proportionality coefficient is The penalty factor is .

[0024] (2) Randomly generate S particle positions within the movable area. The s-th particle is represented as a... Candidate antenna locations: If not satisfied If so, the particle will be regenerated.

[0025] (3) Randomly initialize the velocity of each particle. The maximum value in each direction The speed is set to the corresponding movement range. , This indicates a uniform distribution. The channel response is recalculated based on the initial position, and the result is obtained. .

[0026] (4) Calculate the fitness of each particle using the penalized fitness function: in .

[0027] (5) Initialize the optimal position of the individual as And select the particle with the highest fitness from all particles as the initial global guide particle. At the same time, the historical best solution is initialized as .

[0028] (6) In the t-th iteration, the inertia weight is updated in a linear decreasing manner: (7) For the s-th particle, generate And update the velocity and position of all particles: And cut into Updated later. If the boundary is exceeded, the image will be projected back to the movable area. (8) Recalculate based on the new position , , and and calculate .like Then let Otherwise, .

[0029] (9) Select the current optimal particle from the particles obtained in the (t+1)th iteration: ;like Then update Otherwise, calculate the simulated annealing acceptance probability: Randomly generated ,like Then let Otherwise, .

[0030] (10) Update the annealing temperature .like or If yes, then stop; otherwise, let Then return to (6) to continue iterating. The algorithm outputs the following upon termination: .

[0031] The above-described invention is merely a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several foreseeable improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A weighted energy efficiency optimization method for a MA-SR system for near-field secure transmission, characterized in that, Includes the following steps: Step 1: Establish the primal optimization problem P1 for the MA-SR system for near-field secure transmission, with the goal of maximizing the system's weighted energy efficiency. The constraints include base station transmit power constraints, RIS reflector modulus constraints, eavesdropper decoding main signal rate constraints, user decoding main signal rate constraints, secondary device decoding main signal rate constraints, secondary device decoding secondary signal rate constraints, antenna movement range constraints, and minimum spacing between antennas constraints. Step 2: Iteratively solve the original optimization problem P1 using an alternating optimization framework. By fixing some variables, iteratively optimize the beam vector, RIS reflection matrix, and antenna position until the result converges.

2. The weighted energy efficiency optimization method for MA-SR systems for near-field secure transmission according to claim 1, characterized in that, The alternating optimization iterative process in step 2 specifically includes the following steps: Step a: Initialize system parameters and optimize variables; Step b: Update the beam vector based on the stored RIS reflection matrix and antenna position. Specifically, this includes introducing auxiliary variables to transform the original optimization problem P1, replacing the original objective function by optimizing the lower bound of the original objective function, transforming the objective fraction using the Dinkelbach method to obtain the transformed problem P1.1, and then solving it with the help of the CVX toolbox. Step c: Update the RIS reflection matrix based on the beam vector updated in step b and the stored antenna position. Specifically, this includes introducing auxiliary variables to transform the original optimization problem P1, replacing the original objective function by optimizing the lower bound of the original objective function, and introducing a penalty factor to penalize the equality constraint on the objective function. Then, by introducing new optimization variables, we obtain problem P2.1, and then solve it using CVX. Step d: Using the updated RIS reflection matrix from step c and the stored beam vector, the original optimization problem is first transformed into P3, and then the particle swarm optimization algorithm (PSO) is used to solve the antenna position subproblem to update the antenna position variables. Step e: Calculate the weighted energy efficiency of the current system. If its relative change is less than the threshold and the maximum number of iterations has not been reached, return to step b; otherwise, output the optimization result.

3. The weighted energy efficiency optimization method for MA-SR systems for near-field secure transmission according to claim 2, characterized in that, The original optimization problem P1 in step b is: ； in, and These are the weighting coefficients for each communication user and secondary device, respectively, and their sum is 1; Beam vector; To control circuit power consumption; This refers to static power consumption. This refers to the base station power threshold. The coefficient of the i-th reflecting unit; This is the RIS reflection matrix; These are the local coordinates of the i-th and j-th cells of the base station, respectively. Let x be the x-coordinate of the i-th cell of the base station. Let be the ordinate of the i-th cell of the base station; It is the maximum lateral movement distance of the antenna. is the maximum longitudinal movement distance of the antenna; N is the number of RIS reflector elements; It is the minimum spacing between antennas; The threshold for decoding the main signal for the eavesdropper; The threshold for decoding the main signal for communication users; The threshold for decoding the main signal for secondary devices; The threshold for decoding secondary signals for secondary devices; Let be the rate at which the i-th user decodes the main signal; The rate at which secondary devices decode secondary signals; The rate at which the eavesdropper decodes the main signal; The rate at which the secondary device decodes the main signal; , , The definition is as follows: ； ； ； It is the symbol length; It is the channel vector from the base station to the secondary device. It is the channel matrix from the base station to the RIS. It is the channel vector from the base station to the eavesdropper. It is the channel vector from the base station to the i-th user. It is the channel vector from RIS to the i-th user. It is the channel vector from RIS to the eavesdropper; Indicates conjugate transpose; It is the noise power at the i-th user. It is the noise power at the eavesdropper's location. This refers to the noise power at the secondary equipment; the specific definitions of each channel vector and matrix are as follows: ； in, Where M is the subcarrier wavelength, M is the number of antennas, and e represents the natural exponent. It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution. The nth element in this vector L is the distance from the base station to the i-th user, and L is the number of paths. These are the global coordinates of the m-th antenna; Let be the local coordinates of the i-th antenna; It is the location of the i-th communication user. It is the location of the m-th scatterer near the i-th communication user; ； in, It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution, i.e. It is the distance from RIS to the i-th user; Let be the local coordinates of the i-th unit in the RIS; ； in, It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution, i.e. It is the distance from the base station to the i-th eavesdropper; That's the location of the eavesdropper. These are the coordinates of the m-th scattering object near the eavesdropper; ； in, It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution, i.e. It's the distance from RIS to the eavesdropper; ； in, It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution, i.e. It is the distance from the base station to the SU; It is the location of the secondary equipment. It is the location of the m-th scatterer near the secondary device; ； in, It is the loss coefficient of L+1 paths, which follows a complex Gaussian distribution, i.e. It is the distance from RIS to the i-th eavesdropper; ,in, It is the distance between the base station and the RIS. Indicates a complex Gaussian distribution; The auxiliary variables introduced in step b include Using Dinkelbach's transformation on the target fraction, we obtain the following P1.1: ； in, These represent weighting coefficients, which are positive numbers between 0 and 1, and their sum is 1. Represents the square of the modulus; Indicates the length of the secondary symbol; Let represent the value of × in the t-th iteration, and y be the auxiliary variable that the Dinkelbach method needs to introduce. The channel matrices are defined as follows, taking the real part: ； Solving P1.1 involves the following steps: Step 1.1: Initialize parameters; Step 1.2: Solve for P1.1 using the CVX optimization tool; Step 1.3: Update y for round t+1 based on the parameter values ​​from round t. : ； Step 1.4: Repeat steps 1.2 and 1.3 until the objective function value converges.

4. The weighted energy efficiency optimization method for MA-SR systems for near-field secure transmission according to claim 2, characterized in that, Step c involves introducing auxiliary variables and penalty factors, followed by variable substitution. ,in This means taking the diagonal elements to form a column vector, resulting in problem P2.1 as follows: ； Where C is the penalty factor. yes The parameters of the i-th element are defined as follows: ； Solve problem P2.1 using the CVX tool.

5. The weighted energy efficiency optimization method for MA-SR systems for near-field secure transmission according to claim 2, characterized in that, Step d: The original optimization problem is transformed into P3: ； Where A is the antenna movement region, the specific steps involved in solving this problem using PSO are as follows: Step 2.1: For problem P3, use PSO to optimize the position of the movable antenna; set the number of particles to... The maximum number of iterations is The current iteration number is The maximum and minimum inertia weights are respectively , The learning factor is The initial annealing temperature is The cooling coefficient is The convergence threshold is The maximum speed proportionality coefficient is The penalty factor is ; Step 2.2: Randomly generate S particle positions within the movable area. , where the s-th particle The candidate antenna positions are: If not satisfied Then the particle is regenerated, where, This represents the initial local coordinates of the i-th antenna in the s-th particle; Step 2.3: Randomly initialize the velocity of each particle. , in each direction The maximum speed is set to the corresponding movement range. , This indicates a uniform distribution; the channel response is recalculated based on the initial position, and the rates are obtained. ; Step 2.4: Calculate the fitness of each particle using the penalized fitness function. ； in These are the local coordinates of the i-th antenna in the s-th particle. ; Step 2.5: Initialize the optimal position of the s-th particle as follows: And select the particle with the highest fitness from the particles as the initial guiding particle. At the same time, the historical best solution is initialized as ,in This indicates finding the variable that maximizes the inner function; Step 2.6: In the t-th iteration, the inertia weight is updated in a linear decreasing manner: ； Step 2.7: For the s-th particle, generate... , Indicates a uniform distribution; and updates the velocity and position of all particles: ； And cut into ,in It is the velocity of the s-th particle in the t-th iteration. It is the maximum speed of the s-th particle. Then update the position of the s-th particle. If the boundary is exceeded, the image will be projected back to the movable area. ； in, Let x and y be the x and y coordinates of the i-th antenna in the s-th particle, respectively. These represent taking the minimum and maximum values ​​within the parentheses, respectively. Step 2.8: Recalculate based on the new position , , and and calculate ;like Then let Otherwise, ; Step 2.9: Select the current optimal particle from the particles obtained in the (t+1)th iteration: ;like Then update Otherwise, calculate the simulated annealing acceptance probability: ； Randomly generated ,like Then let Otherwise, ; Step 2.10: Update annealing temperature ;like or If yes, then stop; otherwise, let Then return to step 2.6 to continue iterating; the algorithm outputs the following after termination: .

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