A fluid antenna assisted ISAC system joint beamforming and position optimization method based on a quantum particle swarm optimization algorithm

Abstract

The application discloses a fluid antenna assisted ISAC system joint beam forming and position optimization method based on a quantum particle swarm optimization algorithm. Specifically, an ISAC multi-user system model equipped with a two-dimensional fluid antenna is established, and a beam forming optimization problem is constructed; a weighted least mean square error algorithm is used to convert a communication and rate target function, so that a complex fractional problem is converted into an integral problem, and solving is simplified; an alternating optimization algorithm is used to decompose the original joint optimization problem into multiple sub-problems; an auxiliary variable and a receiving beam former are alternately solved, an iterative solution of a beam forming vector is solved by using a successive convex approximation algorithm, and a fluid antenna position problem is solved by using a quantum particle swarm optimization algorithm. The method of the application effectively improves the communication and rate under the restrictions of the fluid antenna position, the minimum perceived beam pattern gain and the maximum base station transmission power, and is superior to a traditional ISAC system equipped with a fixed antenna.

Description

Technical Field

[0001] This invention relates to the field of wireless communication and signal processing technology, specifically to a method for joint beamforming and position optimization of a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm. Background Technology

[0002] With the gradual development of 6G technology, the rise of numerous emerging industries and the use of new communication equipment have led to spectrum congestion and increased costs, which have become major challenges restricting the development of future 6G network systems. Therefore, it is necessary to explore new communication technologies to address these key issues facing 6G. In response to these challenges, Integrated Sensing and Communication (ISAC) technology can effectively solve these problems. By adopting shared spectrum resources and hardware devices, antenna systems no longer need to allocate dedicated spectrum or deploy independent hardware for communication or sensing systems, effectively reducing spectrum resource consumption and lowering hardware costs. However, with the further increase in communication and sensing requirements, ISAC systems face challenges such as spectrum efficiency bottlenecks and insufficient utilization of spatial resources. To further enhance the depth of the physical layer, fluid antenna systems have been proposed and introduced into the communication field. Traditional Multiple Input Multiple Output (MIMO) systems use fixed-position antennas (FPA) to achieve communication and sensing functions, resulting in insufficient utilization of wireless channel resources. Fluid antennas can freely change their position and physical characteristics, providing additional DoF to ISAC systems, thus effectively overcoming the inherent limitations of fixed antennas in terms of space resource utilization. Fluid antennas can utilize their shape and positional flexibility to select optimal channel conditions within a specific space, fully leveraging space resources to improve performance.

[0003] Fluid antenna-assisted ISAC systems actively adapt to the wireless channel environment by dynamically reconfiguring antenna positions, introducing additional spatial dimension gain to the system. This fully utilizes channel resources within the field response region, effectively suppressing interference and improving the signal-to-interference-plus-noise ratio (SINR), while significantly enhancing the communication and sensing performance of the ISAC system. The advantage of fluid antenna-assisted ISAC systems in beamforming lies in the joint optimization of antenna position and beamforming vector, achieving superior communication and sensing performance. However, this also results in a tight coupling between beamforming vector and antenna position variables, making the joint optimization problem extremely challenging. Therefore, this invention will further investigate the beamforming problem of fluid antenna-assisted ISAC systems, achieving joint optimization of beamforming vector and fluid antenna position, and promoting the application and development of fluid antenna technology in ISAC systems. Summary of the Invention

[0004] The purpose of this invention is to propose a joint beamforming and position optimization method for a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm. By jointly optimizing the beamforming vector and the fluid antenna position, communication and data rate are maximized under the constraints of fluid antenna position, minimum sensing beammap gain and maximum base station transmit power, thereby improving communication performance.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] This invention provides a method for joint beamforming and position optimization of a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm. The method includes the following steps:

[0007] (1) Construct a fluid antenna-assisted ISAC system model;

[0008] (2) Establish a joint optimization beamforming and antenna position problem with the goal of maximizing communication and rate, and use the weighted minimum mean square error algorithm to transform the objective function into a problem of minimizing the weighted mean square error;

[0009] (3) The problem is decomposed into subproblems using an alternating optimization algorithm, and the algorithm variables are initialized.

[0010] (4) Solve for auxiliary variables and receiving beamformer;

[0011] (5) The successive convex approximation algorithm is used to solve for the transmitted beamforming vector;

[0012] (6) The position of the fluid antenna is solved using the quantum particle swarm optimization algorithm;

[0013] (7) Alternately execute steps (4), (5), and (6) until the objective function converges or the maximum number of iterations is reached, and output the optimal beamforming vector and fluid antenna position.

[0014] Furthermore, step 1, for the fluid antenna-assisted ISAC system, considers the far-field scenario, where the base station is configured with... The root fluid antenna is responsible for simultaneously transmitting communication and sensing signals. ≥2, is A single fixed antenna provides communication to a user and sensing to a target, achieving dual communication and sensing functions. The movable area of ​​the fluid antenna is set to a size of [size missing]. square area , Let the side length be , and use a two-dimensional Cartesian coordinate system to locate the antenna position. Indicates the base station The Cartesian coordinates of the root fluid antenna, where , , , Indicates transpose. , They represent the first Root fluid antenna in , Coordinates on the coordinate axes express The location of the root antenna. The fluid antennas at the base station can move freely within the movable area. To avoid coupling effects between antennas in the base station area, the location of each pair of fluid antennas is... , Minimum distance constraint needs to be guaranteed between them. , , For wavelength, Describes the Euclidean norm of a vector. Indicates the first root antenna and the first Root antenna position , The Euclidean distance between them. Therefore, the first... The communication signal received at each user can be expressed as: , ,definition The transmitted signal symbol, To launch to the The signal symbols of each user are independent complex Gaussian random variables, following zero mean and unit variance, and satisfying the following... , Indicates the expectation. This indicates a modulo operation. In order to target the Beamforming vectors for each user , Represents the set of complex numbers. Indicates the first The mean of the users is 0, and the variance is... Gaussian white noise, This represents a cyclically symmetric complex Gaussian distribution. This indicates the power of the noise. Indicates from the base station to the... The channel vector for each user is represented as: ,in, It is a column vector of all 1s. Represents the set of real numbers. For base station to the Number of transmit channel paths per user For base station and the The transmit response matrix for communication between individual users can be represented as: , Indicates the base station and the first When a user communicates, the base station at the first... Transmit field response vector of the root fluid antenna: , The imaginary unit, It is a natural constant. , Indicates the corresponding first The reference origin at the base station corresponding to the transmission path and the first The propagation difference at the location of the root fluid antenna, where , It is given by the following formula: , Base station and the When a user communicates, the base station is at the first... The elevation and azimuth angles of the transmission path, where , Indicates the base station and the first The path response diagonal matrix for individual user communication for The diagonal element represents the corresponding first element. The channel coefficients of the transmission path, therefore the first... The signal-to-interference-plus-noise ratio (SINR) at each user location is: , In order to target the The beamforming vector for each user, and the corresponding communication and rate, are expressed as follows: ;

[0015] For the sensing channel, when the base station senses a target, the base station transmits the following response matrix: , This indicates the number of transmission paths from the base station to the target. Indicates the first The transmit field response vector of a root fluid antenna can be expressed in the following form: , The first time the base station senses the target The reference origin at the base station corresponding to the transmission path and the first The propagation difference at the location of the root fluid antenna. , It is given by the following formula: , When the base station senses the target, the base station is at the first... The elevation and azimuth angles of the launch path, where, Therefore, the corresponding sensing beammap gain is: ,in To obtain the trace of the matrix, This indicates the conjugate transpose.

[0016] Furthermore, step 2 proposes a beamforming problem for a fluid antenna-assisted ISAC system that maximizes communication and rate. The goal is to jointly optimize the beamforming vector and the fluid antenna position while limiting the sensing beammap gain and the base station transmit power. The problem is as follows:

[0017] ;

[0018] Among them, constraint C1 is the feasible area constraint for the antenna at the base station. Indicates size is The square feasible region; C2 is the antenna spacing constraint at the base station, indicating that the spacing between any two antennas must be greater than [missing information]. , Let the minimum spacing constraint be represented as... C3 represents the sensing beammap gain constraint. C4 represents the minimum sensing beammap gain; C4 is the transmit power constraint. This represents the maximum transmit power. For objective functions with fractional and logarithmic structures, a weighted minimum mean square error algorithm is used. This algorithm replaces the original objective function with the weighted mean square error between the received and transmitted signals. Indicates the first The estimated signal received by each user. For the first Individual user receives beamformer This indicates taking the conjugate, therefore corresponding to the first... The weighted mean square error for each user is: , Taking the real part, the original communication and rate maximization problem is transformed into minimizing the weighted mean square error problem:

[0019] ;

[0020] in, Let be a scalar, representing the first... The auxiliary variables for each user are transformed into a form that is easier to solve, as the original complex fractional and logarithmic structures are now converted into a form that is easier to solve.

[0021] Furthermore, in step 3, to address the non-convexity of the objective function and constraints, an alternating optimization algorithm is employed, with optimization variables including auxiliary variables. and receiving beamformer Transmit beamforming vector Fluid antenna position Therefore, initialization , , , .

[0022] Furthermore, step 4 involves optimizing auxiliary variables. and receiving beamformer At that time, by fixing the beamforming vector Fluid antenna position Solve the subproblem. Then, by taking the derivative and setting the derivative value to 0, find the optimal closed-form solution for the auxiliary variables and the receiving beamformer.

[0023] Furthermore, step 5 involves solving for the beamforming vector by fixing the position of the fluid antenna. Auxiliary variables and receiving beamformer The problem is transformed into a question about beamforming vectors. The subproblem is specifically addressed by employing a successive convex approximation algorithm to handle the non-convex perceptual constraints. A first-order Taylor expansion is used to find the lower bound of the original constraints, resulting in linearized convex function constraints. At this point, the problem is transformed into a convex problem, which can be solved using a convex optimization solver. The current beamforming vector from the alternating optimization algorithm is used as the initial value for the successive convex approximation algorithm. The algorithm iteratively solves the problem until the objective function converges or the maximum number of iterations is reached, outputting the current optimal beamforming vector.

[0024] Furthermore, step 6 involves fixing the auxiliary variable. Receiver beamformer and beamforming vector Under the given conditions, the quantum particle swarm optimization algorithm is used to solve the fluid antenna position optimization subproblem, including the following steps:

[0025] (S1) Initialization Phase: First, the quantum particle swarm algorithm introduces... A population of particles, each representing a potential solution for the antenna position, is initialized for each particle. Initial position: The position vector contains The coordinate information of the root antenna on a two-dimensional plane, its dimension is , Representing the The first particle root antenna , Axis coordinates, settings , The upper limit of the axis coordinates is The lower limit is A hot-start strategy is adopted, where 30% of the particles are initialized with Gaussian perturbations near the current fluid antenna position during alternating optimization, thereby accelerating convergence and ensuring the monotonicity of the alternating optimization algorithm. The positions of the remaining particles are uniformly sampled within the feasible region to ensure population diversity. The quantum particle swarm optimization algorithm uses the probability amplitude of the qubit as the real-valued encoding of the particle position. The qubit can be represented by the probability amplitude as follows: ,satisfy First, the values ​​in the physical space are mapped to the range of values ​​for the quantum probability amplitude by normalization: And further converted into phase form: ,in, Indicates the first The first particle The initial phase of each qubit. , The quantum code corresponding to the particle is obtained: The initial fitness and the optimal fitness of all particles are calculated to obtain the initial individual optimal fitness and the global optimal fitness, where the quantum bit... state and The probability magnitude row vectors of the state are expressed as cosine and sine components, respectively: ,

[0026] ;

[0027] (S2) Solution Space Transformation: The range of values ​​for the probability amplitude of a qubit in the quantum particle swarm optimization algorithm is within... In order to evaluate fitness, it needs to be mapped to the domain of the actual problem: In the middle, the first is obtained through mapping. Cosine and sine components of quantum particles under round iteration , Corresponding cosine and sinusoidal fluid antenna positions , And calculate fitness based on location. For the current iteration round, , This represents the maximum number of iterations.

[0028] (S3) Fitness Function Definition and Constraint Handling: In order to evaluate the quality of particles, the fitness function is defined as follows: Fitness function for round iteration: The function consists of two parts: the objective function, which is the original minimized objective function. Penalty term: A penalty function is introduced to address the antenna spacing constraints and sensing performance constraints. If a particle's position does not meet the constraints, its fitness value is increased through a penalty factor, causing it to be eliminated in the iteration. For each iteration, since the particle's qubit encoding consists of cosine and sine components, two candidate positions are mapped out through solution space transformation. and Using the fitness function to respectively and Calculations are performed to obtain the corresponding , The better value between the two is taken as the current fitness of the particle, i.e. If the current particle's fitness If the individual's fitness is better than its optimal fitness, then update the individual's optimal phase. If the individual's optimal fitness is better than the global optimal fitness, then update the global optimal phase. and the global optimal fitness;

[0029] (S4) Particle State Iterative Update: The quantum particle swarm optimization algorithm explores the optimal path by comprehensively utilizing the individual experience of the particles and the global experience of the swarm. It employs a quantum rotation gate to realize position evolution. Particle velocity updates are equivalent to qubit phase increment updates, while particle position updates are reflected in the qubit probability amplitude updates. In the first iteration, the... The first particle The phase increment of each qubit is expressed as: ,in, Define the phase increment of the previous round. , For inertial weights, For the individual optimal phase The Dimensional elements With particles The Current phase of each qubit The difference, Global optimal phase The Dimensional elements With particles The Current phase of each qubit The difference in phase difference needs to be considered. Furthermore, to ensure that particles rotate along the shortest path towards their individual / global optimum, periodic boundary treatment is required for the phase difference. and These are individual learning and global learning factors, respectively. and These are two random parameters uniformly distributed in [0,1]. The position of the particle is obtained by updating the probability amplitude of the qubit through a quantum rotation gate.

[0030] ;

[0031] in, For particles The The first qubit Phase in round iteration, For the updated number The phase in the round of iteration, thus obtaining the first... The quantum code corresponding to the next-generation position of each particle;

[0032] (S5) Mutation processing: To avoid getting trapped in local optima, each updated particle is processed according to the mutation probability. The mutation operation is performed by randomly selecting half of the qubits from the particle and using a quantum NOT gate to implement a phase transformation. This ensures the diversity of the population and enables the algorithm to escape local optima.

[0033] (S6) Looping and Convergence: Repeatedly execute solution space transformation, fitness evaluation, individual / global optimal update, probability amplitude update of qubits and mutation operation until the maximum number of iterations is reached or the convergence condition is met, and finally output the global optimal fluid antenna position.

[0034] Furthermore, step 7 involves alternately executing steps 4, 5, and 6. When the relative change of the minimum mean square error objective function is less than the threshold or the number of iterations is greater than the maximum number, the alternating optimization ends, and the optimal beamforming vector and fluid antenna position are output.

[0035] Compared with existing technologies, the advantages of this invention are: This invention can maximize communication and data rate by jointly optimizing the beamforming vector and antenna position under constraints of fluid antenna location, minimum sensing beammap gain, and maximum base station transmit power. To effectively solve the non-convex optimization problem, a weighted minimum mean square error algorithm is used to transform the communication and data rate objective functions; an alternating optimization algorithm is used to decompose the original joint optimization problem into multiple non-convex sub-problems; and each non-convex sub-problem is solved using a successive convex approximation algorithm and a quantum particle swarm optimization algorithm. This invention can effectively improve communication and data rate and is superior to traditional ISAC systems equipped with FPA. Attached Figure Description

[0036] Figure 1 This is a flowchart of a method for joint beamforming and position optimization of a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm according to the present invention;

[0037] Figure 2 A schematic diagram illustrating the construction of a fluid antenna-assisted ISAC system model for this invention;

[0038] Figure 3 This is a convergence graph of the algorithm proposed in the simulation experiment of this invention with the number of iterations;

[0039] Figure 4 This is a graph showing how communication and speed vary with the size of the movable area in the simulation experiment of this invention;

[0040] Figure 5 This is a graph showing the changes in communication and speed as a function of signal-to-noise ratio in the simulation experiment of this invention. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0042] like Figure 1-2 As shown: Step (1): Constructing a fluid antenna-assisted ISAC system model:

[0043] This step is used to construct the channel and signal model of the fluid antenna-assisted ISAC system, providing a foundation for the optimization problem and algorithm formulation:

[0044] For fluid antenna-assisted ISAC systems, considering far-field scenarios, the base station is configured with... The root fluid antenna is responsible for simultaneously transmitting communication and sensing signals. ≥2, is A single fixed antenna provides communication to a user and sensing to a target, achieving dual communication and sensing functions. The movable area of ​​the fluid antenna is set to a size of [size missing]. square area , Let the side length be , and use a two-dimensional Cartesian coordinate system to locate the antenna position. Indicates the base station The Cartesian coordinates of the root fluid antenna, where , , , Indicates transpose. , They represent the first Root fluid antenna in , Coordinates on the coordinate axes express The location of the root antenna. The fluid antennas at the base station can move freely within the movable area. To avoid coupling effects between antennas in the base station area, the location of each pair of fluid antennas is... , Minimum distance constraint needs to be guaranteed between them. , , For wavelength, Describes the Euclidean norm of a vector. Indicates the first root antenna and the first Root antenna position , The Euclidean distance between them. Therefore, the first... The communication signal received at each user can be expressed as: , ,definition The transmitted signal symbol, To launch to the The signal symbols of each user are independent complex Gaussian random variables, following zero mean and unit variance, and satisfying the following... , Indicates the expectation. This indicates a modulo operation. In order to target the Beamforming vectors for each user , Represents the set of complex numbers. Indicates the first The mean of the users is 0, and the variance is... Gaussian white noise, This represents a cyclically symmetric complex Gaussian distribution. This indicates the power of the noise. Indicates from the base station to the... The channel vector for each user is represented as: ,in, It is a column vector of all 1s. Represents the set of real numbers. For base station to the Number of transmit channel paths per user For base station and the The transmit response matrix for communication between individual users can be represented as: , Indicates the base station and the first When a user communicates, the base station at the first... Transmit field response vector of the root fluid antenna: , The imaginary unit, It is a natural constant. , Indicates the corresponding first The reference origin at the base station corresponding to the transmission path and the first The propagation difference at the location of the root fluid antenna, where , It is given by the following formula: , Base station and the When a user communicates, the base station is at the first... The elevation and azimuth angles of the transmission path, where , Indicates the base station and the first The path response diagonal matrix for individual user communication for The diagonal element represents the corresponding first element. The channel coefficients of the transmission path, therefore the first... The signal-to-interference-plus-noise ratio (SINR) at each user location is: , In order to target the The beamforming vector for each user, and the corresponding communication and rate, are expressed as follows: ;

[0045] For the sensing channel, when the base station senses a target, the base station transmits the following response matrix: , This indicates the number of transmission paths from the base station to the target. Indicates the first The transmit field response vector of a root fluid antenna can be expressed in the following form: , The first time the base station senses the target The reference origin at the base station corresponding to the transmission path and the first The propagation difference at the location of the root fluid antenna. , It is given by the following formula: , When the base station senses the target, the base station is at the first... The elevation and azimuth angles of the launch path, where, Therefore, the corresponding sensing beammap gain is: ,in To obtain the trace of the matrix, This indicates the conjugate transpose.

[0046] Step (2): Establish a joint optimization beamforming and antenna location problem with the goal of maximizing communication and rate, and use the weighted minimum mean square error algorithm to transform the objective function into a problem of minimizing the weighted mean square error:

[0047] A beamforming problem for a fluid antenna-assisted ISAC system that maximizes communication and data rate is proposed. The goal is to jointly optimize the beamforming vector and the fluid antenna position while constraining the sensing beammap gain and the base station transmit power. The problem is as follows:

[0048] ;

[0049] Among them, constraint C1 is the feasible area constraint for the antenna at the base station. Indicates size is The square feasible region; C2 is the antenna spacing constraint at the base station, indicating that the spacing between any two antennas must be greater than [missing information]. , Let the minimum spacing constraint be represented as... C3 represents the sensing beammap gain constraint. C4 represents the minimum sensing beammap gain; C4 is the transmit power constraint. This represents the maximum transmit power of the base station. For objective functions with fractional and logarithmic structures, a weighted minimum mean square error algorithm is used. This algorithm replaces the original objective function with the weighted mean square error between the received and transmitted signals. Indicates the first The estimated signal received by each user. For the first Individual user receives beamformer This indicates taking the conjugate, therefore corresponding to the first... The weighted mean square error for each user is: , Taking the real part, the original communication and rate maximization problem is transformed into minimizing the weighted mean square error problem:

[0050] ;

[0051] in, Let be a scalar, representing the first... The auxiliary variables for each user are transformed into a form that is easier to solve, as the original complex fractional and logarithmic structures are now converted into a form that is easier to solve.

[0052] Step (3): Decompose the problem into subproblems using the alternating optimization algorithm and initialize the algorithm variables;

[0053] To address the non-convexity of the objective function and constraints, an alternating optimization algorithm is employed. Optimization variables include auxiliary variables. Receiver beamformer Transmit beamforming vector and fluid antenna position Therefore, initialization , , , .

[0054] Step (4): Solve for auxiliary variables and receiver beamformer:

[0055] To solve for the auxiliary variables and the receiving beamformer, the beamforming vector is first fixed. Fluid antenna position The original optimization problem is transformed into:

[0056] ;

[0057] The problem then becomes and The unconstrained minimization problem can be solved by respectively applying... , Find the derivative and set its value to 0. (Auxiliary variable) and receiving beamformer The solution is:

[0058] ;

[0059] .

[0060] in, This indicates finding the inverse of a matrix or taking the reciprocal of a scalar.

[0061] Step (5): Solve for the transmitted beamforming vector using the successive convex approximation algorithm:

[0062] Next, the beamforming vector is solved by fixing the position of the fluid antenna. Auxiliary variables and receiving beamformer The original optimization problem is transformed into:

[0063] ;

[0064] For the non-convex constraint C1, considering It is a positive semi-definite matrix, and the left side is a matrix about... convex function, To transform it into a convex constraint, a successive convex approximation algorithm is used to apply C1 in... First-order Taylor expansion is used here:

[0065] ;

[0066] in In the successive convex approximation algorithm, the previous iteration is... The value of is then changed, and the constraint changes from a non-convex constraint to a convex constraint. The original problem is transformed into:

[0067] ;

[0068] It can be solved directly through a convex optimization solver. The current beamforming vector of the alternating optimization algorithm is used as the initial value of the successive convex approximation algorithm. The successive convex approximation algorithm is used to iterate until the objective function converges or the maximum number of iterations is reached, and the current optimal beamforming vector is output.

[0069] Step (6): Solve for the fluid antenna position using the quantum particle swarm optimization algorithm:

[0070] To solve the fluid antenna position optimization problem, a fixed beamforming vector is used. Auxiliary variables and receiving beamformer The problem is transformed into:

[0071] ;

[0072] The corresponding quantum particle swarm optimization algorithm is as follows:

[0073] (S1) Initialization phase:

[0074] First, the algorithm introduces... A population of particles, each representing a potential solution for the antenna position. The position of each particle is initialized using a warm-start strategy: 30% of the particles are initialized near the current fluid antenna position through Gaussian perturbation, accelerating convergence and ensuring the monotonicity of the alternating optimization algorithm; the positions of the remaining particles are uniformly sampled within the feasible region to ensure population diversity. The position vector contains... The coordinate information of the root antenna on a two-dimensional plane, its dimension is ,make Represents particles Initial position:

[0075] ;

[0076] in, Representing the The first particle root antenna , Axis coordinates, settings , The upper limit of the axis coordinates is The lower limit is Based on the concept of quantum coding, the state of a single quantum bit It can be represented as state and The superposition of states is represented as: It can satisfy the normalization condition. of and Representing the probability amplitude, this invention uses the probability amplitude of the qubit for real-number encoding, and introduces the phase of the qubit. ,make , A qubit can be represented by its probability amplitude as: ,satisfy Therefore, the physical space values ​​are first normalized: The range of values ​​for the probability amplitude mapped to a qubit: Furthermore, the normalized position is converted into phase form, assuming the initial phase is a cosine component, taking into account the inverse cosine function. The range of values ​​is limited to To ensure the diversity of initial states of qubits and the completeness of the search space, a random symbolic operator is introduced. Extend the phase, that is:

[0077] ;

[0078] in It is a random variable that takes the value 1 or -1 with equal probability. express The The element of dimension, due to the even symmetry of the cosine function, i.e.: This operation extends the quantum phase search range to At the same time, the corresponding physical position remains unchanged. The phase form representing the initial position of the fluid antenna. Indicates the first The first particle The initial phase of qubits, where, , At this time, the first The quantum code of the current position of a particle is represented by the probability amplitude of the qubit as follows:

[0079] ;

[0080] A particle represents two potential solutions, and its initial fitness and the optimal fitness of all particles are calculated to obtain the initial individual optimal fitness and the global optimal fitness. (Quantum bits in quantum encoding) state and The probability magnitude row vectors of the state are expressed as cosine and sine components, respectively:

[0081] ;

[0082] ;

[0083] (S2) Solution space transformation:

[0084] The range of values ​​for the probability amplitude of a qubit in the quantum particle swarm optimization algorithm is within... Between. To evaluate fitness, it needs to be mapped to the domain of the actual problem: In the middle. Therefore, in the first In rounds of iteration, For the current iteration round, , For the maximum number of iterations, the number of iterations is... The first particle One quantum bit: The mapped fluid antenna position is:

[0085] ;

[0086] ;

[0087] , Representing the cosine components respectively Sine component The corresponding fluid antenna position vector is used to calculate the fitness based on the fluid antenna position.

[0088] (S3) Definition of fitness function:

[0089] The fitness function is used to evaluate the performance of each particle, that is, to determine whether the particle's position can achieve the desired performance requirements. For the fluid antenna position optimization problem, there are antenna spacing constraints C2 and sensing performance constraints C3. Therefore, considering the constraints, a penalty function is introduced:

[0090] ;

[0091] in, express The corresponding antenna position coordinates , Indicates the first In the first iteration, the... The first particle root and first The coordinates of the root antenna, The penalty factor, representing the constraint, can adjust the severity of the penalty and is generally set to a large value. It is an indicator function that returns 1 when the internal conditions are met and 0 when they are not, ensuring that the fitness function is effectively increased when the position and perception constraints are not met.

[0092] Therefore, the fitness function for the current minimization problem is defined as:

[0093] ;

[0094] To optimize the objective function of the problem, for minimization problems, a large penalty function is added to the fitness function to ensure that the fitness of the current position is no better than that of other positions. At this point, by setting penalty functions for sensing constraints and antenna spacing constraints, the original problem is transformed, and the obtained solution satisfies the constraints of the original problem.

[0095] For each iteration, since the quantum bit encoding of a particle consists of cosine and sine components, the solution space transformation maps to the positions of the two candidate fluid antennas. and The fitness function was used to respectively... and Calculations are performed to obtain the corresponding , The better value between the two is taken as the current fitness of the particle, i.e. If the current particle's fitness If the individual's fitness is better than its optimal fitness, then update the individual's optimal phase. If the individual's optimal fitness is better than the global optimal fitness, then update the global optimal phase. and the global optimal fitness;

[0096] (S4) Particle state update:

[0097] After fitness calculation and comparison, the first... Individual optimal phase of each particle and global optimal phase For the minimization problem, the th Particles The optimal position of an individual is:

[0098] ;

[0099] The globally optimal position is:

[0100] ;

[0101] in, and For particles Individual optimal phase The corresponding fluid antenna position, and Global optimal phase The corresponding fluid antenna position, For the individual optimal phase The dimensional elements, Global optimal phase The In the quantum particle swarm optimization algorithm, the position evolution is realized by using quantum rotation gates. The particle velocity update is equivalent to the phase increment update of the qubit, and the particle position update is reflected as the probability amplitude update of the qubit.

[0102] In the During the round of iteration, the first The first particle Phase increment of each qubit Determined by the following formula:

[0103] ;

[0104] in, Define the phase increment of the previous iteration. , and These are the individual learning and global learning factors, used to determine the step size for each particle to move towards the individual and global optimal phases; and These are two random parameters uniformly distributed in [0,1], designed to improve the randomness of the search for escaping local optima; This represents the inertia weight. To balance the search speed and accuracy of particles, its value gradually decreases as the number of iterations increases, and it takes the following form:

[0105] ;

[0106] and yes Maximum and minimum value limits;

[0107] For the individual optimal phase The Dimensional elements With particles The Current phase of each qubit The difference, Global optimal phase The Dimensional elements With particles The Current phase of each qubit The difference, and in order to ensure that the particle rotates to the shortest path towards the individual optimum / global optimum, requires periodic boundary treatment of the phase difference, expressed as:

[0108]

[0109] ;

[0110] After obtaining the number After the phase increment of each particle, the probability amplitude is updated through a quantum rotation gate:

[0111] ;

[0112] Get the first The next round of quantum encoding for each particle is as follows:

[0113] ;

[0114] (S5) Mutation treatment:

[0115] To avoid getting trapped in local optima, each updated particle is processed according to its mutation probability. Perform a mutation operation. Randomly select half of the qubits from the particle and use a quantum NOT gate to implement a phase transition:

[0116] ;

[0117] This ensures the diversity of the population, enabling the algorithm to escape local optima.

[0118] (S6) Cycles and Convergence:

[0119] Repeat the solution space transformation, fitness evaluation, individual / global optimal update, quantum bit probability amplitude update and mutation operation until the maximum number of iterations is reached or the convergence condition is met, and finally output the global optimal fluid antenna position.

[0120] Step (7): Alternately execute steps (4), (5), and (6). When the relative change of the minimum mean square error objective function is less than the threshold or the number of iterations is greater than the maximum number, end the alternating optimization and output the optimal beamforming vector and fluid antenna position.

[0121] The above seven steps enable the joint optimization of beamforming vectors and fluid antenna position under the constraints of fluid antenna position, minimum sensing beammap gain, and maximum base station transmit power, thereby maximizing communication and data rate.

[0122] This invention uses MATLAB simulations to verify the effectiveness of the proposed fluid antenna-assisted beamforming scheme for an ISAC system. The number of fluid antennas at the base station is set. The number of users is 4. The number is 3, and it is equipped with a single fixed antenna. The number of transmission paths and the number of sensing channel paths are... The movable region of the fluid antenna has a side length of The square area, in which , The wavelength is set to 0.06m. This is the parameter setting for the quantum particle swarm optimization algorithm, where the number of particles is [value missing]. The maximum number of iterations for a particle is 200. The individual learning factor is 100. The global learning factor is 1.4. The maximum inertia weight is 1.4. The minimum inertia weight is 0.9. The value is 0.4, and the convergence threshold is... Punishment factor The mutation probability is 10. The signal-to-noise ratio (SNR) at the base station is =9dB, minimum sensing beammap gain is =10dB.

[0123] To demonstrate the advantages of this invention, the proposed design is compared with that of a fixed antenna (where the antenna position remains constant and only the beamforming vector is optimized) and an alternating position selection (APS) scheme (where the movable area of ​​the antenna is quantized into a distance of...). The discrete candidate positions are compared with the discrete position optimization scheme (which alternately optimizes the beamforming vector and the discrete position of the antenna to maximize the system objective function) and the separate optimization scheme (which optimizes the beamforming vector and the fluid antenna position in two stages).

[0124] Figure 3 The convergence graph of the algorithm is shown. The algorithm proposed in this invention has good convergence. As the number of iterations increases, the proposed scheme can converge to the optimal value with a finite number of iterations. Furthermore, as the SNR increases, the communication and speed of the proposed algorithm also increase. This experimental result proves the effectiveness of the algorithm proposed in this invention.

[0125] Figure 4 The experiment demonstrates how communication and speed change with the increase of the mobile area. Experimental results show that the communication and speed of the proposed scheme significantly improve with the expansion of the mobile area A. This is because a larger mobile space allows the antenna to more flexibly find a better channel. However, when the mobile area grows to a certain size, the communication and speed of the fluid antenna scheme stabilize and no longer increase significantly. At this point, the antenna is close to the maximum gain of the proposed scheme, indicating that the antenna's space requirements are not infinite. Therefore, the fluid antenna should choose an appropriate mobile area size. Furthermore, during the change process, the fluid antenna consistently maintains optimal communication and speed levels, outperforming other benchmark schemes, demonstrating the superiority and effectiveness of the proposed scheme.

[0126] Figure 5 The diagram illustrates the impact of changes in communication and data rate with transmit SNR, intuitively reflecting the influence of different transmit SNR states on the communication performance of each scheme in the ISAC system. The diagram clearly shows that the communication and data rate of all schemes exhibit a monotonically increasing trend with increasing transmit SNR. In terms of performance, compared to other benchmark schemes, the proposed scheme is significantly superior in both communication and data rate and their growth rate. Furthermore, there is a significant performance gap between the APS scheme and the proposed scheme. This is because the APS scheme discretizes the antenna movement area into a finite number of candidate positions, limiting the optimization accuracy of the antenna position. In contrast, the proposed scheme, through continuous position optimization, can more fully explore the optimal position within the antenna field response area, thereby achieving higher communication and data rate. Compared to the fixed antenna scheme, the proposed scheme exhibits higher communication and data rate and a faster growth rate. By adjusting the antenna position, it actively avoids channel areas with poor signal transmission environments, demonstrating superior anti-interference capabilities and achieving more significant performance enhancements under high SNR conditions.

[0127] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A method for joint beamforming and position optimization of a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm, characterized in that, Includes the following steps: (1) Construct a fluid antenna-assisted ISAC system model; (2) Establish a joint optimization beamforming and antenna position problem with the goal of maximizing communication and rate, and use the weighted minimum mean square error algorithm to transform the objective function into a problem of minimizing the weighted mean square error; Step (2) establishes a joint optimization beamforming and antenna location problem with the goal of maximizing communication and rate, and uses the weighted minimum mean square error algorithm to transform the objective function into a problem of minimizing the weighted mean square error, specifically: A beamforming problem for a fluid antenna-assisted ISAC system that maximizes communication and data rate is proposed. The goal is to jointly optimize the beamforming vector and the fluid antenna position while constraining the sensing beammap gain and the base station transmit power. The problem is as follows: ； Among them, constraint C1 is the feasible area constraint for the antenna at the base station. Indicates size is The square feasible region; C2 is the antenna spacing constraint at the base station, indicating that the spacing between any two antennas must be greater than [missing information]. , Let the minimum spacing constraint be represented as... C3 represents the sensing beammap gain constraint. C4 represents the minimum sensing beammap gain; C4 is the transmit power constraint. Indicates the maximum transmission power of the base station. Indicates the base station Cartesian coordinates of a root fluid antenna express The location of the root antenna; In order to target the Beamforming vectors for each user In order to target the Beamforming vectors for each user; For objective functions with fractional and logarithmic structures, a weighted minimum mean square error algorithm is used. This algorithm replaces the original objective function by calculating the weighted mean square error between the received and transmitted signals. Indicates the first The estimated signal received by each user. Indicates the first The mean for each user is 0. For the first Individual user receives beamformer This indicates taking the conjugate, therefore corresponding to the first... The weighted mean square error for each user is: , Indicates taking the real part, The power representing the noise. Indicates from the base station to the... The channel vectors of each user are transformed from the original problem of maximizing communication and rate into a problem of minimizing the weighted mean square error: ； in, Let be a scalar, representing the first... The auxiliary variables for each user are transformed from complex fractional and logarithmic structures into easily solvable forms. (3) The problem is decomposed into subproblems using an alternating optimization algorithm, and the algorithm variables are initialized. (4) Solve for auxiliary variables and receiving beamformer; (5) The successive convex approximation algorithm is used to solve for the transmitted beamforming vector; (6) The position of the fluid antenna is solved using the quantum particle swarm optimization algorithm; (7) Alternately execute steps (4), (5), and (6) until the objective function converges or the maximum number of iterations is reached, and output the optimal beamforming vector and fluid antenna position.

2. The method for joint beamforming and position optimization of a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm according to claim 1, characterized in that, Step (1) involves constructing a fluid antenna-assisted ISAC system model, specifically as follows: For fluid antenna-assisted ISAC systems, considering far-field scenarios, the base station is configured with... The root fluid antenna is responsible for simultaneously transmitting communication and sensing signals. ≥2, is A single fixed antenna provides communication to a user and sensing to a target, achieving dual communication and sensing functions. The movable area of ​​the fluid antenna is set to a size of [size missing]. square area , Let the side length be , and use a two-dimensional Cartesian coordinate system to locate the antenna position. Indicates the base station The Cartesian coordinates of the root fluid antenna, where , , , Indicates transpose. , They represent the first Root fluid antenna in , Coordinates on the coordinate axes express The location of the root antenna; The fluid antennas at the base station can move freely within the movable area. To avoid coupling effects between antennas in the base station area, a minimum distance constraint must be maintained between each pair of fluid antennas. , , For wavelength, Describes the Euclidean norm of a vector. Indicates the first root antenna and the first Root antenna position , The Euclidean distance between them, the first The expression for the communication signals received at each user is: , ,definition The transmitted signal symbol, To launch to the The signal symbols of each user are independent complex Gaussian random variables, following zero mean and unit variance, and satisfying the following... , Indicates the expectation. This indicates a modulo operation. In order to target the Beamforming vectors for each user , Represents the set of complex numbers. Indicates the first The mean of the users is 0, and the variance is... Gaussian white noise, This represents a cyclically symmetric complex Gaussian distribution. The power representing the noise. Indicates from the base station to the... The channel vector for each user is represented as: ,in, A column vector consisting entirely of 1s. Represents the set of real numbers. For base station to the Number of transmit channel paths per user For base station and the The transmit response matrix for communication between individual users is represented as follows: ; Indicates the base station and the first When a user communicates, the base station at the first... Transmit field response vector of the root fluid antenna: , The imaginary unit, It is a natural constant. , Indicates the corresponding first The reference origin at the base station corresponding to the transmission path and the first The propagation difference at the location of the root fluid antenna, where , It is given by the following formula: , Base station and the When a user communicates, the base station is at the first... The elevation and azimuth angles of the transmission path. Indicates the base station and the first The path response diagonal matrix for communication between users, where for The diagonal element represents the corresponding first element. The channel coefficients of the transmission path, therefore the first... The signal-to-interference-plus-noise ratio (SIR) at each user location is: , In order to target the The beamforming vector for each user, and the corresponding communication and rate, are expressed as follows: ; For the sensing channel, when the base station senses a target, the base station transmits the following response matrix: , This indicates the number of transmission paths from the base station to the target. Indicates the first The transmit field response vector of the root fluid antenna can be expressed in the following form: , The first time when the base station senses the target The reference origin at the base station corresponding to the transmission path and the first The propagation difference at the location of the root fluid antenna. , It is given by the following formula: , When the base station senses the target, the base station is at the first... The elevation and azimuth angles of the transmission paths, therefore the corresponding sensing beam pattern gain is: ,in To obtain the trace of the matrix, This indicates the conjugate transpose.

3. The method for joint beamforming and position optimization of a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm according to claim 2, characterized in that, The optimization variables in the alternating optimization algorithm in step (3) include auxiliary variables. Receiver beamformer Transmit beamforming vector Fluid antenna position Therefore, initialization , , , .

4. The method for joint beamforming and position optimization of a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm according to claim 3, characterized in that, The solution of auxiliary variables and receiving beamformer in step (4) are specifically as follows: Optimize auxiliary variables and receiving beamformer At that time, by fixing the beamforming vector Fluid antenna position Solve the subproblem. Then, by taking the derivative and setting the derivative value to 0, find the optimal closed-form solution for the auxiliary variables and the receiving beamformer.

5. The method for joint beamforming and position optimization of a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm according to claim 4, characterized in that, The method for solving the transmit beamforming vector in step (5) is as follows: By fixing the position of the fluid antenna Auxiliary variables and receiving beamformer The problem is transformed into a question about beamforming vectors. The beamforming vector is solved by subproblems; The specific processing method is to use a successive convex approximation algorithm to process non-convex perceptual constraints. A first-order Taylor expansion is used to find the lower bound of the original constraint, resulting in a linearized convex function constraint. At this point, the problem is transformed into a convex problem, which is solved by a convex optimization solver. The current beamforming vector of the alternating optimization algorithm is used as the initial value of the successive convex approximation algorithm. The successive convex approximation algorithm is used to iterate until the objective function converges or the maximum number of iterations is reached, and the current optimal beamforming vector is output.

6. The method for joint beamforming and position optimization of a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm according to claim 5, characterized in that, The quantum particle swarm optimization algorithm is used to solve for the position of the fluid antenna, which includes the following steps: (S1) Initialization Phase: First, the quantum particle swarm algorithm introduces... A population of particles, each representing a potential solution for the antenna position, is initialized for each particle. Initial position: The position vector contains The coordinate information of the root antenna on a two-dimensional plane, its dimension is , Representing the The first particle root antenna , Axis coordinates, settings , The upper limit of the axis coordinates is The lower limit is A hot-start strategy is adopted, where 30% of the particles are initialized with Gaussian perturbations near their current fluid antenna positions during alternating optimization, thus accelerating convergence and ensuring the monotonicity of the alternating optimization algorithm. The positions of the remaining particles are uniformly sampled within the feasible region to ensure population diversity. The quantum particle swarm optimization algorithm uses the probability amplitude of the qubit as the real-valued encoding of the particle position. The qubit can be represented by the probability amplitude as follows: ,satisfy First, the values ​​in the physical space are mapped to the range of values ​​for the quantum probability amplitude by normalization: And further converted into phase form: ,in, Indicates the first The first particle The initial phase of each qubit. , The quantum code corresponding to the particle is obtained: The initial fitness and the optimal fitness of all particles are calculated to obtain the initial individual optimal fitness and the global optimal fitness, where the quantum bit... state and The probability magnitude row vectors of the state are expressed as cosine and sine components, respectively: , ； (S2) Solution Space Transformation: The range of values ​​for the probability amplitude of a qubit in the quantum particle swarm optimization algorithm is within... In order to evaluate fitness, it needs to be mapped to the domain of the actual problem: In the middle, the first is obtained through mapping. Cosine and sine components of quantum particles under round iteration , Corresponding cosine and sinusoidal fluid antenna positions , And calculate fitness based on location. For the current iteration round, , This represents the maximum number of iterations. (S3) Fitness Function Definition and Constraint Handling: In order to evaluate the quality of particles, the fitness function is defined as follows: Fitness function for round iteration: The function consists of two parts: the objective function, which is the original minimized objective function. Penalty term: A penalty function is introduced to address the antenna spacing constraints and sensing performance constraints. If a particle's position does not meet the constraints, its fitness value is increased through a penalty factor, causing it to be eliminated in the iteration. For each iteration, since the particle's qubit encoding consists of cosine and sine components, two candidate positions are mapped out through solution space transformation. and Using the fitness function to respectively and Calculations are performed to obtain the corresponding , The better value between the two is taken as the current fitness of the particle, i.e. If the current particle's fitness If the individual's fitness is better than its optimal fitness, then update the individual's optimal phase. If the individual's optimal fitness is better than the global optimal fitness, then update the global optimal phase. and the global optimal fitness; (S4) Particle State Iterative Update: The quantum particle swarm optimization algorithm explores the optimal path by comprehensively utilizing the individual experience of the particles and the global experience of the swarm. It employs a quantum rotation gate to realize position evolution. Particle velocity updates are equivalent to qubit phase increment updates, while particle position updates are reflected in the qubit probability amplitude updates. In the first iteration, the... The first particle The phase increment of each qubit is expressed as: ,in, Define the phase increment of the previous round. , For inertial weights, For the individual optimal phase The Dimensional elements With particles The Current phase of each qubit The difference, Global optimal phase The Dimensional elements With particles The Current phase of each qubit The difference in phase difference needs to be considered. Furthermore, to ensure that particles rotate along the shortest path towards their individual / global optimum, periodic boundary treatment is required for the phase difference. and These are individual learning and global learning factors, respectively. and These are two random parameters uniformly distributed in [0,1]. The position of the particle is obtained by updating the probability amplitude of the qubit through a quantum rotation gate. ； in, For particles The The first qubit Phase in round iteration, For the updated number The phase in the round of iteration, thus obtaining the first... The quantum code corresponding to the next-generation position of each particle; (S5) Mutation processing: To avoid getting trapped in local optima, each updated particle is processed according to the mutation probability. The mutation operation is performed by randomly selecting half of the qubits from the particle and using a quantum NOT gate to implement a phase transformation. This ensures the diversity of the population and enables the algorithm to escape local optima. (S6) Looping and Convergence: Repeatedly execute solution space transformation, fitness evaluation, individual / global optimal update, probability amplitude update of qubits and mutation operation until the maximum number of iterations is reached or the convergence condition is met, and finally output the global optimal fluid antenna position.

7. The method for joint beamforming and position optimization of a fluid antenna-assisted ISAC system based on quantum particle swarm optimization algorithm according to claim 6, characterized in that, The method for outputting the optimal beamforming vector and fluid antenna position by alternately executing steps (4), (5), and (6) in step (7) until the objective function converges or the maximum number of iterations is reached includes: Alternate optimization of auxiliary variables Receiver beamformer Transmit beamforming vector and fluid antenna position When the relative change of the minimum mean square error objective function is less than the threshold or the number of iterations is greater than the maximum number, the alternating optimization ends and the optimal beamforming vector and fluid antenna position are output.

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