Fluid antenna position and radar communication precoding matrix optimization method in URLLC scene

Abstract

The invention discloses a fluid antenna position and radar communication precoding matrix optimization method in a URLLC scene. The method comprises an integrated architecture supporting communication and perception of multiple user terminals and a single perception target; constructing a communication signal model between the base station and the user terminal in the URLLC scene and a sensing signal model between the base station and the detection target; establishing a mathematical model of a radar communication signal optimization problem by taking maximization of a radar sensing signal-to-noise ratio as a target and taking base station transmitting power, URLLC time delay requirements and fluid antenna position limitation as constraints; the optimization problem is decomposed into three sub-problems, an alternating iteration optimization algorithm is adopted, the three sub-problems are alternately optimized, and a convergence solution is obtained through iteration. According to the invention, the URLLC technology and the multiple-input-multiple-output antenna array and fluid antenna technology are utilized, communication and radar sensing are executed on the same frequency spectrum at the same time, and the requirements of communication and radar sensing in a future network are met.

Description

Technical Field

[0001] The present invention belongs to the technical field of dual-function radar communication, and in particular relates to a method for optimizing a fluid antenna position and a radar communication precoding matrix in a URLLC scenario. Background Art

[0002] In the future intelligent process, wireless communication technology is positioned as the core support for innovative fields such as industrial Internet of Things, smart transportation, telemedicine and environmental monitoring, and is used to promote the deep integration of communication, perception, computing and decision-making capabilities. In this context, both academia and industry believe that future wireless systems need to break through the traditional functional boundaries and achieve the synergistic coexistence of perception and communication. In response to this demand, Integrated Sensing and Communications (ISAC) came into being and quickly became the focus of research on 6G and next-generation communication networks. The core idea of ​​ISAC is to deeply integrate radar environmental perception with wireless data transmission through unified signal design and hardware architecture, reuse spectrum resources and equipment hardware, thereby significantly improving spectrum utilization, reducing deployment energy consumption and hardware costs, and achieving two-way enhancement of perception and communication functions, such as optimizing communication link resource allocation through perception information, or using communication signals to assist high-precision target positioning and environmental modeling.

[0003] In recent years, the exploration of ISAC technology has continued to become a hot topic in the field of wireless communication and perception integration. However, existing research has mostly focused on improving spectrum efficiency and perception accuracy, but few works have deeply analyzed the stringent constraints on ISAC systems in ultra-reliable low-latency communication (URLLC) scenarios. In traditional ISAC designs, the coordination of perception and communication functions is often based on static or quasi-static environment assumptions, which makes it difficult to cope with the high dynamics, extremely low latency, and ultra-high reliability requirements required by URLLC. Especially in scenarios such as industrial automation and emergency obstacle avoidance in the Internet of Vehicles, the real-time nature of perception data is highly coupled with the robustness of the communication link. If communication delays or interruptions cause delayed updates of perception information, it may directly lead to system-level security risks.

[0004] As a core technology supporting mission-critical applications, URLLC ensures service quality through short frame transmission, resource reservation, reliable channel coding and other mechanisms, but its strict latency and reliability constraints pose new challenges to the deep integration of perception functions. For example, how to design waveforms to balance perception resolution and communication bit error rate, the solution to this problem urgently needs to break through the traditional ISAC framework and build a cross-layer optimization theory for URLLC.

[0005] On the other hand, the evolution of ISAC technology continues to drive wireless networks towards multifunctional integration, and the rise of fluid antennas (FAs) has injected new transformative potential into this field. Fluid antennas can flexibly adapt to complex electromagnetic environments by dynamically adjusting antenna shape, position or polarization characteristics, significantly improving channel freedom and interference management capabilities. However, existing ISAC research is mostly based on fixed antenna architectures, which makes it difficult to cope with performance degradation problems caused by spatial correlation, multipath fading and burst interference in high-mobility scenarios (such as high-speed Internet of Vehicles, drone swarms) or densely deployed environments (such as industrial Internet of Things). Especially in URLLC-enabled ISAC systems, traditional fixed antennas are limited in freedom and it is difficult to simultaneously optimize the beamforming of perception waveforms and communication signals under extremely low latency constraints, resulting in reduced perception resolution or communication reliability that is difficult to meet stringent QoS requirements. It is worth noting that the deep coupling of fluid antennas with NOMA and URLLC still faces many challenges, such as the coordinated design of dynamic antenna parameters and ISAC waveforms, the fast feedback mechanism of channel state information (CSI) under ultra-low latency constraints, and the suppression of mutual coupling effects of fluid antennas in high-density deployment scenarios. To solve these problems, it is necessary to build an interdisciplinary theoretical framework that integrates electromagnetics, information theory and optimization algorithms to unleash the full-dimensional potential of fluid antennas in the next-generation intelligent ISAC system.

[0006] In view of this, it is necessary to provide a method for optimizing the fluid antenna position and radar communication precoding matrix in URLLC scenarios to solve the above problems. Summary of the invention

[0007] The present invention aims to solve one of the technical problems existing in the related art at least to a certain extent.

[0008] The purpose of the present invention is to provide a method for optimizing the fluid antenna position and radar communication precoding matrix in a URLLC scenario. Based on the URLLC scenario, the fluid antenna technology is introduced to simultaneously perform radar perception and communication functions on the same spectrum to meet the needs of communication and radar perception in future networks.

[0009] In order to achieve the above-mentioned object, the present invention provides a method for optimizing the fluid antenna position and radar communication precoding matrix in a URLLC scenario, comprising the following steps: S100, establishing an integrated architecture of communication and perception, wherein components of the integrated architecture include a base station, multiple user terminals, and a single detection target; The base station has a planar fluid antenna array for sending signals to the user terminal, the signals including communication signals and radar signals; each of the multiple user terminals has a communication function, and the communication with the base station meets the URLLC requirements; the single detection target is a point target, the point target receives the signal sent by the base station and reflects the signal, and the base station receives the reflected signal of the detection target and senses it; Based on this, the integrated architecture is constructed as an ISAC system that supports multiple user terminals and a single sensing target; S200, constructing a communication signal model between a base station and a user terminal in a URLLC scenario, and a perception signal model between a base station and a detection target; S300, with the goal of maximizing the radar perception signal-to-noise ratio, and with the base station transmission power, URLLC delay requirements and fluid antenna position restrictions as constraints, a mathematical model for radar communication signal optimization is established; S400, decomposing the optimization problem into three sub-problems, namely, a sub-problem with the fluid antenna position as the optimization variable, a sub-problem with the radar precoding matrix as the optimization variable, and a sub-problem with the communication precoding matrix as the optimization variable; An alternating iterative optimization algorithm is used to optimize one variable each time, fix the remaining two variables, alternately optimize the three sub-problems and iterate to obtain a convergent solution.

[0010] A further preferred technical solution of the present invention is that the communication signal model between the base station and the user terminal in the URLLC scenario in step S200 is expressed as:

[0011] In the formula, Indicates k Communication signals received by a user terminal; For the k The precoding matrix of the communication symbols of the user terminal is For the base station to i Communication symbols transmitted by a user terminal; For the i The precoding matrix of the communication symbols of the user terminal is For the base station to i Communication symbols transmitted by a user terminal; is Gaussian white noise, following the distribution ; The collection of communication symbols transmitted by the base station to the user terminal satisfy , the set of communication symbols transmitted by the base station to the point target satisfy , the two are uncorrelated and statistically independent, satisfying ; T represents transpose, H represents conjugate transpose, K represents the total number of user terminals, M represents the total number of antennas of the base station, is a complex set, represents the mathematical expectation, is the K*K identity matrix, is the M*M identity matrix; For the k The communication channel between a user terminal and the base station is expressed as:

[0012] in, For base stations and k Path response between user terminals; is the number of channel paths; is the distance between the kth terminal and the base station Path response of the paths; is the field response matrix of the base station, where For the m The antenna and k The field response matrix between user terminals, is an imaginary unit, is the carrier wavelength, Indicates the location of the antenna, and User Terminal k The elevation and azimuth angles between the base station and For the m The root antenna and the origin of the antenna array l The propagation distance of the channels is different; , are the horizontal and vertical coordinates of the mth fluid antenna.

[0013] Preferably, the perception signal model between the base station and the detection target in step S200 is expressed as:

[0014] In the formula, represents the sensing signal received by the base station from the target; represents the Doppler shift of the target, represents the path delay of the signal to and from the target and; Indicates that the base station is in the time slot n The signal emitted at is expressed as:

[0015] is the target response matrix; is the reflection coefficient of the perceived target, It is k The transmitting antenna of each user terminal is steered into an array. and are the elevation angle and azimuth angle between the base station and the point target, respectively. is the set of antenna positions; is a set of precoding matrices for radar symbols; is a set of precoding matrices for communication symbols.

[0016] Preferably, the radar perception signal-to-noise ratio in step S300 is expressed as:

[0017] In the formula, is the comprehensive coefficient and The product of is the covariance matrix of the signal sent by the base station; represents the Frobenius norm; is the variance of radar Gaussian white noise.

[0018] Preferably, the URLLC delay in step S300 is expressed as:

[0019] In the formula, The base station sends k The length of the data packet of each user terminal, It is k The maximum delay that a user terminal can tolerate is It is k The achievable rate of a user terminal is expressed as follows:

[0020] In the formula, is bandwidth; , Gauss The inverse of a function; It is k The channel tolerance of user terminals is expressed as ; It is k The signal-to-interference-and-noise ratio of a user terminal.

[0021] Preferably, the mathematical model of the radar communication signal optimization problem established in step S300 is expressed as:

[0022]

[0023]

[0024]

[0025]

[0026] in, and are the mth and nth antenna position coordinates respectively; Constraint C1 indicates that the maximum transmission power of the base station cannot exceed , constraint C2 represents the URLLC delay requirement, and constraint C3 represents that all antenna positions need to be within the array area Constraint C4 indicates that the distance between any pair of antennas must be greater than D This ensures that the mutual coupling between antennas can be ignored.

[0027] Preferably, the specific steps of step S400 are: S410, decomposing the optimization problem into three sub-problems, namely, a sub-problem with the fluid antenna position as the optimization variable, a sub-problem with the radar precoding matrix as the optimization variable, and a sub-problem with the communication precoding matrix as the optimization variable; S420, solving the sub-problem with the fluid antenna position as the optimization variable, using the continuous convex approximation method to process the two sub-formulas of the URLLC rate, and then using the second-order Taylor expansion to process the objective function as a quadratic convex function, the communication rate and the fluid antenna spacing requirement after the convex approximation are processed as linear constraints, and finally using the convex optimization tool to solve the fluid antenna position; S430, solving the sub-problem with the radar precoding matrix as the optimization variable, organizing the problem into a semidefinite programming problem by using the SDR method, and then relaxing the problem into a standard semi-positive definite problem by discarding the rank 1 constraint, and using CVX to solve it to obtain the radar precoding matrix; S440, solving the sub-problem with the communication precoding matrix as the optimization variable, first processing the communication rate expression, using Lagrange dual transformation to perform concave transformation on the logarithmic term, using second-order Taylor expansion and Dinkelbach transformation to perform convex approximation on the radical term, converting the delay constraint into a convex problem, then performing concave transformation on the objective function, and finally using the interior point method to solve and obtain the communication precoding matrix; S450, repeat steps S420-S440 to perform iterative solution until the model converges.

[0028] Preferably, step S420 solves the sub-problem with the fluid antenna position as the optimization variable, and the specific method is: S421, the sub-problem of taking the fluid antenna position as the optimization variable is expressed as:

[0029]

[0030]

[0031]

[0032] S422, using the continuous convex approximation method to process the two minor formulas of the URLLC rate, first, process , according to the Taylor expansion of the logarithmic function, it is expanded as follows:

[0033] In the formula, is a For the sake of simplicity, let ; yes In the r The value of the iteration; Then, Substitute the expression into Get , for this formula, using the first-order Taylor expansion we get:

[0034] In the formula, is a The relevant comprehensive coefficient; Finally, the URLLC rate expression is expressed as:

[0035] in, ; Then the constraint C1 in the subproblem where the fluid antenna position is the optimization variable is expressed as:

[0036] In the formula, ; S423, using a second-order Taylor expansion to process the objective function into a quadratic convex function, the communication rate after convex approximation and the fluid antenna spacing requirements; including: The objective function is processed as follows:

[0037] in, is the objective function In the r The function value of the iteration; Representation function exist The gradient at It is a satisfying A positive real number, yes The Hessian matrix of The communication rate is handled as follows: Will Substituting the expression into constraint C1 yields:

[0038] After deformation, we get:

[0039] In the formula, For convenience of representation, let ; Then, the second-order Taylor expansion is used to construct The upper bound function of :

[0040] In the formula, is the objective function In the r The function value of the iteration; Representation function exist The gradient at It is a satisfying A positive real number, yes The Hessian matrix of The fluid antenna spacing requirements are handled as follows:

[0041] The subproblem with the fluid antenna position as the optimization variable is simplified to:

[0042]

[0043]

[0044]

[0045] The simplified objective function is about The quadratic convex function of , where the constraints are all linear, is solved using optimization tools.

[0046] Preferably, step S430 solves the sub-problem with the radar precoding matrix as the optimization variable, and the specific method is: S431, the sub-problem with the radar precoding matrix as the optimization variable is expressed as:

[0047]

[0048]

[0049] S432, use the SDR method to organize this sub-problem into a semi-definite programming problem, assuming , , and ; Then the sub-problem is expressed as:

[0050]

[0051]

[0052]

[0053]

[0054] By abandoning the rank 1 constraint, the problem is transformed into a standard semi-definite problem; S433, solve this semi-positive definite problem using the convex optimization tool CVX, let represents the optimal solution of the relaxed problem, and finally the optimal solution of this subproblem is:

[0055] in, yes The largest eigenvalue, is the corresponding eigenvector.

[0056] Preferably, step S440 solves the sub-problem with the communication precoding matrix as the optimization variable, and the specific method is: S441, the sub-problem with the communication precoding matrix as the optimization variable is expressed as:

[0057]

[0058]

[0059] The objective function contains the variables in the original objective function. Since the objective function and constraint C1 are about Convex function, only constraint C2 needs to be processed; S442, Processing rate expression: First, use the logarithmic term Lagrange dual transformation performs concave transformation, note ,but:

[0060]

[0061] In the formula, and All are sets of auxiliary variables; ,and About convex; when Fixed, optimal By calculation Get, that is:

[0062] At the same time, the best Update via:

[0063] Then, the radical terms are convexly approximated using second-order Taylor expansion and Dinkelbach transformation; ,for , whose convexity is determined by Decide; For single fraction terms Using the Dinkelbach transformation, we define for:

[0064] Will Converts to:

[0065] In the formula, is a set of auxiliary variables, the first item About The convex function of About is a concave function; at the same time In the iteration, Updated by:

[0066] Will Converted to a concave function, we have the following inequality:

[0067] final, is approximated as:

[0068] In the formula, , and ; In the r In +1 iterations it is approximated as:

[0069] S443, processing target function: Since the objective function is about is convex, and can be converted to a concave function using a first-order Taylor expansion. To simplify the expression, let .

[0070] exist The expansion of can be written as: In the formula, The expression is:

[0071] According to the above conversion, the sub-problem with the communication precoding matrix as the optimization variable is converted to:

[0072]

[0073]

[0074] This question is about is convex and is solved by the interior point method of CVX.

[0075] Beneficial effects: The present invention utilizes URLLC technology, multiple-input multiple-output antenna arrays, and fluid antenna technology at the hardware level to simultaneously perform communication and radar sensing on the same spectrum, meeting the requirements of communication and radar sensing in future networks. At the same time, the fluid antenna position and radar communication precoding matrix optimization method in the URLLC scenario proposed by the present invention is used to implement the fluid antenna array to simultaneously perform radar sensing and communication at the software level, and effectively reduce interference between user terminals, by solving the fluid antenna position and radar communication precoding matrix to meet the requirements of radar sensing and communication transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 Schematic diagram of the integrated architecture of communication and sensing established for the present invention.

[0077] Figure 2 The present invention is a flow chart of the method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario. DETAILED DESCRIPTION

[0078] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments, and they should not be understood as limitations on the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms used are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0079] Example: The following combination Figure 1-Figure 2 The present invention describes the method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario. The specific steps are as follows: Figure 2 As shown, including: S100. Build an integrated architecture for communication and perception, which is constructed as an ISAC system that supports multiple user terminals and a single perception target.

[0080] The integrated architecture is Figure 1 As shown, it includes a base station, multiple user terminals and a single detection target.

[0081] The base station has a planar fluid antenna array for sending signals to the user terminal, which include communication signals and radar signals; each of the multiple user terminals has a communication function, and the communication with the base station meets the URLLC requirements; the single detection target is a point target, the point target receives the signal sent by the base station and reflects the signal, and the base station receives the reflected signal of the detection target and senses it. The URLLC communication delay and signal-to-noise ratio (SNR) are used as performance indicators of user terminal communication and point target radar perception, respectively.

[0082] S200: construct a communication signal model between the base station and the user terminal in the URLLC scenario, and a perception signal model between the base station and the detection target.

[0083] S210: Construct a communication signal model between the base station and the user terminal in the URLLC scenario: Specifically, assuming there is K user terminals, the base station’s antenna array is equipped with M The communication symbols and radar symbols sent by the base station are encoded separately in the time slot. n The signal sent by the base station It can be expressed as:

[0084] is a set of precoding matrices for radar symbols; It is a collection of communication symbols transmitted by the base station to the point target; is a set of precoding matrices for communication symbols; It is a collection of communication symbols transmitted by the base station to the user terminal.

[0085] and satisfy , satisfy , the two are uncorrelated and statistically independent, satisfying ; T represents transpose, H represents conjugate transpose, K represents the total number of user terminals, M represents the total number of antennas of the base station, is a complex set, represents the mathematical expectation, is the K*K identity matrix, is the M*M identity matrix; Therefore, the covariance matrix of the base station transmit signal can be expressed as:

[0086] Based on this, in the time slot n Department, k The communication signal received by each user It can be expressed as:

[0087] In the formula, Indicates k Communication signals received by a user terminal; For the k The precoding matrix of the communication symbols of the user terminal is For the base station to i Communication symbols transmitted by a user terminal; For the i The precoding matrix of the communication symbols of the user terminal is For the base station to i Communication symbols transmitted by a user terminal; is Gaussian white noise, following the distribution ; For the k The communication channel between a user terminal and the base station is expressed as:

[0088] in, , For base stations and k Path response between user terminals; is the number of channel paths, is the distance between the kth terminal and the base station Path response of the paths; is the field response matrix of the base station, where For the m The antenna and k The field response matrix between user terminals, is an imaginary unit, is the carrier wavelength, Indicates the location of the antenna, and User Terminal k The elevation and azimuth angles between the base station and For the m The root antenna and the origin of the antenna array l The propagation distance of the channels is different; , are the horizontal and vertical coordinates of the mth fluid antenna.

[0089] S220: construct a perception signal model between the base station and the detection target: The base station uses the transmitted signal to perform radar perception on the point target, and the received perception signal can be expressed as:

[0090] In the formula, represents the sensing signal received by the base station from the target; represents the Doppler shift of the target, represents the path delay of the signal to and from the target and; Indicates that the base station is in the time slot n The signal emitted at is expressed as:

[0091] is the target response matrix; is the reflection coefficient of the perceived target, It is k The transmitting antenna of each user terminal is steered into an array. and are the elevation angle and azimuth angle between the base station and the point target, respectively. is the set of antenna positions.

[0092] S300. With the goal of maximizing the radar perception signal-to-noise ratio, and with the base station transmission power, URLLC delay requirements and fluid antenna position restrictions as constraints, a mathematical model for the radar communication signal optimization problem is established.

[0093] Specifically, the radar perception signal-to-noise ratio is expressed as:

[0094] In the formula, is the comprehensive coefficient and The product of is the covariance matrix of the signal sent by the base station; represents the Frobenius norm; is the variance of radar Gaussian white noise.

[0095] URLLC delay, expressed as:

[0096] In the formula, The base station sends k The length of the data packet of each user terminal, It is k The maximum delay that a user terminal can tolerate is It is k The achievable rate of a user terminal is expressed as follows:

[0097] In the formula, is bandwidth; , Gauss The inverse of a function; It is k The channel tolerance of user terminals is expressed as ; It is k The signal-to-interference-and-noise ratio of a user terminal.

[0098] The optimization problem of maximizing the radar perception signal-to-noise ratio is:

[0099]

[0100]

[0101]

[0102]

[0103] in, and are the mth and nth antenna position coordinates respectively; Constraint C1 indicates that the maximum transmission power of the base station cannot exceed , constraint C2 represents the URLLC delay requirement, and constraint C3 represents that all antenna positions need to be within the array area Constraint C4 indicates that the distance between any pair of antennas must be greater than D To ensure that the mutual coupling between antennas can be ignored. This problem is a non-convex optimization problem.

[0104] S400, decomposing the optimization problem into three sub-problems, using an alternating iterative optimization algorithm, optimizing one variable each time, fixing the remaining two variables, alternately optimizing the three sub-problems and iterating to obtain a convergent solution.

[0105] S410, decomposing the optimization problem into three sub-problems, namely, a sub-problem with the fluid antenna position as the optimization variable, a sub-problem with the radar precoding matrix as the optimization variable, and a sub-problem with the communication precoding matrix as the optimization variable.

[0106] S420, for the sub-problem with the fluid antenna position as the optimization variable, the continuous convex approximation method is used to process the two sub-formulas of the URLLC rate, and then the second-order Taylor expansion is used to process the objective function as a quadratic convex function. The communication rate and fluid antenna spacing requirements after the convex approximation are linear constraints, and finally the convex optimization tool is used to solve the fluid antenna position. The specific method is: S421, the sub-problem of taking the fluid antenna position as the optimization variable is expressed as:

[0107]

[0108]

[0109]

[0110] S422, using the continuous convex approximation method to process the two minor formulas of the URLLC rate, first, process , according to the Taylor expansion of the logarithmic function, it is expanded as follows:

[0111] In the formula, is a For the sake of simplicity, let ; yes In the r The value of the iteration; Then, Substitute the expression into Get , for this formula, using the first-order Taylor expansion we get:

[0112] In the formula, is a The relevant comprehensive coefficient; Finally, the URLLC rate expression is expressed as:

[0113] in, ; Then the constraint C1 in the subproblem where the fluid antenna position is the optimization variable is expressed as:

[0114] In the formula, ; S423, using a second-order Taylor expansion to process the objective function into a quadratic convex function, the communication rate after convex approximation and the fluid antenna spacing requirements; including: The objective function is processed as follows:

[0115] in, is the objective function In the r The function value of the iteration; Representation function exist The gradient at It is a satisfying A positive real number, yes The Hessian matrix of The communication rate is handled as follows: Will Substituting the expression into constraint C1 yields:

[0116] After deformation, we get:

[0117] In the formula, For convenience of representation, let ; Then, the second-order Taylor expansion is used to construct The upper bound function of :

[0118] In the formula, is the objective function In the r The function value of the iteration; Representation function exist The gradient at It is a satisfying A positive real number, yes The Hessian matrix of The fluid antenna spacing requirements are handled as follows:

[0119] The subproblem with the fluid antenna position as the optimization variable is simplified to:

[0120]

[0121]

[0122]

[0123] The simplified objective function is about The quadratic convex function of , where the constraints are all linear, is solved using optimization tools.

[0124] S430, solving the sub-problem with the radar precoding matrix as the optimization variable, organizing the problem into a semidefinite programming problem by the SDR method, and then relaxing the problem into a standard semi-positive definite problem by discarding the rank 1 constraint, and using CVX to solve the problem to obtain the radar precoding matrix; the specific method is: S431, the sub-problem with the radar precoding matrix as the optimization variable is expressed as:

[0125]

[0126]

[0127] S432, use the SDR method to organize this sub-problem into a semi-definite programming problem, assuming , , and ; Then the sub-problem is expressed as:

[0128]

[0129]

[0130]

[0131]

[0132] By abandoning the rank 1 constraint, the problem is transformed into a standard semi-definite problem; S433, solve this semi-positive definite problem using the convex optimization tool CVX, let represents the optimal solution of the relaxed problem, and finally the optimal solution of this subproblem is:

[0133] in, yes The largest eigenvalue, is the corresponding eigenvector.

[0134] S440, for solving the sub-problem with the communication precoding matrix as the optimization variable, first process the communication rate expression, use the Lagrange dual transformation to perform concave transformation on the logarithmic term, use the second-order Taylor expansion and Dinkelbach transformation to perform convex approximation on the radical term, convert the delay constraint into a convex problem, then perform concave transformation on the objective function, and finally use the interior point method to solve and obtain the communication precoding matrix. The specific method is: S441, the sub-problem with the communication precoding matrix as the optimization variable is expressed as:

[0135]

[0136]

[0137] The objective function contains the variables in the original objective function. Since the objective function and constraint C1 are about Convex function, only constraint C2 needs to be processed; S442, Processing rate expression: First, the logarithmic terms Use Lagrange dual transformation to perform concave transformation, ,but:

[0138]

[0139] In the formula, and All are sets of auxiliary variables; ,and About convex; when Fixed, optimal By calculation Get, that is:

[0140] At the same time, the best Update via:

[0141] Then, the radical terms are convexly approximated using second-order Taylor expansion and Dinkelbach transformation; ,for , whose convexity is determined by Decide; For single fraction terms Using the Dinkelbach transformation, we define for:

[0142] Will Converts to:

[0143] In the formula, is a set of auxiliary variables, the first item About The convex function of About is a concave function; at the same time In the iteration, Updated by:

[0144] Will Converted to a concave function, we have the following inequality:

[0145] final, is approximated as:

[0146] In the formula, , and ; In the r In +1 iterations it is approximated as:

[0147] S443, processing target function: Since the objective function is about is convex, and can be converted to a concave function using a first-order Taylor expansion. To simplify the expression, let . exist The expansion of can be written as: In the formula, The expression is:

[0148] According to the above conversion, the sub-problem with the communication precoding matrix as the optimization variable is converted to:

[0149]

[0150]

[0151] This question is about is convex and is solved by the interior point method (IPM) of CVX.

[0152] S450, repeat steps S420-S440 to perform iterative solution until the model converges and a converged solution is obtained.

[0153] In summary, the present invention proposes a multi-user terminal ISAC fluid antenna communication and perception system solution in the URLLC scenario. The fluid antenna array simultaneously performs radar perception and communication, and effectively reduces the interference between user terminals. The requirements of radar perception and communication transmission are met by solving the fluid antenna position and radar communication precoding matrix.

[0154] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0155] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing fluid antenna position and radar communication precoding matrix in URLLC scenario, characterized in that: The steps include: S100, establishing an integrated architecture of communication and perception, wherein components of the integrated architecture include a base station, multiple user terminals, and a single detection target; The base station has a planar fluid antenna array for sending signals to the user terminal, the signals including communication signals and radar signals; each of the multiple user terminals has a communication function, and the communication with the base station meets the URLLC requirements; the single detection target is a point target, the point target receives the signal sent by the base station and reflects the signal, and the base station receives the reflected signal of the detection target and senses it; Based on this, the integrated architecture is constructed as an ISAC system that supports multiple user terminals and a single sensing target; S200, constructing a communication signal model between a base station and a user terminal in a URLLC scenario, and a perception signal model between a base station and a detection target; S300, with the goal of maximizing the radar perception signal-to-noise ratio, and with the base station transmission power, URLLC delay requirements and fluid antenna position restrictions as constraints, a mathematical model for radar communication signal optimization is established; S400, decomposing the optimization problem into three sub-problems, namely, a sub-problem with the fluid antenna position as the optimization variable, a sub-problem with the radar precoding matrix as the optimization variable, and a sub-problem with the communication precoding matrix as the optimization variable; An alternating iterative optimization algorithm is used to optimize one variable each time, fix the remaining two variables, alternately optimize the three sub-problems and iterate to obtain a convergent solution.

2. The method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario according to claim 1, characterized in that: The communication signal model between the base station and the user terminal in the URLLC scenario in step S200 is expressed as: ； In the formula, Indicates k Communication signals received by a user terminal; For the k The precoding matrix of the communication symbols of the user terminal is For the base station to i Communication symbols transmitted by a user terminal; For the i The precoding matrix of the communication symbols of the user terminal is For the base station to i Communication symbols transmitted by a user terminal; is Gaussian white noise, following the distribution ; The collection of communication symbols transmitted by the base station to the user terminal satisfy , the set of communication symbols transmitted by the base station to the point target satisfy , the two are uncorrelated and statistically independent, satisfying ; T represents transpose, H represents conjugate transpose, K represents the total number of user terminals, M represents the total number of antennas of the base station, is a complex set, represents the mathematical expectation, is the K*K identity matrix, is the M*M identity matrix; For the k The communication channel between a user terminal and the base station is expressed as: ； in, For base stations and k Path response between user terminals; is the number of channel paths; is the distance between the kth terminal and the base station Path response of the paths; is the field response matrix of the base station, where For the m The antenna and k The field response matrix between user terminals, is an imaginary unit, is the carrier wavelength, Indicates the location of the antenna, and User Terminal k The elevation and azimuth angles between the base station and For the m The root antenna and the origin of the antenna array l The propagation distance of the channels is different; , are the horizontal and vertical coordinates of the mth fluid antenna.

3. The method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario according to claim 2, characterized in that: The sensing signal model between the base station and the detection target in step S200 is expressed as: ； In the formula, represents the sensing signal received by the base station from the target; represents the Doppler shift of the target, represents the path delay of the signal to and from the target and; Indicates that the base station is in the time slot n The signal emitted at is expressed as: ； is the target response matrix; is the reflection coefficient of the perceived target, It is k The transmitting antenna of each user terminal is steered into an array. and are the elevation angle and azimuth angle between the base station and the point target, respectively. is the set of antenna positions; is a set of precoding matrices for radar symbols; is a set of precoding matrices for communication symbols.

4. The method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario according to claim 1, characterized in that: The radar sensing signal-to-noise ratio in step S300 is expressed as: ； In the formula, is the comprehensive coefficient and The product of is the covariance matrix of the signal sent by the base station; represents the Frobenius norm; is the variance of radar Gaussian white noise.

5. The method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario according to claim 4, characterized in that: The URLLC delay in step S300 is expressed as: ； In the formula, The base station sends k The length of the data packet of each user terminal, It is k The maximum delay that a user terminal can tolerate is It is k The achievable rate of a user terminal is expressed as follows: ； In the formula, is bandwidth; , Gauss The inverse of a function; It is k The channel tolerance of a user terminal is expressed as ; It is k The signal-to-interference-and-noise ratio of a user terminal.

6. The method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario according to claim 5, characterized in that: The mathematical model of the radar communication signal optimization problem established in step S300 is expressed as: ； ； ； ； ； in, and are the mth and nth antenna position coordinates respectively; Constraint C1 indicates that the maximum transmission power of the base station cannot exceed , constraint C2 represents the URLLC delay requirement, and constraint C3 represents that all antenna positions need to be within the array area Constraint C4 indicates that the distance between any pair of antennas must be greater than D This ensures that the mutual coupling between antennas can be ignored.

7. The method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario according to claim 1, characterized in that: The specific steps of step S400 are: S410, decomposing the optimization problem into three sub-problems, namely, a sub-problem with the fluid antenna position as the optimization variable, a sub-problem with the radar precoding matrix as the optimization variable, and a sub-problem with the communication precoding matrix as the optimization variable; S420, solving the sub-problem with the fluid antenna position as the optimization variable, using the continuous convex approximation method to process the two sub-formulas of the URLLC rate, and then using the second-order Taylor expansion to process the objective function as a quadratic convex function, the communication rate and the fluid antenna spacing requirement after the convex approximation are processed as linear constraints, and finally using the convex optimization tool to solve the fluid antenna position; S430, solving the sub-problem with the radar precoding matrix as the optimization variable, organizing the problem into a semidefinite programming problem by using the SDR method, and then relaxing the problem into a standard semi-positive definite problem by discarding the rank 1 constraint, and using CVX to solve it to obtain the radar precoding matrix; S440, solving the sub-problem with the communication precoding matrix as the optimization variable, first processing the communication rate expression, using Lagrange dual transformation to perform concave transformation on the logarithmic term, using second-order Taylor expansion and Dinkelbach transformation to perform convex approximation on the radical term, converting the delay constraint into a convex problem, then performing concave transformation on the objective function, and finally using the interior point method to solve and obtain the communication precoding matrix; S450, repeat steps S420-S440 to perform iterative solution until the model converges.

8. The method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario according to claim 7, characterized in that: Step S420 solves the sub-problem with the fluid antenna position as the optimization variable. The specific method is: S421, the sub-problem of taking the fluid antenna position as the optimization variable is expressed as: ； ； ； ； S422, using the continuous convex approximation method to process the two minor formulas of the URLLC rate, first, process , according to the Taylor expansion of the logarithmic function, it is expanded as follows: ； In the formula, is a For the sake of simplicity, let ; yes In the r The value of the iteration; Then, Substitute the expression into Get , for this formula, using the first-order Taylor expansion we get: ； In the formula, is a The relevant comprehensive coefficient; Finally, the URLLC rate expression is expressed as: ； in, ; Then the constraint C1 in the subproblem where the fluid antenna position is the optimization variable is expressed as: ； In the formula, ; S423, using a second-order Taylor expansion to process the objective function into a quadratic convex function, the communication rate after convex approximation and the fluid antenna spacing requirements; including: The objective function is processed as follows: ； in, is the objective function In the r The function value of the iteration; Representation function exist The gradient at It is a satisfying A positive real number, yes The Hessian matrix of The communication rate is handled as follows: Will Substituting the expression into constraint C1 yields: ； After deformation, we get: ； In the formula, For convenience of representation, let ; Then, the upper bound function constructed by the second-order Taylor expansion is: ； In the formula, is the objective function In the r The function value of the iteration; Representation function exist The gradient at It is a satisfying A positive real number, yes The Hessian matrix of The fluid antenna spacing requirements are handled as follows: ； The subproblem with the fluid antenna position as the optimization variable is simplified to: ； ； ； ； The simplified objective function is about The quadratic convex function of , where the constraints are all linear, is solved using optimization tools.

9. The method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario according to claim 7, characterized in that: Step S430 solves the sub-problem with the radar precoding matrix as the optimization variable. The specific method is: S431, the sub-problem with the radar precoding matrix as the optimization variable is expressed as: ； ； ； S432, use the SDR method to organize this sub-problem into a semi-definite programming problem, assuming , , and ; Then the sub-problem is expressed as: ； ； ； ； ； By abandoning the rank 1 constraint, the problem is transformed into a standard semi-definite problem; S433, solve this semi-positive definite problem using the convex optimization tool CVX, let represents the optimal solution of the relaxed problem, and finally the optimal solution of this subproblem is: ； in, yes The largest eigenvalue, is the corresponding eigenvector.

10. The method for optimizing the fluid antenna position and radar communication precoding matrix in the URLLC scenario according to claim 7, characterized in that: Step S440 solves the sub-problem with the communication precoding matrix as the optimization variable, and the specific method is: S441, the sub-problem with the communication precoding matrix as the optimization variable is expressed as: ； ； ； The objective function contains the variables in the original objective function. Since the objective function and constraint C1 are about Convex function, only constraint C2 needs to be processed; S442, processing rate expression: First, the logarithmic terms Use Lagrange dual transformation to perform concave transformation, ,but: ； ； In the formula, and All are sets of auxiliary variables; ,and About convex; when Fixed, optimal By calculation Get, that is: ； At the same time, the best Update via: ； Then, the radical terms are convexly approximated using the second-order Taylor expansion and Dinkelbach transformation; ,for , whose convexity is determined by Decide; For single fraction terms Using the Dinkelbach transformation, we define for: ； Will Converts to: ； In the formula, is a set of auxiliary variables, the first item About The convex function of About is a concave function; at the same time In the iteration, Updated by: ； Will Converted to a concave function, we have the following inequality: ； final, is approximated as: ； In the formula, , and ; In the r In +1 iterations it is approximated as: ； S443, processing target function: Since the objective function is about is convex, and can be converted into a concave function using a first-order Taylor expansion; to simplify the expression, let ; exist Expanded writing: ； In the formula, The expression is: ； According to the above conversion, the sub-problem with the communication precoding matrix as the optimization variable is converted to: ； ； ； This question is about is convex and is solved by the interior point method of CVX.

Images