Optimization Method for Fluid Antenna Position and Radar Communication Precoding Matrix in URLLC Scenarios

Abstract

The present invention discloses an optimization method for the position of a fluid antenna and the radar communication precoding matrix in a URLLC scenario, including an integrated architecture that supports communication and sensing for multiple user terminals and a single sensing target; constructing a communication signal model between a base station and a user terminal in a URLLC scenario, as well as a sensing signal model between the base station and a detection target; aiming at maximizing the radar sensing signal-to-noise ratio, and taking the base station transmission power, URLLC delay requirements, and fluid antenna position constraints as constraints, establishing a mathematical model for the radar communication signal optimization problem; decomposing the optimization problem into three sub-problems, adopting an alternating iterative optimization algorithm, alternately optimizing the three sub-problems and iteratively obtaining a convergent solution. The present invention utilizes URLLC technology, multiple-input multiple-output antenna arrays, and fluid antenna technology to simultaneously perform communication and radar sensing on the same spectrum, meeting the requirements of communication and radar sensing in future networks.

Description

Technical Field

[0001] The present invention belongs to the technical field of dual-functional radar communication, and particularly relates to an optimization method for the position of a fluid antenna 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, intelligent transportation, remote medical treatment, and environmental monitoring, to promote the deep integration of communication, sensing, computing, and decision-making capabilities. In this context, both the academic and industrial circles believe that future wireless systems need to break through the traditional functional boundaries and achieve the coexistence and symbiosis of sensing and communication. In response to this demand, Integrated Sensing and Communications (ISAC) has emerged and quickly become a key research direction for 6G and the next-generation communication networks. The core idea of ISAC is to deeply integrate radar environmental sensing and wireless data transmission through unified signal design and hardware architecture, reuse spectrum resources and device hardware, thereby significantly improving spectrum utilization, reducing deployment energy consumption and hardware costs, and at the same time achieving two-way enhancement of sensing and communication functions. For example, optimizing the communication link resource allocation through sensing information, or using communication signals to assist high-precision target positioning and environmental modeling.

[0003] In recent years, the exploration of ISAC technology has continuously become a hot topic in the field of wireless communication and sensing integration. However, existing research mostly focuses on improving spectrum efficiency and sensing accuracy, and there is little work on deeply analyzing the strict constraints on ISAC systems in the ultra-reliable low-latency communication (URLLC) scenario. In traditional ISAC designs, the coordination of sensing and communication functions often assumes a static or quasi-static environment, making it difficult to meet the high dynamics, extremely low latency, and ultra-high reliability requirements of URLLC. Especially in scenarios such as industrial automation and emergency obstacle avoidance in vehicle-to-everything (V2X), the real-time nature of sensing data and the robustness of communication links are highly coupled. If the communication latency or interruption causes the sensing information update to lag, it may directly trigger system-level security risks.

[0004] As a core technology to support mission-critical applications, URLLC guarantees service quality through mechanisms such as short-frame transmission, resource reservation, and reliable channel coding. However, its strict latency and reliability constraints pose new challenges to the deep integration of sensing functions. For example, how to design waveforms to balance sensing resolution and communication bit error rate. Solving this problem urgently requires breaking through the traditional ISAC framework and constructing a cross-layer optimization theory for URLLC.

[0005] On the other hand, the evolution of ISAC technology has also continuously driven the wireless network towards multi-functional integration, and the rise of Fluid Antennas (FAs) has injected new transformative potential into this field. By dynamically adjusting the antenna morphology, position, or polarization characteristics, fluid antennas can flexibly adapt to complex electromagnetic environments, significantly enhancing the channel degrees of freedom and interference management capabilities. However, existing ISAC research is mostly based on fixed antenna architectures, making it difficult to address performance degradation problems caused by spatial correlation, multipath fading, and burst interference in high-mobility scenarios (such as high-speed vehicle-to-everything (V2X) networks and drone swarms) or dense deployment environments (such as industrial Internet of Things). Especially in URLLC-enabled ISAC systems, due to limited degrees of freedom, traditional fixed antennas are difficult to synchronously optimize the beamforming of sensing waveforms and communication signals under extremely low latency constraints, resulting in a decrease in sensing resolution or communication reliability that cannot meet the 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 co-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. Solving these problems requires constructing 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 an optimization method for the position of fluid antennas and the radar communication precoding matrix in the URLLC scenario to solve the above problems. Summary of the Invention

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

[0008] The object of the present invention is to provide an optimization method for the position of fluid antennas and the radar communication precoding matrix in the URLLC scenario. Based on the URLLC scenario, the fluid antenna technology is introduced to simultaneously perform radar sensing and communication functions on the same spectrum, meeting the requirements of communication and radar sensing in future networks.

[0009] To achieve the above object, the present invention provides an optimization method for the position of fluid antennas and the radar communication precoding matrix in the URLLC scenario, including the following steps:

[0010] S100. Establish an integrated architecture for communication and sensing, and the components of this integrated architecture include a base station, multiple user terminals, and a single detection target;

[0011] Among them, the base station has a planar fluid antenna array for sending signals to the user terminal, and the signals 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 signals sent by the base station and reflects the signals, and the base station receives the signals reflected by the detection target and performs sensing;

[0012] Accordingly, the integrated architecture is constructed as an ISAC system that supports multiple user terminals and a single sensing target;

[0013] S200. Construct a communication signal model between the base station and the user terminal in the URLLC scenario, and a sensing signal model between the base station and the detection target;

[0014] S300. With the goal of maximizing the radar sensing signal-to-noise ratio and subject to the base station transmission power, URLLC delay requirements, and fluid antenna position limitations, establish a mathematical model for the radar communication signal optimization problem;

[0015] S400. Decompose the optimization problem into three sub-problems, namely, the sub-problem with the fluid antenna position as the optimization variable, the sub-problem with the radar precoding matrix as the optimization variable, and the sub-problem with the communication precoding matrix as the optimization variable;

[0016] Adopt an alternating iterative optimization algorithm, optimize one variable each time, fix the remaining two variables, alternately optimize the three sub-problems, and iterate to obtain a convergent solution.

[0017] 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:

[0018]

[0019] In the formula, represents the communication signal received by the k th user terminal; is the precoding matrix of the communication symbol of the k th user terminal, is the communication symbol transmitted by the base station to the i th user terminal; is the precoding matrix of the communication symbol of the i th user terminal, is the communication symbol transmitted by the base station to the i th user terminal; is Gaussian white noise, following the distribution ;

[0020] The set of communication symbols transmitted by the base station to the user terminal satisfies , the set of communication symbols transmitted by the base station to the point target Satisfy , the two are uncorrelated and statistically independent, and satisfy ; T represents transpose, H represents conjugate transpose, K is the total number of user terminals, M is the total number of antennas of the base station, is the set of complex numbers, represents the mathematical expectation, is the K*K identity matrix, is the M*M identity matrix;

[0021] is the k th communication channel between the user terminal and the base station, expressed as:

[0022]

[0023] where, is the path response between the base station and the k th user terminal; is the number of signal path; is the path response of the th path between the kth terminal and the base station;

[0024] is the field response matrix of the base station, where is the m th antenna and the k th user terminal field response matrix, is the imaginary unit, is the carrier wavelength, represents the position of the antenna, and are the elevation angle and azimuth angle between the user terminal k and the base station respectively, is the m th root antenna and the origin of the antenna array of the l th channel propagation distance difference; 、 are the horizontal and vertical coordinates of the

[0025] Preferably, the sensing signal model between the base station and the detection target in step S200 is expressed as:

[0026]

[0027] In the formula, represents the sensing signal received by the base station from the target; represents the Doppler frequency shift of the target, Indicates the sum of the path delays of the signal to and from the target; Indicates the signal transmitted by the base station in the time slot n The expression is:

[0028]

[0029] is the target response matrix; is the reflection coefficient of the sensing target, is the k th transmitting antenna steering array of the user terminal, and are the elevation angle and azimuth angle between the base station and the point target respectively, is the set of antenna positions; is the set of precoding matrices for radar symbols; is the set of precoding matrices for communication symbols.

[0030] Preferably, the radar sensing signal-to-noise ratio in step S300 is expressed as:

[0031]

[0032] In the formula, is the product of the comprehensive coefficient and , is the covariance matrix of the signal transmitted by the base station; represents the Frobenius norm; is the variance of the radar Gaussian white noise.

[0033] Preferably, the URLLC delay in step S300 is expressed as:

[0034]

[0035] In the formula, is the data packet length sent by the base station to the k th user terminal, is the k th maximum delay tolerable by the user terminal, is the k th achievable rate of the user terminal, and its expression is as follows:

[0036]

[0037] In the formula, is the bandwidth; , is the Gaussian inverse function of the function; is the k th channel tolerance of the user terminal, expressed as ; is the signal-to-interference-plus-noise ratio of the k th user terminal.

[0038] Preferably, the mathematical model of the radar communication signal optimization problem established in step S300 is expressed as:

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] Wherein, and are the coordinate positions of the mth and nth antennas respectively;

[0045] Constraint C1 means that the maximum transmission power of the base station cannot exceed , constraint C2 represents the URLLC delay requirement, constraint C3 means that all antenna positions need to be within the array area ), constraint C4 means that the spacing between any pair of antennas needs to be greater than D to ensure that the mutual coupling between antennas can be ignored.

[0046] Preferably, the specific steps of step S400 are:

[0047] S410. Decompose the optimization problem into three sub-problems, namely the sub-problem with the fluid antenna position as the optimization variable, the sub-problem with the radar precoding matrix as the optimization variable, and the sub-problem with the communication precoding matrix as the optimization variable;

[0048] S420. Solve the sub-problem with the fluid antenna position as the optimization variable. Use the successive convex approximation method to process the two sub-expressions of the URLLC rate, then use the second-order Taylor expansion to process the objective function as a quadratic convex function, process the convex-approximated communication rate and the fluid antenna spacing requirement as linear constraints, and finally use the convex optimization tool to solve the fluid antenna position;

[0049] S430. Solve the sub-problem with the radar precoding matrix as the optimization variable. Through the SDR method, organize the problem into a semidefinite programming problem, then relax the problem into a standard semidefinite problem by discarding the rank-1 constraint, and use CVX to solve it to obtain the radar precoding matrix;

[0050] S440. For the solution of the sub-problem with the communication precoding matrix as the optimization variable, first, process the communication rate expression. Use the Lagrangian dual transformation for concave transformation of the logarithmic term, and use the second-order Taylor expansion and Dinkelbach transformation for convex approximation of 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 for the communication precoding matrix;

[0051] S450. Repeat steps S420 - S440 for iterative solution until the model converges.

[0052] Preferably, step S420 for the solution of the sub-problem with the fluid antenna position as the optimization variable is as follows:

[0053] S421. Express the sub-problem with the fluid antenna position as the optimization variable as:

[0054]

[0055]

[0056]

[0057]

[0058] S422. Use the sequential convex approximation method to process the two sub-expressions of the URLLC rate. First, process , according to the Taylor expansion of the logarithmic function, it expands to:

[0059]

[0060] In the formula, is a constant related to . For the sake of simplicity of expression, let ; is the value of at the r th iteration;

[0061] Then, substitute the expression of into to get . For this formula, use the first-order Taylor expansion to get:

[0062]

[0063] In the formula, is a comprehensive coefficient related to ;

[0064] Finally, the URLLC rate expression is expressed as:

[0065]

[0066] Among them, ;

[0067] Then the constraint C1 in the sub-problem with the fluid antenna position as the optimization variable is expressed as:

[0068]

[0069] In the formula, ;

[0070] S423. Use the second-order Taylor expansion to handle the objective function as a quadratic convex function and the requirements for the communication rate and the fluid antenna spacing after convex approximation; including:

[0071] The processing of the objective function is as follows:

[0072]

[0073] Among them, is the function value of the objective function at the r th iteration; represents the gradient of the function at ; is a positive real number that satisfies , is 's Hessian matrix;

[0074] The processing of the communication rate is as follows:

[0075] Substitute the expression of into the constraint C1 to get:

[0076]

[0077] Perform deformation to get:

[0078]

[0079] In the formula, , for the convenience of representation, let ;

[0080] Then, construct the upper bound function of through the second-order Taylor expansion:

[0081]

[0082] In the formula, is the function value of the objective function at the r th iteration; Denote the function at the gradient; is a positive real number satisfying ; is the Hessian matrix of;

[0083] The processing of the fluid antenna spacing requirement is as follows:

[0084]

[0085] The sub-problem with the fluid antenna position as the optimization variable is simplified to:

[0086]

[0087]

[0088]

[0089]

[0090] The simplified objective function is a quadratic convex function with respect to , and the constraints are all linear, which are solved by an optimization tool.

[0091] Preferably, step S430 solves the sub-problem with the radar precoding matrix as the optimization variable. The specific method is as follows:

[0092] S431. Express the sub-problem with the radar precoding matrix as the optimization variable as:

[0093]

[0094]

[0095]

[0096] S432. Use the SDR method to transform this sub-problem into a semidefinite programming problem. Let , , and ; then this sub-problem is expressed as:

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] By abandoning the rank 1 constraint, the problem is transformed into a standard semi-positive definite problem;

[0103] 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:

[0104]

[0105] in, yes The largest eigenvalue, is the corresponding eigenvector.

[0106] Preferably, step S440 solves the sub-problem with the communication precoding matrix as the optimization variable, and the specific method is:

[0107] S441, the sub-problem with the communication precoding matrix as the optimization variable is expressed as:

[0108]

[0109]

[0110]

[0111] 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;

[0112] S442, Processing rate expression:

[0113] First, use the logarithmic term Lagrange dual transformation performs concave transformation, note ,but:

[0114]

[0115]

[0116] In the formula, and All are sets of auxiliary variables; ,and About convex; when Fixed, optimal By calculation Get, that is:

[0117]

[0118] Meanwhile, the optimal is updated by the following formula:

[0119]

[0120] Then, a convex approximation is performed on the radical term using the second-order Taylor expansion and the Dinkelbach transformation; denote , for , its convexity and concavity are determined by ;

[0121] For the single-fraction term , the Dinkelbach transformation is used, and is defined as:

[0122]

[0123] Convert to:

[0124]

[0125] wherein is a set of auxiliary variables, the first term is a convex function with respect to , and is a concave function with respect to ; meanwhile, in the -th iteration, is updated by the following formula:

[0126]

[0127] Convert to a concave function, and there is the following inequality:

[0128]

[0129] Finally, is approximated as:

[0130]

[0131] wherein , and ;

[0132] In the r +1-th iteration, it is approximated as:

[0133]

[0134] S443. Processing objective function:

[0135] Since the objective function is convex with respect to it is converted to a concave function using first-order Taylor expansion. To simplify the expression, let .

[0136] The expansion at can be written as:

[0137] wherein, The expression of

[0138]

[0139] According to the above conversion, the sub-problem with the communication precoding matrix as the optimization variable is converted to:

[0140]

[0141]

[0142]

[0143] This problem is convex with respect to and is solved by the interior point method of CVX.

[0144] Beneficial effects: The present invention utilizes URLLC technology, multi-input multi-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, by using the method for optimizing the position of the fluid antenna and the radar communication precoding matrix in the URLLC scenario proposed by the present invention, the fluid antenna array can simultaneously perform radar sensing and communication at the software level, effectively reducing interference between user terminals, and meeting the requirements of radar sensing and communication transmission by solving the position of the fluid antenna and the radar communication precoding matrix. Description of the Drawings

[0145] Figure 1 It is a schematic diagram of the integrated architecture of communication and sensing established for the present invention.

[0146] Figure 2 It is a flowchart of the method for optimizing the position of the fluid antenna and the radar communication precoding matrix in the URLLC scenario of the present invention. Detailed Embodiments

[0147] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will describe the technical solutions in the present invention clearly and completely in conjunction with the accompanying drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments, and they should not be construed as limiting the present invention. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall 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 the purpose of description and cannot be construed as indicating or implying relative importance.

[0148] Embodiment: The following will describe the method for optimizing the position of the fluid antenna and the radar communication precoding matrix in the URLLC scenario provided by the present invention in conjunction with Figure 1 - Figure 2 which describes the method for optimizing the position of the fluid antenna and the radar communication precoding matrix in the URLLC scenario provided by the present invention. The specific steps are as Figure 2 shown and include:

[0149] S100. Construct an integrated architecture for communication and sensing, which is constructed to support an ISAC system for multiple user terminals and a single sensing target.

[0150] This integrated architecture is as Figure 1 shown and includes a base station, multiple user terminals, and a single detection target.

[0151] Among them, the base station has a planar fluid antenna array for sending signals to the user terminals, and the signals 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, which receives the signals sent by the base station and reflects the signals, and the base station receives the reflected signals from the detection target and performs sensing. The URLLC communication delay and signal-to-noise ratio (SNR) are used as the performance indicators for user terminal communication and point target radar sensing respectively.

[0152] S200. Construct a communication signal model between the base station and the user terminals in the URLLC scenario, and a sensing signal model between the base station and the detection target.

[0153] S210. Construct a communication signal model between the base station and the user terminals in the URLLC scenario:

[0154] Specifically, assuming there are K user terminals, the antenna array of the base station is equipped with M fluid antennas, the communication symbols and radar symbols sent by the base station are separately encoded, and at time slot n , the signal sent by the base station can be expressed as:

[0155]

[0156] is a set of precoding matrices for radar symbols;

[0157] is a set of communication symbols transmitted by the base station to point targets;

[0158] is a set of precoding matrices for communication symbols;

[0159] is a set of communication symbols transmitted by the base station to user terminals.

[0160] And satisfies , satisfies , both are uncorrelated and statistically independent, and satisfy ; T represents transpose, H represents conjugate transpose, K is the total number of user terminals, M is the total number of antennas of the base station, is a set of complex numbers, represents mathematical expectation, is a K*K identity matrix, is an M*M identity matrix;

[0161] Therefore, the covariance matrix of the signal transmitted by the base station can be expressed as:

[0162]

[0163] Based on this, at time slot n , the communication signal k received by the th user can be expressed as:

[0164]

[0165] In the formula, represents the communication signal received by the k th user terminal; is the precoding matrix of the communication symbol of the k th user terminal, is the communication symbol transmitted by the base station to the i th user terminal; is the precoding matrix of the communication symbol of the i th user terminal, is the communication symbol transmitted by the base station to the i th user terminal; is Gaussian white noise, following the distribution ;

[0166] is the kThe communication channel between a user terminal and a base station is expressed as:

[0167]

[0168] where , is the path response between the base station and the k th user terminal; is the number of signal path, is the path response of the th path between the kth terminal and the base station; is the field response matrix of the base station, where is the field response matrix between the m th antenna and the k th user terminal, is the imaginary unit, is the carrier wavelength, represents the position of the antenna, and are the elevation angle and azimuth angle between the user terminal k and the base station respectively, is the m th channel propagation distance difference between the l th root antenna and the origin of the antenna array; , are the horizontal and vertical coordinates of the mth fluid antenna.

[0169] S220. Construct the sensing signal model between the base station and the detection target:

[0170] The base station uses the transmitted signal to perform radar sensing on a point target, and the received sensing signal can be expressed as:

[0171]

[0172] In the formula, represents the sensing signal received by the base station from the target; represents the Doppler frequency shift of the target, represents the sum of the path delays of the signal traveling to and from the target; represents the signal transmitted by the base station at the time slot n , and its expression is:

[0173]

[0174] is the target response matrix; is the reflection coefficient of the sensed target, is the transmitting antenna steering array of the k th user terminal, and are the elevation angle and azimuth angle between the base station and the point target, respectively, is the set of antenna positions.

[0175] S300. A mathematical model of the radar communication signal optimization problem is established with the goal of maximizing the radar sensing signal-to-noise ratio, subject to the base station transmission power, URLLC delay requirements, and fluid antenna position constraints.

[0176] Specifically, the radar sensing signal-to-noise ratio is expressed as:

[0177]

[0178] where is the product of the comprehensive coefficient and ; is the covariance matrix of the signal transmitted by the base station; represents the Frobenius norm; is the variance of the radar Gaussian white noise.

[0179] The URLLC delay, expressed as:

[0180]

[0181] where is the length of the data packet sent by the base station to the k th user terminal, is the maximum tolerable delay of the k th user terminal, is the achievable rate of the k th user terminal, and its expression is as follows:

[0182]

[0183] where is the bandwidth; , is the inverse function of the Gaussian function; is the channel tolerance of the k th user terminal, expressed as ; is the signal-to-interference-plus-noise ratio of the k th user terminal.

[0184] The optimization problem of maximizing the radar sensing signal-to-noise ratio is:

[0185]

[0186]

[0187]

[0188]

[0189]

[0190] Among them, and are the m-th and n-th antenna position coordinates respectively;

[0191] Constraint C1 means that the maximum transmission power of the base station cannot exceed , constraint C2 represents the URLLC delay requirement, constraint C3 means that all antenna positions need to be within the array region and constraint C4 means that the spacing between any pair of antennas needs to be greater than D to ensure that the mutual coupling between antennas can be ignored. This problem is a non-convex optimization problem.

[0192] S400. Decompose the optimization problem into three sub-problems, adopt an alternating iterative optimization algorithm, optimize one variable each time, fix the remaining two variables, and alternately optimize the three sub-problems and iterate to obtain a convergent solution.

[0193] S410. Decompose the optimization problem into three sub-problems, namely the sub-problem with the fluid antenna position as the optimization variable, the sub-problem with the radar precoding matrix as the optimization variable, and the sub-problem with the communication precoding matrix as the optimization variable.

[0194] S420. Solve the sub-problem with the fluid antenna position as the optimization variable. Use the successive convex approximation method to handle the two sub-expressions of the URLLC rate, then use the second-order Taylor expansion to handle the objective function as a quadratic convex function, handle the communication rate and the fluid antenna spacing requirement after convex approximation as linear constraints, and finally use a convex optimization tool to solve the fluid antenna position. The specific method is as follows:

[0195] S421. Represent the sub-problem with the fluid antenna position as the optimization variable as:

[0196]

[0197]

[0198]

[0199]

[0200] S422. Use the successive convex approximation method to handle the two sub-expressions of the URLLC rate. First, handle , according to the Taylor expansion of the logarithmic function, its expansion is:

[0201]

[0202] In the formula, is a constant related to For the sake of simplicity of expression, let ; is at the r iteration value;

[0203] Then, substitute the expression of into to obtain . For this formula, use the first-order Taylor expansion to get:

[0204]

[0205] In the formula, is a comprehensive coefficient related to ;

[0206] Finally, the URLLC rate expression is expressed as:

[0207]

[0208] Among them, ;

[0209] Then the constraint C1 in the sub-problem with the fluid antenna position as the optimization variable is expressed as:

[0210]

[0211] In the formula, ;

[0212] S423. Use the second-order Taylor expansion to process the objective function as a quadratic convex function, the communication rate after convex approximation, and the fluid antenna spacing requirements; including:

[0213] The processing of the objective function is as follows:

[0214]

[0215] Among them, is the function value of the objective function at the r iteration; represents the gradient of the function at ; is a positive real number that satisfies , is 's Hessian matrix;

[0216] The processing of the communication rate is as follows:

[0217] Substitute Substitute the expression into the constraint C1 to obtain:

[0218]

[0219] Perform transformation to obtain:

[0220]

[0221] In the formula, For the convenience of representation, let ;

[0222] Then, construct the upper bound function of through second-order Taylor expansion:

[0223]

[0224] In the formula, is the function value of the objective function at the r th iteration; represents the gradient of the function at ; is a positive real number that satisfies , is 's Hessian matrix;

[0225] The processing of the fluid antenna spacing requirement is as follows:

[0226]

[0227] Simplify the sub-problem with the fluid antenna position as the optimization variable to:

[0228]

[0229]

[0230]

[0231]

[0232] The simplified objective function is a quadratic convex function with respect to , and the constraints are all linear, which are solved by an optimization tool.

[0233] S430. Solve the sub-problem with the radar precoding matrix as the optimization variable. Through the SDR method, organize the problem into a semidefinite programming problem, then relax the problem to a standard semidefinite problem by discarding the rank-1 constraint, and use CVX to solve it to obtain the radar precoding matrix; the specific method is:

[0234] S431. Express the sub - problem with the radar precoding matrix as the optimization variable as follows:

[0235]

[0236]

[0237]

[0238] S432. Use the SDR method to transform this sub - problem into a semidefinite programming problem. Let , , and ; then this sub - problem is expressed as:

[0239]

[0240]

[0241]

[0242]

[0243]

[0244] By relaxing the rank - 1 constraint, transform this problem into a standard semidefinite problem;

[0245] S433. Solve this semidefinite problem using the convex optimization tool CVX. Let represent the optimal solution of the relaxed problem. Finally, the optimal solution of this sub - problem is:

[0246]

[0247] where, is the largest eigenvalue, and

[0248] S440. For the sub - problem solution with the communication precoding matrix as the optimization variable, first process the communication rate expression. Use the Lagrange dual transformation for concave transformation of the logarithmic term, use the second - order Taylor expansion and Dinkelbach transformation for convex approximation of the radical term, transform the delay constraint into a convex problem, then perform a concave transformation on the objective function, and finally use the interior - point method to solve for the communication precoding matrix. The specific method is as follows:

[0249] S441. Express the sub - problem with the communication precoding matrix as the optimization variable as follows:

[0250]

[0251]

[0252]

[0253] The objective function therein contains the part in the original objective function that contains variables Since the objective function and constraint C1 are convex functions with respect to , only constraint C2 needs to be processed;

[0254] S442. Processing rate expression:

[0255] First, perform concave transformation on the logarithmic term using Lagrangian dual transformation. Denote , then:

[0256]

[0257]

[0258] In the formula, and are both sets of auxiliary variables; , and is convex with respect to ; when is fixed, the optimal is obtained by calculating , that is:

[0259]

[0260] Meanwhile, the optimal is updated by the following formula:

[0261]

[0262] Then, perform convex approximation on the radical term using second-order Taylor expansion and Dinkelbach transformation; Denote , for , its convexity and concavity are determined by ;

[0263] Perform Dinkelbach transformation on the single-fraction term , and define as:

[0264]

[0265] Convert to:

[0266]

[0267] In the formula, is a set of auxiliary variables, and the first item is with respect to a convex function of is with respect to a concave function of; meanwhile, in the th iteration, is updated by the following formula:

[0268]

[0269] Converting to a concave function, there is the following inequality:

[0270]

[0271] Finally, is approximated as:

[0272]

[0273] wherein, , and ;

[0274] In the r +1th iteration, it is approximated as:

[0275]

[0276] S443. Process the objective function:

[0277] Since the objective function is convex with respect to , use the first-order Taylor expansion to convert it to a concave function. To simplify the expression, let . The expansion at can be written as:

[0278] wherein, the expression of

[0279]

[0280] According to the above conversion, the sub-problem with the communication precoding matrix as the optimization variable is converted to:

[0281]

[0282]

[0283]

[0284] The problem is about is convex and is solved by the interior point method (IPM) of CVX.

[0285] S450. Repeat steps S420 - S440 for iterative solution until the model converges to obtain a convergent solution.

[0286] In summary, the present invention proposes a multi - user terminal ISAC fluid antenna communication and sensing system solution in the URLLC scenario. The fluid antenna array simultaneously performs radar sensing and communication, effectively reducing interference between user terminals, and satisfies the requirements of radar sensing and communication transmission by solving the fluid antenna position and the radar communication precoding matrix.

[0287] Through the description of the above - mentioned embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general - purpose hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the essence of the above - mentioned technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer - readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing 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.

[0288] 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 them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of each embodiment 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, and 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-positive 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.

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