A movable antenna design method for a C2I integrated system

Abstract

This invention discloses a movable antenna design method for integrated sensing and communication systems, relating to the field of wireless communication technology. By deploying linear movable antenna arrays at both the transmitter and receiver ends, antenna position, communication, and sensing beamforming are jointly optimized. First, a system model incorporating a weighted sum of communication rate and sensing accuracy is established. Then, an optimization problem is constructed with the Cramer-Rao bound weighted sum of total rate and angle estimation as the objective. By decomposing the problem into two sub-problems—beamforming and antenna position—alternating optimization methods such as regularized zero-filling, characteristic beamforming, and gradient projection are employed. A two-stage algorithm prioritizing sensing and balancing collaborative approaches is designed to achieve a dynamic trade-off between communication and sensing performance. This invention significantly improves system spatial diversity, reduces channel correlation, and significantly improves communication rate and sensing accuracy compared to fixed arrays at the same signal-to-noise ratio, making it suitable for 6G high-dynamic, multi-user, multi-target scenarios.

Description

Technical Field

[0001] This invention relates to the field of integrated sensing and communication system technology in sixth-generation (6G) mobile communication technology, and in particular to a design method for a movable antenna for an integrated sensing and communication system. Background Technology

[0002] With the development of 6G (Sixth Generation) communication systems, higher demands are being placed on wireless communication networks. 6G wireless communication networks not only require higher communication speeds and reliability, but also strive to achieve intelligent sensing of the physical world, building a new paradigm of integrated communication and sensing.

[0003] However, due to the static characteristics of its physical structure, traditional fixed array antennas have fixed aperture, geometric layout and beam direction. At the hardware level, they are limited by the static physical constraints of fixed array antennas. At the system design level, there is a lack of effective models to cope with the complexity of multiple users and multiple targets. At the algorithm level, there is a lack of models that can deeply integrate spatial degrees of freedom and signal degrees of freedom. It is difficult to dynamically adapt to the real-time changes in the spatial distribution and channel state of communication users and sensing targets in the ISAC system, resulting in inherent limitations in resource utilization and performance improvement. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a movable antenna design method for integrated communication and sensing systems. By jointly optimizing the positions of the movable antennas at the transmitting and receiving ends and the corresponding communication and sensing beamforming vectors, a weighted and optimized target including the communication rate and the Cramer-Rao bound of the sensing target angle estimation is established, thereby achieving synchronous optimization of communication rate and sensing accuracy.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A movable antenna design method for an integrated sensing and communication system, proposed according to the present invention, includes:

[0007] Step S1: Deploy movable antennas at the transmitting and receiving ends of the integrated sensing and communication system, respectively, and their positions can be dynamically adjusted within a preset spatial area;

[0008] Step S2: Establish the channel and signal model;

[0009] Step S3: Based on the channel and signal model established in step S2, describe the communication rate and the sensing accuracy based on Cramer-Rao bound, and construct a joint optimization problem by weighting the communication rate and the sensing accuracy based on Cramer-Rao bound.

[0010] Step S4: Decompose the joint optimization problem constructed in Step S3 using the weighted sum of communication rate and sensing accuracy based on Cramer-Rhodes bounds into two sub-problems, namely, the first sub-problem and the second sub-problem; wherein,

[0011] First sub-problem: Optimize beamforming with a fixed movable antenna position;

[0012] The second sub-problem: Optimizing the position of a movable antenna under fixed beamforming;

[0013] Step S5: Alternately optimize the first and second stages. When the weighted sum of the communication rate and the sensing accuracy based on the Cramer-Rao boundary reaches its maximum, determine the location layout and beamforming of the movable antennas. In the first stage, based on the principle of sensing priority, the location and beamforming of the movable antennas at the transmitting and receiving ends are initially determined through gradient search and null-space beamforming. In the second stage, under the premise of satisfying the sensing performance constraints, the location and beamforming of the movable antennas at the transmitting and receiving ends are jointly optimized using the block coordinate descent method.

[0014] As a further optimization of the movable antenna design method for an integrated sensing system described in this invention, in step S1, the transmitting end Tx is configured with N movable antennas, and the receiving end Rx is configured with M movable antennas, where M ≥ N. The antenna position vector of the transmitting end Tx is... superscript This represents the matrix transpose operation. For the first in Tx The location of a movable antenna, N≥ ≥1, the antenna position vector of the receiver Rx superscript This represents the matrix transpose operation. For the first in Rx The location of a movable antenna, M≥ The movable space regions of the movable antennas configured with ≥1, Tx, and Rx are respectively denoted as... and Each movable antenna is connected to the RF chain via a flexible cable; K communication users and P perceived targets Use respectively and To indicate, Let K represent the k-th communication user, where 1 ≤ k ≤ K. Let p represent the p-th perceived target, where 1 ≤ p ≤ P.

[0015] As a further optimization of the movable antenna design method for an integrated sensing system described in this invention, in step S2, the communication rate and the sensing accuracy based on the Cramer-Rhodes boundary include:

[0016] The communication rate of the k-th user The signal-to-interference-plus-noise ratio of the kth communication user , This represents the conjugate transpose of the channel matrix from the transmitter Tx to the k-th communication user. This represents beamforming of the signal transmitted to the k-th communication user. This represents the beamforming of the signal transmitted to the i-th communication user. This represents beamforming of the signal transmitted to the p-th sensing target. The Gaussian white noise transmitted to the k-th communication user; the Cramer-Rao boundary sensing accuracy of the p-th sensing target. , This represents the inverse of the Fisher information matrix of the p-th perceived target. Represents the conjugate transpose operator; defines the beamforming matrix for the communication portion of the transmitted signal. Beamforming matrix of the sensing part , , , 1≤k≤K, 1≤p≤P, Received beamforming vector , Beamforming for the p-th sensing target arriving at the receiver Rx; define the angle parameter vector. The angle parameter of the p-th perceived target Let AoA represent the angle of arrival (AoA) of the p-th sensing target at the receiving base station; define the Fisher information matrix. , , Indicates the transmission signal The covariance matrix, The variance of the additive white Gaussian noise of the p-th perceived target Represents the real part of the result of the operation. Represents the trace of a matrix. Represents the received channel matrix. This represents the angle of arrival (AoA) of the i-th sensing target at the receiving base station. Indicates the first The angle of arrival (AoA) of the sensing target at the receiving base station; , This is the channel response from the transmitter Tx to the p-th target and back to the receiver Rx, after receiving beamforming. , This represents the channel matrix from the sensing target p to the receiver Rx. Let represent the reflectance coefficient of the p-th perceived target. Let Tx be the conjugate transpose of the channel matrix from the transmitter Tx to the p-th sensing target. Let Rx represent the Gaussian white noise at the receiver for the p-th sensing target.

[0017] As a further optimization of the mobile antenna design method for an integrated sensing system described in this invention, the communication rate and sensing accuracy based on the Cramer-Rao boundary are established under the channel premise of the channel matrix from the transmitter Tx to the communication user, the channel matrix from the transmitter Tx to the sensing target, and the channel matrix from the sensing target to the receiver Rx, including:

[0018] Channel matrix from transmitter Tx to the k-th communication user Channel matrix from transmitter Tx to the p-th sensing target and the channel matrix from the p-th sensing target to the receiver Rx They are represented as follows:

[0019] , and ;

[0020] in, , and , , , Let Rx represent the field response vectors from the transmitter to the k-th communication user, from the base station to the p-th sensing target, and from the p-th sensing target to the receiver, respectively, and have the following... , and

[0021] , This indicates the position of the nth movable antenna at the transmitter Tx. This indicates the position of the m-th movable antenna at the receiver Rx. , , Let Tx represent the field response vectors from the transmitter Tx to the k-th communication user, from the base station to the p-th sensing target, and from the p-th sensing target to the receiver Rx, respectively, where 1 ≤ n ≤ N, 1 ≤ m ≤ M. This represents the matrix transpose operator, where e is the natural base and j is the imaginary unit. , , Let represent the path response vectors from the base station to the k-th communication user, from the transmitter Tx to the p-th sensing target, and from the p-th sensing target to the receiver Rx, respectively. , , These represent the distance from the transmitter to the k-th user. The angle of arrival of the path, the angle from the transmitter to the p-th sensing target. The angle of arrival of each path is the angle of arrival of the q-th path from the p-th sensing target to the receiver, 1 ≤ ≤ ,1≤ ≤ , and These represent the number of transmission and reception paths, respectively.

[0022] As a further optimization scheme for the mobile antenna design method for a sensing-integrated system described in this invention, in step S3, a joint optimization problem is constructed by weighting the communication rate and the sensing accuracy based on the Cramer-Rao boundary.

[0023] ;

[0024] in, and These represent the optimization weights for communication and sensing performance, respectively. This represents the weight of the Cramer-Rhodes bound for the p-th perceived target. , Indicates a weighted sum. This represents the communication rate of the k-th user. Describes the Cramer-Rhodes bound for the p-th perceived target. Let AoA represent the angle of arrival (AoA) of the p-th sensing target at the receiving base station;

[0025] By jointly optimizing the positions of the transceiver antennas, the communication and sensing transmit beamform matrix, and the receive beamforming matrix, we seek the best performance of the integrated sensing system.

[0026] As a further optimization scheme of the movable antenna design method for an integrated sensing system described in this invention, in step S4, the beamforming optimization under a fixed antenna position and the antenna position optimization under a fixed beamforming position are respectively expressed as follows:

[0027] Given a fixed antenna position, a regularized zero-filling algorithm is used for communication beamforming to balance interference suppression and noise enhancement:

[0028] ;

[0029] in, This represents the beamforming from the transmitter to the communication user calculated by the regularized zero-fill algorithm. This represents the joint channel matrix from transmission to all K communication users. This represents an identity matrix of dimension K*K. , , For regularization parameters, for sensing beamforming, characteristic beamforming is used to maximize the target direction gain, and receiving beamforming is as follows:

[0030] ;

[0031] in, This represents the receiving beamforming vector of the p-th sensing target. This represents the channel matrix from the p-th sensing target to Rx. This means retrieving all elements from the p-th column of the matrix;

[0032] Considering the trade-off between communication and sensing, the transmit beamforming used for sensing employs a method that maximizes SINR:

[0033] ;

[0034] in, The table shows the optimal transmit beamforming vector for the p-th sensing target. This represents a vector of variables during the solution process. This represents the channel matrix from the base station to the p-th sensing target. The covariance matrix representing interference and noise. , This represents the transmit beamforming vector from the transmitter to the k-th communication user. Indicates the noise variance. Represents an identity matrix of dimension N*N; It is a generalized Rayleigh quotient problem, the solution of which is the eigenvector corresponding to the largest generalized eigenvalue;

[0035] Given a fixed beamforming matrix, the gradient of the constructed joint optimization problem with respect to the antenna position is:

[0036] ;

[0037] in, This represents the gradient with respect to the position vector of the movable antenna at the transmitting end. This represents an optimization problem in the construction process. Indicates communication rate. This represents the weight of the p-th perceived target. Describes the Cramer-Rhodes bound for the p-th perceived target. This represents the gradient with respect to the position vector of the movable antenna at the receiving end. This represents the communication rate of the k-th user. This represents the weight of the p-th perceived target;

[0038] The gradient components of the communication rate are calculated using the chain rule: , ;and ;

[0039] in, This represents the signal-to-interference-plus-noise ratio (SIR) of the k-th communication user. This represents the conjugate transpose of the channel matrix from the transmitter to the k-th communication user. This represents the transmit beamforming vector of the k-th communication user. This represents the transmit beamforming vector of the i-th communication user. This represents the received beamforming vector of the p-th sensing target. Let represent the conjugate transpose of the channel matrix from the transmitter to the p-th sensing target. This represents the noise variance transmitted to the k-th communication user;

[0040] The gradient components of CRB are:

[0041] ,

[0042] in, This represents the Fisher information for the p-th perceived target;

[0043] Due to constraints on the antenna position, the projection gradient descent method is used to obtain the new antenna position:

[0044] ;

[0045] in, and For the projection operator to the feasible set, and Step size, This indicates the new location of the movable antenna on the transmitter. This indicates the new movable antenna position at the receiver. This represents the Fisher information matrix.

[0046] As a further optimization of the movable antenna design method for an integrated sensing system described in this invention, step S5 includes:

[0047] The first step is CRB-driven perception-priority optimization. To maximize perception performance, the beamforming vector is designed to be aligned with the target direction.

[0048] ;

[0049] in, This represents the received beamforming vector of the p-th sensing target. Represents the principal eigenvectors of the matrix. Represents the norm of a matrix;

[0050] Communication beamforming design is performed in the null space of the sensing channel:

[0051] ;

[0052] Among them, and there are , , This represents the transmit beamforming vector of the k-th communication user. This represents the projected channel matrix from the transmitter to the k-th communication user. This indicates that the k-th column is extracted from the projected channel matrix. Represents the null projection matrix. This represents the channel matrix from the transmitter to the k-th communication user. It is the sensing channel matrix column space basis;

[0053] CRB optimization for antenna location uses gradient direction search:

[0054] ;

[0055] in, This represents the update amount of the position vector of the movable antenna at the transmitting end. This indicates the step size for updating the position of the movable antenna at the transmitting end. Indicates the position of the movable antenna at the transmitting end. This represents the update amount of the position vector of the movable antenna at the receiving end. This indicates the step size for updating the position of the movable antenna at the receiving end. This indicates the location of the movable antenna at the receiving end.

[0056] As a further optimization scheme for the movable antenna design method for a communication and sensing integrated system described in this invention, in step S3, the optimization variables in the joint optimization problem include the positions of the movable antennas at the transmitting and receiving ends, the communication and sensing beamforming matrix, power constraints, movement range constraints, minimum spacing constraints, and sensing performance lower limit constraints.

[0057] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0058] (1) Higher spatial freedom and performance improvement: By modeling the position of the transmitting antenna as a one-dimensional Wiener process, this invention can effectively enhance the spatial diversity of the antenna array, reduce channel correlation, and thus improve the system's anti-interference capability and spectral efficiency. By deploying movable antennas at both the transmitting and receiving ends, this invention effectively overcomes the aperture and geometric limitations caused by the fixed physical position of traditional fixed array antennas, introduces flexible spatial freedom, and can dynamically adjust the antenna layout according to real-time communication and sensing requirements.

[0059] (2) Coordinated optimization and flexible trade-off between communication and sensing: This invention introduces adjustable weighting parameters to distinguish the importance of different communication users and sensing targets and to allocate performance in a customized manner. A two-stage alternating optimization algorithm driven by Cramer-Rao bound (CRB) is adopted. In the first stage, the sensing accuracy is improved first, and in the second stage, the communication rate is optimized under the sensing constraints. This maximizes the multi-user communication capacity while ensuring high-precision sensing of multiple targets, and realizes efficient coordination and dynamic balance between communication and sensing functions.

[0060] (3) Adapting to complex environments and multi-target, multi-user scenarios: Unlike traditional integrated sensing and communication systems that are optimized only for a single target or a single user, this invention supports serving multiple communication users and multiple sensing targets simultaneously. By jointly optimizing antenna positions and beamforming, the system can better distinguish and suppress interference between users and between targets, improving the overall system performance in complex electromagnetic environments, and is especially suitable for high-density, high-dynamic application scenarios in 6G networks.

[0061] (4) The system is flexible in configuration and supports customized services: By setting independent weights for different targets and users, the system can flexibly adjust the resource allocation strategy according to actual task requirements (such as focusing on monitoring a certain target or prioritizing the communication of a certain user), improve the intelligence and personalized service level of the integrated sensing and communication system, and provide feasible technical support for on-demand services in future networks. Attached Figure Description

[0062] Figure 1 This is an overall flowchart of a movable antenna array for 6G wireless channel modeling provided by an embodiment of the present invention;

[0063] Figure 2 This is a schematic diagram of the optimization process of the optimization algorithm provided in this invention;

[0064] Figure 3 This is the convergence graph of the optimization algorithm provided in this invention.

[0065] Figure 4 This is an antenna performance diagram provided by an embodiment of the present invention;

[0066] Figure 5This is an antenna performance diagram provided by an embodiment of the present invention;

[0067] Figure 6 This is an antenna performance diagram provided by an embodiment of the present invention. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0069] A method for designing a movable antenna for a sensing-integrated system includes:

[0070] Step S1: Deploy movable antennas at the transmitting and receiving ends of the integrated sensing and communication system, respectively, and their positions can be dynamically adjusted within a preset spatial area;

[0071] Step S2: Establish the channel and signal model;

[0072] Step S3: Based on the channel and signal model established in step S2, describe the communication rate and the sensing accuracy based on Cramer-Rao bound, and construct a joint optimization problem by weighting the communication rate and the sensing accuracy based on Cramer-Rao bound.

[0073] Step S4: Decompose the joint optimization problem constructed in Step S3 using the weighted sum of communication rate and sensing accuracy based on Cramer-Rhodes bounds into two sub-problems, namely, the first sub-problem and the second sub-problem; wherein,

[0074] First sub-problem: Optimize beamforming with a fixed movable antenna position;

[0075] The second sub-problem: Optimizing the position of a movable antenna under fixed beamforming;

[0076] Step S5: Alternately optimize the first and second stages. When the weighted sum of the communication rate and the sensing accuracy based on the Cramer-Rao boundary reaches its maximum, determine the location layout and beamforming of the movable antennas. In the first stage, based on the principle of sensing priority, the location and beamforming of the movable antennas at the transmitting and receiving ends are initially determined through gradient search and null-space beamforming. In the second stage, under the premise of satisfying the sensing performance constraints, the location and beamforming of the movable antennas at the transmitting and receiving ends are jointly optimized using the block coordinate descent method.

[0077] In step S1, the transmitting end Tx is configured with N movable antennas, and the receiving end Rx is configured with M movable antennas, where M ≥ N. The antenna position vector of the transmitting end Tx is... superscript This represents the matrix transpose operation. For the first in Tx The location of a movable antenna, N≥ ≥1, the antenna position vector of the receiver Rx superscript This represents the matrix transpose operation. For the first in Rx The location of a movable antenna, M≥ The movable space regions of the movable antennas configured with ≥1, Tx, and Rx are respectively denoted as... and Each movable antenna is connected to the RF chain via a flexible cable; K communication users and P perceived targets Use respectively and To indicate, Let K represent the k-th communication user, where 1 ≤ k ≤ K. Let p represent the p-th perceived target, where 1 ≤ p ≤ P.

[0078] In step S2, the communication rate and the sensing accuracy based on the Cramer-Rhodes boundary include:

[0079] The communication rate of the k-th user The signal-to-interference-plus-noise ratio of the kth communication user , This represents the conjugate transpose of the channel matrix from the transmitter Tx to the k-th communication user. This represents beamforming of the signal transmitted to the k-th communication user. This represents the beamforming of the signal transmitted to the i-th communication user. This represents beamforming of the signal transmitted to the p-th sensing target. The Gaussian white noise transmitted to the k-th communication user; the Cramer-Rao boundary sensing accuracy of the p-th sensing target. , This represents the inverse of the Fisher information matrix of the p-th perceived target. Represents the conjugate transpose operator; defines the beamforming matrix for the communication portion of the transmitted signal. Beamforming matrix of the sensing part , , , 1≤k≤K, 1≤p≤P, Received beamforming vector , Beamforming for the p-th sensing target arriving at the receiver Rx; define the angle parameter vector. The angle parameter of the p-th perceived target Let AoA represent the angle of arrival (AoA) of the p-th sensing target at the receiving base station; define the Fisher information matrix. , , Indicates the transmission signal The covariance matrix, The variance of the additive white Gaussian noise of the p-th perceived target Represents the real part of the result of the operation. Represents the trace of a matrix. Represents the received channel matrix. This represents the angle of arrival (AoA) of the i-th sensing target at the receiving base station. Indicates the first The angle of arrival (AoA) of the sensing target at the receiving base station; , This is the channel response from the transmitter Tx to the p-th target and back to the receiver Rx, after receiving beamforming. , This represents the channel matrix from the sensing target p to the receiver Rx. Let represent the reflectance coefficient of the p-th perceived target. Let Tx be the conjugate transpose of the channel matrix from the transmitter Tx to the p-th sensing target. Let Rx represent the Gaussian white noise at the receiver for the p-th sensing target.

[0080] The communication rate and sensing accuracy based on the Cramer-Rhodes boundary are established under the channel premise of the channel matrix from the transmitter Tx to the communication user, the channel matrix from the transmitter Tx to the sensing target, and the channel matrix from the sensing target to the receiver Rx, including:

[0081] Channel matrix from transmitter Tx to the k-th communication user Channel matrix from transmitter Tx to the p-th sensing target and the channel matrix from the p-th sensing target to the receiver Rx They are represented as follows:

[0082] , and ;

[0083] in, , and , , , Let Rx represent the field response vectors from the transmitter to the k-th communication user, from the base station to the p-th sensing target, and from the p-th sensing target to the receiver, respectively, and have the following... , and

[0084] , This indicates the position of the nth movable antenna at the transmitter Tx. This indicates the position of the m-th movable antenna at the receiver Rx. , , Let Tx represent the field response vectors from the transmitter Tx to the k-th communication user, from the base station to the p-th sensing target, and from the p-th sensing target to the receiver Rx, respectively, where 1 ≤ n ≤ N, 1 ≤ m ≤ M. This represents the matrix transpose operator, where e is the natural base and j is the imaginary unit. , , Let represent the path response vectors from the base station to the k-th communication user, from the transmitter Tx to the p-th sensing target, and from the p-th sensing target to the receiver Rx, respectively. , , These represent the distance from the transmitter to the k-th user. The angle of arrival of the path, the angle from the transmitter to the p-th sensing target. The angle of arrival of each path is the angle of arrival of the q-th path from the p-th sensing target to the receiver, 1 ≤ ≤ ,1≤ ≤ , and These represent the number of transmission and reception paths, respectively.

[0085] In step S3, a joint optimization problem is constructed by weighting the communication rate and the sensing accuracy based on the Cramer-Rhodes bound;

[0086] ;

[0087] in, and These represent the optimization weights for communication and sensing performance, respectively. This represents the weight of the Cramer-Rhodes bound for the p-th perceived target. , Indicates a weighted sum. This represents the communication rate of the k-th user. Describes the Cramer-Rhodes bound for the p-th perceived target. Let AoA represent the angle of arrival (AoA) of the p-th sensing target at the receiving base station;

[0088] By jointly optimizing the positions of the transceiver antennas, the communication and sensing transmit beamform matrix, and the receive beamforming matrix, we seek the best performance of the integrated sensing system.

[0089] In step S4, the beamforming optimization under a fixed antenna position and the antenna position optimization under fixed beamforming are respectively expressed as:

[0090] Given a fixed antenna position, a regularized zero-filling algorithm is used for communication beamforming to balance interference suppression and noise enhancement:

[0091] ;

[0092] in, This represents the beamforming from the transmitter to the communication user calculated by the regularized zero-fill algorithm. This represents the joint channel matrix from transmission to all K communication users. This represents an identity matrix of dimension K*K. , , For regularization parameters, for sensing beamforming, characteristic beamforming is used to maximize the target direction gain, and receiving beamforming is as follows:

[0093] ;

[0094] in, This represents the receiving beamforming vector of the p-th sensing target. This represents the channel matrix from the p-th sensing target to Rx. This means retrieving all elements from the p-th column of the matrix;

[0095] Considering the trade-off between communication and sensing, the transmit beamforming used for sensing employs a method that maximizes SINR:

[0096] ;

[0097] in, The table shows the optimal transmit beamforming vector for the p-th sensing target. This represents a vector of variables during the solution process. This represents the channel matrix from the base station to the p-th sensing target. The covariance matrix representing interference and noise. , This represents the transmit beamforming vector from the transmitter to the k-th communication user. Indicates the noise variance. Represents an identity matrix of dimension N*N; It is a generalized Rayleigh quotient problem, the solution of which is the eigenvector corresponding to the largest generalized eigenvalue;

[0098] Given a fixed beamforming matrix, the gradient of the constructed joint optimization problem with respect to the antenna position is:

[0099] ;

[0100] in, This represents the gradient with respect to the position vector of the movable antenna at the transmitting end. This represents an optimization problem in the construction process. Indicates communication rate. This represents the weight of the p-th perceived target. Describes the Cramer-Rhodes bound for the p-th perceived target. This represents the gradient with respect to the position vector of the movable antenna at the receiving end. This represents the communication rate of the k-th user. This represents the weight of the p-th perceived target;

[0101] The gradient components of the communication rate are calculated using the chain rule: , ;and ;

[0102] in, This represents the signal-to-interference-plus-noise ratio (SIR) of the k-th communication user. This represents the conjugate transpose of the channel matrix from the transmitter to the k-th communication user. This represents the transmit beamforming vector of the k-th communication user. This represents the transmit beamforming vector of the i-th communication user. This represents the received beamforming vector of the p-th sensing target. Let represent the conjugate transpose of the channel matrix from the transmitter to the p-th sensing target. This represents the noise variance transmitted to the k-th communication user;

[0103] The gradient components of CRB are:

[0104] ,

[0105] in, This represents the Fisher information for the p-th perceived target;

[0106] Due to constraints on the antenna position, the projection gradient descent method is used to obtain the new antenna position:

[0107] ;

[0108] in, and For the projection operator to the feasible set, and Step size, This indicates the new location of the movable antenna on the transmitter. This indicates the new movable antenna position at the receiver. This represents the Fisher information matrix.

[0109] Step S5 includes:

[0110] The first step is CRB-driven perception-priority optimization. To maximize perception performance, the beamforming vector is designed to be aligned with the target direction.

[0111] ;

[0112] in, This represents the received beamforming vector of the p-th sensing target. Represents the principal eigenvectors of the matrix. Represents the norm of a matrix;

[0113] Communication beamforming design is performed in the null space of the sensing channel:

[0114] ;

[0115] Among them, and there are , , This represents the transmit beamforming vector of the k-th communication user. This represents the projected channel matrix from the transmitter to the k-th communication user. This indicates that the k-th column is extracted from the projected channel matrix. Represents the null projection matrix. This represents the channel matrix from the transmitter to the k-th communication user. It is the sensing channel matrix column space basis;

[0116] CRB optimization for antenna location uses gradient direction search:

[0117] ;

[0118] in, This represents the update amount of the position vector of the movable antenna at the transmitting end. This indicates the step size for updating the position of the movable antenna at the transmitting end. Indicates the position of the movable antenna at the transmitting end. This represents the update amount of the position vector of the movable antenna at the receiving end. This indicates the step size for updating the position of the movable antenna at the receiving end. This indicates the location of the movable antenna at the receiving end.

[0119] In step S3, the optimization variables in the joint optimization problem include the positions of the movable antennas at the transmitter and receiver, the communication and sensing beamforming matrix, power constraints, movement range constraints, minimum spacing constraints, and sensing performance lower limit constraints.

[0120] To achieve the objectives of this invention, a movable antenna design for an integrated sensing and communication system is proposed. The design process is as follows: Figure 1 As shown, the specific steps are as follows:

[0121] S1. The transmitting end is equipped with N movable antennas, and the receiving end is equipped with M movable antennas (M≥N). Each communication user and sensing target is equipped with a fixed-position antenna. Assume that Tx and Rx both use linear movable antenna arrays, and their antenna position vectors are represented as follows: and The movable spatial regions of the Tx and Rx antennas are denoted as follows: and Each antenna module is connected to the RF chain via a flexible cable. K communication users and P sensing targets are respectively... and To represent. The system model is as follows: Figure 2 As shown.

[0122] S2, the communication rate of the kth user The signal-to-interference-plus-noise ratio of the kth communication user The Lamar-Robben boundary for the perception of the p-th target can be represented as: .in This represents the conjugate transpose operator. The beamforming matrices for the communication and sensing components of the transmitted signal are defined as follows: and The received beamforming vector is Define the angle parameter vector as follows: , representing the angle of arrival (AoA) of the sensed target at the receiving base station. Meanwhile, the Fisher information matrix can be defined as follows: , Indicates the transmission signal The covariance matrix. ,in .

[0123] S3. The constructed joint optimization problem is:

[0124]

[0125] in, and These represent the optimization weights for communication and sensing performance, respectively. This represents the weight of the CRB for the p-th sensing target. By jointly optimizing the positions of the transmitting and receiving antennas, the communication and sensing transmit beamforming matrices, and the receive beamforming matrix, optimal system performance can be sought. This optimization process requires simultaneously incorporating constraints such as the upper limit of transmit power for the communication and sensing components, the spatial movement range of the movable antennas, the minimum distance between antennas, and sensing performance constraints, making the optimization more practically meaningful.

[0126] S4. Given a fixed antenna position, for communication beamforming, we employ the Regularized Zero-fill (RZF) algorithm to balance interference suppression and noise enhancement:

[0127]

[0128] in, , For regularization parameters, characteristic beamforming is used to maximize the target direction gain for sensing beamforming; receiving beamforming is similar.

[0129]

[0130] Considering the trade-off between communication and sensing, the transmit beamforming used for sensing employs a method that maximizes SINR:

[0131]

[0132] in, This is the generalized Rayleigh quotient problem, whose solution is the eigenvector corresponding to the largest generalized eigenvalue.

[0133] Given a fixed beamforming matrix, the gradient of the objective function with respect to the antenna position is:

[0134]

[0135] The gradient component of the communication rate can be calculated using the chain rule: , And in the above formula Similarly, the gradient components of CRB are:

[0136] ,in This represents the Fisher information for the p-th target. Due to constraints on antenna position, we employ the projective gradient descent method:

[0137]

[0138] in, and For the projection operator to the feasible set, and The step size.

[0139] S5. The proposed two-stage algorithm is as follows:

[0140] The first step is CRB-driven perception-priority optimization. To maximize perception performance, the beamforming vector is designed to be aligned with the target direction.

[0141]

[0142] in This represents the principal eigenvector of the matrix. To reduce interference with sensing, communication beamforming is designed within the null space of the sensing channel:

[0143]

[0144] in It is the sensing channel matrix The column space basis, and has , CRB optimization for antenna location can be achieved using gradient direction search:

[0145]

[0146] The second step of the algorithm is a communication-sensing balance optimization, which uses the block coordinate descent method to alternately optimize communication beamforming and sensing beamforming. In this stage, antenna position optimization must ensure that the CRB value does not increase significantly.

[0147] S6. The performance of the proposed movable antenna-enhanced integrated sensing and communication system and its two-stage optimization algorithm was evaluated through numerical simulation using a simulation platform. We compared the communication rate, sensing accuracy (measured by the angle estimation CRB), and communication-sensing weighted sum performance of the movable antenna system and the traditional fixed array system at different signal-to-noise ratios. Figure 3 This demonstrates how the performance of the antenna weighted sum changes with the number of iterations under different weights. Figure 4 This demonstrates the improved communication speed of this movable array antenna compared to traditional fixed array antennas. Figure 5 This demonstrates the improved sensing accuracy of the movable array antenna compared to traditional fixed array antennas. Figure 6 This demonstrates the weighted improvement in communication rate and sensing accuracy of the movable array antenna compared to a traditional fixed array antenna.

[0148] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method for a movable antenna for a sensor-integrated system, characterized in that, include: Step S1: Deploy movable antennas at the transmitting and receiving ends of the integrated sensing and communication system, respectively, and their positions can be dynamically adjusted within a preset spatial area; Step S2: Establish the channel and signal model; Step S3: Based on the channel and signal model established in step S2, describe the communication rate and the sensing accuracy based on Cramer-Rao bound, and construct a joint optimization problem by weighting the communication rate and the sensing accuracy based on Cramer-Rao bound. Step S4: Decompose the joint optimization problem constructed in Step S3 using the weighted sum of communication rate and sensing accuracy based on Cramer-Rhodes bounds into two sub-problems, namely, the first sub-problem and the second sub-problem; wherein, First sub-problem: Optimize beamforming with a fixed movable antenna position; The second sub-problem: Optimizing the position of a movable antenna under fixed beamforming; Step S5: Alternately optimize the first and second stages. When the weighted sum of the communication rate and the sensing accuracy based on the Cramer-Rao boundary reaches its maximum, determine the location layout and beamforming of the movable antennas. In the first stage, based on the principle of sensing priority, the location and beamforming of the movable antennas at the transmitting and receiving ends are initially determined through gradient search and null-space beamforming. In the second stage, under the premise of satisfying the sensing performance constraints, the location and beamforming of the movable antennas at the transmitting and receiving ends are jointly optimized using the block coordinate descent method.

2. The movable antenna design method for an integrated sensing and communication system according to claim 1, characterized in that, In step S1, the transmitting end Tx is configured with N movable antennas, and the receiving end Rx is configured with M movable antennas, where M ≥ N. The antenna position vector of the transmitting end Tx is... superscript This represents the matrix transpose operation. For the first in Tx The location of a movable antenna, N≥ ≥1, the antenna position vector of the receiver Rx superscript This represents the matrix transpose operation. For the first in Rx The location of a movable antenna, M≥ ≥1, the movable space regions of the movable antennas configured in Tx and Rx are respectively denoted as and Each movable antenna is connected to the RF chain via a flexible cable; K communication users and P perceived targets Use respectively and To indicate, Let K represent the k-th communication user, where 1 ≤ k ≤ K. Let p represent the p-th perceived target, where 1 ≤ p ≤ P.

3. The movable antenna design method for an integrated sensing and communication system according to claim 1, characterized in that, In step S2, the communication rate and the sensing accuracy based on the Cramer-Rhodes boundary include: The communication rate of the k-th user The signal-to-interference-plus-noise ratio of the kth communication user , This represents the conjugate transpose of the channel matrix from the transmitter Tx to the k-th communication user. This represents beamforming of the signal transmitted to the k-th communication user. This represents the beamforming of the signal transmitted to the i-th communication user. This represents beamforming of the signal transmitted to the p-th sensing target. The Gaussian white noise transmitted to the k-th communication user; the Cramer-Rao boundary sensing accuracy of the p-th sensing target. , This represents the inverse of the Fisher information matrix of the p-th perceived target. Represents the conjugate transpose operator; defines the beamforming matrix for the communication portion of the transmitted signal. Beamforming matrix of the sensing part , , , 1≤k≤K, 1≤p≤P, Received beamforming vector , Beamforming for the p-th sensing target arriving at the receiver Rx; define the angle parameter vector. The angle parameter of the p-th perceived target Let AoA represent the angle of arrival (AoA) of the p-th sensing target at the receiving base station; define the Fisher information matrix. , , Indicates the transmission signal The covariance matrix, The variance of the additive white Gaussian noise of the p-th perceived target Represents the real part of the result of the operation. Represents the trace of a matrix. Represents the received channel matrix. This represents the angle of arrival (AoA) of the i-th sensing target at the receiving base station. Indicates the first The angle of arrival (AoA) of the sensing target at the receiving base station; , This is the channel response from the transmitter Tx to the p-th target and back to the receiver Rx, after receiving beamforming. , This represents the channel matrix from the sensing target p to the receiver Rx. Let represent the reflectance coefficient of the p-th perceived target. Let Tx be the conjugate transpose of the channel matrix from the transmitter Tx to the p-th sensing target. Let Rx represent the Gaussian white noise at the receiver for the p-th sensing target.

4. The movable antenna design method for an integrated sensing and communication system according to claim 3, characterized in that, The communication rate and sensing accuracy based on the Cramer-Rhodes boundary are established under the channel premise of the channel matrix from the transmitter Tx to the communication user, the channel matrix from the transmitter Tx to the sensing target, and the channel matrix from the sensing target to the receiver Rx, including: Channel matrix from transmitter Tx to the k-th communication user Channel matrix from transmitter Tx to the p-th sensing target and the channel matrix from the p-th sensing target to the receiver Rx They are represented as follows: , and ; in, , and , , , Let Rx represent the field response vectors from the transmitter to the k-th communication user, from the base station to the p-th sensing target, and from the p-th sensing target to the receiver, respectively, and have the following... , and , This indicates the position of the nth movable antenna at the transmitter Tx. This indicates the position of the m-th movable antenna at the receiver Rx. , , Let Tx represent the field response vectors from the transmitter Tx to the k-th communication user, from the base station to the p-th sensing target, and from the p-th sensing target to the receiver Rx, respectively, where 1 ≤ n ≤ N, 1 ≤ m ≤ M. This represents the matrix transpose operator, where e is the natural base and j is the imaginary unit. , , Let represent the path response vectors from the base station to the k-th communication user, from the transmitter Tx to the p-th sensing target, and from the p-th sensing target to the receiver Rx, respectively. , , These represent the distance from the transmitter to the k-th user. The angle of arrival of the path, the angle from the transmitter to the p-th sensing target. The angle of arrival of each path is the angle of arrival of the q-th path from the p-th sensing target to the receiver, 1 ≤ ≤ ,1≤ ≤ , and These represent the number of transmission and reception paths, respectively.

5. The movable antenna design method for an integrated sensing and communication system according to claim 1, characterized in that, In step S3, a joint optimization problem is constructed by weighting the communication rate and the sensing accuracy based on the Cramer-Rhodes bound; ； in, and These represent the optimization weights for communication and sensing performance, respectively. This represents the weight of the Cramer-Rhodes bound for the p-th perceived target. , Indicates a weighted sum. This represents the communication rate of the k-th user. Describes the Cramer-Rhodes bound for the p-th perceived target. Let AoA represent the angle of arrival (AoA) of the p-th sensing target at the receiving base station; By jointly optimizing the positions of the transceiver antennas, the communication and sensing transmit beamform matrix, and the receive beamforming matrix, we seek the best performance of the integrated sensing system.

6. The movable antenna design method for an integrated sensing and communication system according to claim 1, characterized in that, In step S4, the beamforming optimization under a fixed antenna position and the antenna position optimization under fixed beamforming are respectively expressed as: Given a fixed antenna position, a regularized zero-filling algorithm is used for communication beamforming to balance interference suppression and noise enhancement: ； in, This represents the beamforming from the transmitter to the communication user calculated by the regularized zero-fill algorithm. This represents the joint channel matrix from transmission to all K communication users. This represents an identity matrix of dimension K*K. , , For regularization parameters, for sensing beamforming, characteristic beamforming is used to maximize the target direction gain, and receiving beamforming is as follows: ； in, This represents the receiving beamforming vector of the p-th sensing target. This represents the channel matrix from the p-th sensing target to Rx. This means retrieving all elements from the p-th column of the matrix; Considering the trade-off between communication and sensing, the transmit beamforming used for sensing employs a method that maximizes SINR: ； in, The table shows the optimal transmit beamforming vector for the p-th sensing target. This represents a vector of variables during the solution process. This represents the channel matrix from the base station to the p-th sensing target. The covariance matrix representing interference and noise. , This represents the transmit beamforming vector from the transmitter to the k-th communication user. Indicates the noise variance. Represents an identity matrix of dimension N*N; It is a generalized Rayleigh quotient problem, the solution of which is the eigenvector corresponding to the largest generalized eigenvalue; Given a fixed beamforming matrix, the gradient of the constructed joint optimization problem with respect to the antenna position is: ； in, This represents the gradient with respect to the position vector of the movable antenna at the transmitting end. This represents an optimization problem in the construction process. Indicates communication rate. This represents the weight of the p-th perceived target. Describes the Cramer-Rhodes bound for the p-th perceived target. This represents the gradient with respect to the position vector of the movable antenna at the receiving end. This represents the communication rate of the k-th user. This represents the weight of the p-th perceived target; The gradient components of the communication rate are calculated using the chain rule: , ;and ; in, This represents the signal-to-interference-plus-noise ratio (SIR) of the k-th communication user. This represents the conjugate transpose of the channel matrix from the transmitter to the k-th communication user. This represents the transmit beamforming vector of the k-th communication user. This represents the transmit beamforming vector of the i-th communication user. This represents the received beamforming vector of the p-th sensing target. Let represent the conjugate transpose of the channel matrix from the transmitter to the p-th sensing target. This represents the noise variance transmitted to the k-th communication user; The gradient components of CRB are: ， in, This represents the Fisher information for the p-th perceived target; Due to constraints on the antenna position, the projection gradient descent method is used to obtain the new antenna position: ； in, and For the projection operator to the feasible set, and Step size, This indicates the new location of the movable antenna on the transmitter. This indicates the new movable antenna position at the receiver. This represents the Fisher information matrix.

7. The movable antenna design method for an integrated sensing and communication system according to claim 1, characterized in that, Step S5 includes: The first step is CRB-driven perception-priority optimization. To maximize perception performance, the beamforming vector is designed to be aligned with the target direction. ； in, This represents the received beamforming vector of the p-th sensing target. Represents the principal eigenvectors of the matrix. Represents the norm of a matrix; Communication beamforming design is performed in the null space of the sensing channel: ； Among them, and there are , , This represents the transmit beamforming vector of the k-th communication user. This represents the projected channel matrix from the transmitter to the k-th communication user. This indicates that the k-th column is extracted from the projected channel matrix. Represents the null projection matrix. This represents the channel matrix from the transmitter to the k-th communication user. It is the sensing channel matrix column space basis; CRB optimization for antenna location uses gradient direction search: ； in, This represents the update amount of the position vector of the movable antenna at the transmitting end. This indicates the step size for updating the position of the movable antenna at the transmitting end. Indicates the position of the movable antenna at the transmitting end. This represents the update amount of the position vector of the movable antenna at the receiving end. This indicates the step size for updating the position of the movable antenna at the receiving end. This indicates the location of the movable antenna at the receiving end.

8. The movable antenna design method for an integrated sensing and communication system according to claim 1, characterized in that, In step S3, the optimization variables in the joint optimization problem include the positions of the movable antennas at the transmitter and receiver, the communication and sensing beamforming matrix, power constraints, movement range constraints, minimum spacing constraints, and sensing performance lower limit constraints.

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