ISAC near-field channel robust beam forming optimization method and device based on MMSE estimation

Abstract

The invention provides an ISAC near-field channel robust beam forming optimization method and device based on MMSE estimation. The method comprises the following steps: carrying out system modeling and signal configuration on an ISAC system; accurately modeling a near field communication channel by adopting a spherical wave model, calculating to obtain an SINR (Signal to Interference plus Noise Ratio) of a user, and introducing an outage probability constraint; establishing a sensing model under a far-field condition, and estimating a target response matrix by adopting an MMSE criterion to obtain a sensing MSE; introducing an enhanced waveform to improve the perception DoF, and updating the SINR; an enhanced covariance matrix is introduced, the minimum perception MSE is used as an optimization target, the outage probability constraint, the total power constraint and the positive semi-definite constraint updated according to the updated SINR are used as constraint conditions, and an ISAC near-field channel robust beam forming optimization problem is constructed; a non-convex problem is converted into a convex form through combination of semi-definite relaxation SDR and an optimization framework of a spherical boundary and S-lema, and a beam forming optimization matrix is solved and obtained by obeying the constraint of a linear matrix inequality LMI. According to the invention, beam forming can be optimized.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and radar sensing technology, and in particular to an ISAC near-field channel robust beamforming optimization method and apparatus based on MMSE estimation. Background Technology

[0002] With the rapid development of wireless networks towards 6G systems, Integrated Sensing and Communication (ISAC) systems have become a core paradigm for next-generation wireless networks, improving dual-function efficiency by simultaneously achieving information transmission and environmental perception. This system can be applied to autonomous vehicles, smart city systems, and automated industrial processes, providing highly reliable, low-latency communication and precise environmental perception capabilities. Unlike traditional wireless systems, ISAC utilizes shared spectrum and hardware resources, improving spectrum efficiency and reducing deployment costs, thus addressing spectrum congestion issues. Advances in high-frequency technologies such as millimeter waves and massive MIMO (Massively Interactive) antenna arrays have provided ISAC with higher communication throughput and more precise sensing capabilities.

[0003] In existing technologies, beamforming optimization of ISAC systems is mainly based on far-field assumptions and uses plane wave models. These schemes can cause serious errors in high-frequency bands, especially when users are located in the near-field region of large-scale antenna arrays, because spherical waves dominate in the near-field environment. In addition, existing technologies have the following drawbacks: they do not take into account imperfect channel state information (CSI), making them susceptible to environmental interference and reducing robustness; they use the minimum mean squared error (MMSE) criterion for sensing performance but do not optimize for the near field, resulting in increased target estimation errors; and they do not fully consider the probability of interruption in communication QoS constraints, leading to unstable performance in actual deployments. Summary of the Invention

[0004] To address the technical problems existing in the prior art, this invention provides a robust beamforming optimization method and apparatus for ISAC near-field channels based on MMSE estimation. The technical solution is as follows:

[0005] On the one hand, a robust beamforming optimization method for ISAC near-field channels based on MMSE estimation is provided, which includes:

[0006] S1. Perform system modeling and signal configuration for the integrated sensing and communication (ISAC) system, wherein the transmission signal matrix of the ISAC system is used to simultaneously realize communication and sensing functions;

[0007] S2. Based on the transmitted signal matrix, a spherical wave model is used to accurately model the near-field communication channel, capturing distance and angle dependence. Based on the channel matrix obtained from the modeling, the signal-to-interference-plus-noise ratio (SINR) of the user is calculated, and based on the SINR, an interruption probability constraint is introduced.

[0008] S3. Based on the transmitted signal matrix, establish a sensing model under far-field conditions, and estimate the target response matrix of the sensing model using the minimum mean square error (MMSE) criterion to obtain the sensing mean square error (MSE).

[0009] S4. For the transmitted signal matrix, an enhanced waveform is introduced to improve the sensing degree of freedom (DoF), and the SINR is updated according to the enhanced waveform;

[0010] S5. Based on the enhanced waveform, an enhanced covariance matrix is ​​introduced. The minimization of the perceived MSE is taken as the optimization objective. The interruption probability constraint, total power constraint, and positive semidefinite constraint updated according to the updated SINR are taken as constraints to construct the ISAC near-field channel robust beamforming optimization problem.

[0011] S6. For the ISAC near-field channel robust beamforming optimization problem, the non-convex problem is transformed into a convex form by using the optimization framework of semi-definite relaxation SDR combined with spherical bound and S-lemma, and is subject to the linear matrix inequality (LMI) constraint, and the beamforming optimization matrix is ​​obtained by solving.

[0012] Optionally, S1 specifically includes:

[0013] The ISAC system is configured with One transmitting antenna and One receiving antenna, of which To ensure information loss is avoided during sensing tasks, a single base station simultaneously serves [number of tasks]. A single-antenna communication user, and senses environmental targets by reflecting echoes, sets... To support the generation of independent beams for different users;

[0014] Transmitted signal matrix , The frame length is used to simultaneously implement communication and sensing functions, specifically represented as follows: ,in For beamforming matrices, each In order to target the User's beam vector, For a data signal matrix, satisfying I is the identity matrix, ensuring signal orthogonality, and the signal covariance matrix is... .

[0015] Optionally, S2 specifically includes:

[0016] Regarding the first One user, the user is located in the Fresnel region of the antenna array in the high-frequency band, channel vector Represented as:

[0017] (1)

[0018] in For complex gain, The near-field guidance vector is expanded as follows:

[0019] (2)

[0020] Where the distance function for:

[0021] (3)

[0022] in Antenna spacing, For carrier wavelength, As the starting angle, For radial distance, the model captures the distance and angle dependence of the spherical wavefront;

[0023] The signal received by the user terminal is ,in For the channel matrix, It is additive white Gaussian noise with a mean of zero and a variance of 1. The complex Gaussian distribution, in a real-world deployment environment, considering the incomplete Channel State Information (CSI), is modeled as follows: ,in To estimate the channel, Gaussian error, The error covariance matrix is ​​calculated to obtain the first... The user's SINR is:

[0024] (4)

[0025] An interruption probability constraint is introduced to reflect the communication performance of the quantized system:

[0026] (5)

[0027] in The minimum SINR threshold, This represents the maximum interruption probability.

[0028] Optionally, S3 specifically includes:

[0029] The perception task assumption is applicable to distant targets under far-field conditions, and the received echo signal is:

[0030] (6)

[0031] in The target response matrix, The interference response matrix, For additive white Gaussian noise, variance Target response matrix ,in The number of scattering points is denoted by , and is an unknown quantity. The reflection coefficient follows a Swerling 1 model with unit variance Gaussian. For angle, and The receiving guidance vector for far-field transmission, and the interference response matrix. , For the interference reflection coefficient, the covariance matrix is ​​defined as follows: and ;

[0032] Estimate using MMSE criterion To obtain perceived performance:

[0033] (7)

[0034] Therefore, the perceived MSE is:

[0035] (8).

[0036] Optionally, S4 specifically includes:

[0037] Because of the basic signal rank The severely limited DoF of perception resulted in a high MSE, therefore an enhanced waveform was introduced:

[0038] (9)

[0039] in For the additional beamforming matrix, For additional data streams, satisfy ;

[0040] Then update SINR as follows:

[0041] (10).

[0042] Optionally, S5 specifically includes:

[0043] Introducing an enhanced covariance matrix:

[0044] (11)

[0045] Substitute formula (11) into (8) and define ,in for Obtained through Cholesky decomposition, ignoring... The irrelevant constant term, MSE simplifies to:

[0046] (12)

[0047] The parameters are defined as follows:

[0048] : Normalization factor, where Represents frame length, Represents perceived noise power. This represents the receiving antenna, used to balance the strength of the sensed signal;

[0049] The normalized form of the target covariance is used to capture the relative strength of the target and the disturbance.

[0050] : Quadratic normalized covariance, used to simplify matrix inversion operations;

[0051] The constraints include: interruption probability constraint (5) and total power constraint. ,in For the total transmit power budget and the positive semidefinite constraints ;

[0052] The following is a robust beamforming optimization problem for the ISAC near-field channel:

[0053] (13)

[0054] st

[0055] (14) (15).

[0056] Optionally, S6 specifically includes:

[0057] The ISAC near-field channel robust beamforming optimization problem is a non-convex problem. The SDR method is used to reconstruct the problem to obtain a feasible solution.

[0058] First, define and Then we get ;

[0059] Next, we introduce auxiliary variables. Applying the Schur complement principle, the constraint on variable M is equivalent to an LMI constraint, thus the original objective function (13) is transformed back into , and variables The following constraints must be met:

[0060] (16)

[0061] Next, the interruption probability constraint (14) is reconstructed:

[0062] First let ,in Then the constraint is equivalent to The parameter expansion is as follows:

[0063] ;

[0064] ;

[0065]

[0066] The constraint region is approximated by using the spherical boundary method. ,in , Chi-square distribution The scaled form of the inverse cumulative distribution function is used to define the radius of the error sphere, ensuring that the obtained conditions are probabilistically accurate. Covering the error space and applying the S-lemma theorem by introducing auxiliary variables The interruption probability constraint (14) is transformed into an LMI constraint:

[0067] (17)

[0068] After reconstruction, constraint (15) has a rank of 1. Relaxation is represented as:

[0069] (18)

[0070] The final convex optimization problem is:

[0071] (19)

[0072] st (16), (17), (18)

[0073] The convex optimization problem is solved using the CVX tool to obtain the beamforming optimization matrix.

[0074] On the other hand, a robust beamforming optimization device for the ISAC near-field channel based on MMSE estimation is provided, the device comprising:

[0075] The system modeling module is used to perform system modeling and signal configuration for the Integrated Sensing and Communication (ISAC) system, wherein the transmission signal matrix of the ISAC system is used to simultaneously realize communication and sensing functions.

[0076] The communication channel modeling module is used to accurately model the near-field communication channel using a spherical wave model based on the transmitted signal matrix, capture distance and angle dependence, calculate the user's signal-to-interference-plus-noise ratio (SINR) based on the modeled channel matrix, and introduce an interruption probability constraint based on the SINR.

[0077] The sensing model building module is used to build a sensing model under far-field conditions based on the transmitted signal matrix, and to estimate the target response matrix of the sensing model using the minimum mean square error (MMSE) criterion to obtain the sensing mean square error (MSE).

[0078] An introduction module is used to introduce an enhancement waveform into the transmitted signal matrix to improve the sensing degree of freedom (DoF), and to update the SINR based on the enhancement waveform;

[0079] The construction module is used to introduce an enhanced covariance matrix based on the enhanced waveform, take minimizing the perceived MSE as the optimization objective, and take the interruption probability constraint, total power constraint and positive semidefinite constraint updated according to the updated SINR as the constraint conditions to construct the ISAC near-field channel robust beamforming optimization problem.

[0080] The solution module is used to solve the ISAC near-field channel robust beamforming optimization problem by using a semidefinite relaxation SDR combined with spherical bounds and S-lemma optimization framework to transform the non-convex problem into a convex form and subject it to the linear matrix inequality (LMI) constraint, thereby obtaining the beamforming optimization matrix.

[0081] On the other hand, an electronic device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction, which is loaded and executed by the processor to implement the above-described ISAC near-field channel robust beamforming optimization method based on MMSE estimation.

[0082] On the other hand, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, the at least one instruction being loaded and executed by a processor to implement the above-described ISAC near-field channel robust beamforming optimization method based on MMSE estimation.

[0083] The beneficial effects of the technical solution provided by this invention include at least the following:

[0084] This invention significantly reduces perceived MSE in near-field channels (e.g., 2 dB lower than far-field designs and 6.5 dB lower than non-robust designs at SINR=20 dB) and improves communication rates (e.g., 10% higher than far-field designs and 15% higher than non-robust designs at SINR=20 dB). Through robust optimization, it ensures stable communication QoS even under imperfect CSI, improving overall system efficiency and reliability. Attached Figure Description

[0085] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0086] Figure 1 This is a flowchart of an ISAC near-field channel robust beamforming optimization method based on MMSE estimation provided in an embodiment of the present invention;

[0087] Figure 2 This is a general block diagram of an ISAC near-field channel robust beamforming optimization method based on MMSE estimation provided in an embodiment of the present invention;

[0088] Figure 3 This is a schematic diagram of the ISAC system provided in an embodiment of the present invention;

[0089] Figure 4 This is a schematic diagram of the near-field channel model provided in an embodiment of the present invention;

[0090] Figure 5 This is a block diagram of an ISAC near-field channel robust beamforming optimization device based on MMSE estimation provided in an embodiment of the present invention;

[0091] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0092] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0093] This invention provides a robust beamforming optimization method for near-field channels in single-base station ISAC based on MMSE estimation. This method addresses the shortcomings of existing technologies in near-field channel modeling inaccuracies, sensitivity to imperfect CSI, and trade-offs between sensing and communication performance. It introduces a spherical wave channel model, enhances waveform design, employs MMSE-driven sensing optimization, and combines semi-definite relaxation with a spherical bounding method to create a robust optimization framework. This minimizes the sensing MSE while ensuring robust communication QoS under outage probability constraints. This method is applicable to ISAC systems in high-frequency bands (such as mmWave) and can significantly improve overall system efficiency and reliability. The following details the system architecture, model establishment, optimization design, and solution process, including specific technical means, working principles, structural features, and their role in the invention. The entire method is based on matrix operations and convex optimization tools (such as CVX), requiring no specific hardware circuitry and relying only on a standard computing environment.

[0094] This invention provides a robust beamforming optimization method for ISAC near-field channels based on MMSE estimation. This method can be implemented by an electronic device, which can be a terminal or a server. Figure 1 The flowchart of this method is shown below. Figure 2 The diagram shown is an overall block diagram of the method. The processing flow may include the following steps:

[0095] S1. Perform system modeling and signal configuration for the integrated sensing and communication (ISAC) system, wherein the transmission signal matrix of the ISAC system is used to simultaneously realize communication and sensing functions;

[0096] Optionally, S1 specifically includes:

[0097] like Figure 3 As shown, the ISAC system is configured with One transmitting antenna and One receiving antenna, of which To ensure information loss is avoided during sensing tasks (in accordance with MIMO radar configuration specifications), a single base station can simultaneously serve... A single-antenna communication user, and uses reflected echoes to sense environmental targets (such as vehicles, drones), sets... To support the generation of independent beams for different users;

[0098] Transmitted signal matrix , The frame length is used to simultaneously implement communication and sensing functions, specifically represented as follows: ,in For beamforming matrices, each In order to target the User's beam vector, For a data signal matrix, satisfying I is the identity matrix, ensuring signal orthogonality, and the signal covariance matrix is... .

[0099] The various parameter configurations are shown in Table 1:

[0100] Table 1: ISAC System Configuration Parameter Settings

[0101]

[0102]

[0103] This step works by fusing communication and sensing functions through a shared signal framework: the communication signal also serves as a radar detection wave, improving spectrum utilization. Structural features include a matrix-style signal representation, facilitating subsequent optimization.

[0104] Purpose: To establish a unified basic model, ensure that sensing and communication share resources, and avoid the waste of resources caused by independent design.

[0105] S2. Based on the transmitted signal matrix, a spherical wave model is used to accurately model the near-field communication channel, capturing distance and angle dependence. Based on the channel matrix obtained from the modeling, the signal-to-interference-plus-noise ratio (SINR) of the user is calculated, and based on the SINR, an interruption probability constraint is introduced.

[0106] Optionally, S2 specifically includes:

[0107] like Figure 4 As shown, for the first One user, the user is located in the Fresnel region of the antenna array in the high-frequency band, channel vector Represented as:

[0108] (1)

[0109] in For complex gain, The near-field guidance vector is expanded as follows:

[0110] (2)

[0111] Where the distance function for:

[0112] (3)

[0113] in Antenna spacing (usually set to) (to avoid grid lobes) For carrier wavelength, As the starting angle, For radial distance, the model captures the distance and angle dependence of the spherical wavefront (compared to existing far-field planar waveguide vectors). (forming a stark contrast)

[0114] The signal received by the user terminal is ,in For the channel matrix, It is additive white Gaussian noise with a mean of zero and a variance of 1. The complex Gaussian distribution, in a real-world deployment environment, considering the incomplete Channel State Information (CSI), is modeled as follows: ,in To estimate the channel, Gaussian error, The error covariance matrix is ​​calculated to obtain the first... The user's SINR is:

[0115] (4)

[0116] An interruption probability constraint is introduced to reflect the communication performance of the quantized system:

[0117] (5)

[0118] in The minimum SINR threshold, This represents the maximum interruption probability.

[0119] The principle behind this step is to accurately describe the near-field propagation characteristics using a spherical wave model, thus avoiding beam pointing offset caused by far-field assumptions.

[0120] Function: To provide an accurate communication model foundation and solve the inaccuracies of existing technologies in high-frequency near-field environments.

[0121] S3. Based on the transmitted signal matrix, establish a sensing model under far-field conditions, and estimate the target response matrix of the sensing model using the minimum mean square error (MMSE) criterion to obtain the sensing mean square error (MSE).

[0122] Optionally, S3 specifically includes:

[0123] The perception task assumption is applicable to distant targets under far-field conditions, and the received echo signal is:

[0124] (6)

[0125] in The target response matrix, This is the interference response matrix (simulating clutter or interference echo). For additive white Gaussian noise, variance Target response matrix ,in The number of scattering points is denoted by , and is an unknown quantity. The reflection coefficient follows a Swerling 1 model with unit variance Gaussian. For angle, and The receiving guidance vector (plane wave form) for far-field transmission, and the interference response matrix. , For the interference reflection coefficient, the covariance matrix is ​​defined as follows: (Target covariance matrix) and (Interference covariance matrix);

[0126] Estimate using MMSE criterion To obtain perceived performance:

[0127] (7)

[0128] Therefore, the perceived MSE is:

[0129] (8).

[0130] This step works by quantizing sensing accuracy through MMSE and extracting target information using echo signals. Structural features include a matrix-based response model, supporting operations such as Cholesky decomposition.

[0131] Function: Define the perception optimization goal.

[0132] S4. For the transmitted signal matrix, an enhanced waveform is introduced to improve the sensing degree of freedom (DoF), and the SINR is updated according to the enhanced waveform;

[0133] Optionally, S4 specifically includes:

[0134] Because of the basic signal rank The severely limited DoF of perception resulted in a high MSE, therefore an enhanced waveform was introduced:

[0135] (9)

[0136] in For the additional beamforming matrix, For additional data streams, satisfy ;

[0137] Then update SINR as follows:

[0138] (10).

[0139] This step works by extending the receptive space through the addition of DoF. Its structural features include an extended matrix form, which facilitates covariance calculation.

[0140] Function: To improve sensing performance without significantly sacrificing communication rate.

[0141] S5. Based on the enhanced waveform, an enhanced covariance matrix is ​​introduced. The minimization of the perceived MSE is taken as the optimization objective. The interruption probability constraint, total power constraint, and positive semidefinite constraint updated according to the updated SINR are taken as constraints to construct the ISAC near-field channel robust beamforming optimization problem.

[0142] Optionally, S5 specifically includes:

[0143] Introducing an enhanced covariance matrix:

[0144] (11)

[0145] Substitute formula (11) into (8) and define ,in for Obtained through Cholesky decomposition, ignoring... The irrelevant constant term, MSE simplifies to:

[0146] (12)

[0147] The parameters are defined as follows:

[0148] : Normalization factor, where Represents frame length, Represents perceived noise power. This represents the receiving antenna, used to balance the strength of the sensed signal;

[0149] The normalized form of the target covariance is used to capture the relative strength of the target and the disturbance.

[0150] : Quadratic normalized covariance, used to simplify matrix inversion operations;

[0151] The constraints include: interruption probability constraint (5) and total power constraint. ,in For the total transmit power budget (e.g., 50 dBm) and the positive semidefinite constraint ;

[0152] The following is a robust beamforming optimization problem for the ISAC near-field channel:

[0153] (13)

[0154] st

[0155] (14) (15).

[0156] By establishing the optimization problem described above, a balance between perception and communication constraints can be ensured, enabling dual-function collaboration.

[0157] S6. For the ISAC near-field channel robust beamforming optimization problem, the non-convex problem is transformed into a convex form by using the optimization framework of semi-definite relaxation SDR combined with spherical bound and S-lemma, and is subject to the linear matrix inequality (LMI) constraint, and the beamforming optimization matrix is ​​obtained by solving.

[0158] Optionally, S6 specifically includes:

[0159] The ISAC near-field channel robust beamforming optimization problem is a non-convex problem. The SDR method is used to reconstruct the problem to obtain a feasible solution.

[0160] First, define and Then we get ;

[0161] Next, we introduce auxiliary variables. Applying the Schur complement principle, the constraint on variable M is equivalent to an LMI constraint, thus the original objective function (13) is transformed back into , and variables The following constraints must be met:

[0162] (16)

[0163] Next, the interruption probability constraint (14) is reconstructed:

[0164] First let ,in Then the constraint is equivalent to The parameter expansion is as follows:

[0165] ;

[0166] ;

[0167]

[0168] The constraint region is approximated by using the spherical boundary method. ,in , Chi-square distribution The scaled form of the inverse cumulative distribution function is used to define the radius of the error sphere, ensuring that the obtained conditions are probabilistically accurate. Covering the error space and applying the S-lemma theorem by introducing auxiliary variables The interruption probability constraint (14) is transformed into an LMI constraint:

[0169] (17)

[0170] After reconstruction, constraint (15) has a rank of 1. Relaxation is represented as:

[0171] (18)

[0172] The final convex optimization problem is:

[0173] (19)

[0174] st (16), (17), (18)

[0175] The convex optimization problem is solved using the CVX tool to obtain the beamforming optimization matrix.

[0176] If the result ( If the rank of a given eigenvalue is greater than 1, then eigenvalue decomposition (taking the eigenvector corresponding to the largest eigenvalue as the eigenvalue) can be used. ) or Gaussian randomization (from Generate random vectors And scale to meet power) to restore rank 1 solution.

[0177] The above steps work by transforming a non-convex problem into a convex form through SDR (LMI constraints ensure global optimality and convergence), and using spherical bounds and S-lemma to handle randomness and ensure robustness.

[0178] Function: To achieve robust optimization and ensure performance even under CSI error.

[0179] The embodiments of this invention include at least the following innovative points, which are the biggest differences between the embodiments of this invention and the prior art. These innovations can solve the problems of inaccurate near-field modeling, imperfect sensitivity of CSI, and trade-offs between communication and sensing performance, and highlight the advantages of the embodiments of this invention in the ISAC near-field environment (MSE reduction of 2-6.5 dB, communication rate improvement of 10-15%):

[0180] (1) Near-field spherical wave channel model: through the formula Sum Distance Function The capture of distance and angle dependence is the basis of the embodiments of the present invention.

[0181] (2) MMSE-driven perception optimization: The target response moment is estimated using the MMSE criterion. Error formula This is the core of perceived performance as an optimization goal.

[0182] (3) Robust SINR design under interruption probability constraints: through This is used to quantify the QoS of communication, which is the core of communication performance.

[0183] (4) Enhanced waveform design: Introducing additional beamforming Increasing the degree of freedom is key to improving perception DoF.

[0184] (5) SDR combined with sphere bounds and S-lemma optimization framework: transforming non-convex problems into convex forms And it must comply with the relevant LMI constraints, which is the key to solving complex optimization problems.

[0185] like Figure 5 As shown, this embodiment of the invention also provides an ISAC near-field channel robust beamforming optimization device based on MMSE estimation, the device comprising:

[0186] The system modeling module 510 is used to perform system modeling and signal configuration for the integrated sensing and communication (ISAC) system, wherein the transmission signal matrix of the ISAC system is used to simultaneously realize communication and sensing functions.

[0187] The communication channel modeling module 520 is used to accurately model the near-field communication channel using a spherical wave model based on the transmitted signal matrix, capture distance and angle dependence, calculate the user's signal-to-interference-plus-noise ratio (SINR) based on the modeled channel matrix, and introduce an interruption probability constraint based on the SINR.

[0188] The sensing model establishment module 530 is used to establish a sensing model under far-field conditions based on the transmitted signal matrix, and to estimate the target response matrix of the sensing model using the minimum mean square error (MMSE) criterion to obtain the sensing mean square error (MSE).

[0189] The module 540 is used to introduce an enhanced waveform into the transmitted signal matrix to improve the sensing degree of freedom (DoF), and to update the SINR based on the enhanced waveform;

[0190] The construction module 550 is used to introduce an enhanced covariance matrix based on the enhanced waveform, take minimizing the perceived MSE as the optimization objective, and take the interruption probability constraint, total power constraint and positive semidefinite constraint updated according to the updated SINR as the constraint conditions to construct the ISAC near-field channel robust beamforming optimization problem.

[0191] The solver module 560 is used to solve the ISAC near-field channel robust beamforming optimization problem by using a semidefinite relaxation SDR combined with a spherical boundary and S-lemma optimization framework to transform the non-convex problem into a convex form and subject it to the linear matrix inequality (LMI) constraint, thereby obtaining the beamforming optimization matrix.

[0192] The ISAC near-field channel robust beamforming optimization device based on MMSE estimation provided in this embodiment of the invention has a functional structure that corresponds to the ISAC near-field channel robust beamforming optimization method based on MMSE estimation provided in this embodiment of the invention, and will not be described again here.

[0193] Figure 6 This is a schematic diagram of the structure of an electronic device 600 provided in an embodiment of the present invention. The electronic device 600 may vary considerably due to different configurations or performance. It may include one or more central processing units (CPUs) 601 and one or more memories 602. The memory 602 stores at least one instruction, which is loaded and executed by the processor 601 to implement the steps of the above-described ISAC near-field channel robust beamforming optimization method based on MMSE estimation.

[0194] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions that can be executed by a processor in a terminal to complete the aforementioned ISAC near-field channel robust beamforming optimization method based on MMSE estimation. For example, the computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, or optical data storage device.

[0195] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware or by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0196] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robust beamforming optimization method for ISAC near-field channels based on MMSE estimation, characterized in that, The method includes: S1. Perform system modeling and signal configuration for the integrated sensing and communication (ISAC) system, wherein the transmission signal matrix of the ISAC system is used to simultaneously realize communication and sensing functions; S2. Based on the transmitted signal matrix, a spherical wave model is used to accurately model the near-field communication channel, capturing distance and angle dependence. Based on the channel matrix obtained from the modeling, the signal-to-interference-plus-noise ratio (SINR) of the user is calculated, and based on the SINR, an interruption probability constraint is introduced. S3. Based on the transmitted signal matrix, establish a sensing model under far-field conditions, and estimate the target response matrix of the sensing model using the minimum mean square error (MMSE) criterion to obtain the sensing mean square error (MSE). S4. For the transmitted signal matrix, an enhanced waveform is introduced to improve the sensing degree of freedom (DoF), and the SINR is updated according to the enhanced waveform; S5. Based on the enhanced waveform, an enhanced covariance matrix is ​​introduced. The minimization of the perceived MSE is taken as the optimization objective. The interruption probability constraint, total power constraint, and positive semidefinite constraint updated according to the updated SINR are taken as constraints to construct the ISAC near-field channel robust beamforming optimization problem. S6. For the ISAC near-field channel robust beamforming optimization problem, the non-convex problem is transformed into a convex form by using the optimization framework of semi-definite relaxation SDR combined with spherical bound and S-lemma, and is subject to the linear matrix inequality (LMI) constraint, and the beamforming optimization matrix is ​​obtained by solving.

2. The method according to claim 1, characterized in that, S1 specifically includes: The ISAC system is configured with One transmitting antenna and One receiving antenna, of which To ensure information loss is avoided during sensing tasks, a single base station simultaneously serves [number of tasks]. A single-antenna communication user, and senses environmental targets by reflecting echoes, sets... To support the generation of independent beams for different users; Transmitted signal matrix , The frame length is used to simultaneously implement communication and sensing functions, specifically represented as follows: ,in For beamforming matrices, each In order to target the User's beam vector, For a data signal matrix, satisfying I is the identity matrix, ensuring signal orthogonality, and the signal covariance matrix is... .

3. The method according to claim 2, characterized in that, S2 specifically includes: Regarding the first One user, the user is located in the Fresnel region of the antenna array in the high-frequency band, channel vector Represented as: （1） in For complex gain, The near-field guidance vector is expanded as follows: （2） Where the distance function for: （3） in Antenna spacing, For carrier wavelength, Starting angle For radial distance, the model captures the distance and angle dependence of the spherical wavefront; The signal received by the user terminal is ,in For the channel matrix, It is additive white Gaussian noise with a mean of zero and a variance of 1. The complex Gaussian distribution, in a real-world deployment environment, considering the incomplete Channel State Information (CSI), is modeled as follows: ,in To estimate the channel, Gaussian error, Let be the error covariance matrix, and calculate the th . The user's SINR is: （4） An interruption probability constraint is introduced to reflect the communication performance of the quantized system: （5） in The minimum SINR threshold, This represents the maximum interruption probability.

4. The method according to claim 3, characterized in that, S3 specifically includes: The perception task assumption is applicable to distant targets under far-field conditions, and the received echo signal is: （6） in The target response matrix, The interference response matrix, For additive white Gaussian noise, variance Target response matrix ,in The number of scattering points is denoted by , and is an unknown quantity. The reflection coefficient follows a Swerling 1 model with unit variance Gaussian. For angle, and The receiving guidance vector for far-field transmission, and the interference response matrix. , For the interference reflection coefficient, the covariance matrix is ​​defined as follows: and ; Estimate using MMSE criterion To obtain perceived performance: （7） Therefore, the perceived MSE is: （8）。 5. The method according to claim 4, characterized in that, S4 specifically includes: Because of the basic signal rank The severely limited DoF of perception resulted in a high MSE, therefore an enhanced waveform was introduced: （9） in For the additional beamforming matrix, For additional data streams, satisfy ; Then update SINR as follows: （10）。 6. The method according to claim 5, characterized in that, S5 specifically includes: Introducing an enhanced covariance matrix: （11） Substitute formula (11) into (8) and define ,in for Obtained through Cholesky decomposition, ignoring... The irrelevant constant term, MSE simplifies to: （12） The parameters are defined as follows: : Normalization factor, where Represents frame length, Represents perceived noise power. This represents the receiving antenna, used to balance the strength of the sensed signal; The normalized form of the target covariance is used to capture the relative strength of the target and the disturbance. : Quadratic normalized covariance, used to simplify matrix inversion operations; The constraints include: interruption probability constraint (5) and total power constraint. ,in For the total transmit power budget and the positive semidefinite constraints ; The following is a robust beamforming optimization problem for the ISAC near-field channel: （13） st （14） （15）。 7. The method according to claim 6, characterized in that, S6 specifically includes: The ISAC near-field channel robust beamforming optimization problem is a non-convex problem. The SDR method is used to reconstruct the problem to obtain a feasible solution. First, define and Then we get ; Next, we introduce auxiliary variables. Applying the Schur complement principle, the constraint on variable M is equivalent to an LMI constraint, thus the original objective function (13) is transformed back into , and variables The following constraints must be met: （16） Next, the interruption probability constraint (14) is reconstructed: First let ,in Then the constraint is equivalent to The parameter expansion is as follows: ； ； ； The constraint region is approximated by using the spherical boundary method. ,in , Chi-square distribution The scaled form of the inverse cumulative distribution function is used to define the radius of the error sphere, ensuring that the obtained conditions are probabilistically accurate. Covering the error space and applying the S-lemma theorem by introducing auxiliary variables The interruption probability constraint (14) is transformed into an LMI constraint: （17） After reconstruction, constraint (15) has a rank of 1. Relaxation is represented as: （18） The final convex optimization problem is: （19） st (16), (17), (18) The convex optimization problem is solved using the CVX tool to obtain the beamforming optimization matrix.

8. A robust beamforming optimization device for ISAC near-field channels based on MMSE estimation, characterized in that, The device includes: The system modeling module is used to perform system modeling and signal configuration for the Integrated Sensing and Communication (ISAC) system, wherein the transmission signal matrix of the ISAC system is used to simultaneously realize communication and sensing functions. The communication channel modeling module is used to accurately model the near-field communication channel using a spherical wave model based on the transmitted signal matrix, capture distance and angle dependence, calculate the user's signal-to-interference-plus-noise ratio (SINR) based on the modeled channel matrix, and introduce an interruption probability constraint based on the SINR. The sensing model building module is used to build a sensing model under far-field conditions based on the transmitted signal matrix, and to estimate the target response matrix of the sensing model using the minimum mean square error (MMSE) criterion to obtain the sensing mean square error (MSE). An introduction module is used to introduce an enhancement waveform into the transmitted signal matrix to improve the sensing degree of freedom (DoF), and to update the SINR based on the enhancement waveform; The construction module is used to introduce an enhanced covariance matrix based on the enhanced waveform, take minimizing the perceived MSE as the optimization objective, and take the interruption probability constraint, total power constraint and positive semidefinite constraint updated according to the updated SINR as the constraint conditions to construct the ISAC near-field channel robust beamforming optimization problem. The solution module is used to solve the ISAC near-field channel robust beamforming optimization problem by using a semidefinite relaxation SDR combined with spherical bounds and S-lemma optimization framework to transform the non-convex problem into a convex form and subject it to the linear matrix inequality (LMI) constraint, thereby obtaining the beamforming optimization matrix.

9. An electronic device comprising a processor and a memory, wherein the memory stores at least one instruction, characterized in that, The processor loads and executes at least one instruction to implement the ISAC near-field channel robust beamforming optimization method based on MMSE estimation as described in any one of claims 1-7.

10. A computer-readable storage medium storing at least one instruction, characterized in that, The at least one instruction is loaded and executed by the processor to implement the ISAC near-field channel robust beamforming optimization method based on MMSE estimation as described in any one of claims 1-7.

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