Millimeter wave ISAC system perception performance optimization method based on sub-connection hybrid precoding

Abstract

The invention relates to a millimeter wave ISAC system perception performance optimization method based on sub-connection hybrid precoding. The method comprises the following steps: establishing an echo signal model containing an interference source; constructing an optimization problem with the aim of minimizing the Cramer-Rao bound; solving a digital and analog precoder by adopting an alternating optimization strategy; wherein the digital precoding is converted into second-order cone programming through successive convex approximation, and the analog precoding realizes efficient solution under constant modulus constraint through Riemannian manifold optimization. According to the method, collaborative optimization of the communication performance and the sensing performance of the millimeter wave ISAC system is realized through a hybrid precoding algorithm of alternate iteration optimization, a digital precoder design based on a successive convex approximation method and an analog precoder design based on Riemannian manifold optimization.

Description

Technical Field

[0001] This invention relates to the field of wireless communication and sensing fusion technology, specifically to a method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding. Background Technology

[0002] With the continuous advancement of 6th Generation Mobile Networks (6G), Integrated Sensing and Communications (ISAC) has gradually become one of the core technologies supporting key application scenarios such as intelligent transportation and unmanned systems. ISAC systems can simultaneously achieve information transmission and environmental perception on the same resource platform, not only improving the utilization efficiency of spectrum, energy, and hardware resources, but also providing technical support for real-time perception and feedback in highly dynamic environments.

[0003] In the implementation path of ISAC (Inter-Independent Sensing and Communication), the millimeter-wave band, with its abundant bandwidth resources and high spatial resolution, can simultaneously meet the requirements of high-speed communication and high-precision sensing, and is widely regarded as an ideal choice for building high-performance ISAC systems. Especially in typical scenarios such as vehicle-to-everything (V2X), security monitoring, and autonomous driving, the synergistic effect of millimeter-wave sensing and communication can significantly enhance the robustness and response speed of the system.

[0004] However, millimeter-wave systems face challenges such as high hardware complexity and high energy consumption in practical deployments. Due to the large propagation loss of high-frequency signals, large-scale antenna arrays are required to achieve beam gain, which significantly increases the hardware complexity and energy consumption of the system, limiting its promotion in low-cost, lightweight applications.

[0005] To address the aforementioned issues, existing research has attempted to employ hybrid precoding techniques to reduce hardware complexity and energy consumption. Hybrid precoding combines the high flexibility of all-digital precoding with the low hardware complexity of all-analog precoding, effectively reducing system energy consumption and hardware complexity by decreasing the number of radio frequency chains. However, because hybrid precoding reduces the number of radio frequency chains, it decreases the degrees of freedom in precoding, inhibiting the flexibility of transmit beam design. This limitation not only affects the optimization space for communication performance but also weakens the sensing accuracy and stability of the system in complex environments. Therefore, achieving efficient and robust sensing performance optimization under a hybrid precoding architecture has become one of the key issues in current millimeter-wave ISAC system research. Summary of the Invention

[0006] The purpose of this invention is to provide a method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding. This method achieves coordinated optimization of the communication and sensing performance of the millimeter-wave ISAC system through an alternating iterative optimization hybrid precoding algorithm, a digital precoder design based on successive convex approximation, and an analog precoder design based on Riemannian manifold optimization.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding, wherein the ISAC system includes... root transmitting antenna, There are K data streams and K users, and each user has... The system uses a single receiving antenna to simultaneously sense one target, and operates in the millimeter-wave frequency band. The method includes the following steps:

[0008] Step 1: Construct a millimeter-wave ISAC system model, including the channels of each communication user, the transmit steering vector, and the base station's transmit signal model under the sub-connection hybrid precoder architecture;

[0009] Step 2: Establish a communication signal-to-interference-plus-noise ratio (SINR) model for communication users and a radar sensing echo model based on interference sources and array structures;

[0010] Step 3: Establish a joint optimization problem with the goal of minimizing the target arrival angle's Cramer-Rao bound as the optimization objective. The joint optimization problem is a non-convex optimization problem.

[0011] Step 4: Transform the non-convex optimization problem into a standard second-order cone programming form using the successive convex approximation method, and improve convergence by employing the Armijo step size search criterion;

[0012] Step 5: The Riemannian manifold optimization method is used to optimize the simulation precoding matrix. In this method, a user-adaptive penalty factor is introduced to transform the communication constraints into penalty terms and incorporate them into the objective function. The solution that satisfies the constant modulus constraint is iteratively updated in the manifold space.

[0013] Step 6: Using an alternating optimization strategy, iteratively design the digital precoder and the analog precoder until convergence. The initial values ​​are set by extracting the line-of-sight components from the channel sparsity characteristics to form a subspace.

[0014] Further, step 1 includes:

[0015] The base station performs hybrid precoding on the transmitted symbol vector, where the number of radio frequency chains is... and satisfy The base station's transmitted signal first undergoes processing by a hybrid precoder, that is, it sequentially passes through a digital precoding matrix. RF chain and analog precoding matrix The signal is then transmitted into space via a transmitting antenna; the transmitted signal is t, the communication user's channel is H, and the receiving and transmitting turning vectors are respectively... and ;

[0016] The transmitted signal is represented as , Analog pre-encoder ,in And each element conforms to the norm constraint, where .

[0017] Further, step 2 includes:

[0018] Digital precoder is represented as ,in, Here is the digital precoder corresponding to the k-th communication user; the received signal of the k-th communication user is represented as... ,in, It is Gaussian white noise from the k-th communication user; under the assumption that the data streams are independent, it satisfies The signal-to-interference-plus-noise ratio (SIR) of the k-th communication user is expressed as: .

[0019] Further, step 3 includes:

[0020] Step 3.1: There are J interference source targets in the radar echo transmission, and the locations of the interference sources are... Received The echo signal is represented as ,in, It is the reflection coefficient corresponding to the target. It is the reflection coefficient from the i-th interference source target term. and These are the receiving steering vector and the sending steering vector, respectively. It is Gaussian white noise, with a mean of 0 and a covariance of . The complex Gaussian distribution; , These are the target angle and the j-th interference source target angle, respectively;

[0021] Step 3.2: According to Send signal The covariance matrix is ​​expressed as:

[0022]

[0023] The Cramer-Rao boundary for estimating the target angle of arrival is expressed as:

[0024]

[0025] in, , The derivative of the steering vector is expressed as: ,in, The wavelength of the signal is represented by λ, and the distance between the antennas is d. For angle;

[0026] Step 3.3: The joint optimization problem is expressed as:

[0027]

[0028] in, Indicates power budget constraints, Represented as a limited analog pre-encoder Dimensions and models; This indicates that a lower limit has been set for the SINR of all communication users.

[0029] Further, step 4 includes:

[0030] Step 4.1: The original Cramer-Rao bound minimization problem is equivalently transformed into a maximization problem of a new objective function. The joint optimization problem is then transformed into:

[0031]

[0032] Among them, the middle part of the optimization target is used This indicates that the power constraint of the hybrid precoding matrix is ​​equivalently transformed into... The joint optimization problem is transformed into:

[0033]

[0034] Introducing auxiliary variables The joint optimization problem is transformed into a second-order cone programming form joint optimization problem:

[0035]

[0036] in, This is represented as the equivalent channel for the k-th communication user;

[0037] Step 4.2: In each iteration, precode the digital vector from the previous iteration. Performing a first-order Taylor expansion, it can be expressed as: ,in, It is a function used to extract the real part of complex numbers, which can be further expressed in Taylor expansion as: Introducing intermediate variables Add additional constraints ; to remove interference items Represented in vector form, the constructed second-order cone form constraint is expressed as:

[0038]

[0039] Let vector If the expression equals the left-hand side, then the joint optimization problem can be expressed as:

[0040]

[0041] Step 4.3: Based on the Armijo criterion, an adaptive step size adjustment mechanism is used to linearly approximate the objective function in the joint optimization problem in the nth iteration as follows: Its gradient is expressed as ,in, It is a function The gradient of the variable x; using the Armijo step size search criterion Updated to ,in, It is the step size, which must satisfy the Armijo condition. ,in, This is the step size tolerance parameter, and a backoff factor is used. Gradually reduce.

[0042] Further, step 5 includes:

[0043] Step 5.1: Given a digital precoding matrix Optimize the analog precoding matrix The joint optimization problem is expressed as:

[0044]

[0045] in, , Through matrix transformation, the objective function of the joint optimization problem is expressed as: Where vec(·) represents the vectorization operation, Indicates the Kronecker product; Non-zero elements extracted as ,in, This represents a function used to extract non-zero elements; extraction The non-zero elements corresponding to u in the matrix are mapped to... In, it is represented as: ,in, This represents the row (column) index of the m-th sub-block in the original matrix; This represents extracting the sub-block corresponding to the m-th row and n-th column from the entire large matrix; the objective function is transformed into... ;

[0046] Step 5.2: Let , , Then the communication SINR constraint is converted to The joint optimization problem can be transformed into the following expression:

[0047]

[0048] The communication SINR constraint is incorporated into the objective function, and slack variables are introduced. ,in The communication SINR constraint is rewritten as follows: ,in, The objective function with the communication SINR penalty term is rewritten as follows: ,in, Represented as , It is a punishment factor. During the iteration process, according to The value is updated dynamically.

[0049] Step 5.3: The joint optimization problem is finally expressed as:

[0050]

[0051] in, The feasible region of the optimization problem is defined as follows: ,in, express The previous point lies on the unit circle in the N-dimensional complex plane; therefore, the optimization problem can be expressed as follows: Furthermore, at a certain point The tangent space at a point is defined as ,in, express The tangent vector at that point, Represented as the Hadamard product, express The complex conjugate of ; the formula for calculating the Euclidean gradient is expressed as By using the Euclidean gradient Projecting onto this tangent space, we obtain the Riemann gradient as follows: ;pass Update the variable on the manifold, the updated variable is... ,in, Step size, This involves remapping the variables back to the manifold, represented as... After each iteration, when the current error function of communication user k... This will weight and enhance the penalty factor. The specific update mechanism for the penalty factor is as follows:

[0052]

[0053] in, , It's about updating the step size. It is a tolerance parameter.

[0054] Further, step 6 includes:

[0055] First, initialize the analog precoding matrix. The line-of-sight components of all users are represented as a matrix. ,in, Let the set of antennas connected to the r-th RF chain and corresponding to the r-th subarray be represented as:

[0056] ,

[0057] right Perform singular value decomposition and take the first part of the dominant subspace. Column, specifically represented as ,in, and They are The left singular matrix and the right singular matrix, yes The former Listing subarrays; then The initial value is represented as:

[0058] .

[0059] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to implement the above-described method.

[0060] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] 1. This invention aims to minimize the Cramer-Rao bound, replacing the traditional beammap approximation method, and establishes a more realistic lower bound model for perception error, effectively enhancing the accuracy of target angle of arrival estimation and significantly improving the perception performance and estimation accuracy of the system in multi-target and multi-interference environments.

[0063] 2. This invention introduces a communication signal-to-interference-plus-noise ratio constraint to optimize sensing accuracy without sacrificing communication performance, thereby achieving coordinated optimization of communication and sensing. It is particularly suitable for typical 6G application scenarios such as intelligent transportation and autonomous driving, which have high requirements for both performance.

[0064] 3. This invention adopts a sub-connected hybrid precoding structure, which utilizes the sparsity of the sub-connection structure to extract non-zero values ​​from the analog precoding matrix. While maintaining system performance, it effectively reduces the number of radio frequency chains, thereby reducing energy consumption and implementation costs.

[0065] 4. This invention proposes an optimization mechanism with adaptive step size and per-user penalty factor, and combines it with the Riemannian manifold optimization algorithm to improve the convergence speed and robustness of the overall algorithm, and ensure the stability and practicality of the optimization process in complex channels and interference environments. Attached Figure Description

[0066] Figure 1 This is a flowchart of a method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding, provided in an embodiment of the present invention.

[0067] Figure 2 This is an architecture diagram of the millimeter-wave ISAC system provided in an embodiment of the present invention;

[0068] Figure 3 This is a graph showing the relationship between the Cramer-Rao boundary and the communication signal-to-interference-plus-noise ratio threshold under different radio frequency chain numbers in this embodiment of the invention.

[0069] Figure 4 This is a comparison diagram of the influence of the number of radio frequency chains on the Cramer-Rao boundary under different transmit power conditions in the embodiments of the present invention;

[0070] Figure 5 This is a performance curve of the root mean square error (RMSE) of the MUSIC algorithm as a function of radar signal-to-noise ratio under different precoding schemes in this embodiment of the invention.

[0071] Figure 6 This is a performance curve of the root mean square error (RMSE) of the MLE algorithm as a function of radar signal-to-noise ratio under different precoding schemes in this embodiment of the invention.

[0072] Figure 7 This is a graph showing the convergence of the objective function under different radio frequency chain configurations in this embodiment of the invention. Detailed Implementation

[0073] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0074] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0075] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0076] like Figure 1-2 As shown, this embodiment provides a method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding. The ISAC system includes... root transmitting antenna, There are K data streams and K users, and each user has... The system uses a single receiving antenna to simultaneously sense one target and operates in the millimeter-wave band.

[0077] The base station performs hybrid precoding on the transmitted symbol vector, where the number of radio frequency chains is... and satisfy The base station's transmitted signal first undergoes processing by a hybrid precoder, that is, it sequentially passes through a digital precoding matrix. RF chain and analog precoding matrix The signal is then transmitted into space via a transmitting antenna; the transmitted signal is t, the communication user's channel is H, and the receiving and transmitting turning vectors are respectively... and .

[0078] Specifically, the method includes the following steps:

[0079] Step 1: Construct a millimeter-wave ISAC system model, including the channels of each communication user, the transmit steering vector, and the base station's transmit signal model under the sub-connection hybrid precoder architecture.

[0080] The transmitted signal is represented as , Analog pre-encoder ,in And each element conforms to the norm constraint, where .

[0081] Step 2: Establish a communication signal-to-interference-plus-noise ratio (SINR) model for communication users and a radar sensing echo model based on interference sources and array structures, and use the Cramer-Rao boundary of the target arrival angle as a sensing accuracy indicator.

[0082] Digital precoder is represented as ,in, Here is the digital precoder corresponding to the k-th communication user; the received signal of the k-th communication user is represented as... ,in, It is Gaussian white noise from the k-th communication user; under the assumption that the data streams are independent, it satisfies The signal-to-interference-plus-noise ratio (SIR) of the k-th communication user can be expressed as: .

[0083] Step 3: Under the premise of satisfying the communication signal-to-interference-plus-noise ratio constraint, constant mode constraint and transmit power constraint, establish a joint optimization problem with minimizing the target angle of arrival's Cramer-Rao bound as the optimization objective.

[0084] Step 3.1: There are J interference source targets in the radar echo transmission, and the locations of the interference sources are... Received The echo signal is represented as ,in, It is the reflection coefficient corresponding to the target. It is the reflection coefficient from the i-th interference source target term. and These are the receiving steering vector and the sending steering vector, respectively. It is Gaussian white noise, with a mean of 0 and a covariance of . The complex Gaussian distribution; , These are the target angle and the j-th interference source target angle, respectively.

[0085] Step 3.2: According to Send signal The covariance matrix can be expressed as:

[0086]

[0087] The Cramer-Rao boundary for estimating the target angle of arrival is expressed as:

[0088]

[0089] in, , The derivative of the steering vector is expressed as: ,in, The wavelength of the signal is represented by λ, and the distance between the antennas is d. For angle.

[0090] Step 3.3: The joint optimization problem is expressed as:

[0091]

[0092] in, Indicates power budget constraints, Represented as a limited analog pre-encoder Dimensions and models; This indicates that a lower limit has been set for the SINR of all communication users.

[0093] Step 4: The joint optimization problem is a non-convex optimization problem. The non-convex optimization problem is transformed into a standard second-order cone programming form by the successive convex approximation method, and the Armijo step size search criterion is used to improve convergence.

[0094] Step 4.1: The original Cramer-Rao bound minimization problem is equivalently transformed into a maximization problem of a new objective function. The joint optimization problem is then transformed into:

[0095]

[0096] Among them, the middle part of the optimization target is used This indicates that the power constraint of the hybrid precoding matrix is ​​equivalently transformed into... The joint optimization problem is transformed into:

[0097]

[0098] Introducing auxiliary variables The joint optimization problem is transformed into a second-order cone programming form joint optimization problem:

[0099]

[0100] in, This is represented as the equivalent channel for the k-th communication user.

[0101] Step 4.2: In each iteration, precode the digital vector from the previous iteration. Performing a first-order Taylor expansion, it can be expressed as: ,in, It is a function used to extract the real part of complex numbers, and its Taylor expansion can be further expressed as: Introducing intermediate variables Add additional constraints ; to remove interference items Represented in vector form, the constructed second-order cone form constraint is expressed as:

[0102]

[0103] Let vector If the expression equals the left-hand side, then the joint optimization problem can be expressed as:

[0104]

[0105] Step 4.3: Based on the Armijo criterion, an adaptive step size adjustment mechanism is used to linearly approximate the objective function in the joint optimization problem in the nth iteration as follows: Its gradient is expressed as ,in, It is a function The gradient of the variable x; using the Armijo step size search criterion Updated to ,in, It is the step size, which must satisfy the Armijo condition. ,in, This is the step size tolerance parameter, and a backoff factor is used. Gradually reduce.

[0106] Step 5: The Riemannian manifold optimization method is used to optimize the simulation precoding matrix. In this method, a user-adaptive penalty factor is introduced to transform the communication constraints into penalty terms and incorporate them into the objective function. The solution that satisfies the constant modulus constraint is then iteratively updated within the manifold space.

[0107] Step 5.1: Given a digital precoding matrix Optimize the analog precoding matrix The joint optimization problem is expressed as:

[0108]

[0109] in, , Through matrix transformation, the objective function of the joint optimization problem can be expressed as: Where vec(·) represents the vectorization operation, Indicates the Kronecker product; Non-zero elements extracted as ,in, This represents a function used to extract non-zero elements; extraction The non-zero elements corresponding to u in the matrix are mapped to... In, it is represented as: ,in, This represents the row (column) index of the m-th sub-block in the original matrix; This represents extracting the sub-block corresponding to the m-th row and n-th column from the entire large matrix; the objective function can be transformed into... .

[0110] Step 5.2: Let , , Then the communication SINR constraint can be converted into The joint optimization problem can be transformed into the following expression:

[0111]

[0112] The communication SINR constraint is incorporated into the objective function, and slack variables are introduced. ,in The communication SINR constraint is rewritten as follows: ,in, The objective function with the communication SINR penalty term is rewritten as follows: ,in, Represented as , It is a punishment factor. During the iteration process, according to The value is updated dynamically.

[0113] Step 5.3: The joint optimization problem is finally expressed as:

[0114]

[0115] in, The feasible region of the optimization problem is defined as follows: ,in, express The previous point lies on the unit circle in the N-dimensional complex plane; therefore, the optimization problem can be expressed as follows: Furthermore, at a certain point The tangent space at a point is defined as ,in, express The tangent vector at that point, Represented as the Hadamard product, express The complex conjugate of ; the formula for calculating the Euclidean gradient is expressed as By using the Euclidean gradient Projecting onto this tangent space, we can obtain the Riemann gradient as follows: ;pass Update the variable on the manifold, the updated variable is... ,in, Step size, This involves remapping the variables back to the manifold, represented as... After each iteration, when the current error function of communication user k... This will weight and enhance the penalty factor. The specific update mechanism for the penalty factor is as follows:

[0116]

[0117] in, , It's about updating the step size. It is a tolerance parameter.

[0118] Step 6: Using an alternating optimization strategy, design a hybrid precoding joint optimization algorithm to iteratively design the digital precoder and analog precoder until convergence. The initial values ​​are set by extracting the line-of-sight components from the channel sparsity characteristics to form a subspace.

[0119] First, initialize the analog precoding matrix. The line-of-sight components of all users are represented as a matrix. ,in, Let the set of antennas connected to the r-th RF chain and corresponding to the r-th subarray be represented as:

[0120] ,

[0121] right Perform singular value decomposition and take the first part of the dominant subspace. Column, specifically represented as ,in, and They are The left singular matrix and the right singular matrix, yes The former Listing subarrays; then The initial value is represented as:

[0122] .

[0123] The following simulation uses an example, with the following parameter settings: the transmitter uses 64 transmitting antennas, and the communication user distance is... Base station operating frequency Corresponding wavelength Total transmit power budget Number of non-line-of-sight paths .

[0124] Figure 3This is a graph showing the relationship between the Cramer-Rao bound and the communication signal-to-interference-plus-noise ratio (SINR) threshold for different numbers of radio frequency (RF) chains. As the SINR threshold increases, the Cramer-Rao bound for different numbers of RF chains increases. In the low SINR threshold range, the Cramer-Rao bound remains at a low level, indicating that the system can achieve high sensing accuracy. However, when the SINR threshold exceeds 10 dB, the Cramer-Rao bound shows a significant upward trend, directly reflecting the trade-off between communication and sensing performance. Furthermore, the use of hybrid precoding with different RF chains also significantly affects the Cramer-Rao bound. When the number of RF chains is high, especially at low SINR thresholds, the Cramer-Rao bound value approaches that of a fully digital precoder. Reducing the number of RF chains decreases the system's sensing accuracy, a phenomenon particularly pronounced in the higher SINR threshold range.

[0125] Figure 4 This is a comparison chart showing the impact of the number of RF chains on the Cramer-Rao bound under different transmit power conditions. The chart shows a positive correlation between system sensing performance and the number of RF chains. As the number of RF chains increases, the Cramer-Rao bound gradually decreases, verifying that more RF chains provide better sensing performance. Furthermore, with the same RF chain configuration, the Cramer-Rao bound further decreases with increasing transmit power, indicating that increasing transmit power effectively enhances sensing accuracy. When the number of RF chains is 64, the system adopts a fully digital precoding architecture, at which point the Cramer-Rao bound reaches its minimum, and the system's sensing performance is optimal. Clearly, the method proposed in this chapter significantly reduces the hardware overhead of the system implementation while ensuring the required sensing accuracy.

[0126] Figure 5 This is a performance curve showing the root mean square error (RMSE) of the MUSIC algorithm under different precoding schemes as a function of radar signal-to-noise ratio (SNR). As can be seen from the graph, the RMSE decreases with increasing radar SNR. Compared to traditional beam approximation-based all-digital precoding schemes, the precoding scheme proposed in this chapter decreases the RMSE much faster, especially at high SNRs, where its RMSE approaches the theoretical minimum error. Traditional methods, on the other hand, decrease the RMSE more slowly and consistently fail to achieve the sensing accuracy of the precoding scheme proposed in this chapter. Simulation results demonstrate that the precoding scheme proposed in this chapter has significant advantages in improving the performance of the MUSIC algorithm, particularly under low radar SNR conditions, where it can significantly reduce direction estimation errors.

[0127] Figure 6The graph shows the performance curves of the root mean square error (RMSE) of the MLE algorithm under different precoding schemes as a function of radar signal-to-noise ratio (SNR). As can be seen from the graph, consistent with the MUSIC algorithm, the RMSE gradually decreases with increasing radar SNR. Compared to traditional beammap approximation methods, the RMSE of the proposed precoding scheme based on minimizing the Cramer-Rao bound continuously decreases, and even approaches the theoretical minimum error under low radar SNR conditions. In contrast, traditional beammap approximation methods can only approach the performance of the proposed precoding scheme under high radar SNR conditions. Simulation results demonstrate the effectiveness of the proposed precoding optimization method in improving the sensing accuracy of the MLE algorithm, especially in low SNR environments.

[0128] Figure 7 This figure shows the convergence curves of the objective function of the proposed algorithm under different radio frequency chain configurations, where "LT" represents the number of radio frequency chains. As can be seen from the figure, the convergence speed of the system significantly improves with the increase of the number of radio frequency chains, especially at "LT=16", where the objective function value quickly stabilizes within a smaller number of iterations, exhibiting optimal convergence characteristics. In contrast, the convergence speeds of "LT=8" and "LT=4" are relatively slower; however, the difference narrows rapidly with the increase of the number of iterations. Clearly, the direct alternating iteration method and the initial value setting based on the line-of-sight component proposed in this chapter effectively accelerate the convergence process, even with a small number of radio frequency chains, effectively promoting the stable convergence of the objective function, verifying the robustness and efficiency of the proposed optimization algorithm.

[0129] This embodiment also provides a computer device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to implement the method described above.

[0130] This embodiment also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method.

[0131] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0132] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0133] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0134] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0135] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding, wherein the ISAC system includes... root transmitting antenna, There are K data streams and K users, and each user has... The system uses a single receiving antenna to simultaneously sense one target. It operates in the millimeter-wave frequency band and is characterized by... The method includes the following steps: Step 1: Construct a millimeter-wave ISAC system model, including the channels of each communication user, the transmit steering vector, and the base station's transmit signal model under the sub-connection hybrid precoder architecture; Step 2: Establish a communication signal-to-interference-plus-noise ratio (SINR) model for communication users and a radar sensing echo model based on interference sources and array structures; Step 3: Establish a joint optimization problem with the goal of minimizing the target arrival angle's Cramer-Rao bound as the optimization objective. The joint optimization problem is a non-convex optimization problem. Step 4: Transform the non-convex optimization problem into a standard second-order cone programming form using the successive convex approximation method, and improve convergence by employing the Armijo step size search criterion; Step 5: The Riemannian manifold optimization method is used to optimize the simulation precoding matrix. In this method, a user-adaptive penalty factor is introduced to transform the communication constraints into penalty terms and incorporate them into the objective function. The solution that satisfies the constant modulus constraint is iteratively updated in the manifold space. Step 6: Using an alternating optimization strategy, iteratively design the digital precoder and the analog precoder until convergence. The initial values ​​are set by extracting the line-of-sight components from the channel sparsity characteristics to form a subspace.

2. The method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding according to claim 1, characterized in that, Step 1 includes: The base station performs hybrid precoding on the transmitted symbol vector, where the number of radio frequency chains is... and satisfy The base station's transmitted signal first undergoes processing by a hybrid precoder, that is, it sequentially passes through a digital precoding matrix. RF chain and analog precoding matrix The signal is then transmitted into space via a transmitting antenna; the transmitted signal is t, the communication user's channel is H, and the receiving and transmitting turning vectors are respectively... and ; The transmitted signal is represented as , Analog pre-encoder ,in And each element conforms to the norm constraint, where .

3. The method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding according to claim 2, characterized in that, Step 2 includes: Digital precoder is represented as ,in, Here is the digital precoder corresponding to the k-th communication user; the received signal of the k-th communication user is represented as... ,in, It is Gaussian white noise from the k-th communication user; under the assumption that the data streams are independent, it satisfies The signal-to-interference-plus-noise ratio (SIR) of the k-th communication user is expressed as: .

4. The method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding according to claim 3, characterized in that, Step 3 includes: Step 3.1: There are J interference source targets in the radar echo transmission, and the locations of the interference sources are... Received The echo signal is represented as ,in, It is the reflection coefficient corresponding to the target. It is the reflection coefficient from the i-th interference source target term. and These are the receiving steering vector and the sending steering vector, respectively. It is Gaussian white noise, with a mean of 0 and a covariance of . The complex Gaussian distribution; , These are the target angle and the j-th interference source target angle, respectively; Step 3.2: According to Send signal The covariance matrix is ​​expressed as: The Cramer-Rao boundary for estimating the target angle of arrival is expressed as: in, , The derivative of the steering vector is expressed as: ,in, The wavelength of the signal is represented by λ, and the distance between the antennas is d. For angle; Step 3.3: The joint optimization problem is expressed as: in, Indicates power budget constraints, Represented as a limited analog pre-encoder Dimensions and models; This indicates that a lower limit has been set for the SINR of all communication users.

5. The method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding according to claim 4, characterized in that, Step 4 includes: Step 4.1: The original Cramer-Rao bound minimization problem is equivalently transformed into a maximization problem of a new objective function. The joint optimization problem is then transformed into: Among them, the middle part of the optimization target is used This indicates that the power constraint of the hybrid precoding matrix is ​​equivalently transformed into... The joint optimization problem is transformed into: Introducing auxiliary variables The joint optimization problem is transformed into a second-order cone programming form joint optimization problem: in, This is represented as the equivalent channel for the k-th communication user; Step 4.2: In each iteration, precode the digital vector from the previous iteration. Performing a first-order Taylor expansion, it can be expressed as: ,in, It is a function used to extract the real part of complex numbers, which can be further expressed in Taylor expansion as: Introducing intermediate variables Add additional constraints ; to remove interference items Represented in vector form, the constructed second-order cone form constraint is expressed as: Let vector If the expression equals the left-hand side, then the joint optimization problem can be expressed as: Step 4.3: Based on the Armijo criterion, an adaptive step size adjustment mechanism is used to linearly approximate the objective function in the joint optimization problem in the nth iteration as follows: Its gradient is expressed as ,in, It is a function The gradient of the variable x; using the Armijo step size search criterion Updated to ,in, It is the step size, which must satisfy the Armijo condition. ,in, This is the step size tolerance parameter, and a backoff factor is used. Gradually reduce.

6. The method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding according to claim 5, characterized in that, Step 5 includes: Step 5.1: Given a digital precoding matrix Optimize the analog precoding matrix The joint optimization problem is expressed as: in, , Through matrix transformation, the objective function of the joint optimization problem is expressed as: Where vec(·) represents the vectorization operation, Indicates the Kronecker product; Non-zero elements extracted as ,in, This represents a function used to extract non-zero elements; extraction The non-zero elements corresponding to u in the matrix are mapped to... In, it is represented as: ,in, This represents the row (column) index of the m-th sub-block in the original matrix; This represents extracting the sub-block corresponding to the m-th row and n-th column from the entire large matrix; the objective function is transformed into... ; Step 5.2: Let , , Then the communication SINR constraint is converted to The joint optimization problem can be transformed into the following expression: The communication SINR constraint is incorporated into the objective function, and slack variables are introduced. ,in The communication SINR constraint is rewritten as follows: ,in, The objective function with the communication SINR penalty term is rewritten as follows: ,in, Represented as , It is a punishment factor. During the iteration process, according to The value is updated dynamically. Step 5.3: The joint optimization problem is finally expressed as: in, The feasible region of the optimization problem is defined as follows: ,in, express The previous point lies on the unit circle in the N-dimensional complex plane; therefore, the optimization problem can be expressed as follows: Furthermore, at a certain point The tangent space at a point is defined as ,in, express The tangent vector at that point, Represented as the Hadamard product, express The complex conjugate of ; the formula for calculating the Euclidean gradient is expressed as By using the Euclidean gradient Projecting onto this tangent space, we obtain the Riemann gradient as follows: ;pass Update the variable on the manifold, the updated variable is... ,in, Step size, This involves remapping the variables back to the manifold, represented as... After each iteration, when the current error function of communication user k... This will weight and enhance the penalty factor. The specific update mechanism for the penalty factor is as follows: in, , It's about updating the step size. It is a tolerance parameter.

7. The method for optimizing the sensing performance of a millimeter-wave ISAC system based on sub-connection hybrid precoding according to claim 6, characterized in that, Step 6 includes: First, initialize the analog precoding matrix. The line-of-sight components of all users are represented as a matrix. ,in, Let the set of antennas connected to the r-th RF chain and corresponding to the r-th subarray be represented as: ， right Perform singular value decomposition and take the first part of the dominant subspace. Column, specifically represented as ,in, and They are The left singular matrix and the right singular matrix, yes The former Listing subarrays; then The initial value is represented as: 。 8. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-7.

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