A Synesthetic Fusion Hybrid Waveform Design Method Based on Synergistic Index Optimization

Abstract

The application discloses a kind of based on collaborative index optimization's general sense fusion mixed waveform design method, establishes MIMO-ISAC base station equipped with N t Transmitting antenna and N r Receiving antenna, construct shared signal and performance index model, realize the target while base station serves multiple communication users is perceived;Under the condition of satisfying transmitting power level maximum constraint and waveform constant modulus constraint, the problem model of collaborative optimization parameter estimation performance and communication service quality is established;For the nonlinear characteristics of problem model, the geometric characteristics of non-convex constraint are excavated, the constant modulus constraint is associated with Riemann manifold in nature, so that the constrained non-convex optimization problem is converted into an unconstrained convex optimization problem on manifold;SM-RMTR optimization algorithm is proposed to solve, and the integrated sensing and communication system target parameter estimation performance optimization waveform is obtained based on the solving result.In the case of constant waveform modulus, the application can realize more efficient and more accurate target detection and parameter estimation.

Description

Technical Field

[0001] This invention belongs to the field of integrated sensing and communication, specifically involving a hybrid waveform design method based on collaborative index optimization, particularly for performance optimization of integrated waveform target parameter estimation in point target detection and multi-user communication scenarios. Background Technology

[0002] With the rapid development of electronic information technology, sensing and communication systems are showing increasing commonalities in spectrum utilization, structural design, and signal processing technologies. Coupled with the explosive growth in the number of network-connected devices, spectrum resources are becoming increasingly scarce, and inter-device interference is becoming more and more serious. In this context, Integrated Sensing and Communication (ISAC) technology has emerged. This technology utilizes the same hardware and radio signals to accomplish the dual tasks of radar detection and communication transmission, offering multiple advantages such as efficient use of spectrum resources, reduced inter-device interference, and endowing information networks with comprehensive, multi-dimensional communication and sensing capabilities. To meet the strong demand for high-performance conditions in future networks and smart applications, innovating and optimizing specific waveform design methods for integrated sensing and communication has become particularly important. This not only concerns efficient target detection and data transmission but also involves factors such as the complexity, reliability, and flexibility of the integrated system. Its successful implementation is expected to significantly improve the performance and efficiency of wireless communication systems, while bringing significant benefits to economic and social development.

[0003] Current research primarily focuses on optimizing the sensing performance of integrated communication-sensing waveforms as a single limiting metric. This involves constructing an optimization problem model with the limiting metric as the cost function under constraints of signal-to-interference plus-noise ratio (SINR) and transmit power. Solution algorithms for this model are mainly limited to deriving closed-form solutions, semidefinite relaxation (SDR) techniques, and the alternating direction method of multipliers (ADMM). These methods do not adequately consider the degrees of freedom of the problem model and practical engineering issues. When the integrated system fails to operate effectively within its maximum detection range, or when using nonlinear amplifiers, signal distortion leading to power loss affects the accurate assessment of the transmitter and receiver system performance. Therefore, further research and design of integrated waveform problem models and optimization algorithms are needed to reduce target estimation errors and improve the quality and accuracy of integrated waveform sensing performance. Summary of the Invention

[0004] Purpose of the invention: This invention proposes a synergistic index optimization-based hybrid waveform design method. Under the condition of constant waveform modulus, this invention can achieve more efficient and more accurate target detection and parameter estimation.

[0005] Technical solution: The present invention provides a synesthetic fusion hybrid waveform design method based on synergistic index optimization, comprising the following steps:

[0006] (1) Establish a system equipped with N t One transmitting antenna and N r A multi-user multiple-input multiple-output (MIMO) ISAC base station model with one receiving antenna;

[0007] (2) Construct a shared signal and performance index model to enable the base station to perceive the target while serving multiple communication users;

[0008] (3) Based on the shared signal and performance index model, under the conditions of satisfying the maximum constraint of transmit power level and the constant modulus constraint of waveform, a problem model of collaborative optimization parameter estimation performance and communication service quality is established.

[0009] (4) In view of the nonlinear characteristics of the problem model, we explore the geometric properties of nonconvex constraints, associate constant modulus constraints with Riemannian manifolds in terms of properties, and transform the constrained nonconvex optimization problem into an unconstrained convex optimization problem on the manifold.

[0010] (5) A Synergistic Metrics-based Riemannian Manifold-Trust Region (SM-RMTR) algorithm is proposed to solve the unconstrained convex optimization problem model. Based on the solution results, the target parameter estimation performance optimization waveform of the integrated sensing and communication system is obtained.

[0011] Furthermore, the base station model employs a uniform linear array for antenna layout, with an antenna spacing of half a wavelength, enabling it to provide communication services to K single-antenna users while sensing a single point target.

[0012] Furthermore, the implementation process of step (2) is as follows:

[0013] According to the MIMO-ISAC base station model, the base station's transmitted signal is represented as:

[0014] T = W ISAC S c (1)

[0015] In the formula, Represents the beamforming matrix. This represents the baseband data stream, which follows an independent white Gaussian distribution, where L is the number of symbols contained in a signal frame. The data streams are independent of each other, i.e.:

[0016] The signal stream at the user receiver is represented as follows:

[0017] R c =CT+N c (2)

[0018] In the formula, Let the Gaussian white noise matrix be , and the variance be . This represents the channel matrix between the base station and downlink communication users;

[0019] In multi-user communication scenarios, the SINR calculation formula for the k-th downlink communication user is as follows:

[0020]

[0021] According to the expression for the base station's transmitted signal, the echo signal received by the base station is represented as follows:

[0022] R r =FT+N r (4)

[0023] In the formula, The variance is The additive white Gaussian noise matrix; The point target response matrix is ​​represented by F = αU(θ)V. H (θ) = αP(θ); α represents the target received amplitude response affected by the radar cross section (RCS) and two-way propagation loss, and θ represents the relative azimuth angle. Indicates the transmitting antenna steering vector. Indicates the receiving antenna steering vector;

[0024] Based on the base station model and the echo signal expression of the base station receiver, the center of the uniform antenna array is selected as the reference phase point. The transmitting antenna steering vector and its derivative are then expressed as:

[0025]

[0026] In the formula, v i This represents the i-th element of V;

[0027] According to the echo signal R received by the base station r The Cramer-Rao Bound (CRB) relation at angle θ where the target is located is:

[0028]

[0029] In the formula, Q T The sample covariance matrix of the transmitted signal T is expressed as:

[0030]

[0031] By establishing a shared signal and performance index model as shown in equations (1)(2)(3)(4)(7), the base station can perceive the target while serving multiple communication users.

[0032] Furthermore, the implementation process of step (3) is as follows:

[0033] Based on the antenna steering vector and its derivative expression, and by the existence of symmetry between them, it can be proved that:

[0034]

[0035] In the formula, v and u represent v(θ) and u(θ) respectively;

[0036] Based on the orthogonality of the steering vector, the CRB relation at the target angle θ simplifies to:

[0037]

[0038] Under the constraints of user SINR and transmitter power, minimizing the CRB estimation problem at the target angle θ is equivalently transformed into maximizing the radiated power at the target angle θ. The integrated beam optimization problem is expressed as follows:

[0039]

[0040] In the formula, ||·|| F Denotes the norm, Γ k P represents the lower bound of the SINR that guarantees user communication. T Indicates the transmission power;

[0041] By taking parameter estimation CRB and communication quality SINR as joint optimization objectives, the explicit SINR constraint is transformed into an implicit constraint, and the optimization problem is further formulated as follows:

[0042]

[0043] The tradeoff optimization problem after introducing the maximum transmit power level constraint and the constant waveform modulus constraint is expressed as follows:

[0044]

[0045] Furthermore, the implementation process of step (4) is as follows:

[0046] The inherent geometric structure of the constraints is visualized. Embedding the constraints into the search space and mapping them into the solution space results in the following smooth, flowing representation:

[0047]

[0048] In the formula, It is a complex circular manifold;

[0049] Based on the structure of the complex circular manifold, the tangent space is used to approximate the linear space around any point on the manifold:

[0050]

[0051] In the formula, Represents the tangent vector;

[0052] By defining an inner product that satisfies bilinearity, symmetry, and positive definiteness, a specific structure on the manifold can be constructed, namely the Riemannian metric:

[0053]

[0054] Based on the Riemannian complex circular manifold structure and the non-convex optimization problem constructed above, we obtain the unconstrained convex optimization problem based on the Riemannian manifold:

[0055]

[0056] Furthermore, the implementation process of step (5) is as follows:

[0057] The Euclidean gradient of the objective function with respect to the beamforming matrix is ​​derived, and the Riemann gradient is characterized based on the mapping relationship between the Euclidean and Riemann gradients. An initial iteration point and trust region radius are selected. A local quadratic approximation model is constructed and solved using the objective function and Riemann gradient. The ratio of the predicted reduction to the actual reduction of the objective function is evaluated, and the trust region radius is dynamically updated. This process is iterated until the convergence criterion is met, and finally, the optimal beam matrix w that satisfies the optimization objective of the problem model is extracted. opt .

[0058] Furthermore, the derivation process of the Euclidean gradient of the objective function with respect to the beamforming matrix is ​​as follows:

[0059] Decompose the objective function:

[0060]

[0061] The objective functions of each sub-item with respect to w were calculated. k Euclidean gradient:

[0062]

[0063] Calculate the sum gradient of the Euclidean gradients of each component. Merge W again ISAC Gradients of all columns yield Euclidean gradients.

[0064] Furthermore, the process of characterizing the Riemann gradient implementation based on the mapping relationship between the Euclidean gradient and the Riemann gradient is as follows:

[0065] The Riemann gradient is an orthogonal projection of the Euclidean gradient, characterized as:

[0066]

[0067] In the formula, represents the orthogonal projection operator; ⊙ represents the Hadamard product, indicating the multiplication of corresponding elements;

[0068] Introducing Riemannian connection theory, the Riemannian Hessian can be expressed as:

[0069]

[0070] In the formula, It is expressed as the directional derivative of the Euclidean gradient along the tangent vector;

[0071] We establish a Riemannian manifold optimization strategy centered on the shrinkage operator, obtain the point closest to the manifold in the tangent space, and define the shrinkage operator as:

[0072]

[0073] Furthermore, the process for selecting the trust region radius is as follows:

[0074] Using the Riemann gradient and Riemann Hessian information, the optimization problem is represented as the following trust region form:

[0075]

[0076] In the formula, For Levi-Civita connection, η k Indicates the radius of the trust region;

[0077] New trust region radius η k+1 The selection is based on the trust region descent ratio, which is expressed as:

[0078]

[0079] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows:

[0080] 1. This invention uses the sensing performance index CRB and the communication quality index SINR as co-optimization objectives. Under the premise of implicitly satisfying the user's communication quality, it minimizes the target parameter estimate CRB, thereby improving beam sensing performance and the degree of freedom of the optimization model.

[0081] 2. This invention establishes a new framework for a trade-off optimization problem based on the maximum constraint of transmit power level and the constant modulus constraint of waveform, in order to improve target detection performance, optimize system efficiency and reduce power loss caused by signal distortion;

[0082] 3. This invention proposes an SM-RMTR optimization algorithm based on a complex circular Riemannian manifold, which achieves a solution to the problem model with lower complexity and better optimization results. It effectively solves the local optimum problem in traditional algorithms and ensures the stability and effectiveness of the algorithm under multiple constraints. Compared with existing waveform performance optimization models and corresponding SDR and ADMM solution algorithms, the integrated waveform under this invention exhibits superior target parameter estimation performance. Attached Figure Description

[0083] Figure 1 This is a flowchart of the present invention;

[0084] Figure 2 This is a schematic diagram illustrating the modeling of shared signals and performance indicators in the embodiment;

[0085] Figure 3 This is a schematic diagram illustrating the modeling of the collaborative index optimization problem in the embodiment.

[0086] Figure 4 The diagram below shows the detailed solution principle of the SM-RMTR optimization algorithm in the embodiment.

[0087] Figure 5 This is a simulation result of the transmitted signal beam after implementing the method in the embodiment;

[0088] Figure 6 This is a simulation result of the arrival direction estimation after implementing the method in the example;

[0089] Figure 7 The figure shows the simulation results of the angle estimation error after implementing the method in the example. Detailed Implementation

[0090] The present invention will now be described in further detail with reference to the accompanying drawings.

[0091] like Figure 1As shown, this invention provides a synergistic waveform design method based on synergistic index optimization. This method comprehensively considers the synergistic optimization between the target parameter estimation index (CRB) and the communication service quality index (SINR), and formulates a problem model by combining the constant modulus constraint of waveform and the maximum transmit power constraint under practical engineering conditions. To address the non-convex and nonlinear characteristics of the problem model, the SM-RMTR algorithm is proposed to solve the model with lower computational complexity and achieve better optimization results. Specifically, it includes the following steps:

[0092] Step 1: Establish a system equipped with N t One transmitting antenna and N r This is a MIMO-ISAC base station model with K receiving antennas. The base station model uses a uniform linear array (ULA) for antenna layout, with an antenna spacing of half a wavelength. It can sense a single point target while providing communication services to K single-antenna users.

[0093] The MIMO-ISAC system model consists of a base station, a single point target, and K single-antenna users. The base station uses N uniform linear arrays, which are divided into N... t One transmitting antenna and N r There are K receiving antennas. While serving K downlink communication users, the base station also performs target tracking and parameter estimation based on the echo signals.

[0094] Specifically in this embodiment, N t =16, N t =20, K=4.

[0095] Step 2: As Figure 2 As shown, based on the base station model established in step 1, a shared signal and performance index model is constructed.

[0096] Based on the established base station model, the base station's transmitted signal is obtained:

[0097] T = W ISAC S c (1)

[0098] In the formula, Represents the beamforming matrix. This represents the baseband data stream, which follows an independent white Gaussian distribution, where L is the number of symbols contained in a signal frame, and the data streams are independent of each other.

[0099] Based on the established base station model and base station transmitted signal model, calculate the signal flow at the user receiver:

[0100] R c =CT+N c (2)

[0101] In the formula, Let the Gaussian white noise matrix be , and the variance be . This represents the channel matrix between the base station and downlink communication users.

[0102] Based on the obtained user receiver signal stream, in the case of multi-user communication, calculate the SINR of the k-th downlink communication user:

[0103]

[0104] Based on the established base station transmit signal model, calculate the echo signal flow at the base station receiver:

[0105] R r =FT+N r (4)

[0106] In the formula, The variance is expressed as The additive white Gaussian noise matrix, The point target response matrix is ​​represented by F = αu(θ)V. H (θ) = αP(θ). α represents the target received amplitude response influenced by both the target RCS and two-way propagation loss, and θ represents the relative azimuth angle. Indicates the transmitting antenna steering vector. This represents the receiving antenna steering vector.

[0107] Based on the base station model and the echo signal expression of the base station receiver, the center of the uniform antenna array is selected as the reference phase point. The transmitting antenna steering vector and its derivative are then expressed as:

[0108]

[0109] In the formula, v i This represents the i-th element of V;

[0110] According to the echo signal R received by the base station r The CRB relation for the Cramer-Rao boundary at angle θ where the target is located is:

[0111]

[0112] In the formula, Q T The sample covariance matrix of the transmitted signal T is expressed as:

[0113]

[0114] By establishing a shared signal and performance index model as shown in formulas (1)(2)(3)(4)(7), the base station can perceive the target while serving multiple communication users.

[0115] In this specific embodiment, L = 30. θ = 0°, α = 0.1.

[0116] Step 3: As Figure 3 As shown, based on the shared signal and performance index model established in step 2, a problem model for collaborative optimization of parameter estimation performance and communication service quality is established under the constraints of maximum transmit power level and constant waveform modulus.

[0117] Based on the antenna steering vector and its derivative expression, and by the existence of symmetry between them, it can be proved that:

[0118]

[0119] Based on the orthogonality of the steering vector, the Cramer-Rao boundary (CRB) at the target angle θ can be simplified as follows:

[0120]

[0121] Based on the CRB expression, and under the conditions of satisfying the user SINR constraint and the transmitter power constraint, the problem of minimizing the CRB estimation at the target angle θ is equivalently transformed into the problem of maximizing the radiated power at the target angle θ. The integrated beam optimization problem is expressed as follows:

[0122]

[0123] In the formula, ||·|| F Denotes the norm, Γ k P represents the lower bound of the SINR that guarantees user communication. T Indicates the transmission power.

[0124] To further optimize waveform performance and the problem model, parameter estimation (CRB) and communication quality (SINR) are used as joint optimization objectives, transforming explicit SINR constraints into implicit ones. The optimization problem is further formulated as follows:

[0125]

[0126] According to the optimization problem expression, in practical radar and communication systems, it is essential to ensure that the base station can operate efficiently within its maximum detection range and maintain the constant envelope characteristic of the waveform. To avoid distortion caused by amplitude nonlinearity, the trade-off optimization problem after introducing the maximum transmit power level constraint and the constant waveform modulus constraint is expressed as follows:

[0127]

[0128] Specifically in this embodiment, Γ k =15dB, P T=30dBm.

[0129] Step 4: Based on the nonlinear characteristics of the problem model, explore the geometric properties of the nonconvex constraints, and associate the constant modulus constraints with the Riemannian manifold in terms of properties, so that the constrained nonconvex optimization problem is transformed into an unconstrained convex optimization problem on the manifold.

[0130] The inherent geometric structure of the constraints is visualized. Embedding the constraints into the search space and mapping them into the solution space results in the following smooth, flowing representation:

[0131]

[0132] In the formula, It is a complex circular manifold.

[0133] Based on the structure of the complex circular manifold, the linear space surrounding any point on the manifold can be approximated by the tangent space:

[0134]

[0135] In the formula, This represents the tangent vector.

[0136] Based on the established tangent space structure, the inner product of the tangent space should satisfy bilinearity, symmetry, and positive definiteness. By defining inner products that satisfy these properties, a specific structure on the manifold is constructed, namely the Riemannian metric:

[0137]

[0138] Based on the Riemannian complex circular manifold structure and the non-convex optimization problem constructed above, we obtain the unconstrained convex optimization problem based on the Riemannian manifold:

[0139]

[0140] Step 5: Propose the SM-RMTR optimization algorithm to solve the optimization problem model established in Step 4, and obtain the target parameter estimation performance optimization waveform of the integrated sensing and communication system based on the solution results.

[0141] The Euclidean gradient of the objective function with respect to the beamforming matrix is ​​derived, and the Riemann gradient is characterized based on the mapping relationship between the Euclidean and Riemann gradients. An initial iteration point and trust region radius are selected. A local quadratic approximation model is constructed and solved using the objective function and Riemann gradient. The ratio of the predicted reduction to the actual reduction of the objective function is evaluated, and the trust region radius is dynamically updated. This process is iterated until the convergence criterion is met, and finally, the optimal beam matrix w that satisfies the optimization objective of the problem model is extracted. opt .

[0142] To develop the SM-RMTR optimization algorithm, it is necessary to calculate the Riemann gradient and Riemann Hessian of the objective function. The objective function contains complex fractional terms and polynomial summation terms. To facilitate subsequent computation, the objective function is decomposed as follows:

[0143]

[0144] The objective functions of each sub-item with respect to w were calculated. k Euclidean gradient:

[0145]

[0146] Calculate the sum gradient of the Euclidean gradients of each component. Merge W again ISAC Gradients of all columns yield Euclidean gradients.

[0147] The Riemann gradient is an orthogonal projection of the Euclidean gradient, characterized as:

[0148]

[0149] In the formula, represents the orthogonal projection operator; ⊙ represents the Hadamard product, indicating the multiplication of corresponding elements;

[0150] The Riemannian Hessian is a generalization of the second-order partial derivatives of real-valued functions in Euclidean space. It considers the curvature and geometric properties of manifolds and introduces the Riemannian connection theory. Therefore, the Riemannian Hessian can be expressed as:

[0151]

[0152] In the formula, It is expressed as the directional derivative of the Euclidean gradient along the tangent vector.

[0153] To ensure that the points updated along the gradient direction still lie on the manifold, a Riemannian manifold optimization strategy centered on the shrinkage operator is established to obtain the points in the tangent space closest to the manifold. The shrinkage operator is defined as:

[0154]

[0155] Using the Riemann gradient and Riemann Hessian information, the optimization problem in step four can be represented as the following trust region form:

[0156]

[0157] In the formula, For Levi-Civita connection, η k Indicates the radius of the trust region.

[0158] New trust region radius η k+1 The selection is based on the trust region descent ratio, which can be expressed as:

[0159]

[0160] like Figure 4 As shown, the specific process of solving the problem model using the integrated SM-RMTR optimization algorithm is as follows:

[0161] ① Initialization: Starting from the initial point, select an initial trust region radius, which defines the size of the local neighborhood searched by the algorithm.

[0162] ② Constructing a local model: At the current iteration point, a local quadratic approximation model is constructed using the objective function and its gradient. This local model is effective within the trust region.

[0163] ③ Solve the subproblem: Solve the optimization problem of this local model within the current trust region. The solution to this subproblem provides a potential new iteration point.

[0164] ④ Evaluation and Update: Compare the reduction predicted by the local model with the actual reduction of the objective function. If the actual reduction is close enough to the predicted reduction, accept the point and increase the radius of the confidence region as needed; if the actual reduction is much smaller than the prediction, reject the point and decrease the radius of the confidence region.

[0165] ⑤ Iteration: Use the newly found point as the starting point for the next iteration and repeat steps ②-④.

[0166] ⑥ Convergence check: Check whether the algorithm meets the convergence criteria, such as whether the gradient norm is small enough or whether the preset number of iterations has been reached. If the convergence criteria are met, stop iterating; otherwise, continue to step ②.

[0167] like Figure 5 As shown, the radiated power of the transmitted signal beam under the SM-RMTR algorithm at the target azimuth is higher than that of the SDR and ADMM algorithms, verifying its superiority in improving the target detection performance of the signal waveform. Furthermore, the sidelobe levels under the SM-RMTR algorithm are generally lower than those of the comparative algorithms, further confirming its excellent performance in energy concentration and target estimation. Figure 6 As shown, the peak-to-peak value of the SM-RMTR algorithm at the target azimuth is significantly higher than that of the SDR and ADMM algorithms, verifying its significant advantage in enhancing target detection performance. Furthermore, its main peak is sharper and more concentrated, indicating higher spatial resolution, providing more accurate target information, and also demonstrating a significant advantage in suppressing signals from non-target directions. Figure 7As shown, with the continuous improvement of the radar echo signal-to-noise ratio (SNR), the target angle estimation error under each optimization algorithm gradually decreases, and the root mean square error (RMSE) curves all take the corresponding CRB curve as their lower bound. The CRB and RMSE curves under the SM-RMTR algorithm are significantly lower than their corresponding curves under SDR technology and ADMM algorithm, indicating its significant advantage in improving the accuracy of waveform target angle estimation. This verifies the efficiency of the optimization algorithm presented in this paper in processing nonlinear and multidimensional data, and demonstrates its ability to better adapt to complex signal environments and optimize parameter estimation performance.

[0168] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for designing a mixed waveform based on a cooperative index optimization, characterized in that, The method comprises the following steps: (1) Establish a MIMO-ISAC base station model equipped with N t transmit antennas and N r receive antennas; (2) Constructing a shared signal and performance index model to realize target sensing while the base station serves multiple communication users; (3) Based on the shared signal and performance index model, a problem model for optimizing parameter estimation performance and communication service quality is established under the conditions of satisfying the maximum constraint of the transmission power level and the constant modulus constraint of the waveform; (4) In view of the nonlinear characteristics of the problem model, the geometric characteristics of the non-convex constraint are mined, the constant modulus constraint is associated with the Riemannian manifold in nature, and the constrained non-convex optimization problem is converted into an unconstrained convex optimization problem on the manifold; (5) The SM-RMTR optimization algorithm is used to solve the unconstrained convex optimization problem model, and the integrated sensing and communication system target parameter estimation performance optimization waveform is obtained based on the solving result; The implementation process of step (5) is as follows: The Euclidean gradient of the target function with respect to the beamforming matrix is derived, and the Riemannian gradient is represented according to the mapping relationship between the Euclidean gradient and the Riemannian gradient; the initial iteration point and the radius of the trust region are selected, the local quadratic approximation model is constructed and solved by using the target function and the Riemannian gradient, the predicted reduction and the proportion of the actual target function reduction are evaluated, the radius of the trust region is dynamically updated, and the iteration is continuously performed until the convergence criterion is reached, and finally the optimal beam matrix W satisfying the optimization target of the problem model is extracted opt .

2. The method of claim 1, wherein, The base station model adopts a uniform linear array for antenna layout, and the antenna spacing is half a wavelength, which provides communication services for K single-antenna users while sensing a single point target.

3. The method of claim 2, wherein, The implementation process of step (2) is as follows: According to the MIMO-ISAC base station model, the base station transmission signal is represented as: T = W ISAC S c (1) wherein denotes a beamforming matrix, denotes a baseband data stream, subject to independent distributed white Gaussian distribution, L is the number of symbols contained in a signal frame, the data streams are independent of each other, i.e. The user receiving end signal flow is represented as: R c = CT + N c (2) In the formula, denotes a Gaussian white noise matrix with variance denotes a channel matrix between the base station and the downlink communication user; In the case of multi-user communication, the SINR calculation formula of the kth downlink communication user is: According to the base station transmission signal expression, the base station receiving end echo signal is represented as: R,=FT+N,(4) wherein represents an additive white Gaussian noise matrix with variance represents a point target response matrix, F = αu(θ)V H (θ) = αP(θ); α represents the target receive amplitude response influenced by the RCS and the two-way propagation loss, θ represents the relative azimuth angle, represents a transmit antenna steering vector, represents a receive antenna steering vector;​ According to the base station model and the base station receiving end echo signal expression, the center of the uniform antenna array is selected as the reference phase point, and the transmission antenna steering vector and its derivative are represented as: wherein v i denotes the i-th element of V. According to the base station received echo signal R,, the Cramer-Rao bound CRB relationship at the target angle θ is: where Q T is the sample covariance matrix of the transmitted signal T, denoted as: By establishing the shared signal and performance index model as shown in formulas (1)(2)(3)(4)(7), the base station serves multiple communication users while sensing the target.

4. The method of claim 3, wherein, The implementation process of step (3) is as follows: According to the expressions of the antenna steering vector and its derivative, it is proved that there is symmetry between them: In the formula, v,u respectively represent V(θ) and u(θ); According to the orthogonal characteristics of the steering vector, the Cramer-Rao bound CRB relationship at the target angle θ is simplified as: Under the conditions of satisfying the user SINR constraint and the transmitter power constraint, the minimum CRB estimation problem at the target angle θ is equivalent to the maximum radiation power problem at the target angle θ, and the integrated beam optimization problem expression is: In the formula, ||·|| F Denotes the norm, Γ k P represents the lower bound of the SINR that guarantees user communication. T Indicates the transmission power; Taking the parameter estimation CRB and the communication quality SINR as the collaborative optimization target, the explicit SINR constraint is converted into implicit satisfaction, and the optimization problem is further expressed as: The trade-off optimization problem after introducing the maximum constraint of the transmission power level and the constant modulus constraint of the waveform is expressed as:

5. The method of claim 4, wherein, The implementation process of step (4) is as follows: The internal geometric structure of the constraint condition is described, the constraint condition is embedded into the search space, and the smooth flow after mapping into the solution space is expressed as: In the formula, is a complex circle manifold; According to the complex circle manifold structure, the tangent space is used to approximately describe the linear space around any point on the manifold: In the formula, denotes the tangent vector; By setting an inner product satisfying bilinearity, symmetry and positive definiteness, a specific structure on the manifold is constructed, that is, the Riemannian metric: According to the Riemannian complex circle manifold structure and the non-convex optimization problem constructed above, an unconstrained convex optimization problem based on the Riemannian manifold is obtained:

6. The method of claim 5, wherein, The process of deriving the Euclidean gradient of the target function with respect to the beamforming matrix is as follows: The target function is decomposed: The Euclidean gradient of each sub-objective function with respect to w is calculated as follows: k w = w + a * g Summing the partial euclidean gradients Recombine W ISAc Summing all column gradients to get euclidean gradient 7. The method of claim 6, wherein, The process of representing the Riemannian gradient according to the mapping relationship between the Euclidean gradient and the Riemannian gradient is as follows: The Riemannian gradient is the orthogonal projection of the Euclidean gradient, and is represented as: In the formula, denotes the orthogonal projection operator; and is the Hadamard product, which denotes multiplication of corresponding elements. The Riemannian connection theory is introduced, and the Riemannian Hessian is expressed as: wherein denotes the directional derivative of the Euclidean gradient along the tangent vector; A Riemannian manifold optimization strategy is established with a shrinkage operator as the core, the point closest to the manifold on the tangent space is obtained, and the shrinkage operator is defined as:

8. The method of claim 7, wherein, The process of selecting the trust region radius is as follows: Using the Riemannian gradient and Riemannian Hessian information, the optimization problem is represented in the following trust region form: wherein is the Levi-Civita connection, η k denotes the radius of the trust region; New radius of confidence domain η k+1 The selection of is based on the confidence domain reduction ratio, which is expressed as:

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