Collaborative index optimization-based common inductance fusion mixed waveform design method

Abstract

The invention discloses a common inductance fusion mixed waveform design method based on collaborative index optimization, which comprises the following steps: establishing an MIMO-ISAC base station equipped with Nt transmitting antennas and Nr receiving antennas, constructing a shared signal and performance index model, and realizing that the base station serves a plurality of communication users and senses a target at the same time; establishing a problem model of collaborative optimization parameter estimation performance and communication service quality under the condition that the maximum constraint of the transmitting power level and the waveform constant modulus constraint are met; aiming at nonlinear characteristics of the problem model, mining geometric characteristics of non-convex constraints, and associating constant modulus constraints with Riemannian manifolds in nature, so that a constrained non-convex optimization problem is converted into an unconstrained convex optimization problem in manifolds; and providing an SM-RMTR optimization algorithm for solving, and obtaining a target parameter estimation performance optimization waveform of the sensing communication integrated system based on a solving result. Under the condition that the waveform modulus is constant, more efficient and more accurate target detection and parameter estimation can be realized.

Description

Technical Field

[0001] The present invention belongs to the field of perception and communication integration, and specifically relates to a synaesthesia fusion hybrid waveform design method based on collaborative index optimization, especially for point target detection and integrated waveform target parameter estimation performance optimization in multi-user communication scenarios. Background Art

[0002] With the rapid development of electronic information technology, perception and communication systems have shown more and more commonalities in spectrum utilization, structural design and signal processing technology. In addition, the explosive growth of the number of devices connected to the network has made spectrum resources increasingly scarce, and the problem of interference between devices has become increasingly serious. In this context, Integrated Sensing and Communication (ISAC) technology has emerged. This technology uses the same set of hardware equipment and radio signals to complete the dual tasks of radar detection and communication transmission. It has multiple advantages such as efficient use of spectrum resources, reducing interference problems between devices, and giving information networks full-domain multi-dimensional communication perception capabilities. In order to meet the strong demand for high-performance conditions for future networks and smart applications, it is particularly important to innovate and optimize specific perception and communication integrated waveform design methods. This is not only related to efficient target detection and data transmission, but also involves the complexity, reliability, flexibility and other factors of the integrated system. Its successful implementation is expected to greatly improve the performance and efficiency of wireless communication systems, while bringing significant benefits to economic and social development.

[0003] Existing research mainly focuses on optimizing the perception performance of the integrated communication-sensing waveform as a single boundary indicator, and constructs an optimization problem model with a boundary indicator as the cost function under the conditions of communication (Signal-to-Interference plus-Noise Ratio, SINR) constraints and transmission power constraints. The solution algorithm for this problem model is mainly limited to deriving closed-form solutions, semidefinite relaxation (Semidefinite Relaxation, SDR) technology, and alternating direction multipliers (Alternating Direction Method of Multipliers, ADMM). These methods do not fully consider the degree of freedom of the problem model and practical engineering problems. When the integrated system fails to operate effectively within its maximum detection range or when a nonlinear amplifier is used, signal distortion causes power loss, which will affect the accurate evaluation of the performance of the transmitter and receiver systems. Therefore, it is necessary to further study and design the integrated waveform problem model and optimization algorithm to reduce the target estimation error and improve the quality and accuracy of the integrated waveform perception performance. Summary of the invention

[0004] Purpose of the invention: The present invention proposes a synaesthesia fusion hybrid waveform design method based on collaborative index optimization. Under the condition that the waveform modulus is constant, the present invention can achieve more efficient and accurate target detection and parameter estimation.

[0005] Technical solution: The synaesthesia fusion hybrid waveform design method based on synergy index optimization described in the present invention comprises the following steps:

[0006] (1) Establish a t transmit antennas and N r A multi-user multiple-input multiple-output (MIMO) ISAC base station model with multiple receiving antennas;

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

[0008] (3) Based on the shared signal and performance indicator model, a problem model for collaborative optimization of parameter estimation performance and communication service quality is established while satisfying the maximum constraint of the transmission power level and the constant modulus constraint of the waveform;

[0009] (4) In view of the nonlinear characteristics of the problem model, the geometric properties of non-convex constraints are explored, and the constant modulus constraints are associated with the Riemann manifold in terms of properties, so that the constrained non-convex optimization problem can be transformed 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 performance optimization waveform of the target parameter estimation of the perception and communication integrated system is obtained.

[0011] Furthermore, the base station model adopts a uniform linear array for antenna layout, and the antenna spacing is half a wavelength. It provides communication services for 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 transmit signal is expressed as:

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

[0015] In the formula, represents the beamforming matrix, S c∈C K×L represents the baseband data stream, which obeys the independently distributed white Gaussian distribution. L is the number of symbols contained in a signal frame. The data streams are independent of each other, that is:

[0016] The signal flow at the user receiving end is expressed as:

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

[0018] Where N c ∈C K×L represents the Gaussian white noise matrix, with variance represents the channel matrix between the base station and the downlink communication user;

[0019] In the case of multi-user communication, the SINR calculation formula for the kth downlink communication user is:

[0020]

[0021] According to the base station transmission signal expression, the base station receiving end echo signal is expressed as:

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

[0023] In the formula, The variance is The additive white Gaussian noise matrix of ; represents the point target response matrix, F = αu(θ)v H (θ) = αP(θ); α∈C represents the target receiving amplitude response affected by the radar cross section (RCS) and the two-way propagation loss, θ represents the relative azimuth, represents the transmitting antenna steering vector, represents the receiving antenna steering vector;

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

[0025]

[0026] In the formula, v i 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) relationship at the target angle θ is:

[0028]

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

[0030]

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

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

[0033] According to the antenna steering vector and its derivative expression, the symmetry between them proves that:

[0034]

[0035] Where, v, u represent v(θ) and u(θ) respectively;

[0036] According to the orthogonal characteristics of the guidance vector, the CRB relation at the target angle θ is simplified to:

[0037]

[0038] Under the condition that the user SINR constraint and the transmitter power constraint are met, the problem of minimizing the CRB estimation at the target angle θ is equivalent to the problem of maximizing the radiation power at the target angle θ. The expression of the integrated beam optimization problem is:

[0039]

[0040] In the formula, ||·|| F represents the norm, Γ k represents the lower bound of SINR to ensure user communication, P T Indicates the transmit power;

[0041] Taking parameter estimation CRB and communication quality SINR as collaborative optimization targets, the explicit SINR constraint is transformed into implicit satisfaction, and the optimization problem is further expressed as:

[0042]

[0043] The trade-off optimization problem after introducing the maximum constraint of the transmit power level and the constant modulus constraint of the waveform is expressed as:

[0044]

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

[0046] The inherent geometric structure of the constraints is vividly expressed. The constraints are embedded in the search space, and the smooth flow after being mapped into the solution space is expressed as:

[0047]

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

[0049] According to 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 setting the inner product that satisfies bilinearity, symmetry, and positive definiteness, a specific structure on the manifold, namely the Riemann metric, is constructed:

[0053]

[0054] According to the Riemann complex circle manifold structure constructed above and the non-convex optimization problem, the unconstrained convex optimization problem based on the Riemann manifold is obtained:

[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 according to the mapping relationship between the Euclidean gradient and the Riemann gradient. The initial iteration point and the trust region radius are selected, and the local quadratic approximation model is constructed and solved using the objective function and the Riemann gradient. The ratio of the predicted reduction to the actual objective function reduction is evaluated, and the trust region radius is dynamically updated. The iteration is continued until the convergence criterion is reached, and finally the optimal beam matrix w that meets the optimization goal of the problem model is extracted. opt .

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

[0059] Decompose the objective function:

[0060]

[0061] Calculate the target function of each sub-project with respect to w k The Euclidean gradient of :

[0062]

[0063] Calculate the sum gradient of each sub-term Euclidean gradient Then merge all column gradients of W to get the Euclidean gradient Grad W f.

[0064] Furthermore, the Riemann gradient implementation process is characterized according to the mapping relationship between the Euclidean gradient and the Riemann gradient as follows:

[0065] The Riemann gradient is an orthogonal projection of the Euclidean gradient and is characterized by:

[0066]

[0067] In the formula, Proj W (·) represents the orthogonal projection operator;

[0068] Introducing Riemann connection theory, the Riemann Hessian is expressed as:

[0069]

[0070] In the formula, DGrad W f[ξ W ] is expressed as the directional derivative of the Euclidean gradient along the tangent vector;

[0071] Establish a Riemann manifold optimization strategy with the contraction operator as the core, obtain the point closest to the manifold in the tangent space, and define the contraction operator as:

[0072]

[0073] Furthermore, the selected trust region radius is implemented as follows:

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

[0075]

[0076] In the formula, For Levi-Civita connection, represents the trust region radius;

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

[0078]

[0079] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects:

[0080] 1. The present invention takes the perception performance index CRB and the communication quality index SINR as collaborative optimization targets, minimizes the target parameter estimation CRB under the premise of implicitly satisfying the user's communication quality, and improves the beam perception performance and the degree of freedom of the optimization model;

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

[0082] 3. The present invention proposes an SM-RMTR optimization algorithm based on complex circle Riemann manifold, which can solve the problem model with lower complexity and obtain better optimization effect, effectively solve the local optimal problem in the traditional algorithm, and ensure the stability and effectiveness of the algorithm under multiple constraints; compared with the existing waveform performance optimization model, and the corresponding SDR and ADMM solution algorithms, the integrated waveform under the present invention shows more excellent target parameter estimation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 is a flow chart of the present invention;

[0084] Figure 2 A schematic diagram of modeling shared signals and performance indicators in an embodiment;

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

[0086] Figure 4 It is a detailed solution principle diagram of the SM-RMTR optimization algorithm in the embodiment;

[0087] Figure 5 This is a diagram of the simulation result of the transmission signal beam after the method is implemented in the embodiment;

[0088] Figure 6 This is a diagram of the simulation result of the arrival direction estimation after the method is implemented in the embodiment;

[0089] Figure 7 Graph showing the angle estimation error simulation results after the method is implemented in the embodiment. DETAILED DESCRIPTION

[0090] The present invention is further described in detail below with reference to the accompanying drawings.

[0091] like Figure 1As shown, the present invention provides a synaesthesia fusion hybrid waveform design method based on collaborative index optimization. The method comprehensively considers the collaborative optimization between the target parameter estimation index CRB and the communication service quality SINR, and combines the waveform constant modulus constraint and the maximum level constraint of the transmission power in the actual engineering background to formulate a problem model. In view of 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 obtain better optimization effect. Specifically, the following steps are included:

[0092] Step 1: Build a N t transmit antennas and N r The MIMO-ISAC base station model has 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 provide communication services for K single-antenna users while sensing a single point target.

[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 transmit antennas and N r While serving K downlink communication users, the base station also performs target tracking and parameter estimation based on the echo signal.

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

[0095] Step 2: If Figure 2 As shown, according to the base station model established in step 1, a shared signal and performance indicator model is constructed.

[0096] According to the established base station model, the base station transmission signal is obtained:

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

[0098] In the formula, represents the beamforming matrix, S c ∈C K×L Represents the baseband data stream, which obeys an independently distributed white Gaussian distribution. L is the number of symbols contained in a signal frame, and the data streams are independent of each other.

[0099] According to the established base station model and base station transmission signal model, the user receiving end signal flow is calculated:

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

[0101] In the formula, represents the Gaussian white noise matrix, with variance Represents the channel matrix between the base station and the downlink communication user.

[0102] According to the obtained user receiving end signal stream, in the case of multi-user communication, calculate the SINR of the kth downlink communication user:

[0103]

[0104] According to the established base station transmission signal model, the echo signal flow at the base station receiving end is calculated:

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

[0106] In the formula, The variance is The additive white Gaussian noise matrix, represents the point target response matrix, F = αu(θ)v H (θ) = αP(θ). α∈C represents the target receiving amplitude response affected by the target RCS and the two-way propagation loss, θ represents the relative azimuth, represents the transmitting antenna steering vector, represents the receiving antenna steering vector.

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

[0108]

[0109] In the formula, v i Represents the i-th element of v;

[0110] According to the echo signal R received by the base station r , the Cramer-Rao bound CRB relationship at the target angle θ is:

[0111]

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

[0113]

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

[0115] Specifically in this embodiment, L=30, θ=0°, α=0.1.

[0116] Step 3: If Figure 3 As shown, based on the shared signal and performance indicator model established in step 2, a problem model of collaborative optimization of parameter estimation performance and communication service quality is established while satisfying the maximum constraint of the transmission power level and the constant modulus constraint of the waveform.

[0117] According to the antenna steering vector and its derivative expression, the symmetry between them can be proved:

[0118]

[0119] According to the orthogonal characteristics of the steering vector, the Cramer-Rao bound CRB at the target angle θ can be simplified as:

[0120]

[0121] According to the CRB expression, under the condition of satisfying the user SINR constraint and the transmitter power constraint, the problem of minimizing the CRB estimation problem at the target angle θ is equivalent to the problem of maximizing the radiation power at the target angle θ. The expression of the integrated beam optimization problem is:

[0122]

[0123] In the formula, ||·|| F represents the norm, Γ k represents the lower bound of SINR to ensure user communication, P T Indicates the transmit power.

[0124] In order to further optimize the waveform performance and problem model, the parameter estimation CRB and the communication quality SINR are taken as the collaborative optimization objectives to convert the explicit SINR constraint into implicit satisfaction. The optimization problem is further expressed as:

[0125]

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

[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 non-convex constraints, associate the constant modulus constraints with the Riemann manifold in terms of properties, and transform the constrained non-convex optimization problem into an unconstrained convex optimization problem on the manifold.

[0130] The inherent geometric structure of the constraints is vividly expressed. The constraints are embedded in the search space, and the smooth flow after being mapped into the solution space is expressed as:

[0131]

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

[0133] According to the structure of the complex circular manifold, the tangent space can be used to approximate the linear space around any point on the manifold:

[0134]

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

[0136] According to the established tangent space structure, the inner product of the tangent space should satisfy bilinearity, symmetry, and positive definiteness. By setting the inner product that satisfies these characteristics, a specific structure on the manifold, namely the Riemann metric, is constructed:

[0137]

[0138] According to the Riemann complex circle manifold structure constructed above and the non-convex optimization problem, the unconstrained convex optimization problem based on the Riemann manifold is obtained:

[0139]

[0140] Step 5: Propose the SM-RMTR optimization algorithm to solve the optimization problem model established in step 4, and obtain the performance optimization waveform of the target parameter estimation of the perception and communication integrated 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 according to the mapping relationship between the Euclidean gradient and the Riemann gradient. The initial iteration point and the trust region radius are selected, and the local quadratic approximation model is constructed and solved using the objective function and the Riemann gradient. The ratio of the predicted reduction to the actual objective function reduction is evaluated, and the trust region radius is dynamically updated. It is continuously iterated until the convergence criterion is reached, and finally the optimal beam matrix w that meets the optimization goal of the problem model is extracted. opt .

[0142] In order 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. In order to facilitate subsequent calculations, the objective function is decomposed:

[0143]

[0144] Calculate the target function of each sub-project with respect to w k The Euclidean gradient of :

[0145]

[0146] Calculate the sum gradient of each sub-term Euclidean gradient Then merge all column gradients of W to get the Euclidean gradient Grad W f.

[0147] The Riemann gradient is an orthogonal projection of the Euclidean gradient and is characterized by:

[0148]

[0149] In the formula, Proj W (·) represents the orthogonal projection operator.

[0150] The Riemann Hessian is a generalization of the second-order partial derivative of a real-valued function in Euclidean space. Considering the curvature and geometric properties of the manifold, the Riemann connection theory is introduced. Therefore, the Riemann Hessian can be expressed as:

[0151]

[0152] In the formula, DGrad W f[ξ W ] is expressed as the directional derivative of the Euclidean gradient along the tangent vector.

[0153] In order to ensure that the updated points along the gradient direction are still on the manifold, a Riemann manifold optimization strategy with the contraction operator as the core is established to obtain the point closest to the manifold in the tangent space. The contraction operator is defined as:

[0154]

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

[0156]

[0157] In the formula, For Levi-Civita connection, represents the trust region radius.

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

[0159]

[0160] like Figure 4 As shown in the figure, the specific process of integrating the SM-RMTR optimization algorithm to solve the problem model is:

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

[0162] ②Build a local model: At the current iteration point, use the objective function and its gradient to build a local quadratic approximation model, which is valid within the trust region.

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

[0164] ④Evaluation and update: Compare the reduction predicted by the local model and the actual reduction of the objective function. If the actual reduction is close enough to the predicted reduction, accept this point and increase the radius of the trust region as appropriate; if the actual reduction is much smaller than the predicted, reject this point and reduce the radius of the trust region.

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

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

[0167] like Figure 5 As shown in the figure, the radiation power of the transmitted signal beam under the SM-RMTR algorithm at the target azimuth is higher than that of the SDR technology and the ADMM algorithm, which verifies its superiority in improving the target detection performance of the signal waveform. In addition, the sidelobe level under the SM-RMTR algorithm is generally lower than that of the comparison algorithm, further confirming its excellent performance in energy concentration and target estimation. Figure 6 As shown in the figure, the peak value of the SM-RMTR algorithm at the target direction is significantly higher than that of the SDR technology and the ADMM algorithm, which verifies its significant advantage in enhancing target detection performance. In addition, its main peak is sharper and more concentrated, indicating that it has a higher spatial resolution, can provide more accurate target information, and has a significant advantage in suppressing signals in non-target directions. Figure 7As shown in the figure, with the continuous improvement of the signal-to-noise ratio (SNR) of the radar echo signal, the target angle estimation error under each optimization algorithm gradually decreases, and the root mean square error (RMSE) curve takes the CRB curve under the corresponding algorithm as the lower bound. The CRB curve and RMSE curve under the SM-RMTR algorithm are significantly lower than the corresponding curves under the SDR technology and ADMM algorithm, indicating that it has significant advantages in improving the accuracy of waveform target angle estimation, verifying the efficiency of the optimization algorithm in this paper in processing nonlinear and multidimensional data, and can better adapt to complex signal environments and optimize parameter estimation performance.

[0168] The above-mentioned embodiments only express several implementation methods of the present invention, and the description is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A synaesthesia fusion hybrid waveform design method based on synergy index optimization, characterized in that: The following steps are involved: (1) Establish a t transmit antennas and N r MIMO-ISAC base station model with 100 receive antennas; (2) Construct a shared signal and performance indicator model to enable the base station to sense the target while serving multiple communication users; (3) Based on the shared signal and performance indicator model, a problem model for collaborative optimization of parameter estimation performance and communication service quality is established while 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 properties of non-convex constraints are explored, and the constant modulus constraints are associated with the Riemann manifold in terms of properties, so that the constrained non-convex optimization problem can be transformed into an unconstrained convex optimization problem on the manifold; (5) An SM-RMTR optimization algorithm is proposed to solve the unconstrained convex optimization problem model. Based on the solution results, the performance optimization waveform of the target parameter estimation of the perception and communication integrated system is obtained.

2. The synaesthesia fusion hybrid waveform design method based on collaborative index optimization according to claim 1 is characterized in that: The base station model adopts a uniform linear array for antenna layout, with an antenna spacing of half a wavelength. It provides communication services for K single-antenna users while sensing a single point target.

3. The synaesthesia fusion hybrid waveform design method based on collaborative index optimization according to claim 1 is characterized in that: The implementation process of step (2) is as follows: According to the MIMO-ISAC base station model, the base station transmit signal is expressed as: T=W ISAC S c (1) In the formula, represents the beamforming matrix, S c ∈C K×L represents the baseband data stream, which obeys the independently distributed white Gaussian distribution. L is the number of symbols contained in a signal frame. The data streams are independent of each other, that is: The signal flow at the user receiving end is expressed as: R c =CT+N c (2) Where N c ∈C K×L represents the Gaussian white noise matrix, with variance represents the channel matrix between the base station and the downlink communication user; In the case of multi-user communication, the SINR calculation formula for the kth downlink communication user is: According to the base station transmission signal expression, the base station receiving end echo signal is expressed as: R r =FT+N r (4) In the formula, The variance is The additive white Gaussian noise matrix of ; represents the point target response matrix, F = αu(θ)v H (θ) = αP(θ); α∈C represents the target receiving amplitude response affected by RCS and two-way propagation loss, θ represents the relative azimuth, represents the transmitting antenna steering vector, represents the receiving antenna steering vector; According to the base station model and the expression of the echo signal at the base station receiver, the center of the uniform antenna array is selected as the reference phase point, and the transmitting antenna steering vector and its derivative are expressed as: In the formula, v i Represents the i-th element of v; According to the echo signal R received by the base station r , the Cramer-Rao bound CRB relationship at the target angle θ is: In the formula, Q T is the sample covariance matrix of the transmitted signal T, expressed as: By establishing a shared signal and performance indicator model as shown in equations (1)(2)(3)(4)(7), the base station can sense the target while serving multiple communication users.

4. The synaesthesia fusion hybrid waveform design method based on collaborative index optimization according to claim 1 is characterized in that: The implementation process of step (3) is as follows: According to the antenna steering vector and its derivative expression, the symmetry between them proves that: Where, v, u represent v(θ) and u(θ) respectively; According to the orthogonal characteristics of the guidance vector, the CRB relation at the target angle θ is simplified to: Under the condition that the user SINR constraint and the transmitter power constraint are met, the CRB estimation problem of minimizing the target angle θ is equivalent to the problem of maximizing the radiation power at the target angle θ. The expression of the integrated beam optimization problem is: In the formula, ||·|| F represents the norm, Γ k represents the lower bound of SINR to ensure user communication, P T Indicates the transmit power; Taking parameter estimation CRB and communication quality SINR as collaborative optimization targets, the explicit SINR constraint is transformed into implicit satisfaction, and the optimization problem is further expressed as: The trade-off optimization problem after introducing the maximum constraint of the transmit power level and the constant modulus constraint of the waveform is expressed as:

5. The synaesthesia fusion hybrid waveform design method based on collaborative index optimization according to claim 1 is characterized in that: The implementation process of step (4) is as follows: The inherent geometric structure of the constraints is vividly expressed. The constraints are embedded in the search space, and the smooth flow after being mapped into the solution space is expressed as: In the formula, is a complex circular manifold; According to the structure of the complex circular manifold, the tangent space is used to approximate the linear space around any point on the manifold: In the formula, represents the tangent vector; By setting the inner product that satisfies bilinearity, symmetry, and positive definiteness, a specific structure on the manifold, namely the Riemann metric, is constructed: According to the Riemann complex circle manifold structure constructed above and the non-convex optimization problem, the unconstrained convex optimization problem based on the Riemann manifold is obtained:

6. The synaesthesia fusion hybrid waveform design method based on collaborative index optimization according to claim 1 is characterized in that: The implementation process of step (5) is as follows: The Euclidean gradient of the objective function with respect to the beamforming matrix is ​​derived, and the Riemann gradient is characterized according to the mapping relationship between the Euclidean gradient and the Riemann gradient. The initial iteration point and the trust region radius are selected, and the local quadratic approximation model is constructed and solved using the objective function and the Riemann gradient. The ratio of the predicted reduction to the actual objective function reduction is evaluated, and the trust region radius is dynamically updated. The iteration is continued until the convergence criterion is reached, and finally the optimal beam matrix w that meets the optimization goal of the problem model is extracted. opt .

7. The synaesthesia fusion hybrid waveform design method based on collaborative index optimization according to claim 6 is characterized in that: The process of deriving the Euclidean gradient of the objective function with respect to the beamforming matrix is ​​as follows: Decompose the objective function: Calculate the target function of each sub-project with respect to w k The Euclidean gradient of : Calculate the sum gradient of each sub-term Euclidean gradient Then merge all column gradients of W to get the Euclidean gradient Grad W f.

8. The synaesthesia fusion hybrid waveform design method based on collaborative index optimization according to claim 6 is characterized in that: The Riemann gradient implementation process is characterized as follows based on the mapping relationship between the Euclidean gradient and the Riemann gradient: The Riemann gradient is an orthogonal projection of the Euclidean gradient and is characterized by: In the formula, Proj W (·) represents the orthogonal projection operator; Introducing Riemann connection theory, the Riemann Hessian is expressed as: In the formula, DGrad W f[ξ W ] is expressed as the directional derivative of the Euclidean gradient along the tangent vector; Establish a Riemann manifold optimization strategy with the contraction operator as the core, obtain the point closest to the manifold in the tangent space, and define the contraction operator as:

9. The synaesthesia fusion hybrid waveform design method based on collaborative index optimization according to claim 6 is characterized in that: The selected trust region radius is implemented as follows: Using Riemann gradient and Riemann Hessian information, the optimization problem is characterized as the following trust region form: In the formula, For Levi-Civita connection, represents the trust region radius; New trust region radius η k+1 The selection of is based on the trust region reduction ratio, which is expressed as:

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