MIMO-DFRC waveform design method based on angle estimation CRB optimization

Abstract

The application relates to a MIMO-DFRC waveform design method based on angle estimation CRB optimization, and the method comprises the following steps: establishing a signal model; deducing angle estimation CRB; establishing a communication CI constraint; establishing a constant modulus constraint; establishing a MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization; converting inequality constraints by adopting the idea of barrier function; and efficiently solving by adopting the Riemann conjugate gradient method. The method adopts the idea of barrier function in the interior point method to process inequality constraints, ensures that the optimization result can strictly meet the established communication service quality requirement, is more applicable and stable in the actual radar communication integrated scene, adopts the Riemann conjugate gradient method to solve the integrated waveform optimization, is higher in calculation efficiency compared with the existing ADMM algorithm, improves the real-time transmission capability of the MIMO radar communication integrated waveform, and is more advantageous in engineering application.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radio communication, and relates to a MIMO-DFRC waveform design method based on angle estimation CRB optimization. BACKGROUND

[0002] In recent years, with the rapid development of wireless communication technology, the number of access devices and service devices based on the internet of things (IoT) technology has increased exponentially. The explosive growth of communication devices has brought increasing demand for electromagnetic spectrum, however, the existing available communication spectrum resources are limited, which makes the communication system gradually seek spectrum resources from the radar working at a higher frequency band. Obviously, with the update and iteration of electronic information technology, the spectrum competition between the radar and the communication system is becoming increasingly severe.

[0003] To solve the problem of spectrum congestion, the radar communication integration (DFRC) system capable of realizing the horizontal fusion of different electronic information systems has attracted widespread attention from the academic and industrial circles. Unlike simply stacking radar and communication devices, the integrated system simultaneously realizes radar detection and communication transmission functions based on the same hardware platform and transmits integrated waveforms, which can comprehensively improve the utilization efficiency of the overall system in terms of space resources, waveform resources and spectrum resources.

[0004] As the information carrier of electromagnetic tasks, the transmitted waveform deeply affects the working efficiency of the system, and the radar communication integrated waveform design is the core key technology of the radar communication integrated system. Since the Cramer-Rao bound (CRB) can represent the lower bound of the estimation variance of any unbiased estimator, and can directly measure the performance limit of target parameter estimation, the CRB of minimizing the radar angle estimation error variance is used to design the radar communication integrated waveform under the premise of guaranteeing the quality of service (QoS) of communication, which can optimize the angle estimation capability of the radar communication integrated system, and is a research hotspot in the field of radar communication integrated waveform design.

[0005] The optimization problem takes the CRB of minimizing the target azimuth angle estimation error variance as the optimization objective function, and constructs a communication multi-user interference (MUI) constraint or a constructive interference (CI) constraint to guarantee the QoS of communication. In addition, to improve the working efficiency of the radio frequency amplifier and prevent nonlinear distortion, a strict waveform constant modulus constraint is adopted.

[0006] The constructed transmit waveform design problem model is a typical single-variable quadratic optimization problem with inequality constraints and constant modulus constraints, and the closest prior art is to: transform the objective function into a convex function, introduce auxiliary variables, adopt an ADMM solving algorithm, construct an augmented Lagrangian function, penalize the inequality constraints to the objective function, and then iteratively solve multiple variables. The prior art also has some disadvantages:

[0007] (1) The ADMM algorithm adopted by the prior art has defects: first, the variable dimension involved in the algorithm is high, and the calculation process is relatively complicated, second, the performance of the ADMM algorithm depends largely on the selection of parameters, and when the parameters are not selected well, the effect of the algorithm is not good, third, the ADMM algorithm lacks a universal convergence criterion for non-convex optimization problems.

[0008] (2) The waveform optimized by the prior art cannot strictly meet the established constraints: when dealing with inequality constraints, the prior art algorithm adopts an external point method to convert the constraints into a penalty term on the objective function, which cannot be completely equal in mathematical principle, therefore, the finally optimized result can only be approximately close to the established constraints, and may slightly exceed the constraints in some cases. SUMMARY

[0009] In view of the problems in the above-mentioned traditional method, the present application provides a MIMO-DFRC waveform design method based on angle estimation CRB optimization, which can optimize the angle estimation capability of the radar communication integrated system.

[0010] In order to achieve the above-mentioned purpose, the embodiments of the present application adopt the following technical solutions:

[0011] On the one hand, a MIMO-DFRC waveform design method based on angle estimation CRB optimization is provided, the MIMO-DFRC system transmits antenna array and receives antenna array are centrally arranged, and both arrays are uniform linear arrays, comprising the steps of:

[0012] Establishing a radar target echo signal model received by the MIMO-DFRC system;

[0013] According to the radar target echo signal model, determining the CRB lower bound of the unbiased estimation equation at the incident angle of the point target relative to the two arrays.

[0014] Constructing a communication CI constraint that satisfies the condition that the distance from the noiseless signal to the CI region decision boundary is always greater than 0.

[0015] Establishing a waveform constant modulus constraint.

[0016] According to the CRB lower bound of the unbiased estimation equation, the communication CI constraint and the waveform constant modulus constraint, a MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization is established.

[0017] Based on the idea of barrier function, the MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization is restructured.

[0018] The Riemann conjugate gradient method is used to solve the MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization, and a MIMO radar communication integrated waveform is obtained.

[0019] One of the above technical solutions has the following advantages and beneficial effects:

[0020] The MIMO-DFRC waveform design method based on angle estimation CRB optimization includes: establishing a signal model; deriving an angle estimation CRB; establishing a communication CI constraint; establishing a constant modulus constraint; establishing a MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization; converting inequality constraints using the barrier function idea; and efficiently solving using the Riemann conjugate gradient method. The method uses the barrier function idea in the interior point method to process inequality constraints, ensuring that the optimization result strictly meets the established communication service quality requirements, making it more applicable and robust in actual radar communication integrated scenarios. The method uses the Riemann conjugate gradient method to optimize and solve the integrated waveform, which is more efficient than existing ADMM algorithms, improves the real-time transmission capability of MIMO radar communication integrated waveforms, and has more advantages in engineering applications. BRIEF DESCRIPTION OF DRAWINGS

[0021] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor.

[0022] Figure 1 The flowchart of the MIMO-DFRC waveform design method based on angle estimation CRB optimization in one embodiment;

[0023] Figure 2 The comparison diagram of the change of the CRB of the present method and the prior art with running time in one embodiment;

[0024] Figure 3 The comparison diagram of the change of the inequality constraint satisfaction of the present method and the prior art with iteration number in one embodiment;

[0025] Figure 4 The comparison diagram of the communication transmission constellation of the waveforms optimized by the present method and the prior art in one embodiment. DETAILED DESCRIPTION

[0026] In order to make the purposes, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and not intended to limit the present application.

[0027] Unless otherwise defined, 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 belongs. The terminology used in the description of the application herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0028] It should be noted that a reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are they necessarily mutually exclusive of one another. One of ordinary skill in the art can understand that the embodiments described herein can be combined with one another. The term "and / or" as used herein refers to any combination of one or more of the associated listed items, as well as all possible combinations of the items, and includes these combinations.

[0029] DFRC: dual functional radar and communication, radar communication integration.

[0030] MIMO: Multiple-Input-Multiple-Output, multiple-input multiple-output, refers to a system with multiple transmitting and receiving antennas.

[0031] ADMM: Alternating Direction Method of Multipliers, an alternating direction multiplier method, is a computational framework for solving optimization problems with separability.

[0032] CRB: cramér-rao bound, cramér-rao bound.

[0033] The embodiments of the present application will be described in detail below with reference to the accompanying drawings of the embodiments of the present application.

[0034] In one embodiment, as shown in Figure 1 , a MIMO-DFRC waveform design method based on angle estimation CRB optimization is provided, the MIMO-DFRC system transmitting antenna array and receiving antenna array are centrally arranged, and the transmitting antenna array and the receiving antenna array are both uniform linear arrays, the number of elements of the transmitting antenna array and the receiving antenna array are and half wavelength. Transmit integrated waveform wherein, is the number of sampling points within a radar pulse. In addition to the target detection function, the integrated waveform can also provide information transmission services for single antenna users in the downlink communication. In order to focus on the angle estimation performance of the MIMO-DFRC system and simplify the problem difficulty, the interference and clutter in space are ignored. It is assumed that there is only one point target in the far field, and the incident angles of the point target relative to the transmitting antenna array and the receiving antenna array are the same, both being The method can include the following processing steps 1 to 7:

[0035] Step 1: Establish a radar target echo signal model received by the MIMO-DFRC system.

[0036] Step 2: According to the radar target echo signal model, determine the CRB lower bound of the unbiased estimation equation at the incident angle of the point target relative to the two arrays.

[0037] Step 3: Construct a communication CI constraint that satisfies the condition that the distance from the noiseless signal to the CI region decision boundary is always greater than 0.

[0038] Specifically, in order to ensure that the communication received signal is correctly detected, it is necessary to always place all noiseless signals in the CI region, that is, to always keep the distance from the nearest CI decision boundary greater than 0, and to design the CRB lower bound of the unbiased estimation equation at the incident angle of the point target relative to the two arrays based on this.

[0039] Step 4: Establish a waveform constant modulus constraint.

[0040] Specifically, in order to make the radio frequency amplifier work at the highest efficiency and avoid nonlinear distortion, a waveform constant modulus constraint is further added.

[0041] Step 5: According to the CRB lower bound of the unbiased estimation equation, the communication CI constraint, and the waveform constant modulus constraint, establish a MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization.

[0042] Step 6: Reconstruct the MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization based on the idea of barrier function.

[0043] Specifically, in order to solve the problem that the waveform optimized by the prior art cannot strictly meet the established constraints, the method adopts the idea of interior point method for optimization design, and transforms the inequality constraint into an obstacle function on the optimization objective function. Unlike the approximate penalty of the exterior point method in the prior art route, the method proposed in the application can ensure that the optimized waveform strictly meets all the constraints.

[0044] Step 7: The Riemann conjugate gradient method is used to optimize and solve the MIMO radar-communication integrated waveform design problem based on the angle estimation CRB optimization, and the MIMO radar-communication integrated waveform is obtained.

[0045] Specifically, the MIMO radar-communication integrated waveform design problem based on the angle estimation CRB optimization is migrated from the Euclidean space to the Riemann space, the inherent defects of the ADMM algorithm are avoided, the popular optimization is used to reduce the computational complexity of the problem, and the real-time transmission capability of the MIMO radar-communication integrated waveform is improved.

[0046] The above MIMO-DFRC waveform design method based on angle estimation CRB optimization includes: establishing a signal model; deriving an angle estimation CRB; establishing a communication CI constraint; establishing a constant modulus constraint; establishing a MIMO radar-communication integrated waveform design problem based on angle estimation CRB optimization; converting the inequality constraint by using the idea of obstacle function; and efficiently solving by using the Riemann conjugate gradient method. The method adopts the idea of obstacle function in the interior point method to process the inequality constraint, so that the optimization result can strictly meet the established communication service quality requirement, and is more applicable and robust in the actual radar-communication integrated scene; the method uses the Riemann conjugate gradient method to optimize and solve the integrated waveform, and compared with the existing ADMM algorithm, the calculation efficiency is higher, the real-time transmission capability of the MIMO radar-communication integrated waveform is improved, and the method has more advantages in engineering application.

[0047] In one embodiment, step 1 includes: establishing a radar target echo signal model received by a MIMO-DFRC system as:

[0048] (1)

[0049] wherein, is a radar target echo signal, is a reflection coefficient of the target, which is assumed to follow a Swerling-II distribution and remains constant within a single pulse; is a Gaussian white noise matrix with a mean value of 0 and a covariance matrix of ; is an incident angle of the point target relative to the two arrays, is a transmitted integrated waveform, is The direction of the launch steering vector, , for Directional receiving guide vector, , The number of elements in the transmitting antenna array. This represents the number of elements in the receiving antenna array.

[0050] In one embodiment, step 2 includes: determining the lower bound of the CRB of the unbiased estimation equation for the point target at the incident angle relative to the two arrays based on the radar target echo signal model:

[0051] (2)

[0052] in, This is the lower bound of the CRB for the unbiased estimating equation. It is the reflectance coefficient of the target. The average noise power, and They represent Directional transmission and reception steering vectors, Let be the incident angle of the point target relative to the two arrays. To transmit an integrated waveform, For waveform vectors, , , , This is the Kronecker product operator. To indicate spatial angular orientation, It is an identity matrix.

[0053] Specifically, target location The lower bound of the CRB for the unbiased estimate variance at a given location can be defined as:

[0054] (3)

[0055] in:

[0056] (4)

[0057] (5)

[0058] (6)

[0059] Further definition , Target location The unbiased estimate of the lower bound of CRB at a given location can be derived as shown in equation (2).

[0060] In one embodiment, step 3 comprises constructing the communication CI constraint that satisfies the condition that the distance from the noiseless signal to the CI region decision boundary is always greater than 0 as:

[0061] (7)

[0062] wherein, i is the total number of communication users Figure 1 ， is the total number of communication users ， is the real part of a complex number, is the waveform vector, let , is the transformed communication channel vector, is the pre-set communication service quality indicator, and the expression of

[0063] (8)

[0064] (9)

[0065] (10)

[0066] wherein, is the communication channel vector between the transmit array and the q th communication user, is the th column of the identity matrix n , is the th element of the th column of the th row of the Kronecker product operator, is the minimum threshold distance from the received signal to the CI region, and is the pre-set communication service quality indicator.

[0067] In one embodiment, the waveform constant modulus constraint in step 4 is:

[0068] (11)

[0069] wherein, is the th element of the waveform vector , , is the number of elements of the transmit antenna array and the number of sampling points within one radar pulse, respectively.

[0070] In one embodiment, step 5 comprises: establishing a MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization according to the CRB lower bound of unbiased estimation equation, communication CI constraint and waveform constant modulus constraint as follows:

[0071] (12)

[0072] wherein, is a waveform vector, is a transformed communication channel vector, is a preset communication quality of service index, , is a target reflection coefficient, is a covariance of a Gaussian white noise matrix, is a transformation matrix, , , is a total number of communication users, is an element of the waveform vector , is an element of the waveform vector , is a number of elements of a transmitting antenna array and a number of sampling points in a radar pulse, respectively.

[0073] Specifically, the optimization problem is established as follows:

[0074] (13)

[0075] Define , the optimization problem based on angle estimation CRB optimization of MIMO radar communication integrated waveform design can be further derived as shown in formula (12).

[0076] In one embodiment, step 6 comprises: using a logarithmic barrier function to force the CI constraint condition to be met throughout the optimization process, converting the MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization into an unconstrained problem on a complex circle manifold , and obtaining a reconstructed MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization as follows:

[0077] (14)

[0078] wherein, is an optimized objective function, represents a penalty parameter of placing a logarithmic barrier function on the objective function, is a transformed communication channel vector, a predetermined communication quality of service index, a waveform vector, , a reflection coefficient of a target, a covariance of a Gaussian white noise matrix, , , a Kronecker product operator, a total number of communication users, a waveform vector an element of the th column of the , , respectively represent the number of elements of a transmit antenna array and the number of sampling points within one radar pulse.

[0079] Specifically, a logarithmic barrier function is used to enforce the CI constraint condition throughout the optimization process. The original MIMO radar communication integrated waveform design problem based on CRB optimization of angle estimation is transformed into an unconstrained problem on a complex circle manifold , and is specifically as follows:

[0080] (15)

[0081] wherein, represents a penalty parameter for placing the logarithmic barrier function on the objective function.

[0082] In one embodiment, step 7 comprises: calculating the Euclidean gradient of the objective function, and defining the orthogonal projection of the Euclidean gradient on the tangent space as the corresponding Riemannian gradient, and is specifically as follows:

[0083] (16)

[0084] wherein, is the Riemannian gradient, is the Euclidean gradient of the objective function, is the objective function, represents the orthogonal projection, is a waveform vector, is a Hadamard product operator.

[0085] Selecting a descent direction and a step size; selecting a negative conjugate gradient direction as the descent direction, and using a backtracking Armijo line search method to search for the step size after the descent direction is determined; specifically, the descent direction of the th iteration is defined as:

[0086] (17)

[0087] wherein, is the The descent direction of the next iteration These are manually set adjustment parameters. Indicates vector transfer operation, and The first Second and third Waveform vector of the next iteration.

[0088] Iterative updates of feasible solutions; specifically including: updating the solutions... From tangent space Mapped to the On the complex circular manifold during the next iteration; when the change in the target value with the number of iterations is less than the preset convergence threshold, the iteration stops, and the integrated MIMO radar-communication waveform is obtained.

[0089] Specifically, the process of solving the problem using the Riemann conjugate gradient method includes:

[0090] (1) First, calculate the Euclidean gradient. Define the Euclidean gradient of the objective function as:

[0091] (18)

[0092] in:

[0093] (19)

[0094] (20)

[0095] The corresponding Riemann gradient It can be defined as the orthogonal projection of the Euclidean gradient onto the tangent space, as shown in Equation (16).

[0096] (2) Select the descent direction and step size.

[0097] Continuing to choose the negative conjugate gradient direction as the descent direction, the... The descent direction of the next iteration is shown in equation (17). The expression is:

[0098] (twenty one)

[0099] In addition, after determining the descent direction, the backtracking Armijo line search method is used to search for the step size.

[0100] (3) Update the feasible solution.

[0101] Finally, the solution still needs to be found From tangent space Mapped to the On the complex circular manifold during the next iteration, the specific operation is shown in equation (17).

[0102] Finally, when the target value does not change significantly with the number of iterations, the algorithm is determined to have converged, and the specific algorithm stop condition is set as:

[0103] (22)

[0104] wherein, is a preset convergence threshold, usually set to a very small value.

[0105] In an embodiment, the solved is mapped from the tangent space to the complex torus at the th iteration, specifically:

[0106] (23)

[0107] wherein, is the solved waveform vector in the tangent space , , , are the 1st, 2nd, and th elements of , is a mapping operation, indicating mapping of the waveform in the tangent space to the complex torus, is the solved waveform vector in the complex torus, , are the number of elements of the transmit antenna array and the number of sampling points in a radar pulse, respectively.

[0108] It should be understood that although each step in the above Figure 1 is shown in sequence according to the arrow, these steps are not necessarily executed in the order indicated by the arrow. Unless explicitly stated herein, the execution of these steps is not strictly limited in sequence, and these steps can be executed in other orders. Moreover, at least a part of the above Figure 2 steps can include multiple sub-steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution sequence of these sub-steps or stages is not necessarily sequential, but can be executed in rotation or alternation with at least a part of other steps or sub-steps or stages of other steps.

[0109] The overall scheme of the high-efficiency MIMO radar communication integrated waveform design method based on angle estimation CRB optimization includes the following steps: establishing a signal model; deriving angle estimation CRB; establishing a communication CI constraint; establishing a constant modulus constraint; establishing a MIMO radar communication integrated waveform design problem based on angle estimation CRB optimization; converting inequality constraints by using the idea of barrier function; and efficiently solving by using popular optimization.

[0110] As can be seen from Figure 3 The running speed of the present technology is better than that of the prior art.

[0111] As can be seen from Figure 4 And ​ As can be seen from the above, the method proposed in the present application can strictly meet the communication CI constraint, while the prior art only approximately meets the constraint and exceeds the constraint boundary in some cases.

[0112] The technical features of the above embodiments can be combined in any manner, and to make the description concise, not all possible combinations of the technical features in the above embodiments are described, however, as long as the combinations of the technical features do not contradict, they should be considered as falling within the scope of the present application.

[0113] The above embodiments only express several implementation manners of the present application, and the description is specific and detailed, but it should not be understood as a limitation on the protection scope of the present application. It should be pointed out that, for those skilled in the art, some modifications and improvements can be made without departing from the concept of the present application, and all of them belong to the protection scope of the present application.

Claims

1. A MIMO-DFRC waveform design method based on angle CRB optimization, characterized in that, The MIMO-DFRC system employs a centralized deployment of transmit and receive antenna arrays, both of which are uniform linear arrays. The steps include: Establish a model of the radar target echo signal received by the MIMO-DFRC system; Based on the radar target echo signal model, the lower bound of the CRB of the unbiased estimation equation for the point target at the incident angle relative to the two arrays is determined as follows: in, This is the lower bound of the CRB for the unbiased estimating equation. It is the reflectance coefficient of the target. The average noise power, and They represent Directional transmission and reception steering vectors, Let be the incident angle of the point target relative to the two arrays. To transmit an integrated waveform, For waveform vectors, , , , This is the Kronecker product operator. To indicate spatial angular orientation, It is the identity matrix; The communication CI constraint that satisfies the condition that the distance from the noise-free signal to the CI region decision boundary is always greater than 0 is constructed as follows: in, i For communication user ID ， ， It is the total number of communication users. ， To take the real part of the complex number, Let be the waveform vector, let , It is the transformed communication channel vector. These are the preset communication service quality indicators. and The expression is: in, For the transmission array and the first q Communication channel vectors between communication users It is the identity matrix The n OK, for , To receive echo signals phase, Kronecker product operator, The minimum threshold distance for receiving signals to the CI area is a preset communication service quality indicator. Establish waveform constant mode constraints; Based on the lower bound of the CRB in the unbiased estimation equation, the communication CI constraint, and the waveform constant modulus constraint, the MIMO radar-communication integrated waveform design problem based on angle estimation CRB optimization is established as follows: in, For waveform vectors, It is the transformed communication channel vector. These are the preset communication service quality indicators. , It is the reflectance coefficient of the target. Let $\mathbf{a}$ be the covariance of the Gaussian white noise matrix. Let be a transformation matrix. This refers to the total number of communication users. Waveform vector The One element, , These represent the number of elements in the transmitting antenna array and the number of sampling points within a radar pulse, respectively. The waveform design problem for integrated MIMO radar communication based on angle estimation CRB optimization is reconstructed based on the idea of ​​obstacle functions. Specifically, this includes: using a logarithmic obstacle function to force the CI constraint to be satisfied throughout the optimization process, transforming the waveform design problem for integrated MIMO radar communication based on angle estimation CRB optimization into a complex circular manifold. The unconstrained problem on the above, the reconstructed MIMO radar-communication integrated waveform design problem based on angle estimation and CRB optimization is: in, For the objective function to be optimized, This represents the penalty parameter for placing the logarithmic barrier function onto the objective function. It is the transformed communication channel vector. These are the preset communication service quality indicators. For waveform vectors, , It is the reflectance coefficient of the target. Let $\mathbf{a}$ be the covariance of the Gaussian white noise matrix. Let be a transformation matrix. This refers to the total number of communication users. Waveform vector The One element, , , These represent the number of elements in the transmitting antenna array and the number of sampling points within a radar pulse, respectively. The Riemann conjugate gradient method is used to optimize and solve a newly constructed MIMO radar-communication integrated waveform design problem based on angle estimation CRB optimization, resulting in an integrated MIMO radar-communication waveform. Specifically, this includes calculating the Euclidean gradient of the objective function, and defining the orthogonal projection of the Euclidean gradient onto the tangent space as the corresponding Riemann gradient: in, For the Riemann gradient, Let be the Euclidean gradient of the objective function. Let be the objective function. Indicates orthographic projection. For waveform vectors, This is the Hadamard product operator; Choose the descent direction and step size; select the negative conjugate gradient direction as the descent direction, and after determining the descent direction, use the backtracking Armijo line search method to search for the step size; specifically, the first... The descent direction of the next iteration is defined as: in, For the first The descent direction of the next iteration These are manually set adjustment parameters. Indicates vector transfer operation, and The first Second and third Waveform vector of the next iteration; Iterative updates of feasible solutions; specifically including: updating the solutions... From tangent space Mapped to the On the complex circular manifold during the next iteration; when the change in the target value with the number of iterations is less than the preset convergence threshold, the iteration stops, and the integrated MIMO radar-communication waveform is obtained.

2. The MIMO-DFRC waveform design method based on angle CRB optimization according to claim 1, characterized in that, The model of the radar target echo signal received by the MIMO-DFRC system is established as follows: in, For radar target echo signals, It is the reflectance coefficient of the target. It is a Gaussian white noise matrix. Let be the incident angle of the point target relative to the two arrays. To transmit an integrated waveform, for The direction of the launch steering vector, , for Directional receiving guide vector, , The number of elements in the transmitting antenna array. This represents the number of elements in the receiving antenna array.

3. The MIMO-DFRC waveform design method based on angle CRB optimization according to claim 1, characterized in that, The constant modulus constraint of the waveform is: in, Waveform vector The One element, , These represent the number of elements in the transmitting antenna array and the number of sampling points within a radar pulse, respectively.

4. The MIMO-DFRC waveform design method based on angle CRB optimization according to claim 1, characterized in that, The solution From tangent space Mapped to the On the complex circular manifold at the next iteration, specifically: in, For tangent space The waveform vector obtained from the above solution. , , They are respectively The 1st, 2nd, and 3rd One element, This is a mapping operation, indicating that the waveform in the tangent space is mapped onto the complex circular manifold. Let be the waveform vector obtained from the solution on the complex circular manifold. , These represent the number of elements in the transmitting antenna array and the number of sampling points within a radar pulse, respectively.

Images