Local mismatched filter design based on radar communication integrated waveform

Abstract

The invention relates to a local mismatched filter design based on a radar communication integrated waveform. The local mismatched filter design comprises the following steps: acquiring M discrete transmitted waveform vectors planned to be transmitted within a coherent processing interval; constructing a weighted summation optimization problem model based on the M transmitted waveform vectors; carrying out iterative solution on the optimization problem model by adopting an alternating direction multiplier method, and outputting M local mismatched filter coefficient vectors; wherein the M local mismatched filter coefficient vectors are respectively matched with the M discrete transmitted waveforms, and are used for carrying out filtering processing on the received echo signal at a receiving end of the radar communication integrated system so as to suppress distance sidelobe modulation and improve the moving target detection performance. The method can be applied to receiving end processing, the RSM effect can be fundamentally suppressed, clutter responses of different pulses can be effectively aligned and cancelled in cancellation processing, and therefore the moving target detection capacity of a system under the strong clutter background is remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of radar systems and wireless communication technology, specifically relating to the design of a local mismatch filter based on an integrated radar-communication waveform. Background Technology

[0002] Integrated Radar and Communications (IRAC) systems, by sharing hardware platforms and spectrum resources, can effectively alleviate the increasingly tense problem of spectrum conflicts and help reduce system costs in terms of size, weight, and power consumption. Therefore, IRAC technology shows great application potential in fields with urgent needs for the fusion of sensing and communication, such as 5G and future 6G mobile communication base stations, autonomous driving, and drone swarms. To improve system resource utilization, a core research direction is to design transmission waveforms that can simultaneously carry out radar detection and wireless communication functions.

[0003] However, IRAC systems face a unique technical challenge in practical applications: Range Sidelobe Modulation (RSM). To improve communication data rates, the IRAC transmit waveform typically changes dynamically with the transmitted communication information. At the radar receiver, to detect moving targets, matched filtering is usually applied to the received waveform. Subsequently, techniques such as Moving Target Indication (MTI) are used to cancel clutter in the matched filter output of continuous pulses, suppressing stationary clutter and highlighting moving targets. However, due to the differences in transmit waveforms between different pulses, the outputs of their respective matched filters exhibit different range sidelobe structures, i.e., the RSM phenomenon. This inconsistency in output structure severely disrupts the coherence upon which clutter cancellation processing depends, leading to a significant decrease in clutter suppression performance and an increase in residual clutter energy after MTI processing, thereby deteriorating the detection performance of moving targets.

[0004] To mitigate the performance degradation caused by RSM within a coherent processing interval, researchers have proposed various design methods for mismatched filters. Early least-squares (LS) methods aimed to design filters whose outputs approximate the desired low sidelobe response to reduce sidelobe levels. To further improve the similarity between the outputs of different filters, the joint least-squares (JLS) method iteratively approximates the average output of all filters. To balance sidelobe suppression and output similarity with signal-to-noise ratio (SNR) loss, the joint weighted optimization (JWO) method was proposed. This method seeks better overall performance by weightedly optimizing three objectives: sidelobe level, output similarity, and SNR loss.

[0005] However, the aforementioned methods such as LS, JLS, and JWO all design Global Mismatch Filters (GMMFs). GMMF design focuses on the filter output across the entire transmit waveform pulse width, thus failing to fully utilize design freedom to some extent. More importantly, in demanding scenarios with low signal-to-clutter-plus-noise ratios (SCNR), the clutter cancellation performance of GMMFs still has significant room for improvement. Therefore, designing a filter that can more effectively suppress RSM, especially significantly improving clutter suppression and target detection performance under low SCNR conditions, has become a pressing technical problem to be solved in this field. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention provides a local mismatch filter design based on an integrated radar-communication waveform. The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a local mismatch filter design based on radar-communication integrated waveforms, including: Obtain the M discrete transmit waveform vectors planned to be transmitted by the radar-communication integrated system within a coherent processing interval; Based on the M transmitted waveform vectors, a weighted summation optimization problem model is constructed with the joint optimization objectives of minimizing the sidelobe level of the local mismatch filter output, the similarity of the filter outputs between different waveforms, and the signal-to-noise ratio loss. The optimization problem model is solved iteratively using the alternating direction multiplier method, outputting M local mismatch filter coefficient vectors; The M local mismatch filter coefficient vectors are respectively matched with the M discrete transmitted waveforms, and are used to filter the received echo signals at the receiving end of the radar-communication integrated system to suppress range sidelobe modulation and improve the moving target detection performance.

[0007] Compared with the prior art, the beneficial effects of the present invention are as follows: To address the problem in existing radar-communication integrated systems where inconsistent sidelobe structures in matched filters due to variations in transmitted waveforms with communication information significantly degrade the clutter cancellation performance of traditional global mismatch filters under low signal-to-noise ratio (SNR) conditions, this invention provides a local mismatch filter design based on radar-communication integrated waveforms. First, all waveform vectors planned for transmission within a coherent processing interval are obtained. Then, a weighted summation optimization model is constructed with the joint optimization objectives of minimizing filter output sidelobe levels, maximizing the similarity of filter outputs between different waveforms, and minimizing SNR loss. Finally, the alternating direction multiplier method is used to efficiently solve this model, ultimately outputting a set of local mismatch filter coefficient vectors corresponding one-to-one with each transmitted waveform. Through this approach, this invention can design a filter bank with low sidelobes, high output consistency, and controllable SNR loss. Applying this filter to receiver processing can fundamentally suppress the RSM effect, enabling effective alignment and cancellation of clutter responses from different pulses during cancellation processing, thereby significantly improving the system's moving target detection capability in strong clutter backgrounds. Attached Figure Description

[0008] Figure 1 This is a schematic flowchart of the design of a local mismatch filter based on an integrated radar-communication waveform provided in an embodiment of the present invention; Figure 2 This is a model diagram of an integrated radar and communication system provided in an embodiment of the present invention; Figure 3 This is a simulation diagram of the filter output within the maximum time delay when processing using the MF method according to an embodiment of the present invention; Figure 4 This is a simulation diagram of the filter output within the maximum time delay when processing using the LS method according to an embodiment of the present invention; Figure 5 This is a simulation diagram of the filter output within the maximum time delay when processing using the JLS method according to an embodiment of the present invention; Figure 6 This is a simulation diagram of the filter output within the maximum time delay when processing using the JWO method according to an embodiment of the present invention; Figure 7 This is a simulation diagram of the filter output within the maximum time delay when processed using the method proposed in this invention, as provided in an embodiment of the invention. Figure 8 This is the input provided in the embodiments of the present invention. The graph shows the relationship between the output SCNR and the input signal-to-noise ratio. Detailed Implementation

[0009] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0010] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0011] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, disclosure, and appended claims in carrying out the claimed invention. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0012] The following is a detailed description of the local mismatch filter design based on the integrated radar-communication waveform proposed in this invention, with reference to the accompanying drawings.

[0013] Figure 1 This is a schematic flowchart illustrating the design of a local mismatch filter based on an integrated radar-communication waveform, as provided in an embodiment of the present invention. Figure 1 As shown, the method includes steps 110-130; specifically: S110: Acquire M discrete transmission waveform vectors that the radar-communication integrated system plans to transmit within a coherent processing interval.

[0014] Here, using Figure 2The system acquires M discrete transmitted waveform vectors; here, the coherent processing interval refers to a continuous period of time during which the waveform sequence (i.e., the M discrete transmitted waveform vectors) that the radar is scheduled to transmit is usually known or predictable (e.g., determined by the communication protocol and radar scheduling).

[0015] S120: Based on M transmitted waveform vectors, a weighted summation optimization problem model is constructed with the joint optimization objectives of minimizing the sidelobe level of the local mismatch filter output, maximizing the similarity of the filter outputs between different waveforms, and minimizing the signal-to-noise ratio loss.

[0016] In one possible implementation, the computational expression for the optimization problem model is: ; ; ; ; in, , and It is an adjustable non-negative weighting factor. ; The sidelobe level of the filter that has the largest difference between its actual output and the output response vector of the corresponding desired low-sidelobe filter among all filters corresponding to M discrete transmit waveform vectors is characterized. Characterizes the average difference between filter outputs for different waveforms. Characterizing the SNR loss within the coherent processing interval, , and They are respectively , and Normalization factor under mismatched filtering conditions , represents the local mismatch filter coefficient vector corresponding to the m-th transmitted waveform. It is the m-th discrete transmitted waveform vector. Let represent the set of M local mismatch filter coefficient vectors. It is to utilize The constructed convolution matrix, It is the desired low-sidelobe filter output response vector. express Norm, express The square of the norm.

[0017] For example*, The optimization problem model does not consider and In the case of mismatched filtering, The minimum value; The optimization problem model does not consider and In the case of mismatched filtering, The minimum value; The optimization problem model does not consider and In the case of mismatched filtering, The minimum value.

[0018] here, This refers to the desired low-sidelobe filter output response vector, specifically the ideal impulse response where the main lobe position is 1 and the sidelobe region is 0. Furthermore, Defined as: ;in This indicates a null trap, which is close to zero. yes The sampling of the main lobe, and yes The number of samples within the main lobe.

[0019] Here, the constructed optimization problem model needs to make Minimize, where The maximum value criterion is adopted to strictly control the sidelobe performance under the worst case, ensuring that the low sidelobe requirement can be met under all waveforms. By minimizing the differences in output responses between all waveform pairs, the output structures of different filters are forced to be highly similar, thus creating favorable conditions for subsequent clutter cancellation processing (such as MTI).

[0020] Here, for The derivation process is briefly described below. Specifically, its definition and derivation are based on the following analysis: (1) The matched filter (MF) is the optimal linear filter in a radar system, and its coefficients are the conjugate of the transmitted waveform (for...). Its corresponding matched filter is It can achieve the maximum output signal-to-noise ratio against an additive white Gaussian noise background.

[0021] (2) The mismatch filter (MMF) intentionally deviates from this optimal criterion, and exchanges a certain amount of SNR loss for improvements in other performance such as sidelobe suppression and waveform consistency.

[0022] Here, for the m-th discrete transmitted waveform vector, the output signal-to-noise ratios after matched filtering and mismatch filtering are respectively: ; in, It is the variance of Gaussian white noise. It refers to the conjugate transpose. It refers to Take the conjugate transpose.

[0023] Therefore, the SNR loss after mismatch filtering corresponding to the m-th discrete transmitted waveform vector is: .

[0024] Assuming that all transmitted waveforms within the coherent processing interval have unit energy, i.e. and impose constraints This ensures that each filter has a consistent unity gain at the target main lobe. Under this condition, the SNR loss simplifies to: .

[0025] Finally, the average SNR loss within the coherent processing interval is defined as the average of this loss across all waveforms, hence: .

[0026] Here, the purpose of normalization is to eliminate the order-of-magnitude differences among the three objective functions caused by their different physical meanings and dimensions, so that the weighted summation... It has practical optimization significance, and the weighting factors can directly reflect the relative importance attached to each objective.

[0027] S130: The optimization problem model is solved iteratively using the alternating direction multiplier method, and M local mismatch filter coefficient vectors are output. The M local mismatch filter coefficient vectors are matched with M discrete transmitted waveforms, which are used to filter the received echo signal at the receiver of the radar-communication integrated system to suppress range sidelobe modulation and improve the moving target detection performance.

[0028] Here, we first introduce the working principle of the Alternating Direction Multiplier Method (ADMM). For the joint optimization problem constructed in this invention, which simultaneously involves multiple competing objectives (low sidelobes, high similarity, low SNR loss) and complex coupling relationships, direct solution is extremely difficult. ADMM transforms this "large and difficult" problem into a series of "small and simple" subproblems through the following three key ideas: (1) Decomposition (Introduction of Auxiliary Variables and Decoupling): First, by introducing auxiliary variables, the intertwined optimization objectives in the original problem are separated. In this invention, this is manifested in assigning optimization tasks of different aspects, such as the filter's output response and the filter coefficients themselves, to different sets of auxiliary variables. Simultaneously, equality constraints are added to ensure that these variables ultimately remain consistent with the original variables. This step achieves the "decoupling" of the problem.

[0029] (2) Alternating Solution (Handling Simplified Subproblems): Subsequently, the algorithm fixes all other variables and optimizes only a specific set of variables. Since the problem has been decoupled, the form of the subproblem to be solved becomes very simple (e.g., it becomes a quadratic programming problem or can be solved directly through thresholding), resulting in high computational efficiency and often yielding closed-form solutions. The algorithm alternately updates all variable sets in a predetermined order (e.g., first updating filter coefficients, then updating auxiliary variables, and finally updating coordination parameters).

[0030] (3) Coordination (Dual Variable Update and Convergence): During the alternating solution process, the relationship between each set of variables is coordinated through dual variables, forcing them to eventually satisfy the equality constraints introduced during decomposition (i.e., ensuring the consistency of the solution). The algorithm determines whether it has converged to the global optimum by monitoring the degree of constraint violation (original residual) and the stability of the solution (dual residual).

[0031] Based on this, S130 includes: using auxiliary variables to transform the optimization problem model into an equivalent form with equality constraints to decouple the coefficient vectors of the M local mismatched filters; introducing corresponding dual variables for the equivalent form and constructing an augmented Lagrangian function containing the dual variables; iteratively updating the filter coefficient vectors, auxiliary variables, and dual variables alternately to minimize the augmented Lagrangian function; stopping the iteration when the preset convergence condition is met, and outputting the updated filter coefficient vectors as the coefficient vectors of the M local mismatched filters.

[0032] For example, in the original optimization problem model, there are three objective functions. , and Both depend on the same set of variables Specifically: (1) Including the max operator, it is necessary to apply to all The corresponding outputs are compared, and the worst one is selected for optimization, which makes all Updates are mutually restrictive.

[0033] (2) Includes double summation, directly measuring any two distinct... The differences between the corresponding outputs cause all The two are closely related.

[0034] (3) Although it is a simple summation form, it is similar to... and Shared variables .

[0035] In the above cases, directly solving such coupled problems has high computational complexity and makes it difficult to take advantage of parallel computing or closed-loop solutions.

[0036] Auxiliary variables are introduced here ( and This transforms the optimization problem model into an equivalent form with equality constraints. In one possible implementation, this equivalent form is expressed as: ; in and .

[0037] In this equivalent form, a penalty parameter is introduced. and dual variables , The augmented Lagrange function can be expressed as: .

[0038] Here, the alternating iterative updates are performed in the following order in each iteration: 1) Fix the auxiliary and dual variables, and update the filter coefficient vector; 2) Fix the updated filter coefficient vector and dual variable from step 1), and update the auxiliary variable; 3) Fix the updated filter coefficient vector and auxiliary variables from steps 1) and 2), and update the dual variables.

[0039] For example, based on the ADMM framework, updates are performed through the following alternating iterations. , , and .

[0040] ; ; .

[0041] Where k refers to the kth iteration and k+1 refers to the (k+1)th iteration.

[0042] when , and Given the above expression, it is equivalent to: ; in , .

[0043] make , and Further simplified to: ; in, , , and , Indicates that all elements are 1 vector.

[0044] Based on this, the corresponding optimal solution is: ; It is obtained through the Lagrange multiplier method, where It is a Lagrange multiplier vector.

[0045] when and Given the condition, the optimal solution is equivalent to: ; in, .

[0046] Based on this, we can obtain The solution is: .

[0047] Will Substituting the solution back into the original expression, we get: ;in, .

[0048] make for No. Small elements, in the above formula The feasible domain can be divided into a range, that is In the m-th interval , Simplified to: .

[0049] right Differentiation yields: ;make We can obtain: .

[0050] Based on the above formula, it can be seen that, It is a monotonically increasing function, therefore In the each interval The optimal solution within is: .

[0051] according to and The formula for expressing this is: ; and, .

[0052] Then, using the given expression formula... , and renew .

[0053] Here, the preset convergence condition is: The number of iterations reaches the preset maximum value, or the original residual is less than the first threshold and the dual residual is less than the second threshold at the same time. The original residual is calculated based on the equality constraints in the equivalent form, while the dual residual is calculated based on the iterative changes of the filter coefficient vector.

[0054] For example, let Repeat the above steps until the maximum number of iterations is reached. or ,in It is a threshold.

[0055] For clarity, the algorithm flow of the proposed S130 is summarized in Table 1 below.

[0056] Table 1

[0057] It should be noted that, in actual implementation, the filter coefficient vector Auxiliary and dual variables can be initialized as zero vectors or based on prior knowledge (e.g., matched filter coefficients). It should be understood that the initialization method does not affect the final convergence result of the algorithm.

[0058] It should be noted that M local mismatch filter coefficient vectors are matched to M transmitted waveform vectors; at the receiving end, each echo pulse is filtered using its corresponding, specially designed LMMF coefficients. Since this set of filters is the product of joint optimization, the main lobe (target information) of its output signal is preserved, while the side lobes are suppressed and structurally highly consistent. Therefore, in subsequent clutter cancellation processing, the response of stationary clutter (mainly present in the side lobes) can be almost perfectly canceled due to the consistent structure, thereby significantly suppressing RSM and greatly improving the detectability of moving targets in clutter backgrounds.

[0059] To address the problem in existing radar-communication integrated systems where inconsistent sidelobe structures in matched filters due to variations in transmitted waveforms with communication information significantly degrade the clutter cancellation performance of traditional global mismatch filters under low signal-to-noise ratio (SNR) conditions, this invention provides a local mismatch filter design based on radar-communication integrated waveforms. First, all waveform vectors planned for transmission within a coherent processing interval are obtained. Then, a weighted summation optimization model is constructed with the joint optimization objectives of minimizing filter output sidelobe levels, maximizing the similarity of filter outputs between different waveforms, and minimizing SNR loss. Finally, the alternating direction multiplier method is used to efficiently solve this model, ultimately outputting a set of local mismatch filter coefficient vectors corresponding one-to-one with each transmitted waveform. Through this approach, this invention can design a filter bank with low sidelobes, high output consistency, and controllable SNR loss. Applying this filter to receiver processing can fundamentally suppress the RSM effect, enabling effective alignment and cancellation of clutter responses from different pulses during cancellation processing, thereby significantly improving the system's moving target detection capability in strong clutter backgrounds.

[0060] The effects of the present invention will be further illustrated below through simulation.

[0061] 1. Simulation conditions: The simulation of this invention was performed in the MATLAB R2020a software environment.

[0062] 2. Simulation content: Simulation results validated the effectiveness of the designed method.

[0063] Several numerical results are presented to verify the performance of the proposed method. Consider an IRAC system that transmits three Orthogonal Frequency Division Multiplexing (OFDM) waveforms in the CPI. The center frequency is 3 GHz, the waveform repetition interval is 80 µs, the waveform width is 20 µs, each OFDM waveform has 128 subcarriers, and Quadrature Phase Shift Keying (QPSK) modulation is used. The subcarrier spacing is 62.5 kHz, and the cyclic prefix is ​​[missing value] times the effective symbol length. The target is located 1 km away at a speed of 20 m / s. Clutter is distributed at distance intervals. The above follows a Rayleigh distribution with a maximum time lag of 10µs. , , 1000 Monte Carlo experiments were performed to generate different QPSK symbols, noise, and clutter.

[0064] In the following simulations, the proposed method is compared with MF, LS, JLS and JWO.

[0065] To measure the SLL of the filter output, the Average Sidelobe Level (ASLL) is introduced, which is defined as: ; in and It is the output of the m-th filter. The peak value of the main lobe and the average level of the side lobes.

[0066] To evaluate the similarity of filter outputs, an average error (AE) is introduced, which is defined as: ; in , is the average value of the filter output.

[0067] Figure 3 This is a simulation diagram of the filter output within the maximum time delay when processing using the MF method according to an embodiment of the present invention. Figure 4 This is a simulation diagram of the filter output within the maximum time delay when using the LS method for processing, as provided in the embodiments of the present invention. Figure 5 This is a simulation diagram of the filter output within the maximum time delay when processing using the JLS method according to an embodiment of the present invention. Figure 6 This is a simulation diagram of the filter output within the maximum time delay when processing using the JWO method according to an embodiment of the present invention. Figure 7 This is a simulation diagram of the filter output within the maximum time delay when processed using the method proposed in this invention, as provided in an embodiment of the invention. Furthermore, the corresponding ASLL, AE, and SNR losses are given in Table 2. Figure 3-7 In the simulation, the waveforms planned to be transmitted by the radar-communication integrated system are represented by waveforms. Waveforms 1, 2, and 3 represent the three orthogonal frequency division multiplexing waveforms in the simulation conditions. Different methods have different filter outputs.

[0068] And in Table 2 Figure 3-7 The output was evaluated. In Table 2, compared to other methods, the proposed LMMF design method has the lowest ASLL and AE. Furthermore, in terms of SNR loss, it outperforms the LS and JLS methods, but is slightly inferior to the JWO method.

[0069] exist Figure 8 The text provides information on input... The relationship between the output signal-to-noise ratio (SCNR) and the input signal-to-noise ratio (SCR) after MTI processing. Figure 4Among other methods, the proposed method achieves the highest output SCNR, indicating that it has the best clutter cancellation performance. Furthermore, at low input SCR, this method significantly outperforms other methods in terms of output SNR; however, the performance improvement decreases as the input SCR increases.

[0070] Table 2

[0071] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A local mismatch filter design based on radar-communication integrated waveform, characterized in that, include: Obtain the M discrete transmit waveform vectors planned to be transmitted by the radar-communication integrated system within a coherent processing interval; Based on the M transmitted waveform vectors, a weighted summation optimization problem model is constructed with the joint optimization objectives of minimizing the sidelobe level of the local mismatch filter output, the similarity of the filter outputs between different waveforms, and the signal-to-noise ratio loss. The optimization problem model is solved iteratively using the alternating direction multiplier method, outputting M local mismatch filter coefficient vectors; The M local mismatch filter coefficient vectors are respectively matched with the M discrete transmitted waveforms, and are used to filter the received echo signals at the receiving end of the radar-communication integrated system to suppress range sidelobe modulation and improve the moving target detection performance.

2. The local mismatch filter design based on radar-communication integrated waveform according to claim 1, characterized in that, The computational expression for the optimization problem model is: ； ； ； ； in, , and It is an adjustable non-negative weighting factor. ; Characterizes the maximum difference between the actual output and the corresponding desired low-sidelobe filter output response vector among all filters corresponding to the M discrete transmitted waveform vectors. This characterizes the average difference between the filter outputs of the different waveforms. Characterizing the SNR loss within the coherent processing interval, , and They are respectively , and Normalization factor under mismatched filtering conditions , represents the local mismatch filter coefficient vector corresponding to the m-th transmitted waveform. It is the m-th discrete transmitted waveform vector. , representing the vector of coefficients of the M local mismatched filters. It is using the above The constructed convolution matrix, It is the desired low-sidelobe filter output response vector. express Norm, express The square of the norm.

3. The design of a local mismatch filter based on an integrated radar-communication waveform according to claim 2, characterized in that, The desired low sidelobe filter output response vector refers to the ideal impulse response with the main lobe position at 1 and the sidelobe region at 0.

4. The design of a local mismatch filter based on an integrated radar-communication waveform according to claim 2, characterized in that, The optimization problem model is iteratively solved using the alternating direction multiplier method, outputting M local mismatch filter coefficient vectors, including: By using auxiliary variables, the optimization problem model is transformed into an equivalent form with equality constraints, thereby decoupling the coefficient vectors of the M local mismatched filters. For the equivalent form, a corresponding dual variable is introduced, and an augmented Lagrangian function containing the dual variable is constructed. The filter coefficient vector, the auxiliary variable, and the dual variable are alternately and iteratively updated to minimize the augmented Lagrangian function; When the preset convergence condition is met, the iteration stops, and the updated filter coefficient vector is output as the M local mismatch filter coefficient vectors.

5. The design of a local mismatch filter based on an integrated radar-communication waveform according to claim 4, characterized in that, The alternating iterative updates are performed in the following order in each iteration: 1) Fix the auxiliary variable and the dual variable, and update the filter coefficient vector; 2) Fix the updated filter coefficient vector and the dual variable from step 1), and update the auxiliary variable; 3) Fix the updated filter coefficient vector and the auxiliary variable in steps 1) and 2) and update the dual variable.

6. The design of a local mismatch filter based on an integrated radar-communication waveform according to claim 4, characterized in that, The preset convergence condition is: The number of iterations reaches the preset maximum value, or the original residual is less than the first threshold and the dual residual is less than the second threshold at the same time. The original residual is calculated based on the equality constraints in the equivalent form, and the dual residual is calculated based on the iterative changes of the filter coefficient vector.

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