Method and device for joint transmission and reception against spectrum dispersion interference based on Riemann element optimization

Abstract

A method and device for joint anti-spectral dispersion interference of transmission and reception based on Riemann element optimization, including taking the integral level of the spectrum dispersion interference component and the integral sidelobe level of the target component as the optimization target, considering the waveform constant modulus constraint, the receiving filter energy constraint and the non-matching filter peak loss constraint, establishing a joint constraint optimization model for anti-spectral dispersion interference; establishing a Riemann element optimization model for radar transmission waveform optimization and a Riemann element optimization model for receiving filter optimization to achieve synchronous update of radar transmission waveform and receiving filter; initializing radar transmission waveform, initializing receiving filter, updating radar transmission waveform and receiving filter by using a meta optimizer based on a forward transfer algorithm, updating meta optimizer model parameters based on a backward transfer algorithm until convergence, and outputting the current radar transmission waveform and receiving filter. The present invention can achieve effective suppression of SMSP and has a faster convergence rate.

Description

Technical Field

[0001] This invention mainly relates to the field of radar active jamming technology, and in particular to a transceiver joint anti-spectrum dispersion jamming method and device based on Riemannian optimization. Background Technology

[0002] Smeared Spectrum (SMSP) jamming is a type of intra-pulse active coherent jamming. In practice, an SMSP jammer first intercepts the radar transmit waveform of an enemy radar system. After downsampling and copying the delayed signal, it generates jamming components, which are then forwarded. Because the SMSP components are strongly correlated with the radar transmit waveform, after matched filtering at the receiver, the jamming components generate a large number of false targets, thus affecting the detection of real targets.

[0003] Extensive research and significant achievements have been made by scholars both domestically and internationally regarding the suppression of SMSP (Small Target Sparingly Phenomena). These methods can be broadly categorized into two types based on their processing mechanisms: passive jamming suppression methods and active jamming suppression methods. Passive jamming suppression methods primarily involve reconstructing the jamming signal based on estimated jamming parameters and then using cancellation strategies to eliminate the influence of false targets on real targets. Active jamming suppression methods, on the other hand, involve the radar system adaptively adjusting its transmission and reception parameters according to environmental parameters before the jamming signal reaches the receiver, actively reducing the system's response to the jamming signal and minimizing the entry of jamming energy into the radar receiver. Summary of the Invention

[0004] To address the joint design problem of radar transmit waveforms and receive filters under SMSP (Signal Scattering Multiplier) conditions, and considering the limitations of receiver-side adaptive signal processing and transmitter-side waveform optimization methods in terms of SMSP resistance, as well as the low efficiency of classical iterative algorithms, this invention proposes a joint transmit-receive anti-scattering interference method and device based on Riemannian optimization. Specifically, it is a solution method for radar transmit waveforms and receive filters based on Riemannian optimization. By using a meta-learning method to simultaneously update the radar transmit waveform and receive filters, it achieves better waveform convergence performance and interference suppression performance.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] On the one hand, this invention provides a joint transmit / receive anti-spectrum dispersion interference method based on Riemannian optimization, comprising:

[0007] With the optimization objective of minimizing the integral level of the spectral dispersion interference component and the integral sidelobe level of the target component, and considering waveform constant mode constraints, receiver filter energy constraints, and unmatched filter peak loss constraints, a joint constraint optimization model for resisting spectral dispersion interference is established.

[0008] Riemannian optimization models for radar transmit waveform optimization and receive filter optimization are established to achieve synchronous updates of radar transmit waveform and receive filter.

[0009] Initialize the radar transmit waveform and the receive filter. Update the radar transmit waveform and the receive filter using the meta-optimizer based on the forward pass algorithm. Update the meta-optimizer model parameters based on the backward pass algorithm until convergence, and output the current radar transmit waveform and the receive filter.

[0010] On the other hand, the present invention provides a transceiver joint anti-spectrum dispersion interference device based on Riemannian optimization, comprising:

[0011] The first module is used to establish a joint constraint optimization model for resisting spectrum dispersion interference, with the optimization objective of minimizing the integral level of the spectrum dispersion interference component and the integral sidelobe level of the target component, while considering waveform constant mode constraints, receiving filter energy constraints and unmatched filter peak loss constraints.

[0012] The second module is used to establish Riemannian optimization models for radar transmit waveform optimization and receive filter optimization, so as to achieve synchronous updates of radar transmit waveform and receive filter.

[0013] The third module is used to initialize the radar transmit waveform and the receive filter. Based on the forward pass algorithm, the meta-optimizer is used to update the radar transmit waveform and the receive filter. Based on the backward pass algorithm, the meta-optimizer model parameters are updated until convergence, and the current radar transmit waveform and receive filter are output.

[0014] On the other hand, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0015] With the optimization objective of minimizing the integral level of the spectral dispersion interference component and the integral sidelobe level of the target component, and considering waveform constant mode constraints, receiver filter energy constraints, and unmatched filter peak loss constraints, a joint constraint optimization model for resisting spectral dispersion interference is established.

[0016] Riemannian optimization models for radar transmit waveform optimization and receive filter optimization are established to achieve synchronous updates of radar transmit waveform and receive filter.

[0017] Initialize the radar transmit waveform and the receive filter. Update the radar transmit waveform and the receive filter using the meta-optimizer based on the forward pass algorithm. Update the meta-optimizer model parameters based on the backward pass algorithm until convergence, and output the current radar transmit waveform and the receive filter.

[0018] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, performs the following steps:

[0019] With the optimization objective of minimizing the integral level of the spectral dispersion interference component and the integral sidelobe level of the target component, and considering waveform constant mode constraints, receiver filter energy constraints, and unmatched filter peak loss constraints, a joint constraint optimization model for resisting spectral dispersion interference is established.

[0020] Riemannian optimization models for radar transmit waveform optimization and receive filter optimization are established to achieve synchronous updates of radar transmit waveform and receive filter.

[0021] Initialize the radar transmit waveform and the receive filter. Update the radar transmit waveform and the receive filter using the meta-optimizer based on the forward pass algorithm. Update the meta-optimizer model parameters based on the backward pass algorithm until convergence, and output the current radar transmit waveform and the receive filter.

[0022] To further enhance the freedom of active anti-interference and improve interference suppression performance, this invention proposes a transceiver joint anti-spectrum dispersion interference method and device based on Riemannian optimization.

[0023] Under the background of SMSP suppression, this invention aims to minimize the integral level of the interference component and the integral sidelobe level of the target component, while simultaneously considering minimizing the peak loss of the unmatched filter, waveform constant mode constraints, and receiver filter energy constraints, to establish a joint constraint optimization model for resisting spectrum dispersion interference. A joint optimization model solution method based on Riemannian optimization is proposed to achieve synchronous updates of the radar transmit waveform and the receiver filter until convergence, outputting the current radar transmit waveform and the unmatched filter used by the radar receiver.

[0024] Compared with the prior art, the technical effects of the present invention are as follows:

[0025] First, it offers a high degree of optimization freedom. Traditional anti-SMSP methods only utilize one degree of freedom at the transmitting or receiving end, while this invention employs a method of joint optimization of the radar transmit waveform and the receiving filter, improving the waveform's anti-interference performance and the algorithm's operating efficiency.

[0026] Second, this invention achieves simultaneous iteration of the radar transmit waveform and the receive filter. For joint optimization problems, the classic solution method employs an alternating optimization strategy, where one variable is fixed while the other is optimized, and this alternation continues until convergence. To address this problem, this invention introduces a meta-learning strategy and utilizes the geometric properties of constant modulus constraints and energy constraints to establish a Riemannian meta-optimization model, enabling simultaneous iteration of the radar transmit waveform and the receive filter, as well as adaptive updates to the optimizer.

[0027] Third, it exhibits excellent anti-SMSP performance. This invention proposes a Riemannian optimization method for the joint optimization of radar transmit waveform and receive filter to effectively suppress SMSP. Compared with classical methods, the method proposed in this invention has a faster convergence rate and superior anti-SMSP performance. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0029] Figure 1 This is a flowchart illustrating an embodiment of a joint transmit / receive anti-spectrum dispersion interference method based on Riemannian optimization;

[0030] Figure 2 These are the matched filtering results of the initial random waveform under SMSP interference conditions, where (a) is the matched filtering result of waveform channel 1 and (b) is the matched filtering result of waveform channel 2.

[0031] Figure 3 The diagrams show the unmatched filtering results output by the Riemann optimization method under SMSP interference. (a) shows the matched filtering results of waveform channel 1 after Riemann optimization based on the scheme provided by this invention, and (b) shows the matched filtering results of waveform channel 2 after Riemann optimization based on the scheme provided by this invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0033] Reference Figure 1One embodiment provides a joint transmit / receive anti-spectrum dispersion interference method based on Riemannian optimization, comprising:

[0034] With the optimization objective of minimizing the integral level of the spectral dispersion interference component and the integral sidelobe level of the target component, and considering waveform constant mode constraints, receiver filter energy constraints, and unmatched filter peak loss constraints, a joint constraint optimization model for resisting spectral dispersion interference is established.

[0035] Riemannian optimization models for radar transmit waveform optimization and receive filter optimization are established to achieve synchronous updates of radar transmit waveform and receive filter.

[0036] Initialize the radar transmit waveform and the receive filter. Update the radar transmit waveform and the receive filter using the meta-optimizer based on the forward pass algorithm. Update the meta-optimizer model parameters based on the backward pass algorithm until convergence, and output the current radar transmit waveform and the receive filter.

[0037] In one embodiment, the established joint constraint optimization model for resisting spectrum dispersion interference is as follows:

[0038] in The dimension is The radar transmit waveform and receive filter matrix, This represents the number of time-domain sampling points for the radar transmitted waveform and the filter. Indicates the number of radar channels; These represent the radar transmit waveform and the receive filter of the m-th channel, respectively. They represent the first Radar transmit waveforms and receive filters for each channel; Represents the Fourier transform matrix. and These are preset parameters, and their value range is usually related to the waveform dimension, typically taking the value of [value missing]. , ; , and express , , corresponding Zero-padding results for dimensions; express The nth element; , , These represent the modulo operation, the vector 2 norm, and the Hadamard product, respectively. This indicates the conjugate transpose. Indicates complex conjugation; Indicates constant modulus constraint of waveform; This indicates a constant energy constraint for the filter. This represents the spectral dispersion interference component, and express corresponding The result of zero padding in the dimension, where Let represent the shift matrix for spectral dispersion interference, and Represented as

[0039]

[0040] in, The sub-pulse length represents the spectral dispersion interference. This represents the number of sub-pulses.

[0041] A Riemannian optimization model for radar transmit waveform optimization is established, including:

[0042] make Indicates the number of network updates. To indicate the network layer number, then in the th... Radar transmission waveform in layered network Updated to:

[0043]

[0044] in, This represents the Riemannian optimization model. The shrinkage operator represents the radar transmitted waveform. express At point The Riemann gradient, express middle Values , Values The objective function value, i.e. , Indicates the first Radar transmission waveform in the layer network.

[0045] Because of the constant modulus constraint, the radar transmitted waveform variable always lies within the Riemannian complex circular manifold. Compared to Riemann gradient for:

[0046]

[0047] in, This indicates the operation of taking the real part. Indicates complex conjugation.

[0048] Establish a Riemannian optimization model for receiver filter optimization, including:

[0049] In the During the next network update, the first The receiver filter of the layer network is updated as follows:

[0050]

[0051] in, This represents the Riemannian optimization model. express Compared to The Riemann gradient, Indicates the first The receiving filter of the layer network, This represents the shrinkage operator of the receiving filter. express middle Values The objective function value at time, i.e. .

[0052] Because the constant energy constraint ensures that the receiver filter variables always lie in a Riemannian complex oblique manifold, the Riemann gradient... for:

[0053]

[0054] in, This indicates summing the matrix column by column. This indicates the operation of taking the real part. This indicates that the input column vector will be complex. To form a new two-dimensional matrix, express .

[0055] In one embodiment of the present invention, updating the radar transmit waveform and receive filter using a meta-optimizer based on a forward pass algorithm includes:

[0056] In the The network parameters are updated for the second time. During the layer forward propagation, the radar transmit waveform and the receive filter can be updated successively to

[0057] ;

[0058] ;

[0059] in, and Using LSTM networks as basic units, meta-optimizers are used to update the radar transmit waveform and receive filter, respectively. and Indicates the network number The model parameters of the meta-optimizer at the next update. and Indicates the state of each unit. and This indicates the update amount of the radar transmit waveform and the receive filter.

[0060] Updating the meta-optimizer model parameters based on the backpropagation algorithm includes:

[0061]

[0062] in, and Meta-optimizer and The learning rate express Adam Optimizer and They represent Relative to model parameters and The gradient.

[0063] The radar transmit waveform and receive filter are initialized. The radar transmit waveform and receive filter are updated using a meta-optimizer based on a forward pass algorithm. The meta-optimizer model parameters are updated using a backward pass algorithm until convergence, at which point the current radar transmit waveform and receive filter are output. The method for setting the iterative convergence condition described in this invention is not limited; those skilled in the art can set it based on conventional methods or common knowledge. In a preferred embodiment, the maximum number of iterations can be set as the convergence condition, or the loss function calculated in the current and subsequent iterations can be used. When the difference is less than the set threshold (the set threshold is set based on experience, such as 0.001), the iteration stops and the radar transmit waveform and receive filter are output.

[0064] The transceiver joint anti-spectral dispersion interference method based on Riemannian optimization provided by this invention is further illustrated by the following numerical simulation experiments:

[0065] Experimental scenario:

[0066] The following experiments were conducted on a computer (2.30GHz i7-12700H kernel, 40.0GB RAM) using PyTorch version 2.2.2. The experiments considered a two-channel radar system with a radar waveform time-domain width of 20µs and a sampling rate of 50MHz. The jammer downsampled the radar waveform. The value is set to 4, the sub-pulse width of the interference component is 250, and the preset parameter values ​​are set to... , For the meta-optimizer, it is configured as a two-layer LSTM network, each layer containing 500 hidden units, and the learning rate of the Adam optimizer is set to 0.0001. The output loss function is then used for the previous two iterations. The algorithm stops running when the error is less than 0.0001, and outputs the optimized radar transmit waveform and receive filter.

[0067] Experimental steps:

[0068] (1) Problem Model: The optimization objective is to minimize the integral level of the spectral dispersion interference component and the integral sidelobe level of the target component. Simultaneously considering waveform constant mode constraints, receiver filter energy constraints, and unmatched filter peak loss constraints, a joint constraint optimization model for resisting spectral dispersion interference is established. Initialize the radar transmit waveform and initialize the receiver filter;

[0069] (2) Establish a Riemannian optimization model for radar transmit waveform optimization and a Riemannian optimization model for receiver filter optimization, so as to realize the synchronous update of radar transmit waveform and receiver filter.

[0070] (3) The radar transmit waveform and receive filter are updated using the meta-optimizer based on the forward pass algorithm, and the meta-optimizer model parameters are updated based on the backward pass algorithm;

[0071] (4) Repeat step (3) until the convergence condition is met, stop iterating and output the current radar transmit waveform and receive filter.

[0072] The methods for implementing each of the above steps can all be the methods described in any of the foregoing embodiments, and will not be repeated here.

[0073] Figure 2 These are matched filtering results of the initialized random waveform under SMSP interference conditions. (a) shows the matched filtering result for waveform channel 1, and (b) shows the matched filtering result for waveform channel 2. The initialized random waveform has a constant amplitude of 1 and a phase value of... The waveforms are randomly distributed between the channels. Due to the effect of SMSP, false targets appear after matched filtering, and the peak heights of the false targets in the two channels are -2.82dB and -6.41dB respectively, which affects target detection.

[0074] Figure 3The diagram shows the unmatched filtering results output by the Riemann optimization method under SMSP interference. (a) is the matched filtering result of waveform channel 1 after Riemann optimization based on the scheme provided by this invention, and (b) is the matched filtering result of waveform channel 2 after Riemann optimization based on the scheme provided by this invention. In the results, only two peaks appear at the target position, and the highest sidelobe values ​​in the two channels are -14.81dB and -13.33dB, respectively, which effectively suppresses SMSP interference.

[0075] Experimental results show that this invention effectively suppresses SMSP and has significant application value in suppressing active radar cognitive interference.

[0076] In one embodiment, a Riemannian-optimized transceiver joint anti-spectrum dispersion interference device is provided, comprising:

[0077] The first module is used to establish a joint constraint optimization model for resisting spectrum dispersion interference, with the optimization objective of minimizing the integral level of the spectrum dispersion interference component and the integral sidelobe level of the target component, while considering waveform constant mode constraints, receiving filter energy constraints and unmatched filter peak loss constraints.

[0078] The second module is used to establish Riemannian optimization models for radar transmit waveform optimization and receive filter optimization, so as to achieve synchronous updates of radar transmit waveform and receive filter.

[0079] The third module is used to initialize the radar transmit waveform and the receive filter. Based on the forward pass algorithm, the meta-optimizer is used to update the radar transmit waveform and the receive filter. Based on the backward pass algorithm, the meta-optimizer model parameters are updated until convergence, and the current radar transmit waveform and receive filter are output.

[0080] The implementation methods of the above modules and the construction of the model can all adopt the methods described in any of the foregoing embodiments, and will not be repeated here.

[0081] On the other hand, the present invention provides a computer device including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the Riemann-optimized joint transmit-receive anti-spectrum dispersion interference method provided in any of the above embodiments. The computer device may be a server. The computer device includes a processor, a memory, a network interface, and a database connected via a system bus. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database of the computer device stores sample data. The network interface of the computer device is used for communication with external terminals via a network connection.

[0082] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the transceiver joint anti-spectral dispersion interference method based on Riemannian optimization provided in any of the above embodiments.

[0083] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0084] Matters not covered in this invention are common knowledge.

[0085] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0086] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0087] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for joint transmission and reception anti-spectral dispersion interference based on Riemann element optimization, characterized in that: include: Taking minimizing the integral level of the spectrum dispersion interference component and the integral sidelobe level of the target component as the optimization goal, while considering the waveform constant modulus constraint, the receiving filter energy constraint and the non-matching filter peak loss constraint, a joint constrained optimization model for resisting spectrum dispersion interference is established as follows: ； in The dimension is Radar transmit waveform and receive filter matrix, is the radar transmission waveform and the number of time domain sampling points of the receiving filter, Indicates the number of radar channels; They represent the radar transmit waveform and receive filter of the mth channel respectively; Respectively represent Radar transmit waveform and receive filter for each channel; represents the Fourier transform matrix, and is the preset parameter; , and express , , Corresponding The zero-padding result of the dimension; express The nth element; , , They represent the modulo operation, the vector two-norm, and the Hadamard product, respectively. represents the conjugate transpose, represents complex conjugate; represents the waveform constant modulus constraint; represents the filter constant energy constraint; represents the spectral dispersion interference component, and express Corresponding The zero-fill result of dimension, where represents the shift matrix of spectral dispersive interference, and Expressed as ； in, represents the sub-pulse length of the spectral dispersive interference, is the number of sub-pulses; A Riemann element optimization model for radar transmit waveform optimization and a Riemann element optimization model for receive filter optimization are established to achieve synchronous update of radar transmit waveform and receive filter. The Riemann element optimization model for radar transmit waveform optimization includes: make Indicates the number of network updates. Represents the number of network layers, then in the Radar transmission waveform in layer network Updated to: ； in, represents the Riemann meta-optimization model, represents the shrinkage operator of the radar transmit waveform, express At the point The Riemann gradient of express middle The value is , The value is The objective function value of , Indicates Radar transmission waveform in layer network; A Riemann element optimization model for receive filter optimization is established, including: In the When the network is updated, The receiving filter of the layer network is updated as: ； in, represents the Riemann meta-optimization model, express Relative to The Riemann gradient of Indicates The receiving filter of the layer network, represents the shrinkage operator of the receive filter, express middle The value is The objective function value when ; Initialize the radar transmit waveform, initialize the receive filter, update the radar transmit waveform and receive filter using the meta-optimizer based on the forward transfer algorithm, update the meta-optimizer model parameters based on the backward transfer algorithm until convergence, and output the current radar transmit waveform and receive filter.

2. The method for jointly resisting spectrum dispersion interference of transmission and reception based on Riemann element optimization according to claim 1 is characterized in that: Due to the waveform constant modulus constraint, the radar transmission waveform variable is always in the Riemann complex circular manifold. Relative to The Riemann gradient for: ； in, represents the real part operation, represents complex conjugate.

3. The method for jointly resisting spectrum dispersion interference of transmission and reception based on Riemann element optimization according to claim 2 is characterized in that: Due to the constant energy constraint, the receiving filter variable is always on the Riemann complex oblique manifold. for: ； in, It means to sum the columns of the matrix. represents the real part operation, Indicates that the input column vector is complex valued to form a new two-dimensional matrix, express The complex conjugate of .

4. The method for jointly resisting spectrum dispersion interference of transmission and reception based on Riemann element optimization according to claim 3 is characterized in that: The radar transmit waveform and receive filter are updated using a meta-optimizer based on a forward pass algorithm, including: In the Update network parameters, During the forward transmission process, the radar transmission waveform and the receiving filter can be updated successively as ； ； in, and The LSTM network is used as the basic unit to update the radar transmission waveform and the meta-optimizer of the receiving filter. and Indicates network The model parameters of the meta-optimizer at the time of update, and Indicates the status of each unit, and Indicates the update amount of the radar transmit waveform and receive filter.

5. The method for jointly resisting spectrum dispersion interference of transmission and reception based on Riemann element optimization according to claim 4 is characterized in that: Update the meta-optimizer model parameters based on the backward pass algorithm, including: ； in, and Representation Meta-Optimizer and The learning rate, express Adam Optimizer, and Respectively Relative to model parameters and gradient.

6. A transmit-receive joint anti-spectral dispersion interference device based on Riemann element optimization, characterized in that: include: The first module is used to establish a joint constraint optimization model for anti-spectral dispersion interference by minimizing the integral level of the spectrum dispersion interference component and the integral sidelobe level of the target component, while considering the waveform constant modulus constraint, the receiving filter energy constraint, and the non-matching filter peak loss constraint, as follows: ； in The dimension is Radar transmit waveform and receive filter matrix, is the radar transmission waveform and the number of time domain sampling points of the receiving filter, Indicates the number of radar channels; They represent the radar transmit waveform and receive filter of the mth channel respectively; Respectively represent Radar transmit waveform and receive filter for each channel; represents the Fourier transform matrix, and is the preset parameter; , and express , , Corresponding The zero-padding result of the dimension; express The nth element; , , They represent the modulo operation, the vector two-norm, and the Hadamard product, respectively. represents the conjugate transpose, represents complex conjugate; represents the waveform constant modulus constraint; represents the filter constant energy constraint; represents the spectral dispersion interference component, and express Corresponding The zero-fill result of dimension, where represents the shift matrix of spectral dispersive interference, and Expressed as ； in, represents the sub-pulse length of the spectral dispersive interference, is the number of sub-pulses; The second module is used to establish a Riemann element optimization model for radar transmit waveform optimization and a Riemann element optimization model for receive filter optimization to achieve synchronous update of radar transmit waveform and receive filter. The Riemann element optimization model for radar transmit waveform optimization includes: make Indicates the number of network updates. Represents the number of network layers, then in the Radar transmission waveform in layer network Updated to: ； in, represents the Riemann meta-optimization model, represents the shrinkage operator of the radar transmit waveform, express At the point The Riemann gradient of express middle The value is , The value is The objective function value of , Indicates Radar transmission waveform in layer network; A Riemann element optimization model for receive filter optimization is established, including: In the When the network is updated, The receiving filter of the layer network is updated as: ； in, represents the Riemann meta-optimization model, express Relative to The Riemann gradient of Indicates The receiving filter of the layer network, represents the shrinkage operator of the receive filter, express middle The value is The objective function value when ; The third module is used to initialize the radar transmit waveform, initialize the receive filter, update the radar transmit waveform and receive filter using the meta-optimizer based on the forward transfer algorithm, update the meta-optimizer model parameters based on the backward transfer algorithm until convergence, and output the current radar transmit waveform and receive filter.

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