Radar transceiver joint anti-intermittent sampling forwarding interference method and device

Abstract

This invention proposes a radar transmit-receive joint anti-intermittent sampling and forwarding interference method and device. The method includes establishing a joint transmit-receive constrained optimization objective function for anti-intermittent sampling and forwarding interference, with the goal of minimizing the integrated level of the interference signal and the integrated sidelobe level of the target signal, while taking into account waveform constant modulus constraints, receive filter energy constraints, and non-matched filter peak loss constraints. This function, which operates in Euclidean space, is converted into an unconstrained optimization objective function in Riemann product manifold space. The unconstrained optimization objective function is solved using an adaptive cubic regularization algorithm based on Riemann product manifolds, achieving simultaneous iteration of the radar transmit waveform and receive filter. This invention considers the joint optimization problem of the transmit waveform and receive filter, improving the anti-ISRJ capability of pulse Doppler radars.

Description

Technical Field

[0001] The present invention mainly relates to the technical field of radar anti-active interference, and in particular to a radar transceiver joint anti-intermittent sampling and forwarding interference method and device. Background Art

[0002] Interrupted-Sampling Repeater Jamming (ISRJ) is a typical coherent jammer based on the undersampling principle and matched filtering characteristics. By sampling and forwarding radar signals in discrete steps, ISRJ can generate highly realistic, densely packed false targets with controllable positions and numbers at the receiving end, thereby achieving deceptive jamming effects and affecting the radar's effective detection of real targets. Furthermore, ISRJ offers advantages such as fast response time and simple implementation. With the rapid development of Digital Radio Frequency Memory (DFRM) technology, its application has become quite feasible. Therefore, research on ISRJ suppression technology plays a vital role in improving our radar's battlefield situational awareness capabilities.

[0003] In response to the ISRJ suppression problem, domestic and foreign scholars have conducted extensive research and achieved certain results. Currently, there are two main mainstream ISRJ suppression methods, namely the receiving end signal processing method and the waveform optimization anti-ISRJ method.

[0004] As for the signal processing method at the receiving end, the research idea is to use the differences between the target signal and the ISRJ signal in different dimensions to construct a set of filters to filter out the interference signal, thereby achieving the purpose of anti-ISRJ.

[0005] The waveform optimization anti-ISRJ method mainly uses waveform optimization to achieve weighted suppression of the pulse compression results of the ISRJ signal and the target signal at the receiving end, under the premise that the interference parameters are accurately known.

[0006] The anti-interference measures of the above two methods are relatively simple and do not fully utilize the freedom of joint processing between the transmitter and the receiver. Due to the limited freedom of waveform optimization, the interference suppression performance of these methods in complex active scenarios is less than ideal. Summary of the Invention

[0007] Aiming at the problem that the anti-ISRJ performance of the ISRJ suppression method in the prior art is limited, in order to further improve the ISRJ suppression performance, the present invention proposes a radar transceiver joint anti-intermittent sampling forwarding interference method and device.

[0008] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] In one aspect, the present invention provides a radar transmission and reception joint anti-intermittent sampling and forwarding interference method, comprising:

[0010] Under the constraints of waveform constant modulus, receive filter energy, and non-matched filter peak loss, a joint transmit-receive constrained optimization objective function for resisting intermittent sampling and forwarding interference is established by minimizing the non-matched filter integrated sidelobe level of the radar transmit waveform and the integrated level of the non-matched filter processing of the intermittent sampling and forwarding interference signal at the radar receiver.

[0011] Converting the transmit-receive joint constrained optimization objective function on the Euclidean space into an unconstrained optimization objective function on the Riemann product manifold space;

[0012] Solving the Euclidean gradient of the unconstrained optimization objective function and converting the Euclidean gradient of the unconstrained optimization objective function into a Riemannian gradient;

[0013] Solving the Euclidean Hessian of the unconstrained optimization objective function and converting the Euclidean Hessian of the unconstrained optimization objective function into a Riemannian Hessian;

[0014] Based on the Riemann gradient and Riemann Hessian of the unconstrained optimization objective function, a second-order Taylor expansion is performed on the unconstrained optimization objective function in the tangent space of the Riemann product manifold to obtain a second-order approximate model of the unconstrained optimization objective function, and a cubic adaptive regularization term is introduced into the second-order approximate model to construct a regularized approximate model;

[0015] Calculating the degree of fit between the regularized approximation model and the unconstrained optimization objective function;

[0016] Based on the degree of fit and the preset regularization parameters and iteration point update criteria, the regularization parameters and iteration point update criteria are updated until the iteration stop condition is met, and the current radar transmit waveform and the unmatched filter used by the radar receiver are output.

[0017] Furthermore, as a preferred embodiment, the established transmit-receive joint constraint optimization objective function for resisting intermittent sampling forwarding interference is:

[0018]

[0019] st|x1|=…=|x N |=1,h H h=N

[0020] The sampling sequence of the radar transmission waveform is x=[x1,…,x N ] T , where x1,…,x Nrepresents the sampling sequence, N represents the number of radar transmission waveform sampling points, (·) T represents the transpose operation, λ represents the Pareto weight; the non-matched filter at the radar receiving end processes the intermittent sampling forwarding interference signal, where the non-matched filter sequence of the non-matched filter at the radar receiving end is expressed as h = [h1,…,h N ] T ,h1,…,h N represents the sampling sequence of the non-matched filter at the radar receiver, (·) H represents the conjugate transpose operation; f IL (x,h) represents the integration level after the radar receiver uses a non-matched filter to process the intermittent sampling forwarding interference signal, f ISL (x,h) represents the non-matched filtered integrated sidelobe level of the radar transmit waveform with peak point constraint.

[0021] Furthermore, as a preferred embodiment, the transmit-receive joint constrained optimization objective function for resisting intermittent sampling and forwarding interference is converted into an unconstrained optimization objective function on the Riemann product manifold space, which is expressed as:

[0022]

[0023] The Cartesian product y=x×h=(x,h) is defined, then the variable y belongs to the space Expressed as and The Riemann product manifold space formed by in represents N-dimensional complex Euclidean space, (·) * Indicates conjugation.

[0024] Furthermore, as a preferred embodiment, at the kth iteration, the variable y corresponding to the kth iteration is y k =(x k ,h k ), in y k =(x k ,h k ) is the regularized approximate model constructed at:

[0025]

[0026] in represents the constructed regularized approximate model, represents the value of the regularized approximate model at 0, represents the adaptive regularization parameter, Represents the regularized approximate model in The gradient at , g(·) represents the Riemannian metric, θ is a sufficiently small constant with a value range of 0 to 1×10 -3 , represents the Riemann Hessian of the unconstrained optimization objective function f(y) corresponding to the k-th iteration, represents the direction vector corresponding to the kth iteration, which is the tangent vector on the tangent space of the Riemann product manifold; gradf(x k ,h k ) represents the Riemann gradient of the unconstrained optimization objective function f(y) corresponding to the k-th iteration.

[0027] Furthermore, as a preferred embodiment, the degree of agreement between the regularized approximation model and the unconstrained optimization objective function is solved by the following formula:

[0028]

[0029] Among them, 0 2N represents a column vector of dimension 2N, Indicates that the regularized approximate model is at 0 2N The value of Represents the contraction operator, which is used to map the iterative points on the tangent space of the Riemann product manifold back to the manifold surface. The calculation method is:

[0030]

[0031] in, represents a point x on the tangent space k The tangent vector at represents the point h on the tangent space k The tangent vector at Represents point x k Along the tangent vector The contraction operator, Indicates point h k Along the tangent vector The contraction operator.

[0032] Furthermore, as a preferred embodiment, the regularization parameter and iteration point update criteria are as follows:

[0033]

[0034]

[0035] in, Represents the lower bound of the regularization parameter, the threshold parameters η1 and η2 satisfy 0<η1<η2<1, and the regularization update coefficients γ1, γ2 and γ3 satisfy 0<γ1<1<γ2<γ3; when When , accept the solution of the regularization subproblem and update the iteration point; when the model fit parameter further satisfies When , update the iteration point and reduce the regularization parameter; when , reject the solution to the regularized subproblem and increase the regularization parameter.

[0036] On the other hand, the present invention provides a radar transmitting and receiving joint anti-intermittent sampling and forwarding interference device, comprising:

[0037] The first module is used to establish a joint transmit-receive constrained optimization objective function for resisting intermittent sampling and forwarding interference by minimizing the unmatched filtering integrated sidelobe level of the radar transmit waveform and the integrated level of the radar receiver after unmatched filtering of the intermittent sampling and forwarding interference signal under the constraints of waveform constant modulus constraint, receive filter energy constraint, and unmatched filtering peak loss constraint.

[0038] The second module is used to convert the transmit-receive joint constraint optimization objective function on the Euclidean space into an unconstrained optimization objective function on the Riemann product manifold space;

[0039] A third module is used to solve the Euclidean gradient of the unconstrained optimization objective function and convert the Euclidean gradient of the unconstrained optimization objective function into a Riemannian gradient;

[0040] A fourth module is used to solve the Euclidean Hessian of the unconstrained optimization objective function and convert the Euclidean Hessian of the unconstrained optimization objective function into a Riemann Hessian;

[0041] A fifth module is configured to perform a second-order Taylor expansion of the unconstrained optimization objective function in the tangent space of the Riemann product manifold based on the Riemann gradient and the Riemann Hessian of the unconstrained optimization objective function to obtain a second-order approximate model of the unconstrained optimization objective function, and introduce a cubic adaptive regularization term into the second-order approximate model to construct a regularized approximate model;

[0042] A sixth module is used to calculate the degree of fit between the regularized approximation model and the unconstrained optimization objective function;

[0043] The seventh module is used to update the regularization parameters and the iteration point update criteria based on the degree of fit and the preset regularization parameters and iteration point update criteria until the iteration stop condition is met, and output the current radar transmission waveform and the non-matched filter used by the radar receiving end.

[0044] In another aspect, the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are performed:

[0045] Under the constraints of waveform constant modulus, receive filter energy, and non-matched filter peak loss, a joint transmit-receive constrained optimization objective function for resisting intermittent sampling and forwarding interference is established by minimizing the non-matched filter integrated sidelobe level of the radar transmit waveform and the integrated level of the non-matched filter processing of the intermittent sampling and forwarding interference signal at the radar receiver.

[0046] Converting the transmit-receive joint constrained optimization objective function on the Euclidean space into an unconstrained optimization objective function on the Riemann product manifold space;

[0047] Solving the Euclidean gradient of the unconstrained optimization objective function and converting the Euclidean gradient of the unconstrained optimization objective function into a Riemannian gradient;

[0048] Solving the Euclidean Hessian of the unconstrained optimization objective function and converting the Euclidean Hessian of the unconstrained optimization objective function into a Riemannian Hessian;

[0049] Based on the Riemann gradient and Riemann Hessian of the unconstrained optimization objective function, a second-order Taylor expansion is performed on the unconstrained optimization objective function in the tangent space of the Riemann product manifold to obtain a second-order approximate model of the unconstrained optimization objective function, and a cubic adaptive regularization term is introduced into the second-order approximate model to construct a regularized approximate model;

[0050] Calculating the degree of fit between the regularized approximation model and the unconstrained optimization objective function;

[0051] Based on the degree of fit and the preset regularization parameters and iteration point update criteria, the regularization parameters and iteration point update criteria are updated until the iteration stop condition is met, and the current radar transmit waveform and the unmatched filter used by the radar receiver are output.

[0052] In another aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the following steps:

[0053] Under the constraints of waveform constant modulus, receive filter energy, and non-matched filter peak loss, a joint transmit-receive constrained optimization objective function for resisting intermittent sampling and forwarding interference is established by minimizing the non-matched filter integrated sidelobe level of the radar transmit waveform and the integrated level of the non-matched filter processing of the intermittent sampling and forwarding interference signal at the radar receiver.

[0054] Converting the transmit-receive joint constrained optimization objective function on the Euclidean space into an unconstrained optimization objective function on the Riemann product manifold space;

[0055] Solving the Euclidean gradient of the unconstrained optimization objective function and converting the Euclidean gradient of the unconstrained optimization objective function into a Riemannian gradient;

[0056] Solving the Euclidean Hessian of the unconstrained optimization objective function and converting the Euclidean Hessian of the unconstrained optimization objective function into a Riemannian Hessian;

[0057] Based on the Riemann gradient and Riemann Hessian of the unconstrained optimization objective function, a second-order Taylor expansion is performed on the unconstrained optimization objective function in the tangent space of the Riemann product manifold to obtain a second-order approximate model of the unconstrained optimization objective function, and a cubic adaptive regularization term is introduced into the second-order approximate model to construct a regularized approximate model;

[0058] Calculating the degree of fit between the regularized approximation model and the unconstrained optimization objective function;

[0059] Based on the degree of fit and the preset regularization parameters and iteration point update criteria, the regularization parameters and iteration point update criteria are updated until the iteration stop condition is met, and the current radar transmit waveform and the unmatched filter used by the radar receiver are output.

[0060] In order to make full use of the freedom of the joint processing of transmission and reception to improve the ISRJ suppression effect, the present invention, under the technical background of active anti-interference, takes cognitive radar interference environment perception as the premise and considers the joint optimization design problem of radar transmission waveform and receiving filter. Specifically, the present invention first considers the waveform constant modulus constraint, the receiving filter energy constraint and the non-matching filter peak loss constraint, and jointly minimizes the non-matching filter integrated sidelobe level (ISL) of the radar transmission waveform and the integrated level (IL) after the radar receiving end performs non-matching filter processing on the intermittent sampling forwarding interference signal, so as to establish a joint constrained optimization objective function for transmission and reception against intermittent sampling forwarding interference. Subsequently, combined with the geometric characteristics of the constraint space, a model solution method based on the Riemannian Product Manifold Adaptive Regularization with Cubic (RPM-ARC) algorithm is proposed to achieve the synchronous iteration of the radar transmission waveform and the receiving filter. Compared with the prior art, the technical effects of the present invention are at least reflected in the following aspects:

[0061] First, it expands the degrees of freedom for waveform-domain active interference mitigation. Existing waveform optimization mitigation methods simply consider adaptive processing at the transmitter or receiver end, limiting their mitigation performance in complex interference scenarios. To expand the degrees of freedom for interference suppression, this paper proposes a combined transmit-receive anti-ISRJ method based on the RPM-ARC algorithm, enabling synchronized updates of the transmit waveform and receive filter.

[0062] Second, it offers excellent interference suppression performance. This paper proposes an RPM-ARC algorithm for solving the transmit-receive joint optimization model for the radar transmit waveform and receive filter. By introducing a cubic regularization term into the second-order approximation model of the unconstrained optimization objective function, the algorithm's computational complexity is reduced, achieving improved convergence performance and ISRJ suppression. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0064] Figure 1 is a flow chart of an embodiment;

[0065] Figure 2 is a graph showing convergence of objective function values ​​in one embodiment;

[0066] Figure 3 is a graph showing a gradient norm value convergence curve in one embodiment;

[0067] Figure 4 FIG. 1 is a diagram showing the matched filtering result output by the Alternating Direction Method of Multipliers (ADMM) when ISRJ single forwarding interference occurs in one embodiment;

[0068] Figure 5 This is a diagram of the unmatched filtering result output by the RPM-ARC algorithm during a single forwarding of the ISRJ in one embodiment;

[0069] Figure 6 This is the matched filtering result output by the ADMM algorithm when ISRJ forwards interference twice in one embodiment;

[0070] Figure 7 This is a diagram showing the non-matched filtering result output by the RPM-ARC algorithm when ISRJ forwards interference twice in one embodiment. DETAILED DESCRIPTION

[0071] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0072] Reference Figure 1 In one embodiment, a radar transmitting and receiving joint anti-intermittent sampling and forwarding interference method is provided, comprising:

[0073] (1) Establish a joint constrained optimization objective function for transmitting and receiving to resist intermittent sampling and forwarding interference;

[0074] In the context of interrupted-sampling repeater jamming (ISRJ) resistance, this embodiment considers waveform constant modulus constraints, receive filter energy constraints, and non-matched filter peak loss constraints to minimize the non-matched filter integrated sidelobe level of the radar transmit waveform and the integrated level of the non-matched filter processing of the interrupted-sampling repeater jamming signal at the radar receiver. This establishes a joint transmit-receive constrained optimization objective function for interrupted-sampling repeater jamming resistance.

[0075] (2) converting the transmit-receive joint constrained optimization objective function on the Euclidean space into an unconstrained optimization objective function on the Riemann product manifold space;

[0076] (3) solving the Euclidean gradient of the unconstrained optimization objective function and converting the Euclidean gradient of the unconstrained optimization objective function into a Riemannian gradient;

[0077] (4) solving the Euclidean Hessian of the unconstrained optimization objective function and converting the Euclidean Hessian of the unconstrained optimization objective function into a Riemannian Hessian;

[0078] (5) constructing a regularized approximation model of the unconstrained optimization objective function;

[0079] Based on the Riemann gradient and Riemann Hessian of the unconstrained optimization objective function, a second-order Taylor expansion is performed on the unconstrained optimization objective function in the Riemann product manifold tangent space to obtain a second-order approximate model of the unconstrained optimization objective function. At the same time, a cubic adaptive regularization term is introduced into the second-order approximate model to construct a regularized approximate model.

[0080] (6) calculating the degree of agreement between the regularized approximation model and the unconstrained optimization objective function;

[0081] (7) Based on the degree of fit and the preset regularization parameters and iteration point update criteria, the regularization parameters and iteration point update criteria are updated until the iteration stop condition is met, and the current radar transmit waveform and the non-matched filter used by the radar receiver are output.

[0082] It is understandable that the present invention does not limit the design of the iteration stop condition. Those skilled in the art can choose to set the verification iteration stop condition, such as setting the maximum number of iterations, based on conventional means in the field, common knowledge and their own experience.

[0083] In one embodiment, a specific process of constructing the transmit-receive joint constraint optimization objective function for resisting intermittent sampling and forwarding interference is proposed, including: assuming that the radar transmission sequence is x = [x1, ..., x N ] T , where x1,…,x N represents the sampling sequence, N is the sequence length, i.e. the number of sampling points of the radar transmission waveform, (·) T represents the vector or matrix transpose operation, then the ISRJ interference signal can be expressed as

[0084] x j =x⊙p,

[0085] Where ⊙ represents the Hadamard product, and p is the jammer sampling vector with the same length as the transmit sequence. The radar receiver non-matched filter sequence is expressed as h = [h1,…,h N ] T ,h1,…,h N represents the sampling sequence of the non-matched filter at the radar receiver, then the IL value of the ISRJ signal after non-matched filtering can be expressed as

[0086]

[0087] Where, (·) H In addition, in order to control the ISRJ peak intensity to achieve further suppression of interference, the peak loss constraint penalty term |(h⊙p) is introduced H xb min | 2 , and then the radar receiver uses a non-matched filter to perform non-matched filtering on the intermittent sampling forwarding interference signal after the integration level f IL (x,h), is:

[0088]

[0089] Among them, β is the penalty factor, b min represents the preset peak value after the ISRJ signal is processed by non-matched filtering, |·| represents the modulus value,

[0090]

[0091] In addition, in order to achieve effective detection of the target, the pulse compression performance of the radar transmission sequence must also be taken into account. After the non-matched filtering of the receiving filter sequence h, the ISL value of the transmission sequence can be expressed as

[0092] ISL=x H Λ H WΛx=h H Φ H WΦh

[0093] Where W is a constant matrix with all diagonal elements 1 except the Nth diagonal element, Λ and Φ are the non-matched filter and waveform correlation matrices, respectively.

[0094]

[0095]

[0096] In order to control the processing gain loss caused by the mismatched filter [K.Zhou,D.Li,Y.Su,and T.Liu,“Joint design of transmit waveform and mismatch filter in the presence of interrupted sampling repeater jamming,”IEEE Signal Processing Letters,vol.27,pp.1610-1614,2020.], the penalty term |h is introduced H xb max | 2 To force the peak point of the radar transmission waveform after non-matched filtering to approach the preset value b max Therefore, the non-matched filtering integrated sidelobe level f of the radar transmit waveform with peak point constraint for obtaining excellent pulse compression performance is ISL (x,h), is:

[0097] f ISL (x,h)=x H Λ H WΛx+α|h H xb max | 2 =h H Φ H WΦh+α|h H xb max | 2

[0098] Among them, α represents the penalty factor.

[0099] To effectively control the gain loss caused by non-matched filtering, both the radar transmit sequence and the receive filter sequence must satisfy energy constraints. Furthermore, to avoid amplifier nonlinear distortion and maintain the radar transmitter at maximum efficiency, the transmit sequence must also satisfy constant modulus constraints. Therefore, within the Pareto multi-objective optimization framework, the established transmit-receive joint design anti-ISRJ model can be expressed as:

[0100]

[0101] st|x1|=…=|x N |=1,h H h=N

[0102] Where λ∈[0,1] represents the Pareto weight. To balance the ISRJ suppression performance and the waveform pulse compression performance, λ is usually set to 0.5.

[0103] In one embodiment, a specific method for converting the transmit-receive joint constrained optimization objective function on the Euclidean space into an unconstrained optimization objective function on the Riemann product manifold space is proposed, including:

[0104] The constant modulus constraint of the transmit waveform and the energy constraint of the receive filter define two smooth search spaces, respectively:

[0105]

[0106]

[0107] in, represents N-dimensional complex Euclidean space, (·) * Indicates conjugation.

[0108] From the perspective of manifold, and They constitute different closed manifold spaces, namely the complex circle manifold (CCM) and the complex sphere manifold (CSM).

[0109] Define the Cartesian product y = x × h, then the variable y belongs to the space It can be expressed as and The Riemann product manifold space formed by this is,

[0110]

[0111] Therefore, the transmit-receive joint constraint optimization objective function on the Euclidean space is converted into an unconstrained optimization objective function on the Riemann product manifold space, which is expressed as:

[0112]

[0113] For the above-mentioned unconstrained optimization objective function f(y), those skilled in the art can select a suitable algorithm from existing optimization algorithms based on experience or common sense to solve it and output the final radar transmit waveform and the unmatched filter used by the radar receiver.

[0114] In a preferred embodiment, a Riemannian Product Manifold Adaptive Regularization with Cubic (RPM-ARC) algorithm is proposed to solve the unconstrained optimization objective function, including:

[0115] Solving the Euclidean gradient of the unconstrained optimization objective function and converting the Euclidean gradient of the unconstrained optimization objective function into a Riemannian gradient;

[0116] Solving the Euclidean Hessian of the unconstrained optimization objective function and converting the Euclidean Hessian of the unconstrained optimization objective function into a Riemannian Hessian;

[0117] Based on the Riemann gradient and Riemann Hessian of the unconstrained optimization objective function, a second-order Taylor expansion is performed on the unconstrained optimization objective function in the tangent space of the Riemann product manifold to obtain a second-order approximate model of the unconstrained optimization objective function, and a cubic adaptive regularization term is introduced into the second-order approximate model to construct a regularized approximate model;

[0118] Calculating the degree of fit between the regularized approximation model and the unconstrained optimization objective function;

[0119] Based on the degree of fit and the preset regularization parameters and iteration point update criteria, the regularization parameters and iteration point update criteria are updated until the iteration stop condition is met, and the current radar transmit waveform and the unmatched filter used by the radar receiver are output.

[0120] Specifically, in one embodiment, a Euclidean gradient calculation process for solving the unconstrained optimization objective function f(y) is given as follows:

[0121] The Euclidean gradient of f(y) can be expressed as the product of the Cartesian coordinates of the gradient of the unconstrained optimization objective function f(y) with respect to x and h, that is:

[0122]

[0123] Among them, the Euclidean gradient of the unconstrained optimization objective function f(x,h) with respect to x can be calculated as:

[0124]

[0125] in,

[0126]

[0127] Similarly, the Euclidean gradient of the unconstrained optimization objective function f(x,h) with respect to h can be calculated as:

[0128]

[0129] in,

[0130]

[0131] Specifically, in one embodiment, a method for converting a Euclidean gradient into a Riemannian gradient is provided, including:

[0132] According to the projection relationship between the Riemann gradient and the Euclidean gradient, the unconstrained optimization objective function f(y) is calculated on the Riemann product manifold. The Riemannian gradient gradf(y) on can be expressed as the Euclidean gradient Gradf(y) on the Euclidean space:

[0133] gradf(y)=(grad x f(x,h),grad h f(x,h))

[0134] =(Proj x {Grad x f(x,h)},Proj h {Grad h f(x,h)})

[0135] Among them, grad x f(x,h) and grad h f(x,h) represents the Riemann gradient of the unconstrained optimization objective function f(y) with respect to x and h, respectively.

[0136] Project x and Proj h are the projection operators on the Complex Circle Manifold (CCM) and the Complex Sphere Manifold (CSM), respectively, which can be expressed as:

[0137]

[0138] Among them, Re(·) represents the real part operation, and express and The tangent space of is parameterized as follows:

[0139]

[0140] In addition, the product manifold tangent space Can be and The Cartesian product representation of

[0141]

[0142] Therefore, grad x f(x,h) and grad h f(x,h) can be expressed by the Euclidean gradient of the unconstrained optimization objective function f(y) with respect to x and h respectively:

[0143]

[0144] Specifically, in one embodiment, a method for solving the Euclidean Hessian of the unconstrained optimization objective function f(y) is provided, including:

[0145] For the unconstrained optimization objective function f(y), it is in the direction ξ y The Euclidean Hessian can be calculated as:

[0146] Hessf(y)[ξ y ]=Hessf(x,h)[ξ (x,h) ]=(Hess x f(x,h)[ξ (x,h) ],Hess h f(x,h)[ξ (x,h) ])

[0147] Among them, Hess x f(x,h)[ξ (x,h) ] represents the Euclidean Hessian of the unconstrained optimization objective function f(y) with respect to x. The calculation process is as follows:

[0148]

[0149] Similarly, the Euclidean Hessian of the unconstrained optimization objective function f(y) with respect to h can be calculated as:

[0150]

[0151] Specifically, in one embodiment, a method for converting the Euclidean Hessian into the Riemannian Hessian is provided, including:

[0152] Unconstrained optimization objective function f(y) on the product manifold The Riemann Hessian on can be composed of the Cartesian product of the Riemann Hessians on each submanifold, that is:

[0153] hessf(y)[ξ y ]=hessf(x,h)[ξ (x,h) ]

[0154] =(hess x f(x,h)[ξ (x,h) ],hess h f(x,h)[ξ (x,h) ])

[0155] Among them, hess x f(x,h)[ξ (x,h) ] and hess h f(x,h)[ξ (x,h) ] represent the Riemann Hessian of the unconstrained optimization objective function f(y) with respect to x and h respectively. ξ (x,h) Represents the direction vector, which is the tangent vector on the tangent space of the Riemann product manifold.

[0156] Using the projection relationship between Riemann Hessian and Euclidean Hessian, the two can be calculated as:

[0157]

[0158] After obtaining the Riemann gradient and Riemann Hessian of the unconstrained optimization objective function f(y), the unconstrained optimization objective function f(y) is Taylor expanded in the tangent space of the Riemann product manifold to obtain a second-order approximate model. At the same time, a cubic adaptive regularization term is introduced into the second-order approximate model to construct a regularized subproblem.

[0159] Specifically, at the kth iteration, the variable y corresponding to the kth iteration is y k =(x k ,h k ), in y k =(x k ,h k ) is the regularized approximate model constructed at:

[0160]

[0161] in represents the constructed regularized approximate model, represents the value of the regularized approximate model at 0, represents the adaptive regularization parameter, Represents the regularized approximate model in The gradient at , g(·) represents the Riemannian metric, θ is a sufficiently small constant with a value range of 0 to 1×10 -3 , represents the Riemann Hessian of the unconstrained optimization objective function f(y) corresponding to the k-th iteration, represents the direction vector corresponding to the kth iteration, which is the tangent vector on the tangent space of the Riemann product manifold; gradf(x k ,h k ) represents the Riemann gradient of the unconstrained optimization objective function f(y) corresponding to the k-th iteration.

[0162] Since the basis vectors on the tangent space cannot be obtained, an iterative algorithm based on the Lanczos strategy can be used to solve the regularized subproblem.

[0163] The model fit parameter is used to measure the degree of fit between the constructed regularized approximate model and the unconstrained optimization objective function f(y). In one embodiment of the present invention, a method for calculating the fit between the regularized approximate model and the unconstrained optimization objective function f(y) is proposed, as follows:

[0164]

[0165] Among them, 0 2N Represents a column vector of dimension 2N. Represents the contraction operator, which is used to map the iterative points on the tangent space back to the manifold surface. The calculation method is:

[0166]

[0167] Next, based on the model fit ρ k The calculation results are used to update the regularization parameters and iteration points. In one embodiment, the update criteria for the regularization parameters and iteration points are as follows:

[0168]

[0169] in, Represents the lower bound of the regularization parameter, the threshold parameters η1 and η2 satisfy 0<η1<η2<1, and the regularization update coefficients γ1, γ2 and γ3 satisfy 0<γ1<1<γ2<γ3; when When , accept the solution of the regularization subproblem and update the iteration point; when the model fit parameter further satisfies When , update the iteration point and reduce the regularization parameter; when , reject the solution to the regularized subproblem and increase the regularization parameter.

[0170] Iterate continuously until the number of iterations reaches the preset maximum value, then stop iterating and output the current radar transmit waveform x and the non-matched filter h used by the radar receiver.

[0171] It is understood that the manner of setting the iteration stopping condition described in the present invention is not limited, and those skilled in the art can set it based on conventional means or common knowledge in the art. In a preferred embodiment, the iteration stopping condition can be set by setting a maximum number of iterations, or the iteration is stopped when the difference between the objective function values ​​calculated between the previous and next iterations is less than a set threshold (the set threshold is set based on experience, such as 0.001).

[0172] The effects of the present invention are further illustrated by the following numerical simulation experiments:

[0173] Experimental scenario:

[0174] The following experiments were conducted on a computer (core 2.30GHz i7-12700H, RAM 40.0GB) using MATLAB version R2022b. During the experiment, the pulse width was set to 50μs, the bandwidth was set to 5MHz, the ISRJ sampling period was set to 10μs, the sampling rate was set to 10MHz, the ISRJ duty cycle was set to 0.25, the ISRJ forwarding delay was set to 10μs, and the interference-to-signal ratio was set to 10dB. The values ​​were set to -30dB, -1dB, the Pareto weight was set to 0.5, the penalty factor α = β = 256, and the algorithm iteration stop condition was set to the gradient norm less than 10 -3 .

[0175] Step 1: In the context of interrupted-sampling repeater jamming (ISRJ) resistance, the optimization criteria are to minimize the integrated sidelobe level of the radar transmit waveform and the integrated level of the radar receiver after the interrupted-sampling repeater jamming signal is processed by the unmatched filter. Meanwhile, the constant modulus constraint, the receive filter energy constraint, and the unmatched filter peak loss constraint are considered. A joint transmit-receive constrained optimization objective function for ISRJ resistance is established. The transmit waveform, receive filter, and maximum number of algorithm iterations are initialized.

[0176] Step 2: Optimization model form conversion: convert the joint constrained optimization objective function of transmitter and receiver on Euclidean space into an unconstrained optimization objective function on Riemann product manifold space.

[0177] Step three, solving the unconstrained optimization objective function based on the Riemannian Product Manifold Adaptive Regularization with Cubic (RPM-ARC) algorithm provided by the present invention.

[0178] Step 4: Determine convergence: If the iteration stop condition is met, output the current radar transmit waveform x and the unmatched filter h used by the radar receiver; otherwise, repeat step 3 until convergence.

[0179] Figure 2 The curve of objective function value changing with the number of iterations is given. Figure 2 It can be seen that as the number of iterations increases, the objective function value decreases monotonically. After the 600th iteration, the convergence condition is reached and the algorithm stops running. Figure 3 The curve of the gradient norm of the objective function changing with the number of iterations during the operation of the algorithm is given. Figure 3 It can be seen that due to the non-convex nature of the optimization problem, the gradient norm change curve shows a downward trend overall, but there are certain fluctuations.

[0180] In order to verify the effectiveness of the RPM-ARC algorithm proposed in this invention, we compared it with an ISRJ suppression method based on the alternating direction multiplier method (ie, the ADMM algorithm). Figure 4 The unmatched filtering results of the ADMM algorithm for ISRJ single forwarding are given. Figure 4 There is a false target in the image, and the highest value is -13.95dB. Figure 5 The unmatched filtering results of the RPM-ARC algorithm output during single ISRJ forwarding are given, and its maximum sidelobe value is -17.10dB, which is more effective in suppressing ISRJ.

[0181] In order to verify the robustness of the algorithm's anti-interference performance, the anti-interference scenario when ISRJ forwards multiple times is further considered. Figure 6 The unmatched filtering results of the ISRJ two-forward ADMM algorithm output are given. Figure 6 There are two batches of false targets, with the highest values ​​of -10.28dB and -11.25dB respectively, which seriously interfere with the detection of the target. Figure 7 The unmatched filtering results of the RPM-ARC algorithm output when the ISRJ is forwarded twice are given. The maximum sidelobe value is -13.90dB, and the interference target generated by the ISRJ is effectively suppressed. The effectiveness of the RPM-ARC algorithm proposed in this invention is further verified.

[0182] In one embodiment, a radar transmitting and receiving joint anti-intermittent sampling and forwarding interference device is provided, comprising:

[0183] The first module is used to establish a joint transmit-receive constrained optimization objective function for resisting intermittent sampling and forwarding interference by minimizing the unmatched filtering integrated sidelobe level of the radar transmit waveform and the integrated level of the radar receiver after unmatched filtering of the intermittent sampling and forwarding interference signal under the constraints of waveform constant modulus constraint, receive filter energy constraint, and unmatched filtering peak loss constraint.

[0184] The second module is used to convert the transmit-receive joint constraint optimization objective function on the Euclidean space into an unconstrained optimization objective function on the Riemann product manifold space;

[0185] A third module is used to solve the Euclidean gradient of the unconstrained optimization objective function and convert the Euclidean gradient of the unconstrained optimization objective function into a Riemannian gradient;

[0186] A fourth module is used to solve the Euclidean Hessian of the unconstrained optimization objective function and convert the Euclidean Hessian of the unconstrained optimization objective function into a Riemann Hessian;

[0187] A fifth module is configured to perform a second-order Taylor expansion of the unconstrained optimization objective function in the tangent space of the Riemann product manifold based on the Riemann gradient and the Riemann Hessian of the unconstrained optimization objective function to obtain a second-order approximate model of the unconstrained optimization objective function, and introduce a cubic adaptive regularization term into the second-order approximate model to construct a regularized approximate model;

[0188] A sixth module is used to calculate the degree of fit between the regularized approximation model and the unconstrained optimization objective function;

[0189] The seventh module is used to update the regularization parameters and the iteration point update criteria based on the degree of fit and the preset regularization parameters and iteration point update criteria until the iteration stop condition is met, and output the current radar transmission waveform and the non-matched filter used by the radar receiving end.

[0190] The implementation methods of the above modules and the construction of the model can adopt the methods described in any of the above embodiments, which will not be repeated here.

[0191] In another aspect, the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the radar transceiver joint anti-intermittent sampling and forwarding interference method provided in any of the above-mentioned embodiments are implemented. 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 is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device is configured to store sample data. The network interface of the computer device is configured to communicate with an external terminal via a network connection.

[0192] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the radar transceiver joint anti-intermittent sampling forwarding interference method provided in any of the above embodiments are implemented.

[0193] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0194] Matters not covered by the present invention are known technologies.

[0195] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, 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.

[0196] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

[0197] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A radar transceiver joint anti-intermittent sampling and forwarding interference method, characterized in that: include: Under the constraints of waveform constant modulus, receive filter energy, and non-matched filter peak loss, a joint transmit-receive constrained optimization objective function for resisting intermittent sampling and forwarding interference is established by minimizing the non-matched filter integrated sidelobe level of the radar transmit waveform and the integrated level of the non-matched filter processing of the intermittent sampling and forwarding interference signal at the radar receiver. The joint constrained optimization objective function of the transmitter and receiver on the Euclidean space is converted into an unconstrained optimization objective function on the Riemann product manifold space: The sampling sequence of the radar transmission waveform is: ,in represents the sampling sequence, Indicates the number of sampling points of radar transmission waveform, represents the transpose operation, represents the Pareto weight; the non-matched filter at the radar receiving end processes the intermittent sampling forwarding interference signal, where the non-matched filter sequence of the non-matched filter at the radar receiving end is expressed as , represents the sampling sequence of the non-matched filter at the radar receiver, represents the conjugate transpose operation; It indicates the integration level after the radar receiver uses a non-matched filter to process the intermittent sampling forwarding interference signal. It represents the non-matched filtered integrated sidelobe level of the radar transmit waveform with peak point constraint; Solving the Euclidean gradient of the unconstrained optimization objective function and converting the Euclidean gradient of the unconstrained optimization objective function into a Riemannian gradient; Solving the Euclidean Hessian of the unconstrained optimization objective function and converting the Euclidean Hessian of the unconstrained optimization objective function into a Riemannian Hessian; Based on the Riemann gradient and Riemann Hessian of the unconstrained optimization objective function, a second-order Taylor expansion is performed on the unconstrained optimization objective function in the tangent space of the Riemann product manifold to obtain a second-order approximate model of the unconstrained optimization objective function, and a cubic adaptive regularization term is introduced into the second-order approximate model to construct a regularized approximate model; The degree of fit between the regularized approximation model and the unconstrained optimization objective function is calculated. The degree of fit between the regularized approximation model and the unconstrained optimization objective function is solved by the following formula: in, represents the constructed regularized approximate model, Indicates the The direction vector corresponding to the iteration is the tangent vector on the tangent space of the Riemann product manifold, Indicates the dimension Column vector of , Represents the regularized approximate model in The value of Represents the contraction operator, which is used to map the iterative points on the tangent space of the Riemann product manifold back to the manifold surface. The calculation method is: in, Represents a point on the tangent space The tangent vector at Represents a point on the tangent space The tangent vector at Indicates a point Along the tangent vector The contraction operator, Indicates a point Along the tangent vector The contraction operator of ; Based on the degree of fit and the preset regularization parameters and iteration point update criteria, the regularization parameters and iteration point update criteria are updated until the iteration stop condition is met, and the current radar transmit waveform and the unmatched filter used by the radar receiver are output.

2. The radar transmitting and receiving joint anti-intermittent sampling and forwarding interference method according to claim 1 is characterized in that: described , expressed as: in, represents the Hadamard product, It represents the sampling sequence of the radar transmission waveform by the intermittent sampling and forwarding jammer. , ， ， is the penalty factor, Indicates the preset peak value after intermittent sampling and forwarding interference signal non-matched filtering processing, Indicates the modulo value.

3. The radar transmitting and receiving joint anti-intermittent sampling and forwarding interference method according to claim 1 is characterized in that: described , expressed as: The function component is introduced The peak value of the unconstrained radar emission waveform after non-matched filtering is close to the preset value , is the penalty factor, ， ， To exclude A constant matrix with 0 diagonal elements and 1 in the remaining diagonal elements.

4. The radar transmitting and receiving joint anti-intermittent sampling and forwarding interference method according to claim 1, 2 or 3, characterized in that: Pareto weight .

5. The radar transmitting and receiving joint anti-intermittent sampling and forwarding interference method according to claim 1, 2 or 3, characterized in that: The transmit-receive joint constrained optimization objective function for resisting intermittent sampling forwarding interference is converted into an unconstrained optimization objective function on the Riemann product manifold space, which is expressed as: The Cartesian product is defined as , then the variable Space Expressed as and The Riemann product manifold space formed by , , ,in express Dimensional European space, Indicates conjugation.

6. The radar transmitting and receiving joint anti-intermittent sampling and forwarding interference method according to claim 5 is characterized in that: In the At the first iteration, The variable corresponding to the iteration for ,exist The regularized approximate model constructed here is: in, represents the constructed regularized approximate model, Represents the regularized approximate model in The value of represents the adaptive regularization parameter, Represents the regularized approximate model in The gradient at represents the Riemannian metric, is a constant with a value range of , Indicates the The corresponding unconstrained optimization objective function at the iteration The Riemann Hessian, Indicates the The direction vector corresponding to the iteration is the tangent vector on the tangent space of the Riemann product manifold; Indicates the The corresponding unconstrained optimization objective function at the iteration The Riemann gradient of .

7. The radar transmitting and receiving joint anti-intermittent sampling and forwarding interference method according to claim 6 is characterized in that: The regularization parameters and iteration point update criteria are as follows: ， in, Represents the lower bound of the regularization parameter, and the threshold parameter satisfies , the regularization update coefficient satisfies ;when When , accept the solution of the regularization subproblem and update the iteration point; when the model fit parameter further satisfies When , update the iteration point and reduce the regularization parameter; when , reject the solution to the regularized subproblem and increase the regularization parameter.

8. Radar transceiver joint anti-intermittent sampling and forwarding interference device, characterized in that: include: The first module is used to establish a joint transmit-receive constrained optimization objective function for resisting intermittent sampling and forwarding interference by minimizing the unmatched filtering integrated sidelobe level of the radar transmit waveform and the integrated level of the radar receiver after unmatched filtering of the intermittent sampling and forwarding interference signal under the constraints of waveform constant modulus constraint, receive filter energy constraint, and unmatched filtering peak loss constraint. The second module is used to convert the transmit-receive joint constraint optimization objective function on the Euclidean space into an unconstrained optimization objective function on the Riemann product manifold space, which is: The sampling sequence of the radar transmission waveform is: ,in represents the sampling sequence, Indicates the number of sampling points of radar transmission waveform, represents the transpose operation, represents the Pareto weight; the non-matched filter at the radar receiving end processes the intermittent sampling forwarding interference signal, where the non-matched filter sequence of the non-matched filter at the radar receiving end is expressed as , represents the sampling sequence of the non-matched filter at the radar receiver, represents the conjugate transpose operation; It indicates the integration level after the radar receiver uses a non-matched filter to process the intermittent sampling forwarding interference signal. It represents the non-matched filtered integrated sidelobe level of the radar transmit waveform with peak point constraint; A third module is used to solve the Euclidean gradient of the unconstrained optimization objective function and convert the Euclidean gradient of the unconstrained optimization objective function into a Riemannian gradient; A fourth module is used to solve the Euclidean Hessian of the unconstrained optimization objective function and convert the Euclidean Hessian of the unconstrained optimization objective function into a Riemann Hessian; A fifth module is configured to perform a second-order Taylor expansion of the unconstrained optimization objective function in the tangent space of the Riemann product manifold based on the Riemann gradient and the Riemann Hessian of the unconstrained optimization objective function to obtain a second-order approximate model of the unconstrained optimization objective function, and introduce a cubic adaptive regularization term into the second-order approximate model to construct a regularized approximate model; The sixth module is used to calculate the degree of fit between the regularized approximation model and the unconstrained optimization objective function. The degree of fit between the regularized approximation model and the unconstrained optimization objective function is solved by the following formula: in, represents the constructed regularized approximate model, Indicates the dimension Column vector of , Represents the regularized approximate model in The value of Represents the contraction operator, which is used to map the iterative points on the tangent space of the Riemann product manifold back to the manifold surface. The calculation method is: in, Represents a point on the tangent space The tangent vector at Represents a point on the tangent space The tangent vector at Indicates a point Along the tangent vector The contraction operator, Indicates a point Along the tangent vector The contraction operator of The seventh module is used to update the regularization parameters and the iteration point update criteria based on the degree of fit and the preset regularization parameters and iteration point update criteria until the iteration stop condition is met, and output the current radar transmission waveform and the non-matched filter used by the radar receiving end.

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