A joint transmit-receive method to combat intermittent sampling and forwarding interference based on Riemann product manifold space

Abstract

This invention proposes a joint transmit-receive anti-intermittent sampling and forwarding interference (ISRJ) method based on a Riemann product manifold space. The method includes establishing a joint constrained optimization objective function for anti-ISRJ by minimizing the unmatched filtering integrated sidelobe level of the radar transmit waveform and the integrated level of the intermittent sampling and forwarding interference signal after the radar receiver performs non-matched filtering on the radar transmit waveform, subject to waveform constant modulus constraints, receive filter energy constraints, and non-matched filter peak loss constraints. The method then converts the joint constrained optimization objective function for anti-ISRJ into an unconstrained optimization objective function on a Riemann product manifold space. The method then solves the unconstrained optimization objective function to output the radar transmit waveform and the non-matched filter sequence used by the radar receiver. This method considers the joint optimization problem of the transmit waveform and receive filter, improves the anti-ISRJ capability of the pulse Doppler radar, and can simultaneously update the transmit waveform and receive filter with good convergence.

Description

Technical Field

[0001] The present invention mainly relates to the technical field of radar anti-active interference, in particular to a Riemann product manifold space-based method for jointly transmitting and receiving to resist intermittent sampling and forwarding interference. Background Art

[0002] With the widespread application of digital radio frequency memory (DFRM) technology in modern electronic warfare, interrupted-sampling repeater jamming (ISRJ) has become an important countermeasure against classic pulse Doppler radars. In actual operation, the DFRM device in ISRJ begins partial sampling and forwarding after detecting the opposing radar's transmit waveform. Because the ISRJ signal is partially coherent with the radar's transmit waveform, it can also achieve a certain gain after matched filtering with the radar transmit signal at the receiver. For a classic linear frequency modulation signal, the corresponding ISRJ pulse compression result will appear as a cluster of false targets, where the number of peak points is equal to the number of interference slice forwards, and the peak spacing corresponds to the interference slice delay.

[0003] Currently, there are two main technical routes for research results against ISRJ:

[0004] The first is interference identification and suppression at the receiving end. Current receiver-side interference suppression methods typically estimate interference parameters based on radar echo data processing, then reconstruct the interference signal. Finally, cancellation methods are used to suppress the ISRJ component in the radar echo. However, the interference suppression performance of these methods is highly dependent on the interference parameter estimation results. When the estimation results are biased, the impact of ISRJ on target detection is often ineffective.

[0005] Second, waveform optimization is performed on the radar transmitter to minimize ISRJ signals from entering the radar receiver. Current ISRJ mitigation methods based on waveform optimization typically design a transmit waveform with low ISRJ response characteristics, assuming precise interference parameters are known, to minimize interference energy from entering the radar receiver. Due to the limited degrees of freedom in waveform optimization, these methods offer less than ideal interference mitigation performance in complex active scenarios. Summary of the Invention

[0006] Aiming at the technical problems existing in the prior art, in order to give full play to the freedom of radar signal processing and further improve the ISRJ suppression performance, the present invention proposes a joint transmit-receive anti-intermittent sampling forwarding interference method based on Riemann product manifold space.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] On the one hand, the present invention provides a Riemann product manifold space-based joint transmission and reception anti-intermittent sampling forwarding interference method, comprising:

[0009] Under the constraints of waveform constant modulus, receive filter energy, and non-matched filter peak loss, a joint constrained optimization objective function for resisting intermittent sampling forwarding interference is established by minimizing the non-matched filter integrated sidelobe level of the radar transmit waveform and the integrated level of the intermittent sampling forwarding interference signal processed by the radar receiver through non-matched filtering.

[0010] Converting the joint constrained optimization objective function for resisting intermittent sampling and forwarding interference into an unconstrained optimization objective function on a Riemann product manifold space;

[0011] The unconstrained optimization objective function is solved to output the radar transmit waveform x and the unmatched filter h used by the radar receiver.

[0012] Furthermore, in a preferred embodiment, the established joint constrained optimization objective function for resisting intermittent sampling and forwarding interference is:

[0013]

[0014] st|x1|=…=|x N |=1,h H h=N

[0015] Assume that the discrete form of radar emission waveform is x=[x1,…,x N ] T , where x1,…,x N Represents the N sampling points of the radar signal, where N represents the number of sampling points of the radar transmission waveform, (·) T represents the transpose operation, λ∈[0,1] represents the Pareto weight; an unmatched filter h=[h1,…,h N ] T Process the intermittent sampling and forwarding interference signal, h1,…,h N represents the N sampling points of the receiving filter, (·) 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.

[0016] Furthermore, in a preferred embodiment, the 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:

[0017]

[0018] 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.

[0019] Furthermore, in a preferred embodiment, solving the unconstrained optimization objective function includes:

[0020] Solving the Euclidean gradient of the unconstrained optimization objective function and converting the Euclidean gradient into a Riemannian gradient;

[0021] Solving the Euclidean Hessian of the unconstrained optimization objective function and converting the Euclidean Hessian into a Riemannian Hessian;

[0022] 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 f(y) in the tangent space of the Riemann product manifold to obtain a second-order approximate model of the unconstrained optimization objective function for constructing a trust region subproblem;

[0023] Calculating the degree of fit between the second-order approximation model and the unconstrained optimization objective function;

[0024] Based on the degree of fit and the preset trust region parameters and iteration point update criteria, the trust region parameters and iteration points are updated until the iteration stop condition is met, and the current radar transmit waveform x and the unmatched filter h used by the radar receiver are output.

[0025] The method for 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).

[0026] On the other hand, the present invention provides a Riemann product manifold space-based transmitting and receiving joint anti-intermittent sampling forwarding interference device, comprising:

[0027] The first module is used to establish a joint 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 intermittent sampling and forwarding interference signal after the radar receiver performs unmatched filtering under the constraints of waveform constant modulus, receiving filter energy, and unmatched filtering peak loss.

[0028] The second module is used to convert the joint constrained optimization objective function for resisting intermittent sampling and forwarding interference into an unconstrained optimization objective function on the Riemann product manifold space;

[0029] The third module is used to solve the unconstrained optimization objective function and output the radar transmission waveform x and the unmatched filter h used by the radar receiving end.

[0030] 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:

[0031] Under the constraints of waveform constant modulus, receive filter energy, and non-matched filter peak loss, a joint constrained optimization objective function for resisting intermittent sampling forwarding interference is established by minimizing the non-matched filter integrated sidelobe level of the radar transmit waveform and the integrated level of the intermittent sampling forwarding interference signal processed by the radar receiver through non-matched filtering.

[0032] Converting the joint constrained optimization objective function for resisting intermittent sampling and forwarding interference into an unconstrained optimization objective function on a Riemann product manifold space;

[0033] The unconstrained optimization objective function is solved to output the radar transmit waveform x and the unmatched filter h used by the radar receiver.

[0034] 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:

[0035] Under the constraints of waveform constant modulus, receive filter energy, and non-matched filter peak loss, a joint constrained optimization objective function for resisting intermittent sampling forwarding interference is established by minimizing the non-matched filter integrated sidelobe level of the radar transmit waveform and the integrated level of the intermittent sampling forwarding interference signal processed by the radar receiver through non-matched filtering.

[0036] Converting the joint constrained optimization objective function for resisting intermittent sampling and forwarding interference into an unconstrained optimization objective function on a Riemann product manifold space;

[0037] The unconstrained optimization objective function is solved to output the radar transmit waveform x and the unmatched filter h used by the radar receiver.

[0038] The present invention considers the joint optimization problem of the transmitting waveform and the receiving filter under the background of the problem of resisting intermittent sampling repeater jamming (ISRJ). Specifically, the present invention first establishes a joint constrained optimization objective function by minimizing the waveform non-matched filter integrated sidelobe level (ISL) of the radar transmitting waveform and the intermittent sampling repeater jamming (ISRJ) signal integrated level (IntegratedLevels, IL) under the waveform constant modulus constraint, the receiving filter energy constraint and the non-matched filter peak loss constraint, and then proposes a method for solving the unconstrained optimization objective function based on the Riemannian Product Manifold Trust Region (RPM-TR) algorithm, thereby realizing the synchronous update of the transmitting 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:

[0039] First, it expands the degrees of freedom for suppressing Interrupted-Sampling Repeater Jamming (ISRJ). Traditional ISRJ suppression methods focus solely on the transmitter or receiver, while this invention considers the joint optimization of the transmit waveform and the receive filter, improving the pulse Doppler radar's resistance to ISRJ.

[0040] Second, the transmit waveform and receive filter are updated simultaneously. For joint optimization problems, the classic approach is to employ an alternating optimization strategy, where one variable is fixed and the other is optimized, alternating optimization until convergence. However, this approach transforms the multi-constrained optimization problem in Euclidean space into an unconstrained optimization problem in the space of a Riemann product manifold and uses a gradient-based method to achieve the simultaneous update of the transmit waveform and receive filter.

[0041] Third, it offers excellent convergence performance. This paper proposes an RPM-TR algorithm for joint optimization of the transmit waveform and receive filter to effectively mitigate ISRJ. Compared to classical methods, this method boasts a superlinear convergence rate, can achieve lower objective function values, and exhibits superior ISRJ mitigation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] 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.

[0043] Figure 1 is a flow chart of an embodiment;

[0044] Figure 2 is a graph showing changes in the objective function value versus the number of iterations in one embodiment;

[0045] Figure 3 is a graph showing a change in the gradient norm value versus the number of iterations in one embodiment;

[0046] Figure 4 This is a diagram showing the matched filtering results of a linear frequency modulation waveform during a single forwarding of an ISRJ in one embodiment;

[0047] Figure 5 This is a diagram of the unmatched filtering result output by the RPM-TR algorithm during a single forwarding of the ISRJ in one embodiment;

[0048] Figure 6 This is a diagram showing the matched filtering results of a linear frequency modulation waveform when the ISRJ forwards twice in one embodiment;

[0049] Figure 7 This is a diagram of the unmatched filtering result output by the RPM-TR algorithm when ISRJ forwards twice in one embodiment. DETAILED DESCRIPTION

[0050] 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.

[0051] Reference Figure 1 In one embodiment, a method for jointly transmitting and receiving to resist intermittent sampling and forwarding interference based on a Riemann product manifold space is provided, comprising:

[0052] (1) Establish a joint constrained optimization objective function to resist intermittent sampling and forwarding interference.

[0053] In this embodiment, a joint constrained optimization objective function for resisting intermittent sampling and forwarding interference is established by minimizing the unmatched filtering integrated sidelobe level of the radar transmit waveform and the integrated level of the radar receiving end after unmatched filtering of the intermittent sampling and forwarding interference signal, taking into account the waveform constant modulus constraint, the receive filter energy constraint, and the unmatched filtering peak loss constraint.

[0054]

[0055] st|x1|=…=|x N |=1,h H h=N

[0056] Assume that the discrete form of radar emission waveform is x=[x1,…,x N ] T , where x1,…,x N Represents the N sampling points of the radar signal, where N represents the number of sampling points of the radar transmission waveform, (·) T represents the transpose operation, λ∈[0,1] represents the Pareto weight; an unmatched filter h=[h1,…,h N ] T Process the intermittent sampling and forwarding interference signal, h1,…,h N represents the N sampling points of the receiving filter, (·) 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.

[0057] (2) converting the joint constrained optimization objective function for resisting intermittent sampling and forwarding interference into an unconstrained optimization objective function on the Riemann product manifold space;

[0058] (3) Solve the unconstrained optimization objective function and output the radar transmit waveform and the non-matched filter used by the radar receiver.

[0059] In an electronic countermeasure environment, the IRSJ jammer first detects and receives radar signals, and then partially forwards the received radar signals to interfere with the enemy radar.

[0060] Assume that the discrete form of radar emission waveform is x=[x1,…,x N ] T , where x1,…,x N Represents the N sampling points of the radar signal, where N represents the number of sampling points of the radar transmission waveform, (·) Trepresents the transposition operation. Then the interference signal x forwarded by the IRSJ jammer is j It can be expressed as:

[0061] x j =x⊙p,

[0062] Where ⊙ represents the Hadamard product, p=[p1,…p n ,…,p N ] T It represents the sampling vector of the radar transmission waveform of the IRSJ jammer, p n ∈{0,1}. At the radar receiver, a non-matched filter h=[h1,…,h N ] T Process the ISRJ signal, where h1,…,h N Represents the N sampling points of the receiving filter, then the IL value after ISRJ signal processing can be calculated as:

[0063]

[0064] in,(·) H Represents the conjugate transpose operation.

[0065] At the same time, in order to control the peak intensity of the ISRJ signal after being processed by the non-matched filter to effectively suppress the ISRJ, the function component |(h⊙p) is introduced H xb min 2 , and then the radar receiver uses a non-matched filter to process the intermittent sampling forwarding interference signal through non-matched filtering. IL (x,h), we have:

[0066]

[0067] in,

[0068]

[0069] β is the penalty factor, b min represents the preset peak value of the ISRJ signal after unmatched filtering, and |·| represents the modulus value.

[0070] In order to simultaneously obtain a low sidelobe waveform with excellent pulse compression performance, the ISL value of the radar transmit waveform is further minimized. After the non-matched filtering process with the non-matched filter h, the ISL value of the radar transmit waveform can be expressed as:

[0071] ISL=x H Λ H WΛx=h H ΦH WΦh

[0072] in,

[0073] is the non-matched filter and waveform correlation matrix, and W is a constant matrix with all diagonal elements being 1 except the Nth diagonal element being 0.

[0074] Since the non-matched filtering process under white noise conditions will cause processing gain loss, the present invention sets a preset value b for controlling the peak level of the waveform non-matched filtering. max , by introducing the function component |h H xb max | 2 To force the peak value of the radar transmission waveform after non-matched filtering to be close to the preset peak level b max Therefore, the non-matched filtering integrated sidelobe level f of the radar transmission waveform with peak point constraint is ISL (x,h) can be expressed as:

[0075] 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

[0076] Among them, α is the penalty factor.

[0077] In actual radar operating scenarios, to maintain the radar transmitter at maximum efficiency while effectively controlling processing gain loss, the transmit waveform and receive filter should satisfy constant modulus constraints and energy constraints, respectively. Thus, within the Pareto optimization framework, the joint constrained optimization objective function for resisting intermittent sampling and forwarding interference is established, expressed as:

[0078]

[0079] st|x1|=…=|x N |=1,h H h=N

[0080] Where λ∈[0,1] represents the Pareto weight. To balance the anti-ISRJ requirement and waveform pulse compression performance, λ is usually set to 0.5.

[0081] In one embodiment, the 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:

[0082]

[0083] 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

[0084] in represents N-dimensional complex Euclidean space, (·) * represents the conjugate. Then the constant modulus constraint and energy constraint respectively limit the smooth search space and Considering the dimension of the manifold, and Any point on it is differentiable everywhere, and the two actually constitute different closed manifold spaces, namely the complex circle manifold (CCM) and the complex sphere manifold (CSM).

[0085] For the above unconstrained optimization objective function, 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 x and the unmatched filter h used by the radar receiver.

[0086] In a preferred embodiment, a method for solving the unconstrained optimization objective function is proposed, comprising:

[0087] Solving the Euclidean gradient of the unconstrained optimization objective function and converting the Euclidean gradient into a Riemannian gradient;

[0088] Solving the Euclidean Hessian of the unconstrained optimization objective function and converting the Euclidean Hessian into a Riemannian Hessian;

[0089] 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 f(y) in the tangent space of the Riemann product manifold to obtain a second-order approximate model of the unconstrained optimization objective function for constructing a trust region subproblem;

[0090] Calculating the degree of fit between the second-order approximation model and the unconstrained optimization objective function;

[0091] Based on the degree of fit and the preset trust region parameters and iteration point update criteria, the trust region parameters and iteration points are updated until the iteration stop condition is met, and the current radar transmit waveform x and the unmatched filter h used by the radar receiver are output.

[0092] Specifically, in one embodiment, a Euclidean gradient calculation process for solving the unconstrained optimization objective function f(y) is given as follows:

[0093]

[0094] in,

[0095]

[0096]

[0097]

[0098] Specifically, in one embodiment, a method for converting a Euclidean gradient into a Riemannian gradient is provided, including:

[0099] For the established Riemann product manifold The Riemannian gradient gradf(y) and the Euclidean gradient Gradf(y) of the unconstrained optimization objective function f(y) have the following projection relationship:

[0100] gradf(y)=(grad x f(x,h),grad h f(x,h))

[0101] =(Proj x {Grad x f(x,h)},Proj h {Grad h f(x,h)})

[0102] Among them, Proj x and Proj h Riemannian manifold space and The projection operator on has the following form:

[0103]

[0104] Among them, Re(·) means taking the real part of each element. and express and The tangent space of , its parameterized expressions are:

[0105]

[0106] In addition, the product manifold tangent space Can be and The Cartesian product representation is:

[0107]

[0108] 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:

[0109]

[0110] Specifically, in one embodiment, a Euclidean Hessian calculation process for solving the unconstrained optimization objective function f(y) is given as follows:

[0111] For the unconstrained optimization objective function f(y), it is along the direction ξ y The Euclidean Hessian can be calculated as

[0112] 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) ])

[0113] 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:

[0114]

[0115] Similarly, the Euclidean Hessian of the unconstrained optimization objective function f(y) with respect to h is calculated as follows:

[0116]

[0117] Converting Euclidean Hessian to Riemannian Hessian: 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,

[0118] hessf(y)[ξy ]=hessf(x,h)[ξ (x,h) ]

[0119] =(hess x f(x,h)[ξ (x,h) ],hess h f(x,h)[ξ (x,h) ])

[0120] 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 objective function 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 product manifold. Using the projection relationship between the Riemann Hessian and the Euclidean Hessian, the two can be calculated as:

[0121]

[0122] In one embodiment, at the current kth iteration, the corresponding variable y is y k =(x k ,h k ), the corresponding second-order approximate model m k (ξ (x,h) )for:

[0123]

[0124]

[0125] where ξ( x,h ) represents the direction vector, which is the tangent vector on the tangent space of the Riemann product manifold; Δ k represents the trust region radius at the current k-th iteration, g(·) represents the Riemann metric, which can be a complex Euclidean inner product, hessf(x k ,h k )[ξ (x,h) ] and gradf(x k ,h k ) represent the Riemann gradient and Riemann Hessian of the unconstrained optimization objective function at the current k-th iteration, x k ,h k They represent the radar transmission waveform x corresponding to the current k-th iteration and the non-matched filter used by the radar receiver. is a linear Euclidean space. The trust region subproblem can be solved using the solution method on the Euclidean space to obtain the displacement vector of the current iteration point.

[0126] In one embodiment, a method for calculating the degree of fit between the second-order approximation model and the unconstrained optimization objective function is proposed. Specifically, the degree of fit between the second-order approximation model and the unconstrained optimization objective function is calculated by the following formula: k :

[0127]

[0128] 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 of the Riemann product manifold back to the manifold surface. The calculation method is:

[0129]

[0130] 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 .

[0131] In one embodiment, a trust region parameter and iteration point update criterion is proposed as follows:

[0132]

[0133] The threshold parameter ρ2∈(ρ1,1];Δ k represents the trust region radius at the current k-th iteration; when the second-order approximation model calculated at the current k-th iteration fits the unconstrained optimization objective function ρ k When the value is less than the threshold parameter ρ1, the second-order approximation model does not conform to the unconstrained optimization objective function, the solution of the trust region subproblem should be discarded, and the trust region radius should be reduced; when ρ k When the value is greater than or equal to the threshold parameter ρ1 and close to 1, the second-order approximation model is closer to the unconstrained optimization objective function. At this time, the trust region radius is expanded and the solution of the trust region subproblem is accepted. For other cases, the trust region radius is kept unchanged and the solution of the acceptance region subproblem is accepted.

[0134] The method for 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).

[0135] The effect of the Riemann product manifold space-based joint transmit-receive anti-intermittent sampling forwarding interference method provided by the present invention is further illustrated by the following numerical simulation experiments:

[0136] 1. Experimental scenario:

[0137] 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 .

[0138] 2. Experimental content

[0139] 2.1) Problem Modeling: Considering the waveform constant modulus constraint, the receive filter energy constraint, and the unmatched filter peak loss constraint, a joint constrained optimization objective function for combating intermittent sampling forwarding interference is established by minimizing the unmatched filter integrated sidelobe level of the radar transmit waveform and the integrated level of the unmatched filter processing of the intermittent sampling forwarding interference signal at the radar receiver. Initialize the radar transmit waveform, the unmatched filter used by the radar receiver, and the algorithm iteration stop condition.

[0140] 2.2) Optimization model form conversion: Using the waveform constant modulus constraint and the receiving filter energy constraint, the joint constrained optimization objective function in the Euclidean space is transformed into an unconstrained optimization objective function in the Riemann product manifold space.

[0141] 2.3) Iteratively solve the unconstrained optimization objective function on the Riemann product manifold space.

[0142] 2.4) Convergence determination: If the iteration stopping condition is met, the radar transmit waveform and the unmatched filter used by the radar receiver are output; otherwise, step 2.3 is repeated until convergence.

[0143] The implementation method of each of the above steps can adopt the method described in any of the above embodiments, which will not be repeated here.

[0144] Figure 2 The graph shows how the objective function value changes with the number of iterations during the execution of the RPM-TR algorithm. As can be seen from the figure, the objective function value decreases monotonically with increasing iterations, reaching convergence after the 400th iteration, and the algorithm stops running. Figure 3A graph showing the gradient norm of the objective function versus the number of iterations is given. As can be seen from the figure, due to the strong non-convexity of the optimization model, the gradient norm curve fluctuates significantly, but generally shows a downward trend. Figure 4 The results of matched filtering of the linear frequency modulation waveform during a single ISRJ forwarding are shown. The figure contains a number of false targets, with the highest value being -9.89dB, which seriously interferes with target detection. Figure 5 The unmatched filtering result of the RPM-TR algorithm output during a single forwarding of the ISRJ is given. The maximum sidelobe value is -15.40dB, and the interference target generated by the ISRJ is effectively suppressed.

[0145] 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 results of matched filtering of the linear frequency modulation waveform during the two retransmissions of the ISRJ are shown. There are two groups of false targets in the figure, with the highest values ​​of -7.87dB and -5.62dB respectively, which seriously interfere with the detection of the target. Figure 7 The unmatched filtering result of the RPM-TR algorithm output when the ISRJ is forwarded twice is given. The highest sidelobe value is -12.52dB, and the interference target generated by the ISRJ is effectively suppressed.

[0146] In one embodiment, a Riemann product manifold space-based joint transmitting and receiving device for resisting intermittent sampling and forwarding interference is provided, comprising:

[0147] The first module is used to establish a joint 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 intermittent sampling and forwarding interference signal after the radar receiver performs unmatched filtering under the constraints of waveform constant modulus, receiving filter energy, and unmatched filtering peak loss.

[0148] The second module is used to convert the joint constrained optimization objective function for resisting intermittent sampling and forwarding interference into an unconstrained optimization objective function on the Riemann product manifold space;

[0149] The third module is used to solve the unconstrained optimization objective function and output the radar transmission waveform x and the unmatched filter h used by the radar receiving end.

[0150] 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.

[0151] On the other hand, 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, it implements the steps of the Riemann product manifold space-based joint transmit-receive anti-intermittent sampling forwarding interference method provided in any of the above-mentioned 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 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.

[0152] 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 jointly transmitting and receiving to resist intermittent sampling forwarding interference based on the Riemann product manifold space provided in any of the above embodiments are implemented.

[0153] 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).

[0154] Matters not covered by the present invention are known technologies.

[0155] 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.

[0156] 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.

[0157] 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 joint transmit-receive anti-intermittent sampling forwarding interference method based on Riemann product manifold space, characterized in that: include: Under the constraints of waveform constant modulus, receive filter energy, and non-matched filter peak loss, a joint constrained optimization objective function for resisting intermittent sampling forwarding interference is established by minimizing the non-matched filter integrated sidelobe level of the radar transmit waveform and the integrated level of the intermittent sampling forwarding interference signal processed by the radar receiver through non-matched filtering. Assume that the discrete form of the radar transmission waveform is ,in Represents radar signal sampling points, Indicates the number of sampling points of radar transmission waveform, represents the transpose operation, Represents Pareto weight; non-matched filter is used at the radar receiver Process the intermittent sampling and forwarding interference signal, Indicates the receive filter sampling points, 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; Converting the joint constrained optimization objective function for resisting intermittent sampling and forwarding interference into an unconstrained optimization objective function on a Riemann product manifold space; Solve the unconstrained optimization objective function and output the radar transmission waveform and the non-matched filter used at the radar receiver .

2. The Riemann product manifold space-based transmit-receive joint anti-intermittent sampling forwarding interference method according to claim 1, characterized in that: The radar receiving end uses a non-matching filter to perform non-matching filtering on the intermittent sampling forwarding interference signal. , expressed as: in, represents the Hadamard product, represents the sampling vector of the radar transmission waveform of the jammer, , ， ， is the penalty factor, Indicates the preset peak value of the ISRJ signal after non-matched filtering. Indicates the modulo value.

3. The Riemann product manifold space-based transmit-receive joint anti-intermittent sampling forwarding interference method according to claim 1, characterized in that: Unmatched Filtering Integrated Sidelobe Level of Radar Transmitted Waveform with Peak Point Constraint , expressed as: in, is the penalty factor, is the preset value used to control the peak level of the waveform unmatched filter, and are the non-matched filter and radar transmit waveform correlation matrices, ， ， To exclude A constant matrix with 0 diagonal elements and 1 in the remaining diagonal elements.

4. The Riemann product manifold space-based transmit-receive joint anti-intermittent sampling forwarding interference method according to claim 1, 2 or 3, characterized in that: Pareto weight The value is 0.

5.

5. The Riemann product manifold space-based joint transmit-receive anti-intermittent sampling forwarding interference method according to claim 1, 2 or 3, characterized in that: The 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: 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 Riemann product manifold space-based joint transmit-receive anti-intermittent sampling forwarding interference method according to claim 5, characterized in that: Solving the unconstrained optimization objective function includes: Solving the Euclidean gradient of the unconstrained optimization objective function and converting the Euclidean gradient into a Riemannian gradient; Solving the Euclidean Hessian of the unconstrained optimization objective function and converting the Euclidean Hessian into a Riemannian Hessian; Based on the Riemann gradient and Riemann Hessian of the unconstrained optimization objective function, the objective function is tangent to the Riemann product manifold space. Performing a second-order Taylor expansion to obtain a second-order approximate model of the unconstrained optimization objective function for constructing a trust region subproblem; Calculating the degree of fit between the second-order approximation model and the unconstrained optimization objective function; Based on the degree of agreement and the preset trust region parameters and iteration point update criteria, the trust region parameters and iteration points are updated until the iteration stop condition is met, and the current radar transmission waveform is output. and the non-matched filter used at the radar receiver .

7. The Riemann product manifold space-based joint transmit-receive anti-intermittent sampling forwarding interference method according to claim 6, characterized in that: In the current At the iteration, the corresponding variable for , the corresponding second-order approximate model for: in represents the direction vector, which is the tangent vector on the tangent space of the Riemann product manifold; Indicates the current The trust region radius at the iteration, represents the Riemannian metric; and Respectively represent the current The Riemann gradient and Riemann Hessian of the unconstrained optimization objective function at the iteration, Respectively represent the current The radar emission waveform corresponding to the iteration and the non-matched filter used at the radar receiver.

8. The Riemann product manifold space-based joint transmit-receive anti-intermittent sampling forwarding interference method according to claim 7, characterized in that: The degree of agreement between the second-order approximation model and the unconstrained optimization objective function is calculated by the following formula: : in, Indicates the dimension Column vector 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, Indicates a point The direction vector at Indicates a point The direction vector at .

9. The Riemann product manifold space-based joint transmit-receive anti-intermittent sampling forwarding interference method according to claim 8, characterized in that: The trust region parameters and iteration point update criteria are as follows: ， The threshold parameter , ; Indicates the current The radius of the trust region at the iteration; when the current The degree of agreement between the second-order approximate model calculated by the iteration and the unconstrained optimization objective function The value is less than the threshold parameter When , the second-order approximation model does not conform to the unconstrained optimization objective function, the solution of the trust region subproblem should be discarded and the trust region radius should be reduced; when The value is greater than or equal to the threshold parameter When is close to 1, the second-order approximation model is relatively close to the unconstrained optimization objective function. At this time, the trust region radius is expanded and the solution of the trust region subproblem is accepted. For other cases, the trust region radius is kept unchanged and the solution of the acceptance region subproblem is accepted.

10. A joint transmitting and receiving device for resisting intermittent sampling and forwarding interference based on Riemann product manifold space, characterized in that: include: The first module is used to establish a joint 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 intermittent sampling and forwarding interference signal after the radar receiver performs unmatched filtering under the constraints of waveform constant modulus, receiving filter energy, and unmatched filtering peak loss. Assume that the discrete form of the radar transmission waveform is ,in Represents radar signal sampling points, Indicates the number of sampling points of radar transmission waveform, represents the transpose operation, Represents Pareto weight; non-matched filter is used at the radar receiver Process the intermittent sampling and forwarding interference signal, Indicates the receive filter sampling points, 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; The second module is used to convert the joint constrained optimization objective function for resisting intermittent sampling and forwarding interference into an unconstrained optimization objective function on the Riemann product manifold space; The third module is used to solve the unconstrained optimization objective function and output the radar transmission waveform and the non-matched filter used at the radar receiver .

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