Transmit-receive design method for clutter suppression of tangential maneuvering target detection

Abstract

The application discloses a clutter suppression transceiver design method for tangential maneuvering target detection, first, a slow-time echo model of a target, clutter and noise is established under an initial phase agile signal system, then a slow-time window function is introduced at a signal processing end to construct a clutter energy target function, and a clutter energy minimization problem is established under constant modulus constraint, peak matching constraint and signal-to-noise ratio loss constraint, an SISWP algorithm is proposed, the original optimization problem is converted into a sub-problem based on an inter-pulse initial phase and a window function, a QRARC algorithm and a KKT condition are alternately iterated, and finally, the transmission and reception joint optimization design of clutter suppression is realized. The method of the application does not depend on prior knowledge of the clutter distribution, has good robustness, realizability and generalization, fully utilizes the waveform optimization degree of freedom of the transmission end of the airborne radar, further strengthens the suppression effect of the waveform on the range ambiguity clutter by introducing new optimization variables at the signal processing end, and greatly improves the detection performance on the tangential maneuvering target.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a clutter suppression transceiver design method for detecting tangentially maneuvering targets. Background Technology

[0002] Clutter suppression is a major challenge for airborne radar in detecting tangentially maneuvering targets. On the one hand, the direction of motion of tangentially maneuvering targets is perpendicular to the radar main lobe beam, causing the target to fall into the main lobe clutter region. On the other hand, in order to ensure the effectiveness of target coherent accumulation, airborne radar often operates at medium and high pulse repetition frequencies (PRF), making it highly susceptible to range ambiguity folding clutter, which ultimately leads to false detection or missed detection of targets, seriously affecting the detection performance of airborne radar.

[0003] Studies have shown that airborne radar can reconstruct clutter spectra by designing inter-pulse signal parameters according to the detection scenario, thereby avoiding target aliasing with strong clutter. The initial phase codeword is a typical inter-pulse design parameter, offering higher hardware feasibility and more flexible optimization methods. Fuzzy function shaping is one method for implementing inter-pulse initial phase design. Fuzzy function shaping does not rely on prior information about clutter distribution and can suppress fuzzy clutter with unknown terrain within the interval. Therefore, fuzzy function shaping based on inter-pulse initial phase codeword design is considered a technical approach to solving this type of problem. The paper "Quartic Gradient Descent for Tractable Radar Slow-Time Ambiguity Function Shaping, IEEE Transactions on Aerospace and Electronic Systems, vol.56, no.2, pp.1474-1489, Apr.2020" designs the inter-pulse initial phase using a manifold algorithm to achieve clutter interval suppression based on ambiguity function shaping. However, this study only considers the design of the transmitted waveform and does not optimize the signal processing end, resulting in limited clutter suppression performance and difficulty in solving the problem of detecting tangentially maneuvering targets in strong clutter. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a clutter suppression transceiver design method for tangential maneuvering target detection, achieving joint optimization design of transmission and reception for clutter suppression.

[0005] The technical solution adopted in this invention is: a clutter suppression transceiver design method for detecting tangentially maneuvering targets, the specific steps of which are as follows:

[0006] S1. Establish a slow-time total echo model for initial-phase agile airborne radar.

[0007] S2. Based on step S1, process the echo signal and construct a joint optimization problem for clutter suppression based on range ambiguity;

[0008] S3. Solve the joint optimization problem based on the SISWP algorithm to complete the clutter suppression transceiver design for tangential maneuvering target detection.

[0009] Furthermore, step S1 is specifically as follows:

[0010] S11. Establish a slow-time initial phase agile target echo model;

[0011] Given an airborne radar transmitting an inter-pulse initial phase agile signal, which transmits P pulses within one CPI, with the corresponding inter-pulse initial phase codeword being c, the expression for the inter-pulse initial phase agile transmission signal model s(t) is as follows:

[0012]

[0013] Where p∈{1,2,...,P} represents the p-th pulse, t represents the signal time, c(p) represents the initial phase codeword of the p-th pulse, u(t) represents the pulse signal, and T represents the pulse repetition period.

[0014] Given a moving target within the detection range of an airborne radar, with a two-way propagation delay of τ relative to the airborne radar and a radial velocity of v relative to the airborne radar, then the initial phase agile target echo model r T The expression for (t) is as follows:

[0015]

[0016] Where C represents the speed of light, α represents the target echo amplitude, and f0 represents the signal carrier frequency.

[0017] By down-converting the echo, we obtain the initial phase agile target echo model for down-conversion. The expression is as follows:

[0018]

[0019] in, f represents the new target complexity. d Indicates the Doppler shift of the target.

[0020] Let the impulse response of the matched filter be u. * (-t), (·) * The conjugate operator is used for matched filtering of the target echo signal, and at time... If the sample is taken at a certain location, then the processed signal model The expression is as follows:

[0021]

[0022] in, This indicates the target complexity after the update, and This represents the expected value of the statistical expression, v. d ∈[-1 / 2,1 / 2] represents the normalized Doppler frequency of the target. The definition of the intrapulse waveform ambiguity function is given by [formula missing]. Indicates the delay parameter. This represents the Doppler frequency shift parameter.

[0023] According to the echo model Intrapulse waveform blurring function χ u (0,v d The ambiguity function χ is independent of the initial phase codeword c. u (0,v d If ) = 1, then the target's slow-time echo model v T The expression is as follows:

[0024]

[0025] in, The steering vector representing the target echo, (·) T represents the transpose operator, and ⊙ represents the Hadamard product operator.

[0026] S12. Establish a slow-time total echo model;

[0027] A discrete airborne clutter model is constructed based on the equidistant ring Doppler clutter partitioning criterion. Continuous ground clutter is discretized into multiple range cells. The normalized Doppler frequency shift of all clutter cells is set to the range [-1 / 2, 1 / 2]. The normalized Doppler frequency shift of the i-th clutter cell on the same range ring is v. i =-1 / 2+i / P,i∈{1,2,...,P}.

[0028] Let n be the number of range ambiguities corresponding to the maximum detectable range of the airborne radar, and n0 be the number of target range ambiguities. Treat all clutter elements as a single stationary ground target. Then, the matched filtering and sampling process for the clutter signal is similar to that for the target echo. The processed slow-time clutter echo model v C The expression is as follows:

[0029]

[0030] Where r∈{n0-n,n0-n+1,...,n0} represents the number of times a clutter element is blurred relative to a tangentially maneuvering target. Clutter elements on the same range ring have the same number of range blurs. η0(r,i) represents the complex amplitude of the echo of the i-th clutter element on the range ring after r-times of range blur. J represents the steering vector of the echo from the i-th clutter cell on the range ring. r The displacement matrix representing the r-th order range-ambiguous clutter cell echo relative to the target echo is defined as follows:

[0031]

[0032] Where x and y represent the elements in the x-th row and y-th column of the matrix.

[0033] The echo signal actually received by the airborne radar also includes a variance of For a complex Gaussian white noise signal, assuming the slow-time echo model of the noise is n, the expression for the slow-time total echo model r of the initial-phase agile airborne radar under clutter conditions is as follows:

[0034]

[0035] Among them, noise This represents complex Gaussian white noise, n1,...,n P Let each represent an element of the noise vector n. It represents a P-dimensional complex number.

[0036] Furthermore, step S2 is specifically as follows:

[0037] S21. Introduce the window function into the initial phase compensation Doppler filter matrix to handle the slow-time total echo model;

[0038] A slow-time real window is configured at the signal processing end. w1,...,w P Let each represent an element of the noise vector w. Let c represent a P-dimensional real number, and let c be the s-th filter vector of the filter matrix. Fs =w⊙c⊙p(v s ),s∈{1,2,...,P}, Let y represent the output model y of the echo model after being filtered by the s-th filter steering vector. s The expression for (c,w) is as follows:

[0039]

[0040] in,(·) H v represents the conjugate transpose of a vector or matrix. is =v i -vs v s =-1 / 2+s / P represents the s-th normalized Doppler filter frequency, q(v is ) = J -r p(v is ) represents the steering vector of the clutter unit echo, and J -r The direction of displacement and J r on the contrary, This represents the signal noise output by the filter vector.

[0041] S22. Construct the signal-to-interference-plus-noise ratio (SINR) energy model for the target matched filter output;

[0042] Assume there is a new clutter echo complex amplitude. When replacing η0(r,i), q(v) is ) simplified to p(v i This does not affect the output model; let the s-th filter vector be the target peak matching vector (v). s =v d Then, the expression for the SINR model g(c,w) based on the filtered output is as follows:

[0043]

[0044] in, g(c,w) serves as the objective function for the optimization problem.

[0045] S23, Expression and simplification optimization issues;

[0046] Based on steps S21-S22, c and w are used as the two independent variables of the objective function to maximize SINR. A constant modulus constraint is applied to c, and a target matching peak constraint and a maximum signal-to-noise ratio loss constraint are applied to w. The optimization problem is... It is expressed as follows:

[0047]

[0048] Where 1 represents a column vector with all elements equal to 1, and L represents the maximum signal-to-noise ratio loss.

[0049] The problem Substituting the constraints into the original objective function g(c,w), simplifying and taking its reciprocal, we obtain a new minimization objective function g0(c,w), expressed as follows:

[0050]

[0051] in, These two represent the updated clutter unit complex amplitude and noise variance, respectively.

[0052] The simplified send / receive design optimization problem The expression is as follows:

[0053]

[0054] Furthermore, step S3 is specifically as follows:

[0055] S31. Construct sub-optimization problems for inter-pulse initial phase and window function;

[0056] With w fixed, the noise energy is constant. The problem is... It can be transformed into a C-based subproblem. The expression is as follows:

[0057]

[0058] Where g1(c,w) represents a subproblem The objective function, A ri (w) = diag(w) * J r diag(p(v i The original objective function g(c,w) is transformed into a quartic form with c as the variable.

[0059] Fixed c, problem It can be transformed into a subproblem based on w. The expression is as follows:

[0060]

[0061] Where g2(c,w) represents a subproblem The objective function, I P Let w represent an identity matrix of size P×P, where the original objective function is transformed into a quadratic form with w as the variable.

[0062] S32. Based on the inter-pulse initial phase problem obtained in step S31, solve it using the QRARC algorithm;

[0063] Under the constant modulus constraint, |c(i)|=1,i=1,2,...,P is regarded as the product of P complex circles of size 1, and the manifold complex circles of the subproblem are constructed. The expression is as follows:

[0064]

[0065] In the manifold model, For a point on the manifold circle, the Riemann gradient grad g1(c,w) at that point is expressed as follows:

[0066]

[0067] in, This represents the tangent space projection operation. Let g1(c,w) = ▽(g1(c,w)) represent the tangent space, and let g1(c,w) = ▽(g1(c,w)) represent the Euclidean gradient.

[0068] Combining the complex circle projection formula for manifolds, the Riemann-Hess matrix Hess g1(c,w) is solved by projecting the Euclidean directional derivative onto the tangent space, as shown in the following expression:

[0069]

[0070] in, Let g1(c,w) represent the direction vector corresponding to the directional derivative of the objective function at c, and Dgrad g1(c,w) and DGrad g1(c,w) represent the directional derivatives of the Riemann gradient and Euclidean gradient, respectively.

[0071] Given tangent space Given a linear Euclidean space, we establish an adaptive cubic regularization term for the QRARC iteration. The expression is as follows:

[0072]

[0073] in, Let a represent the regularization coefficient, and ||·|| represent the L2 norm; let a and b both represent complex circles. The tangent vector on, In the definition, the Riemannian metric on the complex circle of the manifold is the complex Euclidean inner product, i.e.<a,b> =Re[a H b).

[0074] Let regularization model The corresponding constraint is the second-order θ-stationary point, when the regularized model... When the minimum value is reached, the direction vector becomes the optimal search step size. This is used to construct the optimal search step size for the s-th iteration. The expression for the Euclidean space subproblem is as follows:

[0075]

[0076] Where, λ min (·) represents finding the minimum eigenvalue of a matrix, ▽ 2 This represents the second-order gradient operator, which stops the QRARC iteration of the subproblem when its constraints are not met.

[0077] During the iteration process, a set of orthogonal vectors {Q1, Q2, ..., Q} is generated. N The expression for} and the symmetric matrix Tl is as follows:

[0078]

[0079] T l (a,b)= a ,Hess g(Q b )>,a,b∈{1,...,N} (22)

[0080] Let Tl M (M < N) indicates that T l For an M×M principal subarray, then Use {Q1,Q2,...,Q M The regularization model corresponding to Zhang Cheng's subspace is represented by the following expression:

[0081]

[0082] in, Let M be a real number, and let the orthogonal vector and the elements of y represent the direction vector. Equation (23) is used to calculate the global minimum point of the cubic regularized model.

[0083] Then, the constraints of equation (20) are verified, and the following is obtained. The equivalent calculation method is as follows:

[0084]

[0085] Where m represents the number of iterations of the QRARC algorithm, and T l (1:M+1,1:m) represents the matrix T l T is composed of the first M+1 rows and the first m columns. l The submatrix.

[0086] Define the regularization ratio ρ as follows:

[0087]

[0088] Introducing constants like The optimized search step size Desirable, and called To achieve a successful step size, update the solution c. (m+1) :

[0089]

[0090] Where Ret(·) denotes the contraction operator; if The resulting step size This is called the "maximum success step size," and the regularization coefficient is appropriately reduced in the next iteration. ​The value of .

[0091] Before performing iterative calculations, the algorithm convergence threshold ε is set as needed. When the gradient of the objective function g1(c,w) is less than the set ε, the subproblem iteration based on the QRARC algorithm stops.

[0092] S33. Based on the window function subproblem obtained in step S31, solve it using KKT;

[0093] Based on the optimization result c obtained in step S32, eigenvalue decomposition is performed on B(c) to obtain B(c) = QΛQ H .

[0094] Where Λ=diag(λ) represents the eigenvalues ​​of B(c) λ=[λ1,λ2,...,λ P ] T The diagonal matrix formed by these two matrices, Q, represents a unitary matrix of size P×P that satisfies QQ. H =Q H Q = I P .make The problem Transform into The expression is as follows:

[0095]

[0096] question The Lagrange function is expressed as:

[0097]

[0098] Here, μ1 and μ2 represent the Lagrange multipliers for the equality constraints and inequality constraints of the problem, respectively.

[0099] Based on the KKT conditions, we obtain the problem. The optimality conditions are as follows:

[0100]

[0101] Based on the aforementioned optimality condition, relevant algebraic operations yield a simplified system of equations:

[0102]

[0103] in, and They represent and The i-th element,

[0104] When μ2 = 0, the vector elements in the system of equations λ i and The value of μ1 is not constant, and it is impossible to determine a specific μ1 to satisfy the system of equations, so the system of equations has no solution. When μ2 > 0, we first use the bisection method to solve G(μ2) = 0 to get μ2, and then substitute it into the other two systems of equations to get μ1 and the optimized slow time window function w.

[0105] S34. Based on steps S32-S33, alternately optimize sub-problems to implement the transmit / receive design;

[0106] First, set the convergence threshold for the joint iterative optimization. Then, based on the window function w obtained in step S33, step S32 is repeated to further optimize the inter-pulse initial phase codeword c, and then the optimization is carried out alternately in a loop. In the SISWP algorithm, steps S32-S33 are called a joint iteration.

[0107] If the difference between the objective functions of two algorithm iterations is less than a pre-set threshold The iteration stops, and the optimized slow time window function and inter-pulse initial phase codeword are finally obtained, completing the clutter suppression transceiver design for tangential maneuvering target detection.

[0108] The beneficial effects of this invention are as follows: First, under an initial-phase agile signal system, a slow-time echo model of the target, clutter, and noise is established. Then, a slow-time window function is introduced at the signal processing end to construct a clutter energy objective function. Under constant-mode constraints, peak-matching constraints, and signal-to-noise ratio loss constraints, a clutter energy minimization problem is established. The SISWP algorithm is proposed, transforming the original optimization problem into a sub-problem based on inter-pulse initial phase and the window function. The QRARC algorithm and KKT conditional iterative methods are used alternately to ultimately achieve a joint optimization design for clutter suppression in both transmission and reception. This invention does not rely on prior knowledge of clutter distribution, exhibiting good robustness, feasibility, and generalizability. It fully utilizes the waveform optimization degrees of freedom at the airborne radar transmitter and introduces new optimization variables at the signal processing end to further enhance the waveform's suppression effect on range-ambiguous clutter, significantly improving the detection performance against tangentially maneuvering targets. Attached Figure Description

[0109] Figure 1 This is a flowchart of a clutter suppression transceiver design method for detecting tangentially maneuvering targets according to the present invention.

[0110] Figure 2 This is a scene diagram of tangential maneuvering target detection in an embodiment of the present invention.

[0111] Figure 3 This is a graph showing the change in normalized signal-to-interference-plus-noise ratio (SINR) and iteration count during the algorithm optimization process in this embodiment of the invention.

[0112] Figure 4 This is a fuzzy function graph for algorithm optimization in an embodiment of the present invention.

[0113] Figure 5 This is a comparison diagram of the RD plane for tangential maneuvering target detection based on the algorithm optimization in this embodiment of the invention.

[0114] Figure 6 This is a tangent plane distance map of the RD plane for target detection within the region, optimized by the algorithm in this embodiment of the invention. Detailed Implementation

[0115] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0116] like Figure 1 The flowchart shown is a clutter suppression transceiver design method for tangential maneuvering target detection according to the present invention. The specific steps are as follows:

[0117] S1. Establish a slow-time total echo model for initial-phase agile airborne radar.

[0118] S2. Based on step S1, process the echo signal and construct a joint optimization problem for clutter suppression based on range ambiguity;

[0119] S3. Solve the joint optimization problem based on the (Sequential Iteration of Slow-time Window and Phase-code) SISWP algorithm to complete the clutter suppression transceiver design for tangential maneuvering target detection.

[0120] In this embodiment, step S1 is specifically as follows:

[0121] S11. Establish a slow-time initial phase agile target echo model;

[0122] Assuming an airborne radar transmits an inter-pulse initial phase agile signal, transmitting P pulses within one CPI (pulse repetition interval), with the corresponding inter-pulse initial phase codeword being c, the expression for the inter-pulse initial phase agile transmission signal model s(t) is as follows:

[0123]

[0124] Where p∈{1,2,…,P} represents the p-th pulse, t represents the signal time, c(p) represents the initial phase codeword of the p-th pulse, u(t) represents the pulse signal, and T represents the pulse repetition period.

[0125] Given a moving target within the detection range of an airborne radar, with a two-way propagation delay of τ relative to the airborne radar and a radial velocity of v relative to the airborne radar, then the initial phase agile target echo model r T The expression for (t) is as follows:

[0126]

[0127] Where C represents the speed of light, α represents the target echo amplitude, and f0 represents the signal carrier frequency.

[0128] By down-converting the echo, we obtain the initial phase agile target echo model for down-conversion. The expression is as follows:

[0129]

[0130] in, f represents the new target complexity. d Indicates the Doppler shift of the target.

[0131] Let the impulse response of the matched filter be u. * (-t), (·) * The conjugate operator is used for matched filtering of the target echo signal, and at time... If the sample is taken at a certain location, then the processed signal model The expression is as follows:

[0132]

[0133] in, This indicates the target complexity after the update, and This represents the expected value of the statistical expression, v. d ∈[-1 / 2,1 / 2] represents the normalized Doppler frequency of the target. The definition of the intrapulse waveform ambiguity function is given by [formula missing]. Indicates the delay parameter. This represents the Doppler frequency shift parameter.

[0134] According to the echo model Intrapulse waveform blurring function χ u (0,v d The ambiguity function χ is independent of the initial phase codeword c. u (0,v d If ) = 1, then the target's slow-time echo model v T The expression is as follows:

[0135]

[0136] in, The steering vector representing the target echo, (·) T represents the transpose operator, and ⊙ represents the Hadamard product operator.

[0137] S12. Establish a slow-time total echo model;

[0138] To construct a discrete airborne clutter model based on the equidistant ring Doppler clutter partitioning criterion, continuous ground clutter is discretized into multiple range cells. The normalized Doppler frequency shift of all clutter cells is set to the range [-1 / 2, 1 / 2]. The normalized Doppler frequency shift of the i-th clutter cell on the same range ring is v. i =-1 / 2+i / P,i∈{1,2,…,P}.

[0139] Let n be the number of range ambiguities corresponding to the maximum detectable range of the airborne radar, and n0 be the number of target range ambiguities. Treat all clutter elements as a single stationary ground target. Then, the matched filtering and sampling process for the clutter signal is similar to that for the target echo. The processed slow-time clutter echo model v C The expression is as follows:

[0140]

[0141] Where r∈{n0-n,n0-n+1,…,n0} represents the number of times a clutter cell is blurred relative to a tangentially maneuvering target. Clutter cells on the same range ring have the same number of range blurs. η0(r,i) represents the complex amplitude of the echo of the i-th clutter cell on the range ring after r-times of range blur. J represents the steering vector of the echo from the i-th clutter cell on the range ring. r The displacement matrix representing the r-th order range-ambiguous clutter cell echo relative to the target echo is defined as follows:

[0142]

[0143] Where x and y represent the elements in the x-th row and y-th column of the matrix.

[0144] The echo signal actually received by the airborne radar also includes a variance of For a complex Gaussian white noise signal, assuming the slow-time echo model of the noise is n, the expression for the slow-time total echo model r of the initial-phase agile airborne radar under clutter conditions is as follows:

[0145]

[0146] Among them, noise Represents complex Gaussian white noise, n1,…,n P Let each represent an element of the noise vector n. It represents a P-dimensional complex number.

[0147] In this embodiment, step S2 is specifically as follows:

[0148] S21. Introduce the window function into the initial phase compensation Doppler filter matrix to handle the slow-time total echo model;

[0149] A slow-time real window is configured at the signal processing end. w1,…,w P Let each represent an element of the noise vector w. Let c represent a P-dimensional real number, and let c be the s-th filter vector of the filter matrix. Fs =w⊙c⊙p(v s ),s∈{1,2,…,P}, Let y represent the output model y of the echo model after being filtered by the s-th filter steering vector. s The expression for (c,w) is as follows:

[0150]

[0151] in,(·) H v represents the conjugate transpose of a vector or matrix. is =v i -v s v s =-1 / 2+s / P represents the s-th normalized Doppler filter frequency, q(v is ) = J -r p(v is ) represents the steering vector of the clutter unit echo, and J -r The direction of displacement and J r on the contrary, This represents the signal noise output by the filter vector.

[0152] S22. Construct the signal-to-interference-plus-noise ratio (SINR) energy model for the target matched filter output;

[0153] Assume there is a new clutter echo complex amplitude. When replacing η0(r,i), q(v) is ) simplified to p(v i This does not affect the output model; let the s-th filter vector be the target peak matching vector (v). s =v d Then, the expression for the SINR model g(c,w) based on the filtered output is as follows:

[0154]

[0155] in, g(c,w) serves as the objective function for the optimization problem.

[0156] S23, Expression and simplification optimization issues;

[0157] Based on step S21, c and w are used as the two independent variables of the objective function to maximize SINR (Signal-to-Interference-plus-Noise Ratio). A constant modulus constraint is applied to c, and a target matching peak constraint and a maximum signal-to-noise ratio loss constraint are applied to w. The optimization problem is... It is expressed as follows:

[0158]

[0159] Where 1 represents a column vector with all elements equal to 1, and L represents the maximum signal-to-noise ratio loss.

[0160] The problem Substituting the constraints into the original objective function g(c,w), simplifying and taking its reciprocal, we obtain a new minimization objective function g0(c,w), expressed as follows:

[0161]

[0162] in, These two represent the updated clutter unit complex amplitude and noise variance, respectively.

[0163] The simplified send / receive design optimization problem The expression is as follows:

[0164]

[0165] In this embodiment, step S3 is specifically as follows:

[0166] S31. Construct sub-optimization problems for inter-pulse initial phase and window function;

[0167] With w fixed, the noise energy is constant. The problem is... It can be transformed into a C-based subproblem. The expression is as follows:

[0168]

[0169] Where g1(c,w) represents a subproblem The objective function, A ri (w) = diag(w) * J r diag(p(v i The original objective function g(c,w) is transformed into a quartic form with c as the variable.

[0170] Fixed c, problem It can be transformed into a subproblem based on w. The expression is as follows:

[0171]

[0172] Where g2(c,w) represents a subproblem The objective function, I P Let w represent an identity matrix of size P×P, where the original objective function is transformed into a quadratic form with w as the variable.

[0173] S32. Based on the inter-pulse initial phase problem obtained in step S31, solve it using the (Quartic Riemannian Adaptive Regularization with Cubics) QRARC algorithm;

[0174] Under the constant modulus constraint, |c(i)|=1,i=1,2,...,P is regarded as the product of P complex circles of size 1, and the manifold complex circles of the subproblem are constructed. The expression is as follows:

[0175]

[0176] In the manifold model, For a point on the manifold circle, the Riemann gradient (tangent vector) grad g1(c,w) at that point is expressed as follows:

[0177]

[0178] in, This represents the tangent space projection operation. Let g1(c,w) = ▽(g1(c,w)) represent the tangent space, and let g1(c,w) = ▽(g1(c,w)) represent the Euclidean gradient.

[0179] Combining the complex circle projection formula for manifolds, the Riemann-Hess matrix Hess g1(c,w) is solved by projecting the Euclidean directional derivative onto the tangent space, as shown in the following expression:

[0180]

[0181] in, Let g1(c,w) represent the direction vector corresponding to the directional derivative of the objective function at c, and Dgrad g1(c,w) and DGrad g1(c,w) represent the directional derivatives of the Riemann gradient and Euclidean gradient, respectively.

[0182] Given tangent space Given a linear Euclidean space, we establish an adaptive cubic regularization term for the QRARC iteration. The expression is as follows:

[0183]

[0184] in, Let a represent the regularization coefficient, and ||·|| represent the L2 norm; let a and b both represent complex circles. The tangent vector on, In the definition, the Riemannian metric on the complex circle of the manifold is the complex Euclidean inner product, i.e.<a,b> =Re[a H b).

[0185] To make the regularization model To avoid saddle points, a regularization model is established that exhibits monotonically decreasing properties. The corresponding constraint is the second-order θ-stationary point. When the regularized model... When the minimum value is reached, the direction vector becomes the optimal search step size. This is used to construct the optimal search step size for the s-th iteration. The expression for the Euclidean space subproblem is as follows:

[0186]

[0187] Where, λ min (·) represents finding the minimum eigenvalue of a matrix, ▽ 2 This represents the second-order gradient operator, which stops the QRARC iteration of the subproblem when its constraints are not met.

[0188] To further transform the objective function and constraints, a set of orthogonal vectors {Q1, Q2, ..., Q} is generated during the iteration process. N} and symmetric matrix T l The expression is as follows:

[0189]

[0190] T l (a,b)= a ,Hess g(Q b )>,a,b∈{1,...,N} (22)

[0191] Let Tl M (M < N) indicates that T l For an M×M principal subarray, then Use {Q1,Q2,...,Q M The regularization model corresponding to Zhang Cheng's subspace is represented by the following expression:

[0192]

[0193] in, Let M be a real number, and let the orthogonal vector and the elements of y represent the direction vector. Equation (23) is used to calculate the global minimum point of the cubic regularized model.​

[0194] To avoid calculating ζ and calling the Riemann matrix linear operator, the constraints of problem (20) are verified, and the following is obtained: The equivalent calculation method is as follows:

[0195]

[0196] Where m represents the number of iterations of the QRARC algorithm, and T l (1:M+1,1:m) represents the matrix T l T is composed of the first M+1 rows and the first m columns. l The submatrix.

[0197] To quantify the consistency between the approximate model and the objective function, a regularization ratio ρ is defined, expressed as follows:

[0198]

[0199] Introducing constants like The optimized search step size Desirable, and called To achieve a successful step size, update the solution c. (m+1) :

[0200]

[0201] Where Ret(·) denotes the contraction operator; if The resulting step size This is called the "maximum success step size," and the regularization coefficient is appropriately reduced in the next iteration. The value of .

[0202] Before performing iterative calculations, the algorithm convergence threshold ε is set as needed. When the gradient of the objective function g1(c,w) is less than the set ε, the subproblem iteration based on the QRARC algorithm stops.

[0203] S36. Based on the window function subproblem obtained in step S31, the (Karush-Kuhn-Tucker) KKT method is used to solve it.

[0204] Based on the optimization result c obtained in step S32, eigenvalue decomposition is performed on B(c) to obtain B(c) = QΛQ H .

[0205] Where Λ=diag(λ) represents the eigenvalues ​​of B(c) λ=[λ1,λ2,...,λ P ] T The diagonal matrix formed by these two matrices, Q, represents a unitary matrix of size P×P that satisfies QQ. H =Q HQ = I P .make The problem Transform into The expression is as follows:

[0206]

[0207] question The Lagrange function is expressed as:

[0208]

[0209] Here, μ1 and μ2 represent the Lagrange multipliers for the equality constraints and inequality constraints of the problem, respectively.

[0210] Based on the KKT conditions, we obtain the problem. The optimality conditions are as follows:

[0211]

[0212] Based on the aforementioned optimality condition, relevant algebraic operations yield a simplified system of equations:

[0213]

[0214] in, and They represent and The i-th element,

[0215] When μ2 = 0, the vector elements in the system of equations λ i and The value of μ1 is not constant, and it is impossible to determine a specific μ1 to satisfy the system of equations, so the system of equations has no solution. When μ2 > 0, we first use the bisection method to solve G(μ2) = 0 to get μ2, and then substitute it into the other two systems of equations to get μ1 and the optimized slow time window function w.

[0216] S34. Based on steps S32-S33, alternately optimize sub-problems to implement the transmit / receive design;

[0217] First, set the convergence threshold for the joint iterative optimization. Then, based on the window function w obtained in step S33, step S32 is repeated to further optimize the inter-pulse initial phase codeword c, and then the optimization is carried out alternately in a loop. In the SISWP algorithm, steps S32-S33 are called a joint iteration.

[0218] If the difference between the objective functions of two algorithm iterations is less than a pre-set threshold The iteration stops, and the optimized slow time window function and inter-pulse initial phase codeword are finally obtained, completing the clutter suppression transceiver design for tangential maneuvering target detection.

[0219] In this embodiment, the detection scenario for tangentially maneuvering targets is specifically as follows: Figure 2 As shown, the backscattering rate of clutter in the detection environment conforms to the hilly Morchin model. The airborne radar transmitting antenna is set to a planar phased array operating in a front-side array mode. The phased array elevation angle is β = 5° (looking up). The azimuth angle of the main lobe beam is the normal direction of the phased array. The number of transmitted pulses is P = 128, and the pulse width is T. p =50μs, pulse repetition period is T=500μs, carrier frequency is f0=500MHz, flight altitude is H=8km, speed is V=50m / s, radial distance between the tangentially maneuvering target and the airborne radar is R=235km, and the target cross-section in the actual detection environment is σ t =10m 2 With speed v T It moves in the direction perpendicular to the main lobe beam.

[0220] Then, the clutter model is divided into equidistant Doppler segments. Clutter elements at the same distance form equidistant rings. Among them, equidistant ring 1 corresponds to strong clutter, and equidistant ring 2 is at the same distance as the target. Tangential maneuvering targets are folded into the strong clutter region in the range dimension. On the other hand, strong clutter elements and tangential maneuvering targets in the main lobe beam direction have the same radial relative velocity v = Vsin to the airborne radar. Given the known target location within the ambiguity interval, the waveform is optimized, and the initial phase c is optimized. (0) The time window is randomly generated in a uniform distribution between [0, 2π], and the initial value of the slow time window function is w. (0) =1, noise variance is σ 2 =1×10 -4 The maximum signal-to-noise ratio loss is L = 3dB. The fuzzy shaping parameter expression is set according to the optimization distance interval of interest as follows:

[0221]

[0222] like Figure 3 As shown, in this embodiment, the SINR rising curve and the optimized fuzzy function graph are plotted based on the SISWP algorithm for optimization iteration. It can be seen that the optimization algorithm of the present invention has high convergence efficiency and significant effect, with a theoretical average energy suppression of 55dB within the region of interest. Figure 4 As shown, the method of the present invention creates extremely deep grooves in the third fuzzy interval of the fuzzy function, thereby realizing the shaping of the asymmetric fuzzy function.

[0223] like Figure 5 As shown, when a tangentially maneuvering target exists within the region of interest, the transceiver design method and algorithm proposed in this invention are evaluated. Figure 5 (a) is the RD plane for tangential maneuvering target detection using inter-pulse constant parameter signals; Figure 5 (b) is the optimized RD plane for tangential maneuvering target detection using the initial phase agile signal. The signal-to-clutter-to-noise ratio in the region of interest is improved by 26 dB. The results show that the method and algorithm of this invention can realize tangential maneuvering target detection in cluttered environments and effectively suppress the influence of range ambiguity clutter on target detection.

[0224] like Figure 6 As shown, using the inter-pulse constant parameter signal as a comparison, the optimized tangential target detection RD plane range profile is analyzed. Within the three range ambiguity intervals [225km, 300km], the clutter energy of the inter-pulse constant parameter signal is very high, completely overwhelming the tangential maneuvering target; under the optimized inter-pulse initial phase agile signal system, the strong range folding clutter is significantly suppressed, and tangential maneuvering target detection can be successfully achieved.

[0225] In summary, the above embodiments demonstrate that the transmit / receive design method proposed in this invention can effectively suppress range ambiguity clutter, thereby achieving tangential maneuvering target detection. This invention's method, based on an airborne radar slow-time echo model under an inter-pulse initial-phase agile signal system, introduces a slow-time window function at the signal processing end and constructs a mathematical model of clutter energy as the objective function of the problem. It then establishes an optimization problem by combining constant modulus constraints, peak matching constraints, and signal-to-noise ratio loss constraints. This invention's method not only considers the design of the transmitted signal waveform but also takes into account the optimization degrees of freedom in signal processing, enabling more effective suppression of range ambiguity clutter in the range of interest where the tangential maneuvering target is located, thereby achieving tangential maneuvering target detection within the clutter region. Furthermore, this invention's method does not rely on prior information about clutter and terrain, making it applicable to various terrains.

[0226] Those skilled in the art will recognize that the embodiments described above are intended to help readers understand the principles of the present invention, and should be considered that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention can be modified and varied. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A clutter suppression transceiver design method for detecting tangentially maneuvering targets, the specific steps of which are as follows: S1. Establish a slow-time total echo model for initial-phase agile airborne radar. The specific steps of S1 are as follows: S11. Establish a slow-time initial phase agile target echo model; The airborne radar is configured to transmit an inter-pulse initial phase agile signal, which transmits P pulses within one CPI. The corresponding inter-pulse initial phase codeword is: Then the pulse-first phase agile transmit signal model The expression is as follows: （1）； in, This represents the p-th pulse, and t represents the signal time. This represents the initial phase codeword of the p-th pulse. This represents a pulse signal, where T represents the pulse repetition period; Suppose there is a moving target within the detection range of the airborne radar, and its two-way propagation delay relative to the airborne radar is... If the radial velocity relative to the airborne target is v, then the initial phase agile target echo model... The expression is as follows: （2）； Where C represents the speed of light. Indicates the target echo amplitude. Indicates the signal carrier frequency; By down-converting the echo, we obtain the initial phase agile target echo model for down-conversion. The expression is as follows: （3）； in, Indicates the new target range. Indicates the Doppler shift of the target; The impulse response of the matched filter is set as follows: , The conjugate operator is used for matched filtering of the target echo signal, and at time... If the sample is taken at a certain location, then the processed signal model The expression is as follows: （4）； in, This indicates the target complexity after the update, and , This indicates the calculation of statistical expectation. Represents the normalized Doppler frequency of the target. The definition of the intrapulse waveform ambiguity function is given by [formula missing]. Indicates the delay parameter. Indicates the Doppler frequency shift parameter; According to the echo model Intrapulse waveform ambiguity function Coding with the first encounter Irrelevant, let the fuzzy function Then the target's slow-time echo model The expression is as follows: （5）； in, The steering vector representing the target echo. This represents the transpose operator. This represents the Hadama product operator; S12. Establish a slow-time total echo model; A discrete airborne clutter model is constructed based on the equidistant ring Doppler clutter partitioning criterion. Continuous ground clutter is discretized into multiple range cells, and the normalized Doppler frequency shift value range for all clutter cells is set to be [value missing]. The normalized Doppler frequency shift of the i-th clutter unit on the same distance ring is , ; The maximum detectable range of the airborne radar is set to correspond to the number of range ambiguities. The number of fuzzy operations for the target distance is If all clutter units are treated as a single stationary ground target, then the matched filtering and sampling process of the clutter signal is similar to that of the target echo. The processed slow-time clutter echo model... The expression is as follows: （6）； in, This indicates the number of ambiguities a clutter element has relative to a tangentially maneuvering target. Clutter elements on the same range ring have the same number of range ambiguities. This represents the complex amplitude of the echo of the i-th clutter cell on the r-th distance ambiguity range loop. This represents the steering vector of the echo from the i-th clutter cell on the range loop. The displacement matrix representing the r-th order range-ambiguous clutter cell echo relative to the target echo is defined as follows: （7）； Where x and y represent the elements in the x-th row and y-th column of the matrix; The echo signal actually received by the airborne radar also includes a variance of Given a complex Gaussian white noise signal, let the slow-time echo model of the noise be... Then, the slow-time total echo model of initial-phase agile airborne radar in clutter environment The expression is as follows: （8）； Among them, noise This represents complex Gaussian white noise. Representing noise respectively Elements of a vector Represents a P-dimensional complex number; S2. Based on step S1, process the echo signal and construct a joint optimization problem for clutter suppression based on range ambiguity; A slow time window function is introduced at the signal processing end to construct the clutter energy objective function, and a clutter energy minimization problem is established under constant mode constraint, peak matching constraint and signal-to-noise ratio loss constraint. S3. Solve the joint optimization problem based on the SISWP algorithm and complete the clutter suppression transceiver design for tangential maneuvering target detection; The Sequential Iteration of Slow-time Window and Phase-code (SISWP) algorithm is proposed, which transforms the original optimization problem into a subproblem based on the inter-pulse initial phase and window function. The algorithm uses Quartic Riemannian Adaptive Regularization with Cubics (QRARC) and KKT conditional alternation to finally achieve a joint optimization design for clutter suppression in both transmission and reception.

2. The clutter suppression transceiver design method for tangential maneuvering target detection according to claim 1, characterized in that, Step S2 is as follows: S21. Introduce the window function into the initial phase compensation Doppler filter matrix to handle the slow-time total echo model; A slow-time real window is configured at the signal processing end. , Representing noise respectively Elements of a vector Let P be a real number, and let the s-th filter vector of the filter matrix be... , This represents the s-th filter steering vector, and the output model of the echo model after filtering by this vector. The expression is as follows: （9）； in, This represents the conjugate transpose of a vector or matrix. , This represents the s-th normalized Doppler filter frequency point. This represents the steering vector of the clutter cell echo, and displacement direction and on the contrary, This represents the signal noise output by the filter vector; S22. Construct the signal-to-interference-plus-noise ratio (SINR) energy model for the target matched filter output; Assume there is a new clutter echo complex amplitude. replace At that time, Simplified to This does not affect the output model; let the s-th filter vector be the target peak matching vector. Then, based on the SINR model of the filtered output The expression is as follows: （10）； in, , As the objective function of the optimization problem; S23, Expression and simplification optimization issues; Based on steps S21-S22, adopt and As two optimization variables in the objective function to maximize SINR, for Using constant modulus constraints, for The optimization problem is solved by employing target matching peak constraints and maximum signal-to-noise ratio loss constraints. It is expressed as follows: （11）； in, This represents a column vector where all elements are 1, and L represents the maximum signal-to-noise ratio loss. The problem Substituting the constraints into the original objective function Simplifying and taking the reciprocal yields a new minimization objective function. The expression is as follows: （12）； in, , These two represent the updated clutter unit complex amplitude and noise variance, respectively; The simplified send / receive design optimization problem The expression is as follows: （13）。 3. The clutter suppression transceiver design method for tangentially maneuvering target detection according to claim 2, characterized in that, Step S3 is as follows: S31. Construct sub-optimization problems for inter-pulse initial phase and window function; fixed Then the noise energy is constant, the problem Can be converted to based on subproblems The expression is as follows: （14）； in, Representing subproblems The objective function, Original objective function Transform into The variable is a quartic form; fixed ,question Can be converted to based on subproblems The expression is as follows: （15）； in, Representing subproblems The objective function, , Indicates size is The identity matrix is ​​obtained, and the original objective function is transformed into the identity matrix. The quadratic form of the variable; S32. Based on the inter-pulse initial phase problem obtained in step S31, solve it using the QRARC algorithm; Under constant modulus constraints, View as Construct a manifold of complex circles for the subproblem of a product of complex circles of size 1. The expression is as follows: （16）； In the manifold model, That is, the Riemann gradient at a point on the manifold circle. The expression is as follows: （17）； in, This represents the tangent space projection operation. Represents the tangent space. Represents the Euclidean gradient; By combining the complex circular projection formula of a manifold, the Riemann-Hess matrix is ​​solved by projecting the Euclidean directional derivative onto the tangent space. The expression is as follows: （18）； in, Indicates the objective function in The direction vector corresponding to the directional derivative at that point. and Let represent the directional derivatives of the Riemannian gradient and the Euclidean gradient, respectively; Given tangent space Given a linear Euclidean space, we establish an adaptive cubic regularization term for the QRARC iteration. The expression is as follows: （19）； in, Represents the regularization coefficient. To find the L2 norm; let... and Both represent complex circles The tangent vector on, In the definition, the Riemannian metric on the complex circle of the manifold is the complex Euclidean inner product, i.e. ; Let regularization model The corresponding constraint is second-order. The plateau point, when the regularized model When the value is minimized, the direction vector is the optimal search step size, and the th step size is constructed. Optimal search step size in the next iteration The expression for the Euclidean space subproblem is as follows: （20）； in, This indicates finding the smallest eigenvalue of a matrix. This represents the second-order gradient operator, which stops the QRARC iteration of the subproblem when its constraints are not met. A set of orthogonal vectors is generated during the iteration process. and symmetric matrices The expression is as follows: （21）； （22）； set up express of Submatrix, then use The regularization model corresponding to Zhang Cheng's subspace is represented by the following expression: （23）； in, , Representing M-dimensional real numbers using orthogonal vectors and sums The elements in the vector represent the direction vector. , and equation (23) is used to calculate the global minimum point of the cubic regularized model; Then, the constraints of equation (20) are verified, and the following is obtained. The equivalent calculation method is as follows: （24）； in, This indicates the number of iterations in the QRARC algorithm. Represented by matrix The former line and front Composed of columns The submatrix; Define regularization ratio The expression is as follows: ； Introducing constants ,like The optimized search step size Desirable, and called To achieve a successful step size, update the solution. : （26）； in, Represents the contraction operator; if The resulting step size This is called the "maximum success step size," and the regularization coefficient is appropriately reduced in the next iteration. The value; Before performing iterative calculations, set the algorithm convergence threshold as needed. When the objective function The gradient is less than the set value. When the iteration of the subproblem based on the QRARC algorithm stops, the iteration stops. S33. Based on the window function subproblem obtained in step S31, solve it using KKT; Based on the optimization results obtained in step S32 ,right Eigenvalue decomposition yields ; in, express eigenvalues The diagonal matrix formed Represent a A unitary matrix of size that satisfies ;make , , the problem Transform into The expression is as follows: （27）； question The Lagrange function is expressed as: （28）； in, and Let represent the Lagrange multipliers for the equality constraints and inequality constraints of the problem, respectively; Based on the KKT conditions, we obtain the problem. The optimality conditions are as follows: （29）； Based on the aforementioned optimality condition, relevant algebraic operations yield a simplified system of equations: （30）； in, and They represent and The i-th element, ; when When, the vector elements in the system of equations , and The value is not constant, and a specific value cannot be determined. To satisfy the system of equations, the system of equations has no solution; when First, the bisection method is used to solve the problem. get Then substitute it into the other two systems of equations to get Compared with the optimized slow time window function ; S34. Based on steps S32-S33, alternately optimize sub-problems to implement the transmit / receive design; First, set the convergence threshold for the joint iterative optimization. Then, based on the window function obtained in step S33 Repeat step S32 to generate the initial phase codeword between pulses. Continue optimizing, then iterate and alternate optimizations; in the SISWP algorithm, steps S32-S33 are called a joint iteration; If the difference between the objective functions of two algorithm iterations is less than a pre-set threshold If the iteration stops, the optimized slow time window function and inter-pulse initial phase codeword are finally obtained, completing the clutter suppression transceiver design for tangential maneuvering target detection.

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