Sky-wave over-the-horizon radar clutter suppression method based on low-rank group sparse representation

Abstract

The application discloses a sky wave over-the-horizon radar clutter suppression method based on low rank group sparse representation, comprising the following steps: S1, according to the characteristic analysis of echo signals, the regularization constraint is carried out on each component of the echo signals, and the equality constraint is carried out through a discrete Fourier matrix, so as to construct a target function; S2, the equality constraint of the target function is eliminated through an augmented Lagrange function; S3, the regularization parameter of the target function is initialized and set, and the iteration convergence condition of an algorithm is set; S4, for an unconstrained convex optimization problem, all variables to be solved are updated alternately until the iteration converges, and the result after the clutter component is eliminated is obtained, so that the clutter suppression is realized. The application distinguishes each component of the echo signals by using the low rank, column sparsity and group sparsity, and carries out the constraint by using the nuclear norm, the norm, the group sparse regularization term and the Frobenius norm, and the solution is carried out through a convex optimization algorithm framework, so that the ground sea clutter can be effectively suppressed, and the target signal-to-noise ratio is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar detection, more particularly, to a sky wave over-the-horizon radar clutter suppression method based on low rank group sparse representation. BACKGROUND

[0002] The sky wave over-the-horizon radar (OTHR) works in the high frequency band (5-30MHz), and detects the targets beyond the horizon by using the refraction and reflection effect of the ionosphere on the high frequency electromagnetic wave, and the detection distance range is 800-3000km, which is a special system long-range early warning radar. The OTHR preliminarily suppresses the clutter by pulse compression and coherent accumulation, and then performs target detection in the range-doppler (RD) domain. However, the sea clutter and the ground clutter will produce spectral peaks much larger than the target energy at the Bragg frequency and the zero frequency, and in addition, in the actual situation, due to the influence of the ionosphere, the ground and sea clutter shape usually occurs the widening and frequency shift phenomenon, which further expands the coverage range of the clutter, thereby seriously affecting the detection performance of the low radial velocity target. Therefore, suppressing the main peak of the clutter and detecting the target therein through the clutter suppression processing is one of the key steps to improve the low radial velocity target detection performance of the OTHR. SUMMARY

[0003] The present application aims to provide a sky wave over-the-horizon radar clutter suppression method based on low rank group sparse representation, so as to overcome the defects existing in the prior art.

[0004] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows:

[0005] The sky wave over-the-horizon radar clutter suppression method based on low rank group sparse representation comprises the following steps:

[0006] S1, according to the characteristic analysis of the echo signal, the components of the echo signal are subjected to regularization constraint, and the equality constraint is performed through the discrete Fourier matrix, so as to construct a target function;

[0007] S2, the equality constraint of the target function is eliminated through the augmented Lagrange function;

[0008] S3, the regularization parameter of the target function is initialized and set, and the iteration convergence condition of the algorithm is set;

[0009] S4, for the unconstrained convex optimization problem, all variables to be solved are updated alternately until the iteration converges, and the result after removing the clutter components is obtained, so as to realize the clutter suppression.

[0010] Further, the step S1 specifically comprises:

[0011] S10, signal modeling, the two-dimensional data of a beam channel is represented as M is the number of accumulated pulses, N is the number of range cells, and the slow-time signal of the nth range cell is represented as It is decomposed into target component, clutter component and noise component, and the following is obtained:

[0012] y n (m) = s n (m) + c n (m) + w n (m), m = 1, 2, …, M,

[0013] In the formula, s n (m), c n (m) and w n (m) represent the slow-time components of the target, clutter and noise respectively, and the noise component is subject to zero-mean complex Gaussian distribution with variance σ 2 , that is,

[0014] The target component s n (m) is represented as:

[0015]

[0016] In the formula, a s,k represents the amplitude of the kth target, f d,k represents the Doppler frequency of the kth target, f d,k = 2v k / ξ, v k is the radial velocity of the target, ξ is the wavelength of the radar, T r is the pulse repetition period, is the phase disturbance term of the target caused by the ionosphere;

[0017] The clutter component c n (m) is represented as:

[0018]

[0019] In the formula, c sea (m) and c ground (m) are the slow-time components of the sea clutter and the ground clutter respectively, a c1 , a c2 and a g are the amplitudes of the positive and negative Bragg peaks of the sea clutter and the amplitude of the ground clutter respectively, and are the phase disturbance terms of the positive and negative Bragg peaks of the sea clutter and the ground clutter caused by the ionosphere respectively, f b is the Bragg frequency;

[0020] RD matrix Y and RD matrix are denoted as:

[0021]

[0022] where S, C and W denote the range-slow time domain components of target, clutter and noise, respectively, and S', C' and W' denote the RD domain components of target, clutter and noise, respectively;

[0023] S11, Objective function construction, RD matrix X is obtained by performing FFT on all columns of range-slow time matrix Y, which is denoted as a discrete Fourier matrix:

[0024] X = AY = A (S + C + W)

[0025] = S' + C' + W',

[0026] where is a normalized discrete Fourier matrix, and the (i, j)th element of is:

[0027]

[0028] By using the low-rank property of slow time domain clutter component C, the column sparsity of frequency domain clutter component C', and the block sparsity of frequency domain target component S', each component is separated, and the following equation constraint is obtained:

[0029]

[0030] s.t. X = S' + C' + W', C' = AC,

[0031] where μ1 and μ2 are regularization parameters, and ||C|| * is the nuclear norm of matrix C, and ||C'| 2,1 is the norm of matrix C', and are denoted as:

[0032]

[0033] where σ Ci is the ith singular value of matrix C, the nuclear norm is the sum of singular values of a matrix, and [C'] :,i is the ith column of matrix C', and the norm of matrix is the sum of the norms of each column of matrix, and φ group (·) is a block sparsity constraint, which is defined as:

[0034]

[0035] where G D and GR The total number of groups in the Doppler dimension and the distance dimension, respectively, satisfying G D G R =G, For the indicator set, satisfying

[0036] Considering the influence of noise components, the objective function is rewritten as:

[0037]

[0038] stX=S′+C′+W′,C′=AC,

[0039] In the formula, μ3 is the regularization parameter.

[0040] Further, step S2 specifically includes:

[0041] S21. Introduce a new variable. To decouple, the objective function is equivalent to

[0042]

[0043] stX=S′+C′+W′, C′=AZ, C=Z.

[0044] S22. Construct the equivalent objective function as an augmented Lagrangian function, and obtain:

[0045]

[0046] In the formula, U1, U2, For the introduced intermediate variable, λ > 0 is the parameter of the quadratic penalty term;

[0047] S23. The optimal solution for each component C, C', S', W', Z is expressed as:

[0048]

[0049] Furthermore, in step S3:

[0050] set up μ3=MN / 300, τ=1.1, λ=10 -6 , λ max =10 6 ε = 10 -8 In the CIT mode for oceanographic observation, the Doppler step size is set to s. D =4, in both short-range air-to-sea and air-to-surface CIT modes, s D =2, in all modes, the distance step size is set to s R =4, when satisfied

[0051] max{||X-S′ (k) -C′ (k) -S′ (k) || ∞ ,||C′ (k) -AZ (k) || ∞ ,||C (k) -Z (k) || ∞}<ε

[0052] time, where ||J|| ∞ = max{|J (i,j) |}.

[0053] Further, the step S4 specifically comprises:

[0054] S41, updating variable C:

[0055]

[0056] where, is the reduced singular value decomposition of E, σ(E) is the singular value vector of E, Diag(·) is the diagonal matrix composed of vectors, is the norm proximity operator of matrix, denoted as:

[0057]

[0058] S42, updating variable C′:

[0059]

[0060] where, is the norm proximity operator of matrix, the i-th row is defined as:

[0061]

[0062] S43, updating variable S′, decomposed into updating G sub-problems

[0063]

[0064] where, is the norm proximity operator of matrix, defined as:

[0065]

[0066] S44, updating variable Z:

[0067]

[0068] S45, updating variable W':

[0069]

[0070] S46, updating intermediate variables U1, U2 and U3:

[0071]

[0072] In the formula, τ is an iteration step length, satisfying The above variables are alternately updated until iteration converges, obtaining the RD domain target component S' and noise component W' after clutter elimination, and realizing clutter suppression.

[0073] Compared with the prior art, the advantages of the present application are that: the sky wave over-the-horizon radar clutter suppression method based on low rank group sparse representation provided by the present application distinguishes each component of echo signals by using low rank, column sparsity and group sparsity, and is constrained by nuclear norm, Frobenius norm, and is solved through a convex optimization algorithm framework, so that the ground sea clutter can be effectively suppressed, the target signal-to-noise ratio is improved, and the target detection performance of the OTHR is improved. BRIEF DESCRIPTION OF DRAWINGS

[0074] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0075] Figure 1 is a flow chart of the sky wave over-the-horizon radar clutter suppression method based on low rank group sparse representation of the present application.

[0076] Figure 2 is a schematic diagram of the objective function construction of the present application.

[0077] Figure 3 is an algorithm execution flow chart proposed by the present application.

[0078] Figure 4 is the clutter suppression result of the OTHR in three modes of the present application, (a) is the RD map in the air mode, (b) is the clutter suppression result of the proposed method, (c) is the clutter suppression result of the proposed method, (d) is the RD map in the long CIT mode against the sea, (e) is the clutter suppression result of the proposed method, and (f) is the clutter suppression result of the proposed method.

[0079] Figure 5Fig. 3 is a clutter suppression performance comparison chart of the three modes of the OTHR according to the present application, (a) is a detection performance curve in the air mode, (b) is a detection performance curve in the long sea CIT mode, and (c) is a detection performance curve in the short sea CIT mode. DETAILED DESCRIPTION

[0080] The preferred embodiments of the present application are described in detail below with reference to the accompanying drawings, so that the advantages and features of the present application can be more easily understood by those skilled in the art, and the scope of protection of the present application can be more clearly defined.

[0081] Referring to Figure 1 The embodiment shown discloses a sky wave over-the-horizon radar clutter suppression method based on low-rank group sparse representation, including the following steps:

[0082] Step S1, according to the characteristic analysis of the echo signal, the components of the echo signal are regularized constrained, and the equality constraint is performed through the discrete Fourier matrix to construct a target function.

[0083] Step S2, the equality constraint of the target function is eliminated through an augmented Lagrange function.

[0084] Step S3, the regularization parameter of the target function is initialized and set, and the iteration convergence condition of the algorithm is set.

[0085] Step S4, for the unconstrained convex optimization problem, all variables to be solved are updated alternately until the iteration converges, and the result after removing the clutter components is obtained to realize clutter suppression.

[0086] Specifically, the step S1 specifically includes:

[0087] Step S10, signal modeling

[0088] The OTHR clutter suppression processing is performed after digital beam forming (DBF) and pulse compression. At this time, the two-dimensional data of a certain beam channel is represented as M is the number of accumulated pulses, N is the number of distance units, and the slow time domain signal of the nth distance unit is represented as It is decomposed into target components, clutter components and noise components, and the following is obtained:

[0089] y n (m)=s n (m)+c n (m)+w n (m),m=1,2,…,M,

[0090] In the formula, s n (m), c n (m) and wn (m) denote the slow time components of the target, clutter and noise, respectively, with the noise component obeying a zero-mean complex Gaussian distribution with variance σ 2 , i.e.

[0091] The target component s n (m) is expressed as:

[0092]

[0093] where a s,k is the amplitude of the kth target, f d,k is the Doppler frequency of the kth target, f d,k = 2v k / ξ, v k is the radial velocity of the target, ξ is the radar operating wavelength, and T r is the pulse repetition period, is the phase perturbation term of the target caused by the ionosphere;

[0094] The clutter component c n (m) is expressed as:

[0095]

[0096] where c sea (m) and c ground (m) are the slow time components of the sea clutter and the ground clutter, respectively, a c1 , a c2 and a g are the amplitudes of the positive and negative Bragg peaks of the sea clutter and the amplitude of the ground clutter, respectively, and are the phase perturbation terms of the positive and negative Bragg peaks of the sea clutter and the ground clutter caused by the ionosphere, respectively, f b is the Bragg frequency;

[0097] The range-slow time matrix Y and the RD matrix are expressed as:

[0098]

[0099] where S, C and W denote the range-slow time components of the target, clutter and noise, respectively, and S', C' and W' denote the RD components of the target, clutter and noise, respectively;

[0100] Step S11, construction of the objective function

[0101] The objective function is constructed by regularizing constraints according to the characteristics of each component of the OTHR echo signal and by equation constraints through a discrete Fourier matrix.Figure 2 To construct a schematic diagram of the objective function, we first illustrate each echo signal component in the measured data; then, we approximate the measured data as a theoretical model and construct corresponding regularization constraints; finally, we construct the objective function by combining equality constraints. The RD matrix X is obtained by performing an FFT on all columns of the distance-slow-time matrix Y, and is expressed in the form of a discrete Fourier matrix:

[0102] X = AY = A(S + C + W)

[0103] =S′+C′+W′,

[0104] In the formula, The normalized discrete Fourier matrix has the following element as its (i,j)th element:

[0105]

[0106] By utilizing the low-rank property of the slow-time clutter component C, the column sparsity of the frequency-domain clutter component C′, and the block sparsity of the frequency-domain target component S′, the components are separated, and the following equation constraints are combined to obtain:

[0107]

[0108] stX=S′+C′+W′,C′=AC,

[0109] In the formula, μ1 and μ2 are regularization parameters, ||C|| * Let ||C′|| be the nuclear norm of matrix C. 2,1 For matrix C′ Norms, respectively, represent:

[0110]

[0111] In the formula, σ Ci Let [C'] be the i-th singular value of matrix C, and let [C'] be the nuclear norm, which is the sum of the singular values ​​of the matrix. :,i Let be the i-th column of matrix C′. The norm is the norm of each column of a matrix. The sum of norms, φ group (·) represents a block sparsity constraint, defined as:

[0112]

[0113] In the formula, G D and G R The total number of groups in the Doppler dimension and the distance dimension, respectively, satisfying G D G R =G, For the indicator set, satisfying

[0114] Considering the influence of noise components, the objective function is rewritten as:

[0115]

[0116] s.t.X=S′+C′+W′,C′=AC,

[0117] where μ3 is a regularization parameter.

[0118] Specifically, the step S2 specifically comprises:

[0119] Step S21, introducing a new variable Decoupling, the objective function is equivalent to

[0120]

[0121] s.t.X=S′+C′+W′,C′=AZ,C=Z.

[0122] Step S22, the equivalent objective function is constructed as an augmented Lagrangian function, and the following is obtained:

[0123]

[0124] where U1, U2, is an intermediate variable introduced, and λ>0 is a quadratic penalty parameter;

[0125] S23, the optimization solution of each component C, C', S', W', and Z is represented as:

[0126]

[0127] The above formula is a convex optimization problem without equality constraints, and each variable can be solved by ADMM alternately updated.

[0128] Specifically, in the step S3:

[0129] Variable initial value C (0) ,C′ (0) ,S′ (0) ,W′ (0) ,Z (0) , and is set to The parameters μ1 and μ2 affect the clutter suppression performance. If there is too much clutter residual in the experiment, μ1 should be reduced or μ2 should be increased, and vice versa. The parameter μ3 affects the denoising performance. In the experiments in this paper, the parameters are set as follows:

[0130] μ3=MN / 300, τ=1.1,

[0131] λ = 10 -6 , λ max = 10 6 , ε = 10 -8 , in the long CIT mode, the Doppler step size is set to s D = 4, in the short CIT and air mode, s D = 2, in all modes, the range step size is set to s R = 4, when max{||X-S′

[0132] ||C′ (k) -S′ (k) || (k) || ∞ ,||C′ (k) -AZ (k) || ∞ ,||C (k) -Z (k) || ∞} < ε

[0133] ,||J|| ∞ = max{|J (i,j) |}.

[0134] In particular, the step S4 specifically comprises:

[0135] Step S41, updating the variable C:

[0136]

[0137] wherein, is the reduced singular value decomposition of E, σ(E) is the singular value vector of E, Diag(·) is a diagonal matrix composed of vectors, is the norm proximity operator of matrix, denoted as:

[0138]

[0139] Step S42, updating the variable C′:

[0140]

[0141] wherein, is the norm proximity operator of matrix, the i-th row is defined as:

[0142]

[0143] Step S43, updating the variable S′, decomposed into updating G sub-problems

[0144]

[0145] wherein, is the matrix norm is the matrix norm

[0146]

[0147] Step S44, update variable Z:

[0148]

[0149] Step S45, update variable W':

[0150]

[0151] S46, update intermediate variables U1, U2 and U3:

[0152]

[0153] wherein, τ is the iteration step, satisfying

[0154] Alternately update the above variables until the iteration converges, to obtain the RD target component S' and the noise component W' after clutter rejection, and realize clutter suppression, Figure 3 is the algorithm flow chart for solving the target function, given the input distance-time matrix X and the discrete Fourier matrix A, under the parameter initialization setting, execute the algorithm, and the output RD target component S', RD clutter component C' and RD noise component W' can be obtained. Remove the noise component W' to realize OTHR clutter suppression.

[0155] Figure 4 is the clutter suppression result under the three modes of OTHR. Figure 4 (a)-(c) are the clutter suppression and target detection results under the air-to-air mode; Figure 4 (d)-(f) are the clutter suppression and target detection results under the long CIT sea-to-air mode. In Figure 4 most targets are located in the high-intensity sea clutter spectrum peak, and it is difficult to detect such targets without clutter suppression processing. The present application can effectively suppress the clutter component and retain the target component, effectively improve the target detection performance, and maintain a low false alarm.

[0156] Figure 5 is the performance comparison and analysis of clutter suppression under the three modes of OTHR. Figure 5 (a) is the detection performance curve under the air-to-air mode, Figure 5 (b) is the detection performance curve under the long CIT sea-to-air mode,Figure 5 (c) Target detection performance curves under the short-range CIT mode. Ten tests were conducted respectively. 3 This Monte Carlo experiment compared four existing clutter suppression methods. Figure 5 In this context, FFT represents the detection performance curve obtained by directly detecting the RD map after coherent accumulation without clutter suppression processing. Figure 5 In (a), except when the input SCNR is below -40dB, where the detection probability of RPCA is slightly higher than that of the proposed method, the proposed method has the highest detection probability in all other cases. Figure 5 In (b), except when the input SCNR is below -38dB, in which case the detection probability of SVD is slightly higher than that of the proposed method, the detection probability of the proposed method is the highest in all other cases. Figure 5 In (c), the detection probability of the proposed method is consistently higher than that of other comparative methods.

[0157] This invention utilizes low-rank property, column sparsity, and group sparsity to distinguish the components of the echo signal, based on the kernel norm, By constraining the norm, group sparse regularization term, and Frobenius norm, and solving the problem through a convex optimization algorithm framework, it is possible to effectively suppress land and sea clutter, improve the target signal-to-noise ratio, and thus improve the target detection performance of OTHR.

[0158] Although embodiments of the present invention have been described in conjunction with the accompanying drawings, the patent owner may make various modifications or alterations within the scope of the appended claims, as long as they do not exceed the protection scope described in the claims of the present invention, they shall be within the protection scope of the present invention.

Claims

1. A sky wave over the horizon radar clutter suppression method based on low rank group sparse representation, characterized in that, The method comprises the following steps: S1, according to the characteristic analysis of the echo signal, using low rank, column sparsity and group sparsity to distinguish each component of the echo signal, using nuclear norm, l 2,1 norm, group sparse regularization term and Frobenius norm to regularize and constrain each component of the echo signal, and using discrete Fourier matrix for equality constraint to construct an objective function; S2, eliminating the equality constraint of the objective function by using an augmented Lagrange function; S3, initializing the regularization parameter of the objective function, and setting the iteration convergence condition of the algorithm; S4, for the unconstrained convex optimization problem, all variables to be solved are updated alternately until the iteration converges, and the result after removing the clutter component is obtained to achieve clutter suppression.

2. The sky-wave over-the-horizon radar clutter suppression method based on low-rank group sparse representation according to claim 1, characterized in that, The step S1 specifically comprises: S10, signal modeling, the two-dimensional data of a certain beam channel is represented as M is the number of accumulated pulses, N is the number of range cells, and the slow-time signal of the nth range cell is represented as It is decomposed into target components, clutter components and noise components, and the following is obtained: y n (m) = s n (m) + c n (m) + w n (m), m = 1, 2,..., M, where s n (m), c n (m), and w n (m) represent the target component, the clutter component, and the noise component, respectively, and the noise component follows a zero-mean complex Gaussian distribution with variance σ 2 , i.e., w n (m) ~ CN(0, σ 2 ); Target component s n (m) + is represented as: where a s,k denotes the amplitude of the kth target, f d,k denotes the Doppler frequency of the kth target, f d,k = 2v k / ξ, v k is the radial velocity of the target, ξ is the radar operating wavelength, T r is the pulse repetition period, is the target phase perturbation term caused by the ionosphere; clutter component c n (m) is represented as: where c sea (m) and c ground (m) are the slow time components of the sea clutter and ground clutter, respectively, a c1 , a c2 , and a g are the amplitudes of the positive and negative Bragg peaks of the sea clutter and the amplitude of the ground clutter, respectively, and are the phase perturbation terms of the positive and negative Bragg peaks of the sea clutter and the ground clutter caused by the ionosphere, respectively, f b is the Bragg frequency; Distance slow time matrix Y and RD matrix are represented as: In the formula, S, C and W respectively represent the distance slow time domain components of the target, clutter and noise, and S', C' and W' respectively represent the RD domain components of the target, clutter and noise; S11, target function construction, the RD matrix X is obtained by performing FFT on all columns of the distance slow time matrix Y, and is expressed in the form of a discrete Fourier matrix: X = AY = A (S + C + W) = S' + C' + W', wherein is the normalized discrete Fourier matrix whose (i,j)th element is: By using the low rank of the slow time domain clutter component C, the column sparsity of the frequency domain clutter component C', and the block sparsity of the frequency domain target component S', each component is separated, and the equation constraint is obtained: s.t.X = S' + C' + W', C' = AC, where μ1and μ2are regularization parameters, ||C||F * is the nuclear norm of matrix C, ||C' || 2,1 is the l 2,1 norm of matrix C', respectively. where σi Ci is the i-th singular value of matrix C, the nuclear norm is the sum of the singular values of a matrix, [C'] :,i is the i-th column of matrix C', l 2,1 norm is the sum of the l2-norms of each column of a matrix, φ group (·) is the block-sparse constraint, defined as: In the formula, G D and G R are the total number of Doppler and distance dimensions, respectively, satisfying G D G R = G, I i,j is an index set, satisfying |I i,j | = s D s R ; Considering the influence of the noise component, the objective function is rewritten as: s.t.X = S' + C' + W', C' = AC, In the formula, μ3 is a regularization parameter.

3. The sky-wave over-the-horizon radar clutter suppression method based on low-rank group sparse representation according to claim 2, characterized in that, The step S2 specifically comprises: S21, introduce a new variable Decoupling, equivalent the objective function to s.t.X = S' + C' + W', C' = AZ, C = Z. S22, the equivalent objective function is constructed into an augmented Lagrange function, and the following formula is obtained: wherein is an introduced intermediate variable, λ > 0 is a quadratic penalty parameter; S23, the optimization solution of each component C, C', S', W' and Z is represented as:

4. The sky-wave over-the-horizon radar clutter suppression method based on low-rank group sparse representation according to claim 3, characterized in that, In the step S3: Setting μ3 = MN / 300, τ = 1.1, λ = 10 -6 , λ max = 10 6 , ε = 10 -8 In the sea-long CIT mode, the Doppler step size is set to s D = 4, in the sea-short CIT and air modes, s D = 2, and in all modes, the range step size is set to s R = 4 when the following is satisfied max{||XS′ (k) -C′ (k) -S′ (k) || ∞ ,||C′ (k) -THE (k) || ∞ ,||C (k) -Z (k) || ∞ }<ε At this time, the iteration converges, where ||J ∞ = max{|J (i,j) |}.

5. The sky-wave over-the-horizon radar clutter suppression method based on low-rank group sparse representation according to claim 4, characterized in that, The step S4 specifically comprises: S41, updating the variable C: wherein is the reduced singular value decomposition of E, σ(E) is the singular value vector of E, Diag(·) is the diagonal matrix of the vector, is the l1 norm proximity operator of matrix, denoted as: S42, updating the variable C': wherein l is a matrix 2,1 The norm neighborhood operator, the i-th row is defined as: S43, updating the variable S', which is decomposed into updating G sub-problems wherein is the l2 norm of a matrix, defined as: S44, updating the variable Z: S45, updating the variable W': S46, updating the intermediate variables U1, U2 and U3: where τ is the iteration step size, satisfying The above variables are updated alternately until the iteration converges, and the RD domain target component S' and the noise component W' after removing the clutter are obtained, and the clutter suppression is realized.

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