Blind separation anti-main lobe intermittent sampling cyclic-retransmission interference method based on tensor decomposition

Abstract

The application discloses a blind separation anti-main lobe intermittent sampling cyclic repetition jamming method based on tensor decomposition, which is applied to the technical field of radar anti-jamming and aims at the problem that the existing blind separation algorithm is not applicable to all DRFM jamming. Firstly, the second-order time delay correlation matrix of multiple received signals is calculated and is reconstructed into a high-order tensor form; secondly, an optimization problem about an array manifold matrix is established based on a tensor decomposition principle and an ELS-ALS algorithm is adopted to solve the optimization problem; finally, the left inverse of the estimated array manifold matrix is calculated, the received signal is multiplied by the left inverse, the separated target echo and jamming signal are obtained, the separated target echo is processed, target range Doppler information is acquired, and the suppression of the main lobe intermittent sampling cyclic repetition jamming is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar anti-jamming, and particularly relates to a space-time joint blind separation anti-jamming signal processing technology. BACKGROUND

[0002] With the rapid development of electronic countermeasure technology, the main lobe digital radio frequency memory (DRFM) jamming seriously affects the detection performance of the radar due to its strong energy and high similarity in space, time and frequency domains with the target echo. Therefore, it has important theoretical value and practical significance to improve the anti-main lobe DRFM jamming capability of the radar and ensure the correct detection of the target in a complex electromagnetic environment.

[0003] The existing anti-main lobe DRFM jamming methods mainly focus on waveform design and signal processing. The waveform design anti-jamming mainly utilizes the prior information of the jamming, increases the difference between the target echo and the jamming signal by designing the inter-pulse or intra-pulse waveform. Kai Zhou et al. in the document “Joint design of transmit waveform and mismatch filter in the presence of interrupted sampling repeater jamming, IEEE Signal Process Lett., vol. 27, pp. 1610-1614, Sep. 2020.” jointly design the radar waveform and the mismatch filter by minimizing the autocorrelation sidelobe level of the mismatch filter and the output sidelobe level of the jamming after the mismatch filter, which can effectively resist the interrupted sampling repeater jamming, but this method needs to accurately perceive the related parameters of the jamming. Blind separation as a signal processing method is applied to the field of radar anti-jamming due to its characteristic of not needing any prior information. Gemo Geng et al. in the document “Mainlobe jamming suppression via blind source separation,” 2018 IEEE Radar Conference, OK, USA, Jun. 2018, pp. 0914-0918.” realize the suppression of multi-main lobe jamming by the JADE (joint approximate diagonalization of eigenmatrices) blind separation algorithm, but this method is not suitable for all DRFM jamming, especially the slice repeater type jamming consistent with the pulse width of the target echo, such as the interrupted sampling jamming. SUMMARY

[0004] To solve the above technical problems, the application provides a blind separation anti-main lobe intermittent sampling cyclic repetition jamming method based on tensor decomposition.

[0005] The technical scheme adopted by the application is as follows: a blind separation anti-main lobe intermittent sampling cyclic repetition jamming method based on tensor decomposition, and the application scene is as follows: considering an M-element uniform receiving linear array with an element spacing of d, there is a target and a supporting jammer in the radar far-field detection area; the target echo and the jamming signal are both narrowband signals, the first element is taken as a reference element, and the backscattering component generated by the radar signal irradiating the jammer is ignored; the method comprises the following steps:

[0006] S1, the radar M-element receiving signal is expressed in the following matrix form:

[0007] x(t)=As(t)+n(t)

[0008] wherein x(t) is a receiving signal vector, A is an array manifold matrix, s(t) is a signal vector containing a target echo and a jamming echo, and n(t) is an M-way noise signal vector; the jamming type of the jamming echo is intermittent sampling cyclic repetition jamming;

[0009] S2, R second-order time delay correlation matrices C of receiving signals are calculated according to x(t) r , and a third-order time delay correlation tensor T of the receiving signals is composed according to C r The CP decomposition form of the tensor T is as follows:

[0010]

[0011] wherein is a vector outer product, a n and b n are the n-th column vectors of A and B respectively;

[0012] S3, the array manifold matrix is estimated by using tensor decomposition;

[0013] S4, the estimated array manifold matrix A is used to realize signal separation:

[0014] S6, the target signal separated is subjected to pulse compression and MTD processing to realize jamming suppression.

[0015] ​​​The beneficial effects of the present application: the existing blind source separation algorithm is not applicable to all DRFM interference, especially the problem that the slice retransmission type interference consistent with the target echo pulse width, such as intermittent sampling cycle retransmission interference, etc. The present application firstly calculates the second order time delay correlation matrix of multiple received signals, and reconstructs it into a high order tensor form. Secondly, based on the tensor decomposition principle, an optimization problem about array manifold matrix is established and the ELS-ALS algorithm is used to solve the optimization problem. Finally, the left inverse of the estimated array manifold matrix is obtained, and the received signal is multiplied by the left inverse to obtain the separated target echo and interference signal. The target distance Doppler information is obtained by processing the separated target echo, and the suppression of the main lobe intermittent sampling cycle retransmission interference is realized. The method of the present application has the following advantages:

[0016] 1. The present application can realize effective suppression of intermittent sampling cycle retransmission interference without losing target distance Doppler information.

[0017] 2. The present application realizes interference suppression based on the principle of blind source separation, and is suitable for the scene lacking prior information of interference, and is closer to the actual application environment. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 The flow chart of the method of the present application is shown in the figure.

[0019] Figure 2 The schematic diagram of the receiving array is shown in the figure.

[0020] Figure 3 The flow chart of the ELS-ALS algorithm is shown in the figure.

[0021] Figure 4 The signal processing result diagram before interference suppression is shown in the figure.

[0022] Figure 5 The signal processing result diagram after interference suppression of the present method is shown in the figure.

[0023] Among them, (a) is the signal processing result after interference suppression of the separated signal 1 using the method of the present application, and (b) is the signal processing result after interference suppression of the separated signal 2 using the method of the present application.

[0024] Figure 6 The signal processing result diagram after JADE interference suppression is shown in the figure.

[0025] Among them, (a) is the signal processing result after interference suppression of the separated signal 1 using JADE, and (b) is the signal processing result after interference suppression of the separated signal 2 using JADE. DETAILED DESCRIPTION

[0026] The specific implementation steps of the present application are described as follows: Figure 1

[0027] ​Step 1: Establish a radar received signal model:

[0028] Consider an M-element uniform receiving linear array with an element spacing of d. Assume there is a point target and a support jammer within the radar's far-field detection area, as shown in the attached figure. Figure 2 As shown. Both the target echo and the jamming signal are narrowband signals. Taking the first array element as the reference element, ignoring the backscattering component generated by the radar signal illuminating the jammer, after down-conversion, the baseband echo x received by the m-th array element is... m The expression for (t) is:

[0029]

[0030] Where s(t) is the radar echo, θ0 is the target angle information, and θ J Let J(t) be the angle of the jammer, J(t) be the jamming signal, and n be the angle of the jammer. m (t) represents the Gaussian white noise received by the m-th array element, where m = 1, 2, ..., M, and λ is the carrier wavelength.

[0031] The radar M-element received signal can be represented in the following matrix form.

[0032] x(t)=As(t)+n(t) (2)

[0033] Where x(t)=[x1(t),x2(t),…,x M (t)] T The received signal vector is represented by the superscript T, which stands for transpose; n(t) is the M-channel noise signal vector, defined as n(t) = [n1(t), n2(t), ..., n M (t)] T Its mean is 0 and its variance is σ. 2 The covariance matrix is ​​σ 2 I M I M Let A be an M-dimensional identity matrix; A = [a(θ0), a(θ...] J Let ] be the array manifold matrix, and let a(θ) be defined as:

[0034]

[0035] Where θ = θ0 or θ J s(t)=[s(t),J(t)] T The signal vector containing both the target echo and the interference echo can be called the source signal.

[0036] Step 2: Received signal reconstruction and tensor modeling:

[0037] Step 2-1: Calculate the second-order time delay correlation matrix C of the R received signals. r :

[0038] The R second-order time-delay correlation matrices of M received signals x(t) can be expressed as

[0039] C r = E[x(t)x T (t+τ r )] = AB r A H , r = 1,..., R (4)

[0040] where

[0041] B r = E[s(t)s T (t+τ r )] (5)

[0042] B r is the second-order time-delay correlation matrix of source signals, and the number of source signals N = 2 in the method discussed in the present application; if each component of the source signals is independent, B r is a diagonal matrix; τ r is the time delay of the rth second-order time-delay correlation matrix.

[0043] Step 2-2: Reconstructing the second-order time-delay correlation matrix C r into a tensor form

[0044] represents the complex field, and is composed of the third-order time-delay correlation tensor of the received signals according to the following formula

[0045]

[0046] where fold(·) represents tensor folding.

[0047] Step 2-3: Expressing the tensor as a CP (Canonical Polyadic) decomposition form:

[0048] Each slice C r in the tensor can be expressed as

[0049]

[0050] where (·) * represents the conjugate operation, and the matrix is defined as r The diagonal elements of the matrix B rn (r = 1,..., R) are spliced into a row vector and placed in the rth row of B, that is, (B)r nn . Thus, the above equation can be expressed as

[0051]

[0052] According to the definition of vector outer product and the principle of tensor CP decomposition, the above equation can be expressed as the CP decomposition form of tensor

[0053]

[0054] where, is the vector outer product, a n and b n are the nth column vectors of A and B, respectively, is the definition symbol, i.e., define as as a simplified representation of

[0055] Step 3: Estimate the array manifold matrix A using tensor decomposition:

[0056] Since the uniqueness of tensor CP decomposition, the estimation of the array manifold matrix can be achieved by tensor decomposition.

[0057] Step 3-1: Establish an optimization problem based on tensor decomposition:

[0058] By minimizing the cost function

[0059]

[0060] The optimal estimated array manifold matrix is obtained, where is the iteration factor matrix, and are the nth column vectors of and , respectively, is the 2-norm operation.

[0061] Step 3-2: Solve the optimization problem using the ELS-ALS (enhanced line search alternating least square) algorithm to estimate the array manifold matrix A.

[0062] This method selects the ELS-ALS algorithm to solve the optimization problem, and the algorithm flow is as follows: Figure 3 ​​​The algorithm guarantees the convergence performance by calculating the optimal iteration step. Before the kth iteration, the linear regression prediction value of the iteration factor matrix is calculated

[0063]

[0064] where ρ is the relaxation factor, and its value is determined by the ELS preprocessing. According to A (new) , A *(new) , B (new) The kth iteration result can be obtained as

[0065]

[0066] where C (k) represents the kth-order expansion of the tensor , ⊙ represents the Khatri-Rao product of matrices, and represents the pseudo-inverse of the matrix. The factor matrix is updated every iteration until the algorithm stopping condition is reached, i.e.

[0067]

[0068] where k max is the maximum number of iterations, and k max takes a value of 500 in this embodiment, and ε represents the residual error for stopping calculation, and ε takes a value of 10 -8 in this embodiment. Finally, the estimated array manifold matrix

[0069] Step 4: The estimated array manifold matrix is used to realize signal separation:

[0070] The left inverse of the estimated array manifold matrix is calculated, and the left multiplication of the received signal is performed to realize signal separation.

[0071]

[0072] where represents the left inverse, and is the estimated separation signal.

[0073] Step 5: Pulse compression and MTD processing are performed on the separated target signal to realize interference suppression.

[0074] Simulation verification and analysis

[0075] Simulation parameters:

[0076] A 16-element uniform linear array is considered, and the element spacing is 0.15 m. The radar beam is directed at θ0= 45°, the radar transmitted signal is a linear frequency modulation signal, the pulse repetition period is 200 μs, and the pulse width Tp = 20us, bandwidth B = 3MHz, carrier frequency f0 = 1GHz, sampling frequency f s = 10MHz, and the number of pulses is 64.

[0077] Assume that the target is located at angle θ0 = 45° and at the 600th range cell, and the target Doppler frequency is 1000Hz, the jammer is located at angle θ J = 47° and at the 600th range cell, and the Doppler frequency is 0Hz. The selected jamming type is intermittent sampling and cyclic repetition jamming, the number of jammer slices is 4, and the number of repetitions is 4. The signal-to-noise ratio SNR = 10dB and the jammer-to-noise ratio JNR = 35dB are set.

[0078] Simulation analysis:

[0079] Fig. 1 is a radar receiving signal jamming suppression pre-signal processing result diagram, it can be seen that the processed range-Doppler plane simultaneously exists jamming and target, and the target detection is affected by jamming. Figure 4 Figs. 2 and 3 are radar receiving signal jamming suppression post-signal processing result diagrams of the method and the JADE method respectively. Figure 5 It can be seen from Fig. 2 that after the anti-jamming processing of the method, the target echo and the jamming signal are effectively separated, wherein the separated signal 1 is the target echo, the separated signal 2 is the jamming signal, and the range-Doppler information obtained by processing the separated signal 1 is consistent with the set true target range-Doppler information, effectively realizing jamming suppression. Figure 6 Figs. 2 and 3 are radar receiving signal jamming suppression post-signal processing result diagrams of the method and the JADE method respectively. Figure 5 It can be seen from Fig. 2 that after the anti-jamming processing of the method, the target echo and the jamming signal are effectively separated, wherein the separated signal 1 is the target echo, the separated signal 2 is the jamming signal, and the range-Doppler information obtained by processing the separated signal 1 is consistent with the set true target range-Doppler information, effectively realizing jamming suppression. Figure 6 Figs. 2 and 3 are radar receiving signal jamming suppression post-signal processing result diagrams of the method and the JADE method respectively.

[0080] In summary, the method for suppressing main lobe intermittent sampling and cyclic repetition jamming based on tensor decomposition can effectively suppress main lobe intermittent sampling and cyclic repetition jamming, and enhance the detection capability of radar in a complex electromagnetic environment.

[0081] Those skilled in the art will appreciate that the embodiments described herein are presented for the purpose of helping the reader understand the principles of the present application, and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. The present application can have various modifications and changes for those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the scope of protection of the claims of the present application.

Claims

1. A method for blind separation anti-main lobe intermittent sampling cyclic-retransmission jamming based on tensor decomposition, characterized in that, The application scenario is specifically: considering that an M-element uniform receiving linear array has an element spacing d, there is a point target and a support jammer in a radar far-field detection area; the target echo and the jamming signal are narrowband signals, taking the first element as a reference element, and ignoring a backscattering component generated by the radar signal irradiating to the jammer; the method comprises the following steps: S1, the radar M-element receiving signal is expressed in the following matrix form: x(t) = As(t) + n(t) Wherein, x(t) is a receiving signal vector, A is an array manifold matrix, s(t) is a signal vector containing target echo and jamming echo, n(t) is an M-way noise signal vector; the jamming type of the jamming echo is intermittent sampling and cyclic repetition jamming; S2. Compute R received signal second-order time-delay correlation matrices C from x(t) r r ​​ S3, using tensor decomposition to estimate the array manifold matrix; S4, using the obtained estimated array manifold matrix to realize signal separation; S5, performing pulse compression and MTD processing on the separated target signal to realize jamming suppression.

2. The method of claim 1, wherein, The R second-order time delay correlation matrix of the M-way receiving signal x(t) is expressed as: C r = E [x(t)x T (t+τ r )] = AB r A H , r = 1,..., R where E[] denotes the mathematical expectation, the superscript T denotes the transpose, B r is the second-order time-delay correlation matrix of the source signal, the superscript H denotes the conjugate transpose, τ r is the time delay of the rth second-order time-delay correlation matrix.

3. The method of claim 2, wherein, Step S2 further comprises: decomposing the third-order time-delay correlation tensor into a CP decomposition form, and the specific process is as follows: Third order time-delay dependent tensor each slice C r the element in the pth row and qth column of C is denoted as where (·) * denotes the conjugate operation, and defines the matrix The matrix B r is then formed by concatenating the diagonal elements of B rn (r = 1,..., R) into a row vector, placed in the rth row of B, i.e., (B) r nn ; thus, the above expression can be written as​ According to the definition of vector outer product and the principle of tensor CP decomposition, the CP decomposition form of the third-order time-delay correlation tensor T is obtained as follows: T = ååååaiklmlnqiklmn where is the vector cross product, a n and b n are the nth column vectors of A and B, respectively, is the defining symbol, i.e., to define as a simplification of 4. The method of claim 3, wherein, Step S3 is specifically: based on tensor decomposition, an optimization problem is established, then an enhanced line search alternating least square algorithm is used to solve the optimization problem, and estimation of the array manifold matrix is realized.

5. The method of claim 4, wherein, The optimization problem expression is: By minimizing the cost function wherein is the iteration factor matrix, and are the column vectors of the nth column of and are the column vectors of the nth column of is the 2-norm operation.

6. The method of claim 5, wherein, Step S5 is specifically: The estimated array manifold matrix is The estimated array manifold matrix is The left inverse is calculated and left multiplied by the received signal to achieve signal separation: wherein denotes a left inverse, is the estimated separated signal.

Images