A two-pulse group coding agile convex optimization mismatch filtering anti-range deception jamming method

Abstract

The present application belongs to the field of radar, and is a two-pulse group coding agile convex optimization mismatch filtering anti-range deception jamming method. The method divides the transmitted pulse sequence into two pulse groups according to the odd and even pulses, and respectively gives independent phase coding to form distinguishable pulse group waveforms. The receiving end respectively constructs a mismatch filtering model based on the two pulse group signals, and sets the main lobe amplitude retention, side lobe amplitude limitation and mismatch filtering loss constraint to establish a convex optimization solving framework to obtain the optimal filter weight coefficients of each pulse group. The optimized filter can suppress the non-main pulse group component introduced by the deception jamming, so that it does not form a significant peak value in the filtering output, while maintaining the main lobe gain and range resolution ability of the real target. The present application combines pulse group coding agility and convex optimization constraint, realizes the simultaneous suppression of the main peak and side lobe of the jamming, and significantly improves the anti-range deception jamming performance of the system.

Description

Technical Field

[0001] This invention belongs to the field of radar, specifically relating to a two-pulse group coding agile convex optimization mismatch filtering method to resist range deception interference. Technical Background

[0002] In environments with strong range deception jamming, separating the target from the jammer in the radar echo has always been a challenge. Traditional phase-coded agile waveform diversity methods utilize the delay in the relay of deception jamming, which can suppress the main lobe of range deception jamming, but still leaves a significant amount of residual sidelobe energy. If the jamming energy is large, its sidelobes can easily mask the target, leading to missed detection. Summary of the Invention

[0003] This invention overcomes the limitations of existing phase-coded agile waveform diversity methods in resisting range-deception interference. It proposes a two-pulse group coding agile convex-optimized mismatch filtering method to address the problem of deception interference forming a pseudo-peak in the range dimension, affecting target detection. This method constructs two distinct pulse group signals by dividing the transmitted pulses into odd and even groups and encoding them separately. At the receiver, convex-optimized mismatch filter models are established based on the pulse group echoes, and the optimal filter weights are obtained through main lobe preservation, side lobe suppression, and mismatch loss constraints. The optimized filters are then used to process the echoes, significantly suppressing the deception interference components in the filtered output while preserving the main lobe response of the true target, thus achieving effective detection and estimation of range-dimensional targets. This method can significantly improve the anti-interference capability and target resolution performance of the system in complex environments with range-deception interference, enhancing the reliability of radar range-dimensional detection.

[0004] To achieve the above objectives, the present invention employs the following technical methods.

[0005] A two-pulse group coding agile convex optimization mismatch filtering method to resist range spoofing interference mainly includes the following steps:

[0006] Step 1: Construct two pulse groups of random phase-coded transmission signals. Divide the radar transmission pulse into two pulse groups according to the pulse parity, and generate different random binary phase coding sequences for the two pulse groups to form two sets of phase-coded transmission signals with waveform diversity characteristics.

[0007] Step 2: Construct the corresponding pulse group signal matrix based on the two pulse group transmission signals, and establish a linear relationship model between the output of the mismatch filter and the filter coefficients.

[0008] Step 3: Construct a multi-constraint convex optimization model for solving the mismatch filter coefficients of the two pulse groups, and calculate the optimal mismatch filter weight vector that satisfies the constraints.

[0009] Step 4: Use the optimal filter coefficients to perform mismatch filtering on the echoes of the two pulse groups respectively, so as to achieve target recognition and anti-distance spoofing interference.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0011] To address the problem that traditional matched filtering or waveform diversity methods cannot effectively detect targets in the presence of range spoofing interference, a novel anti-range spoofing interference method based on two-pulse group coding agility and convex optimized mismatch filtering is proposed. This method effectively solves the problem of target main lobe being masked and unreliable detection under strong interference environments. The method constructs a discriminative transmitted waveform through two-pulse group phase coding and utilizes convex optimized mismatch filtering to preserve the target main lobe and suppress interference sidelobes, thus preventing spoofing interference from forming significant peaks in the filtered output and improving the detectability of the target echo. By processing the two pulse group signals separately and fusing their filtering results, the prominence of the true target component is enhanced, improving the accuracy of target parameter estimation and the system's anti-interference performance. Attached Figure Description

[0012] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0013] Figure 1 This is a schematic diagram of a two-pulse group coding agile convex optimization mismatch filtering anti-distance spoofing interference method.

[0014] Figure 2 This is a diagram showing the radar echo matched filtering result of a traditional inter-pulse non-agile phase-coded waveform simulated on the MATLAB platform.

[0015] Figure 3 This is a diagram showing the radar echo matched filtering results of a two-pulse group coded agile transmit waveform simulated on the MATLAB platform.

[0016] Figure 4 This is a diagram showing the radar echo mismatch filtering results of a two-pulse group coded agile transmit waveform simulated on the MATLAB platform. Detailed Implementation

[0017] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0018] like Figure 1 The diagram shows the principle of a two-pulse group coding agile convex optimization mismatch filtering method to resist range spoofing interference, which includes the following steps:

[0019] Step 1: Construct two pulse groups of random phase-coded transmission signals. Divide the radar transmission pulse into two pulse groups according to the pulse parity, and generate different random binary phase coding sequences for the two pulse groups to form two sets of phase-coded transmission signals with waveform diversity characteristics.

[0020] Specifically, step 1 includes the following sub-steps:

[0021] Sub-step 1.1: Based on the parity of the pulse number, divide the radar pulses into two pulse groups: pulses with odd numbers correspond to pulse group 1; pulses with even numbers correspond to pulse group 2.

[0022] Let the complex envelope sequences of the transmitted signals of the two pulse groups be represented as follows:

[0023] x1(k),x2(k),k=1,2,…,K (1)

[0024] Where K is the number of sampling points for each pulse.

[0025] Sub-step 1.2: Generate random 0 / 1 base code sequences of length K for each of the two pulse groups to achieve waveform diversity between the pulse groups. Let the random binary codes of pulse group 1 and pulse group 2 be respectively...

[0026] c1=[c1(1),c1(2),…,c1(K)] (2)

[0027] c2=[c2(1),c2(2),…,c2(K)] (3)

[0028] Each symbol satisfies

[0029] c1(k), c2(k)∈{0,1} (4)

[0030] And it requires that the two sets of codes be different, that is

[0031] c1≠c2 (5)

[0032] This ensures that the two pulse groups have different phase encoding structures.

[0033] Sub-step 1.3: Map the binary code to a binary phase code, where symbol 0 maps to phase 0 and symbol 1 maps to phase π. Therefore, the phase sequences of the two pulse groups are as follows:

[0034]

[0035] Substituting into the exponential form, we can obtain the two-phase phase-coded transmission signals of pulse group 1 and pulse group 2.

[0036]

[0037]

[0038] Step 2: Construct the corresponding pulse group signal matrix based on the two pulse group transmission signals, and establish a linear relationship model between the output of the mismatch filter and the filter coefficients.

[0039] Specifically, step 2 includes the following sub-steps:

[0040] Sub-step 2.1: Let the order of the mismatch filter for the phase-coded signal be M. Pad the pulse group transmission signal obtained in step 1 with zeros at both ends to form an M×1 order vector. Then, the signals of the two pulse groups after zero-padding are represented as follows:

[0041]

[0042]

[0043] Where s(m), m = 1, 2, ..., M represent the elements of vector s.

[0044] Sub-step 2.2: Let the coefficients of its M-order mismatched filter be expressed as...

[0045] w = [w1, w2, ..., w M ] T (11)

[0046] Construct an M×(2M-1) dimensional Toeplitz structure matrix X1 using the transmitted signal of pulse group 1.

[0047]

[0048] The mismatch filter output of pulse group 1 can be expressed as:

[0049]

[0050] The main lobe is

[0051]

[0052] The side lobes are

[0053]

[0054] Where X 1SL The sidelobe matrix obtained by removing the Mth column element from matrix X1.

[0055] Sub-step 2.3: Construct an M×(2M-1) dimensional Toeplitz matrix X2 based on the pulse group 2 transmitted signal.

[0056]

[0057] Then its mismatch filter output can be expressed as

[0058]

[0059] The main lobe is

[0060]

[0061] The side lobes are

[0062]

[0063] Where X 2SL The sidelobe matrix obtained by removing the Mth column element from matrix X2.

[0064] Step 3: Construct a multi-constraint convex optimization model for solving the mismatch filter coefficients of the two pulse groups, and calculate the optimal mismatch filter weight vector that satisfies the constraints.

[0065] Specifically, step 3 includes the following sub-steps:

[0066] Sub-step 3.1: One of the important properties of convex optimization methods is that the solution obtained is the global optimum. The general form of a convex optimization problem is:

[0067] In the formula, f0(x) is the objective function, x is the solution vector, and f p (x) is a convex inequality constraint, h i (x) represents the linear equality constraint, and P and Q represent the number of inequality constraints and equality constraints, respectively.

[0068] Sub-step 3.2: The mismatch filter coefficients for pulse group 1 and pulse group 2 can be solved using a similar method. Taking pulse group 1 as an example: Let the mismatch filter coefficient w of pulse group 1 be the solution vector, and the objective function be the highest sidelobe amplitude in the mismatch filter output of pulse group 2, i.e., the interference sidelobe amplitude. The formula is as follows:

[0069] Among them ||·|| ∞ This indicates that the Chebyshev norm of a vector is calculated, which is the maximum absolute value among the elements of the vector.

[0070] Sub-step 3.3: To ensure target detection performance, the following three constraints are proposed for the convex optimization problem:

[0071] First, the target main lobe amplitude is kept constant, i.e.

[0072]

[0073] This constraint ensures that the target can still form the main lobe peak through mismatch filtering.

[0074] Secondly, the highest sidelobe amplitude in the mismatch filtering output of pulse group 1 signal, i.e., the target sidelobe amplitude, is constrained to not exceed the threshold α, as shown in the formula:

[0075]

[0076] This constraint can reduce the target sidelobe level, lower the false alarm rate, and prevent large targets from masking small targets.

[0077] Third, the mismatch filter loss is defined as...

[0078]

[0079] Where ||·||2 represents the 2-norm of the vector, after normalizing the signal and ensuring that the mismatch filtering loss is less than a predetermined value βdB, the target constraint can be expressed as:

[0080]

[0081] Sub-step 3.4: The design model for the mismatch filter of pulse group 1 can be expressed as follows:

[0082]

[0083] in and All are convex functions, satisfying convex optimization form.

[0084] Range deception jamming typically involves a jammer intercepting the radar's transmitted signal and delaying it by one pulse repetition cycle before retransmitting it. This results in the target component and the jamming component in the echo within one pulse repetition cycle being encoded into two separate pulse groups. Because the correlation between the jamming signal components and the filter coefficients is low, the mismatched filter output does not exhibit a significant main lobe peak. Simultaneously, the jamming sidelobe amplitude is suppressed to an optimal level after objective function optimization. With the target component under strict constraints, the sidelobe ratio of the target peak can be increased while maintaining a constant target main lobe amplitude, thereby enhancing target detection performance.

[0085] Sub-step 3.5: Solve the established convex optimization problem to obtain the optimal mismatch filter coefficient vector that satisfies the constraints.

[0086] Step 4: Use the optimal filter coefficients to perform mismatch filtering on the echoes of the two pulse groups respectively, so as to achieve target recognition and anti-distance spoofing interference.

[0087] The two sets of optimal mismatch filter coefficients obtained are used to perform mismatch filtering on the echo signals of the two pulse groups, respectively. The mismatch filtering formula is as follows:

[0088] z(k)=r(k)*w (27)

[0089] Where r(k) represents the echo signal sequence, * represents the convolution operation, and z(k) is the mismatch filtering result of the filter output.

[0090] Table 1 Simulation parameter settings

[0091]

[0092] Based on the parameters in Table 1, the radar's transmission frequency f0 is 3 GHz, transmitting 32 pulses. The radar pulse repetition period is 1000 μs, therefore the maximum unambiguous range of the radar is 150 km. The convex optimization constraint threshold α is 0.0562, meaning the target sidelobe is below -25 dB. The convex optimization constraint threshold β is 10, meaning the mismatch filtering loss is less than 10 dB.

[0093] To verify the target detection performance of the present invention under interference conditions, one target scattering point and one interference scattering point were set in a radar observation scenario, and the simulated data of their velocity and distance parameters are shown in Table 2.

[0094] Table 2 Target and Interference Parameter Settings

[0095]

[0096] As shown in Table 3, the target and the interference belong to two different range gates, both with a velocity of 0 and the same power.

[0097] Depend on Figure 2 Therefore, using the radar echo matched filtering result with the traditional inter-pulse non-agile phase-coded waveform, the target forms a matched filter peak at 30km. Range deception jamming, after matched filtering, forms a false target peak at 90km, the same height as the real target, making it ineffective against the jamming.

[0098] Depend on Figure 3 The radar echo matched filtering results using two-pulse group coding of the agile transmit waveform show a target peak sidelobe ratio of 16.1 dB and a signal-to-noise ratio of 46.8 dB. While the interference main lobe is suppressed by the matched filter due to its non-coherence, a relatively high range-dimensional sidelobe of -15.6 dB still exists, which can easily obscure small targets.

[0099] Depend on Figure 4The radar echo mismatch filtering results using the two-pulse group encoded agile transmit waveform show a target peak sidelobe ratio of 22.7 dB, an improvement of 6.6 dB compared to the matched filtering result. The interference sidelobe amplitude is also -22.7 dB, a decrease of 7.1 dB compared to the matched filtering result. The target signal-to-noise ratio is 43.6 dB, a decrease of 3.2 dB compared to the matched filtering result. Due to the presence of noise, the obtained indicators are slightly lower than the set convex optimization constraint value. This method, based on suppressing the interference main lobe of the agile waveform, simultaneously suppresses both target and interference sidelobes through convex optimization, at the cost of a decrease in the target signal-to-noise ratio.

[0100] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A two-pulse group coding agile convex optimization mismatch filtering method to resist range spoofing interference, characterized in that, Includes the following steps: Step 1: Construct two pulse groups of random phase-coded transmission signals. Divide the radar transmission pulse into two pulse groups according to the pulse parity, and generate different random binary phase coding sequences for the two pulse groups to form two sets of phase-coded transmission signals with waveform diversity characteristics. Step 2: Construct the corresponding pulse group signal matrix based on the two pulse group transmission signals, and establish a linear relationship model between the output of the mismatch filter and the filter coefficients. Step 3: Construct a multi-constraint convex optimization model for solving the mismatch filter coefficients of the two pulse groups, and calculate the optimal mismatch filter weight vector that satisfies the constraints. Step 4: Use the optimal filter coefficients to perform mismatch filtering on the echoes of the two pulse groups respectively, so as to achieve target recognition and anti-distance spoofing interference.

2. The two-pulse group phase-encoded agile waveform construction according to claim 1, characterized in that, Step 1 includes the following steps: Sub-step 1.1: Based on the parity of the pulse number, divide the radar pulses into two pulse groups: pulses with odd numbers correspond to pulse group 1; pulses with even numbers correspond to pulse group 2. Let the complex envelope sequences of the transmitted signals of the two pulse groups be represented as follows: xx(k),x2(k),k=1,2,…,K (1) Where K is the number of sampling points for each pulse. Sub-step 1.2: Generate random 0 / 1 binary code sequences of length K for each of the two pulse groups to achieve waveform diversity between the pulse groups. Let the random binary codes of pulse group 1 and pulse group 2 be respectively... C1=[c1(1),c1(2),…,c1(K)] (2) c2=[c2(1),c2(2),…,c2(K)] (3) Each symbol satisfies c1(k), c2(k)∈{0,1} (4) And it requires that the two sets of codes be different, that is c1≠c2 (5) to ensure that the two pulse groups have different phase coding structures. Sub-step 1.3: Map the binary code to a binary phase code, where symbol 0 maps to phase 0 and symbol 1 maps to phase π. Therefore, the phase sequences of the two pulse groups are as follows: Substituting into the exponential form, we can obtain the two-phase phase-coded transmission signals of pulse group 1 and pulse group 2.

3. The method for constructing a pulse group signal matrix according to claim 2, characterized in that, Step 2 includes the following steps: Sub-step 2.1: Let the order of the mismatch filter for the phase-coded signal be M. Pad the pulse group transmitted signal obtained in step 1 with zeros at both ends to form an M × 1 order vector. Then, the signals of the two pulse groups after zero-padding are represented as follows: Where s(m), m = 1, 2, ..., M represent the elements of vector s. Sub-step 2.2: Let the coefficients of its M-order mismatched filter be expressed as... w=[w1,w2,…,w M ] T (11) Construct an M×(2M-1) dimensional Toeplitz structure matrix X1 using the transmitted signal of pulse group 1. The mismatch filter output of pulse group 1 can be expressed as: The main lobe is The side lobes are Where X 1SL The sidelobe matrix obtained by removing the Mth column element from matrix X1. Sub-step 2.3: Construct an M×(2M-1) dimensional Toeplitz matrix X2 based on the pulse group 2 transmitted signal. Then its mismatch filter output can be expressed as The main lobe is The side lobes are Where X 2SL The sidelobe matrix obtained by removing the Mth column element from matrix X2.

4. The solution for the multi-constraint convex optimization mismatch filter according to claim 3, characterized in that, Step 3 includes the following steps: Sub-step 3.1: One of the important properties of convex optimization methods is that the solution obtained is the global optimum. The general form of a convex optimization problem is: In the formula, f0(x) is the objective function, x is the solution vector, and f p (x) is a convex inequality constraint, h i (x) represents the linear equality constraint, and P and Q represent the number of inequality constraints and equality constraints, respectively. Sub-step 3.2: The mismatch filter coefficients for pulse group 1 and pulse group 2 can be solved using a similar method. Taking pulse group 1 as an example: Let the mismatch filter coefficient w of pulse group 1 be the solution vector, and the objective function be the highest sidelobe amplitude in the mismatch filter output of pulse group 2, i.e., the interference sidelobe amplitude. The formula is as follows: Among them ||·|| ∞ This indicates that the Chebyshev norm of a vector is calculated, which is the maximum absolute value among the elements of the vector. Sub-step 3.3: To ensure target detection performance, the following three constraints are proposed for the convex optimization problem: First, the target main lobe amplitude is kept constant, i.e. This constraint ensures that the target can still form the main lobe peak through mismatch filtering. Secondly, the highest sidelobe amplitude in the mismatch filtering output of pulse group 1 signal, i.e., the target sidelobe amplitude, is constrained to not exceed the threshold α, as shown in the formula: This constraint can reduce the target sidelobe level, lower the false alarm rate, and prevent large targets from masking small targets. Third, the mismatch filter loss is defined as... Where ||·||2 represents the 2-norm of the vector, after normalizing the signal and ensuring that the mismatch filtering loss is less than a predetermined value βdB, the target constraint can be expressed as: Sub-step 3.4: The design model for the mismatch filter of pulse group 1 can be expressed as follows: in and All are convex functions, satisfying convex optimization form. Range deception jamming typically involves a jammer intercepting the radar's transmitted signal and delaying it by one pulse repetition cycle before retransmitting it. This results in the target component and the jamming component in the echo within one pulse repetition cycle being encoded into two separate pulse groups. Because the correlation between the jamming signal components and the filter coefficients is low, the mismatched filter output does not exhibit a significant main lobe peak. Simultaneously, the jamming sidelobe amplitude is suppressed to an optimal level after objective function optimization. With the target component under strict constraints, the sidelobe ratio of the target peak can be increased while maintaining a constant target main lobe amplitude, thereby enhancing target detection performance. Sub-step 3.5: Solve the established convex optimization problem to obtain the optimal mismatch filter coefficient vector that satisfies the constraints.

5. The method for mismatch filtering the received echo signal according to claim 4, characterized in that, Step 4: Use the two sets of optimal mismatch filter coefficients obtained to perform mismatch filtering on the echo signals of the two pulse groups. The mismatch filtering formula is as follows: z(k)=r(k)*w (27) Where r(k) represents the echo signal sequence, * represents the convolution operation, and z(k) is the mismatch filtering result of the filter output.

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