Time-frequency cooperative multi-subpulse adaptive matched filtering main lobe intermittent sampling interference resisting method

Abstract

The invention discloses a time-frequency cooperative multi-sub-pulse adaptive matched filtering main lobe intermittent sampling interference resisting method, which comprises the following steps of: modeling a radar multi-sub-pulse transmitting signal to obtain an echo signal, modeling a radar system total receiving signal, filtering an interference signal, recovering a target signal, and obtaining a pulse pressure result. According to the method, multi-channel pulse compression is completed, then distance gate alignment is carried out, finally, distance and speed information of a real target is further highlighted through intra-sub-pulse coherent accumulation and inter-sub-pulse coherent accumulation, and intermittent sampling interference is effectively suppressed. According to the method, a multi-sub-pulse structure is utilized, the interception length of a single sub-pulse by a jammer can be reduced, so that the interference degree of the single sub-pulse is reduced, and the intermittent sampling interference can be effectively suppressed under the condition that interference prior information does not need to be known.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a time-frequency collaborative multi-subpulse adaptive matching filtering method for anti-main lobe intermittent sampling interference. Background Art

[0002] Modern radar systems always face the severe problem of interference in tasks such as detection, estimation, tracking, and imaging. According to the spatial distribution of interference sources in the beam pattern, interference can be divided into two major categories: sidelobe interference and main lobe interference. Current radar technologies have developed various effective means to deal with sidelobe interference, including sidelobe blanking, sidelobe cancellation, and low-sidelobe beam design. However, when encountering main lobe interference, if the conventional anti-interference strategies for sidelobe interference are directly used, problems such as main lobe distortion of the beam may occur. Therefore, developing new main lobe interference suppression technologies is crucial for enhancing the survival ability and detection ability of radar systems in complex electromagnetic environments.

[0003] The literature "Y Gao, H Fan, L Ren, et al. Joint design of waveform and mismatched filter for interrupted sampling repeater jamming suppression. IEEE Trans. Aerosp. Electron. Syst., 2023" jointly optimizes the transmitted waveform and the mismatched filter based on the objective function of minimizing the sum of the peak sidelobe level of the target signal pulse compression result and the integrated sidelobe level of the interference signal pulse compression result, improving the radar's anti-main lobe intermittent sampling interference ability. The literature "Y Li, J Wang, Y Wang, et al. Random-frequency-Coded waveform optimization and signal coherent accumulation against compound deception jamming. IEEE Trans. Aerosp. Electron. Syst., 2023, 59(4): 4434 - 4449" constructs an inter-pulse and intra-pulse joint frequency-coded waveform to achieve effective suppression of multi-deception interference. However, the above anti-interference technologies require accurate prior information about the interference. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a time-frequency collaborative multi-subpulse adaptive matching filtering method for anti-main lobe intermittent sampling interference, which can effectively suppress intermittent sampling interference without knowing the prior information about the interference.

[0005] The technical solution adopted by the present invention is as follows: a time-frequency collaborative multi-subpulse adaptive matching filtering method for anti-main lobe intermittent sampling interference, and the specific steps are as follows:

[0006] S1. Modeling the radar multi-subpulse transmitted signal;

[0007] S2. Based on step S1, obtaining the echo signal and modeling the total received signal of the radar system;

[0008] S3. Based on step S2, filtering out the interference signal and then recovering the target signal to obtain the pulse compression result and complete multi-channel pulse compression;

[0009] S4. Based on step S3, performing range gate alignment and sampling the aligned result to obtain the fast and slow time dimension matrix;

[0010] S5. Based on step S4, performing in-subpulse coherent integration, that is, using multi-channel discrete Fourier transform MC-DFT to integrate each subpulse;

[0011] S6. Based on step S5, performing inter-subpulse coherent integration to effectively suppress the intermittent sampling interference.

[0012] Further, the specific steps of step S1 are as follows:

[0013] It is set that during the tracking process, the radar emits a multi-subpulse signal with M subpulses, the pulse duration is T, and the pulse repetition interval PRI is T P , and the coherent processing interval CPI is T CPI , and there are N PRIs in one CPI. Set the pulse width of the m-th subpulse to T m , then the above parameter expressions are as follows:

[0014]

[0015] T CPI =NT P

[0016] Then the transmission sequence x m (t) of the m-th subpulse is expressed as follows:

[0017]

[0018] Among them, represents the imaginary unit, t represents time, and p m (t) represents a linear frequency modulation LFM signal with a time width of T m and a bandwidth of B; f0 represents the carrier frequency, and f m represents the frequency offset of the m-th subpulse, and f m= b(m)Δf, m = 1, 2, ..., M, where Δf represents the frequency offset step, b(m) represents the number of frequency offset steps of the m-th sub-pulse, and b(m) is obtained by sampling without replacement from the frequency offset step sequence b = [0, 1, ..., M - 1].

[0019] Finally, for the multi-sub-pulse signal, the expression of the transmitted signal in one CPI is as follows:

[0020]

[0021] where t m represents the transmission time of the m-th sub-pulse, and t1 = 0,

[0022] Furthermore, the specific steps of step S2 are as follows:

[0023] Set the scenario. There is a point target equipped with a self-defense jammer in the detection and surveillance area of the radar system, that is, there is a point target transmitting main lobe intermittent sampling jammer ISJ in the airspace. Then the target echo y T (t) is expressed as follows:

[0024]

[0025] where c represents the speed of light, R and v respectively represent the distance and radial velocity of the target relative to the radar system, and α represents the influence of target reflectivity and channel propagation on the signal.

[0026] According to different forwarding schemes, intermittent sampling jammers can be divided into three categories: intermittent sampling repeated forwarding jammer ISRJ, intermittent sampling cyclic forwarding jammer ISCJ, and intermittent sampling direct forwarding jammer ISDJ. Set the sampling duration of the jammer during the radar signal transmission as T a , and the sampling period as T b . The specific type of interference is randomly selected among ISRJ, ISCJ, and ISDJ. Then the signal y J,I (t) intercepted by the interference is expressed as follows:

[0027] y J,I (t) = s(t)J(t)

[0028] where J(t) represents the interception strategy of the jammer, and the specific expression is as follows:

[0029]

[0030] where rect(t) represents the rectangular pulse function, with a value of 1 when 0 ≤ t ≤ 1. δ(t) represents the impulse function, and K represents the number of interceptions. Then the total interference signal y J,T (t) is expressed as follows:

[0031]

[0032] Among them, Q represents the number of forwarding times, and τ q represents the start time of the q-th forwarding.

[0033] The intermittent sampling interference is self-defense interference. The distance and radial velocity of the jammer are considered to be the same as those of the target. Then, the interference signal y J (t) received by the radar system is expressed as follows:

[0034] y J (t) = βy J,T (t - 2(R - vt) / c)

[0035] Among them, β represents the influence of target reflectivity and channel propagation on the signal. Then, the total received signal y(t) of the radar system is expressed as follows:

[0036] y(t) = y T (t) + y J (t) + n(t)

[0037] Among them, n(t) represents Gaussian white noise with a mean of 0 and a variance of σ 2 .

[0038] Furthermore, the specific steps of step S3 are as follows:

[0039] S31. Interference signal filtering;

[0040] According to the different carrier frequencies of each sub-pulse, the received signal is respectively down-converted by -(f0 + f i ), i = 1, 2,..., M and band-pass filtered, and the resulting expression is as follows:

[0041]

[0042] Among them, represents the total received signal after being down-converted by -(f0 + f i ) and band-pass filtered, respectively represent the i-th sub-pulse, the interference and noise based on intercepting the i-th sub-pulse.

[0043] Based on M different sub-pulses, design a filter (·) * represents the conjugate operation. Apply the i-th filter to The resulting pulse compression result z i (t) is expressed as follows:

[0044]

[0045] For a specific time τ corresponding to the pulse compression result z i (t), z i (τ) has the following specific expression:

[0046]

[0047] where

[0048]

[0049] Then the expression can be obtained as follows:

[0050]

[0051] where z T,i (τ, u), z J,i (τ, u), z n,i (τ, u) is the expansion of z T,i (τ), z J,i (τ), z n,i (τ). For the expanded dimension u, it is called the matching dimension.

[0052] Then, interference discrimination and separation are performed along the matching dimension. Assume that the power of the target echo received by the receiver is A T , and the power of the interference signal is A J . Then, in the expansion of z T,i (τ), z J,i (τ), z n,i (τ) along the matching dimension, the amplitudes of z T,i (τ, u), z J,i (τ, u), z n,i (τ, u) are respectively σ, and A J >> A T , σ 2 ≥ A T .

[0053] Assume that during the tracking process, the known range τ where the target is located ALL , and in the time-delay - matching plane z ALL corresponding to the range τ where the target is located i (τ ALL , u), z T,i (τ, u), z J,i (τ, u) and z n,i (τ, u) appear at different positions respectively. Then, along the time-delay dimension, the time-delay - matching plane can be divided into several parts along the time-delay dimension, including: τ with only noise n , and τ with both target echo and noise T, τ with both interference signal and noise J , τ with target, interference and noise existing simultaneously T,J . Then there are 3 cases, specifically as follows:

[0054] (1) When τ T ≠τ J , that is, when the true target and the false target do not overlap, at the delay τ J corresponding to the false target, z i (τ J ) has a large amplitude only in some regions in the matching dimension expansion, and the amplitudes in other regions are all close to 0;

[0055] (2) At the delay τ T corresponding to the true target, and at the τ n with only noise, because σ 2 ≥A T , the target signal is submerged by the noise, and z i (τ T ) and z i (τ n ) have small amplitudes for all u in the matching dimension;

[0056] (3) When interference, target and noise exist at the same moment τ T,J , the zi(τ T,J ) corresponding to this moment in the matching dimension expansion can be subdivided into 2 parts: z i (τ T,J ,u T ) with only target and noise existing, z i (τ T,J ,u J ) with target, interference and noise existing simultaneously.

[0057] Based on the above 3 cases, using the target interference separation method, first, for any moment τ, calculate the minimum value z i (τ,u)| and the maximum value z min corresponding to this moment, uniformly sample H points in the amplitude range [z max ,z min ,z max to obtain the threshold sequence z H =[z1,z2,…,z H , for each threshold value, divide |z i (τ,u)| into 2 parts: z i,1 (τ,u) less than the threshold value, z i,2 (τ,u) greater than the threshold value, and then calculate the overall variance var(|z i,1 (τ,u)|),var(|zi,2 (τ, u)|), the optimization problem expression is set as follows:

[0058]

[0059] where z h = z min +(h - 1)((z max - z min ) / H), h = 1, 2, …, H. zh that satisfies the optimization problem is the optimal threshold.

[0060] Finally, the corresponding threshold is adaptively obtained according to the signals corresponding to different time delays. The part exceeding the threshold is considered as interference signal and set to zero.

[0061] S32. Target signal recovery;

[0062] For the processed z i (τ, u), it only has the target signal and the interference signal, as well as some filtered parts with an amplitude of 0. Then, the zeroed parts are compensated, and most of the target signals are retained after filtering out the interference signals.

[0063] Among them, the compensation includes: phase compensation and amplitude compensation, which are specifically as follows:

[0064] (1) Phase compensation: For each time delay τ with a part having an amplitude of 0, using the periodicity of the phase of the target signal expanded along the matching dimension, directly copy the phase of the non-zero part in this time delay.

[0065] (2) Amplitude compensation: For each time delay τ with a part having an amplitude of 0, its amplitude is equal to the mean value of the amplitude of the non-zero part in this time delay.

[0066] S33. Obtain the pulse compression result;

[0067] After performing the interference signal filtering and target signal recovery operations in the matching dimension, sum z i (t, u) along the u dimension, and the pulse compression result z i (t) can be obtained. The expression of the pulse compression result is as follows

[0068]

[0069] where γ i (t - (n - 1)T P - t i - 2R / c) represents the complex envelope of the output result of the i-th pulse and the i-th matched filter after interference suppression processing. and represent the interference output and the noise output respectively.

[0070] Further, the specific steps of step S4 are as follows:

[0071] Based on the output of the first filter and the known sub - pulse durations, there is a time deviation between the nth pulse output by the ith filter and its first pulse output Compensate for the delay by translating the corresponding filter output in the range dimension and truncate the part of the signal that exceeds zero delay. The translated result z i (t) is expressed as follows:

[0072]

[0073] Finally, sample the aligned result to obtain the fast - slow time - dimension matrix A represents the number of sampling points for each T P .

[0074] Further, the specific steps of step S5 are as follows:

[0075] Set the maximum unambiguous velocity of the multi - sub - pulse signal to v max , and uniformly sample U points in the velocity measurement range [-v max , v max to obtain the velocity measurement sequence v U = [v1, v2, …, v U .

[0076] Among them, v u = -v max +(u - 1)(2v max / U), u = 1, 2, …, U, then the row - vector expression is defined as follows:

[0077]

[0078] Among them, [·] T represents the transpose operation.

[0079] Then, the transformation matrix corresponding to the ith sub - pulse is obtained as H i = [h i,1 , h i,2 , …, h i,U T , then the MC - DFT processing expression of the fast - slow time - dimension matrix Z i corresponding to the ith sub - pulse obtained through step S4 is as follows:

[0080] R i = H i Z i

[0081] Among them, R​i Represents the R-D diagram of the i-th sub-pulse.

[0082] Further, the specific steps of step S6 are as follows:

[0083] After obtaining the R-D diagrams of M sub-pulses, a three-dimensional matrix of U×A×M is formed. After performing FFT transformation of P points along the third dimension and obtaining the FFT transformation result of length P, it is tiled along the range dimension to achieve coherent accumulation between sub-pulses and high-precision ranging. Finally, a two-dimensional matrix R of U×(A×P) dimension is obtained F , R F The horizontal and vertical coordinates corresponding to the maximum value of R are the distance and velocity of the real target.

[0084] Wherein, U represents the length of the velocity measurement sequence, P represents the number of FFT points, and P > M.

[0085] Advantages of the present invention: The method of the present invention first models the radar multi-sub-pulse transmitted signal to obtain the echo signal, models the total received signal of the radar system, then filters out the interference signal and restores the target signal to obtain the pulse compression result, completes multi-channel pulse compression, then performs range gate alignment, and finally further highlights the distance and velocity information of the real target through intra-sub-pulse coherent accumulation and inter-sub-pulse coherent accumulation, realizing effective suppression of intermittent sampling interference. The method of the present invention uses a multi-sub-pulse structure, which can reduce the interception length of a single sub-pulse by the jammer, thereby reducing the interference degree on a single sub-pulse, and can effectively suppress intermittent sampling interference without knowing the prior information of the interference. Description of the Drawings

[0086] Figure 1 Is a flowchart of a time-frequency cooperative multi-sub-pulse adaptive matching filtering method for anti-main-lobe intermittent sampling interference of the present invention.

[0087] Figure 2 Is the time domain / frequency domain diagram of the multi-sub-pulse signal in Simulation 1 of the embodiment of the present invention.

[0088] Figure 3 Is a schematic diagram of the pulse compression results of different transmitted signals in Simulation 1 of the embodiment of the present invention.

[0089] Figure 4 Is the R-D diagram of different sub-pulses in Simulation 1 of the embodiment of the present invention.

[0090] Figure 5 Is the final output R-D diagram of different transmitted signals in Simulation 1 of the embodiment of the present invention.

[0091] Figure 6 Is the time domain / frequency domain diagram of the multi-sub-pulse signal in Simulation 2 of the embodiment of the present invention.

[0092] Figure 7 Schematic diagram of the pulse compression results of different transmitted signals in Simulation 2 in the embodiments of the present invention.

[0093] Figure 8 R-D diagram of different sub-pulses in Simulation 2 in the embodiments of the present invention.

[0094] Figure 9 Final output R-D diagram of different transmitted signals in Simulation 2 in the embodiments of the present invention. Detailed implementation manners

[0095] The method of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0096] As Figure 1 shown, the flowchart of a time-frequency collaborative multi-sub-pulse adaptive matching filtering method for anti-main lobe intermittent sampling interference of the present invention is as follows:

[0097] S1. Model the radar multi-sub-pulse transmitted signal;

[0098] S2. Based on step S1, obtain the echo signal and model the total received signal of the radar system;

[0099] S3. Based on step S2, filter out the interference signal and then recover the target signal to obtain the pulse compression result and complete multi-channel pulse compression;

[0100] S4. Based on step S3, perform range gate alignment and sample the aligned result to obtain the fast and slow time dimension matrix;

[0101] S5. Based on step S4, perform in-sub-pulse coherent integration, that is, use multi-channel discrete Fourier transform (MC-DFT) to integrate each sub-pulse;

[0102] S6. Based on step S5, perform inter-sub-pulse coherent integration to effectively suppress the intermittent sampling interference.

[0103] In this embodiment, step S1 is specifically as follows:

[0104] It is assumed that during the tracking process, the radar transmits a multi-sub-pulse signal with M sub-pulses, the pulse duration is T, the pulse repetition interval PRI is T P , the coherent processing interval CPI is T CPI , and there are N PRIs in one CPI. Set the pulse width of the m-th sub-pulse to T m , then the above parameter expressions are as follows:

[0105]

[0106] T CPI = NT P

[0107] Then the transmission sequence x of the m-th sub-pulse m (t) is expressed as follows:

[0108]

[0109] where represents the imaginary unit, t represents time, and p m (t) represents a linear frequency modulation signal (LFM) with a time width of T m and a bandwidth of B; f0 represents the carrier frequency, and f m represents the frequency offset of the m-th sub-pulse. To ensure the orthogonality of each sub-pulse in the frequency domain, there is f m = b(m)Δf, m = 1, 2,..., M, Δf represents the frequency offset step, and b(m) represents the number of frequency offset steps of the m-th sub-pulse. b(m) is obtained by sampling without replacement from the frequency offset step sequence b = [0, 1,..., M - 1].

[0110] Finally, for the multi-sub-pulse signal, the expression of the transmitted signal in one CPI is as follows:

[0111]

[0112] where t m represents the transmission time of the m-th sub-pulse. Without loss of generality, t1 = 0,

[0113] In this embodiment, the step S2 is specifically as follows:

[0114] Set the scenario. There is a point target equipped with a self-defense jammer in the detection and monitoring area of the radar system, that is, there is a point target that emits interrupted sampling jamming (ISJ) in the airspace. Then the target echo y T (t) is expressed as follows:

[0115]

[0116] where c represents the speed of light, and R and v respectively represent the distance and radial velocity of the target relative to the radar system, and α represents the influence of the target reflectivity and channel propagation on the signal.

[0117] According to different forwarding schemes, interrupted sampling jamming can be divided into three categories: Interrupted Sampling Repeater Jamming (ISRJ), Interrupted Sampling Cycling Jamming (ISCJ), and Interrupted Sampling Direct Jamming (ISDJ). Set the sampling duration of the jammer during the radar signal transmission as T a , and the sampling period as T b . If the specific type of jamming is randomly selected among ISRJ, ISCJ, and ISDJ, then the signal y J,I (t) intercepted by the jamming is expressed as follows:

[0118] y J,I (t) = s(t)J(t)

[0119] where J(t) represents the interception strategy of the jammer, and the specific expression is as follows:

[0120]

[0121] where rect(t) represents the rectangular pulse function, with a value of 1 when 0 ≤ t ≤ 1. δ(t) represents the impulse function, and K represents the number of interceptions. Then the total jamming signal y J,T (t) is expressed as follows:

[0122]

[0123] where Q represents the number of forwarding times, and τ q represents the start time of the q-th forwarding.

[0124] The interrupted sampling jamming is self-defense jamming. The distance and radial velocity of the jammer are considered to be the same as those of the target. Then the jamming signal y J (t) received by the radar system is expressed as follows:

[0125] y J (t) = βy J,T (t - 2(R - vt) / c)

[0126] where β represents the influence of the target reflectivity and channel propagation on the signal. Then the total received signal y(t) of the radar system is expressed as follows:

[0127] y(t) = y T (t) + y J (t) + n(t)

[0128] where n(t) represents Gaussian white noise with a mean of 0 and a variance of σ 2 .

[0129] In this embodiment, step S3 is specifically as follows:

[0130] S31. Interference signal filtering;

[0131] According to the different carrier frequencies of each sub-pulse, the received signal is respectively down-converted by -(f0 + f i ), i = 1, 2,..., M and band-pass filtered to effectively filter out the interference and most of the noise that do not intercept the sub-pulse, and the resulting expression is as follows:

[0132]

[0133] where represents the total received signal after down-conversion by -(f0 + f i ) and band-pass filtering, respectively represent the i-th sub-pulse, the interference and noise based on intercepting the i-th sub-pulse.

[0134] Based on M different sub-pulses, a filter (·) * represents the conjugate operation. Since the pulse width of each pulse is relatively narrow, the Doppler frequency shift caused by the time difference within the pulse can be ignored. Applying the i-th filter to the obtained pulse compression result z i (t) has the following expression:

[0135]

[0136] For a specific time τ corresponding to z i (t) in the pulse compression result, z i (τ), the specific expression is as follows:

[0137]

[0138] where

[0139]

[0140] Then the following expression can be obtained:

[0141]

[0142] where z T,i (τ, u), z J,i (τ, u), z n,i (τ, u) are z T,i (τ), z J,i(τ),z n,i (τ) expansion. For the dimension u obtained by expansion, it is called the matching dimension.

[0143] Then, interference identification and separation are performed from the matching dimension. Set the power of the target echo received by the receiver to be A T , and the power of the interference signal to be A J . Then z T,i (τ),z J,i (τ),z n,i In the expansion of (τ) along the matching dimension, z T,i (τ,u),z J,i (τ,u),z n,i (τ,u) amplitudes are respectively σ, and A J >>A T ,σ 2 ≥A T .

[0144] Set that during the tracking process, the known range τ where the target is located ALL . Because the target echo, interference signal, and noise occupy different times in one PRT, in the range τ where the target is located ALL corresponding time-delay - matching plane z i (τ ALL ,u), z T,i (τ,u),z J,i (τ,u) and z n,i (τ,u) appear at different positions respectively. Then, along the time-delay dimension, the time-delay - matching plane can be divided into several parts along the time-delay dimension, including: τ with only noise n , τ with both target echo and noise T , τ with both interference signal and noise J , τ with target, interference, and noise all present T,J . Then there are 3 cases, specifically as follows:

[0145] (1) When τ T ≠τ J , that is, when the real target and the false target do not overlap, at the time-delay τ corresponding to the false target J , the expansion of z i (τ J ) in the matching dimension only has a large amplitude in some areas, and the amplitudes in other areas are all close to 0;

[0146] (2) At the time-delay τ corresponding to the real target T , and at the τ with only noise n , because σ 2 ≥A T , the target signal is submerged by the noise, zi (τ T ) and z i (τ n ) have smaller amplitudes for all u in the matching dimension;

[0147] (3) When the interference, target, and noise exist at the same moment τ T,J , the corresponding zi(τ T,J ) in the expansion of the matching dimension can be subdivided into 2 parts: z where only the target and noise exist i (τ T,J , u T ), and z where the target, interference, and noise exist simultaneously i (τ T,J , u J ).

[0148] Based on the above 3 cases, using the target interference separation method, first, for any moment τ, calculate the minimum value z i (τ, u)| and the maximum value z min corresponding to this moment, and uniformly sample H points in the amplitude range [z max , z min to obtain the threshold sequence z max = [z1, z2,..., z H . For each threshold value, divide |z H (τ, u)| into 2 parts: z i (τ, u) less than the threshold value and z i,1 (τ, u) greater than the threshold value. Then calculate the overall variance var(|z i,2 (τ, u)|), var(|z i,1 (τ, u)|). Then set the optimization problem expression as follows: i,2

[0149]

[0150] where z h = z min + (h - 1)((z max - z min ) / H), h = 1, 2,..., H. The zh that satisfies the optimization problem is the optimal threshold.

[0151] Finally, adaptively obtain the corresponding threshold according to the signals corresponding to different time delays. The part exceeding the threshold is considered as the interference signal and is set to zero.

[0152] Among them, for τ n with only noise and τ T with both target echo and noise, at this time, the threshold value obtained according to the above formula is relatively small itself, and all signals can be retained to reduce the loss of the target signal; for τ with both interference signals and noise J,l , because the power of the interference signal is high and the threshold value is large, the z greater than this threshold value i,1 (τ, u) can be regarded as a signal with both interference and noise and set it to 0, only retaining the noise part less than the threshold value; for τ with the target, interference and noise existing simultaneously ALL , similarly because the power of the interference signal is high and the threshold value is large, the z greater than this threshold value i,1 (τ, u) can be regarded as the part where the target, interference and noise exist simultaneously and set it to 0, only retaining the part where the target and noise exist simultaneously and are less than the threshold value.

[0153] S32. Target signal recovery;

[0154] For the processed z i (τ, u), it only has the target signal and the interference signal, as well as some parts that have been filtered out with an amplitude of 0. Then, the zeroed parts are compensated, the interference signal is filtered out, and most of the target signals are retained.

[0155] Among them, the compensation includes: phase compensation and amplitude compensation, which are specifically as follows:

[0156] (1) Phase compensation: For each delay τ with a part having an amplitude of 0, using the periodicity of the phase of the target signal expanded along the matching dimension, directly copy the phase of the non-zero part in this delay.

[0157] (2) Amplitude compensation: For each delay τ with a part having an amplitude of 0, its amplitude is equal to the average value of the amplitudes of the non-zero parts in this delay.

[0158] S33. Obtain the pulse compression result;

[0159] After performing the interference signal filtering and target signal recovery operations in the matching dimension, sum the obtained z i (t, u) along the u dimension, and the pulse compression result z i (t) can be obtained. The expression of the pulse compression result is as follows

[0160]

[0161] Among them, γ i (t - (n - 1)T P - t i - 2R / c) represents the complex envelope of the output result of the i-th pulse and the i-th matched filter after interference suppression processing. and respectively represent the interference output and the noise output.

[0162] In this embodiment, the step S4 is specifically as follows:

[0163] Based on the output of the first filter and the known sub-pulse durations, there is a time deviation between the nth pulse output by the ith filter and its first pulse output Compensate for the delay by translating the corresponding filter output in the range dimension and truncate the part of the signal that exceeds zero delay. The translation result z i (t) is expressed as follows:

[0164]

[0165] Finally, sample the aligned result to obtain the fast and slow time dimension matrix A represents the number of sampling points for each T P .

[0166] In this embodiment, the step S5 is specifically as follows:

[0167] Set the maximum unambiguous velocity of the multi-sub-pulse signal to v max , and uniformly sample U points in the velocity measurement range [-v max , v max to obtain the velocity measurement sequence v U = [v1, v2,..., v U .

[0168] Among them, v u = -v max + (u - 1)(2v max / U), u = 1, 2,..., U, then the row vector expression is defined as follows:

[0169]

[0170] Among them, [·] T represents the transpose operation.

[0171] Then, the transformation matrix corresponding to the ith sub-pulse is obtained as H i = [h i,1 , h i,2 ,..., h i,U T , then the MC-DFT processing expression of the fast and slow time dimension matrix Z i corresponding to the ith sub-pulse obtained through step S4 is as follows:

[0172] R i = H i Z i

[0173] Among them, R​i It represents the R-D (Range-Doppler) map of the i-th sub-pulse.

[0174] In this embodiment, the step S6 is specifically as follows:

[0175] After obtaining the R-D maps of M sub-pulses, a three-dimensional matrix of U×A×M is formed. After performing FFT transformation of P points along the third dimension and obtaining the FFT transformation result with a length of P, it is tiled along the range dimension to achieve coherent accumulation between sub-pulses and high-precision ranging. Finally, a two-dimensional matrix R of U×(A×P) dimensions is obtained F , R F The horizontal and vertical coordinates corresponding to the maximum value of R are the distance and speed of the real target.

[0176] Among them, U represents the length of the velocity measurement sequence. To improve the accuracy of coherent accumulation between sub-pulses, it is set that P represents the number of FFT points, and P > M.

[0177] This embodiment also conducts simulation verification and analysis, which are specifically as follows:

[0178] (1) Simulation 1: Adaptive matching filtering of multi-sub-pulse structure against single intermittent sampling interference;

[0179] Simulation parameters:

[0180] The target distance and speed are set to 100 km and 150 m / s, and the radar parameters are set as follows: The radar carrier frequency is 3 GHz, the signal pulse duration T = 50 μs, the pulse repetition interval T P = 100 μs, the number of repeated pulses within the CPI is 100, the pulse width of a single sub-pulse T m ranges from [5 μs, 20 μs], the frequency offset step of the sub-pulse signal Δf = 40 MHz, the bandwidth of the sub-pulse signal B = 20 MHz, the sampling rate is 400 MHz, the signal-to-noise ratio at the receiving end SNR = -10 dB, and the jam-to-noise ratio at the receiving end JNR = 45 dB. At the same time, it is compared with a conventional LFM signal with a time width of 50 μs, a bandwidth of 20 MHz, and a carrier frequency of 3 GHz. The relevant parameters of the interference set by the target carrying the jammer are: the interference sampling duration is 2 μs, and the interference sampling period is 10 μs.

[0181] Simulation analysis:

[0182] Figure 2 is the time domain / frequency domain diagram of the multi-sub-pulse signal in Simulation 1 of this embodiment, Figure 2 (a) is the time domain diagram of the multi-sub-pulse signal, Figure 2 (b) is the frequency domain diagram of the multi-sub-pulse signal. As can be seen from Figure 2 , the multi-sub-pulse signals are spliced into a continuous signal in the time domain, and the frequencies of each sub-pulse signal are orthogonal to each other.

[0183] Figure 3 This is the pulse compression result of different transmitted signals in Simulation 1 of this embodiment. Figure 3 (a) is the pulse compression result of the multi-subpulse signal. Figure 3 (b) is the pulse compression result of the existing LFM signal. As can be seen from Figure 3 (a), in the case of transmitting a multi-subpulse signal, each subpulse undergoes interference suppression by the method of the present invention, and most of the interference can be directly filtered out while performing pulse compression; as can be seen from Figure 3 (b), in the case of transmitting the existing LFM signal, the matched filtering result is greatly affected by the interference signal.

[0184] Figure 4 This is the R-D diagram of different subpulses in Simulation 1 of this embodiment. Figure 4 (a) is the R-D of the first subpulse of the multi-subpulse signal. Figure 4 (b) is the R-D of the second subpulse of the multi-subpulse signal. As can be seen from Figure 4 it, performing coherent integration within the subpulse on the pulse compression result after interference suppression processing can highlight the range and velocity information of the target while suppressing interference.

[0185] Figure 5 This is the final output R-D diagram of different transmitted signals in Simulation 1 of this embodiment. Figure 5 (a) is the final output R-D diagram of the multi-subpulse signal with interference. Figure 5 (b) is the final output R-D diagram of the LFM signal with interference. Figure 5 (c) is the final output R-D diagram of the LFM signal without interference. As can be seen from Figure 5 (a), performing coherent integration between subpulses on the result of coherent integration within the subpulse can further improve the signal-to-noise ratio. Through this diagram, it can be obtained that there is a point target at 100 km and 149.62 m / s, which is consistent with the simulation parameter settings, verifying the effectiveness of the method of the present invention. As can be seen from Figure 5 (b), in the case of transmitting the existing LFM signal, the target position cannot be correctly obtained. As can be seen from Figure 5 (c), compared with the LFM signal without interference, the method of the present invention can effectively filter out the intermittent sampling interference with a signal-to-noise ratio loss of 2.83 dB.

[0186] (2) Simulation 2: Adaptive matched filtering of the multi-subpulse structure against multiple intermittent sampling interferences;

[0187] Simulation parameters:

[0188] The target distance and speed are set to 160 km and 100 m / s respectively. The radar parameters are set as follows: the radar carrier frequency is 3 GHz, the signal pulse duration T = 50 μs, the pulse repetition interval T P = 100 μs, the number of repeated pulses within a CPI is 30, the pulse width of a single sub-pulse T m ranges from [5 μs, 20 μs], the frequency deviation step of the sub-pulse signal Δf = 40 MHz, the bandwidth of the sub-pulse signal B = 20 MHz, the sampling rate is 400 MHz, the signal-to-noise ratio at the receiving end SNR = 0 dB, and the jam-to-noise ratio at the receiving end JNR = 60 dB. At the same time, it is compared with a conventional LFM signal with a pulse width of 50 μs, a bandwidth of 20 MHz, and a carrier frequency of 3 GHz. It is considered that the target carries 3 jammers, and each jammer works independently. The signal patterns generated by each jammer are randomly selected among ISRJ, ISCJ, and ISDJ. The relevant parameters of the jammer interference are set as follows: the interference sampling duration is randomly selected between [2 μs, 5 μs], and the interference sampling period is randomly selected between [10 μs, 20 μs].

[0189] Simulation analysis:

[0190] Figure 6 This is the time-domain / frequency-domain diagram of the multi-sub-pulse signal in Simulation 2 of this embodiment, Figure 6 (a) is the time-domain diagram of the multi-sub-pulse signal, Figure 6 (b) is the frequency-domain diagram of the multi-sub-pulse signal. It can be seen from Figure 6 that the multi-sub-pulse signals are spliced into a continuous signal in the time domain, and the frequencies of each sub-pulse signal are orthogonal to each other.

[0191] Figure 7 This is the pulse compression result of different transmitted signals in Simulation 2 of this embodiment, Figure 7 (a) is the pulse compression result of the multi-sub-pulse signal, Figure 7 (b) is the pulse compression result of the existing LFM signal. It can be seen from Figure 7 (a) that in the case of transmitting the multi-sub-pulse signal, each sub-pulse suppresses interference through the method of the present invention, and most of the interference can be directly filtered out while performing pulse compression; it can be seen from Figure 7 (b) that in the case of transmitting the existing LFM signal, the matched filtering result is greatly affected by the interference signal.

[0192] Figure 8 This is the R-D diagram of different sub-pulses in Simulation 2 of this embodiment, Figure 8 (a) is the R-D of the first sub-pulse of the multi-sub-pulse signal, Figure 8 (b) is the R-D of the second sub-pulse of the multi-sub-pulse signal. It can be seen from Figure 8It can be seen that performing coherent integration within sub-pulses on the pulse compression result after interference suppression processing can highlight the range and velocity information of the target while suppressing interference.

[0193] Figure 9 This is the final output R-D map of different transmitted signals in Simulation 2 of this embodiment. Figure 9 (a) is the final output R-D map of the multi-sub-pulse signal with interference. Figure 9 (b) is the final output R-D map of the LFM signal with interference. Figure 9 (c) is the final output R-D map of the LFM signal without interference. From Figure 9 (a), it can be seen that performing coherent integration between sub-pulses on the result of coherent integration within sub-pulses can further improve the signal-to-noise ratio. Through this figure, it can be obtained that there is a point target at 160 km and 99.66 m / s, which is consistent with the simulation parameter settings, verifying the effectiveness of the method of the present invention. From Figure 9 (b), it can be seen that when transmitting the existing LFM signal, the target position cannot be correctly obtained. From Figure 9 (c), it can be seen that compared with the LFM signal without interference, the method of the present invention can effectively filter out the intermittent sampling interference when the signal-to-noise ratio loss is 1.50 dB.

[0194] In summary, due to the characteristics of intermittent sampling interference, the jammer intercepts a part of the target signal. The method of the present invention uses a multi-sub-pulse structure, which can reduce the interception length of a single sub-pulse by the jammer, thereby reducing the interference degree on a single sub-pulse. Moreover, the method of the present invention uses the partial interception characteristic of the jammer to filter out the interference during the matched filtering process and recover the target signal. Then, through coherent integration within sub-pulses and coherent integration between sub-pulses, the range and velocity information of the real target are further highlighted. Without the need to know the prior information of the interference, the effective suppression of intermittent sampling interference is achieved.

[0195] Those of ordinary skill in the art will realize that the embodiments described herein are for helping the reader understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, various changes and modifications can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A method for time-frequency coordinated multi-sub-pulse adaptive matched filtering to resist main lobe intermittent sampling interference, the specific steps are as follows: S1. Radar multi-pulse emission signal modeling; S2. Based on step S1, an echo signal is obtained and a total received signal of the radar system is modeled; S3, based on step S2, after filtering out the interference signal, recover the target signal, obtain the pulse compression result, and complete the multi-channel pulse compression; S4, based on step S3, performing range gate alignment, and sampling the aligned result to obtain a fast and slow time dimension matrix; S5, based on step S4, performing coherent accumulation within the sub-pulse, that is, using multi-channel discrete Fourier transform MC-DFT to accumulate each sub-pulse; S6. Based on step S5, perform coherent accumulation between sub-pulses to effectively suppress the interference of intermittent sampling.

2. According to claim 1, a method for time-frequency coordinated multi-sub-pulse adaptive matched filtering to resist main lobe intermittent sampling interference is characterized in that: The step S1 is specifically as follows: It is assumed that during the tracking process, the radar transmits a multi-sub-pulse signal with M sub-pulses, the pulse duration is T, and the pulse repetition interval PRI is T P , the coherent processing interval CPI is T CPI , there are N PRIs in one CPI; Set the pulse width of the mth sub-pulse to T m , then the above parameter expressions are as follows: T CPI =NT P Then the transmission sequence x of the mth sub-pulse is m (t) is expressed as follows: in, represents an imaginary unit, t represents time, and p m (t) represents the time width T m , a linear frequency modulation LFM signal with a bandwidth of B; f0 represents the carrier frequency, f m represents the frequency deviation of the mth sub-pulse, and f m =b(m)Δf,m=1,2,...,M, Δf represents the frequency deviation step, b(m) represents the number of frequency deviation steps of the m-th sub-pulse, and b(m) is obtained by sampling without replacement in the frequency deviation step sequence b=[0,1,...,M-1]; Finally, for multi-sub-pulse signals, the expression of the transmitted signal in a CPI is as follows: Among them, t m represents the emission time of the mth sub-pulse, and t1=0, 3. The method for anti-mainlobe intermittent sampling interference by time-frequency coordinated multi-sub-pulse adaptive matched filtering according to claim 1 is characterized in that: The step S2 is specifically as follows: Set the scenario, there is a point target equipped with a self-defense jammer in the radar system detection and monitoring area, that is, there is a point target transmitting main lobe intermittent sampling jammer ISJ in the airspace, then the target echo y T (t) is expressed as follows: Where c represents the speed of light, R and v represent the distance and radial velocity of the target relative to the radar system, respectively, and α represents the impact of target reflectivity and channel propagation on the signal; According to different forwarding schemes, intermittent sampling interference can be divided into three categories: intermittent sampling repeated forwarding interference ISRJ, intermittent sampling cyclic forwarding interference ISCJ and intermittent sampling direct forwarding interference ISDJ; the sampling time of the jammer during the radar signal transmission process is set to T a , the sampling period is T b , the specific type of interference is randomly selected from ISRJ, ISCJ and ISDJ, then the signal y intercepted by the interference J,I (t) is expressed as follows: y J,I (t)=s(t)J(t) Among them, J(t) represents the interception strategy of the jammer, and the specific expression is as follows: Where rect(t) represents a rectangular pulse function, and when 0≤t≤1, the value is 1; δ(t) represents a pulse function, and K represents the number of intercepts; then the total interference signal y J,T (t) is expressed as follows: Among them, Q represents the number of forwarding times, τ q Indicates the start time of the qth forwarding; The intermittent sampling interference is a self-defense interference. The distance and radial velocity of the jammer are considered to be consistent with the target. The interference signal y received by the radar system is J (t) is expressed as follows: the J (t)=βy J,T (t-2(R-vt) / c) Among them, β represents the impact of target reflectivity and channel propagation on the signal; then the total received signal y(t) of the radar system is expressed as follows: y(t)=y T (t)+y J (t)+n(t) Among them, n(t) means that the mean is 0 and the variance is σ 2 Gaussian white noise.

4. The method for resisting mainlobe intermittent sampling interference by time-frequency coordinated multi-sub-pulse adaptive matched filtering according to claim 1, characterized in that: The step S3 is specifically as follows: S31, interference signal filtering; According to the different carrier frequencies of each sub-pulse, the received signal is -(f0+f i ),i=1,2,...,M down-conversion and bandpass filtering, the resulting expression is as follows: in, Indicates that after -(f0+f i ) is the total received signal after down-conversion and band-pass filtering, denote the ith sub-pulse, the interference and the noise based on intercepting the ith sub-pulse respectively; Based on M different sub-pulses, design the filter (·) * represents the conjugate operation; the i-th filter is applied to The pulse compression result z i (t) is expressed as follows: The pulse compression result z i (t) corresponds to a specific time τ in z i (τ), the specific expression is as follows: in, Then the expression is as follows: Among them, z T,i (τ,u),z J,i (τ,u),z n,i (τ,u) is z T,i (τ),z J,i (τ),z n,i (τ) is expanded; the dimension u obtained by the expansion is called the matching dimension; Then, the interference is identified and separated from the matching dimension, and the power of the target echo received by the receiver is set to A. T , the power of the interference signal is A J ; then z T,i (τ),z J,i (τ),z n,i (τ) In the expansion along the matching dimension, z T,i (τ,u),z J,i (τ,u),z n,i The amplitudes of (τ,u) are And A J >>A T ,σ 2 ≥A T ; Set the range τ where the target is known during tracking ALL , within the range of the target ALL The corresponding delay-matching plane z i (τ ALL ,u),z T,i (τ,u),z J,i (τ,u) and z n,i (τ,u) appear at different positions respectively, then along the delay dimension, the delay-matching plane can be divided into several parts along the delay dimension, including: τ with only noise n , τ with both target echo and noise T , with both interference signal and noise τ J , τ where target, interference and noise exist simultaneously T,J ; There are three situations, as follows: (1) When τ T ≠τ J , that is, when the real target and the false target do not overlap, the false target corresponds to the delay τ J Place, z i (τ J ) In the expansion of the matching dimension, only some areas have large amplitudes, and the amplitudes in other areas are close to 0; (2) The time delay τ corresponding to the real target T , and τ with only noise n Because σ 2 ≥A T , the target signal is drowned by the noise, z i (τ T ) and z i (τ n ) has a small amplitude on all u of the matching dimension; (3) When interference, target and noise exist at the same time τ T,J , the z corresponding to this moment i (τ T,J ) In the expansion of the matching dimension, it can be divided into two parts: z where only the target and noise exist i (τ T,J ,u T ), target, interference and noise exist simultaneously i (τ T,J ,u J ); Based on the above three situations, the target interference separation method is adopted. First, for any time τ, the corresponding |z i The minimum value z of (τ,u)| min and the maximum value z max , in the amplitude range [z min ,z max ] uniformly sample H points and obtain the threshold sequence z H =[z1,z2,…,z H ], for each threshold value, |z i (τ,u)| is divided into two parts: z less than the threshold value i,1 (τ,u), z greater than the threshold i,2 (τ,u), and then calculate the overall variance var(|z i,1 (τ,u)|),var(|z i,2 (τ,u)|), then the optimization problem expression is set as follows: Among them, z h =z min +(h-1)((z max -z min ) / H), h=1,2,…,H; zh that satisfies the optimization problem is the optimal threshold; Finally, the corresponding threshold is adaptively obtained according to the corresponding signals with different time delays, and the part exceeding the threshold is considered as an interference signal and is set to zero; S32, target signal recovery; For the processed z i (τ,u), which only contains the target signal and the interference signal, as well as a part of the filtered part with an amplitude of 0, and then compensates for the zeroed part, filters out the interference signal and retains most of the target signal; The compensation includes phase compensation and amplitude compensation, which are as follows: (1) Phase compensation: For each time delay τ with a zero amplitude, the phase of the non-zero portion of the time delay is directly copied by utilizing the periodicity of the target signal phase unfolded along the matching dimension. (2) Amplitude compensation: For each delay τ with a zero amplitude portion, its amplitude is equal to the mean amplitude of the non-zero amplitude portion of the delay; S33, obtaining pulse pressure results; After filtering out interference signals and restoring target signals in the matching dimension, the obtained z i (t,u) is summed along the u dimension to obtain the pulse compression result z i (t); The pulse compression result expression is as follows Among them, γ i (t-(n-1)T P -t i -2R / c) represents the complex envelope of the output result of the ith pulse and the ith matched filter after interference suppression processing; and Represent interference output and noise output respectively.

5. The method for anti-mainlobe intermittent sampling interference by time-frequency coordinated multi-sub-pulse adaptive matched filtering according to claim 1 is characterized in that: The step S4 is specifically as follows: Based on the output of the first filter and the known duration of each sub-pulse, the nth pulse output by the ith filter is time-delayed relative to its first pulse output. The corresponding filter output is translated in the distance dimension to compensate for the delay, and the part of the signal that exceeds the zero delay is truncated. The translation result z after the zero delay truncation process is i (t) is expressed as follows: Finally, the aligned results are sampled to obtain the fast and slow time dimension matrix A represents each T P The number of sampling points.

6. The method for resisting main lobe intermittent sampling interference by time-frequency coordinated multi-sub-pulse adaptive matched filtering according to claim 1, characterized in that: The step S5 is specifically as follows: Set the maximum unambiguous speed of the multi-pulse signal to v max , in the speed range [-v max ,v max ] uniformly sample U points and obtain the speed measurement sequence v U =[v1,v2,…,v U ]; Among them, v u =-v max +(u-1)(2v max / U), u=1,2,…,U, then the row vector expression is defined as follows: in,[·] T Represents a transpose operation; Then the transformation matrix corresponding to the i-th sub-pulse is H i =[h i,1 ,h i,2 ,…,h i,U ] T , then the fast and slow time dimension matrix Z corresponding to the i-th sub-pulse obtained in step S4 is i The MC-DFT processing expression is as follows: R i =H i Z i Among them, R i represents the RD diagram of the i-th sub-pulse.

7. The method for resisting main lobe intermittent sampling interference by time-frequency coordinated multi-sub-pulse adaptive matched filtering according to claim 1, characterized in that: The step S6 is specifically as follows: After obtaining the RD diagrams of M sub-pulses, a three-dimensional matrix of U×A×M is formed. The FFT transformation of P points is performed along the third dimension. After obtaining the FFT transformation result of length P, it is tiled along the distance dimension to achieve coherent accumulation and high-precision ranging between sub-pulses, and finally a two-dimensional matrix R of U×(A×P) dimensions is obtained. F , R F The horizontal and vertical coordinates corresponding to the maximum value of are the distance and speed of the real target; Wherein, U represents the length of the speed measurement sequence, P represents the number of FFT points, and P>M.

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