LFM Signal and Method Based on Random Inter-Pulse Frequency and Intra-Pulse Phase Code Modulation

Abstract

This invention proposes an LFM signal based on random inter-pulse frequency and intra-pulse phase coding modulation, relating to the field of electromagnetic wave waveform modulation technology. This signal inherits the high resolution of LFM signals, has lower range-Doppler (RD) sidelobes, and eliminates the RD coupling effect, so that the false targets generated by ISRJ only produce a sparse deception effect without spreading or drifting on the RD plane. This invention further designs a corresponding signal processing method, which achieves anti-intermittent sampling and forwarding interference by transmitting the modulated signal RIF-PCLFM, improving waveform detection capability and interference suppression performance, and enhancing interference processing efficiency.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic wave waveform modulation technology, specifically to an LFM pulse train signal and processing method based on joint modulation of random inter-pulse frequency and intra-pulse phase coding. Background Technology

[0002] Pulse Doppler radar is widely used in aerospace and other fields due to its ability to effectively detect moving targets from strong clutter backgrounds. However, with the continuous development of electronic countermeasures technology, intermittent sample-and-forward jamming (ISRJ) poses a serious threat to traditional radars, especially those using linear frequency modulation (LFM) signals. ISRJ is a coherent jamming technique with flexible modulation and fast response capabilities. The jammer slices, samples, and forwards the intercepted radar signal in real time, simultaneously generating suppression and deception effects at the radar receiver, significantly reducing the radar's target detection and tracking performance.

[0003] To combat ISRJ (Intra-Pulse Signal Jailbreak) interference, existing technologies mainly focus on two directions: intra-pulse waveform design and multi-domain signal processing. The basic idea of ​​waveform design methods is to leverage the characteristic that ISRJ interference signals have at least one sampling slice delay compared to the real echo. Orthogonal phase-coded segments are designed in the radar transmitted waveform, and a matched filter with a time-discontinuous waveform as a reference is used for processing to reduce the pulse compression gain of ISRJ. However, the effectiveness of such methods heavily relies on the accurate estimation of interference parameters (such as the sampling interval). In complex real-world electromagnetic environments, interference parameters are difficult to obtain accurately in real time, and these methods quickly become ineffective once the jammer adaptively changes its sampling strategy. Therefore, their practical engineering application faces significant challenges.

[0004] Multi-domain signal processing methods, particularly those based on range-Doppler (RD) domain processing, employ fully online processing strategies. These methods typically do not rely on prior knowledge of the interference; instead, they utilize the specific distribution characteristics of ISRJ false targets in the RD spectrum after radar coherent processing to design corresponding suppression filters. Because these methods can be directly embedded into standard radar signal processing workflows, they are easy to implement in engineering. However, when applied to processing radar echoes using traditional LFM signals, the false targets formed by ISRJ not only generate multiple spurious peaks in the RD spectrum but also exhibit expansion and drift along the range dimension. This causes the energy of true and false targets to overlap in the RD domain, making effective separation difficult and severely limiting the anti-jamming effectiveness of these methods against LFM radar.

[0005] To address the aforementioned issues, some researchers have proposed a random inter-pulse frequency modulated pulse sequence signal (RIFC-LFM) based on LFM, aiming to constrain the distribution behavior of ISRJ false targets in the RD domain through inter-pulse random frequency modulation, providing a new possibility for interference identification and suppression in the RD domain. However, this technical solution still has significant shortcomings: First, its anti-interference performance mainly relies on the "whitening" effect brought about by inter-pulse random modulation. In harsh environments with low signal-to-interference ratios (e.g., below -30dB), its interference suppression capability rapidly declines or even fails. Second, the proposed interference suppression processing algorithm typically adopts a serial processing architecture, requiring a large number of additional fast Fourier transform operations in each range gate unit, resulting in high computational complexity and making it difficult to meet the stringent requirements of modern radar systems for real-time signal processing. Summary of the Invention

[0006] To address the technical problems of existing anti-intermittent sampling forwarding interference methods, this invention first proposes an LFM pulse train signal RIF-PCLFM based on joint modulation of random inter-pulse frequency and intra-pulse phase coding. This signal inherits the high resolution of LFM signals, has lower range-Doppler (RD) sidelobes, and eliminates the RD coupling effect, so that the false targets generated by ISRJ only produce a sparse deception effect without spreading or drifting on the RD plane. Therefore, this invention further designs a corresponding signal processing method, which realizes anti-intermittent sampling forwarding interference by transmitting the modulated signal RIF-PCLFM, further improving waveform detection capability and interference suppression performance, and enhancing interference processing efficiency.

[0007] The technical solution of this invention is as follows:

[0008] On one hand, this invention proposes an LFM pulse train signal based on joint modulation of random inter-pulse frequency and intra-pulse phase coding, with the baseband using a phase-coded linear frequency modulated signal and random frequency modulation between pulses; the signal model expression is:

[0009]

[0010] in For time, The number of pulses during a coherent processing interval. Indicates the pulse repetition interval. For the first The inter-pulse frequency code of each pulse is taken. and Random values ​​between For bandwidth, It is the symbol for imaginary numbers; Indicates length is The phase-coded linear frequency modulated signal has the following signal model:

[0011]

[0012] in The phase code number within one pulse. The duration of a coded sub-pulse. The modulation slope, , The pulse width. For code number The corresponding intra-pulse coding phase, The rectangle function is defined as follows:

[0013] .

[0014] On the other hand, this invention proposes a signal processing method based on RIF-PCLFM signals to achieve resistance to intermittent sampling and forwarding interference, specifically including the following steps:

[0015] Step 1: After the radar transmits the RIF-PCLFM signal, it receives the echo signal containing the target echo and the ISRJ jamming signal, represented as:

[0016]

[0017] in For the target echo:

[0018]

[0019] in, The complex amplitude of the target echo. Indicates length is Phase-coded linear frequency modulated signal, Delay the target echo. Target Doppler frequency shift;

[0020] This is an ISRJ interference signal:

[0021]

[0022] in, The complex amplitude value of the ISRJ interference signal. To interfere with the number of forwards, To calculate the summation coefficient, For length is Phase-coded linear frequency modulated signal, Indicates the first Secondary interference with forwarding, This refers to the slice sampling width of the ISRJ jammer. For the delay of the ISRJ jammer, For ISRJ jammer frequency shift, , The sampling interval of the ISRJ jammer. These are intermediate parameters, specifically:

[0023]

[0024] in ;

[0025] Step 2: For a coherent processing interval Each echo pulse is individually compressed, and the processing results are stacked into a single pulse. The row matrix, extracted column by column, is as follows:

[0026] y i = [ y 0 ( iT sa ), … , y n ( iT sa ), … , y N − 1 ( iT sa ) ] T ∈ ℂ N × 1

[0027] in For the first The signal obtained by pulse compression processing of each echo pulse. Indicates the first Column fast time index, For fast sampling intervals, express A complex vector with 1 row and 1 column; then along [ y 0 , … , y P r − P − 1 ] Doppler coherence processing is performed along the column direction to obtain the original RD spectrum. ,in express OK Column complex vectors, , , Indicates rounding up;

[0028] Step 3: [Regarding...] Slow-time phase compensation processing is performed to obtain the compensation matrix. :

[0029]

[0030] Compensation matrix Each column corresponds to a different phase compensation value, among which For A diagonal matrix with diagonal elements. The slow-time phase compensation matrix is:

[0031] Ψ = [ ψ ( − P c T sa ) , ψ ( − ( P c − 1 ) T sa ) , … , ψ ( − T sa ) , 0 N × 1 , ψ ( T sa ) , … , ψ ( ( P c − 1 ) T sa ) , ψ ( P c T sa ) ]

[0032] in For slow-time phase compensation vectors, , express OK Columnar complex vectors; The specific expression is:

[0033] ψ ( t ) = [ e j 2 π f 0 t , … , e j 2 π f n t , … , e j 2 π f N − 1 t ] T

[0034] Step 4: [Regarding...] Each column undergoes Doppler coherence processing to obtain the pseudo-target search matrix. ;

[0035] Step 5: Reposition the coordinates:

[0036] if ,make:

[0037]

[0038] Otherwise, let:

[0039]

[0040] in RD spectrum of spurious target; express Column 1 to Column 2 List, express The List to List;

[0041] like ,make Proceed to step 3; otherwise, output the reconstructed pseudo-target RD spectrum. ;

[0042] Step 6: Spectrum of the fake target Normalization and set a threshold ,position Medium amplitude greater than The RD spectrum is eliminated by setting the original RD spectrum to 0 at the False Target Location. The false targets at the corresponding positions are identified; the final output contains only the RD spectrum of the real targets.

[0043] Furthermore, the present invention also proposes an electronic device and a readable storage medium:

[0044] An electronic device includes a processor and a memory, the memory being used to store one or more programs; characterized in that: when the one or more programs are executed by the processor, the above-described method is implemented.

[0045] A readable storage medium storing a computer program, characterized in that: when the computer program is executed by a processor, the above-described method is implemented.

[0046] Beneficial effects:

[0047] The LFM pulse train signal and processing method based on joint modulation of random inter-pulse frequency and intra-pulse phase coding proposed in this invention have the following effects:

[0048] 1. The superior characteristics of the RIF-PCLFM signal are proposed and analytically revealed: In the embodiments, by introducing time delay substitution and piecewise integration techniques, analytical expressions for the self-ambiguity function and cross-ambiguity function (AAF and CAF) are derived, proving that the RIF-PCLFM signal inherits the high resolution of the LFM signal and has low RD sidelobes. Furthermore, due to the combined effect of the whitening term and phase modulation, the range-Doppler coupling effect is removed, which imposes a unique constraint on the false targets generated by ISRJ, namely, it can only produce sparse deception effects without expanding or shifting the RD spectrum.

[0049] 2. Robust suppression of various ISRJ interferences: Utilizing the characteristics of the whitening term in the RIF-PCLFM signal and combining the behavioral characteristics of different types of ISRJ interference, this invention designs a false target identification method based on a fast multi-channel slow-time phase compensation method. Since this process is embedded in the RD coherent processing flow, it maintains the echo gain and can achieve robust suppression of various ISRJ interferences under conditions of input SIR fluctuations and high-speed target movement, without requiring any prior knowledge of the interference.

[0050] 3. Good processing efficiency and scalability: Since the proposed ISRJ interference suppression method is entirely built into the RD processing flow, the time complexity lies only in the additional Fast Fourier Transform (FFT) operation, thus easily meeting real-time processing requirements. Furthermore, to improve the versatility of the RIF-PCLFM signal, this invention uses a random polyphase coding sequence to modulate the signal; combining this with a sequence optimization algorithm can further improve the signal's detection and interference suppression performance.

[0051] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0052] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0053] Figure 1 Flowchart of the anti-interference method proposed in this invention;

[0054] Figure 2 Normalized AF schematic diagram: First column: LFM pulse sequence signal; Second column: RIFC-LFM signal; Third column: RIF-PCLFM signal; First row: Three-dimensional (3D) view; Second row: Two-dimensional (2D) view;

[0055] Figure 3 : CAF diagram of three modes of normalized ISRJ, first column: direct forwarding ISRJ (Q=1), second column: repeated forwarding ISRJ (Q=3), third column: frequency shifting ISRJ;

[0056] Figure 4 : Schematic diagram of distance-Doppler spectrum processing for different signals under direct forwarding ISRJ; Columns 1-3: Processing results of LFM pulse sequence signal, RIFC-LFM signal, and RIF-PCLFM signal; First row: 3D view, second row: 2D view;

[0057] Figure 5 : Schematic diagram of distance-Doppler spectrum processing for different signals under repeated relay ISRJ; Columns 1-3: Processing results of LFM pulse sequence signal, RIFC-LFM signal, and RIF-PCLFM signal; First row: 3D view, second row: 2D view;

[0058] Figure 6 : Schematic diagram of distance-Doppler spectrum processing for different signals under frequency shift ISRJ; Columns 1-3: Processing results of LFM pulse sequence signal, RIFC-LFM signal, and RIF-PCLFM signal; First row: 3D view, second row: 2D view;

[0059] Figure 7 : Schematic diagram of false target reconstruction and elimination under ISRJ direct forwarding; First column: Original RD spectrum before phase compensation, Second column: RD spectrum of false targets after phase compensation, Third column: RD spectrum after interference suppression containing only real targets;

[0060] Figure 8 : Schematic diagram of reconstruction and elimination of false targets under repeated forwarding ISRJ; First column: Original RD spectrum before phase compensation, Second column: RD spectrum of false targets after phase compensation, Third column: RD spectrum after interference suppression containing only real targets;

[0061] Figure 9 : Schematic diagram of false target reconstruction and elimination under frequency shift ISRJ; First column: Original RD spectrum before phase compensation, Second column: RD spectrum of false target after phase compensation, Third column: RD spectrum after interference suppression containing only real target;

[0062] Figure 10Comparison diagram of the reconstructed false target RD spectrum under repeated forwarding ISRJ; First column: false target spectrum after phase compensation processing, second column: false target spectrum after fast phase compensation processing;

[0063] Figure 11 : A comparative diagram of echo processing results under different input SIRs in direct forwarding ISRJ; First column: Echo processing envelope of waveform design methods, Second column: Echo processing envelope based on LFM signal, Third column: Comparison of output SIR and input SIR;

[0064] Figure 12 : A schematic diagram comparing the echo processing results and sampling interval estimation error under direct forwarding ISRJ; First column: Echo processing envelope of waveform design methods, Second column: Echo processing envelope based on LFM signal, Third column: Output SIR and estimation error;

[0065] Figure 13 A comparative diagram of echo processing results under frequency shift ISRJ with different modulation values; First column: Echo processing envelope of waveform design methods; Second column: Echo processing envelope based on LFM signal; Third column: Relationship between output SIR and frequency modulation value. Detailed Implementation

[0066] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0067] To address Intermittent Sample-and-Forward Interference (ISRJ), this embodiment proposes an LFM pulse train signal (RIF-PCLFM) based on joint modulation of random inter-pulse frequency and intra-pulse phase coding, and an anti-ISRJ method based on the RIF-PCLFM signal. By introducing time delay variable substitution and piecewise integration techniques, analytical expressions for the self-ambiguity function and cross-ambiguity function (AAF and CAF) are derived. Based on this, it is verified that the RIF-PCLFM signal inherits the high resolution of the LFM signal, has lower range-Doppler (RD) sidelobes, and eliminates the RD coupling effect, thus exerting a unique constraint on false targets generated by ISRJ, i.e., producing only sparse deception effects rather than spreading or drifting in the RD plane.

[0068] (I) RIF-PCLFM signal model and analysis

[0069] The RIF-PCLFM proposed in this embodiment is a pulse train waveform, in which the baseband uses a phase-coded linear frequency modulated signal, and the pulses are randomly frequency modulated, as expressed in the following expression:

[0070] (1)

[0071] in The number of pulses during a coherent processing interval (CPI). Indicates the pulse repetition interval. For the first The inter-pulse frequency code of each pulse is taken. and Random values ​​between For bandwidth, It is the symbol for imaginary numbers; Indicates length is The phase-coded linear frequency modulated signal has the following signal model:

[0072] (2)

[0073] in The phase code number within one pulse. The duration of a coded sub-pulse. The modulation slope, , The pulse width. For intrapulse coding phase, The rectangle function is defined as follows:

[0074] (3)

[0075] To explore the distribution characteristics of RIF-PCLFM signals in the RD domain and accurately characterize their detection performance, the ambiguity function (AF) is the most effective tool. However, for the signal in equation (2), due to phase coding segmentation, directly deriving its AF expression is not easy. This embodiment uses piecewise integration combined with time delay variable substitution to overcome this difficulty, thereby deriving the analytical expression of the AF for the RIF-PCLFM signal.

[0076] first, AF can be represented as:

[0077] (4)

[0078] in, For time delay variables, For Doppler frequency shift variables, express . conjugate.

[0079] Since ISRJ is a type of interference that completes transmission and reception within a single pulse duration, only the central AF needs to be analyzed. This means... Therefore, by substituting equation (1) into equation (4), we have:

[0080] (5)

[0081] superscript Indicates conjugation, intermediate variable , express The AF, using equation (2), can be The derivation is as follows:

[0082] (6)

[0083] Due to phase encoding segmentation, the two parts summed in the above equation cannot be directly combined. Therefore, we replace the time delay variable with... Let's do further derivation. , τ 0 ∈ [ 0 , T c ] In order to... Calculation We need to discuss two cases separately. First, for Equation (6) can be derived as follows:

[0084] (7)

[0085] in ,

[0086] (8)

[0087] Another situation is Equation (6) can be derived as follows:

[0088] (9)

[0089] Therefore, these two cases can be uniformly written as:

[0090] (10)

[0091] Substituting equation (10) into equation (5), we get:

[0092] (11)

[0093] To better understand the characteristics of RIF-PCLFM signals, one can first observe the zero-delay and zero-Doppler cross-sections. This can be achieved by setting... and The zero Doppler section is given by the following formula:

[0094] (12)

[0095] It can be seen hour, The first zero point is reached. Therefore, the distance resolution is calculated as follows: This means that the RIF-PCLFM signal inherits the high-resolution characteristics of the LFM signal. Similarly, by setting... and This yields a zero-delay section:

[0096] (13)

[0097] From this, we can see that the Doppler resolution of the RIF-PCLFM signal is... Its peak value is It repeats periodically and is composed of one The function is weighted, and its first zero is Further observation of the peak value of AF in equation (11) reveals two findings:

[0098] i) For LFM signals, whenever That is, satisfying When the phase code is in the range, a peak will appear; this is known as the range-Doppler coupling effect. However, for RIF-PCLFM signals, the situation is different. Due to the isolation of the phase code, any original peak will appear as soon as... If it is not equal to 0, it will be Item reduction. This means that for RIF-PCLFM signals, when... At that time, distance and Doppler decouple;

[0099] ii) On the other hand, the frequency coding term between random pulses Can suppress any The amplitude at points that are not equal to 0, i.e., whitening of sidelobes along the distance axis, further reduces the sidelobe level. Figure 2 The AF of RIF-PCLFM, LFM and RIFC-LFM signals is displayed.

[0100] In this embodiment, we will use the number of pulses in a CPI. Set to 128, the number of phase codes within one pulse. Set to 50, bandwidth Set to 50 Pulse width Set to 4 Pulse repetition interval Set to 40 It should be noted that all experiments in this embodiment used random phase coding. From Figure 2 In this study, we can see that the RIF-PCLFM signal provides the lowest sidelobe level (lower sidelobes can be obtained using optimized sequences) and completely eliminates the range-Doppler coupling effect, providing a starting point for subsequent interference suppression.

[0101] (II) ISRJ Interference Signal Model and Analysis

[0102] As an intra-pulse jammer, the intermittent sampling-forward jammer slices, samples, and forwards the intercepted signal within one pulse duration. Its sampling process is modeled as follows:

[0103] (14)

[0104] Indicates the slice sampling width. Indicates the sampling interval. Represents the Dirac function, If we denote the convolution operation, then the RIF-PCLFM signal intercepted by the jammer can be represented as:

[0105] (15)

[0106] in Indicates length is The sampled signal;

[0107] Based on the number of forwardings and whether frequency shift modulation is used, existing ISRJs can be basically divided into three modes.

[0108] If each sample is forwarded once, it is classified as a direct forwarding ISRJ. Ignoring the jammer's delay, the interference signal is represented as:

[0109] (16)

[0110] If each sample piece is forwarded multiple times, it is classified as a duplicate forwarding ISRJ, denoted as:

[0111] (17)

[0112] use Indicates the number of times interference was forwarded. Indicates the first Secondary interference with forwarding.

[0113] If frequency shift is modulated for each sampling slice during forwarding Therefore, it is classified as frequency-shift ISRJ, and is expressed as:

[0114] (18)

[0115] and It can be transformed into:

[0116] (19)

[0117] intermediate parameters , To calculate the summation coefficient, , .

[0118] In summary, the ISRJ interference signal can be uniformly modeled as follows:

[0119] (20)

[0120] Based on the aforementioned unified ISRJ model, the analytical expression of its cross-ambiguity function CAF can be derived, which helps to understand the interference mechanism of ISRJ on RIF-PCLFM signal radar. The CAF is defined as follows:

[0121] (twenty one)

[0122] As mentioned earlier, only the central CAF needs to be considered. Substituting equations (1) and (20) into (21) yields:

[0123] (twenty two)

[0124] make The above equation simplifies to:

[0125] (twenty three)

[0126] Considering that waveforms are typically designed to meet Doppler tolerance requirements, then ,Right now This means that... In this embodiment, the Doppler frequency shift neither exceeds the main lobe nor causes a shift along the time delay axis in a coupled manner. Therefore, in this embodiment, In This can be ignored. It can be observed through equation (23):

[0127] i) If an LFM pulse sequence signal is used, then in order to satisfy False targets can appear at any location. That is, they exist. Cluster with The cluster of false targets is centered around this. This means that by adding appropriate frequency shifts, false targets may be able to guide real targets, which will be explained in detail in Experiment 1 later.

[0128] ii) For RIF-PCLFM signals, according to RIF-PCLFM signal analysis, phase coding will suppress any... The false target, and the random frequency term will whiten any Not equal to The false target, that is This limits the maximum number of signals that the ISRJ can generate at the radar receiver using the RIF-PCLFM signal. A false target.

[0129] We also simulated the normalized CAF, such as Figure 3 As shown. In this embodiment, the jammer sampling interval Set to 2 Interference sampling width Set to 0.5 The number of forwardings in direct forwarding and frequency shift mode Set to 1, the number of relays in repeat relay mode is set to 3, and the jammer modulation frequency in frequency shift mode is set to 3. Set to 2MHz. Note that the frequency-shifted ISRJ does not output false targets because the whitening term requires [a certain threshold] to create false targets. It must be satisfied, although It meets the requirements, but at this time .

[0130] (III) ISRJ Confrontation

[0131] As can be seen from the above two parts of the analysis, the ISRJ false target formed by sampling the RIF-PCLFM signal first undergoes phase coding modulation to suppress the time delay coordinates that need to be suppressed. The false target, and then the random frequency coding term is required. The false targets are whitened so that the number of interfering targets is at most 100. (Frequency shift ISRJ may not generate interfering targets). This embodiment utilizes the whitening characteristic of random frequency coding terms, based on The possible values ​​of the term are subjected to slow-time phase compensation to focus on all possible false target locations. The key to this method is that multiple false targets (with a time delay of ) can be reconstructed by compensating for the random frequency term. The real target cannot be reconstructed, thus achieving identification. In this embodiment, we further extend this method to RIF-PCLFM signal processing. Thanks to phase-coded modulation, we only need to process the phase... The portion is compensated because it is required in the time delay coordinate. The false targets can no longer be reconstructed. In this way, the time complexity is greatly reduced to that of the original method. The output SIR is significantly improved.

[0132] The development process of the proposed method is explained in detail below:

[0133] (1) Echo analysis

[0134] Assuming radial distance There is a target equipped with an ISRJ jammer. At the speed of light, The Doppler frequency shift is the target echo delay. The jammer's delay is Frequency shift is The number of reposts is ,in Therefore, the radar receiver echo signal using RIF-PCLFM signals can be characterized as follows:

[0135] (twenty four)

[0136] For the target echo:

[0137] (25)

[0138] This is an ISRJ interference signal:

[0139] (26)

[0140] in and The complex amplitude values ​​of the target echo and the ISRJ interference signal.

[0141] The echo signal was processed by pulse compression to obtain:

[0142] (27)

[0143] make and ignore In have to:

[0144] (28)

[0145] The result of Doppler coherence processing within CPI was then obtained:

[0146] (29)

[0147] It can be seen from equation (29):

[0148] i) In the RD spectrum, the true target is located at... Place;

[0149] ii) Due to the combined modulation of random frequency and random phase coding, pulse compression processing first requires adjustments to the time delay coordinates. Suppressing false targets, followed by Doppler coherent processing and then... The false target is whitened, and only the desired result is obtained. of A false target;

[0150] iii) If the jammer is in frequency-shift mode, then check hour Will the value lead to If so, it will not create a target of interference.

[0151] (2) Reconstruction of ISRJ interference signal based on slow-time phase compensation:

[0152] Without random inter-pulse frequency coding, false targets will appear. Substituting it into equation (28), we get the first... Slow-time dimensional steering vector of a dummy target :

[0153] a ( − ( f J + lf s ) / k , f d , s ) = [ e j 2 π ( f d , s 0 T r − f 0 ( f J + lf s ) / k ) , … , e j 2 π ( f d , s nT r − f n ( f J + lf s ) / k ) , … , e j 2 π ( f d , s ( N − 1 ) T r − f N − 1 ( f J + lf s ) / k ) ] T (30)

[0154] During the Doppler coherence processing, due to The random variation does not satisfy The target will be whitened. To reconstruct the false target, the latter term of the slow-time dimension steering vector needs to be compensated to restore the linearity of the slow-time dimension phase, thereby refocusing the ISRJ energy during Doppler coherence processing. Therefore, the slow-time dimension phase compensation vector is expressed as... :

[0155] ψ ( ( f J + lf s ) / k ) = [ e j 2 π f 0 ( f J + lf s ) / k , … , e j 2 π f n ( f J + lf s ) / k , … , e j 2 π f N − 1 ( f J + lf s ) / k ] T (31)

[0156] Phase compensation yields:

[0157] a ( − ( f J + lf s ) / k , f d , s ) ⊙ ψ ( ( f J + lf s ) / k ) = [ e j 2 π f d , s 0 T r , … , e j 2 π f d , s nT r , … , e j 2 π f d , s ( N − 1 ) T r ] T (32)

[0158] In addition, three issues need to be considered. First, in order to facilitate the elimination of false targets on the RD spectrum, the phase-compensated false targets need to be shifted along the time delay direction. First, the recovered false targets must correspond to the original false targets. Second, true targets must be removed during reconstruction to achieve identification. Considering that the true target will only remain in the reconstructed spectrum when the phase compensation value is zero, setting the compensation result to zero at this point is sufficient. Third, phase-coded modulation allows us to compensate only those that satisfy... The phase is fixed because false targets outside this range are unrecoverable, which leads to a significant improvement in computational efficiency.

[0159] Based on the above analysis, the following steps in this embodiment realize the reconstruction of false targets based on RIF-PCLFM signals using fast phase compensation:

[0160] Initialization: Initialize the RD spectrum of the dummy target for , , This represents the fast-time sampling interval. The slow-time phase compensation matrix is ​​established as follows: :

[0161] Ψ = [ ψ ( − P c T sa ) , … , ψ ( − T sa ) , 0 N × 1 , ψ ( T sa ) , … , ψ ( P c T sa ) ] (33)

[0162] in The centered zero vector is intended to eliminate the real target.

[0163] make ;

[0164] Pulse compression: For a CPI of Each pulse is individually compressed, and the processing results are stacked into a single pulse. Row matrix, extracted column by column y i = [ y 0 ( iT sa ), … , y n ( iT sa ), … , y N − 1 ( iT sa ) ] T ∈ ℂ N × 1 Subsequently, Doppler coherence processing is performed along the column direction to obtain the original RD spectrum. ,in ;

[0165] Phase compensation: for Slow-time phase compensation processing is performed to obtain ;

[0166] Doppler coherence processing: for Each column undergoes Doppler coherence processing to obtain ;

[0167] Coordinate repositioning:

[0168] if ,make:

[0169] (34)

[0170] Otherwise, let:

[0171] (35)

[0172] like ,make Switch to phase compensation; otherwise, output the reconstructed false target RD spectrum. ;

[0173] Wherein represents Comparison Matrix With matrix For each element at the corresponding position, retain the larger element to form a new matrix.

[0174] After the above steps, all false targets that may mislead the radar are reconstructed. And adjust it through the coordinate repositioning step. Furthermore, it is worth noting that for each The characteristics of the RIF-PCLFM signal allow for the execution of only additional... This FFT operation, compared to the existing technology, requires the execution of... Compared to the previous one, it decreased to .

[0175] (3) Identification and elimination of ISRJ

[0176] Compare and The target in the analysis can identify ISRJs by following these principles:

[0177] i) If the same location is only If a target is formed in the middle, then that position is the true target;

[0178] ii) If and If there are targets at the same location, then they are false targets generated by ISRJ;

[0179] iii) If only one is in the same position If a target is included, then that target is a false target formed by frequency-shifted ISRJ.

[0180] Therefore, we can then design the interference cancellation strategy as follows:

[0181] Initialization: Set the spectrum of the fake target Normalization and set a threshold To make its amplitude smaller than the false target and larger than the clutter, in this embodiment, it was set to 0.65 through multiple experiments;

[0182] Target positioning: Positioning Medium amplitude greater than false target location ;

[0183] Target elimination: by making ,eliminate The false target at the corresponding position in the middle;

[0184] Output: RD spectrum containing only the real target .

[0185] It should be noted that the Doppler frequency shift of the real target is designed to be no more than The main lobe ( Therefore, it is guaranteed that no real target will exist after phase compensation, and all interfering targets only need to satisfy the following: ,Right now It will be in The signal is reconstructed, including both those appearing and those not present in the original RD spectrum. Considering that ISRJ jammers typically need to perform multiple forwards within a sampling interval to ensure radar receiver processing gain, and that the response speed of current advanced jamming equipment is generally on the microsecond scale, we need to maintain [the required parameters] when designing RIF-PCLFM signal parameters. This is easy to satisfy.

[0186] (iv) Numerical Experiments

[0187] To evaluate the detection performance of RIF-PCLFM signals under ISRJ and verify its effectiveness in assisting ISRJ against different interference modes, input SIR fluctuations, and frequency shift variations, this embodiment conducted multiple sets of comparative experiments on a PC with a CPU of 2.30 GHz, an i7-11800H, and 32 GB of RAM. As mentioned above, all simulation experiments involved in this embodiment used random phase coding for the RIF-PCLFM signal, that is, the phase of the sub-pulse was... [ 0 , 2 π ] The noise is randomly and uniformly distributed over the interval. For each experiment in this embodiment, we will assume that the noise is a circularly symmetric, independent, identically distributed, additive complex Gaussian process with a mean of zero. For clarity, the experimental parameter settings in this section are summarized in Table 1.

[0188] Furthermore, to better reflect practical applications, quantization error is also considered. Here, it is treated as a rounding noise with a mean of zero. We assume that the radar system uses... -bit is a 12-bit output A / D converter with a maximum input peak voltage of 1 volt. Then, calculate... The SNR of the bit A / D converter is ,in The load factor can be taken as... Therefore, the SNR of the A / D converter due to quantization error can be measured to be 74.01 dB.

[0189] Table 1 Summary of Experimental Parameter Settings

[0190]

[0191] (1) Differences in the behavior of ISRJ in the range-Doppler spectrum

[0192] Experiment 1: Unlike traditional LFM signals, RIF-PCLFM signals impose unique constraints on the behavior of false targets generated by ISRJ. To illustrate this characteristic, this experiment analyzed the RD spectra of different signal echoes under three ISRJ conditions. The RIFC-LFM signal, a recently proposed LFM-based pulse train signal, was also included in the comparative experiment. In contrast, the signal presented in this embodiment is a composite modulation version developed and improved upon that.

[0193] At the start of the simulation, it was assumed that a moving target with a Doppler frequency shift of 2 kHz existed at a radial distance of 2000 meters, and that the target was equipped with a jammer capable of generating three different types of ISRJ. Other parameters are shown in Table 1. Figure 4 , Figure 5 , Figure 6 The RD spectra after echo processing under three ISRJ conditions—LFM, RIFC-LFM, and RIF-PCLFM—were plotted respectively. The parameters for the LFM and RIFC-LFM signals were determined by selecting the necessary items as shown in Table 1.

[0194] Depend on Figure 4 , Figure 5 , Figure 6 It can be seen that:

[0195] i) In the case of directly forwarding ISRJ, such as Figure 4 As shown, the RD spectrum after LFM signal processing forms a cluster of false targets, in order to Centered on, at intervals Uniformly distributed, amplitude modulated as In contrast, the RD spectrum processed based on RIFC-LFM and RIF-PCLFM signals only generates one false target, located in... The rest did not meet the requirements. And are suppressed and whitened. We can also see that, thanks to the composite modulation effect, the RIF-PCLFM signal helps the radar obtain the flattest sidelobes among the three signals;

[0196] ii) When switching to repeat forwarding mode, such as Figure 5 As shown, the number of false targets increases accordingly. The number of false targets increased to three clusters on the RD spectrum of the LFM signal, with their centroids located at... , and As for the RIFC-LFM and RIF-PCLFM signals, the number of false targets has increased to three, located at... , and The remaining false targets are suppressed and whitened. Similarly, the RD spectrum of the RIF-PCLFM signal after processing still has the flattest sidelobes;

[0197] iii) When frequency shift ISRJ exists, some special effects will occur, such as Figure 6 As shown. In the case of LFM signals, the false target cluster will move along the direction of decreasing distance. , causing the center to move This means it begins to guide the real target. Combined with the increased power of the jammer, the real target is then overwhelmed. For RIFC-LFM and RIF-PCLFM signals, due to... satisfy Simultaneously enable Therefore, false targets will not be formed. On the other hand, the RIF-PCLFM signal still maintains flat sidelobes, which is beneficial to enhancing radar detection performance, and will be discussed in detail in Experiment 4.

[0198] (2) ISRJ adversarial examples

[0199] Experiment 2: We now continue to verify the effectiveness of ISRJ against RIF-PCLFM signals. The signal and interference parameters are shown in Table 1, and the target parameters are the same as in the previous experiment. Similarly, all three types of ISRJ are considered. The false target reconstruction, identification, and elimination processes under direct relay, repeated relay, and frequency-shifted relay ISRJ interference are as follows: Figure 7 , Figure 8 and Figure 9 As shown.

[0200] exist Figure 7 , Figure 8 and Figure 9 In the middle, we found:

[0201] i) When using the RIF-PCLFM signal, directly relaying the ISRJ generates a false target in the original RD spectrum. Its amplitude is approximately 1.37 times that of the real target, and the calculated SIR is -2.78 dB. The Doppler frequency is the same as the real target, which will induce the radar to track the false target. After slow-time phase compensation processing, as... Figure 7 The second column shows the screening out of false targets. Then, the false targets are eliminated according to the processing strategy in the aforementioned ISRJ identification and elimination method. At this time, the SIR is improved to 16.83dB.

[0202] ii) Repeated ISRJ relay generates three false targets with amplitudes approximately 1.4 times that of the true target and a SIR of -2.95 dB. The Doppler frequency remains aligned with the true target. After ISRJ reconstruction based on slow-time phase compensation and ISRJ identification and elimination, the false targets are successfully identified and the interference is eliminated, improving the SIR to 16.19 dB.

[0203] iii) For the case of frequency shift ISRJ, due to the modulation frequency of the jammer Set to 2MHz, so satisfy But it also makes This resulted in no false targets appearing in the original RD spectrum. However, after phase compensation, the false targets were still successfully reconstructed, and interference cancellation was performed, improving the output SIR to 16.83 dB.

[0204] (3) Performance analysis of ISRJ countermeasures

[0205] Experiment 3: In the process of false target reconstruction, a fast phase compensation scheme was designed by utilizing the inherent characteristics of the RIF-PCLFM signal. Compared with existing methods, this theoretically improves computational efficiency. To intuitively verify this, this experiment compares the scheme with existing techniques. The interference and target parameters were set the same as in previous experiments. False targets under repeated forwarding ISRJ were reconstructed using both existing techniques and the fast phase compensation method proposed in this embodiment, resulting in the false target RD spectrum as shown below. Figure 10 As shown in Table 2, the first method uses the RIFC-LFM signal, while the second method corresponds to the proposed RIF-PCLFM signal. Furthermore, we recorded the running times of the two signals in the phase compensation session.

[0206] Table 2 Runtime Comparison (records each) (Time used)

[0207]

[0208] from Figure 10 From Table 2, we obtained the following findings:

[0209] i) As shown on the right side of the figure, since the phase modulation in the RIF-PCLFM signal allows only those that satisfy... Phase compensation is performed (comparison method phase compensation range is...) Therefore, the fast phase compensation method can focus the RD spectrum of the false target within a narrower range. This reduces the average noise amplitude, facilitating rapid location searching for the false target.

[0210] ii) Table 2 shows that the time required for the false target reconstruction process of the proposed signal is half that of the comparison signal. This is because the fast phase compensation method only requires at each position Additional This involves multiple FFT operations, which are required in the comparison method. The second operation .

[0211] Experiment 4: An LFM signal was used as the reference for comparison, and the bandwidth of the phase-coded signal should be consistent with that of the LFM-based signal. Therefore, the number of phase codes within a pulse was set to 200, and waveform design optimization was performed, resulting in a bandwidth of 50 MHz. Then, two time-discontinuous sequences with a phase code length of 100 were optimized and alternated at 50-second intervals to form the transmitted waveform of the waveform design method. For ease of comparison, the target Doppler frequency shift was set to 0, and the number of coherent processing pulses was set to 256, referring to existing technologies.

[0212] To comprehensively analyze the performance of the proposed method, this experiment examined the output SIR variation of each method under conditions of input SIR fluctuation, interference parameter estimation error, and frequency modulation variation of the jammer, respectively. Figure 11 , Figure 12 and Figure 13 For clarity, we plotted the echo processing envelope for each method in each simulation under a specific input parameter, as shown in the first two columns. It should be noted that for the first two experiments, the jammer was assumed to be in direct relay mode; for the latter two experiments, the input SIR was set to -10 dB.

[0213] from Figures 11 to 13 We can observe that:

[0214] i) The output SIR obtained through RIFC-LFM signal processing is generally superior to waveform design methods, such as... Figure 11 As shown, the lowest processable input SIR is -25 dB, at which point the output SIR reaches 2.22 dB, representing a 27.22 dB improvement in SIR. However, it can also be observed that as the input SIR decreases, waveform design methods exhibit a slower rate of output SIR reduction, giving them an increasingly larger advantage over the reference standard (LFM) and a smaller gap compared to the RIFC-LFM signal. For example, when the input SIR is 0 dB, the output SIR of the waveform design method is only slightly better than the reference standard by about 1 dB, but worse than the RIFC-LFM signal by about 14 dB. When the input SIR decreases to -30 dB, the output SIR is about 25 dB higher than the reference standard and only about 4 dB lower than the RIFC-LFM signal. This is because waveform design methods require the matched filter to be referenced to a time-discontinuous waveform, resulting in a partial loss of processing gain, which is not significant at low SIRs. In contrast, the proposed signal essentially integrates the advantages of both methods, maintaining optimal overall output SIR while exhibiting robustness under input SIR fluctuations, with an output SIR of 9.76 dB even when the input SIR is as low as -30 dB. This represents a 39.76 dB improvement in SIR.

[0215] ii) For every 10% error in the estimation of interference parameters, i.e., the jammer sampling interval The deviation of the waveform design method results in an output SIR attenuation of approximately 8 dB, which will reach the baseline when the estimation error reaches 12%. In contrast, the RIFC-LFM signal and the proposed RIF-PCLFM signal do not rely on any prior knowledge of the interference parameters and are therefore almost unaffected by the estimation error. At each data recording point, the output SIR of the proposed method is on average 6.55 dB higher than that of the RIFC-LFM signal.

[0216] iii) As analyzed above, when the jammer's modulation frequency changes, it is processed at the LFM signal receiver as a shift along the direction of decreasing distance, such as... Figure 13 As shown in the second column, the output SIR of the reference LFM signal remains essentially unchanged. On the other hand, waveform design methods are more sensitive to frequency modulation changes, decreasing by as much as 5.52 dB from 0 MHz to 5 MHz, which is an inherent characteristic of phase-coded waveforms. The RIFC-LFM signal, however, does not involve phase coding, and its output SIR remains relatively stable across all frequencies. For the proposed RIF-PCLFM signal, thanks to joint modulation, although the fluctuation is relatively greater than that of the RIFC-LFM signal, the output SIR generally shows an upward trend, being 8.1 dB higher than the RIFC-LFM signal at 6 MHz frequency modulation, a satisfactory result.

[0217] In summary, for the LFM pulse train signal RIF-PCLFM proposed in this invention, which is based on joint modulation of random inter-pulse frequency and intra-pulse phase coding, the AF analytical expression of the signal was derived by means of time delay variable substitution and piecewise integration techniques. Based on this, the good potential of RIF-PCLFM signal on some high-speed mobile platforms was discovered: while inheriting the high resolution of LFM signal, the range-Doppler coupling effect can be almost eliminated, avoiding the ranging error that may be caused by it.

[0218] Further research on the CAF of ISRJ revealed a unique limitation of the RIF-PCLFM signal on the generation of false targets: after processing by the receiver, the ISRJ generated by sampling the RIF-PCLFM signal exhibits a finite number of fixed false targets that no longer obscure or cause real targets to be detected. This characteristic makes it possible to identify and eliminate false targets in the RD spectrum. Therefore, by utilizing the whitening term characteristics of the echo processing results and combining them with slow-time phase compensation techniques, the reconstruction, identification, and elimination of false targets generated by ISRJ were achieved.

[0219] Simulation results show that the proposed method requires no prior knowledge or interference parameter estimation, can handle various types of ISRJ, has low time and space complexity, and high computational efficiency. Competitive comparison experiments demonstrate that the proposed method outperforms state-of-the-art methods in terms of input SIR fluctuations, interference parameter estimation errors, and interference modulation frequency variations, and shows promise for application in various space-based high-speed miniaturized platforms.

[0220] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method of LFM signal processing based on random inter-pulse frequency and intra-pulse phase coding modulation, characterized in that: The anti-intermittent sampling retransmission interference is realized through signal processing, and the signal processing method comprises the following steps: Step 1: after radar transmits a RIF-PCLFM signal, echo signals containing target echoes and ISRJ interference signals are received; The baseband of the RIF-PCLFM signal adopts a phase coding linear frequency modulation signal, and the frequency is randomly modulated between pulses; the signal model expression is: wherein is time, is the number of pulses during one coherent processing interval, denotes the pulse repetition interval, is the pulse-to-pulse frequency code of the th pulse, is the imaginary sign; denotes a phase-coded linear frequency modulated signal of length ; the signal model of the phase-coded linear frequency modulated signal is wherein is the number of phase codes within a pulse, is the duration of one coded sub-pulse, is the modulation slope, , is the bandwidth, is the pulse width, is the number of codes is the corresponding intra-pulse coded phase, is a rectangular function; Step 2: For a coherent processing interval Each echo pulse is individually compressed, and the processing results are stacked into a single pulse. Row matrix, the first row Column vector is ; and along Doppler coherence processing is performed along the column direction to obtain the original RD spectrum. ,in express OK Column real vector, , , Indicates rounding up. Fast sampling interval; Step 3: Slow time phase compensation is performed on to obtain a compensation matrix : wherein is a diagonal matrix with as diagonal elements, is a slow-time dimension phase compensation matrix; ; Step 4: Doppler coherent processing is performed on each column to obtain a false target search matrix ;​ Step 5: coordinate repositioning is performed: If , let: Otherwise, let: wherein is the false target RD profile; represents the first column to the column of represents the column to the column of If , let , go to step 3; otherwise output the reconstructed false target RD spectrum ; Step 6: Spectrum of the fake target Normalization and set a threshold ,position Medium amplitude greater than The RD spectrum is eliminated by setting the original RD spectrum to 0 at the False Target Location. The false targets at the corresponding positions are identified; the final output contains only the RD spectrum of the real targets.

2. The LFM signal processing method based on random inter-pulse frequency and intra-pulse phase coding modulation according to claim 1, characterized in that: inter-pulse frequency code with a random value between is the bandwidth.

3. The LFM signal processing method based on random inter-pulse frequency and intra-pulse phase coding modulation according to claim 1, characterized in that: In step 1, the echo signals received after the radar transmits a RIF-PCLFM signal are expressed as: wherein Target echo: in The complex amplitude of the target echo. Indicates length is Phase-coded linear frequency modulated signal, Delay the target echo. Target Doppler frequency shift; ISRJ for interference signal: wherein is the complex amplitude of the ISRJ jamming signal, is the number of jamming retransmissions, is the summation coefficient, is a phase-coded linear frequency modulated signal of length denotes the jamming retransmission, is the chip sampling width of the ISRJ jammer, is the ISRJ jammer time delay, is the ISRJ jammer frequency shift, , is the sampling interval of the ISRJ jammer, is an intermediate parameter:​ wherein .

4. The LFM signal processing method based on random inter-pulse frequency and intra-pulse phase coding modulation according to claim 1, characterized in that: In step 2, the first Column vector is: wherein is a signal obtained after pulse compression processing for the th echo pulse, is a fast time sampling interval, denotes a row 1 column real vector.

5. The LFM signal processing method based on random inter-pulse frequency and intra-pulse phase coding modulation according to claim 1, characterized in that: In step 3, the slow-time dimension phase compensation matrix is: wherein is the slow-time dimension phase compensation vector, , denotes row column real vectors; is the fast-time sampling interval; is given by 。 6.An electronic device comprising a processor, a memory storing one or more programs; characterized in that: When the one or more programs are executed by the processor, the method in any one of claims 1-5 is realized.

7. A readable storage medium, storing a computer program, characterized in that: When the computer program is executed by the processor, the method in any one of claims 1-5 is realized.

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