An intermittent sampling and forwarding interference suppression method based on phase encoding pulse train signal processing

Abstract

The application discloses an intermittent sampling and forwarding interference suppression method based on phase coding pulse train signal processing, and relates to the field of data processing.The method comprises the following steps: processing a power distribution function of an RD spectrum to obtain a range-Doppler matrix containing only target information, excluding a true target protection area, adopting a two-dimensional switching constant false alarm rate detection algorithm to detect the range-Doppler matrix containing only false targets, and extracting delay coordinates of the false targets; clustering the delay coordinates of the false targets through a mean value drift algorithm, constructing a window function according to a false target clustering center, processing two-dimensional S-CFAR detection results, eliminating the false targets, and obtaining a coarse detection result of the true targets; constructing Doppler vector spaces of the false targets and the true targets, obtaining a slant projection operator, performing Doppler filtering, and obtaining a one-dimensional pulse compression result of a final detection result containing only the true targets. The application can realize fine detection when the clutter or interference power is high.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of data processing, and particularly relates to an intermittent sampling repeater jamming suppression method based on phase coding pulse train signal processing. BACKGROUND

[0002] The intermittent sampling repeater jamming (ISRJ) has good phase correlation, flexible modulation and fast response capability, but can produce suppression and deception effects at the radar receiving end at the same time, which seriously weakens the radar detection capability. However, at present, the interference suppression is mainly realized by using interference parameters, and fine detection when the clutter or interference power is high cannot be realized. SUMMARY

[0003] The purpose of the present application is to provide an intermittent sampling repeater jamming suppression method based on phase coding pulse train signal processing, which can realize fine detection when the clutter or interference power is high.

[0004] To achieve the above purpose, the present application provides the following scheme:

[0005] In a first aspect, the present application provides an intermittent sampling repeater jamming suppression method based on phase coding pulse train signal processing, comprising:

[0006] Sampling, Doppler compensation and pulse compression are performed on the phase coding pulse train signal to obtain an in-phase signal and a quadrature signal;

[0007] A power distribution function of an RD spectrum is obtained based on the in-phase signal and the quadrature signal;

[0008] The power distribution function of the RD spectrum is processed to obtain a range-Doppler matrix containing only target information;

[0009] After excluding a true target protection area based on the range-Doppler matrix, a range-Doppler matrix containing only false targets is obtained;

[0010] A two-dimensional switch constant false alarm rate detection algorithm is used to detect the range-Doppler matrix containing only false targets to obtain a two-dimensional S-CFAR detection result, and a delay coordinate of the false target is extracted;

[0011] The delay coordinate of the false target is clustered by a mean shift algorithm to obtain a false target cluster center formed by the intermittent sampling repeater jamming;

[0012] A window function is constructed according to the false target cluster center, the two-dimensional S-CFAR detection result is processed to eliminate the false target, and a coarse detection result of the true target is obtained;

[0013] Based on the false target cluster center and the true target Doppler shift extracted from the coarse detection result of the true target, a Doppler vector space of the false target and a Doppler vector space of the true target are constructed;

[0014] A slant projection operator along the Doppler vector space of the false target to the Doppler vector space of the true target is obtained, and Doppler filtering is performed based on the slant projection operator to obtain a one-dimensional pulse compression result; the one-dimensional pulse compression result only contains the final detection result of the true target.

[0015] According to the specific embodiments provided in the present application, the present application has the following technical effects:

[0016] The present application provides an intermittent sampling and retransmission jamming suppression method based on phase coding pulse train signal processing. By using a two-dimensional switching constant false alarm rate (2D S-CFAR) detection algorithm and combining a mean shift algorithm originally used for image tracking, false target recognition is realized. Window operation is used to realize coarse detection of the target, and further Doppler filtering is performed using a slant projection operator. The phase correlation accumulation gain can be maintained while suppressing ISRJ, and fine detection can be realized when the clutter or jamming power is high. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0018] Figure 1 A flowchart of an intermittent sampling and retransmission jamming suppression method based on phase coding pulse train signal processing according to an embodiment of the present application is provided.

[0019] Figure 2 A bit coding pulse signal normalization AF array provided by an embodiment of the present application is provided.

[0020] Figure 3 An ISRJ normalization CAF diagram provided by another embodiment of the present application is provided.

[0021] Figure 4 A range-Doppler spectrum diagram of a return provided by an embodiment of the present application is provided.

[0022] Figure 5 A two-dimensional S-CFAR processor target detection flowchart provided by an embodiment of the present application is provided.

[0023] Figure 6 A delay Doppler spectrogram after echo reconstruction under ISRJ interference provided for an embodiment of the present application;

[0024] Figure 7 A delay Doppler matrix after 2D-CFAR detection processing under direct forwarding ISRJ provided for an embodiment of the present application;

[0025] Figure 8 A delay Doppler matrix after 2D-CFAR processing under frequency shift ISRJ provided for an embodiment of the present application;

[0026] Figure 9 A delay Doppler matrix after 2D-CFAR processing under repeated forwarding ISRJ provided for an embodiment of the present application;

[0027] Figure 10 A coarse detection process result under direct forwarding ISRJ provided for an embodiment of the present application;

[0028] Figure 11 A coarse detection process result under frequency shift ISRJ provided for an embodiment of the present application;

[0029] Figure 12 A coarse detection process result under repeated forwarding ISRJ provided for an embodiment of the present application;

[0030] Figure 13 A Doppler filtering result of direct forwarding ISRJ provided for an embodiment of the present application;

[0031] Figure 14 A Doppler filtering result of frequency shift forwarding ISRJ provided for an embodiment of the present application;

[0032] Figure 15 A Doppler filtering result of repeated forwarding ISRJ provided for an embodiment of the present application;

[0033] Figure 16 A comparison of processing results of experiment 3 provided for an embodiment of the present application;

[0034] Figure 17 A comparison of echo processing results under direct forwarding ISRJ under different input SIRs provided for an embodiment of the present application;

[0035] Figure 18 A comparison of the influence of different sampling interval estimation errors on echo processing under direct forwarding ISRJ provided for an embodiment of the present application;

[0036] Figure 19The interference machine under different frequency shift modulation values provided by an embodiment of the present application provides a comparison diagram of echo processing results. DETAILED DESCRIPTION

[0037] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work are within the protection scope of the present application.

[0038] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0039] In an exemplary embodiment, the present application provides an intermittent sampling repeater jamming suppression method based on phase-coded pulse train signal processing, which is executed by a computer device, specifically, can be executed by a terminal or a server, or can be executed by a terminal and a server. In the embodiments of the present application, the method is applied to a server as an example. As shown in the figure, the method comprises the following steps. Figure 1

[0040] Step 100: sampling, Doppler compensation and pulse compression are performed on the phase-coded pulse train signal to obtain an in-phase signal and a quadrature signal.

[0041] Step 101: a power distribution function of an RD spectrum is obtained based on the in-phase signal and the quadrature signal. The power distribution function of the RD spectrum can be seen from the following formula (42).

[0042] Step 102: the power distribution function of the RD spectrum is processed to obtain a distance-Doppler matrix containing only target information.

[0043] Step 103: after excluding a true target protection area based on the distance-Doppler matrix, a distance-Doppler matrix containing only false targets is obtained. The true target protection area can be excluded based on the following formula (49).

[0044] Step 104: a two-dimensional switch constant false alarm rate detection algorithm is used to detect the distance-Doppler matrix containing only false targets to obtain a two-dimensional S-CFAR detection result, and a delay coordinate of the false target is extracted.

[0045] Step 105: the delay coordinate of the false target is clustered by a mean shift algorithm to obtain a false target cluster center formed by the intermittent sampling repeater jamming.

[0046] ​Step 106, a window function is constructed according to the false target clustering center, the two-dimensional S-CFAR detection result is processed, the false target is eliminated, and the coarse detection result of the true target is obtained. Wherein, the true target can be further windowed according to the following formula (55) to obtain the coarse detection result.

[0047] Step 107, based on the false target clustering center and the Doppler frequency shift of the true target extracted from the coarse detection result of the true target, the Doppler vector space of the false target and the Doppler vector space of the true target are constructed. Wherein, the Doppler vector spaces of the false target and the true target can be constructed according to the following formula (57) and formula (59) respectively.

[0048] Step 108, the oblique projection operator along the Doppler vector space of the false target to the Doppler vector space of the true target is obtained, and Doppler filtering is performed based on the oblique projection operator to obtain a one-dimensional pulse compression result. The one-dimensional pulse compression result only contains the final detection result of the true target. Wherein, the Doppler filtering can be implemented according to the following formula (63).

[0049] In the implementation process, the ISRJ cross-ambiguity function (CAF) of the phase-coded pulsetrain (PCPT) signal based on Doppler compensation is derived, it is found that the false target is distributed in parallel along the Doppler axis in the range-Doppler domain, and the delay is fixed. Different types of ISRJ are represented as moving along the Doppler axis and copying along the delay axis in the range-Doppler domain. Based on this, the above steps 100-108 are implemented by using the distribution characteristics of the range-Doppler domain, a two-dimensional switching constant false alarm rate (2D S-CFAR) detection algorithm is proposed, and the mean shift algorithm originally used for image tracking is combined to realize false target recognition, window operation is used to realize coarse detection of the target, and further Doppler filtering is used to realize fine detection when the clutter or interference power is high.

[0050] Further, in combination with the simulation effect, the design idea and specific implementation process of the above intermittent sampling and forwarding jamming suppression method provided in the application are described.

[0051] (I) Analysis of phase-coded pulse sequence signal

[0052] A. Signal model

[0053] Consider that there are pulses in a pulse sequence waveform in a coherent processing interval (CPI):

[0054] (1)

[0055] In the formula, Within the pulse repetition interval, t For time indexing, N This represents the number of pulses within a coherent processing interval. It is a length of The phase-coded single-pulse signal is represented as:

[0056] (2)

[0057] In the formula, M This represents the number of phase-coded sub-pulses within a single pulse. It is a modulation code sequence, represented as:

[0058] (3)

[0059] In the formula, j The imaginary unit, m The phase is modulated by the sub-pulse.

[0060] This application uses a random phase-coded sequence. The duration is The rectangular shaped pulse is represented as:

[0061] (4)

[0062] In the formula, T is the pulse width. The rectangle function is defined as follows:

[0063] (5)

[0064] B. Fuzzy function analysis.

[0065] AF (Asynchronous Signal Analysis) is a very effective signal analysis tool that can be used to analyze the waveform resolution, sidelobe level, and range-Doppler characteristics of echoes. AF can be written as:

[0066] (6)

[0067] In the formula, for AF, For delay, For Doppler frequency, for The echo signal at time e, where e is the natural logarithm.

[0068] Because the interrupt sampling repeater slices, samples, and forwards the intercepted signal within a pulse width, the jammer eliminates the need to analyze the cyclic periodic ambiguity function. This application only considers the central AF, i.e. Based on this, substituting formula (1) into formula (6), we get:

[0069] (7)

[0070] In the formula, This is a radar signal.

[0071] To simplify the calculation, let Then formula (7) becomes:

[0072] (8)

[0073] Referring to formula (2), we have:

[0074] (9)

[0075] In the formula, For rectangular window functions, The code point index is The modulation code sequence at that time, This is the code point index.

[0076] For ease of analysis, the time delay is discretized into a time grid. , ,At Calculate the ambiguity function of a single-pulse signal. ,have:

[0077] (10)

[0078] in, The width of the sub-pulse. The code point index is The modulation code sequence at that time, For Kronecker delta (transliterated as Kronecker symbol), if ,but ,otherwise Substituting formula (10) into formula (8), we get:

[0079] (11)

[0080] In the formula, Phase-coded single-pulse signal The discrete AF is defined as:

[0081] (12)

[0082] To understand this ambiguity function, first observe the zero-Doppler and zero-delay responses. The zero-Doppler response is determined by setting... , resulting in:

[0083] (13)

[0084] where, is the zero-Doppler slice of the pulse train signal ambiguity function.

[0085] By choosing a phase-coded sequence with a "pin-like" ambiguity function , it is possible to obtain:

[0086] (14)

[0087] This means that the range resolution of the PCPT signal is . Similarly, the Doppler resolution can be given by setting , resulting in:

[0088] (15)

[0089] where, is the zero-time-delay slice of the pulse train signal ambiguity function. is the zero-time-delay slice of the single-pulse signal discrete ambiguity function, which is given by:

[0090] (16)

[0091] Thus, the Doppler resolution of the PCPT signal is , and the peaks repeat with a period , which is weighted by a sinc function with the first zero at . Moreover, it is not difficult to find that the peaks of the ambiguity function only appear at . Figure 2 The normalized AF of the phase-coded pulse signal is shown, along with the zero-Doppler slice and the zero-time-delay slice, where, Figure 2 the first row is the phase-coded single-pulse signal, and the second row is the PCPT signal. The first column is the three-dimensional view, the second column is the zero-Doppler slice, and the third column is the zero-time-delay slice. In this simulation, we set , , , , . As can be seen from Figure 2 , the simulation results are in complete agreement with the mathematical analysis.

[0092] (II) ISRJ analysis.

[0093] A. Interference signal model.

[0094] When the sampling repeater is interrupted, and the jammer slices, samples, and forwards the intercepted signal, it sometimes adds extra frequencies, thus creating false targets. The jammer's sampling can be characterized as... :

[0095] (17)

[0096] In the formula, For slice sampling width, For sampling interval, Let be the Dirac function, and l be the jamming slice count. Generally, when the jammer detects the leading edge of a radar signal pulse, it begins slicing, sampling, and forwarding at regular time intervals until it detects the trailing edge of the radar signal pulse. This process continues when a new leading edge is detected. Therefore, the signal intercepted by the jammer can be described by the following formula. :

[0097] (18)

[0098] In the formula, This is the sampling function for the jammer.

[0099] Based on the forwarding strategy and whether frequency shift exists, the most commonly used ISRJs can be divided into three types.

[0100] The first type is direct forwarding of ISRJ, and its mathematical model is (ignoring jammer delay):

[0101] (19)

[0102] In the formula, This is a mathematical model for direct forwarding interference.

[0103] The second type is Repeated Forwarding (ISRJ). This type of jammer repeatedly forwards the intercepted signal within the sampling interval. Its mathematical model is (ignoring the jammer's delay):

[0104] (20)

[0105] In the formula, For the mathematical model of repeated forwarding interference, for The sampling function of the jammer at that time. for The radar signal at that time. This represents the number of times the jammer forwards the signal; the number of repeated forwards increases with the number of times the signal is repeated.

[0106] The third type is frequency-shift ISRJ. The operating characteristics of ISRJ jammers determine that the false targets they produce will at least lag behind the real targets. For those radars using LFM signals, this is manifested in the form of change in target frequency point after pulse compression at the receiving end. Therefore, it is proposed to modulate the frequency of the intercepted signal slice to move the false target in front of the true target. The mathematical model of frequency-shift ISRJ is (ignoring the jammer's delay):

[0107] (21)

[0108] where, is the mathematical model of frequency-shift repeater jamming, is the modulation frequency.

[0109] The above three ISRJs can be uniformly expressed as:

[0110] (22)

[0111] where, is the unified mathematical model description of intermittent sampling repeater jamming. is the jamming signal model within a single radar pulse, and there is:

[0112] (23)

[0113] It is worth noting that, when it is direct repeater ISRJ, , . when it is repeated ISRJ, , . when it is frequency-shift ISRJ, . Where, can be derived as:

[0114] (24)

[0115] where, is the coefficient of the jamming model, and there is:

[0116] (25)

[0117] where, , . Therefore, formula (23) can be derived as:

[0118] (26)

[0119] B. Mutual ambiguity function analysis.

[0120] In order to analyze the characteristics of the false target distribution of ISRJ and its induced effects on the radar using PCPT signal, the CAF of ISRJ is first analyzed mathematically using CAF. The CAF of ISRJ can be written as :

[0121] (27)

[0122] The present application only needs to consider the central CAF. Substituting equation (1) and equation (22) into equation (27), we have

[0123] (28)

[0124] In order to simplify the calculation, let Then equation (28) is transformed into

[0125] (29)

[0126] From the above derivation, it can be seen that the CAF of ISRJ is a superposition of a series of AFs with different delays and Doppler shifts. Directly forwarding ISRJ ( , ) will produce multiple peaks with equal frequency intervals in the zero-delay cut. Repeatedly forwarding ISRJ ( , ) will copy and move the CAF of directly forwarding ISRJ times, accompanied by a time delay . Frequency-shifted ISRJ ( ) will add an additional Doppler shift to the CAF. Figure 3 The CAF shapes of the three types of ISRJ are shown. Through analysis, it is not difficult to find that the distribution of false targets is consistent with the mathematical analysis. In this simulation, the number of pulses , is set, and the rest of the parameters are the same as in the previous experiment. In addition, the number of repeated forwarding times is set, the number of frequency-shifted forwarding times is set, and the frequency shift . Figure 3 The first column is the directly forwarded ISRJ, the second column is the repeatedly forwarded ISRJ, and the third column is the frequency-shifted ISRJ. The first row is the 3D view, and the second row is the 2D view.

[0127] (Three) Reconstruction and elimination of ISRJ based on pulse train signal processing.

[0128] According to the analysis and simulation, it is known that the false targets generated by ISRJ have significant distribution difference in range-doppler (RD) spectrum, which is shown as a series of peaks along the doppler velocity. Considering that the amplitude of ISRJ is usually at least twice the amplitude of target echo, these peaks will induce radar to track false targets. Therefore, in order to take advantage of these characteristics, a doppler compensation technique is proposed to reconstruct the interference peaks before pulse compression, and the position of ISRJ is identified according to the distribution characteristics of false targets. Next, the ISRJ reconstruction method based on doppler compensation is introduced.

[0129] A.ISRJ reconstruction.

[0130] Suppose there is a target, whose time delay and doppler shift are and respectively. An ISRJ jammer is installed near the target, whose retransmission delay is and the frequency shift is , where . Then the echo signal at the radar receiver end can be characterized as:

[0131] (30)

[0132] In the formula, is the echo signal at the radar receiver end, is the radar signal echo, is the interference signal echo.

[0133] Target echo, i.e. ISRJ signal. and are represented as:

[0134] (31)

[0135] (32)

[0136] In the formula, is the complex amplitude of target echo, is the complex amplitude of ISRJ signal, is the true target doppler shift. In order to reconstruct the RD spectrum of the interference signal, the given signal is doppler compensated, and there is:

[0137] (33)

[0138] In the formula, is the echo signal at the radar receiver end after doppler compensation.

[0139] The signal after doppler compensation is pulse compressed to obtain:

[0140] (34)

[0141] where, is the signal after pulse compression processing.

[0142] For simplicity of calculation, let Then, formula (34) is transformed as:

[0143] (35)

[0144] where, is the radar echo coefficient, is the jamming echo coefficient, and

[0145] (36)

[0146] (37)

[0147] Then, the received echoes within a CPI are coherently accumulated, and

[0148] (38)

[0149] Take the frequency-shifted ISRJ as an example, where , Then, the range-Doppler spectrum of the echoes is plotted, as shown in Figure 4 In this simulation, the target range is assumed to be 2000 m, and , are set to 0.5 and 0.1, respectively, and other parameters are the same as before. In addition, the SNR and SIR are set to 10 dB and -15 dB, respectively. Figure 4 The left side is a three-dimensional view, and the right side is a two-dimensional view.

[0150] As can be seen from Figure 4 , the frequency-shifted ISRJ produces a group of peaks along the Doppler axis, and due to the frequency shift, these peaks are shifted, and the maximum amplitude appears at On the other hand, the real target presents a single, lower-amplitude peak, which is away from the false target peak group.

[0151] Therefore, the application proposes a method for identifying false targets generated by ISRJ. That is, by using the characteristic that ISRJ can generate multiple spectral peaks, a group of spectral peak positions is extracted on the RD spectrum by a suitable constant false alarm rate (CFAR) detection method, and clustering is performed to obtain the delay axis coordinates of the false targets, thereby completing the identification process of the false targets. Further, according to the identification result, a window operation is performed on the range-doppler matrix (RDM) after CFAR detection to eliminate the ISRJ, and coarse detection of true targets is realized. However, for PD radars used for airborne or spaceborne surveillance, missile seeker and battlefield surveillance, the large-amplitude clutter background may cause unnecessary false alarms. Therefore, the application also performs Doppler filtering to realize fine detection of real targets.

[0152] B. Target detection under ISRJ, a group of spectral peak positions are extracted on the RD spectrum by a suitable constant false alarm rate (CFAR) detection method, and clustering is performed to obtain the delay axis coordinates of the false targets, thereby completing the identification process of the false targets.

[0153] In the PCPT signal processing process, the radar target detection often faces a non-uniform background, that is, there may be multiple interferences, clutters and noises in the reference window. This leads to some detection problems of the most famous cell-averaging CFAR (CA-CFAR) processor, such as weak targets being masked near strong targets, too many false alarms when clutter transitions, and inability to detect targets near the edge of the clutter. This is because the optimality of the CA-CFAR processor is based on the assumption that the samples in each reference cell are independent and identically distributed (iid) and are dominated by an exponential distribution. When considering interferences and clutters, this assumption is invalid.

[0154] In order to overcome the above-mentioned adverse conditions, the application adopts an algorithm which uses the statistical characteristics of the samples in the test cell to filter suitable reference samples, which is called a switching CFAR (S-CFAR) algorithm. Compared with CA-CFAR in a uniform background, the S-CFAR algorithm can adjust to almost no detection performance degradation, and at the same time, when used for target detection near the edge of the clutter in a non-uniform background, it is superior to the ordering class of constant false alarm rate processing algorithms. In addition, the S-CFAR algorithm allows a larger number of interference targets, and is easier to implement because it does not involve sorting operations. Since the S-CFAR has excellent detection performance and time efficiency, it is generalized to two-dimensional target detection under ISRJ, and coarse detection of true and false targets is realized.

[0155] The standard S-CFAR includes the following two main steps.

[0156] First step: reference cells in the window are divided into two groups, and

[0157] (39)

[0158] That is, if the reference cell is smaller than , it is assigned to the set , otherwise it is assigned to the set . Where is the amplitude of the test cell, and is the scaling factor.

[0159] Second step: represents the potential of the set , when the following conditions are met, the target is determined to exist:

[0160] (40)

[0161] Or:

[0162] (41)

[0163] In the formula, and are threshold multipliers, and is the threshold integer.

[0164] During the operation of the S-CFAR processor, means that the test cell may contain a phase-coded pulse train signal with a large amplitude, in order to improve the detection probability, the reference cells in the set are selected to evaluate the detection threshold. means that the test cell may contain small amplitude noise or clutter samples, at this time the S-CFAR processor switches to all reference cells to estimate the background noise or clutter power, so as to maintain a low false alarm rate. Such operation makes the S-CFAR processor can use the samples in the set , instead of discarding larger amplitude reference samples when is small, thereby reducing the false alarm rate of the clutter edge.

[0165] Further, the excellent detection performance of S-CFAR processor is utilized to solve the problem of 2D multi-target detection under ISRJ. For the radar system explored in this application, the phase-coded pulse train signal is sampled, Doppler compensated and pulse compressed in the radar receiver, and processed into in-phase signal and quadrature signal, which are further processed by the detector. Since it is simpler to calculate the square amplitude of the test sample (by summing the squares of the real and imaginary parts), the square-law detector is recommended, which outputs the power of the RD spectrum, denoted as:

[0166] (42)

[0167] wherein, P RD represents the power of the RD spectrum, and represents the signal after coherent accumulation of the received echo signal within a coherent processing interval.

[0168] Subsequently, the 2D S-CFAR processor receives the input from the range-Doppler video sample detected by the square-law detector, and stores the cells in the CFAR window as reference cells, guard cells and test cells, respectively. Note that the reference cells are used to estimate the background noise or clutter power, and in order to prevent possible power leakage, some cells adjacent to the test cells (guard cells) are excluded from the estimation, and the test cells are the cells that need to give a detection decision. Thus, the principle block diagram of 2D S-CFAR processor target detection under ISRJ can be drawn, as shown in Figure 5 .

[0169] Based on the above description, the scaling factor , the threshold multiplier and , the threshold integer are still not determined. For the problem of 2D multi-target detection, the way of processing the problem of 1D target detection can be referred to. Based on this, the detection probability of the 2D S-CFAR algorithm is:

[0170] (43)

[0171] wherein, , , , are all intermediate quantities and have no special meaning. SNR is the signal-to-noise ratio of the cell sample.

[0172] wherein, (44)

[0173] (45)

[0174] (46)

[0175] (47)

[0176] (48)

[0177] In the formula, and It is also an intermediate quantity and has no special meaning.

[0178] Formula (43) is a formulaic representation of the detection probability of the S-CFAR algorithm under a uniform background. By assigning values... Formula (43) becomes the expression for the false alarm probability. In engineering applications, given the design index of the false alarm probability, the threshold parameters of the two-dimensional S-CFAR detector can be determined from it. Since the interference power is usually unknown, the parameters often need to be optimized based on the simulation results during the radar system design process.

[0179] Typically, the power distribution function in equation (42) is processed by an adjusted two-dimensional S-CFAR processor. After processing, an RDM containing only target information (including real and fake targets) is obtained, denoted as . When multiple true targets exist, new cluster centers may form in the next step of this application. To avoid identifying true targets as interference signals, it is recommended to exclude potential true targets in advance. A true target protection region is created along the delay axis, and simultaneously widened appropriately along the Doppler axis, resulting in an RDM containing only false targets, denoted as... :

[0180] (49)

[0181] in, The maximum possible Doppler frequency shift for the real target can be adjusted based on waveform parameters. This application assigns... Value Then The delayed axis coordinates of the dummy targets in the data are extracted into the set. It should be noted that, due to the false targets formed by ISRJ along the Doppler axis... The intervals are evenly distributed, usually as follows: The difference is several times that of the target peak, so the above operation can eliminate at most one false target peak on the same delay cut, and has little impact on subsequent interference clustering.

[0182] C. ISRJ recognition.

[0183] With the targets detected by the RD spectrum, the identification of the jammer can be performed. In fact, only one-dimensional clustering is needed to achieve effective discrimination, because there is no overlap between false targets and true targets in the delay dimension. But there is still another problem, which is the selection of the number of clusters. Generally, traditional clustering methods, such as k-means type algorithms and their optimized versions, need to determine the number of clusters in advance. This is feasible for most application scenarios, but it is not feasible for the interference clustering of the present application, because it means the pre-knowledge of the ISRJ type and the number of retransmissions, which is impractical.

[0184] A clustering and tracking algorithm, called mean shift algorithm, has been widely used in the research fields of image segmentation, target tracking and computer vision in recent years. Its iterative process is simple, its convergence speed is fast, it does not depend on any prior knowledge, and it does not depend on the predetermined number of clusters. In addition, the well-known k-means type algorithm has been proved to be a special case of the mean shift algorithm. The present application takes advantage of the excellent characteristics of the mean shift algorithm and extends it to the field of interference clustering for identifying the false target positions formed by the ISRJ.

[0185] Definition 1: For each point in the set of delay axis coordinates of the price table , the multivariate kernel density estimator is defined as :

[0186] (50)

[0187] where denotes the weight function, denotes the kernel function, is the bandwidth of the kernel function , is a set of real numbers. Considering that the main lobe width along the delay axis is , , it is recommended to be no less than . Unless otherwise stated, the weight function of the present application is set to 1.

[0188] The present application adopts a Gaussian kernel function, which is defined as :

[0189] (51)

[0190] A contour function is defined as

[0191] (52)

[0192] then

[0193] (53)

[0194] Definition of Mean Shift based on Gaussian Kernel is:

[0195] (54)

[0196] Equation (54) is the gradient ascent direction at where , , , the kernel is called the shadow of the kernel . Now give the implementation steps of the mean shift algorithm, including:

[0197] Step 1: For each , calculate .

[0198] Step 2: For all , perform .

[0199] Step 3: , the algorithm converges, and the output is the cluster center of the false target formed by ISRJ, denoted as .

[0200] According to this, according to the cluster center , a window function is constructed to process the two-dimensional S-CFAR detection result, so as to eliminate false targets and obtain the coarse detection result of true targets , which has:

[0201] (55)

[0202] where is the window function, which is expressed as:

[0203] (56)

[0204] In the formula, is the width of the window function, which is to eliminate the main lobe expansion of the false target. According to equation (14), the range resolution of PCPT signal is , therefore, it is recommended to set as .

[0205] D. Doppler filtering, a Doppler filter is designed to realize fine detection of real targets.

[0206] Generally, the position and velocity information of the true target can be extracted at this time, and the coarse detection result is focused on the true target protection area , referring to equation (49) and equation (55). However, when the clutter amplitude and interference power are large, such as airborne or missile-borne application scenarios, there may still be residual isolated false targets in the coarse detection result , causing false alarms and wasting system resources. In order to reduce the false alarm rate while maintaining the detection probability, it is necessary to further improve the SNR. For this purpose, a Doppler filter based on oblique projection is designed to realize fine detection of the true target.

[0207] Based on the false target delay coordinates extracted by the above mean shift algorithm, and considering the main lobe width, the Doppler vector space of the false target can be obtained, which is expressed as:

[0208] (57)

[0209] where, is the Doppler discrete data vector, which is expressed as:

[0210] (58)

[0211] where, is the radar intermediate frequency (IF) sampling frequency, represents the number of discrete data along the Doppler axis within the detection window, is the Doppler data interval (excluding the main lobe endpoints), . According to the Doppler frequency shift extracted from the coarse detection result, the Doppler vector of the true target is formed, which is expressed as:

[0212] (59)

[0213] where, . Therefore, the oblique projection operator from to can be expressed as:

[0214] (60)

[0215] where, is the orthogonal projection matrix of , which is calculated as:

[0216] (61)

[0217] Since the oblique projection operator can make simultaneously satisfy . The Doppler filter is designed by using this property , which is expressed as:

[0218] (62)

[0219] It makes simultaneously . Thus, the Doppler filtering process is as follows:

[0220] (63)

[0221] So far, the ISRJ is eliminated, and the one-dimensional pulse compression result is obtained, and the output SNR is further improved, which can be used to realize fine detection of the true target.

[0222] Further, based on the above description, the procedure steps of ISRJ elimination and target detection of the PD radar using PCPT signals include:

[0223] Step 1 (square law detector): After Doppler compensation and pulse compression, the power of the RD spectrum is calculated according to formula (42).

[0224] Step 2 (target coarse detection): After excluding the true target protection area according to formula (49), the video samples are detected using a 2D S-CFAR processor, and the delay coordinates of the false targets are extracted as . Then, the meanshift algorithm is used for clustering, and the false target cluster centers formed by the ISRJ are output, denoted as . According to formula (55), the true target is further windowed to obtain the coarse detection result.

[0225] Step 3 (Doppler filtering): Based on the false target cluster center and the true target Doppler shift extracted from the coarse detection result , the Doppler vector spaces of the false target and the true target are constructed according to formulas (57) and (59) respectively. The Doppler filtering is implemented according to formula (63).

[0226] Step 4 (target fine detection): The one-dimensional pulse compression result is output, which only contains the true target detection result with improved SNR, and can be used for fine detection of the target.

[0227] Further, numerical experiment simulation is performed.

[0228] To evaluate the performance of the method provided in this application in ISRJ confrontation, this embodiment carries out a plurality of numerical simulations on a PC with a 2.30 GHz i7-11800H CPU and 32 GB of RAM. Unless otherwise stated, a random PCPT signal will be used, i.e. the phases of the sub-pulses are randomly chosen within an interval . For each example, it will be assumed that the noise is a circularly symmetric, independent, identically distributed, zero-mean additive complex Gaussian process.

[0229] In addition, in order to enhance the proximity of the analysis to the actual system, the quantization error is also considered. Here, the quantization error is considered as a kind of rounding noise with zero mean. Assuming that the radar system uses a 12-bit output word A / D converter with a maximum input peak voltage of 1 volt. Therefore, the quantization level , which also represents twice the maximum rounding error, can be expressed as . The probability density function of the quantization error is defined as , from which the variance is calculated as . The SNR of the A / D converter can be obtained as , where is the load factor, which is taken as 0.5 in this application. Thus, the SNR of a 12-bit output word A / D converter is calculated to be 74.01 dB. Based on this, the following analysis is carried out:

[0230] A. Target detection performance analysis.

[0231] Experiment 1: First, the performance of the 2D S-CFAR processor under three different types of ISRJ is evaluated by comparing it with the classical cell averaging CFAR (CA-CFAR) and order statistic CFAR (OS-CFAR) processors. It is assumed that there is a jammer on a target at a radial distance of 2000 m . The jammer can generate three different types of ISRJ, and the specific parameter settings are shown in Table 1. For the three CFAR processors, the same size of CFAR window is used, with 4 reference cells and 2 guard cells on each side of the distance axis , and 9 reference cells and 10 guard cells on each side of the Doppler axis . The total number of reference cells is calculated to be 402. Assuming that the required false alarm probability of the radar system is , then according to formula (43) and appropriate adjustments, the parameters of the S-CFAR can be determined as: threshold integer , threshold multiplier , and scaling factor The threshold parameters of other CFAR processors are determined according to existing published literature. In testing the OS-CFAR, the threshold is selected as the data in the order to establish the detection threshold.

[0232] Table 1 Parameter setting table in experiments 1, 2

[0233]

[0234] Figures 6-9 The reconstructed delay-Doppler spectra of echoes under three different types of ISRJ interference, and the delay-Doppler matrix after 2D-CFAR processing are plotted respectively. In order to further compare the actual application performance of the CFAR processor, the running time which is very important for real-time detection and tracking of targets is also recorded and listed in Table 2. Figure 6 The left is direct repeater ISRJ, the middle is frequency-shifted repeater ISRJ, and the right is repeated repeater ISRJ. Figure 7 The left is the CA-CFAR detector detection result, the middle is the OS-CFAR detector detection result, and the right is the S-CFAR detector detection result. Figure 8 The left is the CA-CFAR detector detection result, the middle is the OS-CFAR detector detection result, and the right is the S-CFAR detector detection result. Figure 9 The left is the CA-CFAR detector detection result, the middle is the OS-CFAR detector detection result, and the right is the S-CFAR detector detection result.

[0235] From Figures 6-9 and Table 2, it can be seen that:

[0236] 1) There are significant differences in the two-dimensional target detection performance of the three CFAR processors, which is due to the formation of multiple false target peaks around the high-level interference residue of ISRJ. Thus inducing CA-CFAR to miss the real target under repeated repeater ISRJ, indicating that the processor is sensitive to dense false targets, while S-CFAR and OS-CFAR show good robustness.

[0237] 2) The number of targets detected by the CFAR processor is different under different types of ISRJ. When the ISRJ is directly forwarded, the number of targets detected by CA-CFAR, OS-CFAR and S-CFAR is 50, 49 and 52, respectively. The similar detection performance is due to the sparseness of false targets. When the frequency shift mode is switched to, the number of targets detected by CA-CFAR, OS-CFAR and S-CFAR is 56, 49 and 61, respectively. At this time, S-CFAR begins to stand out. With the false targets in the repeated forwarding mode being more dense, OS-CFAR shows better performance, and the number of targets detected by CA-CFAR, OS-CFAR and S-CFAR is 21, 39 and 35, respectively.

[0238] Table 2 Runtime comparison of CFAR processors

[0239]

[0240] B. Coarse detection and Doppler filtering.

[0241] Experiment 2: In this experiment, the effectiveness of the proposed interference countermeasures on three different types of ISRJ is evaluated. In the ISRJ identification process, the minimum distance of the mean shift algorithm is set to , and the bandwidth is set to . According to the target detection results of Experiment 1, the coarse detection process under three ISRJ types of false target detection, ISRJ identification, and true target coarse detection is shown in Figures 10-12 , respectively. The subsequent Doppler filtering process is shown in Figures 13-15 for fine detection. In addition, in order to test the timeliness of the identification process, the running time of the mean shift clustering algorithm and the Doppler filtering process is also recorded, as shown in Table 3. Figure 10 The first column of Table 4 is the detection result after removing the true target protection zone, the second column is the ISRJ identification result of the mean shift algorithm, and the third column is the coarse detection result of the true target after window operation. Figure 11 The first column of Table 4 is the detection result after removing the true target protection zone, the second column is the ISRJ identification result of the mean shift algorithm, and the third column is the coarse detection result of the true target after window operation. Figure 12The first column is the detection result after removing the true target protection zone, the second column is the recognition result of ISRJ by mean shift algorithm, and the third column is the coarse detection result of true target after window operation. Figure 13 The first column is echo delay-Doppler spectrum, the second column is two-dimensional view along Doppler axis, and the third column is Doppler filtering result. Figure 14 The first column is echo delay-Doppler spectrum, the second column is two-dimensional view along Doppler axis, and the third column is Doppler filtering result. Figure 15 The first column is echo delay-Doppler spectrum, the second column is two-dimensional view along Doppler axis, and the third column is Doppler filtering result.

[0242] It can be found that: Figures 10 to 12

[0243] i) The mean shift algorithm accurately identifies the position of the false target by using the distribution characteristics of the false target. Figure 10 The second column of Table 2 is the ISRJ recognition result of mean shift algorithm under straight-transmitting ISRJ (excluding the true target protection zone), which shows that the straight-transmitting ISRJ can generate a group of false targets along the Doppler axis, which are gathered in . Figure 11 The second column of Table 2 is the ISRJ recognition result of mean shift algorithm under straight-transmitting ISRJ (excluding the true target protection zone), which shows that the straight-transmitting ISRJ can generate a group of false targets along the Doppler axis, which are gathered in .The ISRJ recognition result under repeated-transmitting ISRJ is shown in the second column of Table 2, which confirms that the repeated-transmitting ISRJ generates a group of false targets along the delay axis with an interval of . Figure 12 , and .

[0244] ii) After providing the position of the recognized false target, the window operation easily eliminates the three different types of ISRJ while retaining the true target, and the detected targets are 9, 11 and 4, respectively, and the extracted center delay and Doppler frequency shift are and 0.125 MHz. This shows that even under the most challenging frequency-shifted repeated-transmitting ISRJ, the method proposed in the present application can still provide sufficient true target points for radar to extract parameters and make decisions.

[0245] ​​​It should be noted that when the input SIR is large, there are still some residual isolated false targets in the range-Doppler plane after the window operation. The number of these false targets is too small to form a cluster center, and they cannot be identified in the false target clustering step. This is a problem of the coarse detection, but it has little effect on the extraction of the true target Doppler shift in the protected area. Therefore, a Doppler filter is designed to further improve the output SIR.

[0246] To quantitatively describe the performance of the Doppler filtering method, the signal-to-interference ratio improvement factor (SIRIF) is introduced here to represent the ability of the filter to suppress interference and noise, and is defined as:

[0247] (64)

[0248] In the formula, is the SIR before Doppler filtering, which is calculated by Figures 13 to 15 the second column of data.

[0249] From Figures 13 to 15 we can see that:

[0250] i) Since ISRJ produces several groups of peaks with an interval of in the RD spectrum along the Doppler axis, the number of false targets presented in the pulse compression result depends on the number of times ISRJ is repeated. And the false targets still maintain a generally larger amplitude than the true targets after coherent integration, indicating that both the interference slice and the real phase-coded pulse train signal can enjoy the coherent integration gain.

[0251] ii) The Doppler filtering method effectively eliminates the false targets produced by ISRJ and improves the output SIR. The SIRIFs under the three interference modes are calculated to be 15.36 dB, 12.12 dB and 9.13 dB, respectively. This shows that the suppression effect of Doppler filtering on interference and noise decreases with the increase in the number of false targets, but it can still achieve correct fine detection. In engineering applications, this method can be combined with low sidelobe phase-coded waveforms to improve the suppression effect. In addition, increasing the number of phase codes in a single pulse can also improve the output SIR, as shown in the next experiment.

[0252] iii) In addition to suppressing the interference produced by ISRJ, the Doppler filter can also effectively suppress isolated interference or noise in the delay-Doppler spectrum, which is particularly evident in Figure 12 and 13 . In this way, at the same detection probability, the false alarm rate of the radar system can be reduced, thereby avoiding the waste of system resources.

[0253] Considering the practical application, the efficiency of the algorithm is the most important, therefore, the running time of the most time-consuming part in the method provided in the present application is recorded in Table 3, including the mean shift algorithm used in the ISRJ identification process and the Doppler filtering process before fine detection, which takes only milliseconds, basically meeting the engineering requirements of all application scenarios.

[0254] Table 3. Running time of ISRJ identification and Doppler filtering process running parameter table

[0255]

[0256] C. ISRJ countermeasure performance analysis.

[0257] The anti-ISRJ method of phase-coded signal is divided into two categories, namely waveform design method and signal processing method. The waveform design method uses the characteristic that the ISRJ jammer only intercepts part of the radar signal piece, and designs an orthogonal coding segment in the pulse in an offline manner, so that the interference echo is mismatched with the unintercepted signal piece. However, the waveform design method highly depends on the accuracy of the jammer parameter estimation. The signal processing method uses the distribution characteristics of ISRJ target in the range-Doppler spectrum, and eliminates the interference through real-time processing. The method provided in the present application belongs to the signal processing method. Based on this, the most advanced algorithms from the two categories are selected for competitive comparison. In the analysis process, the Doppler shift sensitivity of the signal processing method and the interference parameter estimation error of the waveform design method are comprehensively considered, and the superiority of the method provided in the present application is fully demonstrated.

[0258] Experiment 3: Unlike the processing of LFM signal, phase-coded signal is not suitable for time-frequency domain tool analysis. In this experiment, the related research on ISRJ suppression of single-pulse phase-coded waveform is compared with the method provided in the present application. In order to facilitate comparison, the parameter settings are as follows: phase-coded number is 500, bandwidth is 50 MHz, pulse width is , coherent accumulation pulse number is 1, Doppler data interval , intermediate frequency sampling frequency is 100 MHz, and Doppler axis discrete data number is 401. Other parameters are the same as those in experiment 2. Taking frequency shift retransmission ISRJ as an example, the phase-coded pulse train signal processing results of the two methods are drawn as shown in FIG. 6, under the conditions that the target Doppler shift is 0, and , respectively. Figure 16 Figure 16 ​The first line is the echo delay Doppler spectrum, and the second line is the Doppler filtering result. Figure 16 Columns 1-3 show a Doppler frequency shift of 0. and The processing results at that time.

[0259] It should be noted that this assumes the target's Doppler frequency shift will not reach... This is reasonable for airborne and spaceborne radars, but considering missile-borne radars, if a shorter wavelength carrier frequency is used, the Doppler shift may even exceed [a certain value]. The method proposed in this application can solve this problem.

[0260] from Figure 16 The following findings can be made: i) The Doppler frequency shift of the target manifests as a translation along the Doppler axis in the delayed Doppler spectrum. Under the three Doppler frequency shift conditions, the peak values ​​of the frequency-shifted false targets generated by ISRJ appear at 0.5 MHz, 0.53 MHz, and 0.57 MHz, respectively. ii) When the Doppler frequency shift of the target is less than... At 0.03 MHz, the output SIR processed by the comparison method is slightly worse than that of the method proposed in this application, but the difference is not significant. At this time, taking an S-band radar as an example, its radial velocity is roughly calculated to be less than that of hypersonic speed (Mach 5). iii) When the target is moving at hypersonic speeds, the situation is quite different. From Figure 16 As can be seen from column 3, the output SIR of the comparison method is significantly degraded. Considering that the power of the ISRJ jammer may be higher than the set value, the comparison method will be unable to correctly identify the target. iv) Under different Doppler frequency shifts, the method proposed in this application maintains stable output SIRs of 16.42 dB, 16.23 dB, and 16.03 dB, and the calculated SIRIFs are 18.88 dB, 18.76 dB, and 18.64 dB, respectively. This is attributed to the coarse detection process designed in this application, which extracts the approximate Doppler frequency shift of the target and embeds it into the Doppler filter formula, thereby providing more satisfactory interference suppression results for fine detection.

[0261] Experiment 4: Now we turn our attention to waveform design-based anti-ISRJ methods, delving into the impact of parameter estimation errors, input SIR, and modulation frequency on interference suppression to reveal the superior performance and robustness of the proposed method. The key to waveform design-based methods is to use the estimated interference parameters (i.e., sampling interval)... ) designed to embed orthogonal protection sub-pulse segments, and to achieve mismatch with the jammer signal at the receiver. Therefore, under the premise of accurate estimation of jammer parameters, the orthogonality of the waveform sequence determines the suppression effect of ISRJ. Here, we focus on the three most commonly used algorithms in the field of sequence set design, and select the most representative and advanced algorithms from them. The first is the multi-stage accelerated iterative sequential optimization (MS-AISO), the second is the efficient gradient (EG), and the third is the generalized maximum block improvement (GMBI). Then, following the anti-ISRJ waveform and filter construction strategy in the literature [Z. Ren, M. Jiang, L. Zhang, Orthogonal phase-frequency coded signal in a pulse against interrupted sampling repeater jamming, J. Eng. 2019(21) (November 2019) 7573–7576.] [C. Zhou, F. F. Li, and Q. H. Liu, “An adaptive transmitting scheme for interrupted sampling repeater jamming suppression,” Sensors., vol. 17, no. 11, pp. 2480–2496, 2017.], we carry out comparative experiments. In this experiment, the sequence set design method is used to optimize two groups of time discontinuous sequences with a phase coding length of 250, which are arranged alternately with an interval of 50. In this way, the number of sub-pulse segments is 10, and the width of the sub-pulse segment is . For ease of comparison, the target Doppler shift in the simulation is set to 0, and other parameters are consistent with Experiment 3.

[0262] To show the actual performance of each method in detail, we simulate the jamming suppression results when the input SIR fluctuates, the jammer parameter estimation error, and the modulation frequency changes, and plot them in Figures 17-19Please note that for the first two sets of simulations, it is assumed that the jammer is in direct relay mode; for the latter two sets of simulations, the SIR is set to -10 dB. Observing the simulation results, it is found that: 1) The waveform design method is sensitive to input SIR fluctuations. When the jamming power is low, the output SIR after pulse compression is close to that of the method proposed in this application, but once the jamming power increases, the output SIR will deteriorate significantly. When the input signal-to-noise ratio is less than -20 dB, the waveform design method is basically unable to distinguish the real target. The method proposed in this application has good robustness to input SIR fluctuations, slowly varying within the range of 12.68 dB ~ 19.69 dB. ii) In addition to the influence of input SIR fluctuations, the waveform design method heavily relies on the jamming parameters (i.e., sampling interval). Accurate estimation of the waveform pulse width is crucial. Even a small estimation error can cause ISRJ suppression to fail, especially when the waveform pulse width is... Sampling interval When the error is several times greater than the target value, the estimation error accumulates in the last slice, causing a mismatch between the interference signal and the receiving filter. Under the parameter settings of this application, the jammer can sample and relay 5 times within one pulse, so the estimation error must be less than 5% to correctly identify the real target. Moreover, the proposed method is completely unaffected by the estimation error. iii) When the jammer switches to frequency shift mode, the output SIR of the waveform design method fluctuates to varying degrees, with the MS-AISO method showing the least fluctuation, followed by the EG method, and the GMBI method showing the largest fluctuation, ranging from 8.03 dB to 12.60 dB. On the other hand, although the proposed method decreases between 0 MHz and 1 MHz, it quickly stabilizes around 15 dB, still ensuring accurate identification of the real target. Figure 17 Columns 1 and 2 show the processing results when SIR is 0 and -10, respectively, and column 3 shows the processing results when the output SIR is the same as the input SIR. Figure 18 Columns 1 and 2 show the results after processing with estimation errors of 2% and 3%, respectively. Column 3 shows the output SIR and... Estimation error. Figure 19 Columns 1 and 2 show the processing results when the jammer's frequency shift value is set to 1 MHz and 2 MHz, respectively. Column 3 shows the output SIR and frequency modulation value. The relationship.

[0263] D. Algorithm complexity analysis.

[0264] The computational complexity of the method proposed in this application is analyzed, covering asymptotic time complexity and asymptotic space complexity.

[0265] The time complexity of the ISRJ suppression method proposed in the application mainly depends on the two-dimensional S-CFAR detection, mean shift clustering and Doppler filtering process. The asymptotic time complexity of the two-dimensional S-CFAR processing is , wherein and are respectively the number of data points along the distance (delay) axis and the Doppler axis in the radar two-dimensional detection window. For the mean shift algorithm, the asymptotic time complexity is , wherein represents the number of target points detected in the previous step. The asymptotic time complexity of the Doppler filtering process is , due to the existence of the matrix inversion operation, but since the number of repeated forwarding is limited (for example, at most 3 times), the time actually spent on this operation is very small. In summary, the overall asymptotic time complexity of the method proposed in the application is , which can fully meet the real-time processing requirements in engineering applications. The asymptotic spatial complexity is mainly determined by the RDM in the radar detection window, which occupies .

[0266] In summary, the essence of the application is a PCPT signal processing method based on Doppler compensation. In order to reveal the distribution characteristics of false targets, the CAF of ISRJ is first established. On this basis, a two-step target detection process is designed, including coarse detection and fine detection. For the identification and suppression of ISRJ, two-dimensional S-CFAR algorithm, mean shift algorithm and Doppler filtering method are respectively proposed and used. The simulation results show that the method proposed in the application can effectively suppress various types of ISRJ interference, and has fast calculation speed, low requirement for radar system and no need for prior knowledge of interference parameters. The comparative experiments show that under various preset conditions, the method proposed in the application is superior to the most advanced algorithms of the existing waveform design type and signal processing type, and can be popularized to engineering applications.

[0267] Further, compared with the prior art, the application has the following advantages:

[0268] 1. The application can reveal the range-Doppler domain distribution characteristics of ISRJ: by deriving the ISRJ cross ambiguity function (CAF) of PCPT signal, it is found that the false targets are distributed in parallel along the Doppler axis in the range-Doppler domain, and the delay is fixed. Different types of ISRJ are represented as moving along the Doppler axis and copying along the delay axis in the range-Doppler domain. In actual signal processing, the application reproduces this characteristic through Doppler compensation.

[0269] 2、The application can robustly suppress various types of ISRJ: by using the distance-Doppler domain distribution characteristics, a two-dimensional switching constant false alarm rate (2D S-CFAR) detection algorithm is proposed, and combined with the original average shift algorithm used for image tracking, false target recognition is realized, wherein a Doppler filter is formulated. Thus, without any prior information interference, the input SIR fluctuation and target high-speed motion conditions are realized. Robust suppression of various types of ISRJ.

[0270] 4、The application has real-time processing efficiency: the asymptotic time complexity and asymptotic space complexity of the application mainly depend on the 2D S-CFAR algorithm. Simulation experiments show that by appropriately selecting the radar detection window, the operation efficiency can be as fast as milliseconds, thereby allowing engineering applications on various small platforms.

[0271] 5、Good scalability: since the application is based on PCPT signal processing, it can be combined with inter-pulse waveform diversity technology to realize synchronous suppression of FPFJ and ISRJ in coherent radar, and has broad application prospects.

[0272] In addition, the method proposed in the application can be extended to the cooperative effect of various types of pulse diversity waveforms, such as inter-pulse frequency coding waveforms, pulse diversity phase coding waveforms, or complex modulation waveforms, etc., so as to further enhance the ISRJ suppression effect while taking into account the sidelobe interference and FPFJ suppression.

[0273] Based on the same inventive concept, the embodiments of the application also provide an intermittent sampling and forwarding interference suppression device for implementing the intermittent sampling and forwarding interference suppression method described above. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme described in the above method, so the specific limitations in one or more intermittent sampling and forwarding interference suppression device embodiments provided below can refer to the limitations of the intermittent sampling and forwarding interference suppression method in the above text, which will not be repeated here.

[0274] In an exemplary embodiment, an intermittent sampling and forwarding interference suppression device is provided, comprising:

[0275] A radar receiver is configured to accept a phase-coded pulse train signal, and to sample, Doppler compensate, and pulse compress the phase-coded pulse train signal to obtain an in-phase signal and a quadrature signal.

[0276] A square law detector is connected to the radar receiver and is configured to obtain a power distribution function of an RD spectrum based on the in-phase signal and the quadrature signal.

[0277] The target coarse detector is connected with the square law detector, and is used for processing a power distribution function of the RD spectrum to obtain a range-Doppler matrix containing only target information. Based on the range-Doppler matrix, a range-Doppler matrix containing only false targets is obtained after excluding a true target protection area. A two-dimensional switch constant false alarm rate (S-CFAR) detection algorithm is used to detect the range-Doppler matrix containing only false targets to obtain a two-dimensional S-CFAR detection result, and delay coordinates of the false targets are extracted. A mean shift algorithm is used to cluster the delay coordinates of the false targets to obtain a false target cluster center formed by the intermittent sampling and retransmission interference. A window function is constructed according to the false target cluster center, and the two-dimensional S-CFAR detection result is processed to eliminate the false targets, so as to obtain a coarse detection result of the true target.

[0278] The oblique projection operator obtaining module is connected with the target coarse detector, and is used for constructing a Doppler vector space of the false targets and a Doppler vector space of the true target based on the false target cluster center and a Doppler frequency shift of the true target extracted from the coarse detection result of the true target. An oblique projection operator along the Doppler vector space of the false targets to the Doppler vector space of the true target is obtained.

[0279] The Doppler filter is connected with the oblique projection operator obtaining module, and is used for performing Doppler filtering based on the oblique projection operator to obtain a one-dimensional pulse compression result.

[0280] The target fine detector is connected with the Doppler filter, and is used for analyzing the one-dimensional pulse compression result to obtain a final detection result of the true target.

[0281] In an exemplary embodiment, a computer device can be provided, which can be a server or a terminal. The computer device includes a processor, a memory, an input / output interface (I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for running the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store intermittent sampling and retransmission interference suppression data. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals through a network connection. The computer program is executed by the processor to implement an intermittent sampling and retransmission interference suppression method based on phase-coded pulse train signal processing.

[0282] In an exemplary embodiment, a computer device is provided, comprising a memory and a processor, the memory storing a computer program, and the processor implementing the steps in the above method embodiments when executing the computer program.

[0283] In an exemplary embodiment, a computer readable storage medium is provided, storing a computer program, and the computer program implementing the steps in the above method embodiments when executed by a processor.

[0284] In an exemplary embodiment, a computer program product is provided, comprising a computer program, and the computer program implementing the steps in the above method embodiments when executed by a processor.

[0285] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in the present application are all information and data authorized by the user or authorized by all parties, and the collection, use and processing of related data need to comply with relevant regulations.

[0286] It can be understood by those skilled in the art that all or part of the processes in the above method embodiments can be completed by a computer program instructing related hardware, and the computer program can be stored in a non-volatile computer readable storage medium. When the computer program is executed, it can include the processes of the above method embodiments. Any reference to memory, database or other medium used in the embodiments provided by the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical storage, high-density embedded non-volatile memory, resistive memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration but not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0287] The database involved in each of the embodiments provided in the present application can include at least one of a relational database and a non-relational database. The non-relational database can include a distributed database based on a blockchain, and the like, without being limited thereto. The processor involved in each of the embodiments provided in the present application can be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, and the like, without being limited thereto.

[0288] The technical features of the above embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above embodiments are not described, but it should be considered that any combination of the technical features is within the scope of the present disclosure, as long as there is no contradiction.

[0289] The principles and implementation manners of the present application are described by using specific examples in the present application. The above embodiments are only used to help understand the method of the present application and its core idea. Meanwhile, for those skilled in the art, the specific implementation manners and application ranges will be changed according to the idea of the present application. In summary, the content of the present description should not be understood as a limitation of the present application.

Claims

1. An intermittent sampling repeater jamming rejection method based on phase-coded pulse train signal processing, characterized in that, The intermittent sampling retransmission interference suppression method comprises: sampling, Doppler compensation and pulse compression on the phase-coded pulse train signal to obtain an in-phase signal and a quadrature signal; obtaining a power distribution function of an RD spectrum based on the in-phase signal and the quadrature signal; processing the power distribution function of the RD spectrum to obtain a range-Doppler matrix containing only target information; obtaining a range-Doppler matrix containing only false targets based on the range-Doppler matrix after excluding a true target protection area; detecting the range-Doppler matrix containing only false targets by using a two-dimensional switching constant false alarm rate detection algorithm to obtain a two-dimensional S-CFAR detection result, and extracting delay coordinates of the false targets; clustering the delay coordinates of the false targets by using a mean shift algorithm to obtain a false target cluster center formed by intermittent sampling retransmission interference; processing the two-dimensional S-CFAR detection result by using a window function constructed according to the false target cluster center to eliminate false targets, and obtaining a coarse detection result of true targets; constructing a false target Doppler vector space and a true target Doppler vector space based on the false target cluster center and a true target Doppler shift extracted from the coarse detection result of the true targets; obtaining an oblique projection operator along the false target Doppler vector space to the true target Doppler vector space, and performing Doppler filtering based on the oblique projection operator to obtain a one-dimensional pulse compression result; the one-dimensional pulse compression result contains only a final detection result of true targets.

2. The phase-encoded train signal processing based intermittent sampling repeating jammer rejection method of claim 1, wherein, The power distribution function of the RD spectrum is expressed as: P(t,f) = |y(t,f)| 2 ; wherein P(t,f) represents the power of the RD spectrum, and y(t,f) represents a signal obtained by performing coherent accumulation on echo signals received within one coherent processing interval; The signal obtained by performing coherent accumulation is obtained based on the in-phase signal and the quadrature signal.

3. The phase-encoded train signal processing based intermittent sampling repeating jammer rejection method of claim 1, wherein, The range-Doppler matrix containing only false targets is expressed as: where F d,s is the maximum Doppler shift of the real target, adjusted according to the waveform parameters; P false (t,f) is the range-Doppler matrix, f is the frequency shift, P d (t,f) is the range-Doppler matrix containing only target information, otherwise represents otherwise, if represents if.

4. The phase-encoded train signal processing based intermittent sampling repeating jammer rejection method of claim 1, wherein, The coarse detection result of the true targets is expressed as: P coarse (t,f) = w(t)P d (t,f); where P coarse (t,f) is the coarse detection result of the true target, w(t) is the window function, P d (t,f) is the range-Doppler matrix containing only target information.

5. The phase-encoded train signal processing based intermittent sampling repeating jammer rejection method of claim 1, wherein, The oblique projection operator is expressed as: wherein is a slant projection operator, U s is the Doppler vector space of true targets, H is the conjugate transpose, is the orthogonal projection of the Doppler vector space of false targets, U J is the Doppler vector space of false targets.

6. The phase-encoded train signal processing based intermittent sampling repeating jammer rejection method of claim 1, wherein, In the process of performing Doppler filtering based on the oblique projection operator, a Doppler filter is constructed by using the oblique projection operator to perform Doppler filtering processing.

7. The phase-encoded train signal processing based intermittent sampling repeating jammer rejection method according to claim 6, characterized in that, The Doppler filter is expressed as: where w d is a Proler filter, is a slant projection operator, U s is the Doppler vector space of true targets, H is the conjugate transpose, U J is the Doppler vector space of false targets.

8. The phase-encoded train signal processing based intermittent sampling repeating jammer rejection method of claim 6, wherein, The one-dimensional pulse compression result is expressed as: where y filtered (t) is the one-dimensional pulse compression result, w d is a Proler filter, y vec (t) is the Doppler dispersed data vector, and H is the conjugate transpose.

9. The phase-encoded train signal processing based intermittent sampling repeating jammer rejection method of claim 1, wherein, The false target Doppler vector space is expressed as: where U J is the Doppler vector space of false targets, y vec (*) is the Doppler discrete data vector, c1is the first cluster center of false targets, c k is the kth cluster center of false targets, H is the conjugate transpose, F s is the radar intermediate frequency sampling frequency.

10. The phase-encoded train signal processing based intermittent sampling repeating jammer rejection method of claim 1, wherein, The true target Doppler vector space is expressed as: where U s is the Doppler vector space of true targets, N d is the number of 0 elements, and T is the transpose.

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