Intermittent sampling and forwarding interference suppression method based on phase coding pulse train signal processing

Abstract

The invention 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, and the method comprises the steps: processing a power distribution function of an RD frequency spectrum to obtain a distance-Doppler matrix only containing target information, eliminating a true target protection region, and obtaining a distance-Doppler matrix containing target information; a two-dimensional switching constant false alarm rate detection algorithm is adopted to detect the distance-Doppler matrix only containing the false target, and delay coordinates of the false target are extracted; the delay coordinates of the false targets are clustered through a mean shift algorithm, a window function is constructed according to the clustering center of the false targets, the two-dimensional S-CFAR detection result is processed, the false targets are removed, and a rough detection result of the true targets is obtained; doppler vector spaces of a false target and a true target are constructed, an oblique projection operator is obtained, Doppler filtering is carried out, and a one-dimensional pulse compression result only containing a final detection result of the true target is obtained. According to the invention, fine detection when clutter or interference power is relatively high can be realized.

Description

Technical Field

[0001] This application relates to the field of data processing, and in particular, to an interrupted sampling and repeater jamming suppression method based on phase-coded pulse train signal processing. Background Art

[0002] Interrupted sampling repeater jamming (ISRJ) has good coherence, flexible modulation, and fast response capabilities, but it will simultaneously produce suppression and deception effects at the radar receiving end, seriously weakening the radar detection ability. However, currently, most of them achieve interference suppression by using interference parameters and cannot achieve fine detection when the clutter or interference power is high. Summary of the Invention

[0003] The purpose of this application is to provide an interrupted sampling and repeater jamming suppression method based on phase-coded pulse train signal processing, which can achieve fine detection when the clutter or interference power is high.

[0004] To achieve the above purpose, this application provides the following solutions:

[0005] In the first aspect, this application provides an interrupted sampling and repeater jamming suppression method based on phase-coded pulse train signal processing, including:

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

[0007] Based on the in-phase signals and the quadrature signals, the power distribution function of the RD spectrum is obtained;

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

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

[0010] The two-dimensional switched 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 the delay coordinates of the false targets are extracted;

[0011] The delay coordinates of the false targets are clustered by the mean shift algorithm to obtain the false target clustering center formed by the interrupted sampling and repeater jamming;

[0012] According to the false target clustering center, a window function is constructed to process the two-dimensional S-CFAR detection result, eliminate false targets, and obtain a rough detection result of the true target;

[0013] Construct a Doppler vector space for false targets and a Doppler vector space for true targets based on the false target clustering centers and the Doppler frequency shifts of the true targets extracted from the rough detection results of the true targets.

[0014] Obtain an oblique projection operator from the Doppler vector space of the false targets to the Doppler vector space of the true targets, and perform Doppler filtering 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 results of the true targets.

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

[0016] This application provides an intermittent sampling and repeater jamming suppression method based on phase-coded pulse train signal processing. By adopting a two-dimensional switching constant false alarm rate (2D S-CFAR) detection algorithm and combining the mean shift algorithm originally used for image tracking, false target recognition is achieved. Coarse detection of targets is realized through window operations. Further, Doppler filtering is performed using an oblique projection operator, which can suppress ISRJ while maintaining the coherent integration gain, and achieve fine detection when the clutter or interference power is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of this application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0018] Figure 1 It is a schematic flowchart of an intermittent sampling and repeater jamming suppression method based on phase-coded pulse train signal processing provided by an embodiment of this application;

[0019] Figure 2 It is a normalized AF array diagram of a bit-coded pulse signal provided by an embodiment of this application;

[0020] Figure 3 It is a schematic diagram of ISRJ normalized CAF provided by another embodiment of this application;

[0021] Figure 4 It is a schematic diagram of the range-Doppler spectrum of the echo provided by an embodiment of this application;

[0022] Figure 5 It is a schematic flowchart of the target detection process of a two-dimensional S-CFAR processor provided by an embodiment of this application;

[0023] Figure 6 Schematic diagram of the delayed Doppler spectrogram after echo reconstruction under ISRJ interference provided by an embodiment of the present application;

[0024] Figure 7 Schematic diagram of the delayed Doppler matrix after 2D-CFAR detection processing under direct-forwarding ISRJ provided by an embodiment of the present application;

[0025] Figure 8 Schematic diagram of the delayed Doppler matrix after 2D-CFAR processing under frequency-shifted ISRJ provided by an embodiment of the present application;

[0026] Figure 9 Schematic diagram of the delayed Doppler matrix after 2D-CFAR processing under repeat-forwarding ISRJ provided by an embodiment of the present application;

[0027] Figure 10 Schematic diagram of the result of the coarse detection process under direct-forwarding ISRJ provided by an embodiment of the present application;

[0028] Figure 11 Schematic diagram of the result of the coarse detection process under frequency-shifted ISRJ provided by an embodiment of the present application;

[0029] Figure 12 Schematic diagram of the result of the coarse detection process under repeat-forwarding ISRJ provided by an embodiment of the present application;

[0030] Figure 13 Schematic diagram of the Doppler filtering result of direct-forwarding ISRJ provided by an embodiment of the present application;

[0031] Figure 14 Schematic diagram of the Doppler filtering result of frequency-shifted forwarding ISRJ provided by an embodiment of the present application;

[0032] Figure 15 Schematic diagram of the Doppler filtering result of repeat-forwarding ISRJ provided by an embodiment of the present application;

[0033] Figure 16 Schematic diagram of the comparison of the processing results of Experiment 3 provided by an embodiment of the present application;

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

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

[0036] Figure 19Schematic diagram for comparing echo processing results of a jammer under different frequency shift modulation values provided by an embodiment of the present application. Detailed implementation manners

[0037] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a 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 those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0038] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0039] In an exemplary embodiment, the present application provides an intermittent sampling and forwarding interference suppression method based on phase-coded pulse train signal processing. This method is executed by a computer device, specifically, it can be executed alone by a computer device such as a terminal or a server, or jointly executed by a terminal and a server. In the embodiments of the present application, this method is described by taking its application to a server as an example. As Figure 1 shown, this method includes:

[0040] Step 100: Sample, Doppler compensate, and pulse compress the phase-coded pulse train signal to obtain in-phase signals and quadrature signals.

[0041] Step 101: Obtain the power distribution function of the RD spectrum based on the in-phase signals and quadrature signals. The expression of the power distribution function of the RD spectrum can be seen in the following formula (42).

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

[0043] Step 103: After excluding the true target protection area based on the range-Doppler matrix, obtain a range-Doppler matrix containing only false targets. Among them, the true target protection area can be excluded based on the following formula (49).

[0044] Step 104: Use a two-dimensional switched constant false alarm rate detection algorithm to detect the range-Doppler matrix containing only false targets to obtain a two-dimensional S-CFAR detection result, and extract the delay coordinates of the false targets.

[0045] Step 105: Cluster the delay coordinates of the false targets through a mean shift algorithm to obtain the false target clustering center formed by intermittent sampling and forwarding interference.

[0046] Step 106: Construct a window function based on the false target clustering center, process the two-dimensional S-CFAR detection result, eliminate the false targets, and obtain the rough detection result of the true targets. Among them, the rough detection result can be obtained by further performing a window operation on the true targets according to the following formula (55).

[0047] Step 107: Based on the false target clustering center and the Doppler frequency shift of the true targets extracted from the rough detection result of the true targets, construct the Doppler vector space of the false targets and the Doppler vector space of the true targets. Among them, the Doppler vector spaces of the false targets and the true targets can be constructed according to the following formula (57) and formula (59) respectively.

[0048] Step 108: Obtain the oblique projection operator from the Doppler vector space of the false targets to the Doppler vector space of the true targets, and perform Doppler filtering based on the oblique projection operator to obtain the one-dimensional pulse compression result. The one-dimensional pulse compression result only contains the final detection result of the true targets. Among them, Doppler filtering can be implemented according to the following formula (63).

[0049] During the implementation process, the ISRJ cross-ambiguity function (CAF) of the phase-coded pulse train (PCPT) signal based on Doppler compensation is derived, and it is found that the false targets are parallelly distributed along the Doppler axis in the range-Doppler domain and the delay is fixed. Different types of ISRJ are manifested as moving along the Doppler axis and replicating along the delay axis in the range-Doppler domain. Based on this, using the distribution characteristics in the range-Doppler domain, the above steps 100 - 108 are implemented. By proposing a two-dimensional switched constant false alarm rate (2D S-CFAR) detection algorithm and combining the original mean shift algorithm used for image tracking, false target recognition is achieved. Coarse detection of the targets is realized through window operations, and further Doppler filtering is performed using the oblique projection operator to achieve fine detection when the clutter or interference power is high.

[0050] Furthermore, combined with the simulation results, the design idea and specific implementation process of the above intermittent sampling and repeater interference suppression method provided by this application are described.

[0051] (1) Analysis of phase-coded pulse sequence signals.

[0052] A. Signal model.

[0053] Consider a pulse sequence waveform s(t) with N pulses within a coherent processing interval (CPI):

[0054]

[0055] In the formula, Tr Within the pulse repetition interval, \(t\) is the time index, and \(N\) is the number of pulses within one coherent processing interval. \(s\) p (t) is a phase-coded single pulse signal with a length of \(T\), expressed as:

[0056]

[0057] In the formula, \(M\) is the number of phase-coded sub-pulses within one pulse. \(x(m)\) is the modulation code sequence, expressed as:

[0058]

[0059] In the formula, \(j\) is the imaginary unit, is the sub-pulse modulation phase.

[0060] This application adopts a random phase coding sequence. \(p\) m (t) is a rectangular shaping pulse with a duration of \(T\) c \(=T / M\), expressed as:

[0061]

[0062] In the formula, \(T\) is the pulse width. \(rect()\) is the rectangular function, defined as:

[0063]

[0064] B. Ambiguity function analysis.

[0065] The AF is a very effective signal analysis tool, which can be used to analyze the waveform resolution, sidelobe level, and range-Doppler characteristics of the echo. The AF can be written as:

[0066]

[0067] In the formula, \(\chi(\tau,f\) d ) is the AF of \(s\) p (t), \(\tau\) is the delay, \(f\) d is the Doppler frequency, \(s\) * (t - \(\tau\)) is the echo signal at \(t - \tau\), and \(e\) is the natural logarithm.

[0068] Due to the interrupted sampling repeater, the jammer slices, samples, and forwards the intercepted signal within one pulse width, so there is no need to analyze the cycle period ambiguity function. This application only considers the central AF, that is, \(|\tau|\leq T\) r , based on this, substituting formula (1) into formula (6), we get:

[0069]

[0070] In the formula, \(s\) p(t - nT r ) is the transmitted reference signal, s p (t - nT r ) is the radar signal.

[0071] To simplify the calculation, let t′ = t - nT r , then formula (7) is transformed into:

[0072]

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

[0074]

[0075] In the formula, p m′ (t - τ) is the rectangular window function, x * (m′) is the modulation code sequence at the code position index m′, and m′ is the code position index.

[0076] For ease of analysis, the time delay is discretized into the time grid {τ = kT c}, k ∈ {-M + 1,..., M - 1}, and the ambiguity function χ p (τ, f d ) of the single - pulse signal is calculated at τ = kT, and we have:

[0077]

[0078] Among them, T c is the sub - pulse width, x * (m - k) is the modulation code sequence at the code position index m - k, δ m′+k,m is the Kronecker delta. If m = n, then δ m,n = 1, otherwise δ m,n = 0. Substituting formula (10) into formula (8), we can obtain:

[0079]

[0080] In the formula, is the discrete AF of the phase - coded single - pulse signal s p (t), defined as:

[0081]

[0082] To understand this ambiguity function, first observe the zero - Doppler and zero - delay responses. The zero - Doppler response is obtained by setting f d = 0, and we get:

[0083]

[0084] where χ(kT c , 0) is the zero Doppler section of the ambiguity function of the burst signal.

[0085] By selecting a phase-coded sequence with a "thumbtack-shaped" ambiguity function it is possible to obtain:

[0086] |χ(T c , 0)| ≈ 0 (14)

[0087] This means that the range resolution of the PCPT signal s(t) is cT c / 2. Similarly, the Doppler resolution can be obtained by setting k = 0, giving:

[0088]

[0089] where χ(0, f d ) is the zero delay section of the ambiguity function of the burst signal. is the zero delay section of the discrete ambiguity function of the single pulse signal, and there is:

[0090]

[0091] Therefore, the Doppler resolution of the PCPT signal s(t) is 1 / NT r , and the peak repeats with a period of 1 / T r , and this behavior is weighted by the sinc function, and its first zero is 1 / T c . In addition, it is not difficult to find that the peak of the ambiguity function only appears at {(τ, f d )|τ = 0, f d = 0}. Figure 2 shows the normalized AF of the phase-coded pulse signal, as well as the zero Doppler cut and zero delay cut, where Figure 2 the first row of is the phase-coded single pulse signal, and the second row is the PCPT signal. The first column is the 3D view, the second column is the zero Doppler section, and the third column is the zero delay section. In this simulation, N = 64, M = 500, B = 50 MHz, T r = 100 μs, T = 10 μs. It can be seen from Figure 2 that the simulation results are in complete agreement with the mathematical analysis.

[0092] (II) ISRJ analysis.

[0093] A. Interference signal model.

[0094] When the interrupted sampling repeater, the jammer slices, samples, and forwards the intercepted signal, sometimes an additional frequency is added, thus forming a false target. The sampling of the jammer can be characterized as p(t):

[0095]

[0096] Wherein, T 0 is the slice sampling width, T s is the sampling interval, δ(*) is the Dirac function, and l is the interference slice count. Generally, when the jammer detects the leading edge of the radar signal pulse, the jammer starts slicing, sampling, and forwarding at a certain time interval until the trailing edge of the radar signal pulse is detected and then stops. When a new pulse leading edge is detected, this process continues. Thus, the signal s sample (t) intercepted by the jammer can be described by the following formula:

[0097]

[0098] Wherein, p(t - nT r ) is the sampling function of the jammer.

[0099] According to the forwarding strategy and the presence or absence of frequency shift, the most common ISRJs can be divided into three types.

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

[0101]

[0102] Wherein, s direct is the mathematical model of the direct forwarding interference.

[0103] The second type is the repeat forwarding ISRJ. This type of jammer will repeat and forward the intercepted signal within the sampling interval, and its mathematical model is (ignoring the jammer delay):

[0104]

[0105] Wherein, s repeated (t) is the mathematical model of the repeat forwarding interference, p(t - nT r - qT 0 ) is the sampling function of the jammer at t - nT r - qT 0 and s p (t - nT r - qT 0 ) is the radar signal at t - nT r - qT 0 . Q is the number of times the jammer forwards. As the number of repeat forwarding times increases.

[0106] The third type is the frequency shift ISRJ. The operating characteristics of the ISRJ jammer determine that the false target it generates will at least lag behind the true target by T0 , for radars that use LFM signals, this appears as a change in the target frequency point after pulse compression at the receiving end. Therefore, frequency shift modulation is proposed for the slices of the intercepted signal to move the false target in front of the true target. The mathematical model of frequency shift ISRJ is (ignoring the delay of the jammer):

[0107]

[0108] In the formula, s f-shift (t) is the mathematical model of frequency shift repeater jamming, and f J is the modulation frequency.

[0109] The above three types of ISRJ can be uniformly expressed as:

[0110]

[0111] Among them, s J (t) is the unified mathematical model description of intermittent sampling repeater jamming. s J,n (t) is the interference signal model within a single radar pulse, and there is:

[0112]

[0113] It should be noted that when s J (t) is direct repeater ISRJ, Q = 1, and f J = 0. When s J (t) is repeated repeater ISRJ, Q > 1, and f J = 0. When s J (t) is frequency shift ISRJ, f J ≠0. Among them, p(t)s p (t) can be deduced as:

[0114]

[0115] Among them, a l is the coefficient of the interference model, and there is:

[0116]

[0117] In the formula, f s = 1 / T s , sa(t) = sin(t) / t. Therefore, formula (23) can be deduced as:

[0118]

[0119] B. Cross ambiguity function analysis.

[0120] To deeply analyze the false target distribution characteristics generated by ISRJ and its induction effect on radars using PCPT signals, mathematical analysis was first carried out using CAF. s J The CAF of χ J (τ, f d ) can be written as:

[0121]

[0122] This application only needs to consider the central CAF. Substituting formula (1) and formula (22) into formula (27), we get:

[0123]

[0124] In the formula, is, is.

[0125] To simplify the calculation, let t′ = t - nT r , and then formula (28) is transformed into:

[0126]

[0127] From the above derivation results, it can be seen that the CAF of ISRJ is the superposition of a series of AFs with different delays and Doppler frequency shifts. Directly forwarding ISRJ (Q = 1, f J = 0) will generate multiple peaks with equal frequency intervals f s in the zero-delay cut. Repeatedly forwarding ISRJ (Q > 1, f J = 0) will copy and shift the CAF of directly forwarding ISRJ Q - 1 times, accompanied by a time delay T 0 . The frequency-shifted ISRJ (f J ≠ 0) will add an additional Doppler frequency shift f J to the CAF. Figure 3 shows the CAF shapes of three types of ISRJ. Through analysis, it is not difficult to find that the distribution of false targets is consistent with the mathematical analysis. In this simulation, T s = 2 μs, T 0 = 0.5 μs, and the other parameters are the same as those in the previous experiment. In addition, the number of repeated forwarding times Q = 3 is set, the number of frequency-shifted forwarding times Q = 1 is set, and the frequency shift f J = 0.5 MHz. Figure 3 In, the first column is directly forwarding ISRJ, the second column is repeatedly forwarding ISRJ, and the third column is frequency-shifted ISRJ. The first row is the 3D view, and the second row is the 2D view.

[0128] (III) ISRJ Reconstruction and Elimination Based on Pulse Train Signal Processing.

[0129] According to the previous analysis and simulation, it is known that the false targets generated by ISRJ have significant distribution differences in the range-Doppler (RD) spectrum, manifested as a series of peaks arranged along the Doppler dimension. Considering that the amplitude of ISRJ is usually at least twice that of the target echo amplitude, these peaks will induce the radar to track false targets. Therefore, in order to utilize these characteristics, a Doppler compensation technique is proposed to reconstruct the interference peaks before pulse compression and identify the location of ISRJ according to the distribution characteristics of false targets. Next, the ISRJ reconstruction method based on Doppler compensation will be introduced first.

[0130] A. ISRJ Reconstruction.

[0131] Suppose there is a target with a time delay and Doppler shift of τ s and f d,s . An ISRJ jammer is installed near the target, with a forwarding delay of τ J and a frequency shift of f J , where τ J - τ s ≥T 0 . Then the echo signal at the radar receiver end can be characterized as:

[0132]

[0133] In the formula, r(t) is the echo signal at the radar receiver end, r s,n (t) is the radar signal echo, and r J,n (t) is the interference signal echo.

[0134] Target echo, that is, the ISRJ signal. r s,n (t) and r J,n (t) are respectively expressed as:

[0135]

[0136]

[0137] In the formula, A s is the complex amplitude of the target echo, A J is the complex amplitude of the ISRJ signal, and f d,s is the true target Doppler shift. In order to reconstruct the RD spectrum of the interference signal, Doppler compensation is performed on the given signal r s,n (t) + r J,n (t), and we have:

[0138]

[0139] In the formula, r c,n (t) is the echo signal at the radar receiver end after Doppler compensation reconstruction.

[0140] The signal after Doppler compensation is subjected to pulse compression processing to obtain:

[0141]

[0142] where y n (t,f) is the signal after pulse compression processing.

[0143] To simplify the calculation, let τ′ = τ - nT r , then formula (34) is transformed into:

[0144]

[0145] where A s (n,f) is the radar echo coefficient, and A J (n,f) is the interference echo coefficient, and we have:

[0146]

[0147]

[0148] Then, coherent integration is performed on the echoes received within one CPI, and we have:

[0149]

[0150] Taking frequency shift ISRJ as an example, where Q = 1, f J = 0.5 MHz. Then the range-Doppler spectrum of the echo is plotted, as shown in Figure 4 . In this simulation, it is assumed that the target range is 2000 m, and f d,s = 50 kHz, τ J - τ s = 0.5 μs, and other parameters are the same as those in the previous text. Additionally, the SNR and SIR are set to 10 dB and -15 dB respectively. Figure 4 On the left is the three-dimensional view, and on the right is the two-dimensional view.

[0151] From Figure 4 it can be seen that frequency shift ISRJ generates a set of peaks along the Doppler axis direction, and due to the frequency shift, these peaks are shifted, and the maximum amplitude appears at -(f J + f d,s ). On the other hand, the real target presents a single, lower-amplitude peak, which is at a distance of c(τ J - τ s ) / 2 from the false target peak group.

[0152] Therefore, this application proposes a method for adaptively identifying false targets generated by ISRJ. That is, by utilizing the characteristic that ISRJ can generate multiple spectral peaks, a group of spectral peak positions are extracted on the range-Doppler (RD) spectrum through a suitable constant false alarm rate (CFAR) detection method, and they are clustered to obtain the delay-axis coordinates where the false targets are located, thus completing the process of false target identification. Further, according to the identification result, a window operation is performed on the range-Doppler matrix (RDM) after CFAR detection to eliminate ISRJ and achieve a rough detection of true targets. However, for phased array (PD) radars used in airborne or spaceborne surveillance, missile seekers, and battlefield surveillance, a large-amplitude clutter background may cause unnecessary false alarms. Therefore, this application also performs Doppler filtering to achieve a fine detection of real targets.

[0153] B. Target detection under ISRJ: A group of spectral peak positions are extracted on the RD spectrum through a suitable constant false alarm rate (CFAR) detection method, and they are clustered to obtain the delay-axis coordinates where the false targets are located, thus completing the process of false target identification.

[0154] In the process of processing PCPT signals, radar target detection often faces a non-uniform background, that is, there may be various 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, excessive false alarms during clutter transitions, and the inability to detect targets near the clutter edge. 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 governed by an exponential distribution. When considering interferences and clutters, this assumption is invalid.

[0155] To overcome the above disadvantages, this application adopts an algorithm that utilizes the statistical characteristics of samples in the test cell to filter suitable reference samples, called the switching constant false alarm rate (S-CFAR) processor algorithm. Compared with CA-CFAR in a uniform background, the S-CFAR algorithm can be adjusted to have almost no degradation in detection performance. At the same time, when used for target detection at the clutter edge in a non-uniform background, it is superior to sorting-based constant false alarm rate processing algorithms. In addition, the S-CFAR algorithm allows a larger number of interfering targets and is easier to implement because it does not involve sorting operations. Due to the excellent detection performance and time efficiency of S-CFAR, it is extended to two-dimensional target detection under ISRJ to achieve a rough detection of true and false targets.

[0156] The standard S-CFAR includes the following two main steps.

[0157] Step 1: The 2N ref cells in the reference window are divided into two groups, and there are:

[0158]

[0159] That is, if the reference cell z k is less than αz, it belongs to set S 0 , otherwise it belongs to set S 1 . Where z is the amplitude of the test unit and α is the scale factor.

[0160] Step 2: n 0 represents the cardinality of set S 0 , and when the following conditions are met, it is determined that the target exists:

[0161]

[0162] Or:

[0163]

[0164] In the formula, β 0 and β 1 are threshold multipliers, and N T is the threshold integer.

[0165] During the operation of the S-CFAR processor, n 0 > N T means that the test unit may contain a phase-coded pulse train signal with a relatively large amplitude. To improve the detection probability, the reference cells in set S 0 are selected to evaluate the detection threshold. n 0 ≤ N T means that the test unit may contain noise or clutter samples with a relatively small amplitude. 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 an operation enables the S-CFAR processor to utilize the samples in set S 1 , rather than discarding the reference samples with a relatively large amplitude when n 0 is small, thereby reducing the false alarm rate at the clutter edge.

[0166] Furthermore, taking advantage of the excellent detection performance of the S-CFAR processor, it is extended to solve the two-dimensional multi-target detection problem 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 relatively simple to calculate the squared magnitude of the test sample (by summing the squares of the real and imaginary parts), a square-law detector is recommended, and it outputs the power of the RD spectrum, expressed as:

[0167] P(t,f) = |y(t,f)| 2 (42)

[0168] Wherein, P(t,f) represents the power of the RD spectrum, and y(t,f) represents the signal after coherent accumulation of the received echo signal within a coherent processing interval.

[0169] Subsequently, the 2D S-CFAR processor receives the input from the range-Doppler video samples detected by the square-law, and stores the cells within 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. 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 for which detection decisions need to be given. Thus, the principle block diagram of the two-dimensional S-CFAR processor target detection under the action of ISRJ can be drawn, as Figure 5 shown.

[0170] Based on the above description, the scaling factor α, the threshold multiplier β 0 and β 1 , the threshold integer N T remain undetermined. For the 2D multi-target detection problem, the method of dealing with the one-dimensional target detection problem can be referred to. Based on this, the detection probability of the two-dimensional S-CFAR algorithm is:

[0171]

[0172] Wherein, V(0,n), P d (N ref ,N T ,α,β 0 ,β 1 ,σ), N ref , W(0,n) are all intermediate quantities without special meanings. σ is the signal-to-noise ratio of the cell sample.

[0173] Among them,

[0174]

[0175]

[0176] ρ 0,n =(2N ref -n 0 +n)α(47)

[0177]

[0178] where ρ 0,n and ζ 0,n are also intermediate quantities and have no special meaning.

[0179] Equation (43) is the formula representation of the detection probability of the S-CFAR algorithm in a homogeneous background. By assigning σ = 0, Equation (43) becomes the expression of 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 therefrom. Since the interference power is usually unknown, during the radar system design process, it is often necessary to optimize the parameters according to the simulation results.

[0180] Generally, the two-dimensional S-CFAR processor after adjustment processes the power distribution function P(t,f) in Equation (42) to obtain an RDM that only contains target information (including true targets and false targets), denoted as P d (t,f). When there are multiple true targets, new clustering centers may be formed in the next step of this application. To avoid identifying true targets as interference signals, it is recommended to exclude possible true targets in advance. A true target protection area is created along the delay axis and appropriately widened along the Doppler axis to obtain an RDM that only contains false targets, denoted as P false (t,f):

[0181]

[0182] where F d,s is the maximum possible Doppler frequency shift of the true target and can be adjusted according to the waveform parameters. In this application, F d,s is assigned a value of 2 / T. Then the delay axis coordinates of the false targets in P false (t,f) are extracted into a set It should be noted that since the false targets formed by ISRJ are evenly distributed along the Doppler axis at an interval of f s , usually several times that of F d,s , the above operation eliminates at most one false target peak on the same delay cut, and has little impact on the subsequent interference clustering.

[0183] C. ISRJ identification.

[0184] With the targets detected by the RD spectrum, interference identification can be carried out. In fact, effective discrimination can be achieved only by performing one-dimensional clustering because there is no overlap between false targets and true targets in the delay dimension. However, there is still another problem, that is, the selection of the number of clusters. Generally speaking, traditional clustering methods, such as the k-means type algorithm and its optimized versions, require the number of clusters to be determined in advance. This is feasible for most application scenarios, but not for the interference clustering of this application because it means the prediction of the ISRJ type and the number of relays, which is unrealistic.

[0185] A clustering tracking algorithm widely used in recent years in research fields such as image segmentation, target tracking, and computer vision is called the mean shift algorithm. Its iterative process is simple, the convergence speed is fast, it does not depend on any prior knowledge, nor does it depend on a predetermined number of clusters. In addition, the well-known k-means type algorithm has been proven to be a special case of the mean shift algorithm. This application utilizes the excellent characteristics of the mean shift algorithm and extends it to the field of interference clustering for identifying the positions of false targets formed by ISRJ.

[0186] Definition 1: For each point t in the set of delay axis coordinates of the price list h , the multivariate kernel density estimator is defined as

[0187]

[0188] where w: Ω t →[0,∞] represents the weight function, represents the kernel function, h is the bandwidth of the kernel function K, is the set of real numbers. Considering that the main lobe width along the delay axis of χ(τ,f d ) is 2T c , h is recommended to be set no less than 2T c . Unless otherwise specified, this application sets the weight function w(t h ) to 1.

[0189] This application adopts a Gaussian kernel function, which is defined as K(t):

[0190]

[0191] Define a contour function

[0192]

[0193] Then there is:

[0194] K(t) = k(||t||2 ) (53)

[0195] Define the mean shift based on the Gaussian kernel K as follows:

[0196]

[0197] Equation (54) is the gradient ascent direction at t, where G(t) = g(||t|| 2 ), g(t) = -k'(t), and the kernel K is called the shadow of the kernel G. Now, the implementation steps of the mean shift algorithm are given, including:

[0198] Step 1: For each t ∈ Ω t , calculate m(t).

[0199] Step 2: For all t ∈ Ω t , execute t ← m(t).

[0200] Step 3: When |m(t) - t| < ∈, the algorithm converges, and the clustering center of the false targets formed by ISRJ is output, denoted as

[0201] Accordingly, based on the clustering center construct a window function to process the two-dimensional S-CFAR detection result, so as to eliminate false targets and obtain the rough detection result P coarse (t, f), and there is:

[0202] P coarse (t, f) = w(t)P d (t, f)(55)

[0203] where w(t) is the window function, expressed as:

[0204]

[0205] In the formula, T win is the width of the window function, which is used to eliminate the main lobe expansion of false targets. According to formula (14), the range resolution of the PCPT signal is cT c / 2. Therefore, it is recommended to set T win to 2T c .

[0206] D. Doppler filtering, a Doppler filter is designed to achieve fine detection of real targets.

[0207] Generally, at this time, the position and velocity information of real targets can already be extracted. By focusing on the rough detection result P coarseThe true target protection region of (t, f), referring to Equation (49) and Equation (55). However, when the clutter amplitude and interference power are large, such as in airborne or missile-borne application scenarios, there may still be residual isolated false targets in the coarse detection result P coarse (t, f), causing false alarms and wasting system resources. To reduce the false alarm rate while maintaining the detection probability, the SNR needs to be further improved. For this purpose, a Doppler filter based on oblique projection is designed to achieve fine detection of real targets.

[0208] Based on the false target delay coordinates extracted by the above mean shift algorithm and considering its main lobe width, the Doppler vector space of the false target can be obtained It is expressed as:

[0209]

[0210] Among them, is the Doppler discrete data vector, expressed as:

[0211] y vec (*) = [y(*, -GΔf),..., y(*, 0),..., y(*, GΔf)] T (58)

[0212] In the formula, F s is the radar intermediate frequency (IF) sampling frequency, 2G + 1 represents the number of discrete data along the Doppler axis within the detection window, Δf is the Doppler data interval (excluding the main lobe endpoints), H = T c F s -1. According to the Doppler frequency shift f d,s extracted from the coarse detection result, the Doppler vector of the real target is formed It is expressed as:

[0213]

[0214] Among them, Therefore, the oblique projection operator along U J to U s can be expressed as: In the formula,

[0215]

[0216] In the formula, is the orthogonal projection matrix of U J , calculated as:

[0217]

[0218] Since the oblique projection operator can make while satisfying Utilize this characteristic to design a Doppler filter Expressed as:

[0219]

[0220] It enables while Therefore, the Doppler filtering process is as follows:

[0221]

[0222] So far, the elimination of ISRJ is completed, obtaining a one-dimensional pulse compression result, and the output SNR is further improved, which can be used to achieve fine detection of real targets.

[0223] Furthermore, based on the above description, the program steps for ISRJ elimination and target detection of a PD radar using PCPT signals include:

[0224] Step 1 (Square-law detector): After Doppler compensation and pulse compression, calculate the power of the RD spectrum according to formula (42).

[0225] Step 2 (Coarse target detection): After excluding the real target protection area according to formula (49), use a 2D S-CFAR processor to detect the video sample P false (t,f), extract the delay coordinates of false targets as Then, cluster them through the meanshift algorithm, and output the false target clustering center formed by ISRJ, denoted as According to formula (55), perform a further windowing operation on the real target to obtain the coarse detection result.

[0226] Step 3 (Doppler filtering): Based on the false target clustering center and the Doppler frequency shift f of the real target extracted from the coarse detection result d,s , construct the Doppler vector spaces of false targets and real targets according to formula (57) and formula (59) respectively. Perform Doppler filtering according to formula (63).

[0227] Step 4 (Fine target detection): Output the one-dimensional pulse compression result y filtered (t), which only contains the real target detection result with improved signal-to-noise ratio and can be used for fine target detection.

[0228] Furthermore, conduct numerical experiment simulations.

[0229] To evaluate the performance of the method provided in this application in the ISRJ confrontation, multiple groups of numerical simulations were carried out on a PC with a 2.30GHz i7-11800H CPU and 32GB RAM. Unless otherwise specified, a random PCPT signal will be adopted, that is, the phases of the sub-pulses are randomly selected within the interval [0, 2π]. For each example, it is assumed that the noise is a circularly symmetric, independent, identically distributed, additive complex Gaussian process with a mean of zero.

[0230] In addition, to enhance the proximity of the analysis to the actual system, quantization error is also considered. Here, the quantization error is regarded as a rounding noise with a mean of zero. It is assumed 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 q, which also represents twice the maximum rounding error, can be expressed as q = 2volt / 2 12 . The probability density function of the quantization error is defined as p(e) = 1 / q, and the variance is calculated to be q 2 / 12. The SNR of the A / D converter can be obtained as 6.02b + 4.77 + 10log 10 LF, where LF is the load factor, and in this application, LF is taken as 0.5. Thus, the SNR of the 12-bit output word A / D converter is calculated to be 74.01dB. Based on this, the following analysis is carried out:

[0231] A. Target detection performance analysis.

[0232] Experiment 1: First, by comparing with the classical cell averaging CFAR (CA-CFAR) and order statistic CFAR (OS-CFAR) processors, the performance of the 2D S-CFAR processor under three different types of ISRJ is evaluated. It is assumed that there is a jammer on a target at a radial distance of 2000m (τ s = 13.33μs), and this jammer can generate three different types of ISRJ. The specific parameter settings are shown in Table 1. For the three CFAR processors, CFAR windows of the same size are adopted, with 4 reference cells and 2 guard cells on each side along the range axis (data interval 1 / F s ), and 9 reference cells and 10 guard cells on each side along the Doppler axis (data interval 1 / T r ). The total number of reference cells 2N ref is calculated to be 402. Assuming that the required false alarm probability of the radar system is 10 -6 , then referring to formula (43) and making appropriate adjustments, the parameters of S-CFAR can be determined as: threshold integer N T = N = 201, threshold multiplier β 0 = β1 = 13.6 and the scale factor α = 0.7. The threshold parameters of other CFAR processors are determined according to the existing public literature. When testing OS-CFAR, the data of order 3N / 2 is selected to establish the detection threshold.

[0233] Table 1 Parameter setting table in Experiments 1 and 2

[0234]

[0235] Figures 6 - 9 The reconstructed delay-Doppler spectra of the echoes under three different types of ISRJ interference and the delay-Doppler matrices after 2D-CFAR processing are plotted respectively. To further compare the actual application performance of CFAR processors, the running time, which is important for real-time detection and tracking of targets, is also recorded and listed in Table 2. Figure 6 On the left is the direct retransmission type of ISRJ, in the middle is the frequency shift retransmission type of ISRJ, and on the right is the repeated retransmission type of ISRJ. Figure 7 On the left is the detection result of the CA-CFAR detector, in the middle is the detection result of the OS-CFAR detector, and on the right is the detection result of the S-CFAR detector. Figure 8 On the left is the detection result of the CA-CFAR detector, in the middle is the detection result of the OS-CFAR detector, and on the right is the detection result of the S-CFAR detector. Figure 9 On the left is the detection result of the CA-CFAR detector, in the middle is the detection result of the OS-CFAR detector, and on the right is the detection result of the S-CFAR detector.

[0236] From Figures 6 - 9 and Table 2, it can be seen that:

[0237] 1) There are significant differences in the two-dimensional target detection performance of the three CFAR processors. This is because ISRJ forms multiple false target peaks around the high-level interference residue, thus inducing CA-CFAR to miss real targets under repeated retransmission ISRJ, indicating that the processor is sensitive to dense false targets, while S-CFAR and OS-CFAR show better robustness.

[0238] 2) Under different types of ISRJs, the number of targets detected by the CFAR processor also varies. When directly forwarding the ISRJ, the number of targets detected by CA-CFAR, OS-CFAR, and S-CFAR are 50, 49, and 52 respectively. The similar detection performance is due to the sparsity of false targets. When switching to the frequency shift mode, the number of targets detected by CA-CFAR, OS-CFAR, and S-CFAR are 56, 49, and 61 respectively. At this time, S-CFAR begins to stand out. As the false targets in the repeated forwarding mode are denser, OS-CFAR shows better performance, and the number of targets detected by CA-CFAR, OS-CFAR, and S-CFAR are 21, 39, and 35 respectively. iii) Although OS-CFAR has good detection performance, it has a large defect in terms of time complexity, as shown in Table 2, which greatly hinders its application in engineering. The reason is mainly that the OS-CFAR algorithm requires sorting operations, which is very time-consuming for 2D target detection with a large number of reference units (up to 30 seconds in this experiment). In contrast, the processing speeds of CA-CFAR and S-CFAR are very fast, taking 0.12 seconds to 0.24 seconds. Generally speaking, for target detection under ISRJ, the 2D S-CFAR processor has significant performance advantages.

[0239] Table 2 Runtime comparison table of CFAR processors

[0240] CA - CFAR OS - CFAR S - CFAR Direct - Forwarding ISRJ 0.13s 29.01s 0.24s Frequency - Shift - Forwarding ISRJ 0.13s 31.28s 0.22s Repeated - Forwarding ISRJ 0.12s 27.41s 0.23s

[0241] B. Coarse detection and Doppler filtering.

[0242] Experiment 2: In this experiment, the effectiveness of the proposed interference countermeasures for three different types of ISRJs was evaluated. During the ISRJ identification process, the minimum distance of the mean shift algorithm was set to ∈ = 10 -3 , and the bandwidth was set to h = 2T c = 0.16. According to the target detection results of Experiment 1, the coarse detection processes for the three ISRJ types of false target detection, ISRJ identification, and true target coarse detection are shown respectively as Figures 10 - 12 . The subsequent Doppler filtering process is shown as Figures 13 - 15 for fine detection. In addition, to test the timeliness of the identification process, the running times of the mean shift clustering algorithm and the Doppler filtering process were also recorded, as shown in Table 3. Figure 10 The first column of [] is the detection result after excluding the true target protection area, the second column is the identification result of the ISRJ by 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 [] is the detection result after excluding the true target protection area, 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 12 The first column is the detection result after excluding the true target protection area, the second column is the recognition result of the mean shift algorithm for ISRJ, and the third column is the rough detection result of the true target after window operation. Figure 13 The first column is the echo delay Doppler spectrum, the second column is the two-dimensional view along the Doppler axis, and the third column is the Doppler filtering result. Figure 14 The first column is the echo delay Doppler spectrum, the second column is the two-dimensional view along the Doppler axis, and the third column is the Doppler filtering result. Figure 15 The first column is the echo delay Doppler spectrum, the second column is the two-dimensional view along the Doppler axis, and the third column is the Doppler filtering result.

[0243] From Figures 10 to 12 it can be found that:

[0244] i) The mean shift algorithm uses the distribution characteristics of false targets to accurately identify the positions of false targets. Figure 10 The second column of shows the ISRJ recognition result of the mean shift algorithm under direct retransmission ISRJ (excluding the true target protection area), indicating that direct retransmission ISRJ can generate a set of false targets along the Doppler axis, clustering at τ J ≈13.80 μs. Figure 11 The second column of is the ISRJ recognition result under frequency-shifted ISRJ (excluding the true target protection area), that is, frequency-shifted ISRJ will generate a set of false targets with a displacement of -f along the Doppler axis J clustering at τ J ≈13.80 μs. The ISRJ recognition result under repeated retransmission ISRJ is as shown in the second column of Figure 12 confirming that repeated retransmission ISRJ generates false targets to produce Q = 3 sets of false targets along the delay axis at intervals of T 0 clustering at τ J ≈13.83 μs, τ J +T 0 ≈14.28 μs and τ J +2T 0 ≈14.79 μs.

[0245] ii) After providing the positions of the identified false targets, the window operation easily eliminates three different types of ISRJ while retaining the true targets. The detected targets are 9, 11, and 4 respectively, and the extracted central delay and Doppler frequency shift are 13.32 μs and 0.125 MHz respectively. This shows that even under the most challenging frequency-shifted repeated retransmission ISRJ, the method proposed in this application can still provide sufficient true target points for radar parameter extraction and decision-making.

[0246] It should be noted that when the input SIR is large, residual isolated false targets are still likely to appear in the range-Doppler plane after window operation. The number of these false targets is too small to form a clustering center and cannot be recognized in the false target clustering step. This is a problem with coarse detection, but it has little impact on the extraction of the Doppler frequency shift of real targets within the protected area. Therefore, this application designs a Doppler filter to further improve the output SIR.

[0247] To quantitatively describe the performance of the Doppler filtering method, a signal-to-interference ratio improvement factor (SIRIF) is introduced here to characterize the ability of the filter to suppress interference and noise, which is defined as:

[0248] SIRIF = SIR output - SIR unfiltered .(64)

[0249] In the formula, SIR unfiltered is the SIR before Doppler filtering, which is calculated from the data in the second column of Figures 13 - 15 .

[0250] From Figures 13 to 15 it can be seen that:

[0251] i) Since ISRJ generates several groups of peaks with an interval of T 0 along the Doppler axis in the RD spectrum, the number of false targets presented in the pulse compression result depends on the number of ISRJ retransmissions. And after coherent integration, the false targets still generally have a larger amplitude than the real targets, indicating that both the interference slice and the real phase-coded pulse train signal can enjoy the coherent integration gain.

[0252] ii) The Doppler filtering method effectively eliminates the false targets generated by ISRJ and improves the output SIR. The calculated SIRIFs for the three interference modes are 15.36 dB, 12.12 dB, and 9.13 dB respectively. This shows that the suppression effect of the Doppler filter on interference and noise weakens as the number of false targets increases, 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 codings in a single pulse can also improve the output SIR, as shown in the next experiment.

[0253] iii) In addition to suppressing the interference generated by ISRJ, the Doppler filter can also effectively suppress isolated interference or noise on the delay-Doppler spectrum, which is particularly obvious in Figure 12 and 13 . In this way, at the same detection probability, the false alarm rate of the radar system can be reduced, thus avoiding the waste of system resources.

[0254] Considering the actual application, the efficiency of the algorithm is of utmost importance. Therefore, in Table 3, the running times of the most time-consuming parts of the method provided in this application are recorded, including the mean shift algorithm used in the ISRJ recognition process and the Doppler filtering process before fine detection, both of which are as short as milliseconds, basically meeting the engineering requirements of all application scenarios.

[0255] Table 3 Operating parameter table of ISRJ recognition and Doppler filtering processes during runtime

[0256] ISRJ Mode Mean - Shift Clustering Doppler Filter Formula Direct - Forwarding ISRJ 0.0013s 0.0056s Frequency - Shift - Forwarding ISRJ 0.0016s 0.0060s Repeated - Forwarding ISRJ 0.0011s 0.0070s

[0257] C. ISRJ anti-interference performance analysis.

[0258] The anti-ISRJ methods for phase-coded signals are divided into two categories, namely waveform design methods and signal processing methods. Waveform design methods utilize the characteristic that the ISRJ jammer only intercepts a part of the radar signal segment, and orthogonally coded segments are designed within the pulse in an offline manner to mismatch the interference echo with the un-intercepted signal segment. However, waveform design methods highly depend on the accuracy of the jammer parameter estimation. Signal processing methods utilize the distribution characteristics of ISRJ targets in the range-Doppler spectrum and eliminate interference through real-time processing. The method proposed in this application belongs to the signal processing method. Based on this, the most advanced algorithms are respectively selected from these two types of methods for competitive comparison. During the analysis process, the Doppler frequency 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 of this application is fully demonstrated.

[0259] Experiment 3: Different from the processing of LFM signals, phase-coded signals are not applicable to time-frequency domain tool analysis. In this experiment, the relevant research on ISRJ suppression of single-pulse phase-coded waveforms is compared with the method provided in this application. For the convenience of comparison, the following parameter settings are made: the number of phase encodings M is 500, the bandwidth B is 50 MHz, the pulse width T is 10 μs, the number of coherent accumulated pulses N is 1, the Doppler data interval is 1 / (3T), the intermediate frequency sampling frequency F s is 100 MHz, and the number of discrete data points on the Doppler axis 2G + 1 is 401. Other parameters are the same as those in Experiment 2. Taking the frequency shift retransmission ISRJ as an example, when the target Doppler frequency shifts f d,s are 0, 1 / (3T), and 2 / (3T) respectively, the processed results of the phase-coded pulse train signals of the two methods are plotted as Figure 16 shown. Figure 16 The first row of is the echo delay Doppler spectrum, and the second row is the Doppler filtering result. Figure 16 Columns 1-3 of are the processing results when the Doppler frequency shifts are 0, 1 / (3T), and 2 / (3T).

[0260] It should be noted that it is assumed that the Doppler shift of the target will not reach 1 / 3T, which is reasonable for airborne and spaceborne radars. However, considering missile-borne radars, if a carrier frequency with a shorter wavelength is used, the Doppler shift may even exceed 1 / T. The method proposed in this application can exactly solve this problem.

[0261] From Figure 16 the following findings can be obtained: i) The Doppler shift of the target is manifested as a translation along the Doppler axis in the delay-Doppler spectrum. Under the three Doppler shift conditions, the peaks 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 shift of the target is less than 1 / (3T) (0.03 MHz), the output SIR of 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 hypersonic (5 Mach). iii) When the target is in hypersonic motion, the situation is quite different. As can be seen from the third column of Figure 16 , the output SIR of the comparison method deteriorates significantly. Considering that the power of the ISRJ jammer may be higher than the setting, the comparison method will not be able to correctly identify the target. iv) Under different Doppler 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. By extracting the approximate Doppler shift of the target and embedding it into the Doppler filter formula, a more satisfactory interference suppression result can be provided for fine detection.

[0262] Experiment 4: Now turn the attention to the anti-ISRJ method of waveform design, and deeply explore the influence of parameter estimation error, input SIR, and modulation frequency on interference suppression to reveal the excellent performance and robustness of the proposed method. The key to the waveform design method is to design the waveform according to the estimated interference parameters (i.e., the sampling interval T s)Design a pulse-internal time-discontinuous waveform and embed orthogonal protection sub-pulse segments to achieve mismatch between the receiving end and the interference signal. Therefore, on the premise of accurately estimating the interference parameters, the orthogonality of the waveform sequence determines the suppression effect of ISRJ. Here, three types of algorithms most commonly used in the field of sequence set design are introduced, and the most representative and advanced algorithms are selected 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 strategies in [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.], comparative experiments are carried out. 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 at intervals of 50. In this way, the number of sub-pulse segments is 10, and the width of the sub-pulse segment is 1 μs. For easy comparison, the target Doppler frequency shift in the simulation is set to 0, and other parameters are the same as those in Experiment 3.

[0263] To show the actual performance of each method in detail, the interference suppression results when the input SIR fluctuates, the interference parameter estimation error, and the modulation frequency changes are simulated respectively, and they are plotted in Figures 17 - 19Note that for the first two groups of simulations, it is assumed that the jammer is in the direct - forwarding mode, and for the last two groups of simulations, the SIR is set to - 10 dB. Observing the simulation results, it is found that: 1) The waveform - design - type method is sensitive to the fluctuation of the input SIR. When the interference power is low, the output SIR after pulse compression is close to the method proposed in this application. However, once the interference power increases, the output SIR will deteriorate significantly. When the input signal - to - noise ratio is less than - 20 dB, the waveform - design - type method can basically not distinguish the real target. The method proposed in this application has good robustness to the fluctuation of the input SIR and changes slowly in the range of 12.68 dB to 19.69 dB. ii) In addition to the influence of the input SIR fluctuation, the waveform - design - type method highly depends on the accurate estimation of the interference parameters (i.e., the sampling interval T s ). Even a very small estimation error may lead to the failure of ISRJ suppression. Especially when the waveform pulse width T is several times the sampling interval T s , this will cause the estimation error to accumulate in the last intercepted slice, resulting in the mismatch failure between the interference signal and the receiving filter. Under the parameter - setting conditions of this application, the jammer can sample and forward 5 times within one pulse, so the estimation error should 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 the frequency - shift mode, the output SIR of the waveform - design - type method fluctuates to varying degrees. Among them, the MS - AISO method has the smallest fluctuation, the EG method comes second, and the GMBI method has the largest fluctuation, between 8.03 dB and 12.60 dB. On the other hand, although the proposed method decreases between 0 MHz and 1 MHz, it quickly stabilizes at about 15 dB, still ensuring the accurate identification of the real target. Among them, Figure 17 Columns 1 and 2 are the processing results when the SIR is 0 and - 10, and column 3 is the processing result of the output SIR and the input SIR. Figure 18 Columns 1 and 2 are the processing results when the estimation error is 2% and 3%, and column 3 is the output SIR and the T s estimation error. Figure 19 Columns 1 and 2 are the processing results when the frequency - shift value of the jammer is set to 1 MHz and 2 MHz, and column 3 is the relationship between the output SIR and the frequency - modulation value f J .

[0264] D. Algorithm complexity analysis.

[0265] Analyze the computational complexity of the method proposed in this application, covering the asymptotic time complexity and the asymptotic space complexity.

[0266] The time complexity of the ISRJ suppression method proposed in this application mainly depends on the two - dimensional S - CFAR detection, mean - shift clustering, and Doppler filtering processes. The asymptotic time complexity of the two - dimensional S - CFAR processing is O(Lr L D N ref ), where L r and L D are the number of data points along the range (delay) axis and the Doppler axis within the two-dimensional detection window of the radar, respectively. For the mean shift algorithm, its asymptotic time complexity is O((N det ) 2 ), where N det represents the number of target points detected in the previous step. The asymptotic time complexity of the Doppler filtering process is O(Q 3 ), which is due to the existence of matrix inverse operations. However, since the number of repeated transmissions Q is limited (for example, at most 3 times), this operation actually takes very little time. In summary, the overall asymptotic time complexity of the method proposed in this application is O(L r L D N ref ), which can fully meet the requirements of real-time processing in engineering applications. The asymptotic space complexity is mainly determined by the RDM within the radar detection window, occupying O(L r L D ).

[0267] In summary, the essence of the method proposed in this 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 rough detection and fine detection. For the identification and suppression of ISRJ, the two-dimensional S-CFAR algorithm, the mean shift algorithm, and the Doppler filtering method are respectively proposed and applied. The simulation results show that the method proposed in this application can effectively suppress various types of ISRJ interference, has a fast calculation speed, low requirements for the radar system, and does not require prior knowledge of interference parameters. Comparative experiments show that under various preset conditions, the method proposed in this application is superior to the state-of-the-art algorithms in existing waveform design and signal processing categories and can be extended to engineering applications.

[0268] Furthermore, compared with the prior art, this application also has the following advantages:

[0269] 1. This application can reveal the range-Doppler domain distribution characteristics of ISRJ: By deriving the cross ambiguity function (CAF) of the PCPT signal for ISRJ, it is found that false targets are parallelly distributed along the Doppler axis in the range-Doppler domain and the delay is fixed. Different types of ISRJ show movement along the Doppler axis and replication along the delay axis in the range-Doppler domain. In actual signal processing, this application reproduces this characteristic through Doppler compensation.

[0270] 2. This application can robustly suppress various types of ISRJ: By utilizing the range-Doppler domain distribution characteristics, a two-dimensional switched constant false alarm rate (2D S-CFAR) detection algorithm is proposed, and combined with the mean shift algorithm originally used for image tracking to achieve false target recognition, where Doppler filters are formulated. Thus, without being interfered by any prior information, it can robustly suppress various types of ISRJ under the conditions of input SIR fluctuations and high-speed target motion.

[0271] 4. This application has real-time processing efficiency: The asymptotic time complexity and asymptotic space complexity of this 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, thus allowing engineering applications on various small platforms.

[0272] 5. Good scalability: Since this application is based on PCPT signal processing, it can be combined with the inter-pulse waveform diversity technology to achieve synchronous suppression of FPFJ and ISRJ in coherent radars, with broad application prospects.

[0273] In addition, the method proposed in this application can be extended to various types of pulse diversity waveforms, such as the cooperative effects of inter-pulse frequency-coded waveforms, inter-pulse diversity phase-coded waveforms, or composite modulation waveforms, etc., so as to further enhance the ISRJ suppression effect while taking into account sidelobe interference and FPFJ suppression.

[0274] Based on the same inventive concept, the embodiments of this application also provide an intermittent sampling and forwarding interference suppression device for implementing the intermittent sampling and forwarding interference suppression method involved above. The solution provided by this device to solve the problem is similar to the solution recorded in the above method. Therefore, the specific limitations in one or more embodiments of the intermittent sampling and forwarding interference suppression device provided below can refer to the limitations on the intermittent sampling and forwarding interference suppression method in the above text, and will not be repeated here.

[0275] In an exemplary embodiment, an intermittent sampling and forwarding interference suppression device is provided, including:

[0276] A radar receiver, configured to receive a phase-coded pulse train signal, sample, Doppler compensate, and pulse compress the phase-coded pulse train signal to obtain in-phase signals and quadrature signals.

[0277] A square-law detector, connected to the radar receiver, and configured to obtain the power distribution function of the RD spectrum based on the in-phase signals and quadrature signals.

[0278] The target coarse detector, connected to the square-law detector, is used to process the power distribution function of the RD spectrum to obtain a range-Doppler matrix that only contains target information. After excluding the true target protection area based on the range-Doppler matrix, a range-Doppler matrix that only contains false targets is obtained. The two-dimensional switched constant false alarm rate (S-CFAR) detection algorithm is used to detect the range-Doppler matrix that only contains false targets to obtain the two-dimensional S-CFAR detection result, and the delay coordinates of the false targets are extracted. The mean shift algorithm is used to cluster the delay coordinates of the false targets to obtain the false target cluster center formed by the intermittent sampling and repeater jamming. A window function is constructed according to the false target cluster center to process the two-dimensional S-CFAR detection result, eliminate the false targets, and obtain the coarse detection result of the true target.

[0279] The oblique projection operator acquisition module, connected to the target coarse detector, is used to construct the Doppler vector space of the false targets and the Doppler vector space of the true targets based on the false target cluster center and the true target Doppler frequency shift extracted from the coarse detection result of the true targets. The oblique projection operator from the Doppler vector space of the false targets to the Doppler vector space of the true targets is obtained.

[0280] The Doppler filter, connected to the oblique projection operator acquisition module, is used to perform Doppler filtering based on the oblique projection operator to obtain a one-dimensional pulse compression result.

[0281] The target fine detector, connected to the Doppler filter, is used to analyze the one-dimensional pulse compression result to obtain the final detection result of the true targets.

[0282] In an exemplary embodiment, a computer device is provided. The computer device can be a server or a terminal. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, 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. Among them, 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 the operation of 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 repeater jamming 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. When the computer program is executed by the processor, it implements an intermittent sampling and repeater jamming suppression method based on the processing of phase-coded pulse train signals.

[0283] In an exemplary embodiment, a computer device is provided, which includes a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.

[0284] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0285] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0286] 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 this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use, and processing of relevant data need to comply with relevant regulations.

[0287] Those of ordinary skill in the art can understand that all or part of the processes of implementing the methods in the above embodiments can be completed by instructing relevant hardware through a computer program. 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. Among them, any reference to a memory, database, or other medium used in the various embodiments provided in this application can include at least one of non-volatile and volatile memories. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0288] In each of the embodiments provided in this application, the database involved may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., and is not limited thereto. In each of the embodiments provided in this application, the processor may 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, etc., and is not limited thereto.

[0289] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0290] Specific examples are used in this application to elaborate on the principles and implementation manners of this application. The description of the above embodiments is only used to help understand the method and its core idea of this application; at the same time, for those of ordinary skill in the art, according to the idea of this application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to this application.

Claims

1. A method for suppressing intermittent sampling and forwarding interference based on phase-coded pulse train signal processing, characterized in that: The intermittent sampling forwarding interference suppression method comprises: The phase-coded pulse train signal is sampled, Doppler compensated and pulse compressed to obtain an in-phase signal and an orthogonal 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; After excluding the real target protection area based on the range-Doppler matrix, a range-Doppler matrix containing only false targets is obtained; The two-dimensional switching constant false alarm rate detection algorithm is used to detect the range-Doppler matrix containing only false targets to obtain the two-dimensional S-CFAR detection result, and the delayed coordinates of the false targets are extracted; Clustering the delayed coordinates of the false target by a mean shift algorithm to obtain the clustering center of the false target formed by intermittent sampling and forwarding 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 target and obtain a rough detection result of the true target; Based on the cluster centers of the false targets and the Doppler frequency shift of the true targets extracted from the rough detection results of the true targets, constructing the Doppler vector space of the false targets and the Doppler vector space of the true targets; An oblique projection operator from 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 includes the final detection result of the true target.

2. The intermittent sampling forwarding interference suppression method based on phase-coded pulse train signal processing according to claim 1 is characterized in that: The power distribution function of the RD spectrum is expressed as: P(t,f)=|y(t,f)| 2 ; Where P(t,f) represents the power of the RD spectrum, and y(t,f) represents the signal after coherent accumulation of the echo signal received within a coherent processing interval; The coherently integrated signal is obtained based on the in-phase signal and the orthogonal signal.

3. The intermittent sampling forwarding interference suppression method based on phase-coded pulse train signal processing according to claim 1 is characterized in that: The range-Doppler matrix containing only false targets is expressed as: In the formula, F d,s is the maximum Doppler frequency shift of the real target, which is 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 that contains only target information, otherwise represents other, and if represents if.

4. The intermittent sampling forwarding interference suppression method based on phase-coded pulse train signal processing according to claim 1 is characterized in that: The rough detection result of the true target is expressed as: P coarse (t,f)=w(t)P d (t,f); Where P coarse (t,f) is the rough 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 intermittent sampling forwarding interference suppression method based on phase-coded pulse train signal processing according to claim 1 is characterized in that: The oblique projection operator is expressed as: In the formula, is the oblique projection operator, U s is the Doppler vector space of the true target, H is the conjugate transpose, is the orthogonal projection of the Doppler vector space of the false target, U J is the Doppler vector space of the false target.

6. The intermittent sampling forwarding interference suppression method based on phase-coded pulse train signal processing according to claim 1 is characterized in that: In the process of performing Doppler filtering based on the oblique projection operator, the oblique projection operator is used to construct a Doppler filter to perform Doppler filtering processing.

7. The intermittent sampling forwarding interference suppression method based on phase-coded pulse train signal processing according to claim 6 is characterized in that: The Doppler filter is expressed as: In the formula, w d is the Doppler filter, is the oblique projection operator, U s is the Doppler vector space of the true target, H is the conjugate transpose, U J is the Doppler vector space of the false target.

8. The intermittent sampling forwarding interference suppression method based on phase-coded pulse train signal processing according to claim 6 is characterized in that: The one-dimensional pulse compression result is expressed as: In the formula, y filtered (t) is the one-dimensional pulse compression result, w d is the Doppler filter, y vec (t) is the Doppler discrete data vector, and H is the conjugate transpose.

9. The intermittent sampling forwarding interference suppression method based on phase-coded pulse train signal processing according to claim 1 is characterized in that: The Doppler vector space of the false target is expressed as: Where U J is the Doppler vector space of the false target, y vec (c1-H / F s ) is, y vec (c1+H / F s ) is, y vec (c k -H / F s ) is, y vec (c k +H / F s ) is, y vec (c K -H / F s ) is, y vec (c K +H / F s ) is, c1 is the first cluster center of the false target, c k is the kth cluster center of the false target, H is the conjugate transpose, F s is the radar intermediate frequency sampling frequency.

10. The intermittent sampling forwarding interference suppression method based on phase-coded pulse train signal processing according to claim 1, characterized in that: The Doppler vector space of the true target is expressed as: Where U s is the Doppler vector space of the true target, N d is the number of 0 elements, and T is the transpose.

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