Array radar angle deception jamming generation method based on coherent FDA

Abstract

The invention discloses a coherent FDA-based array radar angle deception jamming generation method, which solves the technical problem of far-field array system angle deception, and comprises the following steps: building a generalized coherent FDA signal model; transmitting a coherent FDA signal based on the frequency step amount and weighted modulation; the deception jamming signals form a non-uniform phase difference in the far-field array; the non-uniform phase difference affects a far-field angle measurement result; and deception on the far-field array is realized. According to the invention, a frequency stepping amount is introduced between adjacent transmitting array elements, and an electromagnetic signal of distance-angle-time-frequency offset joint modulation is formed in a space far field, so that a non-uniform phase difference is generated between different array elements of a receiving array, and further angle measurement and positioning errors of a far-field receiver are caused; a frequency diversity signal is transmitted to destroy a far-field electromagnetic signal equiphase surface, electromagnetic energy regulation and control are realized through weighted modulation, and far-field array angle deception is successfully caused. The method is used for angle cheating of radar investigation equipment in electronic countermeasures and protecting the high-value target of our part.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electronic countermeasures, and mainly relates to array radar angle deception jamming, in particular to an array radar angle deception jamming generation method based on coherent FDA. BACKGROUND

[0002] In the field of modern electronic countermeasures, the working process of high-speed aircraft faces the powerful detection capability of active radar. Modern early warning radars usually adopt a multi-channel array radar system, which has the advantages of high gain, narrow beam, anti-side lobe interference and strong tracking capability, and has extremely important application value in the field of high-value target detection and electronic countermeasures, which poses a strong threat to the normal work of high-speed aircraft.

[0003] In order to protect the effective working state and task completion of high-speed aircraft, an important problem is how to avoid or deceive the effective detection of the opponent's array radar. However, with the in-depth study of electronic warfare, various anti-jamming technologies have been developed and widely applied. For example, for traditional high-power active suppression jamming, side lobe cancellation and side lobe blanking technologies are introduced in radars, and the anti-jamming capability is obviously enhanced. For aiming deception jamming, a new system radar based on frequency agility technology is developed, in addition to moving target detection, constant false alarm detection and coherent accumulation, modern mainstream radar technologies mainly include pulse compression and pulse Doppler technology. Signals with low matching degree to radar transmitted signals cannot obtain coherent processing gain, so the anti-jamming capability is greatly improved. In many cases, the probability of identifying traditional jamming signal by the enemy is getting higher and higher, and it is difficult to effectively jam the new system radar.

[0004] The most representative radar system at present is active phased array, which is also the main technical system of multifunctional radar. The beam scanning characteristic has faster scanning speed than mechanical scanning, can simultaneously detect and master hundreds of batches or even thousands of batches of targets, and can adjust the working mode of the radar according to the target environment and environmental situation, and has strong anti-jamming capability. Of course, phased array also has some shortcomings, for example, in a beam scanning snapshot, the beam propagates along a fixed angle and is independent of distance, but in some anti-jamming and clutter suppression applications, it is hoped that the beam can point to targets at different distances with the same angle.

[0005] In 2006, Antonik et al. first proposed the concept of Frequency Diversity Array (FDA). Unlike the traditional phased array, FDA applies different frequency offsets to each array element, eliminating the need for a phase shifter at the transmitter, thus forming a range-angle coupled beam pattern. While the phased array beam pattern is fixed in angle, the beam pointing is constant. Due to its range dimension beam scanning characteristics, FDA is widely used in radar detection fields such as range clutter suppression, non-fuzzy imaging, and high-precision parameter estimation. In addition, FDA has the potential to produce angle deception jamming by changing the phase of the far-field radiation plane wave, as it can modulate the electromagnetic wave in both range and angle dimensions. Therefore, it has received some attention in the field of jamming technology. Chen Yang et al. introduced the jamming principle of FDA in their published paper "FDA Jamming Technology Progress and Prospect Review" (Firepower and Command Control, 2023, 48(1): 8-13.), comprehensively reviewed the research progress in FDA jamming field, systematically summarized the main technologies of FDA jamming, and analyzed the main application prospects of FDA in the field of jamming.

[0006] To address the problem of passive radar direction finding through jammer signals, Wang Bo et al. disclosed an angle deception method based on FDA amplitude comparison monopulse direction finding system in their published paper "Angle Deception of FDA Amplitude Comparison Monopulse Direction Finding" (Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(03): 643-650.). First, the FDA model is established to calculate the half-power beamwidth of FDA. By utilizing the range dependence of FDA's half-power beamwidth, the beamwidth at the enemy direction finding system is modulated by adjusting the frequency offset, thereby interfering with the enemy direction finding system. The angle deception effect and error influence of FDA jammer on amplitude comparison passive direction finding system are analyzed through simulation system.

[0007] Further, Xie Junwei et al. in the paper "FDA Transmitter Jammer Deception Mechanism for Passive Radar Interferometer Direction Finding System" (Journal of South China University of Technology, 2020, 48(01): 93-103.) discloses a angle deception jamming method for passive interferometer direction finding system, first, on the basis of establishing FDA array model, the FDA array factor and phase pattern with nonlinear frequency increment are obtained by Euler formula; then the signal to angle beta measured by FDA array acting on interferometer and the coordinate position of virtual transmitter in X axis are derived; then, based on the deception of interferometer direction finding, the deception principle and positioning accuracy of FDA jammer to direction finding cross positioning system are analyzed. The simulation results show that: by reasonably selecting the carrier frequency, the number of array elements and the frequency offset, the deception effect of FDA array on interferometer direction finding under far field condition can be realized; while reasonably selecting other parameters, the higher the direction finding accuracy is, the smaller the positioning ambiguity area is, and the positioning of virtual jammer is always outside the actual position of jammer.

[0008] In modern electronic countermeasure and combat system, the direction finding system usually adopts multi-channel active array, which has powerful direction finding and positioning capability. How to use FDA to effectively jam it and make it difficult to accurately detect and locate high-value targets of our side has only received limited attention. Currently, Wang Bo team considers using FDA to interfere with the single pulse direction finding system of the other party, and Xie Junwei team uses FDA to deceive the angle of the interferometer direction finding system, without considering how to deceive the angle of the active array. However, how to use the distance dimension freedom of FDA signal to pull the direction finding result of the active array of the other party to produce angle deception effect, there is no public patent or paper to study, which is still in the blank stage. SUMMARY

[0009] The present application aims at the problems existing in the prior art, and provides a novel and efficient array radar angle deception jamming generation method based on coherent FDA.

[0010] The present application is an array radar angle deception jamming generation method based on coherent FDA, characterized in that a frequency step is introduced between adjacent transmitting array elements to form a distance-angle-time-frequency offset jointly modulated electromagnetic signal in the spatial far field, causing angle measurement and positioning error of the array receiver, including the following steps:

[0011] Step 1, build a generalized coherent FDA signal model: the built generalized coherent FDA signal model is a one-dimensional linear array, which includes M array elements with equal spacing and uniform distribution, each array element is an omnidirectional antenna, and each antenna includes an independent transceiver channel;

[0012] Step 2, the FDA signal model emits a coherent FDA signal based on frequency step and weighted modulation: each array element of the FDA signal model emits a linear frequency modulation waveform, and during signal emission, a frequency step is introduced between adjacent array elements, so that different array elements in the model work at different emission frequencies, and the emission signal forms a frequency offset-time-distance-angle related phase during the propagation in space, which destroys the equal phase plane of the electromagnetic signal in the far field; at the same time, by performing weighted modulation on each array element, an FDA combined signal, i.e. a deception jamming signal, is formed, and the electromagnetic energy at different positions in space is regulated;

[0013] Step 3, the generated deception jamming signal forms a non-uniform phase difference in the far field array: there is an array receiving system composed of N array elements at the space far field, and each array element of the receiving system receives the FDA combined signal at the position, and due to the frequency step introduced by the jammer in the model at the emission end and the weighted modulation, the generated frequency offset-time-distance-angle related phase causes non-uniform phase difference between the signals received by different array elements;

[0014] Step 4, the formed non-uniform phase difference affects the far field angle measurement result: the signals at different receiving array elements are arranged in vector form, and the angle estimation of the signals is performed, and due to the frequency step and the weighted modulation, the non-uniform phase difference between the far field arrays affects the angle measurement result, and the obtained angle measurement result is a biased angle measurement result;

[0015] Step 5, deception to the far field array is realized: the biased angle measurement result causes the far field array to form an angle estimation error and a positioning error, and for a given position of the space far field receiver array, the signal received by the far field receiver is only modulated by the frequency step and the emission weight vector, and the modulation introduces non-uniform phase difference between different receiving array elements, so that the angle estimation result deviates, and the biased angle estimation causes deviation in the positioning of the FDA signal model, thereby realizing the deception effect to the far field array.

[0016] The present application solves the problem of angle deception to the far field array direction finding system.

[0017] Compared with the prior art, the technical advantages of the present application are:

[0018] The emission frequency diversity signal destroys the equal phase plane of the far field electromagnetic signal: by introducing a linearly increasing frequency step between different array elements of the emission array, a coherent FDA combined signal is obtained, a distance-angle-time-frequency offset related phase term is formed in space, and a non-uniform phase difference is generated between different array elements of the far field receiving array, the coherent FDA signal destroys the equal phase plane of the far field electromagnetic signal, solves the problem of angle deception to the far field array direction finding system, causes the angle estimation of the far field array to deviate, and realizes the protection of the high value target of our side.

[0019] The electromagnetic energy is regulated by the weighted modulation: in the process of obtaining the coherent FDA combined signal, the electromagnetic energy at a specific distance-angle position in the space is regulated by the weighted modulation of the transmitting end, the regulation is disorderly, the phase plane at the position is further distorted, and the phase regulation of the far-field array receiving signal is realized. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 The flowchart of the present application is shown in the figure;

[0021] Figure 2 The angle deception jamming scene based on the coherent FDA constructed by the present application is shown in the figure;

[0022] Figure 3 The phase distribution diagram of the coherent FDA combined signal of the present application in the distance-angle space is shown in the figure;

[0023] Figure 4 The phase distribution diagram of the PA combined signal in the distance-angle space is shown in the figure;

[0024] Figure 5 The influence result diagram of the angle of the receiving array on the angle estimation deviation of the present application is shown in the figure;

[0025] Figure 6 The influence result diagram of the distance of the receiving array on the angle estimation deviation of the present application is shown in the figure;

[0026] Figure 7 The influence result diagram of the frequency stepping amount on the angle estimation deviation of the present application is shown in the figure.

[0027] The present application will be described below in conjunction with the accompanying drawings: DETAILED DESCRIPTION

[0028] Example 1

[0029] In the field of modern electronic countermeasures, high-speed aircrafts face strong detection ability of enemy active radars in the working and attacking process. Modern early warning radars usually adopt multi-channel array radar system, which has high gain, narrow beam, strong anti-side lobe interference and tracking ability, and has strong threat to high-value targets. In view of the present situation, the present application carries out technical research and development, and proposes an array radar angle deception jamming generation method based on coherent FDA for electromagnetic space energy regulation, which forms jamming to the radar while protecting high-value targets.

[0030] The application is a kind of array radar angle deception jamming generation method based on coherent FDA, the application introduces frequency step quantity between adjacent transmitting array elements, forms distance-angle-time-frequency offset joint modulation electromagnetic signal in spatial far field, causes non-uniform phase difference between different array elements of receiving array, the phase difference causes angle measurement and positioning error of array receiver, realizes angle deception of far field array system, see Figure 1 , Figure 1 The flow chart of the application includes the following steps:

[0031] Step 1, build a generalized coherent FDA signal model: the generalized coherent FDA signal model built by the application includes a linear transmitting array system, which is composed of M omnidirectional array elements, each array element has independent transmitting and receiving functions and can transmit pre-generated signals.

[0032] Step 2, transmit coherent FDA signals based on frequency step quantity and weighting modulation: during the process of transmitting FDA signals, each array element transmits the same waveform, i.e. linear frequency modulation waveform, which is different from the process of transmitting traditional signals. In the process of transmitting coherent FDA signals, frequency step quantity is introduced between adjacent array elements. The carrier frequency f0 of the signal transmitted by the first transmitting array element is used as the reference carrier frequency, and the carrier frequency of the signal transmitted by the mth array element is written as f m =f0+△f m , where △f is the frequency step quantity used by the mth array element. The frequency step quantity is usually much smaller than the signal bandwidth and can be designed by optimization algorithm in different scenarios. The wave path difference of the transmitted signal in space is related to the frequency of the signal. Different carrier frequencies result in different wave path differences. The difference of wave path differences between different frequency step quantities can be represented by the coupling of frequency step quantity and distance-time. This coupling term causes the coherent FDA signal to form a frequency offset-time-distance-angle related phase during spatial propagation. In the process of transmitting signals by traditional phased array, without using frequency step quantity, the phase of the combined signal at different positions in space is only related to the angle of the position. The phase at different distances for the same angle is the same, i.e. a hemispherical equal phase surface. However, the introduction of frequency step quantity will form a distance-angle beam distribution graph with "S" shape in space, which destroys the equal phase surface of electromagnetic signals in far field. In addition, any weighting modulation is used on each array element during signal transmission. The weighting term can control the electromagnetic energy distribution of FDA combined signal at any distance and angle in space, further enhancing the deception effect of coherent FDA combined signal.

[0033] Step 3, the deception jamming signal forms a non-uniform phase difference in the far-field array: there is an array receiving system composed of N elements at the spatial far field, each element of the receiving system receives the FDA combined signal at the location; the spatial distance-angle plane coordinate system is converted into the XoZ spatial coordinate system, the coherent FDA combined signal at each receiving element position in the XoZ coordinate system can be obtained, the phase of the coherent FDA combined signal at each receiving element is extracted, the phase at each receiving element is related to the position of the element, the angle relative to the transmitting array and the signal propagation time, since the distance and angle of different receiving elements relative to the transmitting array are different, and the distance difference and angle difference between the receiving elements are non-uniform, the phase difference between the signals on the adjacent receiving elements obtained is non-uniform; that is, since the jammer in the model introduces a frequency step at the transmitting end and adopts a weighted modulation, the frequency offset-time-distance-angle related phase makes the signals received by different elements have a non-uniform phase difference.

[0034] Referring to Figure 2 , Figure 2 is a schematic diagram of the angle deception jamming scene based on the coherent FDA constructed by the application, the coherent FDA signal model constructed by the application is composed of M elements, the element spacing is d T , the far-field array receiver is composed of N elements, the element spacing is d R , the signal received by each element of the far-field array receiver is the sum of the M signals transmitted by the coherent FDA signal model constructed by the application, different elements transmit signals of different carrier frequencies, and these signals form a non-uniform phase difference between different elements of the far-field array.

[0035] Step 4, the non-uniform phase difference affects the far-field angle measurement result: the signals at different receiving elements are arranged in vector form, the receiving array processes the vector signal, and the maximum likelihood method is used for angle estimation of the signal, the maximum likelihood method performs exhaustive search in the angle dimension, calculates the spatial spectrum power corresponding to each angle, and takes the angle corresponding to the maximum power as the measured signal incident angle; in the case of transmitting a conventional phased array signal and being received by an array, the path difference between different receiving elements is uniform, and the maximum likelihood method can accurately measure the incident angle of the signal; since the coherent FDA combined signal modulated by the frequency step and the weighting term causes the phase difference between different receiving elements to be non-uniform, the non-uniform phase difference causes the incident angle measured by the array to deviate from the true incident angle, and the obtained angle measurement result is a biased angle measurement result.

[0036] Step 5: Realize deception to far-field array: the receiving array adopts the goniometric result to position the transmitting array, i.e. the interference source, and the biased goniometric result leads to angle estimation error and positioning error of the far-field receiving array; in the actual use of the coherent FDA as angle deception interference, when the position of the far-field receiver array is fixed, the signal incidence angle measured by the array is modulated by the frequency stepping amount and the transmitting weight vector, and the frequency stepping amount and the weight modulation term of the transmitting end can be optimized and designed according to different scenes, so that the signal incidence angle measured by the receiving array deviates more from the real incidence angle, and the greater angle deviation also leads to greater positioning error of the transmitting array, i.e. better angle deception interference effect.

[0037] In order to break through the strong detection capability of the modern far-field array radar system, the application introduces a frequency stepping amount between adjacent transmitting array elements, forms a distance-angle-time-frequency offset jointly modulated electromagnetic signal in the spatial far field, causes angle measurement and positioning error of the array receiver, realizes angle deception to the far-field array direction finding system and protection of high-value targets of our side.

[0038] In the prior art, only the angle deception to the single pulse direction finding system and the interferometer direction finding system is considered, the angle deception mechanism to the array direction finding system is not clearly described, and the problem is not clearly explained in principle. In view of this problem, the idea of the application is to form a distance-angle-time-frequency offset related coherent FDA combined signal in space by adopting frequency stepping amount and weight phase joint modulation at the transmitting end, to obtain the received signal on each array element of the receiving array system and the non-uniform phase difference between adjacent receiving array elements through coordinate transformation, and to cause the angle and positioning result of the receiving array goniometric system to deviate, so as to realize angle deception to the far-field array direction finding system.

[0039] Embodiment 2

[0040] A kind of array radar angle deception interference generation method based on coherent FDA same as embodiment 1, the coherent FDA signal based on frequency stepping amount and weight modulation described in step 2 of the application includes the following steps:

[0041] 2.1 Introduce frequency stepping amount: in the generalized coherent FDA signal model built in the application, a linear transmitting array is included, which is composed of M array elements, and the distance between each two array elements is uniform and is half a wavelength; the first transmitting array element is the reference array element, and the carrier frequency of the signal transmitted at the array element is the reference carrier frequency f0, which is usually 0.5-2GHz in airborne radar, and in the traditional array, the frequency on each transmitting array element is the same; in the coherent FDA, different array elements transmit signals with different carrier frequencies, and the carrier frequency of the signal transmitted at the mth array element is f m =f0+△f m Wherein f mThe carrier frequency of the transmitting signal on the mth array element is f m The frequency step size used on the mth array element is f m m represents the number of transmitting array elements, and m is in the range of m = 1, 2,..., M, M is the total number of transmitting array elements, that is, the size of the transmitting array, and too small M will result in too small design space of the frequency step size and too small available size of the array, and the performance cannot be guaranteed, but the increase of M means the increase of the cost of the front end of the array, so the value of M needs to be demonstrated according to actual needs.

[0042] In the generalized coherent FDA signal model built in the application, see Figure 2 , Figure 2 The angle deception jamming scene based on the coherent FDA built in the application is shown in the figure, and the coherent FDA signal model built in the figure is composed of M array elements, and the array element spacing is d R After introducing the frequency step size, the carrier frequency of the transmitting signal of the mth array element is f m = f0+ f m , f m is the frequency step size used on the mth array element.

[0043] 2.2 Obtain the transmitting signal of the mth array element: after introducing the frequency step size, the transmitting carrier frequency f m of the mth array element is obtained, and the signal of the mth transmitting array element is modulated to the carrier frequency, and the transmitting signal of the mth array element is:

[0044]

[0045] Where E represents the transmitting energy of the entire array, which depends on the transmitting power of the radar, w m is the weighting modulation term used by the mth antenna, which can be arbitrarily modulated to the phase, is the transmitted baseband waveform, in order to perform matched filtering processing in the radar, the transmitted waveform usually uses a linear frequency modulation signal, which has the form:

[0046]

[0047] Where t is time, and j is the imaginary unit; is the pulse gate function, and μ = B / T p is the frequency modulation rate of the linear frequency modulation signal, B is the transmitting signal bandwidth, and T p is the pulse duration; in the actual signal generation process, the transmitting signal is sampled into discrete sampling points, and the sampling rate is F s , the number of sampling points in the pulse duration is F s ·T p .

[0048] 2.3 Forming the coherent FDA combined signal, i.e. the spoof jamming signal: after obtaining the transmitting signal of the mth array element, the transmitting signals of all M array elements are added to obtain the coherent FDA combined signal, i.e. the spoof jamming signal; taking the first transmitting array element of the generalized coherent FDA signal model as a reference array element, the spatial position (θ0, R0) represents a distance of R0 from the first transmitting array element and an angle of θ0 offset from the normal of the transmitting array, and the coherent FDA combined signal at the position is:

[0049]

[0050] where c is the speed of light, R m represents the radial distance between the mth array element and the spatial position (θ0, R0). Under the far-field condition, the narrowband signal has a plane wave assumption, i.e. At this time, the transmitting signal of each array element can be regarded as parallel, and thus the radial distance R m is written as: m R T = R0- (m-1) d T sinθ0. According to the expression of the radial distance, the coherent FDA combined signal at the spatial position (θ0, R0) is written as:

[0051]

[0052] where represents a weighted modulation vector obtained by arranging the weighted modulation terms on the M array elements into a vector form, represents a distance-angle-time steering vector, which contains a distance-angle-time-frequency offset related phase term, and the steering vector is written as:

[0053] d(t, θ0, R0, △f) = v(t, △f) ⊙ a(θ0) ⊙ r(R0, △f)

[0054] where and respectively represent angle-related, time-related, and distance-related transmitting steering vectors, and are respectively written as:

[0055]

[0056] where d T represents the element spacing of the transmitting array, and in engineering, the element spacing is usually half a wavelength to avoid the generation of angle dimension grating lobes, i.e. represents a frequency step amount vector, and is written as:

[0057] △f = [△f1, △f2, …, △f M ] T

[0058] The form of the coherent FDA combined signal of the present application at spatial position (θ0, R0) is the result of the summation of the transmit steering vector and the weighted modulation vector, and the transmit steering vector contains the phase term related to frequency offset-time-distance-angle, which together with the weighted modulation vector controls the electromagnetic energy at spatial position (θ0, R0).

[0059] Referring to Figure 3 , Figure 3 is the phase distribution of the coherent FDA combined signal of the present application in the distance-angle space, and the phase of the coherent FDA combined signal is distributed as "S" in the two-dimensional distance-angle space, which indicates that the electromagnetic energy at spatial position (θ0, R0) is controlled by transmitting the coherent FDA signal based on the frequency step and the weighted modulation, and it is shown that the phase distribution of the coherent FDA combined signal of the present application in space is jointly modulated by distance and angle.

[0060] The present application obtains the electromagnetic signal related to distance-angle-time-frequency offset by changing the carrier frequency of the signal transmitted by each array element and using the weighted modulation term to arbitrarily modulate the phase of the signal transmitted by the array element.

[0061] In order to compare the coherent FDA combined signal of the present application with the existing PA signal without frequency step.

[0062] 2.4. Obtain the phased array combined signal without introducing frequency step: in order to compare the coherent FDA combined signal of the present application, the phased array signal transmitted when no frequency step is introduced between adjacent array elements is given, and the phased array combined signal at spatial position (θ0, R0) can be written as:

[0063]

[0064] wherein represents the transmit steering vector of the phased array, and is

[0065]

[0066] Referring to Figure 4 , Figure 4 is the phase distribution of the PA combined signal in the distance-angle space, and when the signals transmitted by all array elements are located at the same carrier frequency, the phase distribution of the combined signal in space is only affected by the change of angle.

[0067] In the above formula, the phased array combined signal is jointly controlled by its transmit steering vector and weighted modulation vector. However, the transmit steering vector of the phased array only contains angle-related phase terms. Compared with the frequency-offset-time-distance-angle-related phase terms in the coherent FDA combined signal, it lacks the control capability in the frequency-offset-time-distance dimension, cannot generate deceptive interference signals, and cannot control the electromagnetic energy at the spatial position (θ0, R0) in the frequency-offset-time-distance dimension.

[0068] Example 3

[0069] A method for generating angle deception jamming of an array radar based on coherent FDA is the same as that in Examples 1-2. The deception jamming signal described in step 3 of the present invention forms a non-uniform phase difference in the far-field array, comprising the following steps:

[0070] 3.1 Define the XoZ space coordinate system: Construct the XoZ coordinate system in space. The coordinate system takes the position of the first transmitting array element as the coordinate origin (0,0). The coordinates of the mth transmitting array element are written as: ((m-1)d T ,0), for any point in space, the coordinates of the point in the distance-angle coordinate system are (θ,R), and the conversion equation between the distance-angle coordinate system and the XoZ coordinate system is written as:

[0071]

[0072] Where (x, z) represents the coordinates of the spatial position (θ, R) in the XoZ coordinate system, x represents the projection distance between the position and the transmitting array element on the X axis, and z represents the height of the position, that is, the projection distance on the Z axis.

[0073] 3.2 Obtaining the far-field receiver coordinates: Assume that there is an array receiver in the far field of space. The array receiver includes N array elements with equal spacing and uniform distribution, and the array element spacing is half a wavelength, that is, Furthermore, the coordinates of the nth receiving element of the receiver in the XoZ coordinate system are written as:

[0074]

[0075] 3.3 Obtaining the coherent FDA composite signal at each receiving element position: Each receiving element receives the transmitted coherent FDA signal based on the frequency step amount and weighted modulation. According to the above coordinate system conversion formula and the generalized coherent FDA signal model given in 2.3, the FDA composite signal at the nth receiving element of the far-field receiving array is written as:

[0076]

[0077] in Rm,n represents the radial distance between the mthtransmitting element and the nthreceiving element, which is not linearly changed with the transmitting and receiving elements; without considering the waveform envelope and amplitude attenuation, i.e. the approximation in the signal and At this time, the FDA signal at the nthreceiving element of the far-field array is written as:

[0078]

[0079] where β represents the complex amplitude considering the waveform envelope, channel propagation coefficient, and antenna gain, Rm,n represents the radial distance between the mthtransmitting element and the nthreceiving element, which is not linearly changed with the transmitting and receiving elements; without considering the waveform envelope and amplitude attenuation, i.e. the approximation in the signal

[0080] r n =[R 1,n ,R 2,n ,...,R M,n ] T

[0081] Since and the number of transmitting elements m and the number of receiving elements n are not linearly related, the above radial distance vector also does not change linearly with the number of elements.

[0082] 3.4 Obtain the non-uniform phase difference: extract the phase of the FDA combined signal at the nthand (n+1)threceiving elements, and subtract the phases to obtain the phase difference of the coherent FDA combined signal at the nthand (n+1)threceiving elements:

[0083]

[0084] The above phase difference is the result of the joint modulation of the frequency increment and the weighting modulation term. In general cases, the frequency offset increases linearly and the transmitting weight is 1. At this time, the frequency offset modulation vector and the transmitting weight vector can be written as:

[0085] △f=[0,△f,…,(m-1)△f m ,…,(M-1)△f M ] T

[0086] w=[1,1,...,1] T =1 M

[0087] Bring the above frequency modulation vector and transmitting weight vector into the phase difference of the coherent FDA combined signal at the nthand (n+1)threceiving elements, and we have:

[0088]

[0089] where △R n =(R 1,n -R 1,n+1 ) represents the radial distance difference between the nth and n+1th receiving elements and the first transmitting element, and is represented by From the expression of △R n It does not change linearly with the number n of receiving array elements, which causes the phase difference of the coherent FDA combined signals received by different receiving array elements to be non-uniform.

[0090] In order to compare the non-uniform phase difference formed by the coherent FDA combined signal of the present invention with the uniform phase difference obtained by the PA signal without using the frequency step amount, a comparison is made.

[0091] 3.5 Obtaining the uniform phase difference when no frequency step is introduced: When no frequency step is introduced between adjacent array elements, that is, when the phased array signal is transmitted, the phase difference between the signal received by the nth array element and the n+1th receiving array element is written as:

[0092]

[0093] In the above formula, the phase difference between the two receiving elements in PA mode is a uniform quantity that is only related to the direction of arrival angle. However, in FDA mode, the phase difference between the two receiving elements is related to the frequency offset, distance, time, and angle. Because the distances between different receiving elements and the first transmitting element are non-uniform, the phase difference is also non-uniform.

[0094] The deceptive jamming signal of the present invention forms a non-uniform phase difference in the far-field array. The transmitted coherent FDA combined signal and the far-field receiver array are integrated into a coordinate system through coordinate transformation. The non-uniform phase difference between adjacent receiving elements is obtained by phase extraction of the received signal at each receiving element. This non-uniform phase difference is jointly controlled by the frequency step amount and the weighted modulation term, and has a more flexible phase control capability than the existing method of using the same frequency transmission signal.

[0095] Example 4

[0096] A method for generating angle deception jamming for an array radar based on coherent FDA is the same as that in Examples 1-3. The non-uniform phase difference affecting the far-field angle measurement result described in step 4 of the present invention includes the following steps:

[0097] 4.1 Obtaining the vector form of the coherent FDA signal received by the far-field array: Arrange the coherent FDA signal received by each receiving array element into a vector form, and obtain the received echo vector received by the far-field array system as:

[0098]

[0099] in and denote the receive steering vector of the receive array system and the transmit steering matrix of the coherent FDA combined signal respectively, written as

[0100]

[0101] D(t, θ, r, Δf) = [d(t, θ, r1, Δf), d(t, θ, r2, Δf),..., d(t, θ, rM, Δf)] N

[0102] wherein denotes the vector composed of radial distances between all M transmit and N receive elements, written as

[0103]

[0104] The transmit steering matrix of the coherent FDA combined signal of the present application contains all the phase terms of the distance-time correlation generated by the M transmit carrier frequencies, which is jointly modulated by the frequency stepping amount and the transmit weighting vector, and in turn the transmit steering matrix modulates the received echo vector received by the far-field array system.

[0105] For comparison, the vector form of the coherent FDA combined signal of the present application is compared with the vector form of the PA signal without frequency stepping amount.

[0106] 4.2 Obtain the vector form of the far-field array received phased array combined signal: As a comparison, the vector form of the received signal received by the far-field array system when the frequency stepping amount is zero, i.e. the phased array combined signal, is given when the position of the signal transmitting source is unchanged.

[0107]

[0108] wherein denotes the transmit steering vector without frequency modulation, written as

[0109]

[0110] When no frequency modulation is used, the signal received by the far-field array receiver is only related to the angle of the signal relative to the receive array;

[0111] 4.3 Perform angle estimation of the phased array signal: the far-field receiver array uses maximum likelihood angle measurement on the received signal in the phased array mode, the maximum likelihood angle measurement uses angle dimension search, constructs a spatial spectrum for each angle and calculates the power at the angle, and the angle corresponding to the maximum power is taken as the angle measurement result; the maximum likelihood angle measurement result of the phased array signal is:

[0112] ​

[0113] In the above formula, when θ k = -θ, the output power reaches the maximum value, which indicates that the accurate angle measurement result can be obtained in the phased array mode;

[0114] 4.4 Angle estimation of the coherent FDA combined signal is performed to obtain a biased angle measurement result: the far-field receiver array performs maximum likelihood angle measurement on the coherent FDA signal, and the angle estimation result is written as

[0115]

[0116] The real angle value θ k = -θ is substituted into the above formula, and the obtained power is written as:

[0117] P(θ k ) = |b H (θ)diag{b * (θ)}D T (t, θ, r, △f)w| 2

[0118] = |w T D(t, θ, r, △f)1 N | 2

[0119] The power value in the above formula is jointly modulated by the transmission modulation weight w, the frequency offset vector △f and the radial distance vector r, and this angle is not necessarily equal to the real target incident angle; this indicates that in the scenario of given spatial array receiver positions, the angle estimation of the array receiver can be offset by modulating △f and the transmission weight vector w, and the obtained angle measurement result is a biased angle measurement result; in a specific scenario, the frequency step size vector △f can be optimized for a certain scenario to make the angle measurement result deviate greatly from the real angle, but in actual engineering, the hardware system may be difficult to achieve the precision of the theoretical frequency step size, which will cause the angle measurement result obtained by the receiving array system to deviate from the result obtained by theoretical calculation, at this time, the minimum precision constraint that can be reached by the hardware system should be added in the selection of the frequency step size to meet the engineering implementation conditions; in addition, the transmission weight vector w modulus in engineering is usually constant, and the constant modulus constraint also needs to be considered in the process of theoretical optimization to meet the engineering implementation scenario.

[0120] The application arranges the signals received by each receiving element of the far-field array into a vector form, and obtains the angle measurement result of the receiving array system by using the maximum likelihood estimation method, and the non-uniform phase difference between different array elements causes the angle measurement result to be jointly modulated by the frequency step size and the weighting modulation term, the coupling of the frequency step size and the distance causes different receiving elements to be on a non-equal phase surface, and the weighting modulation term can regulate the phase difference between different receiving elements, and through the combination of the two, the non-uniform phase difference between the receiving elements can be effectively modulated, so that the angle measurement result based on the maximum likelihood method is a biased angle measurement result.

[0121] Embodiment 5

[0122] A coherent FDA-based array radar angle deception jamming generation method same as embodiments 1-4, the implementation of the deception to the far-field array in step 5 of the application comprises the following steps:

[0123] According to the angle estimation result of the maximum likelihood angle measurement of the coherent FDA signal obtained in step 4.4, under the given position of the spatial far-field receiver array, the modulation of the frequency step size and the transmission weight vector will affect the angle measurement result of the coherent FDA signal by the far-field array receiver, and affect the positioning result of the FDA signal transmitter, and the angle estimation deviation and the positioning deviation obtained by the far-field receiver are respectively written as:

[0124]

[0125] When the angle estimation deviation obtained by the far-field array receiver is larger, the positioning result of the transmitting array is also larger than the real position of the transmitter, thereby realizing the deception effect on the far-field array.

[0126] The application realizes the deception to the far-field array by the biased angle measurement result of the far-field receiver array to the transmitting array, and the positioning result is deviated, and the far-field array receiver realizes the positioning to the transmitting array through the measured biased angle measurement result, under the given distance between the transmitting array and the receiving array, the larger the angle estimation deviation of the far-field receiver array caused by the frequency modulation and the transmission weighting modulation, the larger the positioning estimation deviation of the transmitting array, thereby realizing the deception effect on the far-field array.

[0127] The present application builds a generalized coherent FDA signal model, and adopts frequency step size and weighted modulation at the transmitting end to form a distance-angle-time-frequency offset related coherent FDA combined signal in space, and regulates the electromagnetic energy at the spatial far field position; the generated coherent FDA combined signal forms a non-uniform phase difference through the far field array, which affects the angle measurement result of the far field array receiver; according to the position of the far field array, the frequency step size and the transmitting weight vector are designed to make the far field array deviate in angle measurement and positioning of the received coherent FDA combined signal, so as to realize the angle deception effect of the far field array, which can be used for deception jamming of radar reconnaissance equipment.

[0128] The technical effects of the present application are verified by the simulation test results as follows:

[0129] Embodiment 6

[0130] A kind of array radar angle deception jamming generation method based on coherent FDA same as embodiment 1-5,

[0131] 1. Simulation conditions:

[0132] The hardware test platform of the simulation test is: the CPU is Intel (R) Core (TM) i7-10700, the main frequency is 2.9GHz, and the memory is 32GB.

[0133] The software test platform of the simulation experiment is: Windows10 operating system, Matlab2019b.

[0134] Simulation parameters: the number of transmitting and receiving elements is 8, the carrier frequency is 1GHz, the transmitting and receiving element spacing is 0.15m, the pulse repetition frequency is 100μs, the pulse width is 10μs, and the bandwidth is 3MHz.

[0135] The above simulation parameters are shown in Table 1:

[0136] Table 1 System simulation parameters

[0137]

[0138] 2. Simulation content:

[0139] Simulation 1, under the above simulation parameters, the phase direction diagram of the transmitting PA combined signal and the coherent FDA combined signal of the present application is simulated, when the PA combined signal is simulated, the frequency step size is 0, when the coherent FDA combined signal is simulated, the frequency step size is 4kHz and the fixed time t=10μs, the simulation results are shown in Figure 3 and Figure 4

[0140] Referring to Figure 3 , Figure 3 ​is a phase distribution diagram of the coherent FDA combined signal in the distance-angle space, which describes the phase distribution of the coherent FDA combined signal in the distance-angle space at a certain moment, Figure 3 The abscissa is the angle, and the ordinate is the distance of signal propagation. The coherent FDA combined signal of the present application changes the phase in space with the distance and the angle by using the frequency step and the weighting modulation between the transmitting elements, and the equal phase surface forms an "S" type curve in space with the change of the distance and the angle. When the angle is fixed, the phase has a certain periodicity in the distance. When the distance is fixed, the equal phase surface does not focus in one direction, but constantly scans all angles in the space.

[0141] Referring to Figure 4 , Figure 4 is a phase distribution diagram of the PA combined signal in the distance-angle space, Figure 4 The abscissa is the angle, and the ordinate is the distance of signal propagation. The transmitting PA signal does not use the frequency step and the weighting modulation at the transmitting end, and the phase change in space is only related to the angle. The phase distribution in space is a straight line along the angle, which indicates that the phase at different distances at the same angle is the same, and the phase of the PA combined signal does not change with the distance.

[0142] As can be seen from the simulation results, the coherent FDA signal of the present application forms a distance-angle two-dimensional phase distribution diagram by introducing the frequency step between the elements, which destroys the equal phase surface of the far-field electromagnetic signal, and can effectively regulate the electromagnetic energy in space,

[0143] Embodiment 7

[0144] A method for generating angle deception jamming of an array radar based on coherent FDA is the same as that in Embodiments 1-5.

[0145] Simulation conditions: as in Embodiment 6.

[0146] Simulation content:

[0147] Simulation 2: Under the above simulation parameters, the maximum likelihood angle estimation result of the far-field array receiver is simulated. At this time, the transmitting signal uses the PA signal (the frequency step is 0), the ULFDA signal (the frequency step increases linearly), the LogFDA signal (the frequency step increases exponentially), and the RandFDA signal (the frequency step increases randomly). The far-field array receiver uses the maximum likelihood method to estimate the angle of the received coherent FDA combined signal, compares the estimation result with the true result, obtains the angle estimation error, and the simulation result is shown in Figure 5 , Figure 6 and Figure 7 .

[0148] Referring to Figure 5, Figure 5 is a graph of the influence of the receiving array angle-angle estimation bias of the application, Figure 5 The abscissa of the graph is the angle of the far-field receiver relative to the FDA transmitting signal model, and the ordinate is the bias between the signal incidence angle estimated by the far-field receiver and the true signal incidence angle. In the experiment, the radial distance between the far-field array receiver and the coherent FDA signal model is fixed, and only the angle between the two is changed. In the graph, the red curve represents the angle estimation bias when the frequency step is 0, that is, when the PA signal is transmitted. The blue curve represents the angle estimation bias when the frequency step is uniformly and linearly increased, that is, when the ULFDA signal is transmitted. The magenta curve represents the angle estimation bias when the frequency step is exponentially increased, that is, when the LogFDA signal is transmitted. The black curve represents the angle estimation bias when the frequency step is randomly selected, that is, when the RandFDA signal is transmitted. The fluctuation of the curve along the ordinate in the graph represents the size of the angle estimation bias. When the far-field array receiver is located at -34°, the coherent FDA signal of the application makes the angle estimation result of the receiver array deviate from the true angle by 12.9°, which has the ability of angle deception. However, the angle estimation result of the PA signal is always 0° deviated from the true angle, which means that the PA signal cannot deceive the receiver array in terms of angle.

[0149] Referring to Figure 6 , Figure 6 is a graph of the influence of the receiving array distance-angle estimation bias of the application, Figure 6 The abscissa of the graph is the radial distance between the far-field receiver and the coherent FDA transmitting signal model, and the ordinate is the bias between the signal incidence angle estimated by the far-field receiver and the true signal incidence angle. In the experiment, the angle between the far-field receiver and the coherent FDA signal model is fixed. The correspondence between the curve color in the graph and the transmitted signal is as follows Figure 5 . The fluctuation of the curve along the ordinate in the graph represents the bias between the angle estimation result of the far-field array receiver and the true angle. In the blue curve, when the radial distance between the receiver array and the transmitting signal model is 146.2 km, the coherent FDA signal of the application makes the angle estimation result of the receiver array deviate from the true angle by 10.7°, which illustrates the angle deception ability of the application to the far-field array receiver. In the red curve, the angle estimation bias is always 0°, which means that the angle estimation result of the PA signal is always equal to the true angle estimation result and does not change with the radial distance. The PA signal cannot deceive the receiver array in terms of angle.

[0150] Referring to Figure 7 , Figure 7 is a graph of the influence of the frequency step-angle estimation bias of the application, Figure 7The abscissa of the figure is the size of the frequency step, and the ordinate is the deviation between the signal incidence angle estimated by the far-field receiver and the true signal incidence angle. In the experiment, the distance and angle of the far-field receiver are fixed, and only the size of the frequency step in the coherent FDA signal model is changed. The blue curve, the magenta curve and the black curve in the figure respectively represent three kinds of coherent FDA transmission signal models, which respectively adopt linearly increasing, exponentially increasing and randomly selected frequency steps. The angle estimation deviation of the three curves increases with the increase of the frequency step, indicating that the size of the frequency step affects the angle estimation deviation. In the blue curve, when the frequency step is 373.1 kHz, the angle measurement result of the receiver array deviates from the true angle by-8.95°, which illustrates the angle deception capability of the far-field array receiver of the application; the red curve represents the deviation between the angle measurement result of the far-field receiver and the true angle when the frequency step is not used. The red curve is always equal to 0, indicating that the PA signal cannot form angle deception to the receiver array.

[0151] The above results verify the correctness, effectiveness and reliability of the application. The results show that the coherent FDA in the application has angle deception capability to the array receiver and can be used in the field of electronic countermeasure to deceive the angle measurement of the array radar, so as to make the angle measurement of the opponent's array radar system invalid and protect the effectiveness of the work of the high-value target.

[0152] In summary, the application discloses a method for generating array radar angle deception jamming based on coherent FDA, and mainly solves the problem that the prior art cannot deceive the angle of the array radar receiver. The implementation scheme is as follows: a generalized coherent FDA signal model is built; a coherent FDA signal based on frequency step and weighted modulation is transmitted; the deception jamming signal forms a non-uniform phase difference in the far-field array; the non-uniform phase difference affects the far-field angle measurement result; and the deception to the far-field array is realized. The application introduces the frequency step between adjacent transmitting array elements, forms a distance-angle-time-frequency offset joint modulated electromagnetic signal in the spatial far field, causes the non-uniform phase difference between different array elements of the receiving array, and causes the angle measurement and positioning error of the array receiver. The application transmits the frequency diversity signal to destroy the equal phase surface of the far-field electromagnetic signal, realizes the electromagnetic energy regulation through the weighted modulation, significantly improves the angle deception jamming capability to the far-field array receiver, and can be used in the electronic countermeasure process to deceive the angle of the radar reconnaissance equipment and protect the high-value target.

[0153] It should be noted that the step numbers in the specification and claims of the application are only for the clear description of the implementation scheme of the application, and the sequence of the numbers is not limited

[0154] Furthermore, the application itself has been described in considerable detail hereinabove, with general and specific reference to certain embodiments of the application. It is to be understood that modifications and improvements to the application have been and are still considered desirable, and as such, go within the scope of the application. Accordingly, the modifications and improvements to the application as described hereinabove are to be considered as within the scope of the application as defined in the following claims.

Claims

1. A method for generating angle deception jamming for array radar based on coherent FDA, characterized in that: By introducing a frequency step between adjacent transmitting array elements, an electromagnetic signal modulated by distance, angle, time, and frequency deviation is formed in the far field, causing angle measurement and positioning errors in the array receiver. The following steps are included: Step 1: Build a generalized coherent FDA signal model: The generalized coherent FDA signal model is a one-dimensional linear array consisting of M equally spaced and evenly distributed array elements. Each element is an omnidirectional antenna, and each antenna contains an independent transmit and receive channel. Step 2: Transmit a coherent FDA signal based on frequency stepping and weighted modulation: The transmission signal of each array element in the FDA signal model is a linear frequency modulation waveform. During the signal transmission process, frequency stepping is introduced between adjacent array elements, so that different array elements operate at different transmission frequencies. During the propagation of the transmitted signal in space, a phase related to frequency deviation, time, distance, and angle is formed, which destroys the isophase surface of the electromagnetic signal in the far field. At the same time, weighted modulation is performed on each array element to form an FDA composite signal, that is, a deceptive interference signal, to achieve electromagnetic energy control at different locations in space. Step 3: The deceptive jamming signal forms a non-uniform phase difference in the far-field array: There is an array receiving system composed of N array elements in the far field of space. Each array element of the receiving system receives the FDA composite signal at its location, so that there is a non-uniform phase difference between the signals received by different array elements. Step 4: Non-uniform phase differences affect far-field angle measurement results: The signals at different receiving array elements are arranged in vector form to estimate the angle of the signal. Due to the frequency step size and weighted modulation, the non-uniform phase difference between the far-field arrays affects the angle measurement result, resulting in a biased angle measurement result. Step 5: Deceiving the far-field array: Biased angle measurement results lead to angle estimation errors and positioning errors in the far-field array. For a given spatial position of the far-field receiver array, the signal received by the far-field receiver is modulated only by the frequency step amount and the transmit weight vector. This modulation introduces non-uniform phase differences between different receiving array elements, causing deviations in the angle estimation results. Biased angle estimation leads to deviations in the positioning of the FDA signal model, thus deceiving the far-field array.

2. The array radar angle deception jamming generation method based on coherent FDA according to claim 1 is characterized in that: The step 2 of transmitting the coherent FDA signal based on the frequency step amount and weighted modulation includes the following steps: 2.1 Introducing frequency stepping: Taking the first transmitting array element as the reference array element, the carrier frequency of the transmitted signal at this array element is the reference carrier frequency f0. Frequency stepping is introduced between adjacent array elements. The carrier frequency of the transmitted signal at the mth array element is written as: f m =f0+Δf m ,m=1,2,...,M, where f m is the carrier frequency of the transmitted signal on the mth array element, Δf m is the frequency step size used on the mth array element, where m represents the number of transmitting array elements; 2.2 Obtain the transmitted signal of the mth array element: Substitute the frequency step amount, and the transmitted signal of the mth array element is written as: Where E represents the emission energy of the entire array, w m is the weighted modulation term of the mth antenna, is the baseband waveform, usually a linear frequency modulation signal, which is in the form of: Where t is time and j is the imaginary unit; is the pulse gate function, μ=B / T p is the modulation frequency of the linear frequency modulation signal, B is the transmission signal bandwidth, T p is the pulse duration; 2.3 Forming a coherent FDA sum signal, i.e., a deceptive jamming signal: The transmit signals of all M array elements are added together to obtain a coherent FDA sum signal, i.e., a deceptive jamming signal. Taking the first transmitting array element as the reference array element, the coherent FDA sum signal at any position (θ0, R0) in space is obtained as: Where c is the speed of light, R m Indicates the radial distance between the mth array element and the spatial position (θ0, R0). In the far field, the transmitted signals of each array element can be regarded as parallel, so the radial distance is written as: R m =R0-(m-1)d T sinθ0, the coherent FDA signal at any position (θ0, R0) in space is written as: in represents the weighted modulation vector, represents the distance-angle-time steering vector, which is written as: d(t,θ0,R0,Δf)=v(t,Δf)ea(θ0)er(R0,Δf) in and They represent the angle-related, time-related, and distance-related launch steering vectors, respectively, and are written as: where d T Represents the element spacing of the transmitting array, usually half a wavelength, that is, represents the frequency offset vector, written as: Δf=[Δf1,Δf2,L,Δf M ] T The coherent FDA combined signal at the spatial position (θ0, R0) is the result of the summation of the transmission steering vector and the weighted modulation vector. The transmission steering vector contains a phase term related to frequency deviation, time, distance and angle. This phase term and the weighted modulation vector jointly regulate the electromagnetic energy at the spatial position (θ0, R0).

3. The method for generating angle deception jamming for array radar based on coherent FDA according to claim 1, wherein the step of forming a non-uniform phase difference of the deception jamming signal in the far-field array comprises the following steps: 3.1 Define the XoZ space coordinate system: Construct the XoZ coordinate system in space. The coordinate system takes the position of the first transmitting array element as the coordinate origin (0,0). The coordinates of the mth transmitting array element are written as: ((m-1)d T ,0), for the spatial position (θ,R), the conversion equation between the distance-angle coordinate system and the XoZ coordinate system is written as: Where (x, z) represents the coordinates of the spatial position (θ, R) in the XoZ coordinate system; 3.2 Obtaining the far-field receiver coordinates: Assume that there is an array receiver in the far field of space. The array receiver includes N array elements with equal spacing and uniform distribution, and the array element spacing is half a wavelength, that is, The coordinates of the nth receiving element of the receiver in the XoZ coordinate system are written as: 3.3 Obtain the coherent FDA sum signal at each receiving element position: According to the coordinate system conversion formula and the FDA signal model given in 2.3, the FDA sum signal at the nth receiving element of the far-field receiving array is written as: in represents the radial distance between the mth transmitting element and the nth receiving element. Without considering the waveform envelope and amplitude attenuation, the FDA signal at the nth receiving element of the far-field array is further written as: Where β represents the complex amplitude after considering the waveform envelope, channel propagation coefficient, and antenna gain. Represents the radial distance vector between the nth receiving element and the M transmitting elements, written as r n =[R 1,n ,R 2,n ,K,R M,n ] T 3.4 Obtaining the non-uniform phase difference: Based on the FDA composite signal at the nth receiving element, the phase difference between the signals received by the nth element and the n+1th receiving element is written as: When a linearly increasing frequency offset is used and the transmit weight is all 1, the above phase difference can be expressed as: where ΔR n =(R 1,n -R 1,n+1 ) represents the radial distance difference between the nth and n+1th receiving elements and the first transmitting element. In FDA mode, the phase difference between two receiving elements is related to frequency offset, distance, time, and angle. Because the distance differences between different receiving elements and the first transmitting element are non-uniform, the phase difference is also non-uniform.

4. The method for generating angle deception jamming of array radar based on coherent FDA according to claim 1, characterized in that: The non-uniform phase difference affecting the far-field angle measurement results described in step 4 includes the following steps: 4.1 Obtaining the vector form of the coherent FDA combined signal received by the far-field array: Arranging the coherent FDA signals received by each receiving array element, the signal form received by the far-field array system can be obtained as follows: in and denote the receiving steering vector and transmitting steering matrix respectively, and D(t,θ,r,Δf)=[d(t,θ,r1,Δf),d(t,θ,r2,Δf),K,d(t,θ,r N ,Δf)] in represents the radial distance vector between all transmitting and receiving array elements, written as The FDA signal received by the array contains the range-time related phase terms generated by all M transmitting carrier frequencies at each receiving element; 4.2 Obtaining the vector form of the phased array combined signal received by the far-field array: For comparison, the signal form of the phased array signal transmitted and received by the far-field array system in the same scenario is given as follows: in represents the launch steering vector of the phased array, which is In phased array mode, the received signal is only related to the direction of arrival angle; 4.3 Angle estimation of phased array signals: Maximum likelihood angle measurement is used for the received signals in phased array mode to obtain: In the above formula, when θ k = -θ, the above formula obtains the maximum value, indicating that accurate angle measurement results can be obtained in the phased array mode; 4.4 Perform angle estimation on the coherent FDA combined signal and obtain the biased angle measurement result: Perform maximum likelihood angle measurement on the coherent FDA signal and write the angle estimation result as When θ k = -θ, the power obtained is written as: The power value here is jointly modulated by the transmit weight w, the frequency offset Δf, and the radial distance r. This phenomenon shows that, given the location of a spatial array receiver, the angle estimate of the array receiver can be offset by modulating Δf and the transmit weight vector w, resulting in a biased angle measurement.

5. The method for generating angle deception jamming of array radar based on coherent FDA according to claim 1, characterized in that: The steps to achieve deception of the far-field array described in step 5 include the following: Based on the maximum likelihood angle estimation results of the coherent FDA signal obtained in step 4.4, given the position of the far-field receiver array, the modulation frequency step amount and the transmission weight vector will affect the angle measurement results of the far-field array receiver for the coherent FDA signal and the positioning results of the FDA signal transmitter. The angle estimation error and positioning error obtained by the far-field receiver are written as: The greater the deviation between the angle estimate obtained by the far-field array receiver and the actual angle, the greater the angle estimation deviation and positioning deviation obtained, thereby achieving a deceptive effect on the far-field array.

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