CN113791392B - Spoofing method based on frequency control array to omnidirectional amplitude comparison single pulse direction finding system - Google Patents
Spoofing method based on frequency control array to omnidirectional amplitude comparison single pulse direction finding system Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/38—Jamming means, e.g. producing false echoes
Abstract
The application discloses a method for positioning deception of an omnidirectional amplitude comparison single-pulse direction finding system based on a frequency control array, which is different from the phased array which controls beam pointing through phase differences among array elements, and a frequency control array (FDA) radar can realize beam control with higher degree of freedom by introducing frequency differences among the array elements. The main lobe energy of the space beam is bent in the energy domain due to the interference effect of field intensity, so that a virtual radiation source is formed, and angle deception is formed on the nAbD direction finding of the reconnaissance receiver. Experiments show that by adopting the deception method, the detection precision of the my radar can be improved, and the deception effect on the enemy jammer can be enhanced.
Description
Technical Field
The application relates to the field of electronic countermeasure, in particular to a spoofing method based on a frequency control array pair omnidirectional amplitude comparison single pulse direction finding system.
Background
Electronic countermeasures are a special combat means in modern warfare, and mainly comprise basic contents such as electronic countermeasures, electronic attack, electronic defense and the like. The essence of direction finding in electron countering scout is to determine or estimate the direction of arrival (DOA) or angle of arrival (AOA) of the incoming wave of the radiation source in space, and is therefore also referred to as passive or passive goniometry. In electronic countermeasure, the jammer emits interference to the enemy target radar, and meanwhile, the radiation signal of the jammer can be captured by the enemy passive detection radar so as to accurately position the jammer, which can pose a serious threat to the safety of the jammer. Therefore, a new system radar needs to be developed to shield an jammer by reducing the interception probability, and the traditional phased array radar changes the phase position between adjacent array elements through a direction shifter to realize the scanning of a beam in space, so that the determining factor of the beam pointing is only the phase position, is irrelevant to the distance, and is easy to be detected by an enemy direction-finding system to interfere and hit the direction of a radiation source.
The frequency diversity array (frequency diverse array, FDA) can synthesize the wave beam with three-dimensional correlation of time-distance-angle by introducing a micro frequency offset between array elements, so that after the radiation signal of the interference machine based on the FDA reaches the signal receiver of the target radar direction-finding system, a virtual radiation source can be formed due to the time-distance-angle correlation characteristic of the wave beam emitted by the FDA, and the positioning of the enemy radar is misled, thereby ensuring that the interference machine on my effectively performs a shielding task.
Disclosure of Invention
Aiming at the problems, the application aims to provide a deception method based on a frequency control array to a full-antenna amplitude-comparison direction-finding system, and the deception effect on an enemy jammer is enhanced while the detection precision of the my radar is improved by using the deception method.
In order to achieve the above purpose, the technical scheme adopted by the application is as follows:
a deception method for a full-antenna amplitude-comparison direction-finding system based on a frequency control array is characterized by comprising the following steps:
step 1: constructing a frequency control array radar system;
step 2: establishing a deception model of the frequency control array radar system on the full-antenna amplitude comparison direction-finding system;
step 3: obtaining a distance expression between the frequency control array elements and the direction finding system array antenna elements and an expression of signals received by the direction finding system;
step 4: and obtaining the DOA estimated angle of the direction finding system based on the deception model of the full-antenna amplitude comparison direction finding system, calculating the angle deviation and the position deviation of the direction finding system on the positioning of the radiation source, and evaluating the positioning deception effect according to the obtained angle deviation and the position deviation.
Further, the specific steps of the step 1 are as follows:
assuming a uniform linear array frequency control array radar composed of N array elements, as shown in figure 1, wherein the number of the frequency control array elements is N, c is the light speed, the frequency increment between two adjacent array elements is delta f, and the initial carrier frequency f 0 The frequency at the nth array element is f n ＝f 0 +Δf, wherein the array element distance is d, and the distance between the target and the frequency control array is R; the pointing angle of the array signal to the far field is theta, and the radiation signal of the array element n in the frequency control array radiation source is assumed to be:
s n (t)＝exp(j2πf n t),n＝0,1,...,N-1 (1)，
the signal emitted by the nth element at the far field observation point (R, θ) is expressed as:
the combined field strength at the far field observation point (R, θ) is:
let γ=Δft+ (f 0 dsin θ)/c-. DELTA.fR/c due to f 0 > N.DELTA.f, then:
taking array factors as follows:
the phase pattern is:
further, the specific steps of the step 2 are as follows:
step 21: expanding an antenna pattern function F (theta) of the four-antenna omnidirectional amplitude monopulse direction finding system into a Fourier series, namely:
wherein N is the number of antennas of the receiving system, F i (θ) is the pattern function of the ith antenna, a k For Fourier series coefficients, k takes 0 and all positive integers, θ s Is the included angle between adjacent antennas and is 2 pi/N;
step 22: with weights cos (iθ) s ),sin(iθ s ) The output signals of the antennas are weighted and summed, which is equivalent to respectively summing the projections of incoming wave signals received by the antennas in two orthogonal directions, and then:
the unfolding is as follows:
wherein L represents an antenna of the same pattern F (θ);
when the antenna graph function is subjected to Fourier expansion, the coefficients of the higher order terms can be reduced rapidly along with the increase of the times, so that when the number of the antennas is large, approximation is obtained:
step 23: and calculating an incoming wave azimuth angle based on the obtained C (theta) and S (theta), wherein the calculation formula is as follows:
step 24: and (3) establishing a positioning deception model based on the incoming wave azimuth angle obtained in the step (23), wherein a receiving antenna of the full-antenna amplitude comparison direction-finding system in the positioning deception model is an array antenna comprising M array elements, and the distance between adjacent array elements in the array antenna of the omnidirectional amplitude comparison single-pulse direction-finding system is d1.
Further, the specific steps of the step 3 are as follows:
step 31: according to the geometric position relation, calculating the distance R' between the frequency control array element n and the array antenna element m of the omnidirectional amplitude comparison single pulse direction finding system, and calculating the formula:
R'＝R-(n-1)dsinθ+(m-1)d1sin(θ-iθ s ) (12)；
step 32: the expression of the signal received by the direction finding system is:
assuming that the gain of each transmitting array element radiation signal and each receiving array element signal is equal to 1, the signal received by the antenna i is:
further, the specific steps of the step 4 are as follows:
step 41: when Deltaf n When=0, the frequency control array is degraded to a phased array, and the signal received by the antenna i is changed to a signal of formula (13):
the phase pattern is:
φ 1 ＝2πf 0 (t-[R-(N-1)dsinθ/2+(M-1)d1sin(θ-iθ s )/2]/c) (16)；
step 42: assuming that each receive channel performs sub-envelope sampling after threshold detection, equation (11) can be expressed as:
wherein,
step 43: in the full-antenna amplitude-comparison direction-finding system, signal processing is carried out according to a phased array system, the form of a received signal is shown as a formula (15), the actually received signal is a frequency control array signal, and an angle estimated value is obtained by utilizing a solve function in MATLAB
Step 44: calculating the angle deviation and the position deviation of the full antenna specific amplitude direction-finding system for positioning the radiation source, wherein the calculation formula is as follows:
angular deviation:
position deviation:
the beneficial effects of the application are as follows:
based on the spoofing principle of the FDA on the direction-finding system, the application establishes a spoofing model of the FDA on the full-antenna amplitude-comparison (nAbd) direction-finding system, and finally verifies the DOA positioning spoofing effect of the FDA on the nAbd in a non-noise environment and a Gaussian white noise environment through simulation analysis, and the experimental effect shows that the spoofing model has good spoofing effect.
Drawings
FIG. 1 is a schematic diagram of a basic FDA array configuration;
FIG. 2 is a schematic diagram of four-antenna omnidirectional amplitude monopulse direction finding;
FIG. 3 is a diagram showing the positional relationship between a nAbd direction finding system and a frequency controlled array radar jammer;
FIG. 4 is a comparison of four FDA array transmit patterns;
FIG. 5 is a diagram showing the effect of frequency offset increment on the positioning spoofing effect of different arrays;
FIG. 6 is a graph of time versus location spoofing effect for different arrays;
FIG. 7 is an effect of signal-to-noise ratio on position estimation;
FIG. 8 is the effect of time on location estimate RMSE under noisy conditions;
fig. 9 is an illustration of the effect of frequency offset delta on location estimate RMSE under noisy conditions.
Detailed Description
In order to enable those skilled in the art to better understand the technical solution of the present application, the technical solution of the present application is further described below with reference to the accompanying drawings and examples.
To further illustrate the spoofing method proposed by the present application, the principles of FDA and nABD direction finding systems will be briefly described.
1. FDA signal model
As shown in figure 1, the FDA array structure has N array elements and f carrier frequency 0 The radiation signal frequency of the nth array element is:
f n ＝f 0 +Δf n ＝f 0 +x n Δf,n＝0,1,2,...,N-1 (1)，
wherein x is n Representing the coding coefficient, wherein Deltaf is the increment of frequency offset between adjacent array elements, deltaf n Indicating the increment of the frequency offset between the nth array element and the initial array element.
It can be known from the formula (1) that if the coding coefficient x is changed n The FDA array with different frequency control functions can be obtained, when x is n When n, the Uniform Linear FDA (ULFDA) is given when x n When=sin (n), it is sinusoidal FDA (sin-FDA), when x n When=log (n+1), log FDA (log-FDA) is used.
Assuming that the distance between two adjacent array elements is d, the pointing angle of an array signal to a far field is theta, the light speed is c, and assuming that the radiation signals of the array element n in the frequency control array radiation source are as follows:
s n (t)＝exp(j2πf n t),n＝0,1,...,N-1 (2)，
at far field observation point (R, θ):
wherein R is ginsengTaking the distance r from the array element to the target point into consideration n =r-ndsin θ, the combined field strength at the far field observation point (R, θ) is:
the following analysis was performed using ULDA as an example:
the combined field intensity at the far field point (R, theta) is:
let γ=Δft+ (f 0 dsin θ)/c-. DELTA.fR/c due to f 0 > N.DELTA.f, the above can be simplified as:
and array factor is taken as:
the phase pattern is:
2. nAbd direction finding system principle
The principle diagram of the omnidirectional amplitude monopulse direction finding system is shown in the attached figure 2, and the system comprises L antennas with the same direction diagram F (theta), wherein the antennas are uniformly distributed within a 360-degree range to form a circular array, and the opening angles of adjacent antennas are as follows: θ s =360°/L, the system makes DOA (Direction ofarrival) estimations from the amplitude information of the signals received by the respective antennas:
the azimuth direction of each antenna is as follows:
F i (θ)＝F(θ-iθ s ),i＝0,1,2…L-1 (9)，
let the amplitude gain of each channel be k i The log output of the signals received by each antenna through the receiving channel is:
s i (t,θ)＝10lg[k i F(θ-iθ s )A(t)](dB),i＝0,1,…L-1 (10)，
a (t) in formula (10) is a magnitude function of the radiated signal;
the nAbd direction-finding system performs unified processing by using the amplitude information of the signals received by the n antennas, so as to perform DOA estimation. The antenna pattern function F (θ) can be expanded into a fourier series, i.e.:
therein, wherein
With weights cos (iθ) s ),sin(iθ s ) The output signals of the antennas are weighted and summed, which is equivalent to respectively summing the projections of incoming wave signals received by the antennas in two orthogonal directions, and then:
the respective formulae (12-1) and (12-2) are developed to obtain:
in general, the coefficients of the higher order terms decrease rapidly with increasing number of times when the antenna pattern functions are fourier-spread, so that approximation is made when the number of antennas is large:
the azimuth angle of the incoming wave is obtained as follows:
in engineering practice, the signal in a pulse envelope is sampled and then statistically averaged, so that the virtual antenna can be realized. By performing the direction finding process, the direction estimation accuracy can be improved. Assuming that each receive channel performs m envelope samples after threshold detection, equation (15) may be expressed as:
wherein,
the above is an introduction to the principle of the transmitting direction diagram of the FDA signal and the na bd direction finding system, generally, n antennas with the same antenna direction diagram function in the na bd direction finding system are uniformly arranged on a circumference to perform omnidirectional direction finding, all the received signals are projected to two orthogonal directions, and the arctangent of the ratio is obtained, so that the DOA estimation can be performed. Compared with the traditional amplitude comparison method which is difficult to have an ideal antenna directional diagram function and the direction finding precision is easy to influence, the nAbd direction finding method directly processes the amplitude information of signals received by n antennas in one circumference, constructs a virtual ideal antenna and greatly improves the direction finding precision. The transmission direction diagram of the frequency control array has distance dependency, beam direction changes along with the change of the distance, bending characteristics are presented on an energy domain, and in view of the fact that the nAbD direction finding system carries out DOA estimation according to the amplitude of a received signal, the virtual radiation source characteristics of the frequency control array can realize positioning deception on the frequency control array, the application provides an FDA-based deception model, and the positioning deception can be carried out on the nAbD direction finding system through the deception model.
3. FDA-based fraud model
The receiving antenna of the omnidirectional amplitude-comparison single-pulse direction-finding system is assumed to be an array antenna comprising M array elements. The spatial positional relationship between the nAbd direction-finding system and the frequency control array is shown in fig. 3. Assuming that the distance between adjacent array elements in the nAbd direction-finding system array antenna is d1, and the distance between the frequency control array element n and the receiving antenna array element m is R':
R'＝R-(n-1)dsinθ+(m-1)d1sin(θ-iθ s ) (17)，
assuming that the gain of each transmitting array element radiation signal and each receiving array element signal is equal to 1, the signal received by the antenna i is:
when Deltaf n When=0, the frequency control array degenerates into a phased array:
φ 1 ＝2πf 0 (t-[R-(N-1)dsinθ/2+(M-1)d1sin(θ-iθ s )/2]/c) (21)，
the angular deviation of the direction finding system to the positioning of the radiation source is:
examples
In order to verify the feasibility and effect of the fraud model proposed by the present application, the following simulation experiment was performed.
Positioning errors are generally used for measuring positioning accuracy, and in the application, the larger the positioning error is, the better the spoofing effect is. In order to verify the spoofing effect of the proposed model, the application analyzes the angle deviation, the distance deviation and the Root Mean Square Error (RMSE) of the DOA positioning of the nAbd direction finding system based on ULDA, log-FDA, sin-FDA and FDA radiation signals.
1. Simulation experiment
(1) Four array emission pattern comparisons
Assuming the far field target coordinates are (60 km,30 °), Δf=6khz, d=0.15m, f 0 =1 GHz, the number of array elements is 30, and the signal to noise ratio and the dry ratio are 10. FIG. 4 is a diagram of the emission patterns of a PA array, ULDMA array, log-FDA array, sin-FDA array, respectively; from fig. 4, it can be verified that the FDA proposed by the present application can perform location spoofing on the nABD direction-finding system that performs DOA estimation using the amplitude response of the radiation signal, compared to the beam bending characteristics of PA in the energy domain. FIGS. 4 (c) - (d) enable the formation of concentrated energy "spot" beams, eliminating ULDA distance-angle coupling;
(2) Positioning spoofing using different FDA arrays under noiseless conditions
Taking the total number of FDA array elements of N=10, d=0.15m and carrier frequency f 0 =1ghz, the number of receiver antennas of the nabd direction-finding system is l=72, and the angle between adjacent antennas is θ s The number of received array elements of each array antenna is m=10, and the distance between adjacent array elements is d1=0.15M. The FDA jammer is 50km away from the direction finding system, and the real incident angle of the radiation signal is 50 degrees. Because of the introduction of the tiny frequency offset increment, the distance-time dependent wave beam generated by the frequency control array has a positioning deception effect on the direction-finding system, so that the influence of two parameters of the frequency offset increment and the time on the deception effect is mainly simulated in the simulation experiment, the influence of different frequency offset increments on the positioning deception effect when t=40 mu s is shown in fig. 5 (a) - (d), and the influence of different initial times at the position of Δf=1 kHz on the positioning deception effect is shown in fig. 6 (a) - (d). As can be seen from fig. 5 and fig. 6, the signal radiated by the conventional phased array radar has no spoofing effect and is easy to intercept by a direction-finding system. The signals radiated by the FDA array have a deception effect on the direction-finding system, wherein the deception effect of the ULDA array is better than that of other two nonlinear frequency control functions. And the optimal spoofing effect can be achieved at a specific frequency offset and a specific time.
(3) Positioning spoofing with different FDA arrays in case of Gaussian white noise
The basic parameters of the FDA transmitting array element and the nAbD direction-finding system in the experiment are consistent with those in the simulation experiment. In an actual electromagnetic environment, internal and external noise is ubiquitous, and the example assumes that the noise is Gaussian white noise. The root mean square error can effectively measure the statistical mean value of the estimation quantity and the true value deviation, and in the experiment, DOA estimation and positioning errors are described by using the root mean square error, so that the quality of the positioning spoofing effect is measured. To ensure randomness of the results, 1000 Monte Carlo experiments were used to calculate the RMSE for the angle estimation error and the distance estimation error. Fig. 7 (a) shows the effect of snr on the angle estimation root mean square error, and fig. 7 (b) shows the effect of snr on the position estimation root mean square error. Fig. 8 (a) shows the effect of time on the estimated rms error of the angle under noise conditions, and fig. 8 (b) shows the effect of time on the estimated rms error of the position under noise conditions. Fig. 9 (a) shows the effect of the frequency offset increment on the angle estimation root mean square error under noise conditions, and fig. 9 (b) shows the effect of the frequency offset increment on the position estimation root mean square error under noise conditions. From simulation results, the frequency control array still has a spoofing effect on the nAbd direction-finding system in a noise environment, and the signal-to-noise ratio, the frequency offset increment and the starting time all have influence on the positioning estimation deviation. As can be seen from fig. 8 and 9, the ul fda spoofing effect is the best among the four arrays, and the spoofing effect is the better when the signal to noise ratio is small, but in most practical scenarios, the signal to noise ratio of the signal received by the direction-finding system is low, so that the frequency control array can exert a good spoofing effect.
The foregoing has outlined the basic principles, features, and advantages of the present application. It will be understood by those skilled in the art that the present application is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present application, and various changes and modifications may be made without departing from the spirit and scope of the application, which is defined in the appended claims. The scope of the application is defined by the appended claims and equivalents thereof.
Claims (2)
1. A deception method for a full-antenna amplitude-comparison direction-finding system based on a frequency control array is characterized by comprising the following steps:
step 1: constructing a frequency control array radar system;
step 2: establishing a deception model of the frequency control array radar system on the full-antenna amplitude comparison direction-finding system;
step 3: obtaining a distance expression between the frequency control array elements and the direction finding system array antenna elements and an expression of signals received by the direction finding system;
step 4: based on a deception model of the full-antenna amplitude-comparison direction-finding system, obtaining a DOA estimated angle of the direction-finding system, calculating angle deviation and position deviation of the direction-finding system on the positioning of a radiation source, and evaluating a positioning deception effect according to the obtained angle deviation and position deviation;
the specific steps of the step 2 are as follows:
step 21: the antenna pattern function F (theta) of the full-antenna amplitude-comparison direction-finding system is expanded into Fourier series, namely:
wherein N is the number of antennas of the receiving system, F i (θ) is the pattern function of the ith antenna, a k For Fourier series coefficients, k takes 0 and all positive integers, θ s Is the included angle between adjacent antennas and is 2 pi/N;
step 22: with weights cos (iθ) s ),sin(iθ s ) The output signals of the antennas are weighted and summed, which is equivalent to respectively summing the projections of incoming wave signals received by the antennas in two orthogonal directions, and then:
the unfolding is as follows:
wherein L represents an antenna of the same pattern F (θ);
when the antenna graph function is subjected to Fourier expansion, the coefficients of the higher order terms can be reduced rapidly along with the increase of the times, so that when the number of the antennas is large, approximation is obtained:
step 23: and calculating an incoming wave azimuth angle based on the obtained C (theta) and S (theta), wherein the calculation formula is as follows:
step 24: establishing a positioning deception model based on the incoming wave azimuth angle obtained in the step 23, wherein a receiving antenna of an all-antenna amplitude comparison direction-finding system in the positioning deception model is an array antenna comprising M array elements, and the distance between adjacent array elements in the array antenna of the all-antenna amplitude comparison direction-finding system is d1;
the specific steps of the step 3 are as follows:
step 31: according to the geometric position relation, calculating the distance R' between the frequency control array element n and the array antenna element m of the full-antenna amplitude-comparison direction-finding system, and calculating the formula:
R'＝R-(n-1)dsinθ+(m-1)d1sin(θ-iθ s ) (12)；
step 32: the expression of the signal received by the direction finding system is:
assuming that the gain of each transmitting array element radiation signal and each receiving array element signal is equal to 1, the signal received by the antenna i is:
the specific steps of the step 4 are as follows:
step 41: when Deltaf n When=0, the frequency control array is degraded to a phased array, and the signal received by the antenna i is changed to a signal of formula (13):
the phase pattern is:
φ 1 ＝2πf 0 (t-[R-(N-1)dsinθ/2+(M-1)d1sin(θ-iθ s )/2]/c) (16)；
step 42: assuming that each receive channel performs m envelope samples after threshold detection, equation (11) can be expressed as:
wherein,
step 43: in the full-antenna amplitude-comparison direction-finding system, signal processing is carried out according to a phased array system, the form of a received signal is shown as a formula (15), the actually received signal is a frequency control array signal, and an angle estimated value is obtained by utilizing a solve function in MATLAB
Step 44: calculating the angle deviation and the position deviation of the full antenna specific amplitude direction-finding system for positioning the radiation source, wherein the calculation formula is as follows:
angular deviation:
position deviation:
2. the spoofing method of the full-antenna amplitude-comparison direction finding system based on the frequency control array according to claim 1, wherein the specific steps of the step 1 are as follows:
assuming a uniform linear array frequency control array radar consisting of N array elements, wherein the number of the frequency control array elements is N, c is the light speed, the frequency increment between two adjacent array elements is delta f, and the initial carrier frequency f 0 The frequency at the nth array element is f n ＝f 0 +△f n The array element distance is d, and the distance between the target and the frequency control array is R; the pointing angle of the array signal to the far field is theta, and the radiation signal of the array element n in the frequency control array radiation source is assumed to be:
s n (t)＝exp(j2πf n t),n＝0,1,...,N-1 (1)，
the signal emitted by the nth element at the far field observation point (R, θ) is expressed as:
the combined field strength at the far field observation point (R, θ) is:
let γ=Δft+ (f 0 dsinθ)/c-ΔfR/cDue to f 0 >>N.DELTA.f, then:
taking array factors as follows:
the phase pattern is:
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