阅读说明：本技术 一种基于频控阵对全向比幅单脉冲测向系统的欺骗方法 (Deception method for omnidirectional amplitude comparison monopulse direction finding system based on frequency control array ) 是由 陈楚舒 盛川 谢军伟 邵雷 张浩为 王博 李正杰 葛佳昂 于 2021-08-05 设计创作，主要内容包括：本发明公开了一种基于频控阵对全向比幅单脉冲测向系统定位欺骗的方法,与相控阵通过阵元之间的相差控制波束指向不同,频控阵(frequencydiversearray,FDA)雷达通过在阵元间引入频差的方式可以实现更高自由度的波束控制。在能量域上即为空间波束主瓣能量由于场强的干涉效应呈现弯曲,形成“虚拟辐射源”,从而对侦察接收机的nABD测向形成角度欺骗。实验表明采用本申请中的欺骗方法,能够提高我方雷达的探测精度,增强对敌方干扰机的欺骗效果。(The invention discloses a method for positioning and cheating an omnidirectional amplitude-comparison monopulse direction-finding system based on a frequency control array, which is different from a phased array in controlling the beam direction through the phase difference between array elements. The energy domain is that the main lobe energy of the space beam is bent due to the interference effect of the field intensity to form a virtual radiation source, so that angle deception is formed on the nABD direction of the reconnaissance receiver. Experiments show that the deception method can improve the detection precision of the radar of the party and enhance the deception effect on the interference machine of the enemy.)

1. A deception method for an all-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 to a full-antenna amplitude comparison direction-finding system;

and step 3: obtaining a distance expression between the frequency control array elements and the array elements of the direction-finding system array antenna and an expression of signals received by the direction-finding system;

and 4, step 4: and obtaining a DOA estimation angle of the direction-finding system based on a deception model of the full-antenna amplitude-comparison direction-finding system, calculating an angle deviation and a position deviation of the direction-finding system for positioning the radiation source, and evaluating a positioning deception effect according to the obtained angle deviation and position deviation.

2. The deception 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:

suppose a uniform linear array frequency-controlled array radar composed of N array elements, as shown in fig. 1, where the number of the frequency-controlled array elements is N, c is the speed of light, the frequency increment between two adjacent array elements is Δ f, and the initial carrier frequency f₀The frequency of the n-th array element is f_n＝f₀+ delta f, array element spacing d, and distance between the target and the frequency control array R; the pointing angle from the array signal to the far field is theta, and the radiation signals of array elements n in the frequency control array radiation source are assumed as follows:

s_n(t)＝exp(j2πf_nt),n＝0,1,...,N-1 (1)，

the signal emitted by the nth array element at a far-field observation point (R, θ) is represented as:

the resultant field strength at the far field observation point (R, θ) is:

let γ be Δ ft + (f)₀dsin θ)/c- Δ fR/c due to f₀> N.DELTA.f, then:

taking the array factor as:

taking a phase direction diagram as follows:

3. the deception method of the full-antenna amplitude comparison direction-finding system based on the frequency control array as claimed in claim 1, wherein the specific steps of the step 2 are as follows:

step 21: an antenna directional pattern function F (theta) of the four-antenna omnidirectional amplitude monopulse direction-finding system is expanded into a Fourier series, namely:

wherein N is the number of antennas of the receiving system, F_i(theta) is the directional diagram function of the ith antenna, a_kFor Fourier series coefficients, k is 0 and all positive integers, θ_sThe included angle between adjacent antennas is 2 pi/N;

step 22: using the weight cos (i θ)_s),sin(iθ_s) The weighted sum of the output signals of each antenna is equivalent to the sum of the projections of the incoming wave signals received by each antenna to two orthogonal directions, and then:

the expansion is as follows:

wherein L represents an antenna of the same pattern F (θ);

when the antenna mapping function is fourier expanded, the coefficients of the higher order terms decrease very fast with increasing order, so when the number of antennas is large, an approximation is taken:

step 23: and calculating the incoming wave azimuth angle based on the obtained C (theta) and S (theta), wherein the calculation formula is as follows:

step 24: and establishing a positioning deception model based on the incoming wave azimuth angle obtained in the step 23, wherein a receiving antenna of a 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 d 1.

4. The deception method of the full-antenna amplitude comparison direction-finding system based on the frequency control array as claimed in claim 1, wherein the specific steps of the step 3 are as follows:

step 31: according to the geometric position relation, calculating the distance R' between a frequency control array element n and an array antenna element m of the omnidirectional amplitude comparison monopulse direction-finding system, and calculating a formula:

R'＝R-(n-1)d sinθ+(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 the gain of each receiving array element signal are both equal to 1, the signal received by the antenna i is:

5. the deception method of the full-antenna amplitude comparison direction-finding system based on the frequency control array as claimed in claim 1, wherein the specific steps of the step 4 are as follows:

step 41: when Δ f_nWhen the frequency control array is degraded to a phased array at 0, the signal received by the antenna i is changed from equation (13):

the phase direction diagram is:

φ₁＝2πf₀(t-[R-(N-1)d sinθ/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 the content of the first and second substances,

step 43: processing signals in the full-antenna amplitude-comparison direction-finding system according to a phased array system, wherein the form of the received signals is as shown in the formula (15), the actually received signals are frequency control array signals, and angle estimation values are obtained in MATLAB by using a solve function

Step 44: calculating the angle deviation and the position deviation of the full-antenna amplitude-comparison direction-finding system for positioning the radiation source, wherein the calculation formula is as follows:

angular deviation:

position deviation:

Technical Field

The invention relates to the field of electronic countermeasure, in particular to a deception method for an omnidirectional amplitude comparison monopulse direction finding system based on a frequency control array.

Background

Electronic countermeasure is a special combat means in modern war, and mainly comprises the basic contents of electronic countermeasure reconnaissance, electronic attack, electronic defense and the like. The direction finding in electronic pair scout is essentially determining or estimating the direction of arrival (DOA) or angle of arrival (AOA) of an incoming wave from a radiation source in space, and is therefore also called passive or passive goniometry. In electronic countermeasure, the jammer of our party releases interference to the target radar of the enemy party, and meanwhile, the radiation signal of the jammer of our party is captured by the passive detection radar of the enemy party so as to accurately position the jammer of our party, which seriously threatens the safety of the jammer of our party. Therefore, a new system radar needs to be developed to shield an interference machine by reducing interception probability, and the traditional phased array radar changes the phase between adjacent array elements through a shifter to realize the scanning of a wave beam in space.

The Frequency Diversity Array (FDA) can synthesize a beam with time-distance-angle three-dimensional correlation by introducing a tiny frequency offset between array elements, so that after a radiation signal of an interference machine based on the FDA reaches a signal receiver of a target radar direction-finding system, a 'virtual radiation source' can be formed due to the time-distance-angle correlation characteristic of the FDA emitted beam, and positioning of an enemy radar is misled, thereby ensuring that the interference machine of our party effectively carries out a shield task.

Disclosure of Invention

Aiming at the existing problems, the invention aims to provide a deception method of a full-antenna amplitude comparison direction-finding system based on a frequency control array, and the deception effect of an enemy jammer is enhanced while the detection precision of the radar of the own party is improved by using the method.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

a deception method for an all-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 to a full-antenna amplitude comparison direction-finding system;

and step 3: obtaining a distance expression between the frequency control array elements and the array elements of the direction-finding system array antenna and an expression of signals received by the direction-finding system;

and 4, step 4: and obtaining a DOA estimation angle of the direction-finding system based on a deception model of the full-antenna amplitude-comparison direction-finding system, calculating an angle deviation and a position deviation of the direction-finding system for positioning the radiation source, and evaluating a positioning deception effect according to the obtained angle deviation and position deviation.

Further, the specific steps of step 1 are:

suppose a uniform linear array frequency-controlled array radar composed of N array elements, as shown in fig. 1, where the number of the frequency-controlled array elements is N, c is the speed of light, the frequency increment between two adjacent array elements is Δ f, and the initial carrier frequency f₀The frequency of the n-th array element is f_n＝f₀+ delta f, array element spacing d, and distance between the target and the frequency control array R; the pointing angle from the array signal to the far field is theta, and the radiation signals of array elements n in the frequency control array radiation source are assumed as follows:

s_n(t)＝exp(j2πf_nt),n＝0,1,...,N-1 (1)，

the signal emitted by the nth array element at a far-field observation point (R, θ) is represented as:

the resultant field strength at the far field observation point (R, θ) is:

let γ be Δ ft + (f)₀dsin θ)/c- Δ fR/c due to f₀> N.DELTA.f, then:

taking the array factor as:

taking a phase direction diagram as follows:

further, the specific steps of step 2 are:

step 21: an antenna directional pattern function F (theta) of the four-antenna omnidirectional amplitude monopulse direction-finding system is expanded into a Fourier series, namely:

wherein N is the number of antennas of the receiving system, F_i(theta) is the directional diagram function of the ith antenna, a_kFor Fourier series coefficients, k is 0 and all positive integers, θ_sThe included angle between adjacent antennas is 2 pi/N;

step 22: using the weight cos (i θ)_s),sin(iθ_s) The weighted sum of the output signals of each antenna is equivalent to the sum of the projections of the incoming wave signals received by each antenna to two orthogonal directions,then there are:

the expansion is as follows:

wherein L represents an antenna of the same pattern F (θ);

when the antenna mapping function is fourier expanded, the coefficients of the higher order terms decrease very fast with increasing order, so when the number of antennas is large, an approximation is taken:

step 23: and calculating the incoming wave azimuth angle based on the obtained C (theta) and S (theta), wherein the calculation formula is as follows:

step 24: and establishing a positioning deception model based on the incoming wave azimuth angle obtained in the step 23, wherein a receiving antenna of a 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 d 1.

Further, the specific steps of step 3 are:

step 31: according to the geometric position relation, calculating the distance R' between a frequency control array element n and an array antenna element m of the omnidirectional amplitude comparison monopulse direction-finding system, and calculating a 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 the gain of each receiving array element signal are both equal to 1, the signal received by the antenna i is:

further, the specific steps of step 4 are:

step 41: when Δ f_nWhen the frequency control array is degraded to a phased array at 0, the signal received by the antenna i is changed from equation (13):

the phase direction diagram is:

φ₁＝2πf₀(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: processing signals in the full-antenna amplitude-comparison direction-finding system according to a phased array system, wherein the form of the received signals is as shown in the formula (15), the actually received signals are frequency control array signals, and angle estimation values are obtained in MATLAB by using a solve function

Step 44: calculating the angle deviation and the position deviation of the full-antenna amplitude-comparison direction-finding system for positioning the radiation source, wherein the calculation formula is as follows:

angular deviation:

position deviation:

the invention has the beneficial effects that:

according to the method, on the basis of the deception principle of the FDA on the direction finding system, a deception model of the FDA on the full antenna amplitude comparison (nABD) direction finding system is established, and finally, the DOA positioning deception effect of the FDA on the nABD direction finding under a non-noise environment and a Gaussian white noise environment is verified through simulation analysis, and the experiment effect shows that the deception model has a good deception effect.

Drawings

Fig. 1 is a schematic diagram of a basic FDA array structure;

FIG. 2 is a four-antenna omnidirectional amplitude monopulse direction-finding schematic;

FIG. 3 is a position relationship between an nABD direction finding system and a frequency control array radar jammer;

fig. 4 is a comparison of the emission patterns of four FDA arrays;

FIG. 5 illustrates the impact of frequency offset increments on the positioning spoofing effect of different arrays;

FIG. 6 is a graph of the effects of time on location spoofing for different arrays;

FIG. 7 is a graph of the effect of signal-to-noise ratio on positioning estimation;

FIG. 8 is a graph of the effect of time on location estimation RMSE under noisy conditions;

FIG. 9 is a graph of the effect of a frequency offset increment on a location estimate RMSE under noisy conditions.

Detailed Description

In order to make those skilled in the art better understand the technical solution of the present invention, the following further describes the technical solution of the present invention with reference to the drawings and the embodiments.

To further illustrate the spoofing method proposed by the present invention, a brief description of the FDA and nABD direction finding system principles will be given first.

1. FDA signal model

As shown in the FDA array structure of FIG. 1, the number of array elements is N, and the carrier frequency is f₀And then the frequency of the radiation signal of the nth array element is:

f_n＝f₀+Δf_n＝f₀+x_nΔf,n＝0,1,2,...,N-1 (1)，

wherein x is_nRepresenting the coding coefficient, and delta f is the increment of frequency deviation between adjacent array elements, delta f_nIndicating the increment of frequency offset between the nth array element and the initial array element.

As can be seen from equation (1), if the coding coefficient x is changed_nObtaining FDA arrays with different frequency control functions when x is_nWhen n, is a uniform linear fda (ulfda), when x_nSin (n), sin-FDA, when x is_nLog (n +1) is log FDA (log-FDA).

Assuming that the distance between two adjacent array elements is d, the pointing angle from the array signal to the far field is theta, the light velocity is c, and assuming that the radiation signals of the array elements n in the frequency control array radiation source are:

s_n(t)＝exp(j2πf_nt),n＝0,1,...,N-1 (2)，

at a far-field observation point (R, θ):

wherein R is the distance from the reference array element to the target point, R_nThe combined field strength at a far-field observation point (R, θ) is:

the following analyses were performed using the example of ULFDA:

the resultant field strength at the far field point (R, θ) is:

let γ be Δ ft + (f)₀dsin θ)/c- Δ fR/c due to f₀> N.DELTA.f, the above formula can be simplified as:

and taking the array factor as:

taking a phase direction diagram as follows:

2. nABD direction finding system principle

Amplitude of omnidirectionalThe schematic diagram of the monopulse direction finding system is shown in fig. 2, and the monopulse direction finding system comprises L antennas with the same directional diagram F (theta), which are uniformly distributed in a range of 360 degrees to form a circular array, and the field angles of the adjacent antennas are as follows: theta_sThe system performs doa (direction of arrival) estimation based on amplitude information of signals received by each antenna:

the azimuth direction of each antenna is as follows:

F_i(θ)＝F(θ-iθ_s),i＝0,1,2…L-1 (9)，

suppose that the amplitude gain of each channel is k_iThen, the logarithmic output of the signal received by each antenna through the receiving channel is:

s_i(t,θ)＝10lg[k_iF(θ-iθ_s)A(t)](dB),i＝0,1,…L-1 (10)，

a (t) in the formula (10) is a function of the amplitude of the radiation signal;

the nABD direction-finding system utilizes the amplitude information of the signals received by the n antennas to carry out unified processing, thereby carrying out DOA estimation. The antenna pattern function F (θ) can be expanded as a fourier series, i.e.:

therein

Using the weight cos (i θ)_s),sin(iθ_s) The weighted sum of the output signals of each antenna is equivalent to the sum of the projections of the incoming wave signals received by each antenna to two orthogonal directions, and then:

the respective formulas (12-1) and (12-2) are developed to obtain:

in general, when the antenna pattern function is subjected to fourier expansion, the coefficients of higher-order terms decrease rapidly with increasing order, so when the number of antennas is large, the approximation is obtained:

obtaining the azimuth angle of the incoming wave as follows:

in engineering practice, a signal in one pulse envelope is sampled and then statistical averaging is carried out, so that the effect of a virtual antenna can be achieved. By performing the direction finding processing in this way, the direction estimation accuracy can be improved. Assuming that each receive channel performs m envelope samples after threshold detection, equation (15) can be expressed as:

wherein the content of the first and second substances,

generally, in the nABD direction finding system, n antennas with the same antenna pattern function are uniformly arranged on a circle, omnidirectional direction finding is performed, all received signals are projected to two orthogonal directions, summation is performed, and arctangent of a ratio is obtained, so that DOA estimation can be performed. Compared with the traditional amplitude comparison method which is difficult to have an ideal antenna directional diagram function and easy to influence the direction finding precision, the nABD direction comparison method directly processes the amplitude information of signals received by n antennas in one circle, constructs a virtual ideal antenna and greatly improves the direction finding precision. The transmitting directional diagram of the frequency control array has distance dependency, the beam direction changes along with the change of the distance, and the beam direction shows bending characteristics on an energy domain, and the nABD direction-finding system carries out positioning cheating on the nABD direction-finding system due to the fact that the DOA estimation is carried out according to the amplitude of a received signal, and therefore the virtual radiation source characteristics of the frequency control array can carry out positioning cheating on the nABD direction-finding system.

3. FDA-based fraud model

The receiving antenna of the omnidirectional amplitude-comparison monopulse direction-finding system is assumed to be an array antenna comprising M array elements. The positional relationship between the nABD direction-finding system and the frequency control array in the space is shown in figure 3. Assuming that the distance between adjacent array elements in the array antenna of the nABD direction-finding system is d1, and the distance between a frequency control array element n and a 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 receiving array element signal is equal to 1, the signal received by the antenna i is:

when Δ f_nWhen 0, the frequency control array is degraded to a phased array:

φ₁＝2πf₀(t-[R-(N-1)dsinθ/2+(M-1)d1sin(θ-iθ_s)/2]/c) (21)，

the angular deviation of the orientation system from the positioning of the radiation source is then:

examples

In order to verify the feasibility and the effect of the deception model provided by the invention, the following simulation experiment is carried out.

Positioning errors are generally used as a measure of positioning accuracy, and in the present invention, a larger positioning error indicates a better spoofing effect. In order to verify the deception effect of the model, the invention analyzes the angular deviation, the distance deviation and the Root Mean Square Error (RMSE) of the DOA positioning of the nABD direction-finding system based on the radiation signals of ULFDA, log-FDA, sin-FDA and FDA.

1. Simulation experiment

(1) Four array emission pattern comparisons

Let the coordinates of the far-field object be (60km,30 °), Δ f 6kHz, d 0.15m, f₀The number of array elements is 30 at 1GHz, and the signal-to-noise ratio and the drying ratio are both 10. FIG. 4 shows PA array, ULFDA array, log-FDA arrayColumn, emission pattern of sin-FDA array; from fig. 4, it can be verified that the FDA proposed in the present invention can perform positioning spoofing on an nABD direction finding system that performs DOA estimation using the amplitude response of a radiation signal, compared to the beam bending characteristics of PA in the energy domain. Fig. 4(c) - (d) enable the formation of energy-concentrated "spot-like" beams, eliminating the ULFDA distance-angle coupling;

(2) location spoofing with different FDA arrays under noiseless conditions

Taking the total number N of array elements of FDA as 10, d as 0.15m, and carrier frequency f₀1GHz, the number L of receiving antennas of the nABD direction finding system is 72, and the included angle between adjacent antennas is theta_sThe receiving array element number of each array antenna is M10, and the distance between adjacent array elements is d1 0.15M. The FDA jammer is 50km away from the direction-finding system, and the true incident angle of a radiation signal is 50 degrees. Due to the introduction of the tiny frequency offset increment, a distance-time dependent beam generated by the frequency control array has a positioning spoofing effect on a direction finding system, so that the influence of two parameters, namely the frequency offset increment and the time, on the spoofing effect is mainly simulated in the simulation experiment, fig. 5(a) - (d) show the influence of different frequency offset increments on the positioning spoofing effect when t is 40 μ s, and fig. 6(a) - (d) show the influence of different starting times at Δ f being 1kHz on the positioning spoofing effect. As can be seen from the attached figures 5 and 6, the signals radiated by the traditional phased array radar have no deception effect and are easy to be intercepted by a direction-finding system. The signals radiated by the FDA array have a deceptive effect on the direction-finding system, wherein the deceptive effect of the ULFDA array is better than that of the other two non-linear frequency control functions. And the optimal deception effect can be achieved at a specific frequency offset and a specific time.

(3) Location spoofing with different FDA arrays in the case of white Gaussian noise

The basic parameters of the FDA transmit array element and the nABD direction finding system in the experiment are the same as those in the simulation experiment described above. In an actual electromagnetic environment, internal and external noise is ubiquitous, and the noise is assumed to be white gaussian noise in the example. The root mean square error can effectively measure the statistical mean value of the deviation between the estimator and the true value, and the root mean square error is used for describing DOA estimation and positioning errors in the experiment and measuring the quality of positioning deception effect. To ensure randomness of the results, the RMSE of the angle estimation error and the distance estimation error was calculated using 1000 monte carlo experiments. Fig. 7(a) shows the effect of the signal-to-noise ratio on the root mean square error of the angle estimation, and fig. 7(b) shows the effect of the signal-to-noise ratio on the root mean square error of the position estimation. Fig. 8(a) shows the effect of time on the root mean square error of the angle estimation under noisy conditions, and fig. 8(b) shows the effect of time on the root mean square error of the position estimation under noisy conditions. Fig. 9(a) shows the influence of the frequency offset increment on the root mean square error of the angle estimation under the noise condition, and fig. 9(b) shows the influence of the frequency offset increment on the root mean square error of the position estimation under the noise condition. From simulation results, in a noise environment, the frequency control array still has a deception effect on the nABD direction finding system, and the positioning estimation deviation is influenced by the signal-to-noise ratio, the frequency offset increment and the starting time. As can be seen from fig. 8 and 9, among the four arrays, the ul fda spoofing effect is the best, and the spoofing effect is the better when the signal-to-noise ratio is small, while in most practical scenarios, the signal-to-noise ratio of the signal received by the direction-finding system is low, so the frequency control array can exert good spoofing effect.

The foregoing has described the general principles, principal features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.