An angle deception method and system for interferometric direction finding systems based on subarray MIMO frequency control array

Abstract

This invention discloses a method and system for angle deception of an interferometric direction finding system based on a subarray MIMO frequency-controlled array. The method includes: constructing a MIMO frequency-controlled array radar transmission model based on subarray partitioning; establishing an angle deception model of the MIMO frequency-controlled array radar for the interferometric direction finding system; obtaining a phase difference expression between two receiving elements of the interferometric direction finding system based on the angle deception model; calculating the deception angle of arrival measured by the interferometric direction finding system based on the interferometric direction finding principle and the phase difference expression; comparing the deception angle of arrival with the true azimuth angle of the target, and evaluating the effectiveness of the deception method based on the deviation between the two. This invention can achieve effective angle deception of the interferometric direction finding system.

Description

Technical Field

[0001] This invention relates to the field of electronic countermeasures technology, and in particular to a method and system for deceiving interferometric direction finding systems based on a subarray MIMO frequency control array. Background Technology

[0002] Electronic reconnaissance is a crucial component of electronic warfare, and one of its core tasks is to achieve direction finding and location by intercepting enemy radiation source signals. Traditional active radars rely on actively radiating electromagnetic waves to detect targets, making them vulnerable to interception and location by enemy passive reconnaissance systems, thus threatening the radar platform's survival. Therefore, researching new radar systems with low interception probability and high countermeasure capabilities is of great significance. Interferometric direction finding systems are a typical type of passive direction finding device. They estimate azimuth by measuring the phase difference between different receiving channels of the incoming wave signal, offering advantages such as high direction finding accuracy and fast response speed. For traditional single-carrier or phased array radiated signals, due to their approximate regular far-field wavefront, interferometric direction finding systems can usually accurately calculate the direction of arrival, making it difficult to effectively deceive them. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide an angle deception method for interferometric direction finding systems based on a subarray MIMO frequency control array, thereby achieving effective angle deception of the interferometric direction finding system.

[0004] Technical Solution: The present invention provides an angle deception method for an interferometric direction finding system based on a subarray MIMO frequency control array, comprising the following steps:

[0005] S1. Construct a multi-subarray MIMO frequency-controlled array radar transmission model. The transmission model consists of multiple frequency-controlled array subarrays. Orthogonal transmission waveforms are used between each subarray in the frequency domain. A set frequency increment is introduced between adjacent array elements within the subarray to form a transmission pattern with range-angle two-dimensional dependence characteristics.

[0006] S2. The interferometric direction finding system includes two receiving array elements. The direction of arrival of the wave is estimated by measuring the phase difference of the received signal, and a deception model of the MIMO frequency-controlled array radar against the interferometric direction finding system is established based on the total phase gradient of the spatial radiation field.

[0007] S3. Based on the deception model, derive the expression for the phase difference between the two receiving array elements of the interferometric direction finding system;

[0008] S4. Based on the principle of interferometric direction finding and the phase difference expression, calculate the direction finding angle measured by the interferometric direction finding system; compare the deviation between the true azimuth angle and the direction finding angle, and evaluate the effectiveness of the deception method based on the deviation between the true azimuth angle and the direction finding angle.

[0009] Furthermore, the construction method for the multi-subarray MIMO frequency-controlled array radar transmission model includes:

[0010] (1) Each subarray is a uniform linear array, and each subarray contains The array element, according to the first The first in the sub-array The carrier frequency of each array element, the first The transmitted signals of each array element and the target and the first The distance between the array elements is calculated. The signals transmitted by each array element arrive at the target, and a basic frequency-controlled array subarray model is established.

[0011] (2) According to the first The transmitted signals of each array element are used to derive the time delay caused by the first element. The phase of each array element, as well as the emission pattern and emission pattern gain;

[0012] (3) The frequency control array subarrays are combined in a linear arrangement to form a complete MIMO frequency control array, and a multi-subarray MIMO frequency control array radar transmission model is established.

[0013] Furthermore, step (3) specifically includes:

[0014] At the far-field target, define For the first The first in the formation The time delay from each array element to the target point is determined by the time delay, the subarray carrier frequency, and the first element. The first in the formation The actual transmitted signal of the nth array element is calculated to obtain the nth... The first in the formation The received signal of each array element at the target.

[0015] In the far-field case, the envelope delay is unified into a common delay: the received signal at the target. Rewritten as:

[0016] ;

[0017] in, Indicates common delay, Indicates time, This represents the distance between the target and the first element of the array. Represents the speed of light. Represents the imaginary unit. Indicates the first The phase corresponding to each array element is expressed as:

[0018] ;

[0019] in, For the first The reference array element carries the frequency in each subarray. This indicates the frequency spacing between adjacent subarray carrier frequencies. The frequency increment between array elements For the first The first in the sub-array Each array element, The spacing between adjacent subarrays The distance between adjacent array elements. This represents the angle of incidence of the target relative to the array reference direction;

[0020] The total radiation field of the entire multi-subarray MIMO frequency-controlled radar transmission model at the far-field target is the superposition of the transmitted signals of all subarrays and all array elements:

[0021] ;

[0022] in, Indicates a distance of , direction is The total radiated signal received at the target location, Indicates the first The first in the formation The transmit carrier frequency corresponding to each array element This indicates that the carrier frequency acts on the phase term of the delayed signal. Indicates the first The first in the formation The baseband signal transmitted by each array element Indicates the number of subarrays. This indicates the number of array elements in each subarray;

[0023] Under the public envelope, The expression simplifies to:

[0024] ;

[0025] Will Substitute the simplified The expression yields:

[0026] .

[0027] Furthermore, the methods for establishing a deception model for interferometric direction-finding systems by MIMO frequency-controlled array radar include:

[0028] (1) The interferometric direction finding system estimates the angle by the phase difference between two receiving array elements, and establishes a deception model by causing the phase difference measured by the interferometer to deviate through waveform distortion;

[0029] (2) Ignore the frequency spacing between the carrier frequencies of adjacent subarrays in space. Frequency increment between array elements The higher-order coupling terms of the multiplication phase express the phase expression of the received signal as consisting of a common time delay term, an inter-subarray frequency control time-varying term, and a spatial phase term. The spatial phase term includes the spatial phase caused by the fundamental carrier frequency, the inter-subarray frequency difference and spatial position coupling term, and the intra-subarray frequency difference and coupling term.

[0030] The received signal expression is further rewritten, and the exponential terms in the rewritten received signal expression are sorted out. The received signal is divided into two parts: inter-subarray and intra-subarray. The phase center form is written out using a geometric series, and the total phase expression near the main lobe is obtained.

[0031] (3) For the total phase expression near the main lobe, respectively and Find the partial derivative. This represents the distance between the target and the first element of the array. The phase gradient is obtained by representing the incident angle of the target relative to the array reference direction.

[0032] Furthermore, step (2) specifically includes: the phase expression of the received signal is:

[0033] ;

[0034] in, Indicates the first The phase corresponding to each array element Indicates the common delay term. This indicates the time-varying term of frequency control between subarrays. This represents the frequency difference and coupling term within the subarray. Indicates time, This represents the distance between the target and the first element of the array. Represents the speed of light. For the first The reference array element carries the frequency in each subarray. This indicates the frequency spacing between adjacent subarray carrier frequencies. The frequency increment between array elements For the first The first in the sub-array Each array element, The spacing between adjacent subarrays The distance between adjacent array elements. This represents the angle of incidence of the target relative to the array reference direction;

[0035] The expression for the received signal is written as:

[0036] ;

[0037] in, Indicates common delay, This represents the received signal at the approximate target location.

[0038] After rearranging the exponent term, the expression for the received signal is divided into two parts: inter-subarray and intra-subarray.

[0039] ;

[0040] ;

[0041] in, This represents the phase increment between subarrays. This represents the phase increment between elements within a subarray.

[0042] Write the phase center form using a geometric series:

[0043] ;

[0044] Substituting the phase center form into the expression for the received signal, we get:

[0045] ;

[0046] The total phase near the main lobe is approximately:

[0047] ;

[0048] in, This indicates the total phase near the main lobe. This represents the phase increment between subarrays. This represents the phase increment between elements within a subarray. The phase is constant;

[0049] Summarized as follows:

[0050] .

[0051] Furthermore, based on the deception model, the expression for the phase difference between the two receiving array elements of the interferometric direction finding system is derived; specifically including:

[0052] The phase difference between the total field phases received by the two receiving array elements is expressed as:

[0053] ;

[0054] in, This represents the phase difference between the signals received by the two receiving elements of the interferometer. and The total field phase received by the two receiving array elements are respectively the total field phases. These are the center positions of the two receiving array elements of the interferometer;

[0055] To each and exist place and Performing a first-order Taylor expansion, we get:

[0056] ;

[0057] in, The distance between the two receiving elements of the interferometer. for In position ,time Spatial gradient at that location Let be the unit vectors in the directions of the two receiving array elements;

[0058] The phase difference between the two array elements is approximately expressed by the first-order spatial expansion of the total phase along the baseline direction as follows:

[0059] ;

[0060] in, Represents the phase function Spatial gradient;

[0061] ;

[0062] in, This represents the distance between the target and the first element of the array. This represents the angle of incidence of the target relative to the array reference direction;

[0063] In the total phase expression near the main lobe and Substitute partial derivatives into the input The expression is used to obtain the phase difference expression between the two receiving array elements of the interferometric direction finding system:

[0064] ;

[0065] in, This represents the distance between the target and the first element of the array. Represents the speed of light. For the first The reference array element carries the frequency in each subarray. This indicates the frequency spacing between adjacent subarray carrier frequencies. The frequency increment between array elements The spacing between adjacent subarrays The distance between adjacent array elements. Indicates the number of subarrays. This indicates the number of array elements in each subarray.

[0066] Furthermore, step S4 specifically involves:

[0067] According to the interferometer direction finding principle formula, the direction finding angle measured by the interferometric direction finding system is expressed as:

[0068] ;

[0069] in, This represents the direction-finding angle measured by the interferometric direction-finding system. Indicates wavelength. This represents the distance between two receiving array elements. This represents the phase difference between the signals received by the two receiving elements of the interferometer.

[0070] Substituting the phase difference into the direction finding angle expression, we get:

[0071] ;

[0072] in, For the first The reference array element carries the frequency in each subarray. Indicates the number of subarrays. This indicates the number of array elements in each subarray. This indicates the frequency spacing between adjacent subarray carrier frequencies. The frequency increment between array elements This represents the incident angle of the target relative to the array reference direction. This represents the distance between the target and the first element of the array. The spacing between adjacent subarrays The distance between adjacent array elements;

[0073] Define the interferometric direction finding angle deviation for:

[0074] ;

[0075] The deviation is approximated as:

[0076] .

[0077] Based on the same inventive concept, the present invention provides an angle deception system for an interferometric direction finding system based on a subarray MIMO frequency control array, comprising:

[0078] The transmission model construction unit is used to construct a multi-subarray MIMO frequency-controlled array radar transmission model. The transmission model consists of multiple frequency-controlled array subarrays. Orthogonal transmission waveforms are used between each subarray in the frequency domain. A set frequency increment is introduced between adjacent array elements within the subarray to form a transmission pattern with range-angle two-dimensional dependence characteristics.

[0079] The deception model building unit, the interferometric direction finding system includes two receiving array elements, estimates the direction of incoming wave by measuring the phase difference of the received signals, and establishes a deception model of the MIMO frequency-controlled array radar on the interferometric direction finding system based on the total phase gradient of the spatial radiation field;

[0080] The phase difference expression derivation unit is used to derive the phase difference expression between two receiving array elements of the interferometric direction finding system based on the deception model.

[0081] The evaluation unit is used to calculate the direction finding angle measured by the interferometric direction finding system based on the interferometric direction finding principle and the phase difference expression; compare the deviation between the true azimuth angle and the direction finding angle; and evaluate the effectiveness of the deception method based on the deviation between the true azimuth angle and the direction finding angle.

[0082] Based on the same inventive concept, the present invention provides an electronic device comprising:

[0083] Memory, used to store computer programs;

[0084] A processor for executing the computer program to implement the method.

[0085] Based on the same inventive concept, the present invention provides a computer program product comprising a computer program / instruction that, when executed by a processor, implements the method described herein.

[0086] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows: (1) Based on the spatial synthetic total field, the present invention establishes a phase deception model for the interferometric direction finding system, clarifies the correspondence between the MIMO frequency control array signal and the phase difference measurement results of the interferometric direction finding system, and provides a theoretical basis for the passive interferometric direction finding deception method based on the transmission signal system; (2) The present invention proposes a transmission structure with multiple subarrays combined. Compared with the single-layer array system, the frequency difference between subarrays, the frequency difference within subarrays, the spacing between subarrays and the spacing between array elements within subarrays can jointly participate in the regulation of the spatial total phase distribution, making the phase gradient deviation more hierarchical and designable, thereby improving the flexibility and controllability of implementing directional deception on the interferometric direction finding system, and having a better deception effect. Attached Figure Description

[0087] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0088] Figure 2 It is the transmission pattern of the frequency-controlled array;

[0089] Figure 3 This is a schematic diagram illustrating the effect of frequency offset between different array elements on the deception effect of interferometric direction finding angle in an example of the present invention;

[0090] Figure 4 This is a schematic diagram illustrating the effect of frequency offset between different subarrays on the deception effect of interferometric direction finding in an example of the present invention;

[0091] Figure 5 This is a schematic diagram illustrating the effect of distance on angle deception effect under different array element numbers in an example of the present invention;

[0092] Figure 6 This is a schematic diagram illustrating the effect of distance on angle deception under different numbers of subarrays in an example of the present invention. Detailed Implementation

[0093] To make the objectives, technical solutions, and effects of this invention clearer, the invention will be described in detail below with reference to specific examples and accompanying drawings. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0094] Frequency-controlled array radar, by introducing frequency offsets between array elements, not only retains all the advantages of phased array radar but also exhibits range-angle coupling characteristics. Its beam direction changes over time, forming a unique "S"-shaped beam pattern, which helps to deceive reconnaissance equipment and reduce the probability of detection and interception. Meanwhile, in frequency-domain orthogonal MIMO radar, phase wavefront distortion causes phase gradient deviation angles, leading to errors in the measurement results of passive interferometric direction finding systems. The combination of multiple subarrays not only alters the spatial distribution of the far-field wavefront but also further enhances the adjustability of the phase gradient deviation, making the interferometric direction finding system more prone to systematic angular deviations.

[0095] This invention proposes an angle deception method for interferometric direction finding systems based on a subarray MIMO frequency control array, such as... Figure 1 As shown, it includes the following steps:

[0096] S1. Establish a multi-subarray MIMO frequency-controlled radar transmission model. This model consists of multiple frequency-controlled subarrays. Each subarray uses orthogonal transmission waveforms in the frequency domain. A predetermined frequency increment is introduced between adjacent elements within a subarray to form a transmission pattern with range-angle two-dimensional dependence. The specific details of establishing the multi-subarray MIMO frequency-controlled radar transmission model are as follows:

[0097] Step 1: Construct the basic frequency-controlled array subarray model. The multi-subarray MIMO frequency-controlled array radar transmission model is constructed from... It consists of several frequency-controlled subarrays, each of which is a uniform linear array. Taking the first subarray as an example... Taking a subarray as an example, it contains There are 1 array elements, and the distance between adjacent array elements is . The first element in the subarray is set as the reference element, and the carrier frequency is... The frequency increment between array elements is Then the first The first in the sub-array Carrier frequency of each element It can be represented as:

[0098] (1)

[0099] The first in the sub-array The transmitted signal of each array element can be represented as:

[0100] (2)

[0101] in, This represents the transmitted signal of an element in the subarray. Indicates time, Represents the imaginary unit, satisfying ;

[0102] For those located The far-field target, the target and the first The distance between individual array elements It can be represented as:

[0103] (3)

[0104] in, This represents the distance between the target and the first element of the array. This represents the angle of incidence of the target relative to the array reference direction;

[0105] No. Each element transmits a signal that reaches the target. The signal is represented as:

[0106] (4)

[0107] in, Indicates the first Each element transmits a signal that reaches the target. The signal Represents the speed of light;

[0108] Step 2: Based on the subarray element transmission signals in Step 1, determine the first time delay caused by the time delay. The phase and emission pattern of each array element; the first Phase of each element Represented as:

[0109] (5)

[0110] Due to the frequency increment between array elements Much smaller than the carrier frequency In reality there are Therefore, the squared term in equation (5) can be ignored. , It can be simplified to:

[0111] (6)

[0112] Therefore, the first Phase difference between each array element and the reference array element for:

[0113] (7)

[0114] Based on the phase difference between array elements according to equation (7), the uniform frequency-controlled array guide vector for:

[0115] (8)

[0116] For a weighted array, the transmit pattern of a frequency-controlled array can be simplified as:

[0117] (9)

[0118] in, For weighted array at distance Direction angle ,time The launch pattern at that location.

[0119] Therefore, the gain of the frequency control array transmission pattern for:

[0120] (10)

[0121] As can be seen from equation (10), the transmission pattern of each frequency-controlled array subarray has range-angle dependent characteristics, and the transmission pattern of the frequency-controlled array is as follows: Figure 2 As shown, and by adjusting the frequency increments between the elements of each subarray... This allows different subarrays to have different spatial energy distribution characteristics.

[0122] Step 3: Combine the frequency control array subarrays established in Step 1 in a linear arrangement to form a complete MIMO frequency control array, and establish a multi-subarray MIMO frequency control array radar transmission model.

[0123] Assumption For the first The carrier frequency of each subarray is such that adjacent elements within the subarray use the same frequency increment. , No. Within the formation The frequency of each array element is:

[0124] (11)

[0125] in, Indicates the first The first in the formation Each array element corresponds to a different carrier frequency, and different subarrays correspond to different carrier frequencies. And satisfy the frequency domain orthogonality condition. To facilitate subsequent analytical derivation, we further assume that the carrier frequencies of each subarray are equally spaced, i.e.

[0126] (12)

[0127] in, Indicates the frequency spacing between adjacent subarray carrier frequencies;

[0128] Therefore:

[0129] (13)

[0130] set up The frequency-controlled subarrays are arranged in a straight line to form a [array containing] A linear MIMO frequency-controlled array with subarrays. The spacing between adjacent subarrays is... ,and Each subarray has an internal spacing of [missing information]. of Each array element has a spacing of [missing information]. A two-level array element structure. Subarrays are assumed to be orthogonal in the frequency domain; different subarrays satisfy frequency domain orthogonality, therefore:

[0131] (14)

[0132] in, Indicates the first The baseband signal transmitted by each subarray Indicates the first The complex conjugate of the baseband signal transmitted by each subarray and Both represent subarray indices;

[0133] Establish a multi-subarray MIMO frequency-controlled radar transmission model; based on the above settings, the first... The first in the formation The actual signal transmitted by each element It can be represented as:

[0134] (15)

[0135] in, The baseband modulation signal representing the transmitted signal;

[0136] At the far-field target, define For the first The first in the formation The time delay from each array element to the target point. Consider the subarray spacing as... The spacing between array elements is In this situation, It can be represented as:

[0137] (16)

[0138] Delay carrier frequency Substituting into (15), we can obtain the first... The first in the formation The received signal of each array element at the target is:

[0139] (17)

[0140] in, This represents the baseband signal delay form when considering the differences in the propagation paths of each array element.

[0141] In the far field case, the envelope delay can be uniformly approximated as a common delay:

[0142] (18)

[0143] in, This indicates the approximate common delay.

[0144] Therefore, the received signal at the target can be written as:

[0145] (19)

[0146] in, Indicates the first The phase corresponding to each array element is expressed as:

[0147] (20)

[0148] The total radiation field of the entire multi-subarray MIMO frequency-controlled radar transmission model at the far-field target is the superposition of the radiated signals of all subarrays and all array elements:

[0149] (twenty one)

[0150] in, Indicates a distance of , direction is The total radiated signal received at the target location, Indicates the first The first in the formation The transmit carrier frequency corresponding to each array element This indicates the phase term of the delayed signal after the carrier frequency is applied;

[0151] According to equation (18), under the common envelope, equation (21) can be simplified to:

[0152] (twenty two)

[0153] In equation (20) Substituting into equation (22), we get:

[0154] (twenty three)

[0155] S2. Establish a deception model for the interferometric direction finding system using a MIMO frequency-controlled array radar; the interferometric direction finding system consists of two receiving array elements, and the direction of arrival is estimated by measuring the phase difference of the received signals; a deception model is established based on the total phase gradient of the spatial radiation field; the specific content is as follows:

[0156] Step 1: Establish a deception model based on the principle of interferometer direction finding. The interferometric direction finding system estimates the angle by the phase difference between two receiving array elements. The deception model is established by causing the phase difference measured by the interferometer to deviate through waveform distortion.

[0157] The deception model described above uses an interferometric direction-finding system with two array elements. It is assumed that the received signals from the two array elements of the interferometer are respectively... and , and This can be simplified as follows:

[0158] (twenty four)

[0159] in, It is Gaussian white noise, and obeys , For noise variance, and These represent the received signal amplitudes of the two array elements, respectively. This represents the original signal received by the array element. This is for additional phase shift.

[0160] (25)

[0161] and These represent the real and imaginary parts of the total received signal synthesized from the two channels of the interferometer, respectively. express The conjugate transpose of;

[0162] The phase difference between the signals received by the two array elements of the interferometer for:

[0163] (26)

[0164] The angle of the incoming wave signal obtained by the interferometer based on the phase difference of the signals received by the two array elements is:

[0165] (27)

[0166] in, This represents the angle measured by the interferometer. Indicates wavelength. This is the distance between the two receiving array elements of the interferometer.

[0167] Step 2, because , In space and and The higher-order coupling terms in the multiplication are relatively small and can be ignored. Therefore, the phase of the received signal obtained from equation (20) in step S1 can be approximated as:

[0168] (28)

[0169] The phase consists of three parts: a common delay term, an inter-subarray frequency control time-varying term, and a spatial phase term. The spatial phase term includes the spatial phase caused by the fundamental carrier frequency, an inter-subarray frequency difference and spatial position coupling term, and an intra-subarray frequency difference and coupling term. Indicates the common delay term. This indicates the time-varying term of frequency control between subarrays. This represents the frequency difference and coupling term within the subarray.

[0170] because For a smaller approximation, the received signal can be written as:

[0171] (29)

[0172] in, This represents the received signal at the approximate target location.

[0173] After rearranging the exponent terms, the signal in equation (29) can be divided into two parts: inter-subarray and intra-subarray.

[0174] (30)

[0175] (31)

[0176] in, This represents the phase increment between subarrays. To represent the phase increment between elements within a subarray;

[0177] Write the phase center form using a geometric series:

[0178] (32)

[0179] Substituting equation (32) into the total field expression (30), we get:

[0180] (33)

[0181] The total phase near the main lobe can be approximated as:

[0182] (34)

[0183] in, Indicates the location The total phase at that point, The phase is constant.

[0184] Summarized as follows:

[0185] (35)

[0186] Step 3: Multi-element vector synthesis signals can cause significant distortion of the equiphase surface at a certain point, a phenomenon known as phase distortion or phase gradient. The definition is:

[0187] (36)

[0188] in, Represents the phase function. Represents a radial unit vector. Represents an angular unit vector;

[0189] For equation (35) Find the partial derivative:

[0190] (37)

[0191] For equation (35) Find the partial derivative:

[0192] (38)

[0193] S3. Based on the deception model established in step S2, derive the expression for the phase difference between the two receiving array elements of the interferometric direction finding system; the specific content is as follows:

[0194] Suppose the interferometric direction finding system consists of two receiving array elements, and the distance between the two receiving array elements of the interferometer is... ,and At this point, the two receiving array elements can be considered as neighboring sampling points on the same local wavefield. Let the center positions of the two array elements be respectively... and , , Let be the unit vectors in the directions of the two receiving array elements. The total field phases received by the two receiving array elements are respectively: and The phase difference is defined as:

[0195] (39)

[0196] in, This represents the phase difference between the signals received by the two receiving elements of the interferometer.

[0197] Can Phase function of the receiving array element at the location exist Perform a first-order Taylor expansion:

[0198] (40)

[0199] in, Indicates position Phase function at that point, Represents the phase function Location Spatial gradient at a given location; This represents the unit vectors indicating the directions of the two receiving array elements;

[0200] Therefore, we can obtain:

[0201] (41)

[0202] Therefore, the phase difference between the two array elements can be approximated by the first-order spatial expansion of the total phase along the baseline direction as follows:

[0203] (42)

[0204] in, This represents the phase difference between the received signals of two array elements. Represents the phase function Spatial gradient;

[0205] (43)

[0206] Substituting equations (37) and (38) into equation (43), we obtain the expression for the phase difference between the two receiving array elements of the interferometric direction finding system:

[0207] (44)

[0208] S4. Based on the interferometric direction finding principle and the phase difference expression in equation (44) of S3, calculate the direction finding angle measured by the interferometric direction finding system; compare the deviation between the true azimuth angle and the direction finding angle, such as... Figure 3-6 As shown, the effectiveness of the deception method is evaluated based on the deviation between the two, specifically as follows:

[0209] According to formula (27) of the interferometer direction finding principle in S2, the direction finding angle measured by the interferometric direction finding system is expressed as:

[0210] (45)

[0211] in, This represents the lateral angle measured by the interferometric direction-finding system. Indicates wavelength. This indicates the distance between two receiving array elements;

[0212] Substituting the phase difference obtained from equation (44) in step S3 into equation (45), we get:

[0213] (46)

[0214] Define the interferometric direction finding angle deviation as:

[0215] (47)

[0216] The deviation can be approximated as:

[0217] (48)

[0218] In this example, the base carrier frequency is set. for The element spacing is half a wavelength. The spacing between two elements in the interferometric direction finding system is similar to the element spacing, and the subarray spacing is set to ten times the element spacing. Both the subarray spacing and the element spacing are much smaller than the distance between the radiation source and the interferometric direction finding system, thus satisfying the approximation conditions in the aforementioned steps. With the true incident angle set to 30°, the number of elements, subarrays, distance, and frequency offset are varied, and the changes in direction finding error and the deception effect are compared under different conditions. Figure 3 This study demonstrates the impact of inter-element frequency offset on the deception effect of interferometric direction-finding systems under different array types. Figure 3 It can be concluded that for MIMO frequency-controlled array radar, the angle measurement error of the interferometric direction finding system increases slowly with the increase of the inter-element frequency offset; under the same frequency offset conditions, the more subarrays there are, the more obvious the angle deviation. Compared with frequency-controlled array radar without subarrays and MIMO radar, multi-subarray MIMO frequency-controlled array radar has a better deception effect on interferometric direction finding systems. Figure 4The effects of different carrier frequency variations between subarrays on the deception effect of the interferometric direction-finding system were compared. Figure 4 It can be concluded that increasing the carrier frequency between different subarrays can significantly improve the angle deception effect, and MIMO frequency-controlled array radar exhibits better deception performance than frequency-controlled array radar without subarrays and MIMO radar. Figure 5 The influence of distance on the angle deception effect of the interferometric direction finding system under different array element numbers was compared. Figure 5 It can be concluded that the more array elements there are, the better the angle deception effect. Figure 6 The effects of distance on the angular deception effect of the interferometric direction finding system under different array configurations were compared. Figure 6 It can be concluded that the more subarrays there are, the better the angle deception effect, and the MIMO frequency-controlled array radar has a better angle deception effect on the interferometric direction finding system than the frequency-controlled array radar without subarrays and the MIMO radar.

[0219] In summary, the MIMO frequency-controlled array radar constructed through subarray partitioning can effectively deceive interferometric direction-finding systems. Compared to traditional frequency-controlled array radars and MIMO radars, the multi-subarray structure proposed in this invention has stronger hierarchy and designability, resulting in superior angle deception performance.

[0220] Based on the same inventive concept, this invention also provides an angle deception system for an interferometric direction finding system based on a subarray MIMO frequency control array, comprising:

[0221] The transmission model construction unit is used to construct a multi-subarray MIMO frequency-controlled array radar transmission model. The transmission model consists of multiple frequency-controlled array subarrays. Orthogonal transmission waveforms are used between each subarray in the frequency domain. A set frequency increment is introduced between adjacent array elements within the subarray to form a transmission pattern with range-angle two-dimensional dependence characteristics.

[0222] The deception model building unit, the interferometric direction finding system includes two receiving array elements, estimates the direction of incoming wave by measuring the phase difference of the received signals, and establishes a deception model of the MIMO frequency-controlled array radar on the interferometric direction finding system based on the total phase gradient of the spatial radiation field;

[0223] The phase difference expression derivation unit is used to derive the phase difference expression between two receiving array elements of the interferometric direction finding system based on the deception model.

[0224] The evaluation unit is used to calculate the direction finding angle measured by the interferometric direction finding system based on the interferometric direction finding principle and the phase difference expression; compare the deviation between the true azimuth angle and the direction finding angle; and evaluate the effectiveness of the deception method based on the deviation between the true azimuth angle and the direction finding angle.

[0225] Based on the same inventive concept, the present invention also provides an electronic device, comprising:

[0226] Memory, used to store computer programs;

[0227] A processor for executing the computer program to implement the method.

[0228] Based on the same inventive concept, the present invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the method described.

[0229] The above description is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the protection scope of the present invention.

Claims

1. A method for deceiving an interferometric direction-finding system based on a subarray MIMO frequency-controlled array, characterized in that, Includes the following steps: S1. Construct a multi-subarray MIMO frequency-controlled array radar transmission model. The transmission model consists of multiple frequency-controlled array subarrays. Orthogonal transmission waveforms are used between each subarray in the frequency domain. A set frequency increment is introduced between adjacent array elements within the subarray to form a transmission pattern with range-angle two-dimensional dependence characteristics. S2. The interferometric direction finding system includes two receiving array elements. The direction of arrival of the wave is estimated by measuring the phase difference of the received signal, and a deception model of the MIMO frequency-controlled array radar against the interferometric direction finding system is established based on the total phase gradient of the spatial radiation field. S3. Based on the deception model, derive the expression for the phase difference between the two receiving array elements of the interferometric direction finding system; S4. Based on the principle of interferometric direction finding and the phase difference expression, calculate the direction finding angle measured by the interferometric direction finding system; compare the deviation between the true azimuth angle and the direction finding angle, and evaluate the effectiveness of the deception method based on the deviation between the true azimuth angle and the direction finding angle.

2. The method according to claim 1, characterized in that, The methods for constructing a multi-subarray MIMO frequency-controlled radar transmission model include: (1) Each subarray is a uniform linear array, and each subarray contains The array element, according to the first The first in the sub-array The carrier frequency of each array element, the first The transmitted signals of each array element and the target and the first Calculate the distance between the nth array elements. The signals transmitted by each array element arrive at the target, and a basic frequency-controlled array subarray model is established. (2) According to the first The transmitted signals of each array element are used to derive the time delay caused by the first element. The phase of each array element, as well as the emission pattern and emission pattern gain; (3) The frequency control array subarrays are combined in a linear arrangement to form a complete MIMO frequency control array, and a multi-subarray MIMO frequency control array radar transmission model is established.

3. The method according to claim 2, characterized in that, Step (3) specifically includes: At the far-field target, define For the first The first in the formation The time delay from each array element to the target point is determined by the time delay, the subarray carrier frequency, and the first element. The first in the formation The actual transmitted signal of the nth array element is calculated to obtain the nth... The first in the formation The received signal of each array element at the target. In the far-field case, the envelope delay is unified into a common delay: the received signal at the target. Rewritten as: ； in, Indicates common delay, Indicates time, This represents the distance between the target and the first element of the array. Represents the speed of light. Represents the imaginary unit. Indicates the first The phase corresponding to each array element is expressed as: ； in, For the first The reference array element carries the frequency in each subarray. This indicates the frequency spacing between adjacent subarray carrier frequencies. The frequency increment between array elements For the first The first in the sub-array Each array element, The spacing between adjacent subarrays. The distance between adjacent array elements. This represents the incident angle of the target relative to the array reference direction; The total radiation field of the entire multi-subarray MIMO frequency-controlled radar transmission model at the far-field target is the superposition of the transmitted signals of all subarrays and all array elements: ； in, Indicates a distance of , direction is The total radiated signal received at the target location Indicates the first The first in the formation The transmit carrier frequency corresponding to each array element This indicates that the carrier frequency acts on the phase term of the delayed signal. Indicates the first The first in the formation The baseband signal transmitted by each array element Indicates the number of subarrays. This indicates the number of array elements in each subarray; Under the public envelope, The expression simplifies to: ； Will Substitute the simplified The expression yields: 。 4. The method according to claim 1, characterized in that, The methods for establishing a deception model for interferometric direction finding systems by MIMO frequency-controlled array radar include: (1) The interferometric direction finding system estimates the angle by the phase difference between two receiving array elements, and establishes a deception model by causing the phase difference measured by the interferometer to deviate through waveform distortion; (2) Ignore the frequency spacing between the carrier frequencies of adjacent subarrays in space. Frequency increment between array elements The higher-order coupling terms of the multiplication phase express the phase expression of the received signal as consisting of a common time delay term, an inter-subarray frequency control time-varying term, and a spatial phase term. The spatial phase term includes the spatial phase caused by the fundamental carrier frequency, the inter-subarray frequency difference and spatial position coupling term, and the intra-subarray frequency difference and coupling term. The received signal expression is further rewritten, and the exponential terms in the rewritten received signal expression are sorted out. The received signal is divided into two parts: inter-subarray and intra-subarray. The phase center form is written out using a geometric series, and the total phase expression near the main lobe is obtained. (3) For the total phase expression near the main lobe, respectively and Find the partial derivative. This represents the distance between the target and the first element of the array. The phase gradient is obtained by representing the incident angle of the target relative to the array reference direction.

5. The method according to claim 4, characterized in that, Step (2) specifically includes: The phase expression of the received signal is: ； in, Indicates the first The phase corresponding to each array element Indicates the common delay term. This indicates the time-varying term of frequency control between subarrays. This represents the frequency difference and coupling term within the subarray. Indicates time, This represents the distance between the target and the first element of the array. Represents the speed of light. For the first The reference array element carries the frequency in each subarray. This indicates the frequency spacing between adjacent subarray carrier frequencies. The frequency increment between array elements For the first The first in the sub-array Each array element, The spacing between adjacent subarrays. The distance between adjacent array elements. This represents the incident angle of the target relative to the array reference direction; The expression for the received signal is written as: ； in, Indicates common delay, This represents the received signal at the approximate target location; After rearranging the exponent term, the expression for the received signal is divided into two parts: inter-subarray and intra-subarray. ； ； in, This represents the phase increment between subarrays. This represents the phase increment between elements within a subarray. Write the phase center form using a geometric series: ； Substituting the phase center form into the expression for the received signal, we get: ； The total phase near the main lobe is approximately: ； in, This indicates the total phase near the main lobe. This represents the phase increment between subarrays. This represents the phase increment between elements within a subarray. The phase is constant; Summarized as follows: 。 6. The method according to claim 1, characterized in that, Based on the deception model, the expression for the phase difference between two receiving array elements in an interferometric direction finding system is derived; specifically including: The phase difference between the total field phases received by the two receiving array elements is expressed as: ； in, This represents the phase difference between the signals received by the two receiving elements of the interferometer. and These represent the total field phases received by the two receiving array elements, These are the center positions of the two receiving array elements of the interferometer; To each and exist place and Performing a first-order Taylor expansion, we get: ； in, The distance between the two receiving elements of the interferometer. for In position ,time Spatial gradient at that location Let be the unit vectors in the directions of the two receiving array elements; The phase difference between the two array elements is approximately expressed by the first-order spatial expansion of the total phase along the baseline direction as follows: ； in, Represents the phase function Spatial gradient; ； in, This represents the distance between the target and the first element of the array. This represents the incident angle of the target relative to the array reference direction; In the total phase expression near the main lobe and Substitute partial derivatives into the input The expression yields the phase difference expression between the two receiving array elements of the interferometric direction finding system: ； in, This represents the distance between the target and the first element of the array. Represents the speed of light. For the first The reference array element carries the frequency in each subarray. This indicates the frequency spacing between adjacent subarray carrier frequencies. The frequency increment between array elements The spacing between adjacent subarrays. The distance between adjacent array elements. Indicates the number of subarrays. This indicates the number of array elements in each subarray.

7. The method according to claim 1, characterized in that, Step S4 is as follows: According to the interferometer direction finding principle formula, the direction finding angle measured by the interferometric direction finding system is expressed as: ； in, This represents the direction-finding angle measured by the interferometric direction-finding system. Indicates wavelength. This represents the distance between two receiving array elements. This represents the phase difference between the signals received by the two receiving elements of the interferometer. Substituting the phase difference into the direction finding angle expression, we get: ； in, For the first The reference array element carries the frequency in each subarray. Indicates the number of subarrays. This indicates the number of array elements in each subarray. This indicates the frequency spacing between adjacent subarray carrier frequencies. The frequency increment between array elements This represents the incident angle of the target relative to the array reference direction. This represents the distance between the target and the first element of the array. The spacing between adjacent subarrays. The distance between adjacent array elements; Define the interferometric direction finding angle deviation for: ； The deviation is approximated as: 。 8. An angle deception system for an interferometric direction finding system based on a subarray MIMO frequency control array, characterized in that, include: The transmission model construction unit is used to construct a multi-subarray MIMO frequency-controlled array radar transmission model. The transmission model consists of multiple frequency-controlled array subarrays. Orthogonal transmission waveforms are used between each subarray in the frequency domain. A set frequency increment is introduced between adjacent array elements within the subarray to form a transmission pattern with range-angle two-dimensional dependence characteristics. The deception model building unit, the interferometric direction finding system includes two receiving array elements, estimates the direction of incoming wave by measuring the phase difference of the received signals, and establishes a deception model of the MIMO frequency-controlled array radar on the interferometric direction finding system based on the total phase gradient of the spatial radiation field; The phase difference expression derivation unit is used to derive the phase difference expression between two receiving array elements of the interferometric direction finding system based on the deception model. The evaluation unit is used to calculate the direction finding angle measured by the interferometric direction finding system based on the interferometric direction finding principle and the phase difference expression; compare the deviation between the true azimuth angle and the direction finding angle; and evaluate the effectiveness of the deception method based on the deviation between the true azimuth angle and the direction finding angle.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the method as described in any one of claims 1-7.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the method described in any one of claims 1-7.

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