A linear sparse array beam property analysis method and device for unmanned aerial vehicle clusters

Abstract

The present invention provides a linear sparse array beam property analysis method and device for a drone cluster, belonging to the field of sparse array beam analysis. Aiming at the near-field sparse distribution characteristics of the drone cluster array, the present invention first constructs an array signal model corresponding thereto, and approximates the phase difference function of each array element signal in the signal model by using Taylor expansion, thereby obtaining a simplified implementation method for near-field beamforming for linear frequency modulation pulse compression processing in the spatial domain. From the perspective of signal spectrum folding caused by spatial undersampling, an analytical expression for the near-field beam grating lobe distribution is analyzed and proposed. The present invention provides theoretical support for improving the communication, electronic reconnaissance, and jamming capabilities of drone clusters using near-field beamforming technology.

Description

Technical Field

[0001] The present invention belongs to the field of sparse array beam analysis, and more specifically, relates to a linear sparse array beam property analysis method and device for a drone cluster. Background Art

[0002] Compared with far-field array beams, near-field sparse arrays have differences in beamforming methods, beam gain variation characteristics, and beam grating lobe distribution characteristics. There is still a lack of research results in related fields, which brings difficulties to the beamforming of UAV clusters, the design and optimization of beam scanning methods, and the suppression or utilization of beam grating lobes.

[0003] In terms of beamforming, patent document 201910916960.5 provides a method of using drone clusters as three-dimensional array antennas, but does not combine the application of drone clusters in the field of electronic countermeasures. The document "Adaptive beamforming algorithm for airborne early warning radar based on SVRGD" provides a beamforming algorithm that searches for the optimal solution through the algorithm, but cannot obtain an analytical solution, that is, it cannot be derived theoretically, and its signal model is a far-field signal model; the document "Microwave Technology and Antennas" derives the array pattern (beamforming pattern) based on far-field approximation.

[0004] In terms of grating lobe position, the document "Two-dimensional phased array-MIMO radar joint transmission subarray division and beamforming design method" takes the maximum output signal-to-interference ratio as the criterion, constructs an optimization model, and optimizes the antenna subarray structure and the beamforming vector of each subarray at the same time; the document "Adaptive beamforming algorithm for airborne early warning radar based on SVRGD" proposes a random variance gradient descent adaptive beamforming algorithm based on machine learning, which improves the stability of short-shot adaptive beamforming in complex environments. Both of the above documents are based on the far-field plane wave radiation model of electromagnetic waves. However, the antenna array formed by the drone cluster can reach thousands of meters in size, resulting in a significant expansion of the near-field range. Due to the limitations of drone size and flight safety, the formation interval of drones is usually much larger than the wavelength. Therefore, the antenna array formed by the drone cluster often presents near-field sparse characteristics, and the far-field beamforming cannot be adapted. Summary of the invention

[0005] In view of the defects of the prior art, the purpose of the present invention is to provide a linear sparse array beam property analysis method and device for UAV clusters, aiming to solve the problems that compared with far-field array beams, near-field sparse arrays are different in beamforming methods, beam gain variation characteristics, beam grating lobe distribution characteristics, etc., and research results in related fields are still lacking, which brings difficulties to the beamforming of UAV clusters, the design and optimization of beam scanning methods, and the suppression or utilization of beam grating lobes.

[0006] To achieve the above object, on the one hand, the present invention provides a linear sparse array beam property analysis method for a UAV cluster, comprising the following steps:

[0007] A near-field sparse antenna array is formed by a formation of N drones, and the array is linearly distributed at equal intervals along the x-axis; and the array element spacing is greater than half a wavelength;

[0008] The array signal model under near-field conditions is constructed by using the phase difference of the received signal of each array element relative to the received signal at the center of the array;

[0009] The distance between the array element and the radiation source is expanded by Taylor series at x=0, and the phase difference function of each array element signal in the array signal model is approximated by Taylor expansion, and the array signal model is approximated as the sampling output of the linear frequency modulation signal at the array element, and the array signal model expression in the form of a rectangular wave is obtained;

[0010] The near-field beamforming is Taylor expanded at x=0 to simplify the near-field beamforming, wherein the simplified near-field beamforming is formed by using a filter to perform pulse compression processing on the received signal in a space-frequency two-dimensional domain;

[0011] According to the characteristic of signal spectrum folding caused by spatial undersampling, the grating lobe distribution equation of multivariate sparse array is obtained by using Nyquist sampling theorem.

[0012] The central frequency of the grating lobe and the bandwidth of the signal corresponding to the grating lobe are obtained by using the sampling output characteristics of the array signal approximated as a linear frequency modulation signal at the array element;

[0013] The position of the grating lobe is obtained by combining the grating lobe distribution equation of the multivariate sparse array, the center frequency of the grating lobe and the bandwidth of the signal corresponding to the grating lobe pointing, wherein the position of the grating lobe is characterized by the angle between the grating lobe and the positive half axis of the y-axis in the coordinate system and the distance between the grating lobe and the center of the array;

[0014] Or when the number of array elements is two, the two array elements are regarded as the intersection of hyperbolas, and the x-axis coordinate of the grating lobe is calculated by the properties of the hyperbola cluster; wherein the coordinate system takes the center of the array as the origin, the x-axis is the straight line where the array is located, and the y-axis is the straight line where the perpendicular line of the array is located.

[0015] Further preferably, the array signal model expression in the rectangular wave form is:

[0016]

[0017] Wherein, rect(·) is a rectangular pulse function, rect(x / L) is the pulse width of the linear frequency modulation signal, which is equal to the total length L of the array antenna; x is the horizontal coordinate of the array element; k = 2π / λ is the wave number; j is the imaginary unit; θ is the angle between the distance from the array element to the radiation source and the y axis; R is the distance from the radiation source to the center of the array; A represents the radiation amplitude of the signal sent by the radiation source; f is the frequency of the radiation signal; t is the time.

[0018] Further preferably, the simplified beamforming expression is:

[0019]

[0020] in, is the pulse compression filter function of s(x); N is the number of array elements.

[0021] Further preferably, the position of the grating lobe is:

[0022]

[0023] Among them, θ I is the angle between the main lobe position of the beam and the line connecting the center of the array and the y-axis; R I is the distance from the main lobe position of the beam to the center of the array; θ m is the angle between the mth grating lobe position of the beam and the line connecting the center of the array and the y-axis; R m is the distance from the mth grating lobe position of the beam to the center of the array; λ is the signal wavelength.

[0024] On the other hand, the present invention provides a linear sparse array beam property analysis device for a drone cluster, comprising:

[0025] The UAV is used to construct a near-field sparse antenna array by setting N of the UAVs, wherein the array is linearly distributed at equal intervals along the x-axis, and the array element spacing is greater than half a wavelength;

[0026] An array signal model acquisition system is used to construct an array signal model under near-field conditions by using the phase difference of the received signal of each array element relative to the received signal at the center of the array; Taylor series expansion is performed on the distance between the array element and the radiation source at x=0, and the phase difference function of each array element signal in the array signal model is approximated, and the array signal model is approximated to the sampling output of the linear frequency modulation signal at the array element, so as to obtain the array signal model expression in the form of a rectangular wave;

[0027] A near-field beamforming system is used to perform Taylor expansion of the near-field beamforming at x=0 to simplify the near-field beamforming, wherein the simplified near-field beamforming is formed by using a filter to perform pulse compression processing on a received signal in a two-dimensional space-frequency domain;

[0028] A grating lobe position acquisition system is used to obtain the grating lobe distribution equation of a multi-element sparse array using the Nyquist sampling theorem based on the characteristic of signal spectrum folding caused by spatial undersampling; obtain the center frequency of the grating lobe and the bandwidth of the signal corresponding to the grating lobe direction using the sampling output characteristics of the array signal being a linear frequency modulation signal at the array element; obtain the position of the grating lobe by combining the grating lobe distribution equation of the multi-element sparse array, the center frequency of the grating lobe and the bandwidth of the signal corresponding to the grating lobe direction; wherein the position of the grating lobe is characterized by the angle between the grating lobe and the positive half axis of the y-axis in the coordinate system, and the distance between the grating lobe and the center of the array; the coordinate system takes the center of the array as the origin, the x-axis as the straight line where the array is located; and the y-axis as the straight line where the perpendicular line of the array is located;

[0029] Or when there are two array elements, the two array elements are regarded as the intersection of a hyperbola, and the x-axis coordinate of the grating lobe is calculated by the properties of the hyperbola cluster.

[0030] Further preferably, the array signal model expression in the rectangular wave form is:

[0031]

[0032] Wherein, rect(·) is a rectangular pulse function, rect(x / L) is the pulse width of the linear frequency modulation signal, which is equal to the total length L of the array antenna; x is the horizontal coordinate of the array element; k = 2π / λ is the wave number; j is the imaginary unit, θ is the angle between the distance from the array element to the radiation source and the y-axis; R is the distance from the radiation source to the center of the array; A represents the radiation amplitude of the signal sent by the radiation source; f is the frequency of the radiation signal; t is the time.

[0033] Further preferably, the simplified beamforming expression is:

[0034]

[0035] in, is the pulse compression filter function of s(x); N is the number of array elements.

[0036] Further preferably, the position of the grating lobe is:

[0037]

[0038] Among them, θ I is the angle between the main lobe position of the beam and the line connecting the center of the array and the y-axis; R I is the distance from the main lobe position of the beam to the center of the array; θ m is the angle between the mth grating lobe position of the beam and the line connecting the center of the array and the y-axis; R m is the distance from the mth grating lobe position of the beam to the center of the array; λ is the signal wavelength.

[0039] In general, the above technical solution conceived by the present invention has the following beneficial effects compared with the prior art:

[0040] The present invention is based on the classic uniform linear array structure. Aiming at the near-field sparse distribution characteristics of the UAV cluster array, the present invention adopts the phase difference of the received signal of each array element relative to the received signal at the center of the array to construct an array signal model under near-field conditions. On this basis, the phase difference function of each array element signal in the signal model is approximated by using the Taylor expansion, and the array signal model is approximated as the sampling output of the linear frequency modulation signal at the array element, and the array signal model expression in the form of a rectangular wave is obtained. Under this premise, the present invention proposes to analyze two major properties of the linear sparse array beam. One is the simplification of near-field beamforming. The near-field beamforming is Taylor expanded at x=0 to simplify the near-field beamforming. The simplified near-field beamforming is formed by using a filter to perform pulse compression processing on the received signal in the space-frequency two-dimensional domain. The other is the acquisition of the grating lobe position. From the perspective of signal spectrum folding caused by spatial undersampling, an analytical expression for the distribution of the grating lobe of the near-field beam is analyzed and proposed. The theoretical support is provided for improving the communication, electronic reconnaissance and jamming capabilities of the UAV cluster by using the near-field beamforming technology.

[0041] The present invention provides an analytical expression for the distribution of the near-field beam grating lobes (when θ I =0, yes And the far-field grating lobe distribution analytical expression By comparison, it can be shown that when θ I = 0, the grating lobes with the same number in the near and far fields are in the same azimuth direction. The difference is that the far field does not consider the influence of the distance direction, while the near field needs to consider the characteristics of the grating lobe in the beam distance direction. The effectiveness of the analysis conclusion of the present invention is proved by simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a schematic diagram of a near-field linear sparse array model provided by an embodiment of the present invention;

[0043] Figure 2 is a schematic diagram of a hyperbolic cluster model of two array elements provided by an embodiment of the present invention;

[0044] FIG. 3( a ) is a diagram of θ provided by an embodiment of the present invention. I = 0° when the beam is formed by the classical method;

[0045] FIG. 3( b ) is a diagram of θ provided by an embodiment of the present invention. I = 0° when the beam is formed by the approximate method;

[0046] FIG. 3( c ) is a diagram of θ provided by an embodiment of the present invention. I =0° when the main lobe power changes with distance;

[0047] FIG. 3( d ) is a graph showing the θ I =0° when the main lobe power changes with the angle;

[0048] FIG. 4( a ) is a diagram of θ provided by an embodiment of the present invention. I =2° beam formed by the classical method;

[0049] FIG. 4( b ) is a diagram of θ provided by an embodiment of the present invention. I = 2° when the beam is formed by the approximate method;

[0050] FIG. 4( c ) is a diagram of θ provided by an embodiment of the present invention. I =2° when the main lobe power changes with distance;

[0051] FIG. 4( d ) is a graph showing the θ I =2° when the main lobe power changes with the angle;

[0052] Figure 5 is a target beam pattern within a curved surface range provided by an embodiment of the present invention;

[0053] FIG6( a ) is a θ-R plane projection diagram of a beam and a grating lobe when the center of the beam points to I (40 km, 0°) according to an embodiment of the present invention;

[0054] FIG6( b ) is a partial θ-R plane projection diagram of the beam and grating lobe when the beam center points to I (40 km, 0°) according to an embodiment of the present invention;

[0055] FIG6( c ) is a projection diagram of the beam and grating lobe on the θ-P plane when the beam center points to I (40 km, 0°) according to an embodiment of the present invention;

[0056] FIG6( d ) is a RP plane projection diagram of the beam and the grating lobe when the beam center points to I (40 km, 0°) according to an embodiment of the present invention;

[0057] Figure 7 It is a beam scanning curved surface range beam diagram provided by an embodiment of the present invention;

[0058] FIG8( a ) is a θ-R plane projection diagram of a beam and a grating lobe when the center of the beam points to I (40 km, 2°) according to an embodiment of the present invention;

[0059] FIG8( b ) is a partial θ-R plane projection diagram of the beam and grating lobe when the beam center points to I (40 km, 2°) according to an embodiment of the present invention;

[0060] FIG8( c ) is a projection diagram of the beam and grating lobe on the θ-P plane when the beam center points to I (40 km, 2°) provided by an embodiment of the present invention;

[0061] FIG8( d ) is an RP plane projection diagram of the beam and grating lobe when the center of the beam points to I (40 km, 2°) provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0062] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0063] Based on the classic uniform linear array structure, the present invention aims at the near-field sparse distribution characteristics of the drone cluster array. First, the corresponding array signal model is constructed, and the phase difference function of each array element signal in the signal model is approximated by using Taylor expansion, and a simplified implementation method of near-field beamforming for linear frequency modulation pulse compression processing in the spatial domain is obtained. Then, from the perspective of signal spectrum folding caused by spatial undersampling, an analytical expression for the near-field beam grating lobe distribution is analyzed and proposed and compared with the analytical expression for the far-field grating lobe distribution. Finally, the effectiveness of the analysis conclusion is proved through simulation, which provides theoretical support for improving the communication, electronic reconnaissance, and jamming capabilities of drone clusters using near-field beamforming technology.

[0064] On the one hand, the present invention provides a linear sparse array beam property analysis method for a drone cluster, which specifically includes the following steps:

[0065] Under near-field conditions, the assumption that electromagnetic waves are plane waves does not hold true, and spherical waves need to be used to describe them, such as Figure 1 As shown in the figure, suppose that the N-element near-field sparse antenna array composed of N UAVs is linearly distributed at equal intervals along the x-axis, the array element spacing is greater than half a wavelength, the total length of the array is L, and the coordinates of the nth array element are (x n ,0),-L / 2≤x n ≤L / 2;

[0066] For any radiation source P in the near field space, according to the spherical wave equation, the radiation signal received at the array element n can be expressed as:

[0067]

[0068] in, is the radiation signal at point P, f is the radiation signal frequency, λ is the signal wavelength, k=2π / λ is the wave number, r nRepresents the distance from antenna element n to point P, n = 1, 2, ..., N; A represents the radiation amplitude of the signal sent by the radiation source;

[0069] Let R be the distance from point P to the center point O of the array, and θ be the angle between OP and the y-axis. Then, according to the law of cosines, r n It can be expressed as:

[0070] Taking the array center O as the reference, the path difference from point P to antenna element n can be expressed as:

[0071]

[0072] Corresponding to the wave path difference, the phase difference of the received signal of each array element relative to the received signal at the array center O is:

[0073]

[0074] Substituting formula (4) into formula (1), the array signal model under near-field conditions can be expressed as:

[0075]

[0076] It can be seen from formula (4) and formula (5) that the signal phase difference between different array elements under near-field conditions is not only related to the angle θ, but also to the distance R. Based on this, in order to make the signals of different array elements be added in phase, the classic near-field beamforming method can be expressed as:

[0077]

[0078] For the array antenna composed of a cluster of drones, although the targets of interest such as wireless communication, electronic reconnaissance and jamming are generally located in the near field area of ​​the antenna array, the distance from the target of interest to the center of the antenna array is usually still much larger than the aperture of the antenna. Using this condition, it can be assumed that R>>L≥2|x in formula (2) n |, and expand it in Taylor series around x = 0 to get:

[0079]

[0080] Using formula (7) to calculate s(x n ) can be approximated to obtain:

[0081]

[0082] in, From formula (8), we can know that s(x n ) can be approximated as the array element coordinate x n is a quadratic function, so in the space-frequency two-dimensional domain s(xn ) can be approximated as the linear frequency modulation signal at the array element x n The sampled output at the position can be expressed in the form of a rectangular wave as follows:

[0083]

[0084] Where rect(·) is a rectangular pulse function, rect(x / L) is the pulse width of the linear frequency modulation signal, which is equal to the total length L of the array antenna, and x is the horizontal coordinate of the array element. Similar to formula (7), the compensation phase in formula (6) is Performing Taylor expansion around x=0 gives an approximate expression for near-field beamforming:

[0085]

[0086] in, represents s(x n ) and h(x n )’s discrete convolution output at 0, h(x) can be expressed as:

[0087]

[0088] When the target of interest is exactly at the peak of the main lobe, R is equal to R t , θ is equal to θ t , the corresponding formula (9) of linear frequency modulation pulse signal can be rewritten as:

[0089]

[0090] Comparing formula (11) and formula (12), we can see that h(x) can be regarded as s t (x); Based on this, the near-field beamforming implementation method of formula (10) is equivalent to using the filter h(x) to perform pulse compression processing on the signal s(x) in the space-frequency two-dimensional domain. When the target of interest is located at the peak point of the main lobe, h(x) and s(x) exactly match, so that the maximum pulse compression processing gain can be obtained; θ t is the angle between the line connecting the target of interest and the center of the array and the y-axis; the small subscript t represents the target of interest; the target of interest is the target in the direction of the main lobe of the array's desired beam; when beamforming is used for reconnaissance, the target is the radiation source; when beamforming is used for interference, the target is the receiver;

[0091] The main lobe is the point of maximum combined power. In practical applications, the array forms the main lobe in the target area of ​​interest; however, due to the sparseness of the array, interfering grating lobes will be formed;

[0092] For the cross-beam synthesis of binary coefficient arrays, such as Figure 2As shown, the two array elements can be regarded as the intersection of hyperbolas, and the grating lobe distribution can be obtained through the properties of the hyperbola cluster.

[0093] Figure 2 The equation of the hyperbolic family shown is:

[0094]

[0095] Wherein, m=0,±1,±2,..., m=0 is the main lobe position, and each m value corresponds to a grating lobe, x and y are the x-axis and y-axis coordinates of the point on the hyperbola, respectively, and L is the distance between two array elements; when the distance between the target of interest and the center of the array, i.e., the investigation distance R0, is constant, y=R0, and the x-axis coordinate of the mth grating lobe can be solved according to the one-to-one correspondence between A, B, C and D and m;

[0096]

[0097] This method is applicable to the derivation of grating lobe distribution of binary sparse array at any target distance;

[0098] At present, the existing technology rarely discusses the distribution of grating lobes of multivariate sparse arrays. According to the above analysis, the signal of each array element can be approximated as a linear frequency modulation signal in the space-frequency two-dimensional domain. The array sparseness is equivalent to undersampling the signal. When the signal is transformed into the frequency domain, the spectrum will be extended with the sampling frequency as the period, that is, the signal spectrum will be folded. When the folded signal spectrum matches the filter function spectrum, grating lobes will appear. The Nyquist sampling theorem is used to solve the grating lobe distribution problem of the multivariate sparse array, that is:

[0099]

[0100] Among them, m = ±1, ±2, ... are the grating lobe numbers, m = 0 is the main lobe, f 0I is the main lobe pointing direction of the array beam I(R I ,θ I ) corresponds to the center frequency of the signal, B wI is the main lobe pointing direction of the array beam I(R I ,θ I ) corresponds to the bandwidth of the signal, f 0m is the center frequency of the mth grating lobe, B wm The mth grating lobe points to I(R I ,θ I ) corresponds to the bandwidth of the signal; using the sampling output characteristics of the array signal as a linear frequency modulation signal at the array element, the signal phase term in equation (12) Take the derivative, and correspond the frequency-space domain to the frequency-time domain by using the array length L, and we have:

[0101]

[0102] Among them, θ m is the angle between the mth grating lobe and the positive half axis of the y-axis, R m is the distance between the mth grating lobe and the array center O, then we can get:

[0103]

[0104] When θ I =0, yes

[0105]

[0106] According to the formula for deriving the far-field uniform linear array grating lobe distribution, the maximum value of the uniform linear array factor appears at ψ my =kdsinθ my =m·2π, m=0,±1,±2,..., where ψ my represents the phase difference between the radiation fields of two adjacent units, d = L / (N-1) is the spacing of uniformly distributed array elements, θ my is the angle between the direction of the mth maximum value of the array and the array normal. It can be solved as follows:

[0107]

[0108] At this time, θ my =θ m , indicating that when θ I When =0, the grating lobes with the same serial number in the near and far fields are in the same azimuth direction, but the far field does not consider the influence in the range direction, while the near field needs to consider the characteristics of the grating lobe in the beam range direction.

[0109] On the other hand, the present invention provides a linear sparse array beam property analysis device for a drone cluster, comprising:

[0110] The UAV is used to construct a near-field sparse antenna array by setting N of the UAVs, wherein the array is linearly distributed at equal intervals along the x-axis, and the array element spacing is greater than half a wavelength;

[0111] An array signal model acquisition system is used to construct an array signal model under near-field conditions by using the phase difference of the received signal of each array element relative to the received signal at the center of the array; Taylor series expansion is performed on the distance between the array element and the radiation source at x=0, and the phase difference function of each array element signal in the array signal model is approximated, and the array signal model is approximated to the sampling output of the linear frequency modulation signal at the array element, so as to obtain the array signal model expression in the form of a rectangular wave;

[0112] A near-field beamforming system is used to perform Taylor expansion of the near-field beamforming at x=0 to simplify the near-field beamforming, wherein the simplified near-field beamforming is formed by using a filter to perform pulse compression processing on a received signal in a two-dimensional space-frequency domain;

[0113] A grating lobe position acquisition system is used to obtain the grating lobe distribution equation of a multi-element sparse array using the Nyquist sampling theorem based on the characteristic of signal spectrum folding caused by spatial undersampling; obtain the center frequency of the grating lobe and the bandwidth of the signal corresponding to the grating lobe direction using the sampling output characteristics of the array signal being a linear frequency modulation signal at the array element; obtain the position of the grating lobe by combining the grating lobe distribution equation of the multi-element sparse array, the center frequency of the grating lobe and the bandwidth of the signal corresponding to the grating lobe direction; wherein the position of the grating lobe is characterized by the angle between the grating lobe and the positive half axis of the y-axis in the coordinate system, and the distance between the grating lobe and the center of the array; the coordinate system takes the center of the array as the origin, the x-axis as the straight line where the array is located; and the y-axis as the straight line where the perpendicular line of the array is located;

[0114] Considering the special case when the array has only two elements, the two elements are regarded as the intersection of hyperbolas, and the x-axis coordinate of the grating lobe is calculated by the properties of the hyperbola cluster.

[0115] Further preferably, the array signal model expression in the rectangular wave form is:

[0116]

[0117] Wherein, rect(·) is a rectangular pulse function, rect(x / L) is the pulse width of the linear frequency modulation signal, which is equal to the total length L of the array antenna; x is the horizontal coordinate of the array element; k = 2π / λ is the wave number; j is the imaginary unit; θ is the angle between the distance from the array element to the radiation source and the y axis; R is the distance from the radiation source to the center of the array; A represents the radiation amplitude of the signal sent by the radiation source; f is the frequency of the radiation signal; t is the time.

[0118] Further preferably, the simplified beamforming expression is:

[0119]

[0120] in, is the pulse compression filter function of s(x); N is the number of array elements.

[0121] Further preferably, the position of the grating lobe is:

[0122]

[0123] Among them, θ I is the angle between the main lobe position of the beam and the line connecting the center of the array and the y-axis; R Iis the distance from the main lobe position of the beam to the center of the array; θ m is the angle between the mth grating lobe position of the beam and the line connecting the center of the array and the y-axis; R m is the distance from the mth grating lobe position of the beam to the center of the array; λ is the signal wavelength.

[0124] Example

[0125] Assume the signal frequency f = 300MHz, and the beam center points to point Iθ I =0° or θ I =2°; number of array elements N = 26, array aperture L = 500λ, observation distance array R t = Main lobe beamforming at [30km, 50km], i.e. θ I =0°, θ t =[-2°,2°] corresponds to the target field strength value; θ I =2°, θ t =[0°,4°] corresponds to the target field strength value; the beam is formed using the classical beamforming method and the approximate beamforming method. Figures 3(a) to 3(d) , Figures 4(a) to 4(d) As shown, Figure 3(a) to 3(b) and Figure 4(a) to 4(b) They are θ I =0° and θ I =2°, the beam has grating lobes because the array element spacing selected in the simulation is greater than λ / 2. Figure 3(c) to 3(d) and Figure 4(c) to 4(d) are θ I =0° and θ I =2° beam main lobe power change;

[0126] Depend on Figures 3(a) to 3(d) and Figures 4(a) to 4(d) It can be seen that, regardless of whether the beam is scanned or not, the beam formed by the classical method is consistent with the beam formed approximately, which verifies that the pulse compression process is applicable to the near-field beamforming method provided by the present invention and the effectiveness of the near-field beamforming method provided by the present invention; after compensation, the peak power of the main lobe of the beam can reach 28dB, and the peak power can reach 28.3dB when the array elements are close to 26;

[0127] Assume that the beam center points to I (40km, 0°) and examine the slant range R t =[30km,50km],θ t = For a target within [-8°, 8°], according to formula (6), its power value varies with angle and distance as follows: Figure 5 As shown;

[0128] The actual beam formed by the array is Figure 5The beam shown is projected onto the θ-R, θ-P, and RP planes respectively, and the grating lobe distribution derivation formula is used to calculate the grating lobe corresponding to the beam pointing, as shown in Figure 6(a) to 6(d) As shown;

[0129] The black dots in Figures 6(a) and 6(b), and the vertical lines in Figure 6(c) are calculated using the grating lobe distribution formula (19). As can be seen from Figure 6(a), as θ m Change, R m There are also certain changes; the power diagram of the distance change is drawn in the azimuth where the grating lobe appears, as shown in Figure 6(c). The peak values ​​of grating lobes with different serial numbers change in the distance upward, and the power of a pair of grating lobes with equal |m| has the same law of change in the distance upward; Figure 6(a) to 6(d) It shows that the grating lobe obtained by the grating lobe distribution formula (18) is consistent with the beam grating lobe distribution, which verifies the effectiveness of the grating lobe distribution solution method of formula (18);

[0130] When scanning the beam, assume that the beam center points to I(40km,2°), and the other simulation conditions remain unchanged. Figure 7 The beam scanning surface range beam diagram shown in FIG. 1 is used to calculate the grating lobe corresponding to the beam pointing using the grating lobe distribution derivation formula, such as Figures 8(a) to 8(b) ;

[0131] Depend on Figure 7 as well as Figures 8(a) to 8(b) It can be seen that the grating lobe distribution obtained by applying formula (18) is consistent with the actual grating lobe distribution of the beam. The peak values ​​of grating lobes with different serial numbers vary in the distance direction. In the scanning case, the characteristics of a pair of grating lobes with equal |m| in the distance direction are also different. Figure 8 shows that the grating lobe obtained by the grating lobe distribution formula (18) is consistent with the beam grating lobe distribution, which verifies the effectiveness of the grating lobe distribution solution method of formula (18).

[0132] Compared with the prior art, the present invention has the following advantages:

[0133] The present invention is based on the classic uniform linear array structure. Aiming at the near-field sparse distribution characteristics of the UAV cluster array, the present invention adopts the phase difference of the received signal of each array element relative to the received signal at the center of the array to construct an array signal model under near-field conditions. On this basis, the phase difference function of each array element signal in the signal model is approximated by using the Taylor expansion, and the array signal model is approximated as the sampling output of the linear frequency modulation signal at the array element, and the array signal model expression in the form of a rectangular wave is obtained. Under this premise, the present invention proposes to analyze two major properties of the linear sparse array beam. One is the simplification of near-field beamforming. The near-field beamforming is Taylor expanded at x=0 to simplify the near-field beamforming. The simplified near-field beamforming is formed by using a filter to perform pulse compression processing on the received signal in the space-frequency two-dimensional domain. The other is the acquisition of the grating lobe position. From the perspective of signal spectrum folding caused by spatial undersampling, an analytical expression for the distribution of the grating lobe of the near-field beam is analyzed and proposed. The theoretical support is provided for improving the communication, electronic reconnaissance and jamming capabilities of the UAV cluster by using the near-field beamforming technology.

[0134] The present invention provides an analytical expression for the distribution of the near-field beam grating lobes (when θ I =0, yes And the far-field grating lobe distribution analytical expression By comparison, it can be shown that when θ I = 0, the grating lobes with the same number in the near and far fields are in the same azimuth direction. The difference is that the far field does not consider the influence of the distance direction, while the near field needs to consider the characteristics of the grating lobe in the beam distance direction. The effectiveness of the analysis conclusion of the present invention is proved by simulation.

[0135] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A linear sparse array beam property analysis method for a drone cluster, characterized in that: The following steps are involved: A near-field sparse antenna array is formed by using drone formations. The array is linearly distributed at equal intervals along the x-axis, and the array element spacing is greater than half a wavelength. The array signal model under near-field conditions is constructed by using the phase difference of the received signal of each array element relative to the received signal at the center of the array; Perform Taylor series expansion on the distance between the array element and the radiation source at x=0, perform approximate processing on the phase difference function of each array element signal in the array signal model, approximate the array signal model to the sampling output of the linear frequency modulation signal at the array element, and obtain the array signal model expression in the form of a rectangular wave; Taylor expansion of the near-field beamforming at x=0 is performed, and the near-field beamforming is simplified based on the array signal model expression in the form of a rectangular wave, wherein the simplified near-field beamforming is formed by using a filter to perform pulse compression processing on the received signal in the space-frequency two-dimensional domain; According to the characteristic of signal spectrum folding caused by spatial undersampling, the grating lobe distribution equation of multivariate sparse array is obtained by using Nyquist sampling theorem. The central frequency of the grating lobe and the bandwidth of the signal corresponding to the grating lobe are obtained by using the sampling output characteristics of the linear frequency modulation signal at the array element; The position of the grating lobe is obtained by combining the grating lobe distribution equation of the multivariate sparse array, the center frequency of the grating lobe and the bandwidth of the corresponding signal of the grating lobe pointing; wherein the position of the grating lobe is characterized by the angle between the grating lobe and the positive half axis of the y-axis in the coordinate system, and the distance between the grating lobe and the center of the array; the coordinate system takes the center of the array as the origin, the x-axis as the straight line where the array is located; and the y-axis as the straight line where the perpendicular line of the array is located; Or when the number of array elements is two, the two array elements are regarded as the intersection of hyperbolas, and the x-axis coordinate of the grating lobe is calculated by the properties of the hyperbola cluster; The simplified beamforming expression is: in, is the pulse compression filter function of s(x); N is the number of array elements; where the array signal model expression in the form of a rectangular wave is: Wherein, rect(·) is a rectangular pulse function, rect(x / L) is the pulse width of the linear frequency modulation signal, which is equal to the total length L of the array antenna; x is the horizontal coordinate of the array element; k = 2π / λ is the wave number; λ is the signal wavelength; j is the imaginary unit; R is the distance from the radiation source to the center of the array; A represents the radiation amplitude of the signal sent by the radiation source; f is the radiation signal frequency; t is the time; x n is the horizontal coordinate of array element n; θ t is the angle between the line connecting the target of interest and the center of the array and the y-axis; the small superscript t represents the target of interest.

2. The linear sparse array beam property analysis method according to claim 1, characterized in that: The positions of the grating lobes are: Among them, θ I is the angle between the main lobe position of the beam and the line connecting the center of the array and the y-axis; R I is the distance from the main lobe position of the beam to the center of the array; θ m is the angle between the mth grating lobe position of the beam and the line connecting the center of the array and the y-axis; R m is the distance from the mth grating lobe position of the beam to the center of the array.

3. A linear sparse array beam property analysis device for a drone cluster, characterized in that: include: A drone, used for constructing a near-field sparse antenna array by arranging N of the drones, wherein the array is linearly distributed at equal intervals along the x-axis, and the array element spacing is greater than half a wavelength; An array signal model acquisition system is used to construct an array signal model under near-field conditions by using the phase difference of the received signal of each array element relative to the received signal at the center of the array; Taylor series expansion is performed on the distance between the array element and the radiation source at x=0, and the phase difference function of each array element signal in the array signal model is approximated, and the array signal model is approximated to the sampling output of the linear frequency modulation signal at the array element, so as to obtain the array signal model expression in the form of a rectangular wave; A near-field beamforming system is used to perform Taylor expansion of the near-field beamforming at x=0 to simplify the near-field beamforming, wherein the simplified near-field beamforming is formed by using a filter to perform pulse compression processing on a received signal in a two-dimensional space-frequency domain; A grating lobe position acquisition system is used to obtain the grating lobe distribution equation of a multi-element sparse array using the Nyquist sampling theorem based on the characteristic of signal spectrum folding caused by spatial undersampling; obtain the center frequency of the grating lobe and the bandwidth of the signal corresponding to the grating lobe direction using the sampling output characteristics of the array signal being a linear frequency modulation signal at the array element; obtain the position of the grating lobe by combining the grating lobe distribution equation of the multi-element sparse array, the center frequency of the grating lobe and the bandwidth of the signal corresponding to the grating lobe direction; wherein the position of the grating lobe is characterized by the angle between the grating lobe and the positive half axis of the y-axis in the coordinate system, and the distance between the grating lobe and the center of the array; the coordinate system takes the center of the array as the origin, the x-axis as the straight line where the array is located; and the y-axis as the straight line where the perpendicular line of the array is located; Or when there are two array elements, it is used to regard the two array elements as the intersection of hyperbolas and calculate the x-axis coordinate of the grating lobe by the properties of the hyperbola cluster; The simplified beamforming expression is: in, is the pulse compression filter function of s(x); N is the number of array elements; Among them, the array signal model expression in the form of a rectangular wave is: Wherein, rect(·) is a rectangular pulse function, rect(x / L) is the pulse width of the linear frequency modulation signal, which is equal to the total length L of the array antenna; x is the horizontal coordinate of the array element; k = 2π / λ is the wave number; λ is the signal wavelength; j is the imaginary unit; R is the distance from the radiation source to the center of the array; A represents the radiation amplitude of the signal sent by the radiation source; f is the radiation signal frequency; t is the time; x n is the horizontal coordinate of array element n; θ t is the angle between the line connecting the target of interest and the center of the array and the y-axis; the small superscript t represents the target of interest.

4. The linear sparse array beam property analysis device according to claim 3, characterized in that: The positions of the grating lobes are: Among them, θ I is the angle between the main lobe position of the beam and the line connecting the center of the array and the y-axis; R I is the distance from the main lobe position of the beam to the center of the array; θ m is the angle between the mth grating lobe position of the beam and the line connecting the center of the array and the y-axis; R m is the distance from the mth grating lobe position of the beam to the center of the array.

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