CN113314843B - Side lobe suppression method suitable for conformal antenna array - Google Patents

Side lobe suppression method suitable for conformal antenna array Download PDF

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CN113314843B
CN113314843B CN202110511901.7A CN202110511901A CN113314843B CN 113314843 B CN113314843 B CN 113314843B CN 202110511901 A CN202110511901 A CN 202110511901A CN 113314843 B CN113314843 B CN 113314843B
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赵勋旺
张世莹
张玉
林中朝
闫聪欢
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Xidian University
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Abstract

The invention discloses a method for suppressing side lobes based on a conformal antenna array. The problem that the prior art can not restrain good side lobes of a complex conformal antenna array is mainly solved. The scheme is as follows: creating a conformal antenna array and a transmitting antenna model; the transmitting antenna transmits electromagnetic wave signals to the conformal antenna array to obtain a far-field directional diagram; determining the angle of the suppressed side lobe according to the far-field directional diagram and obtaining the excitation information at the angle; forming an excitation matrix by the excitation information; calculating to obtain a weight according to the side lobe level design requirement; multiplying the excitation matrix by the weight to obtain the excitation of the conformal antenna array with suppressed sidelobe level; the directional pattern of the conformal antenna array under this excitation is calculated using commercial software. The invention utilizes time reversal and multi-beam superposition to restrain the side lobe of the conformal antenna array, only needs to place a transmitting antenna at the angle of the side lobe to be restrained, and adjusts excitation by changing the weight, thereby achieving the restraint of the side lobe, and having good restraining effect and low cost.

Description

Side lobe suppression method suitable for conformal antenna array
Technical Field
The invention belongs to the technical field of antennas, and particularly relates to a method for suppressing side lobe beams, which can be used for conformal antenna arrays.
Background
In many fields such as radar systems and wireless communication, electromagnetic energy is often reasonably distributed in space by performing beam forming on an antenna array, and the effective utilization rate of the electromagnetic energy is further improved. Under normal conditions, a main lobe beam of a far-field directional diagram of the antenna array is required to point to a specific direction, and a side lobe beam of the antenna array is restrained, so that the electromagnetic compatibility and the anti-interference capability of the system are effectively improved. For a traditional classical antenna array beam forming method, such as a particle swarm optimization algorithm, a genetic algorithm and the like, when beam forming is realized on an antenna array, array antenna excitation meeting design beam requirements needs to be solved, an optimal solution needs to be obtained through a mode of repeated iteration solution, and if beam forming is carried out on a conformal array with a relatively complex antenna form, more iteration times and longer solution time need to be carried out.
The title method is a beam forming method suitable for conformal antenna arrays, and is implemented by time reversal method, which only needs to perform time reversal processing for multiple times to obtain excitation information of multiple single beams, and does not need to perform time-consuming numerical optimization on loss function of beam pattern at each frequency point. When the beam forming is carried out on the large-scale antenna array which is arranged irregularly, the mutual coupling among the array elements and the scattering condition of the carrier do not need to be measured accurately, and the cost can be greatly reduced. However, the method can only realize that the main lobe beam of the far-field directional diagram points to a specific direction, and does not relate to the suppression of the side lobe beam, so that the gain of the side lobe beam is higher, and the requirement of practical application is not met.
Disclosure of Invention
The present invention is directed to provide a method for suppressing sidelobe beams in a conformal antenna array, so as to reduce the gain of the sidelobe beams and meet the requirements of practical applications.
The technical scheme of the invention is as follows: the time reversal method is combined with the multi-beam superposition method to reduce the side lobe gain of the conformal antenna array, and the implementation steps comprise:
(1) establishing a conformal antenna array model consisting of M antenna units and irregular carriers, and setting the working frequency F of each antenna unit to be 450MHz, wherein M is more than or equal to 2;
(2) in conformal array models
Figure BDA0003060712650000021
A first transmitting antenna is arranged at a far-direction area, and a far-field directional diagram of a conformal antenna array model is obtained by a time reversal method under the condition that the transmitting antenna transmits electromagnetic waves w (t), wherein thetarIs the included angle between the incident direction of w (t) of the electromagnetic wave emitted by the first emitting antenna and the + Y axis,
Figure BDA0003060712650000022
the included angle between the incident direction of w (t) of the electromagnetic wave transmitted by the first transmitting antenna and the + X axis;
(3) determining the angle of the suppressed side lobe beam from the far field pattern in (2)
Figure BDA0003060712650000023
And in conformal antenna array model
Figure BDA0003060712650000024
A second transmitting antenna is arranged at a far zone of the direction, and the electromagnetic wave w transmitted by the second transmitting antenna is obtained by utilizing a time reversal method2(t) excitation of the conformal antenna array;
(4) repeating the step (3) N times to obtain N groups of beam directions
Figure BDA0003060712650000025
The excitation matrix S (ω) is composed of the excitation information of (a):
Figure BDA0003060712650000026
wherein S isi(ω) denotes the i-th group beam pointing
Figure BDA0003060712650000027
Excitation information of sij(ω) represents the value of the i-th and j-th excitations, i being 1 to N, j being 1 to M;
(5) according to the design requirement on the side lobe level, calculating and solving the weight occupied by each wave beam in the total field to obtain a weight vector alpha:
α＝(α1 α2 ... αi ... αN)T，
wherein alpha isiRepresenting the weight corresponding to the ith group of excitation, wherein T represents transposition;
(6) obtaining the excitation I (omega) of the conformal antenna array after the side lobe level is suppressed according to an excitation matrix S (omega) formed by a plurality of groups of vectors and a weight vector alpha:
Figure BDA0003060712650000031
wherein, Ij(ω) represents the value of the newly derived j-th excitation;
(7) and applying the excitation signal I (omega) with the side lobe level suppressed to a feed port of the conformal antenna array, and calculating a directional pattern of the conformal antenna array under the excitation by utilizing electromagnetic commercial software.
Compared with the prior art, the invention has the following advantages:
1. the side lobe gain of the conformal antenna array is reduced by utilizing a time reversal technology and a multi-beam superposition method, only a transmitting antenna needs to be placed at the angle of the side lobe to be suppressed on the conformal antenna array, and the value of the angle and the level of the side lobe to be suppressed can be controlled autonomously by changing the weight to adjust the value of excitation;
2. according to the method, only the array model needs to be changed, compared with the traditional optimization method, complicated numerical iteration is not needed, numerical calculation is not needed for each frequency point, and the calculation time can be greatly reduced;
3. according to the invention, because the time reversal technology is utilized to carry out beam forming on the antenna array, namely the far field pattern of the antenna array is calculated, when the beam forming is carried out on the large-scale antenna array which is irregularly arranged, especially the conformal antenna array, mutual coupling among array elements does not need to be considered, and accurate measurement is carried out on the scattering condition of a carrier, so that the cost can be greatly reduced.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram of a conformal antenna array model constructed in the present invention;
FIG. 3 is a xoz plane two-dimensional directional diagram calculated from FIG. 2 using time reversal techniques;
FIG. 4 is a three-dimensional xoz plane pattern calculated using time reversal techniques for FIG. 2;
FIG. 5 is a yoz plane three-dimensional directional diagram calculated by the time reversal technique of the present invention from FIG. 2;
FIG. 6 is a xoz plane three-dimensional pattern after the side lobe of FIG. 3 has been suppressed using the present invention;
FIG. 7 is a three dimensional orientation of the yoz plane after the side lobe of FIG. 3 has been suppressed using the present invention;
FIG. 8 is a two-dimensional comparison of xoz planes before and after the side lobe of FIG. 3 is suppressed using the present invention;
FIG. 9 is a two-dimensional direction comparison of the xoy plane before and after the side lobe of FIG. 3 is suppressed by the present invention.
Detailed Description
The embodiments and effects of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:
referring to fig. 1, the implementation steps of this example are as follows:
step 1, creating a conformal antenna array.
Referring to fig. 2, the conformal antenna array created in this step is composed of 10 × 7 inverted-F antenna elements 1 and a carrier 2, each antenna element 1 is distributed on the surface of the carrier 2, and the interval between the antenna elements in the + X direction is one third wavelength, and the interval between the antenna elements in the + Z direction is one wavelength.
And 2, setting a first transmitting antenna, and transmitting electromagnetic waves to the conformal antenna array to obtain a far-field directional diagram and excitation information.
2.1) placing a first transmitting antenna at a position which is twenty wavelengths away from the antenna array in the direction of the conformal antenna array (-90,0), wherein the transmitting antenna transmits electromagnetic waves with the central frequency of 450MHz to the conformal antenna array;
2.2) calculating a receiving signal Y (t) of a conformal antenna array feeding port of the first transmitting antenna under the condition of transmitting electromagnetic waves by utilizing electromagnetic commercial software:
Y(t)＝[y1(t),y2(t),...,ym(t)...,y70(t)]T，
wherein, ym(T) receiving signals at a feed port of the mth array element, wherein m is more than or equal to 1 and less than or equal to 70, and T represents transposition;
2.3) carrying out time reversal processing on the received signal Y (t) to obtain a received signal Y (-t) after time reversal:
Y(-t)＝[y1(-t),y2(-t),...,ym(-t)...,y70(-t)]T，
wherein, ymThe (-t) is a time domain receiving signal after the feed port of the mth array element is subjected to time reversal;
2.4) performing Fourier transform on the time domain received signal Y (-t) after time reversal to obtain a received signal Y (omega) on a frequency domain:
Figure BDA0003060712650000041
wherein e is-jωtIs a complex exponential signal;
2.5) conjugate the received signal Y (omega) in the frequency domain to obtain the conjugated frequency domain received signal Y*(ω)：
Figure BDA0003060712650000042
Wherein, the upper label*In order to take the conjugate operator out of the conjugate operator,
Figure BDA0003060712650000043
is as followsReceiving signals in frequency domains of m array elements;
2.6) excitation information Y*Frequency domain received signal of m-th array element in (omega)
Figure BDA0003060712650000051
Exciting the conformal antenna array without the transmitting antenna, and calculating a beam pattern of the conformal antenna array under the excitation by utilizing electromagnetic commercial software, wherein a xoz plane two-dimensional pattern obtained by calculation is shown in fig. 3, a xoz plane three-dimensional pattern obtained by calculation is shown in fig. 4, and a yoz plane three-dimensional pattern obtained by calculation is shown in fig. 5.
And 3, determining the angle for inhibiting the side lobe, arranging a transmitting antenna in the side lobe direction, and transmitting electromagnetic waves to the conformal antenna array to obtain excitation information.
3.1) placing a second transmitting antenna at a position which is twenty wavelengths away from the antenna array in the direction of the conformal antenna array (-105,0), wherein the transmitting antenna transmits electromagnetic waves with the central frequency of 450MHz to the conformal antenna array;
3.2) calculating a receiving signal X (t) of a conformal antenna array feeding port of the second transmitting antenna under the condition of transmitting electromagnetic waves by utilizing electromagnetic business software:
X(t)＝[x1(t),x2(t),...,xm(t),...,x70(t)]T，
wherein x ism(t) m is more than or equal to 1 and less than or equal to 70, and the feed port of the mth array element receives signals;
3.3) carrying out time reversal processing on the received signal X (t) to obtain a received signal X (-t) after time reversal:
X(-t)＝[x1(-t),x2(-t),...,xm(-t),...,x70(-t)]T，
wherein x ismThe (-t) is a time domain receiving signal after the feed port of the mth array element is subjected to time reversal;
3.4) carrying out Fourier transform on the time domain received signal X (-t) after time reversal to obtain a received signal X (omega) on a frequency domain:
Figure BDA0003060712650000052
wherein e-jωtIs a complex exponential signal;
3.5) conjugate the received signal X (omega) in the frequency domain to obtain the conjugated frequency domain received signal X*(ω)：
Figure BDA0003060712650000053
Wherein, the upper label*In order to take the conjugate operator out of the conjugate operator,
Figure BDA0003060712650000054
receiving signals for the frequency domain of every m array elements;
3.6) placing a third transmitting antenna at a position twenty wavelengths away from the antenna array in the direction (-75,0) of the conformal antenna array, and repeating the operations of 3.2) -3.5) on the electromagnetic wave with the central frequency of 450MHz transmitted by the conformal antenna array by the transmitting antenna to obtain the frequency domain receiving signal after conjugation
Figure BDA0003060712650000061
And 4, constructing an excitation matrix S (omega).
The frequency domain receiving signal Y conjugated in the (-90,0) direction in the step 2 is transmitted*(ω) as excitation signal S in this direction1(ω)；
The frequency domain received signal X conjugated in the (-105,0) direction in the step 3 is transmitted*(ω) as excitation signal S in this direction2(ω)；
The frequency domain receiving signal conjugated in the (-75,0) direction in the step 3 is received
Figure BDA0003060712650000062
As an excitation signal S in that direction3(ω)；
The three excitation signals are combined into an excitation matrix S (ω):
Figure BDA0003060712650000063
wherein s is1m(ω) is the excitation value of the m-th array element in the (-90,0) direction, s2m(ω) is the excitation value of the m-th array element in the (-75,0) direction, s3mAnd (omega) is the excitation value of the m-th array element in the (-105,0) direction.
And 5, calculating and solving the weight occupied by each beam in the total field according to the level value for inhibiting the side lobe to obtain a weight vector alpha.
5.1) in the example, the level of the suppression side lobe is set to be 20dB, and three groups of electric fields are obtained by performing simulation calculation on the conformal antenna array by using three groups of inversion excitation in three directions of (-90,0), (-75,0) and (-105, 0);
5.2) extracting electric field values at-90 °, -75 °, -105 ° angles in the three sets of electric fields constructs an electric field matrix E:
Figure BDA0003060712650000064
wherein the first column represents electric field values at-90 °, -75 °, -105 ° angles in the (-90,0) direction, the second column represents electric field values at-90 °, -75 °, -105 ° angles in the (-75,0) direction, and the third column represents electric field values at-90 °, -75 °, -105 ° angles in the (-105,0) direction;
5.3) converting the formula according to the level value and the electric field value: 10 log (a) ═ B, obtaining a multiple relation between a product of the electric field value at an angle of-90 ° and the weight vector and a product of the electric field value at an angle of-75 °, -105 ° and the weight vector, wherein a is the electric field value and B is the level value;
since the value of the suppressed sidelobe level is set to 20dB in this example, it can be seen that the product of the electric field value at an angle of-90 ° and the weight vector is 10 times the product of the electric field value at an angle of-75 °, -105 ° and the weight vector, and the following equation set is listed:
Figure BDA0003060712650000071
5.4) solving by the equation set of 5.3) to obtain a weight vector α:
α＝(α1 α2 α3)T，
wherein alpha is1,α2,α3The weights occupied by the excitation in the (-90,0), (-75,0), (-105,0) directions, respectively.
And 6, obtaining the excitation I (omega) of the conformal antenna array for inhibiting the sidelobe level according to an excitation matrix S (omega) formed by the multiple groups of vectors and the weight vector alpha.
Multiplying an excitation matrix S (omega) formed by a plurality of groups of vectors by a weight vector alpha to obtain an excitation I (omega) of the conformal antenna array after the side lobe level is suppressed:
Figure BDA0003060712650000072
wherein, ImAnd (omega) is the new excitation value of the m-th array element.
And 7, utilizing the newly obtained excitation value to suppress the side lobe of the conformal antenna and calculating the directional diagram of the conformal antenna.
7.1) applying the excitation I (omega) of the conformal antenna array obtained in the step 6 after the side lobe level is suppressed to a feed port of the conformal antenna array;
7.2) calculating the directional pattern of the conformal antenna array with the suppressed side lobe beam by using electromagnetic commercial software, such as FEKO, HOBBIES, wherein:
the xoz plane three-dimensional directional diagram after the side lobe is suppressed is shown in fig. 6;
the yoz plane three-dimensional directional diagram after the side lobe suppression is shown in fig. 7;
a two-dimensional direction comparison diagram of the xoz planes before and after the side lobes are suppressed is shown in fig. 8;
a two-dimensional direction comparison graph of the xoy plane before and after the side lobe suppression is shown in fig. 9.
Comparing the xoz plane three-dimensional patterns before and after the side lobe suppression of fig. 4 and 6 and the yoz plane three-dimensional patterns before and after the side lobe suppression of fig. 5 and 7 shows that the side lobe of the conformal antenna array has a significant drop.
As can be seen from fig. 8, at plane xoz, the sidelobe level of the conformal antenna array drops from 13dB to 19.9dB, which substantially satisfies the set value of 20dB, and achieves the expected effect.
As can be seen from fig. 9, on the xoy plane, the sidelobe level of the conformal antenna array is not reduced much because no plane with obvious reduction is intercepted when the two-dimensional cross section is selected.
The results show that the invention can effectively restrain the side lobe of the conformal antenna array.

Claims (3)

1. A method for sidelobe suppression for a conformal antenna array, comprising:
(1) establishing a conformal antenna array model consisting of M antenna units and irregular carriers, and setting the working frequency F of each antenna unit to be 450MHz, wherein M is more than or equal to 2;
(2) in conformal antenna array models
Figure FDA0003598859720000011
A first transmitting antenna is arranged at a far-direction area, and a far-field directional diagram of the conformal antenna array model is obtained by a time reversal method under the condition that the transmitting antenna transmits electromagnetic waves w (t), wherein theta isrIs the included angle between the incident direction of w (t) of the electromagnetic wave emitted by the first emitting antenna and the + Y axis,
Figure FDA0003598859720000012
the included angle between the incident direction of w (t) of the electromagnetic wave transmitted by the first transmitting antenna and the + X axis;
(3) determining the angle of the suppressed side lobe beam from the far field pattern in (2)
Figure FDA0003598859720000013
And in conformal antenna array model
Figure FDA0003598859720000014
DirectionA second transmitting antenna is arranged at the far zone, and the electromagnetic wave w transmitted by the second transmitting antenna is obtained by utilizing a time reversal method2(t) excitation of the conformal antenna array;
(4) repeating the step (3) for N times to obtain N groups of beam directions
Figure FDA0003598859720000015
The excitation matrix S (ω) is composed of:
Figure FDA0003598859720000016
wherein S isi(ω) denotes the i-th group beam pointing
Figure FDA0003598859720000017
Excitation information of sij(ω) represents the value of the ith and jth excitations, i is 1 to N, j is 1 to M, N is 2 or more, M is 2 or more;
(5) according to the design requirement on the side lobe level, calculating and solving the weight occupied by each wave beam in the total field to obtain a weight vector alpha:
α＝(α1 α2...αi...αN)T，
wherein alpha isiRepresenting the weight corresponding to the ith group of excitation, wherein T represents transposition;
the method for calculating and calculating the weight value occupied by each beam in the total field according to the design requirement on the side lobe level comprises the following steps:
5.1) setting the level of a suppressed side lobe to be 20dB, and carrying out simulation calculation on the conformal antenna array by using three groups of inversion excitation in three directions of (-90,0), (-75,0) and (-105,0) to obtain three groups of electric fields;
5.2) extracting electric field values at-90 °, -75 °, -105 ° angles in the three sets of electric fields constructs an electric field matrix E:
Figure FDA0003598859720000021
wherein the first column represents electric field values at-90 °, -75 °, -105 ° angles in the (-90,0) direction, the second column represents electric field values at-90 °, -75 °, -105 ° angles in the (-75,0) direction, and the third column represents electric field values at-90 °, -75 °, -105 ° angles in the (-105,0) direction;
5.3) converting the formula according to the level value and the electric field value: 10 log (a) ═ B, obtaining a multiple relation between a product of the electric field value at an angle of-90 ° and the weight vector and a product of the electric field value at an angle of-75 °, -105 ° and the weight vector, wherein a is the electric field value and B is the level value; the following system of equations is obtained:
Figure FDA0003598859720000022
5.4) solving by the equation set of 5.3) to obtain a weight vector α:
α＝(α1 α2 α3)T，
wherein alpha is1,α2,α3The weights occupied by the excitations in the (-90,0), (-75,0), (-105,0) directions, respectively;
(6) obtaining the excitation I (omega) of the conformal antenna array after the side lobe level is suppressed according to an excitation matrix S (omega) formed by a plurality of groups of vectors and a weight vector alpha:
Figure FDA0003598859720000031
wherein, Ij(ω) represents the value of the newly derived j-th excitation;
(7) and applying the excitation signal I (omega) with the side lobe level suppressed to a feed port of the conformal antenna array, and calculating a directional pattern of the conformal antenna array under the excitation by utilizing electromagnetic commercial software.
2. The method of claim 1, wherein the time reversal method is used in (2) to obtain the far-field pattern of the conformal antenna array by:
(2a) calculating a receiving signal Y (t) of a conformal antenna array feeding port of the first transmitting antenna under the condition of transmitting an electromagnetic wave w (t) by using electromagnetic commercial software:
Y(t)＝[y1(t),y2(t),...,ym(t)...,yM(t)]T，
wherein, ym(t) receiving signals for a feed port of each array element, wherein M is the serial number of each array element, and M is more than or equal to 1 and less than or equal to M;
(2b) and (3) carrying out time reversal processing on the received signal Y (t) to obtain a time reversed received signal Y (-t):
Y(-t)＝[y1(-t),y2(-t),...,ym(-t)...,yM(-t)]T，
wherein y ism(-t) time domain receiving signals after time reversal are carried out on the feed port of each array element;
(2c) performing Fourier transform on the time domain received signal Y (-t) after time reversal to obtain a received signal Y (omega) on a frequency domain:
Figure FDA0003598859720000032
wherein e-jωtIs a complex exponential signal;
(2d) conjugate Y (omega) to obtain frequency domain receiving signal Y*(ω)：
Figure FDA0003598859720000033
Where superscript is the operator of the conjugate,
Figure FDA0003598859720000034
receiving signals for the frequency domain of each array element;
(2e) the conjugated frequency domain receiving signal Y*In (omega)
Figure FDA0003598859720000041
As the excitation signal of the m-th antenna unit, the conformal antenna array without the transmitting antenna is excited, and the beam pattern of the conformal antenna array under the excitation is calculated by utilizing electromagnetic commercial software.
3. The method of claim 1, wherein the time reversal method is used in (3) to obtain the electromagnetic wave w transmitted by the second transmitting antenna2And (t) exciting the conformal antenna array to realize the following steps:
(3a) calculating the electromagnetic wave w emitted by the second transmitting antenna by utilizing electromagnetic commercial software2(t) received signal x (t) of the conformal antenna array feed port in case of (t):
X(t)＝[x1(t),x2(t),...,xm(t),...,xM(t)]T，
wherein x ism(t) receiving signals for a feed port of each array element, wherein M is the serial number of each array element, and M is more than or equal to 1 and less than or equal to M;
(3b) carrying out time reversal processing on the received signal X (t) to obtain a received signal X (-t) after time reversal:
X(-t)＝[x1(-t),x2(-t),...,xm(-t),...,xM(-t)]T，
wherein xm(-t) is the time domain received signal after the feed port of each array element is time-reversed;
(3c) performing Fourier transform on the time domain received signal X (-t) after time reversal to obtain a received signal X (omega) on a frequency domain:
Figure FDA0003598859720000042
wherein e-jωtIs a complex exponential signal;
(3d) the angle of the side lobe beam is suppressed by conjugating X (omega) to obtain excitation information X*(ω)：
Figure FDA0003598859720000043
Where superscript is the operator of the conjugate,
Figure FDA0003598859720000044
the signals are received in the frequency domain for each array element, i.e. the desired excitation information.
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