CN113051745A - Single-point array response control directional diagram synthesis method with minimum error - Google Patents

Single-point array response control directional diagram synthesis method with minimum error Download PDF

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CN113051745A
CN113051745A CN202110293693.8A CN202110293693A CN113051745A CN 113051745 A CN113051745 A CN 113051745A CN 202110293693 A CN202110293693 A CN 202110293693A CN 113051745 A CN113051745 A CN 113051745A
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directional diagram
theta
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pattern
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兰岚
吕微慧
廖桂生
朱圣棋
许京伟
邓敬亚
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Xidian University
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Abstract

The invention discloses a single-point array response control directional diagram comprehensive method with minimum error, which mainly solves the technical problem that the existing single-point array directional diagram cannot be flexibly controlled. The scheme comprises the following steps: 1) initializing and starting an iterative process; 2) selecting an angle to be controlled; 2) obtaining a closed-form solution of the phase response by minimizing the array error; 3) obtaining an updated form of the weight vector; 4) obtaining a directional diagram of the array corresponding to the weight vector; 5) judging whether the obtained directional diagram meets the requirement of an expected directional diagram, and if so, outputting the directional diagram; otherwise, continuing iteration, and readjusting the weight vector to synthesize the directional diagram. According to the method, the array error is minimized, and the accurate calculation form of the virtual interference power is obtained, so that the flexible control of the directional diagram is realized, the distortion phenomenon of the directional diagram is effectively avoided, the flexibility of the directional diagram is obviously improved, and the accurate control of the level of the single-point directional diagram is realized.

Description

Single-point array response control directional diagram synthesis method with minimum error
Technical Field
The invention belongs to the technical field of radar antennas, and particularly relates to a Single-Point Array Response Control-Minimum development (SPARC-MD) directional diagram synthesis method with Minimum error. The method can be used for the directional diagram design of the antenna array which is flexible, stable and fast and meets the specific hardware requirement.
Background
With the increasing complexity of electromagnetic environment, in order to meet the requirement for the pattern shape in practical application, the pattern synthesis technology, i.e. beam forming, is widely used in array beam forming, such as in radar anti-interference, deep nulls need to be formed at specific positions to achieve effective interference suppression, and in remote sensing, the main lobe of a pattern needs to be widened to increase the target detection range. The directional pattern synthesis technique satisfies the requirement of the expected response of the directional pattern by weighting each antenna, including digital weighting and analog weighting.
By using optimization algorithms, such as particle swarm optimization, genetic algorithm, simulated annealing algorithm and other directional diagram comprehensive technologies, because global search is needed, the calculation amount is large, and particularly when the method is applied to a large-scale array, the global search method needs to consume a long time to obtain a satisfactory directional diagram result.
The directional diagram is optimized by using a convex optimization theory, and the comprehensive problem of the directional diagram can be converted into a convex optimization constraint problem through modeling to be solved. However, such an approach does not achieve accurate pattern response control. FUCHS B et al, in the document "Application of constellation relaxation to array synthesis schemes", use the idea of semi-positive relaxation SDR (Semidefinite relaxation) to synthesize patterns, and relax and model non-convex patterns. However, since the problem after relaxation is different from the original problem, only an approximate solution can be obtained by semi-positive relaxation.
The directional diagram is controlled by using the adaptive array theory, the difference value between the directional diagram and the expected directional diagram response is minimized by applying virtual interference in the directional diagram, although the method can realize the effects of widening a zero point, reducing a side lobe and the like, the main lobe area cannot be controlled, and the power of the virtual interference is selected in an empirical mode, so that the expected value of the directional diagram response cannot be accurately achieved.
Disclosure of Invention
The invention aims to provide a method for synthesizing an array response control directional diagram with minimum error aiming at the defects and the defects of the prior art, so as to solve the difficult problem of flexibly controlling the array directional diagram, realize the flexible control of the array directional diagram on a main lobe and a side lobe and effectively improve the performance of an array antenna system.
The idea for realizing the invention is as follows: in the synthesis process of the directional diagram of each step, the angle with the maximum deviation with the expected directional diagram is selected as the angle to be controlled, the array error is minimized under the condition that the angle to be controlled is controlled at an expected level value, and the phase response parameter factor is accurately selected, so that the updating form of the weight vector is obtained, and the directional diagram is obtained. If the obtained directional diagram meets the requirement of the expected directional diagram, stopping iteration and obtaining a satisfactory directional diagram; otherwise, continuing iteration and readjusting the weight vector.
The method comprises the following specific steps:
(1) initialization:
(1.1) presetting an angle as an azimuth angle theta of a desired signal0And sets an initial weight vector w0And the vector is relative to theta0Normalized directional pattern response L of direction0(θ)：
w0＝a(θ0)，
Figure BDA0002983483300000021
Wherein, a (theta)0) A steering vector representing a desired signal, H represents a conjugate transpose;
(1.2) recording the iteration times as k, and setting the iteration termination conditions as follows:
|20log10(Ld(θ))-20log10(Lk(θ))|≤0.5
wherein，Ld(θ) represents a desired pattern, Lk(θ) represents the pattern generated by the kth iteration, 20log10(. cndot.) represents converting.cndot.to a dB value;
(1.3) starting the kth iteration by setting k equal to 1;
(2) respectively selecting directions in a main lobe area and a side lobe area of a directional diagram to obtain an angle to be controlled;
(2a) a main lobe region: selecting the direction theta with the maximum deviation from the expected directional diagram in the main lobe regionk,m：
Figure BDA0002983483300000022
Wherein L isk-1(θ) represents the pattern generated by the (k-1) th iteration, ΩmA main lobe angular region representing a desired directional pattern;
side lobe region: selecting a direction theta in the sidelobe region that is the greatest above the desired levelk,s：
Figure BDA0002983483300000023
Wherein omegasA main lobe angular region representing a desired directional pattern;
(2b) determining an angle theta of the directional diagram to be controlledk：
Figure BDA0002983483300000031
(3) Minimizing the array error and then performing parameter factor selection, i.e. obtaining the phase response phik；
(3a) At the time of ensuring thetakThe level of the direction is accurately controlled to be rhokMeanwhile, the level values of other directions are kept unchanged; obtaining the following selection phikThe constraint formula of (1):
Figure BDA0002983483300000032
wherein L isk(θi,θ0) Denotes θ during the kth iterationiDirection relative to theta0Normalized array pattern response of direction, pkRepresenting an amplitude response;
(3b) defining the response error of the array of two adjacent times as Ji，JiThe set of real and imaginary parts of (1) is a circle
Figure BDA0002983483300000033
Namely:
Figure BDA0002983483300000034
(3c) finding the point on the circle closest to the origin, i.e. the phase response phikApproximate solution of
Figure BDA0002983483300000035
Figure BDA0002983483300000036
Wherein,
Figure BDA0002983483300000037
representing an approximate value of phase response, and representing a phase angle;
(3d) let JiIs zero to obtain a phase response phik：
Figure BDA0002983483300000038
Wherein, the first and second connecting parts are connected with each other; w is ak-1A weight vector, a (theta), representing the k-1 st stepk) Denotes thetakA steering vector of direction;
(4) derivation of the update form of the weight vector:
(4a) the complex factor in the kth iteration is:
Figure BDA0002983483300000039
wherein the amplitude response pk＝Pd(θk)，||·||2A two-norm representing a matrix;
(4b) weight vector w for a given k-1 th iterationk-1The weight vector w of the k-th timekThe following were used:
wk＝wk-1+μka(θk)；
(5) get the weight vector wkPattern P of the corresponding arrayk(θ)：
Figure BDA00029834833000000310
(6) Judging whether k meets the iteration termination condition, if so, judging the directional diagram P obtained in the step (5)k(theta) as a final directional diagram, entering the step (7); otherwise, after adding 1 to k, returning to the step (1.3);
(7) and outputting a final directional diagram.
Compared with the prior art, the invention has the following advantages:
the method and the device solve the problems of poor array response control and poor directional diagram flexibility, break through the thought of the traditional overall directional diagram design, realize directional diagram synthesis by utilizing a single-point accurate control concept, have an analytic expression form and can effectively avoid the distortion phenomenon of the directional diagram;
secondly, the invention defines and minimizes array errors, thereby obtaining a method for accurately selecting virtual interference power, overcoming the defect that the traditional method selects interference power by using an experience mode, and realizing the accurate control of single-point directional diagram level; by applying the method iteratively, the directional diagram is synthesized quickly.
Drawings
FIG. 1 is a flow chart of an implementation of the method of the present invention;
FIG. 2 shows an array error in the present inventionDifference JiA schematic diagram of the trajectory of (a);
FIG. 3 is a simulation comparison of the method of the present invention with a prior art method;
FIG. 4 is a diagram of simulation results of non-equal side lobe level patterns synthesis performed in the present invention;
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, the method for synthesizing a single-point array response control directional diagram with minimum error provided by the present invention specifically includes the following steps:
step 1, initialization:
(1.1) presetting an angle as an azimuth angle theta of a desired signal0And sets an initial weight vector w0And the vector is relative to theta0Normalized directional pattern response L of direction0(θ)：
w0＝a(θ0)，
Figure BDA0002983483300000041
Wherein, a (theta)0) A steering vector representing a desired signal, H represents a conjugate transpose;
(1.2) recording the iteration times as k, and setting the iteration termination conditions as follows:
|20log10(Ld(θ))-20log10(Lk(θ))|≤0.5
wherein L isd(θ) represents a desired pattern, Lk(θ) represents the pattern generated by the kth iteration, 20log10(. cndot.) represents converting.cndot.to a dB value;
(1.3) starting the kth iteration by setting k equal to 1;
step 2, respectively selecting directions in a main lobe area and a side lobe area of the directional diagram to obtain an angle to be controlled;
(2a) a main lobe region: selecting the direction theta with the maximum deviation from the expected directional diagram in the main lobe regionk,m：
Figure BDA0002983483300000051
Wherein L isk-1(θ) represents the pattern generated by the (k-1) th iteration, ΩmA main lobe angular region representing a desired directional pattern;
side lobe region: selecting a direction theta in the sidelobe region that is the greatest above the desired levelk,s：
Figure BDA0002983483300000052
Wherein omegasA main lobe angular region representing a desired directional pattern;
(2b) determining an angle theta of the directional diagram to be controlledk：
Figure BDA0002983483300000053
Step 3, minimizing array error, and then selecting parameter factors, namely obtaining phase response phik；
(3a) At the time of ensuring thetakThe level of the direction is accurately controlled to be rhokMeanwhile, the level values of other directions are kept unchanged; obtaining the following selection phikThe constraint formula of (1):
Figure BDA0002983483300000054
wherein L isk(θi,θ0) Denotes θ during the kth iterationiDirection relative to theta0Normalized array pattern response of direction, θiRepresents an arbitrary direction; rhokRepresenting an amplitude response;
angle theta to be controlledkIn a direction corresponding to a predetermined azimuth angle theta0Normalized array pattern response of Lk(θk,θ0)：
Figure BDA0002983483300000055
(3b) Defining the response error of the array of two adjacent times as JiSpecifically, the following are shown:
Ji＝Lk(θi,θ0)-Lk-1(θi,θ0),
wherein L isk-1(θk,θ0) Denotes θ in the k-1 th iterationkDirection relative to theta0A normalized array pattern response of direction;
Jithe set of real and imaginary parts of (1) is a circle
Figure BDA0002983483300000061
Namely:
Figure BDA0002983483300000062
round (T-shaped)
Figure BDA0002983483300000063
Is centered at
Figure BDA0002983483300000064
Radius of
Figure BDA0002983483300000065
Figure BDA0002983483300000066
Figure BDA0002983483300000067
Wherein the parameter xi0,ξi,ξk,ψ0,ψi,ψkAre respectively defined as follows:
ξ0＝a(θk)Ha(θ0)，
ξi＝a(θk)Ha(θi)，
ξk＝a(θk)Ha(θk)，
Figure BDA0002983483300000068
Figure BDA0002983483300000069
Figure BDA00029834833000000610
(3c) finding the point on the circle closest to the origin, i.e. the phase response phikApproximate solution of
Figure BDA00029834833000000611
Figure BDA00029834833000000612
Wherein,
Figure BDA00029834833000000613
representing an approximate value of phase response, and representing a phase angle;
(3d) let JiIs zero to obtain a phase response phik：
Figure BDA00029834833000000614
Wherein, the first and second connecting parts are connected with each other; w is ak-1A weight vector, a (theta), representing the k-1 st stepk) Denotes thetakA steering vector of direction;
and 4, deriving an updating form of the weight vector:
(4a) the complex factor in the kth iteration is:
Figure BDA00029834833000000615
wherein the amplitude response pk＝Pd(θk)，||·||2A two-norm representing a matrix;
(4b) weight vector w for a given k-1 th iterationk-1The weight vector w of the k-th timekThe following were used:
wk＝wk-1+μka(θk)；
step 5, obtaining a weight vector wkPattern P of the corresponding arrayk(θ)：
Figure BDA0002983483300000071
Step 6, judging whether k meets the iteration termination condition, and if so, judging the directional diagram P obtained in the step 5k(theta) as a final directional diagram, entering the step (7); otherwise, after adding 1 to k, returning to the step (1.3);
and 7, outputting the final directional diagram.
The effect of the present invention will be further described with reference to simulation experiments.
1. Simulation parameters:
the simulation experiment of the invention selects 11 array element non-equidistant linear arrays, and each array element is anisotropic. Taking the center theta of a signal beam 020 °, initial weight vector w0＝a(θ0). Position x of each array elementnAnd array element directional diagram gn(θ) is shown in Table 1.
TABLE 1 non-equidistant linear array element position and array element directional diagram
n xn gn(θ) n xn gn(θ)
1 0.00 1.00cos(1.00θ) 7 3.05 1.02cos(1.00θ)
2 0.45 0.98cos(0.85θ) 8 3.65 1.08cos(0.90θ)
3 1.00 1.05cos(0.98θ) 9 4.03 0.96cos(0.75θ)
4 1.55 1.10cos(0.70θ) 10 4.6 1.09cos(0.92θ)
5 2.10 0.90cos(0.85θ) 11 5.00 1.02cos(0.80θ)
6 2.60 0.93cos(0.69θ)
2. Simulation content and result analysis:
for experimental comparison, precise array response control was simulated simultaneously (A)2RC), an optimal array response control (OPARC), a maximum gain single point array response control (SPARC-MG) algorithm, and a minimum error single point array response control (SPARC-MD) algorithm of the present invention.
Simulation 1, considering two angles to be controlled as theta1，θ2. Take theta1＝-22°,θ2＝23°，θ1Desired level value of direction is p1＝-20dB，θ2Desired level value of direction is p 20 dB. The response control of the array pattern is carried out in two steps by adopting the technology of the invention, and the result is shown in figure 2.
Referring to FIG. 3, a different approach to θ completion is shown2Angular (main lobe region) directional diagramAnd (5) comparing the results after control. As can be seen from the figure, the four methods can all realize the theta pair2And (4) precise control of the direction. However, A2The pattern of the RC algorithm is distorted and is aligned with theta1The level value of the direction produces an effect of 16.15 dB; OPARC algorithm after second step control on θ1The level impact of (3) is 14.65 dB; SPARC-MG Algorithm controls Direction θ for the first step after the second step1An effect of 3.81dB is generated; SPARC-MD Algorithm controls the direction θ for the first step after the second step of control1The level effect of (2.81 dB). From the figure, it is found that the SPARC-MD algorithm is on theta1The level values of the directions have the smallest influence and are superior to the other three algorithms.
Simulation 3, the directional diagrams of unequal sidelobe levels are synthesized by adopting the technology of the invention, and the result is shown in fig. 4.
In conclusion, the method can obtain a satisfactory expected direction diagram, and can flexibly control the direction diagram, thereby proving the effectiveness of the method provided by the invention.
The simulation analysis proves the correctness and the effectiveness of the method provided by the invention.
The invention has not been described in detail in part of the common general knowledge of those skilled in the art.
While the invention has been particularly shown and described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (4)

1. A method for synthesizing a single-point array response control directional diagram with minimum error is characterized by comprising the following steps:
(1) initialization:
(1.1) presetting an angle as an azimuth angle theta of a desired signal0And sets an initial weight vector w0And the vector is relative to theta0Normalized directional pattern response L of direction0(θ)：
w0＝a(θ0)，
Figure FDA0002983483290000011
Wherein, a (theta)0) A steering vector representing a desired signal, H represents a conjugate transpose;
(1.2) recording the iteration times as k, and setting the iteration termination conditions as follows:
|20log10(Ld(θ))-20log10(Lk(θ))|≤0.5
wherein L isd(θ) represents a desired pattern, Lk(θ) represents the pattern generated by the kth iteration, 20log10(. cndot.) represents converting.cndot.to a dB value;
(1.3) starting the kth iteration by setting k equal to 1;
(2) respectively selecting directions in a main lobe area and a side lobe area of a directional diagram to obtain an angle to be controlled;
(2a) a main lobe region: selecting the direction theta with the maximum deviation from the expected directional diagram in the main lobe regionk,m：
Figure FDA0002983483290000012
Wherein L isk-1(θ) represents the pattern generated by the (k-1) th iteration, ΩmA main lobe angular region representing a desired directional pattern;
side lobe region: selecting a direction theta in the sidelobe region that is the greatest above the desired levelk,s：
Figure FDA0002983483290000013
Wherein omegasA main lobe angular region representing a desired directional pattern;
(2b) determining the directional diagram to be controlledAngle of system thetak：
Figure FDA0002983483290000021
(3) Minimizing the array error and then performing parameter factor selection, i.e. obtaining the phase response phik；
(3a) At the time of ensuring thetakThe level of the direction is accurately controlled to be rhokMeanwhile, the level values of other directions are kept unchanged; obtaining the following selection phikThe constraint formula of (1):
Figure FDA0002983483290000022
wherein L isk(θi,θ0) Denotes θ during the kth iterationiDirection relative to theta0Normalized array pattern response of direction, pkRepresenting an amplitude response;
(3b) defining the response error of the array of two adjacent times as Ji，JiThe set of real and imaginary parts of (1) is a circle
Figure FDA0002983483290000023
Namely:
Figure FDA0002983483290000024
(3c) finding the point on the circle closest to the origin, i.e. the phase response phikApproximate solution of
Figure FDA0002983483290000025
Figure FDA0002983483290000026
Wherein,
Figure FDA0002983483290000027
representing an approximate value of phase response, and representing a phase angle;
(3d) let JiIs zero to obtain a phase response phik：
Figure FDA0002983483290000028
Wherein, the first and second connecting parts are connected with each other; w is ak-1A weight vector, a (theta), representing the k-1 st stepk) Denotes thetakA steering vector of direction;
(4) derivation of the update form of the weight vector:
(4a) the complex factor in the kth iteration is:
Figure FDA0002983483290000029
wherein the amplitude response pk＝Pd(θk)，||·||2A two-norm representing a matrix;
(4b) weight vector w for a given k-1 th iterationk-1The weight vector w of the k-th timekThe following were used:
wk＝wk-1+μka(θk)；
(5) get the weight vector wkPattern P of the corresponding arrayk(θ)：
Figure FDA0002983483290000031
(6) Judging whether k meets the iteration termination condition, if so, judging the directional diagram P obtained in the step (5)k(theta) as a final directional diagram, entering the step (7); otherwise, after adding 1 to k, returning to the step (1.3);
(7) and outputting a final directional diagram.
2. The method of claim 1, wherein: the angle theta to be controlled in step (3a)kIn a direction corresponding to a predetermined azimuth angle theta0Normalized array pattern response of Lk(θk,θ0)：
Figure FDA0002983483290000032
3. The method of claim 1, wherein: the array response error of two adjacent times in the step (3b) is JiSpecifically, the following are shown:
Ji＝Lk(θi,θ0)-Lk-1(θi,θ0),
wherein L isk-1(θk,θ0) Denotes θ in the k-1 th iterationkDirection relative to theta0Normalized array pattern response of direction.
4. The method of claim 1, wherein: circle in step (3b)
Figure FDA0002983483290000033
Is centered at
Figure FDA0002983483290000034
Radius of
Figure FDA0002983483290000035
Figure FDA0002983483290000036
Figure FDA0002983483290000037
Wherein the parameter xi0,ξi,ξk,ψ0,ψi,ψkAre respectively defined as follows:
ξ0＝a(θk)Ha(θ0)，
ξi＝a(θk)Ha(θi)，
ξk＝a(θk)Ha(θk)，
Figure FDA0002983483290000041
Figure FDA0002983483290000042
Figure FDA0002983483290000043
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