CN114722868B - Array excitation dynamic range controllable wide beam gain enhancement method - Google Patents

Array excitation dynamic range controllable wide beam gain enhancement method Download PDF

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CN114722868B
CN114722868B CN202210320116.8A CN202210320116A CN114722868B CN 114722868 B CN114722868 B CN 114722868B CN 202210320116 A CN202210320116 A CN 202210320116A CN 114722868 B CN114722868 B CN 114722868B
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雷世文
杨伟
章奥
胡皓全
赵志钦
包永芳
陈波
田径
唐璞
何子远
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a wide beam gain enhancement method with controllable array excitation dynamic range, and belongs to the technical field of antennas. The invention directly optimizes the wide beam gain of the array, and realizes the wide beam gain enhancement under the condition of given expected low side lobe by effectively controlling the excitation of the array. Compared with the traditional beam forming method based on pattern optimization, the method can obtain higher wide beam gain under the same condition.

Description

Array excitation dynamic range controllable wide beam gain enhancement method
Technical Field
The invention belongs to the technical field of antennas, and particularly relates to a wide beam gain enhancement method with controllable array excitation dynamic range.
Background
In the terrestrial mobile reception of satellite multimedia signals, it is often required that the array antenna have a wide beam to ensure that the array receiving antenna carrier (e.g., car, ship, aircraft, etc.) receives the beam in real time at the satellite during rapid position changes. Because of the long-distance fading of satellite multimedia signals, the signals at the receiving end are weak, so that the array receiving antenna is required to have higher gain and lower side lobe so as to resist background noise and machine noise and realize good receiving of the satellite multimedia signals. Meanwhile, since the operating range of the array excitation control element (such as an amplifier) is limited in practical application, the dynamic range of the practical array excitation is required to be controllable.
In order to realize the wide beam forming with controllable array excitation dynamic range, the existing method mainly optimizes an array directional diagram to obtain array excitation distribution meeting the specific array excitation dynamic range, and because the method is mainly designed for waveforms of an array, the optimal array wide beam gain is difficult to ensure.
Disclosure of Invention
The present invention provides a wide beam gain enhancement method with controllable array excitation dynamic range for maximizing the gain of an array given the beam width, desired side lobe level and desired array excitation dynamic range.
The technical scheme adopted by the invention is as follows:
a method of array excitation dynamic range controllable wide beam gain enhancement, comprising:
step S1, pretreatment:
discretizing the value range of the beam direction of the array antenna to obtain a plurality of discrete points, wherein the discrete points are represented as (theta, phi), wherein theta represents a pitch angle of the beam direction, and phi represents an azimuth angle of the beam direction;
according to the formula
Figure BDA0003570171060000011
Calculating a positive definite matrix A, and performing matrix decomposition A=C on the positive definite matrix A H C, obtaining a matrix C, wherein a (theta, phi) represents an array factor of the beam direction (theta, phi);
uniformly discretizing a main lobe area and a side lobe area of the array antenna into L respectively ML And L SL A plurality of discrete angles;
traversing each discrete angle of the main lobe region based on an array factor a of each discrete angle k Calculate matrix B 1 Element b of (2) 1,k ＝C -H a k Obtaining a matrix
Figure BDA0003570171060000012
Wherein the discrete angle number of the main lobe region k=1 ML ；
Traversing each discrete angle of the flap region based on an array factor a of each discrete angle s Calculate matrix B 2 Element b of (2) 2,s ＝C -H a s Obtaining a matrix
Figure BDA0003570171060000021
Wherein the discrete angle number s=1 of the flap region SL ；
Step S2: setting iteration related parameters, including:
setting three thresholds c 0 、c 1 And c 2 Maximum inner circulation times Imax and maximum outer circulation times Omax;
initializing two penalty factors ρ 1 And ρ 2 Initializing the inner circulation times zeta=0 and the outer circulation times r=0;
initializing two pairs of even variables u 1 And u 2 Wherein u is 1 Is L ML Dimension line vector u 2 Is L SL A row vector is maintained;
initializing array excitation w, and obtaining an initial value of a quantity x to be solved according to a formula x=cw; the initialization mode of w can be random initialization or other conventional modes.
Step S3, inner loop update processing:
step S3-1, calculating a first intermediate quantity J and a second intermediate quantity
Figure BDA0003570171060000022
J＝∠(v 1 )
Figure BDA0003570171060000023
Wherein J is L ML The vector of the dimension column is set,
Figure BDA0003570171060000024
is L SL Valien vector, parameter->
Figure BDA0003570171060000025
Parameter->
Figure BDA0003570171060000026
The angle (·) represents the phase of the complex-valued vector element;
step S3-2, calculating a third intermediate quantity t and a fourth intermediate quantity h:
solving so that the cost function
Figure BDA0003570171060000027
The smallest values of t and h are used as the initial solution +.>
Figure BDA0003570171060000028
The initial solving result +.>
Figure BDA0003570171060000029
The third intermediate quantity t and the fourth intermediate quantity h after updating are obtained through reverse arrangement;
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA00035701710600000213
an element representing the kth discrete angle estimate of the main lobe region, i.e. the first intermediate quantity J, +.>
Figure BDA00035701710600000211
An estimate of the s-th discrete angle representing the flap region, i.e. the second intermediate quantity +.>
Figure BDA00035701710600000212
K=1,.. ML ，s＝1,...,L SL ；v 3 ＝v 2 γ, γ represents the arithmetic square root of the desired side lobe level;
step S3-3, updating x:
definition:
Figure BDA0003570171060000031
definition of the definition
Figure BDA0003570171060000032
The updated x is: />
Figure BDA0003570171060000033
Where β represents the desired array excitation dynamic range;
step S3-4, the internal circulation times zeta is increased by 1, whether the internal circulation times zeta reaches the maximum internal circulation times Imax is judged, if yes, step S4 is executed, the internal circulation times zeta=0 are repeated, and otherwise, step S3 is executed;
step S4, outer loop updating processing:
according to the formula
Figure BDA0003570171060000034
Calculating to obtain the measurement value of the external circulation of the wheel; the metric value obtained by the previous round of outer loop calculation and the threshold c 0 Taking the product of (2) as the current outer loop reference value;
if the current metric value is less than or equal to the current outer loop reference value, then only for u 1 And u 2 Update ρ 1 And ρ 2 Respectively the same value as the previous round of external circulation, wherein, after updating
Figure BDA0003570171060000035
Updated +.>
Figure BDA0003570171060000036
If the current metric value is greater than the current outer loop reference value, then p is only 1 And ρ 2 Update u 1 And u 2 Respectively the same value as the previous round of outer circulation, wherein, the updated rho 1 ＝c 1 ρ 1 Updated ρ 2 ＝c 2 ρ 2 ；
After the updating is finished, the outer circulation times r are increased by 1, whether the outer circulation times r reach the maximum outer circulation times Omax is judged, if yes, the step S5 is executed, and if not, the step S3 is executed;
step S5, based on the currently obtained x, according to the formula w=c -1 x is obtained in the expected arrayThe array of optimally wide beam gains under column excitation dynamic range β conditions excites w.
Further, in step S3-2, the result of the initial solution
Figure BDA0003570171060000037
The specific solution of (2) is as follows:
will |v 1 I and V 3 I arrange construction vector according to ascending order of amplitude
Figure BDA0003570171060000038
At the same time according to |v 1 I and V 3 The order of the amplitude of the vector p, the vector +.>
Figure BDA0003570171060000039
And->
Figure BDA00035701710600000310
I.e. vector->
Figure BDA00035701710600000311
The element in (a) is |v 1 The magnitude of the I, and the position index is determined based on the magnitude corresponding to the vector p;
definition g represents a temporary variable, and g is greater than or equal to 0, t k ≥g，h s Not more than g, wherein t k A kth element, h, representing a third intermediate quantity t s The s-th element representing the fourth intermediate amount h, k=1,.. ML ，s＝1,...,L SL ；
If g is E (0, p) 1 ]Then:
Figure BDA0003570171060000041
if g is E [ p ] m ,p m+1 ],m＝1,...,L ML +L SL -1, then
Figure BDA0003570171060000042
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003570171060000043
and k and s satisfy +.>
Figure BDA0003570171060000044
And->
Figure BDA0003570171060000045
If it is
Figure BDA0003570171060000046
The technical scheme provided by the invention has at least the following beneficial effects:
the invention directly optimizes the wide beam gain of the array, and realizes the wide beam gain enhancement under the condition of given expected low side lobe by effectively controlling the excitation of the array. Compared with the traditional beam forming method based on pattern optimization, the method can obtain higher wide beam gain under the same condition.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a diagram showing a comparison between a wide beam gain enhancement method with controllable array excitation dynamic range and two existing gain enhancement modes, wherein the main lobe width is 20 degrees.
Fig. 2 is a diagram showing a comparison between a wide beam gain enhancement method with controllable array excitation dynamic range and two existing gain enhancement modes, wherein the main lobe width is 30 degrees.
Fig. 3 is a diagram showing a comparison between a wide beam gain enhancement method with controllable array excitation dynamic range and two existing gain enhancement modes, wherein the main lobe width is 40 degrees.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in further detail with reference to the accompanying drawings.
In order to realize wide beam forming with controllable array excitation dynamic range, the existing method mainly optimizes an array pattern to obtain array excitation distribution meeting the specific array excitation dynamic range. For an array antenna with arbitrary distribution and containing N array elements, the position of the array element of the arbitrary nth array element is assumed to be
Figure BDA0003570171060000051
The far field pattern of the array can be described as:
Figure BDA0003570171060000052
wherein E (θ, φ) represents the far field pattern, θ represents the angle (pitch angle) of the beam direction in the pitch direction, φ represents the angle (azimuth angle) of the beam direction in the horizontal direction, ω n The complex weighted excitation of the nth element is represented, j represents an imaginary unit, k represents a spatial wave number, w represents the complex weighted excitation of the array, and a represents an array factor.
Wherein, the liquid crystal display device comprises a liquid crystal display device,
w＝[ω 1 ,...,ω N ] T ；
Figure BDA0003570171060000053
ω n 、a n representing the complex weighted excitation and the matrix factor of the nth element, respectively, n=1, …, N, exp () represents an exponential function based on a natural constant e.
Thus, the array gain can be expressed as:
Figure BDA0003570171060000054
wherein the method comprises the steps of
Figure BDA0003570171060000055
a (θ, Φ) represents an array factor in a beam direction (θ, Φ), a superscript "T" represents a transpose of a vector, and a superscript "H" represents an hermitian transpose of a vector.
Given the array elements and form of the array antenna, matrix a θ,φ And A is a known quantity.
The current way to obtain an array excitation profile that meets the dynamic range of a particular array excitation by optimizing the array pattern mainly includes the following two ways:
in the first existing mode, the gain enhancement method under the constraint condition of the array excitation dynamic range based on pattern optimization comprises the following steps:
Figure BDA0003570171060000061
wherein Θ is ML And theta (theta) SL Respectively representing a main lobe region and a side lobe region, f d (θ, φ) is the desired array pattern.
Existing approach-approach to gain enhancement given in array wide beam applications, an array pattern f is desired d (θ, φ) has the form:
Figure BDA0003570171060000062
wherein epsilon and gamma 2 And β represents the main lobe ripple, side lobe level, and excitation dynamic range, respectively. max { |w| } and min { |w| } represent the maximum and minimum values of array excitation, respectively. Such an approach minimizes the main lobe ripple, i.e., achieves as flat a wide beam as possible, given the side lobe level and array excitation dynamic range. The optimization problem indicates that the power difference between the sought array pattern and the desired pattern is required to be as small as possible.
In the second existing mode, a gain enhancement method for minimizing array excitation for a given desired side lobe is satisfied:
Figure BDA0003570171060000063
where X is the N-dimensional matrix to be solved, diag () represents the diagonal matrix, trace (A θ,φ X) represents matrix A θ,φ Trace of X. Finding the optimal solution X of the problem opt After that, the array excitation w is matrix X opt And the corresponding maximum eigenvalue corresponds to the eigenvector.
The existing mode of optimizing an array pattern to obtain an array excitation distribution meeting the dynamic range of specific array excitation is difficult to ensure to obtain optimal array wide beam gain because the mode is designed mainly aiming at the waveform of the array.
Aiming at the defects of the prior art, the embodiment of the invention provides a gain enhancement method which directly takes wide beam gain as an optimization object, and the wide beam gain enhancement of the array is realized under the condition of given expected low side lobe by effectively controlling the excitation of the array, so that the high-precision signal reception is satisfied.
In order to obtain the optimal wide beam gain under the condition of the excitation dynamic range of a specific array, the embodiment of the invention aims to solve the following optimization problem:
Figure BDA0003570171060000071
/>
wherein G is 0 Represents the minimum gain within the broad main lobe, Θ ML And theta (theta) SL Representing the main lobe region and the side lobe region of the array antenna, respectively. Gamma ray 2 And β represents the desired side lobe level and the desired array excitation dynamic range, respectively. max { |w| } and min { |w| } represent the maximum and minimum values of array excitation, respectively. Due to w H Aw describes the radiation power of the array antenna, and therefore, for any non-zero w, there is w H Aw > 0, A is a positive definite matrix, and is known to be a Hermitian matrix by definition of A, so matrix A is a decomposable A=C H C. For the convenience of calculation, the main lobe area and the side lobe area are uniformly discretized into L respectively ML And L SL And a plurality of discrete angles. Let b k ＝C -H a k X=cw, then problem (7) can be converted into:
Figure BDA0003570171060000072
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003570171060000073
t k ∈R + ，h s ∈R + ，/>
Figure BDA0003570171060000079
and->
Figure BDA00035701710600000710
Kth discrete angle estimate representing main lobe region,/->
Figure BDA0003570171060000075
An estimate of the s-th discrete angle representing the flap region,>
Figure BDA0003570171060000076
represents an N-dimensional column vector, R + Representing a positive real number. Intermediate quantity b i ＝C -H a i (i＝1,2,...,L SL +L ML )，a i An array factor representing the i-th discrete angle, i.e. the discrete angle as the beam direction, by +.>
Figure BDA0003570171060000077
Each array element factor is calculated, and a corresponding array factor a is obtained based on N array element factors i θ and φ at this time correspond to the pitch and azimuth angles of the dispersion angle.
Variable is changed
Figure BDA0003570171060000078
Vectorization is as follows:
Figure BDA0003570171060000081
two pairs of even variables are defined:
Figure BDA0003570171060000082
the first two equality constraints in problem (8) are written into the cost function, and the augmented Lagrangian function is constructed as follows:
Figure BDA0003570171060000083
wherein ρ is 1 And ρ 2 For the preset penalty factor to be present,
Figure BDA0003570171060000084
is the two norms of the vector, +.. />
In order to solve the optimization problem given by the formula (11), the embodiment of the invention provides a gain enhancement double-layer iteration method based on a punishment dual decomposition framework:
1) Internal circulation:
1-1) solving for
Figure BDA0003570171060000085
Figure BDA0003570171060000086
Order the
Figure BDA0003570171060000087
Then:
Figure BDA0003570171060000088
wherein, the angle (·) describes the phase of the complex valued vector element.
1-2) solving { t, h }:
introducing a temporary variable g and defining v 3 ＝v 2 The following problem is solved by the demand:
Figure BDA0003570171060000091
will |v 1 I and V 3 I arranges and constructs new vector according to ascending amplitude
Figure BDA0003570171060000092
At the same time according to |v 1 I and V 3 The order of the I in vector p, a new vector is constructed +.>
Figure BDA0003570171060000093
And->
Figure BDA0003570171060000094
Then:
case 1: when g is E (0, p 1 ]In the time-course of which the first and second contact surfaces,
Figure BDA0003570171060000095
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003570171060000096
representation vector->
Figure BDA0003570171060000097
Is the m < th > of 3 The elements.
Case 2: when g is E [ p ] m ,p m+1 ],m＝1,...,L ML +L SL In the case of the time of-1,
Figure BDA0003570171060000098
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003570171060000099
and k and s satisfy +.>
Figure BDA00035701710600000910
And->
Figure BDA00035701710600000911
Figure BDA00035701710600000912
Respectively represent vector +.>
Figure BDA00035701710600000913
Is the m < th > of 1 K elements>
Figure BDA00035701710600000914
Representation vector->
Figure BDA00035701710600000915
P is the s element of (2) m Represents the mth element of vector p.
Case 3: when (when)
Figure BDA00035701710600000916
In the time-course of which the first and second contact surfaces,
Figure BDA00035701710600000917
obtaining the optimal value
Figure BDA00035701710600000918
After that, the value of { t, h } is defined by }>
Figure BDA00035701710600000919
And (5) arranging in reverse order.
1-2) solving for x:
definition of the definition
Figure BDA0003570171060000101
Order the
Figure BDA0003570171060000102
Then
Figure BDA0003570171060000103
2) External circulation: update { u } 1 ,u 2 ,ρ 1 ,ρ 2 }
Definition of the definition
Figure BDA0003570171060000104
The number of iterations of the outer loop is denoted by the superscript "(r)", then:
case 1: when (when)
Figure BDA0003570171060000105
In the time-course of which the first and second contact surfaces,
Figure BDA0003570171060000106
case 2: when (when)
Figure BDA0003570171060000107
When (I)>
Figure BDA0003570171060000108
Wherein c 0 ，c 1 And c 2 Is three preset thresholds.
In a possible implementation manner, the specific flow of the wide beam gain enhancement method with controllable array excitation dynamic range provided by the embodiment of the invention is as follows:
step 1: initializing ρ 1 ∈(0.1,100)，ρ 2 ∈(0.1,100)，c 0 ∈(0.5,0.99)，c 1 ∈(0.5,0.99)，c 2 ∈(0.5,0.99)，
Figure BDA0003570171060000111
The inner circulation times k=0, the outer circulation times r=0, and the maximum inner circulation times Imax e [1000,2000 ]]And the maximum number of outer cycles Omax e [1000,2000 ]]；
Step 2: update using equation (14)
Figure BDA0003570171060000112
Step 3: updating { t, h } using equations (16), (17) and (18): so that the cost function in equation (15)
Figure BDA0003570171060000113
Minimum->
Figure BDA0003570171060000114
After the reverse arrangement, the sequence is { t, h };
step 4: updating x using equation (20);
step 5: k=k+1;
step 6: if k is less than Imax, entering step 2, otherwise entering step 7, and letting k=0;
step 7: updating { u } using equation (21) and equation (22) 1 ,u 2 ,ρ 1 ,ρ 2 }；
Step 8: r=r+1;
step 9: if r is less than Omax, entering step 2, otherwise entering step 10;
step 10: w=c -1 And x, ending.
In order to further verify the technical effect of the wide beam gain enhancement method with controllable array excitation dynamic range provided by the embodiment of the present invention, the embodiment uses a 20 array element linear array with half wavelength uniformly distributed to verify the wide beam gain enhancement method (denoted as M3) provided by the embodiment of the present invention, and compares the wide beam gain enhancement method with the existing mode one (the gain enhancement method under the array excitation dynamic range constraint condition based on pattern optimization, denoted as M1) and the existing mode two (the gain enhancement method satisfying the minimum array excitation of a given desired side lobe, denoted as M2), and the comparison results are shown in fig. 1, fig. 2 and fig. 3.
Table 1 specific parameters of the respective methods corresponding to fig. 1 to 3
Figure BDA0003570171060000115
In this embodiment, the desired side lobe level is-25 dB and the dynamic range of the array excitation is desired to be within 4. From the results of fig. 1 to 3 and table 1, the gain enhancement method M3 provided by the embodiment of the present invention can achieve the maximum main lobe gain under the condition of meeting the-25 dB side lobe level and the array excitation dynamic range within 4. In comparison, the existing method M1 can better control the dynamic range of array excitation, but has lower gain and the side lobe level is far greater than the expected-25 dB; the existing method M2 can well inhibit the side lobe level, obtain the expected side lobe level and obtain the good main lobe gain, but the dynamic range of the array excitation is far greater than the expected value 4, which is unfavorable for engineering realization.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
What has been described above is merely some embodiments of the present invention. It will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the spirit of the invention.

Claims (5)

1. A method for wide beam gain enhancement with controllable array excitation dynamic range, comprising:
step S1, pretreatment:
discretizing the value range of the beam direction of the array antenna to obtain a plurality of discrete points, wherein the discrete points are represented as (theta, phi), wherein theta represents a pitch angle of the beam direction, and phi represents an azimuth angle of the beam direction;
according to the formula
Figure FDA0004180123100000011
Calculating a positive definite matrix A, and performing matrix decomposition A=C on the positive definite matrix A H C, obtaining a matrix C, wherein a (theta, phi) represents an array factor of the beam direction (theta, phi);
uniformly discretizing a main lobe area and a side lobe area of the array antenna into L respectively ML And L SL A plurality of discrete angles;
traversing each discrete angle of the main lobe region based on an array factor a of each discrete angle k Calculate matrix B 1 Element b of (2) 1,k ＝C -H a k Obtaining a matrix
Figure FDA0004180123100000012
Wherein the discrete angle number of the main lobe region k=1 ML ；
Traversing each discrete angle of the flap region based on an array factor a of each discrete angle s Calculate matrix B 2 Element b of (2) 2,s ＝C -H a s Obtaining a matrix
Figure FDA0004180123100000013
Wherein the discrete angle number s=1 of the flap region SL ；
Step S2: setting iteration related parameters, including:
setting three thresholds c 0 、c 1 And c 2 Maximum inner circulation times Imax and maximum outer circulation times Omax;
initializing two penalty factors ρ 1 And ρ 2 Initializing the inner circulation times zeta=0 and the outer circulation times r=0;
initializing two pairs of even variables u 1 And u 2 Wherein u is 1 Is L ML Dimension line vector u 2 Is L SL A row vector is maintained;
initializing array excitation w, and obtaining an initial value of a quantity x to be solved according to a formula x=cw;
step S3, inner loop update processing:
step S3-1, calculating a first intermediate quantity J and a second intermediate quantity
Figure FDA0004180123100000014
J＝∠(v 1 )
Figure FDA0004180123100000015
Wherein J is L ML The vector of the dimension column is set,
Figure FDA0004180123100000016
is L SL Valien vector, parameter->
Figure FDA0004180123100000017
Parameter->
Figure FDA0004180123100000018
The angle (·) represents the phase of the complex-valued vector element;
step S3-2, calculating a third intermediate quantity t and a fourth intermediate quantity h:
solving so that the cost function
Figure FDA0004180123100000019
The smallest values of t and h as the initial solution result
Figure FDA0004180123100000021
The initial solving result +.>
Figure FDA0004180123100000022
The third intermediate quantity t and the fourth intermediate quantity h after updating are obtained through reverse arrangement;
wherein g represents a temporary variable, and g is not less than 0,
Figure FDA0004180123100000023
θ k kth discrete angle estimate representing main lobe region,/->
Figure FDA00041801231000000210
The s-th discrete angle estimate representing the flap region, k=1,.. ML ，s＝1,...,L SL ；v 3 ＝v 2 γ, γ represents the arithmetic square root of the desired side lobe level;
step S3-3, updating x:
definition:
Figure FDA0004180123100000024
definition of the definition
Figure FDA0004180123100000025
The updated x is: />
Figure FDA0004180123100000026
Where β represents the desired array excitation dynamic range;
step S3-4, the number ζ of internal cycles is increased by 1, and then it is determined whether the number ζ of internal cycles reaches the maximum number Imax of internal cycles, if yes, step S4 is executed, and the number ζ=0 of internal cycles is reset, otherwise, step S3 is executed;
step S4, outer loop updating processing:
according to the formula
Figure FDA0004180123100000027
Calculating to obtain the measurement value of the external circulation of the wheel; the metric value obtained by the previous round of outer loop calculation and the threshold c 0 Taking the product of (2) as the current outer loop reference value;
if the current metric value is less than or equal to the current outer loop reference value, then only for u 1 And u 2 Update ρ 1 And ρ 2 Respectively the same value as the previous round of outer loop, wherein u is as follows 1 The updating is as follows:
Figure FDA0004180123100000028
will u 2 Updated to->
Figure FDA0004180123100000029
If the current metric value is greater than the current outer loop reference value, then p is only 1 And ρ 2 Update u 1 And u 2 Respectively the same value as the previous round of outer circulation, wherein, the updated rho 1 ＝c 1 ρ 1 Updated ρ 2 ＝c 2 ρ 2 ；
After the updating is finished, the outer circulation times r are increased by 1, whether the outer circulation times r reach the maximum outer circulation times Omax is judged, if yes, the step S5 is executed, and if not, the step S3 is executed;
step S5, based on the currently obtained x, according to the formula w=c -1 x results in an array stimulus w of optimally wide beam gain at the desired array stimulus dynamic range β.
2. The method of claim 1, wherein in step S3-2, the result of the initial solution is
Figure FDA0004180123100000031
The specific solution of (2) is as follows:
will |v 1 I and V 3 I arrange construction vector according to ascending order of amplitude
Figure FDA0004180123100000032
At the same time according to |v 1 I and V 3 The order of the amplitude of the vector p, the vector +.>
Figure FDA0004180123100000033
And->
Figure FDA0004180123100000034
Definition t k A kth element, h, representing a third intermediate quantity t s The s-th element representing a fourth intermediate quantity h, and t k ≥g，h s ≤g，k＝1,...,L ML ，s＝1,...,L SL ；
If g is E (0, p) 1 ]Then:
Figure FDA0004180123100000035
/>
if g is E [ p ] m ,p m+1 ],m＝1,...,L ML +L SL -1, then
Figure FDA0004180123100000036
Wherein the method comprises the steps of
Figure FDA0004180123100000037
And k and s satisfy +.>
Figure FDA0004180123100000038
And->
Figure FDA0004180123100000039
If it is
Figure FDA00041801231000000311
Then->
Figure FDA00041801231000000310
3. The method according to claim 1 or 2, wherein in step S2, the penalty factorρ 1 And ρ 2 The value ranges of (a) are respectively as follows: ρ 1 ∈(0.1,100)，ρ 2 E (0.1,100), threshold c 0 、c 1 And c 2 The value ranges of (a) are respectively as follows: c 0 ∈(0.5,0.99)，c 1 ∈(0.5,0.99)，c 2 E (0.5,0.99), the maximum number of internal cycles Imax is Imax E [1000,2000 ]]The maximum number of outer cycles Omax is within the range Omax epsilon [1000,2000 ]]。
4. The method according to claim 1 or 2, wherein in step S2, the dual variable u 1 And u 2 All initialized to the zero vector.
5. The method of claim 1, wherein the initial manner of energizing w by the array is: and (5) randomly initializing.
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