CN112162266B - Conformal array two-dimensional beam optimization method based on convex optimization theory - Google Patents
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Abstract
The invention discloses a conformal array two-dimensional wave beam optimization method based on a convex optimization theory, and belongs to the technical field of underwater acoustic array signal processing. The method comprises the following steps: dividing a main lobe area and a side lobe area of the conformal array scanning space; initializing half main lobe width, and setting the narrowest main lobe width under an expected side lobe level through iterative solution; and expressing the beam forming optimization problem into a convex optimization second-order cone constraint form, and solving the optimal solution of the weighting vector by using an inner point method so as to obtain a uniform low-sidelobe two-dimensional beam response diagram. The two-dimensional beam pattern obtained by the invention has lower side lobe level, and the side lobes are uniform side lobes, so that the two-dimensional beam pattern has more excellent beam directivity. The constraint equation designed on the basis of the MVDR method enables the two-dimensional beam forming to obtain higher array gain compared with the traditional method. In addition, the constraint on the norm of the weighting vector in the invention ensures that the two-dimensional beam forming has higher robustness compared with the traditional method.
Description
Technical Field
The invention belongs to the technical field of underwater acoustic array signal processing, and particularly relates to a conformal array two-dimensional beam optimization method based on a convex optimization theory.
Background
When the active sonar is used for detecting water surface targets such as ships, the water surface targets are not at the same height as the sonar platform, and the sonar needs to search in the horizontal direction and in the pitching direction. The conformal array sonar can realize space all-round scanning, and the purpose of reducing algorithm operand and sonar equipment complexity is worked out in the traditional processing means, is equivalent to the one-dimensional array with conformal array and carries out one-dimensional beam forming, is about to each array element series connection processing of every pitch direction is equivalent to an array element, and every equivalent array element has certain directive property in the pitch direction. However, the pitch direction detection range of such processing is limited to around 0 °, the performance of resisting the pitch direction interference is poor, the side lobe level of the beam is high, and the performance is deteriorated under the condition that the loss of the sound propagation path occurs.
A two-dimensional beam forming method based on a product theorem decomposes an area array into a combination of a linear array and a linear array, and respectively carries out beam forming on the two linear arrays to finally obtain a beam pattern of a three-dimensional array, but the method is not suitable for conformal arrays with randomly distributed array element spaces. The numerical synthesis method is based on minimum variance distortion free response (MVDR) beamforming, imposing several virtual interferences in the side lobe region. These interferences may reduce the beam response in the corresponding direction and increasing the interference strength may reduce the corresponding beam response. And adjusting the interference intensity through an iterative method, and controlling the side lobe of the wave beam to reach the expected side lobe level. The numerical synthesis method and the side lobe control method based on the self-adaptive beam forming have the problems that iteration step length is difficult to select, strict control on side lobes is difficult to guarantee, main lobes are easy to widen obviously due to the fact that the iteration process is free of constraint on the main lobes, the narrowest main lobe width under a given side lobe level cannot be obtained, the problems are more obvious when the numerical synthesis method is applied to two-dimensional beam forming, and the algorithm cannot be converged frequently. Furthermore, such methods lack considerations for array gain and robustness in controlling sidelobes.
With the development of optimization theory and the progress of computer technology, a method for performing beam optimization and sidelobe control by using convex optimization theory appears. The convex optimization method can obtain the global optimal solution of the problem, and can avoid the problems of searching step length selection, trapping in local extremum and the like. The convex optimization problem can be conveniently solved according to the existing interior point method. Therefore, the convex optimization theory and the solving algorithm thereof provide a new solving idea and direction for the two-dimensional beam optimization and the sidelobe control of the conformal array.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a conformal array two-dimensional beam optimization method based on a convex optimization theory, which solves the problems that when the conformal array performs two-dimensional beam forming, the side lobe level is too high and the beam stability is difficult to control, and simultaneously improves the array gain and the robustness of beam forming.
The technical problem to be solved by the invention is realized by the following technical scheme:
a conformal array two-dimensional wave beam optimization method based on convex optimization theory comprises the following steps:
(1) performing array flow pattern modeling in a conformal array scanning space to obtain a two-dimensional array flow pattern matrix A;
(2) obtaining a beam response of a target direction according to the azimuth angle and the pitch angle pointed by the target;
(3) dividing a main lobe area and a side lobe area of the conformal array scanning space;
(4) initializing the widths of the azimuth half main lobe and the pitching half main lobe, and setting an expected side lobe level;
(5) calculating the narrowest half main lobe width with a solution through loop iteration, and obtaining a main lobe region and a side lobe region under the narrowest half main lobe width;
(6) solving convex optimization second-order cone constraint by using an interior point method to obtain a beam forming weighting vector w;
(7) and calculating the beam response formed by the two-dimensional beam according to the weighting vector w and the two-dimensional array flow pattern matrix A.
Further, the specific mode of the step (1) is as follows:
(101) uniformly discretizing the radiation space into theta according to azimuth angle and pitch angle1,θ2,…,θP、Wherein theta is1,θ2,…,θP∈[-90°,90°],Subscripts P and Q are the number of discrete azimuth angles and pitch angles respectively;
(102) for an N-element conformal array, the three-dimensional coordinates of hydrophone array element i are represented as ri=[xi,yi,zi]TI is more than or equal to 1 and less than or equal to N; for the direction of radiation spaceThe unit direction vector is expressed asT is the transposition of the matrix;
(103) taking the origin of coordinates as a reference point, the time delay of the array element i relative to the origin of coordinates is:
the N-dimensional steering vector of the array is:
wherein c is underwater sound velocity, f is signal center frequency, j is imaginary number unit, G1、G2,...,GNDirectivity of conformal hydrophone array with value ofPhi is more than 180 degrees and less than or equal to 180 degrees, and phi is an included angle between the array element sound receiving main shaft and the signal incidence direction;
thereby, obtaining an azimuth pitching two-dimensional array flow pattern matrix of the matrix:
where p (-) is the beam response function and superscript H denotes the conjugate transpose.
and
wherein,is the target direction, αaIs the azimuthal half main lobe width, αeIs the pitch half main lobe width.
Further, the specific mode of the step (5) is as follows:
(501) for half the main lobe width, the constraint equation is solved by the interior point method:
Wherein,response of the beam in the target direction, xipqA desired side lobe level; if the equation has a solution, α ═ α -1, and if the equation has no solution, α ═ α + 1;
(502) iterating the loop of the step (501) until alpha is solved and alpha-1 is not solved to obtain the main lobe area theta 'at the moment'main,Comprises the following steps:
and
wherein alpha isaminAnd alphaeminThe narrowest azimuth half main lobe width and the narrowest pitching half main lobe width are obtained respectively.
Further, the convex optimization second order cone constraint in step (6) is expressed as:
Wherein w ═ w1,w2,...,wN]TRepresenting a weight vector, wiIs a weight value of array element i, RnIs a noise covariance matrix;
r in the case of spatial white noisenIs an identity matrix, so the second order cone constraint is simplified as:
And solving the second-order cone constraint through an interior point method to obtain the optimal solution of the weighting vector w under the second-order cone constraint.
Further, the beam response of the two-dimensional beam forming in step (7)The calculation method is as follows:
compared with the prior art, the invention has the following advantages:
1. compared with the traditional method, the two-dimensional beam pattern obtained by the invention has lower side lobe level, and the side lobe is uniform side lobe, so that the invention has better beam directivity.
2. The invention solves the global optimal solution through a convex optimization method, and can obtain the narrowest main lobe under the set expected side lobe level.
3. Compared with the conventional method, the second-order cone constraint beam forming method has higher array gain under the same side lobe level.
4. By constraining the norm of the weighting vector, the robustness of beam forming is higher than that of the traditional method.
Drawings
FIG. 1 is a diagram of a model of an array received signal in an embodiment of the invention;
fig. 2 is a flow chart of two-dimensional beamforming in an embodiment of the invention;
FIG. 3 is a diagram of a division of a main lobe region and a side lobe region in an embodiment of the present invention;
FIG. 4 is a schematic diagram of a conformal array model used in simulation according to an embodiment of the present invention;
FIGS. 5-10 are two-dimensional beamforming beampatterns using Conventional Beamforming (CBF), numerical synthesis (OLEN), and the method of the present invention;
FIGS. 11-14 are graphs comparing the beam optimization results of the method of the present invention with the processing results of the conventional beamforming and numerical synthesis method;
fig. 15 is a comparison of the array gain of the method of the present invention with the gain of a conventional beamforming and numerically synthesized array.
Detailed Description
The technical solution and effects of the present invention will be further described in detail with reference to the accompanying drawings.
A conformal array two-dimensional wave beam optimization method based on a convex optimization theory is provided, and increases the constraint of a side lobe of wave beam response formed by a two-dimensional wave beam on the basis of high array gain obtained by a minimum variance distortion free response (MVDR) wave beam forming method, and represents the constraint as a convex optimization second-order cone constraint problem. The method specifically comprises the following steps:
(1) performing array flow pattern modeling in a conformal array scanning space to obtain a two-dimensional array flow pattern matrix A;
(2) obtaining a beam response of a target direction according to the azimuth angle and the pitch angle pointed by the target;
(3) dividing a main lobe area and a side lobe area of the conformal array scanning space;
(4) initializing the width of the azimuth and the pitch half main lobe, and setting an expected side lobe level;
(5) calculating the narrowest half main lobe width with a solution through loop iteration, and obtaining a main lobe region and a side lobe region under the narrowest half main lobe width;
(6) solving convex optimization second-order cone constraint by using an interior point method to obtain a weighting vector w;
(7) and calculating the beam response formed by the two-dimensional beam according to the weighting vector w and the two-dimensional array flow pattern matrix A.
Wherein, the step (1) comprises the following steps:
(101) uniformly discretizing the radiation space into theta according to azimuth angle and pitch angle1,θ2,…,θP、Wherein theta is1,θ2,…,θP∈[-90°,90°],P and Q are respectively the number of discrete azimuth angles and pitch angles;
(102) for an N-element conformal array, the three-dimensional coordinates of hydrophone array element i are represented asri=[xi,yi,zi]TI is more than or equal to 1 and less than or equal to N; for the radiation space directionThe unit direction vector is expressed asT is the transposition of the matrix;
(103) taking the origin of coordinates as a reference point, the time delay of the array element i relative to the origin of coordinates is:
the N-dimensional steering vector of the array is:
wherein c is underwater sound velocity, f is signal center frequency, j is imaginary number unit, G1、G2,...,GNDirectivity of conformal hydrophone array with value ofPhi is more than 180 degrees and less than or equal to 180 degrees, and phi is an included angle between the array element sound receiving main shaft and the signal incidence direction;
thereby, obtaining an azimuth pitching two-dimensional array flow pattern matrix of the matrix:
wherein the superscript H denotes the conjugate transpose.
and
wherein,is the target direction, αaIn azimuth half main lobe width, αeIs the pitch half main lobe width.
The iteration method in the step (5) specifically comprises the following steps:
(501) for half mainlobe widths, the constraint equation is solved by the interior point method:
wherein,is the beam response of the target direction, ξpqA desired sidelobe level; if the equation has a solution, α ═ α -1, and if the equation has no solution, α ═ α + 1;
(502) iterating the loop of the step (501) until alpha is solved and alpha-1 is not solved, and obtaining the main lobe region theta 'at the moment'main,Comprises the following steps:
and
wherein alpha isaminAnd alphaeminThe narrowest azimuth half main lobe width and the narrowest pitching half main lobe width are obtained respectively.
The convex optimization second order cone constraint in the step (6) is expressed as follows:
wherein w ═ w1,w2,...,wN]TRepresenting a weighted vector, wiWeighted value, R, of array element inIs a noise covariance matrix;
r in the case of spatial white noisenAs an identity matrix, the second order cone constraint is simplified as:
and solving the second-order cone constraint through an inner point method to obtain the optimal solution of the weighting vector w under the second-order cone constraint.
The calculation formula of the beam response formed by the two-dimensional beam in the step (7) is as follows:
the method can be used for optimizing the design of transmitting and receiving beam patterns of an active conformal array sonar system, and the beam directivity of the sonar system is improved.
The following is a more specific example:
FIG. 1 is a diagram of an array received signal model. The figure shows a model of a received signal of a conformal array, taking an N-ary spatial conformal array as an example. The array receives a signal at a far-field point P. Theta andrespectively representing the incidence azimuth angle in the horizontal direction and the incidence pitch angle in the depth direction of the incoming wave signal. Assuming that the conformal array radiates only half-space forward, θ e [ -90 °,90 °]、
The specific flow of the conformal array two-dimensional beam forming method in this example is shown in fig. 2, and the implementation steps are as follows:
step 1: referring to FIG. 1, a conformal array flow pattern is modeled.
(101) Uniformly discretizing the radiation space into theta according to azimuth angle and pitch angle1,θ2,…,θP、Wherein theta is1,θ2,…,θP∈[-90°,90°],P and Q are respectively the number of discrete azimuth angles and pitch angles;
(102) for an N-element conformal array, the three-dimensional coordinates of hydrophone array element i are represented as ri=[xi,yi,zi]TI is more than or equal to 1 and less than or equal to N; for the direction of radiation spaceThe unit direction vector is expressed asT is the transposition of the matrix;
(103) taking the origin of coordinates as a reference point, the time delay of the array element i relative to the origin of coordinates is:
the N-dimensional steering vector of the array is:
wherein c is underwater sound velocity, f is signal center frequency, j is imaginary number unit, G1、G2,...,GNDirectivity of conformal array hydrophonePhi is more than 180 degrees and less than or equal to 180 degrees, and phi is an included angle between the array element sound receiving main shaft and the signal incidence direction;
thereby, obtaining an azimuth pitching two-dimensional array flow pattern matrix of the matrix:
wherein the superscript H denotes the conjugate transpose.
And 3, step 3: referring to fig. 3, the conformal array scanning space is divided into a main lobe area and a side lobe area.
(301) Set the target direction asWidth of azimuth half main lobe is alphaaThe pitch half main lobe width is alphaeThen main lobe region θmain,Comprises the following steps:
and 4, step 4: the half main lobe width sum of azimuth and pitch is initialized, setting the desired side lobe level.
And 5: the iterative solution is performed according to the following manner:
(501) for half the main lobe width, the constraint equation is solved by the interior point method:
wherein ξpqA desired sidelobe level; if the equation has a solution, α ═ α -1, and if not, α ═ α + 1;
(502) iterating the loop of the step (501) until alpha is solved and alpha-1 is not solved, and obtaining the main lobe region theta 'at the moment'main,Comprises the following steps:
wherein alpha isaminAnd alphaeminThe narrowest azimuth half main lobe width and the narrowest pitching half main lobe width are obtained respectively.
Step 6: and solving convex optimization second-order cone constraint to obtain a beam forming weighting vector w.
The beam forming method based on MVDR has higher array gain, and side lobe control is applied to the beam forming method:
forming the MVDR wave beam applying the side lobe control into a second-order cone constraint form of a convex optimization problem:
wherein w ═ w1,w2,...,wN]TRepresenting a weighted vector, wiWeighted value, R, of array element inIs a noise covariance matrix. R in the case of spatial white noisenIs an identity matrix, so the second order cone constraint is simplified as:
weighted vector norm | w | shading2The lower, the more robust the beamforming. By adding the constraint on the norm of the weighting vector | | w | | luminance2Gamma is less than or equal to gamma, and gamma is a set scalar, so that the robustness of beam forming can be improved. Objective function of above second order cone constraintNon-woven cells with constraint | | w |)2The ≦ γ -effect repetition, i.e., this second-order cone constraint, already can improve the robustness of beamforming.
The second-order cone constraint is solved through an interior point method, and an optimal solution of the weighting vector w under the second-order cone constraint can be obtained.
And 7: and according to the solved optimal weighting vector w and the two-dimensional array flow pattern matrix A, calculating to obtain two-dimensional beam forming beam response by the following formula:
the effect of the method can be illustrated by the following simulation:
1. simulation condition and method
An 8-row 216-membered ring belt conformal array was set up as shown in fig. 4. The array surface is hemispherical, 8 rows of curve arrays are arranged on the hemispherical surface in parallel to the horizontal plane, each row of 27 array elements are arranged, the distance between each array element and the origin is 220mm, and the distance between the array elements is 25 mm. At a signal frequency of 30kHz and an acoustic velocity of 1500m/s in water, the half wavelength lambda/2 of the signal is 25 mm. The array element interval is half wavelength, which accords with the sampling theorem. The target orientations were [0 °,0 ° ], [60 °,0 ° ].
2. Simulation content and results
On the premise of not changing the simulation conditions, the conformal array two-dimensional beam optimization method based on the convex optimization theory provided herein is compared with the Conventional Beam Forming (CBF) method and the numerical synthesis method (OLEN), and the obtained two-dimensional beam patterns are respectively shown in fig. 5 to 10. The results shown in fig. 11 to 14 can be obtained by performing azimuth beam slicing and elevation beam slicing in the target pointing direction for each two-dimensional beam pattern, and comparing the one-dimensional beam patterns of each algorithm. It can be found that the two-dimensional beam pattern obtained by the method has a lower side lobe level, and the side lobe is a uniform side lobe, so that the two-dimensional beam pattern has more excellent beam directivity. The expected side lobe level is set to be-30 dB in simulation, and the method can be found to set the expected side lobe level and obtain a beam pattern meeting the setting requirement.
On the premise of not changing the beam direction, the high array gain characteristic of the method is continuously examined when the frequency is different. The results shown in fig. 10 were obtained by simulating the difference between the input and output signal-to-noise ratios, i.e., the array gain, for the three methods at different frequencies. At different frequencies, the method has a higher array gain than the other two methods.
In summary, the method of the present invention is a side lobe control high gain high robustness two-dimensional beam optimization method suitable for any sensor array, and the method mainly includes the following steps: dividing a main lobe area and a side lobe area of a conformal array scanning space; initializing half main lobe width, and setting the narrowest main lobe width under an expected side lobe level through iterative solution; and (3) representing the beam forming optimization problem into a convex optimization second-order cone constraint form, and solving the optimal solution of the weighting vector by using an inner point method, thereby obtaining a uniform two-dimensional beam response diagram with low side lobes.
The two-dimensional beam pattern obtained by the method has lower side lobe level, and the side lobe is uniform side lobe, so that the two-dimensional beam pattern has more excellent beam directivity. In addition, the method of the invention can set the expected side lobe level and can obtain the beam pattern meeting the setting requirement.
The constraint equation designed on the basis of the MVDR method enables the beam forming to obtain higher array gain compared with the traditional method. The constraint of the weighting vector norm of the invention ensures that the beam forming has higher robustness compared with the traditional method, and effectively solves the problems of high sidelobe and poor beam directivity of the two-dimensional beam pattern transmitted and received by the active conformal array sonar system.
Claims (2)
1. A conformal array two-dimensional wave beam optimization method based on a convex optimization theory is characterized by comprising the following steps:
(1) performing array flow pattern modeling in a conformal array scanning space to obtain a two-dimensional array flow pattern matrix A; the concrete mode is as follows:
(101) uniformly discretizing the radiation space into theta according to azimuth angle and pitch angle1,θ2,…,θP、Wherein
θ1,θ2,…,θP∈[-90°,90°],Subscripts P and Q are the number of discrete azimuth angles and pitch angles, respectively;
(102) for an N-element conformal array, the three-dimensional coordinates of hydrophone array element i are represented as ri=[xi,yi,zi]TI is more than or equal to 1 and less than or equal to N; for the radiation space directionThe unit direction vector is expressed asT is the transposition of the matrix;
(103) taking the origin of coordinates as a reference point, the time delay of the array element i relative to the origin of coordinates is:
the N-dimensional steering vector of the array is:
wherein c is underwater sound velocity, f is signal center frequency, j is imaginary number unit, G1、G2,...,GNDirectivity of conformal hydrophone array with value ofPhi is more than 180 degrees and less than or equal to 180 degrees, and phi is an included angle between the array element sound receiving main shaft and the signal incidence direction;
thereby, obtaining an azimuth pitching two-dimensional array flow pattern matrix of the matrix:
where p (-) is the beam response function, superscript H denotes the conjugate transpose;
(2) obtaining a beam response of a target direction according to the azimuth angle and the pitch angle pointed by the target;
(3) dividing a main lobe area and a side lobe area of a conformal array scanning space; wherein, the main lobe area thetamain,Comprises the following steps:
and
wherein,is the target direction, αaIn azimuth half main lobe width, αeThe width of the pitching half main lobe is;
(4) initializing the width of the azimuth and the pitch half main lobe, and setting an expected side lobe level;
(5) calculating the narrowest half main lobe width with a solution through loop iteration, and obtaining a main lobe region and a side lobe region under the narrowest half main lobe width; the concrete method is as follows:
(501) for half mainlobe widths, the constraint equation is solved by the interior point method:
Wherein,response of the beam in the target direction, xipqA desired side lobe level; if the equation has a solution, α ═ α -1, and if the equation has no solution, α ═ α + 1;
(502) iterating the loop of the step (501) until alpha is solved and alpha-1 is not solved, and obtaining the main lobe region theta 'at the moment'main,Comprises the following steps:
and
wherein alpha isaminAnd alphaeminRespectively obtaining the narrowest azimuth half main lobe width and the narrowest pitching half main lobe width;
(6) solving convex optimization second-order cone constraint by using an inner point method to obtain a beam forming weighting vector w; the convex optimization second order cone constraint is expressed as:
Wherein w ═ w1,w2,...,wN]TRepresenting a weight vector, wiWeighted value, R, of array element inIs a noise covariance matrix;
r in the case of spatial white noisenIs an identity matrix, so the second order cone constraint is simplified to:
Solving the second-order cone constraint through an interior point method to obtain an optimal solution of the weighting vector w under the second-order cone constraint;
(7) and calculating the beam response formed by the two-dimensional beam according to the weighting vector w and the two-dimensional array flow pattern matrix A.
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Citations (13)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO2010116153A1 (en) * | 2009-04-09 | 2010-10-14 | Ntnu Technology Transfer As | Optimal modal beamformer for sensor arrays |
WO2012140471A1 (en) * | 2011-04-12 | 2012-10-18 | Agence Spatiale Europeenne | Array antenna having a radiation pattern with a controlled envelope, and method of manufacturing it |
CN103344944A (en) * | 2013-07-02 | 2013-10-09 | 西安电子科技大学 | Radar pulse compression filter optimization design method applied to random signal waveforms |
CN111903233B (en) * | 2008-10-22 | 2014-06-11 | 中国电子科技集团公司第五十四研究所 | Broadband beam forming method based on specific group delay finite impulse response filter |
CN105246005A (en) * | 2015-09-15 | 2016-01-13 | 国家电网公司 | Hybrid gravitational search algorithm-based stereo microphone array optimization design method |
CN105467365A (en) * | 2015-12-08 | 2016-04-06 | 中国人民解放军信息工程大学 | A low-sidelobe emission directional diagram design method improving DOA estimated performance of a MIMO radar |
US9591404B1 (en) * | 2013-09-27 | 2017-03-07 | Amazon Technologies, Inc. | Beamformer design using constrained convex optimization in three-dimensional space |
CN106682405A (en) * | 2016-12-14 | 2017-05-17 | 西北工业大学 | Low-side-lobe beam pattern integrated design method based on convex optimization |
CN106772257A (en) * | 2017-01-10 | 2017-05-31 | 西北工业大学 | A kind of low sidelobe robust adaptive beamforming method |
CN106886656A (en) * | 2017-03-15 | 2017-06-23 | 南京航空航天大学 | A kind of cubical array antenna radiation pattern side lobe suppression method based on improvement MOPSO and convex optimized algorithm |
CN109976154A (en) * | 2019-03-04 | 2019-07-05 | 北京理工大学 | A kind of aerial vehicle trajectory optimization method based on chaos multinomial and the convex optimization of sequence |
CN110398711A (en) * | 2019-08-01 | 2019-11-01 | 天津工业大学 | A kind of Pattern Synthesis method that sonar conformal array is measured based on array manifold |
WO2020000655A1 (en) * | 2018-06-27 | 2020-01-02 | 东南大学 | Efficient digital-analog hybrid beamforming method, apparatus, and device for multi-antenna system |
Family Cites Families (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
KR100350026B1 (en) * | 2000-06-17 | 2002-08-24 | 주식회사 메디슨 | Ultrasound imaging method and apparatus based on pulse compression technique using a spread spectrum signal |
ITGE20130009A1 (en) * | 2013-01-24 | 2014-07-25 | Istituto Italiano Di Tecnologia | METHOD FOR THE CONFIGURATION OF PLANAR TRANSDUCER LINES FOR THE DEVELOPMENT OF SIGNALS WITH BROADBAND THROUGH THREE-DIMENSIONAL BEAMFORMING AND SIGNAL PROCESSING SYSTEMS USING THIS METHOD, IN PARTICULAR ACOUSTIC CAMERA |
CN110501675A (en) * | 2019-07-16 | 2019-11-26 | 北京工业大学 | One kind being based on MIMO radar low sidelobe transmitting pattern design method |
CN111400919B (en) * | 2020-03-20 | 2022-09-06 | 西安电子科技大学 | Low sidelobe beam design method in array antenna |
-
2020
- 2020-09-28 CN CN202011038156.0A patent/CN112162266B/en active Active
Patent Citations (13)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN111903233B (en) * | 2008-10-22 | 2014-06-11 | 中国电子科技集团公司第五十四研究所 | Broadband beam forming method based on specific group delay finite impulse response filter |
WO2010116153A1 (en) * | 2009-04-09 | 2010-10-14 | Ntnu Technology Transfer As | Optimal modal beamformer for sensor arrays |
WO2012140471A1 (en) * | 2011-04-12 | 2012-10-18 | Agence Spatiale Europeenne | Array antenna having a radiation pattern with a controlled envelope, and method of manufacturing it |
CN103344944A (en) * | 2013-07-02 | 2013-10-09 | 西安电子科技大学 | Radar pulse compression filter optimization design method applied to random signal waveforms |
US9591404B1 (en) * | 2013-09-27 | 2017-03-07 | Amazon Technologies, Inc. | Beamformer design using constrained convex optimization in three-dimensional space |
CN105246005A (en) * | 2015-09-15 | 2016-01-13 | 国家电网公司 | Hybrid gravitational search algorithm-based stereo microphone array optimization design method |
CN105467365A (en) * | 2015-12-08 | 2016-04-06 | 中国人民解放军信息工程大学 | A low-sidelobe emission directional diagram design method improving DOA estimated performance of a MIMO radar |
CN106682405A (en) * | 2016-12-14 | 2017-05-17 | 西北工业大学 | Low-side-lobe beam pattern integrated design method based on convex optimization |
CN106772257A (en) * | 2017-01-10 | 2017-05-31 | 西北工业大学 | A kind of low sidelobe robust adaptive beamforming method |
CN106886656A (en) * | 2017-03-15 | 2017-06-23 | 南京航空航天大学 | A kind of cubical array antenna radiation pattern side lobe suppression method based on improvement MOPSO and convex optimized algorithm |
WO2020000655A1 (en) * | 2018-06-27 | 2020-01-02 | 东南大学 | Efficient digital-analog hybrid beamforming method, apparatus, and device for multi-antenna system |
CN109976154A (en) * | 2019-03-04 | 2019-07-05 | 北京理工大学 | A kind of aerial vehicle trajectory optimization method based on chaos multinomial and the convex optimization of sequence |
CN110398711A (en) * | 2019-08-01 | 2019-11-01 | 天津工业大学 | A kind of Pattern Synthesis method that sonar conformal array is measured based on array manifold |
Non-Patent Citations (11)
Title |
---|
A Deep Reinforcement Learning-Based Framework for Dynamic Resource Allocation in Multibeam Satellite Systems;Xin Hu 等;《IEEE Communications Letters 》;20180605;第1612-1615页 * |
Linear sparse array synthesis via convex optimization;Ling Cen 等;《Proceedings of 2010 IEEE International Symposium on Circuits and Systems》;20100803;第4233-4236页 * |
Robust Minimum Sidelobe Beamforming for Spherical Microphone Arrays;Haohai Sun 等;《IEEE Transactions on Audio, Speech, and Language Processing》;20101004;第1045-1051页 * |
Thinned Array Beampattern Synthesis by Iterative Soft-Thresholding-Based Optimization Algorithms;Xiangrong Wang 等;《IEEE Transactions on Antennas and Propagation》;20141020;第6102-6113页 * |
二维束宽恒定的二阶锥规划波束形成方法;张勇 等;《电讯技术》;20160430;第56卷(第4期);第383-388页 * |
基于二阶锥规划的矢量阵波束优化设计及仿真;尚娟 等;《电声技术》;20101130;第34卷(第11期);第68-71页 * |
基于凸优化的共形阵波束优化方法研究;王晓庆 等;《无线电工程》;20200805;第50卷(第8期);第683-689页 * |
基于凸优化的最小旁瓣恒定束宽时域宽带波束形成;范展 等;《电子学报》;20130531;第41卷(第5期);第943-948页 * |
基于凸优化的频率方向二维恒定束宽波束形成技术;张文刚 等;《电子信息对抗技术》;20121130;第27卷(第6期);第67-72页 * |
基于凸优化算法的水声传感器阵列综合;李文强 等;《电子测量与仪器学报》;20171031;第31卷(第10期);第1614-1620页 * |
用于射频识别的低旁瓣圆极化微带天线阵;孙竹 等;《上海大学学报(自然科学版)》;20090228;第15卷(第1期);第51-53、59页 * |
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