CN113849977A - Low-sidelobe phased array optimization method with controllable channel power loss - Google Patents

Low-sidelobe phased array optimization method with controllable channel power loss Download PDF

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CN113849977A
CN113849977A CN202111122007.7A CN202111122007A CN113849977A CN 113849977 A CN113849977 A CN 113849977A CN 202111122007 A CN202111122007 A CN 202111122007A CN 113849977 A CN113849977 A CN 113849977A
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channel
channel power
array
excitation
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刘颜回
白晶晶
吴攀
芮茵
黄杰
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Yangtze River Delta Research Institute of UESTC Huzhou
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Abstract

The invention discloses a low-sidelobe phased array optimization method with controllable channel power loss, relates to the field of phased array antennas, and solves the problems of high channel power loss, low power amplifier efficiency and complex feed network. The method comprises the steps that the scanning wave beams of the phased array antenna share the excitation amplitude, the normal wave beams and a plurality of scanning wave beams are optimized in the minimization of the side lobe level, the power loss of a channel is controlled simultaneously in the optimization process of the minimization of the side lobe level, the constraint on the power loss of the channel is converted into the constraint on the excitation amplitude, the constraint problem after conversion is subjected to convex optimization iterative calculation, whether a given threshold is met or not is judged, or the iteration is terminated when the maximum iteration frequency is reached, the directional diagrams of the scanning wave beams of the phased array antenna are output, and the distribution of the common excitation amplitude meeting the requirements is obtained. The invention saves cost, improves power amplification efficiency and has higher engineering practical value.

Description

Low-sidelobe phased array optimization method with controllable channel power loss
Technical Field
The invention relates to the field of phased array antennas, in particular to a low-sidelobe phased array optimization method with controllable channel power loss.
Background
Phased array antennas are increasingly used in modern communication systems and radar systems due to their flexible beam scanning characteristics. It can be used to form a certain radiation beam over a desired scan angle or to achieve a fast scan of the beam over a certain spatial angular range. In engineering applications, in order to improve the anti-interference capability of the array antenna to noise and other factors, the level of the side lobe of the radiation pattern of the array antenna is required to be as low as possible. On the other hand, in order to improve the radiation efficiency of the antenna, higher requirements are also put forward on the design of a phased array feed system, and the reduction of the channel power loss can not only improve the efficiency of the power amplifier, but also simplify a feed network.
Chinese patent 202110181871.8 discloses a method for rapidly calculating sidelobe of phased array antenna and a sidelobe reduction method [1], which combines genetic algorithm to realize low sidelobe synthesis of array factors of phased array. However, the patent only synthesizes array factors, and neglects the influence of the unit mutual coupling effect. The patent is only applicable to small scan angles (e.g., scan angles within 30 deg.), and the mutual coupling of the cells becomes non-negligible when the desired scan angle is a wide-angle scan. Chinese patent 202010010677.9 discloses an irregular subarray optimization method [2] for ultra-large scan angles, which can achieve larger scan angles with fewer TR components. But the method adjusts both the amplitude and phase of the excitation at different scan angles. This makes the phased array system need to add amplitude modulation modules (such as attenuators) to achieve the effect of beam scanning, and thus makes the feed network become complicated. Documents y.alan, j.puskely, a.roederer, and a.yarooy, "Synthesis of multiple beam linear arrays with uniform amplitudes," in proc.12th eur.conf.antennas Propag (EuCAP), apr.2018.[3] discuss satisfying wide angle scanning of multiple beams with simultaneous side lobe minimization by position optimization, in which the array elements are uniformly activated and the amplifiers powering the array can all achieve energy efficient operation. However, in practical applications, there is another requirement that the array element position is fixed and the amplitude is not adjusted during beam scanning, i.e. different beam amplitudes are shared. If the power loss of the channel can be further reduced on the basis, the power amplification efficiency can be improved, and the cost is saved.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the invention provides a low-side lobe phased array optimization method with controllable channel power loss, which solves the problems of high channel power loss, low power amplifier efficiency and complex feed network.
The basic idea of the invention is as follows:
and performing side lobe level optimization on the normal beam and a plurality of scanning beams simultaneously, controlling the power loss of a channel in the process, and searching the minimum side lobe level value which can be obtained when the amplitudes of a plurality of beams are shared under the constraint condition. Furthermore, the invention can conveniently take mutual coupling into account by using active cell patterns. In the specific implementation process of the invention, an iterative convex optimization idea is introduced, the non-convex constraint condition of the channel power loss in the original comprehensive problem is converted and indirectly converted into the iterative convex optimization problem by constraining the excitation amplitude in an iterative manner, and the judgment condition of the channel power loss obtained by the iteration is added after the convex optimization is completed, so that the control of the channel power loss is finally realized.
The method comprises the steps that normal beams and scanning beams of a phased array antenna share excitation amplitude, the normal beams of the phased array are subjected to phase shifting to obtain a plurality of scanning beams, the normal beams and the scanning beams are optimized in a sidelobe level minimization mode, channel power loss is controlled simultaneously in the optimization process of the sidelobe level minimization, constraint on the channel power loss is converted into constraint on the excitation amplitude, convex optimization iterative computation is carried out on the constraint problem after conversion, whether the channel power loss value of excitation obtained by each iteration meets a preset threshold value or not is judged, the iteration is terminated if the channel power loss value meets the preset threshold value or the maximum iteration number is reached, directional patterns of the scanning beams of the phased array antenna and the common excitation amplitude distribution meeting the requirement are output.
The invention is realized by the following technical scheme:
combining the problem of realizing the minimization of a plurality of beam side lobes under the condition of sharing the feed amplitude with the power loss of a control channel, and expressing the comprehensive problem in a mathematical form;
because the constraint of the channel power loss is a non-convex constraint condition, the invention adopts the idea of iterative convex optimization to carry out conversion processing on the constraint of the power loss;
in each iteration, the constraint on the channel power loss is converted into the constraint on the excitation amplitude, so that the comprehensive problem is converted into a convex optimization problem;
after each convex optimization is finished, judging whether the channel power loss value of the excitation obtained by the iteration meets the condition of a given threshold value;
the condition of iteration termination is that the power loss value of the channel obtained by synthesis meets a given threshold value or reaches the maximum iteration times; if the iteration termination condition is met, outputting the directional diagrams of a plurality of scanning beams and the common excitation amplitude distribution meeting the requirement, and otherwise, continuing the iteration.
The channel power loss can be defined as the ratio of the sum of the actually required power of each channel when the array antenna radiates a certain direction to the total power fed to each channel by the power amplifier, that is, the ratio is
Figure BDA0003277339980000021
Wherein, wnAnd N is the excitation of the nth array element when the array points to the normal beam, and N is the total number of the array elements. Since the multiple beam excitation amplitudes are shared in the present invention, the array channel power loss is the same for different beams.
Further, the multiple beam side lobe minimization problem is combined with the control channel power loss, and the mathematical form can be expressed as:
Figure BDA0003277339980000031
wherein the constraint in equation (2) is that from top to bottom, constraint 1 points to the normal beam
Figure BDA0003277339980000032
The constraint is carried out; constraint 2 controls the channel power loss, where P (w) represents the channel power loss, δmaxA threshold value given to the user; constraint 3 is the simultaneous optimization of the side lobes of the K beams, where
Figure BDA0003277339980000033
For the kth beam of the array, K is the total number of beam formations, and τ is the number of K beams in the corresponding side lobe region
Figure BDA0003277339980000034
Minimum side lobe level value which can be realized simultaneously; the last constraint defines the excitation of the kth beam, which is calculated from the phase relation of the excitation corresponding to the normal beam, wherein
Figure BDA0003277339980000035
For the excitation of the nth array element corresponding to the kth wave beam,
Figure BDA0003277339980000036
a position vector representing the elements of the array,
Figure BDA0003277339980000037
representing the direction vector corresponding to the maximum pointing angle of the kth beam. The above integration problem is a non-convex problem because the constraint of channel power loss is a non-convex constraint.
Further, the constraint on the excitation amplitude converted is: in the l iteration, the excitation amplitude of each array element is constrained to be less than or equal to the product of the maximum value of the excitation amplitude obtained in the (l-1) iteration and a coefficient. Can be described in a mathematical form as
|wn (l)|≤ε·max{|w1 (l-1)|，|w2 (l-1)|，…，|wN (l-1)|},for n＝1,…,N (3)
Wherein epsilon is a positive real number less than 1. If the excitation of the (l-1) th iteration is obtained, the array synthesis problem of the l-th iteration is converted into a convex optimization problem.
Further, the condition for judging whether the channel power loss meets the given threshold is to judge P (w) after the end of the ith convex optimization(l))≤δmaxWhether or not, P (w)(l)) Can be calculated as
Figure BDA0003277339980000038
The invention has the following advantages and beneficial effects:
when the sidelobes of a plurality of scanning beams of the phased array antenna are optimized, the power loss of the channel is controlled, on one hand, the transmission power loss can be reduced, and the effective transmitting power is improved; on the other hand, the feed network can be simplified, and the cost is saved.
The invention is not limited by the structure of the antenna, and can include the influence of mutual coupling of array elements and platform effect, thereby having higher engineering practical value for phased array design.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a diagram of an antenna unit designed for verifying the proposed algorithm in an embodiment of the present invention.
Fig. 3 is a scanning beam pattern without channel power loss control according to an embodiment of the present invention.
Fig. 4 is a corresponding excitation amplitude distribution diagram of fig. 3 in an embodiment of the present invention.
Fig. 5 is a diagram of a scanning beam pattern obtained when controlling channel power loss in an embodiment of the present invention.
Fig. 6 is a corresponding excitation amplitude distribution diagram of fig. 5 in an embodiment of the present invention.
Detailed Description
Hereinafter, the term "comprising" or "may include" used in various embodiments of the present invention indicates the presence of the invented function, operation or element, and does not limit the addition of one or more functions, operations or elements. Furthermore, as used in various embodiments of the present invention, the terms "comprises," "comprising," "includes," "including," "has," "having" and their derivatives are intended to mean that the specified features, numbers, steps, operations, elements, components, or combinations of the foregoing, are only meant to indicate that a particular feature, number, step, operation, element, component, or combination of the foregoing, and should not be construed as first excluding the existence of, or adding to the possibility of, one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing.
In various embodiments of the invention, the expression "or" at least one of a or/and B "includes any or all combinations of the words listed simultaneously. For example, the expression "a or B" or "at least one of a or/and B" may include a, may include B, or may include both a and B.
The terminology used in the various embodiments of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the various embodiments of the invention. As used herein, the singular forms are intended to include the plural forms as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which various embodiments of the present invention belong. The terms (such as those defined in commonly used dictionaries) should be interpreted as having a meaning that is consistent with their contextual meaning in the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein in various embodiments of the present invention.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Step 1: calculating the channel power loss, wherein the channel power loss can be defined as the ratio of the sum of the actually required power of each channel to the total power of each channel fed by the power amplifier when the array antenna radiates a certain direction diagram, namely
Figure BDA0003277339980000051
Wherein, wnAnd N is the excitation of the nth array element when the array points to the normal beam, and N is the total number of the array elements. Since the multiple beam excitation amplitudes are shared in the present invention, the array channel power loss is the same for different beams.
Step 2: the combined problem of achieving multiple beam side lobe minimization with feed amplitude sharing, combined with control channel power loss, is expressed mathematically,
for an N-ary arbitrary array, the direction pattern of the k-th scanning beam radiated by the N-ary arbitrary array can be expressed as
Figure BDA0003277339980000052
In the formula
Figure BDA0003277339980000053
Figure BDA0003277339980000054
Wherein the content of the first and second substances,
Figure BDA0003277339980000055
the active unit directional diagram of the nth array element of the array comprises the mutual coupling of the array elements, the influence of an installation platform and the like, can be obtained through test or electromagnetic simulation software,
Figure BDA0003277339980000056
is the position vector of the nth array element,
Figure BDA0003277339980000057
a direction vector representing the angle of spatial radiation,
Figure BDA0003277339980000058
the excitation vector of the kth beam.
In engineering applications, if multiple beams are desired by phase scanning and the amplitudes of the multiple beams are shared, then the excitation of the kth beam can be represented as
Figure BDA0003277339980000059
Where K is the total number of beams required and w ═ w1,w2,…,wN]TFor the excitation vector corresponding to the normal beam,
Figure BDA00032773399800000510
is the direction vector of the kth beam.
Then the comprehensive problem of the low-sidelobe phased array antenna with controllable channel power loss can be expressed as follows:
Figure BDA00032773399800000511
where the optimization objective is to find the minimum sidelobe level achievable by several beams simultaneously, condition 1 above constrains the normal beam pointing
Figure BDA0003277339980000061
Condition 2 controls channel power loss, where δmaxA threshold value customized for the user; condition 3 optimizes the side lobes of the K beams simultaneously,
Figure BDA0003277339980000062
and tau is the side lobe level value to be optimized for the side lobe area of the kth wave beam. The last condition, which constrains the excitation of the kth beam, is obtained by phase scanning from the corresponding excitation of the normal beam,
Figure BDA0003277339980000063
a direction vector corresponding to the maximum pointing angle of the kth beam; the above integration problem is a non-convex problem because the constraint of channel power loss is a non-convex constraint.
And step 3: because the constraint of the channel power loss is a non-convex constraint condition, the invention adopts the idea of iterative convex optimization to carry out conversion processing on the non-convex constraint condition. In the l-th iteration, the excitation amplitudes of the array elements are constrained to be less than or equal to the product of the maximum value of the excitation amplitudes obtained in the (l-1) -th iteration and a coefficient. Can be described in a mathematical form as
|wn (l)|≤ε·max{|w1 (l-1)|，|w2 (l-1)|,…,|wN (l-1)|},for n＝1,…,N (11)
Wherein epsilon is a positive real number less than 1, and empirically, epsilon generally ranges from 0.8 to 0.99. If the excitation of the (l-1) th iteration is obtained, the array synthesis problem of the l-th iteration is converted into a convex optimization problem, namely
Figure BDA0003277339980000064
And 4, step 4: increasing the judgment P (w) in the first iteration(l))≤δmaxWhether or not a condition is satisfied, wherein
Figure BDA0003277339980000065
And 5: the condition of iteration termination is that the power loss value of the channel obtained by synthesis meets a given threshold value or reaches the maximum iteration times; and if the iteration termination condition is met, outputting the common excitation amplitude and the corresponding excitation phase of the plurality of scanning beams, otherwise, iteratively executing the step 3.
The specific simulation embodiment:
the effectiveness of the invention is verified by taking a 20-element uniform linear array which is arranged on a z-axis array element and has the spacing of 15mm as an example. The dimensions of the antenna elements used in the array are given in fig. 2. The antenna unit is a common microstrip patch antenna, and the working frequency is 10 GHz. The present invention takes into account the effects of coupling by using the active element patterns in the pattern synthesis process. The phased array is assumed to realize a scanning range of +/-45 degrees, and the scanning directional diagrams are in shared amplitude and are rapidly switched in phase. Fig. 3 shows the pattern without constraining the power loss of the channels, in fig. 3 the abscissa is the angle θ (°) and the ordinate is the power pattern (dB); the scanning angles corresponding to the beam curve from left to right in fig. 3 are 7 angles of 45 °, 60 °, 75 °, 90 °, 105 °, 120 °, and 135 °, respectively. As can be seen from the figure, the maximum gain of the beam at this time is 19.57dB, each beam is completely accurate in pointing, the maximum sidelobe level is-25 dB, the corresponding excitation amplitude distribution is as shown in fig. 4, the abscissa is the position (λ) of the array element, and the ordinate is the excitation amplitude; the resulting channel power loss from the excitation amplitude profile was 2.73 dB. The method provided by the invention is utilized to restrain the power loss of the channel, the maximum acceptable loss of the system is set to be 1.5dB, other conditions are unchanged, and the comprehensive directional diagram and the corresponding excitation amplitude distribution are respectively shown in a figure 5 and a figure 6. In fig. 5, the abscissa is an angle θ (°), and the ordinate is a power pattern (dB); in fig. 6, the abscissa is the array element position (λ) and the ordinate is the excitation amplitude.
The maximum gain obtained at this time is 19.87dB, the sidelobe level is raised to-21 dB, and the channel power loss is reduced to 1.45dB, so that the given constraint condition is met. When the given maximum allowed power loss is smaller, the combined sidelobe will generally be higher, since the freedom of excitation will then be smaller. The above results demonstrate the effectiveness of the proposed method of the present invention.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (4)

1. A low sidelobe phased array optimization method with controllable channel power loss is characterized by comprising the following steps:
the method comprises the steps that scanning beams of a phased array antenna share an excitation amplitude, the normal beams of the phased array are subjected to phase shifting to obtain a plurality of scanning beams, the normal beams and the scanning beams are optimized in a sidelobe level minimization mode, channel power loss is controlled simultaneously in the optimization process of the sidelobe level minimization, the constraint on the channel power loss is converted into the constraint on the excitation amplitude, convex optimization iterative computation is adopted for the constraint problem after conversion, whether the channel power loss value of excitation obtained by each iteration meets a preset threshold value or not is judged, the iteration is terminated if the channel power loss value meets the preset threshold value or the maximum iteration number is reached, directional patterns of the scanning beams of the phased array antenna are output, and the common excitation amplitude distribution meeting the requirements is obtained.
2. The method of claim 1, wherein the channel power loss is a ratio of a sum of powers actually required by each channel when the array antenna radiates a certain direction to a total power fed to each channel by the power amplifier, that is, the channel power loss is controllable, that is, the channel power loss is a ratio of a sum of powers actually required by each channel to a total power fed to each channel by the power amplifier
Figure FDA0003277339970000011
Wherein, wnAnd N is the excitation of the nth array element when the array points to the normal beam, and N is the total number of the array elements.
3. The method as claimed in claim 2, wherein the normal beam and the plurality of scanning beams are optimized for minimizing the side lobe level by finding the minimum side lobe level that can be achieved by the normal beam and the plurality of scanning beams simultaneously, and the optimization problem can be expressed as
Figure FDA0003277339970000012
Figure FDA0003277339970000013
Figure FDA0003277339970000014
Representing constrained normal beam pointing angle
Figure FDA0003277339970000015
P(w)≤δmaxWhere P (w) represents the channel power loss, δmaxA threshold value is given to the user that is,
Figure FDA0003277339970000016
side lobes of the K beams are simultaneously optimized, wherein
Figure FDA0003277339970000017
For the kth beam of the array, K is the total number of beam formations, and τ is the number of K beams in the corresponding side lobe region
Figure FDA0003277339970000018
Minimum side lobe level value which can be realized simultaneously;
Figure FDA0003277339970000019
Figure FDA00032773399700000110
indicating the excitation of the nth array element corresponding to the kth beam,
Figure FDA00032773399700000111
the corresponding excitation from the normal beam is obtained by phase relation calculation,
Figure FDA0003277339970000021
a position vector representing the elements of the array,
Figure FDA0003277339970000022
representing the direction vector corresponding to the maximum pointing angle of the kth beam.
4. The method for optimizing the low sidelobe phased array with controllable channel power loss according to claim 3, wherein in the transformation into the constraint on the excitation amplitude, in the I iteration, the excitation amplitude of each array element is constrained to be less than or equal to the product of the maximum value of the excitation amplitude obtained in the (l-1) iteration and a coefficient, namely
|wn (l)|≤ε·max{|w1 (l-1)|，|w2 (l-1)|，…，|wN (l-1)|},for n＝1,…,N (3)
And if the excitation of the (l-1) th iteration is obtained, the array comprehensive problem of the l-th iteration is converted into a convex optimization problem.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114337752A (en) * 2021-12-30 2022-04-12 电子科技大学 High-efficiency side lobe suppression linear array antenna based on three-section type hybrid drive

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114337752A (en) * 2021-12-30 2022-04-12 电子科技大学 High-efficiency side lobe suppression linear array antenna based on three-section type hybrid drive
CN114337752B (en) * 2021-12-30 2022-09-23 电子科技大学 High-efficiency side lobe suppression linear array antenna based on three-section type hybrid drive

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