JPH04321304A - Polarized wave changeover device for phased array antenna - Google Patents

Polarized wave changeover device for phased array antenna

Info

Publication number
JPH04321304A
JPH04321304A JP3116957A JP11695791A JPH04321304A JP H04321304 A JPH04321304 A JP H04321304A JP 3116957 A JP3116957 A JP 3116957A JP 11695791 A JP11695791 A JP 11695791A JP H04321304 A JPH04321304 A JP H04321304A
Authority
JP
Japan
Prior art keywords
phase
vertical
polarized wave
array antenna
antenna
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
JP3116957A
Other languages
Japanese (ja)
Inventor
Yoshihiko Matsuzawa
松澤 佳彦
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
NEC Corp
Original Assignee
NEC Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by NEC Corp filed Critical NEC Corp
Priority to JP3116957A priority Critical patent/JPH04321304A/en
Publication of JPH04321304A publication Critical patent/JPH04321304A/en
Pending legal-status Critical Current

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  • Variable-Direction Aerials And Aerial Arrays (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

PURPOSE:To select a polarized wave optionally by controlling a phase change in each phase shifter. CONSTITUTION:A high frequency signal of an equal amplitude and an equal phase is inputted to input terminals 1a, 1b of adjacent vertical array pairs. The high frequency signal is subject to phase change by a phase depending on the position of the array pair and in the beam scanning direction and inputted to vertical feeding circuits 4a, 4b. The phase shift of the phase shifter in the entire array antenna is controlled by a controller 3. The high frequency signal inputted to the vertical feeding circuits 4a, 4b is distributed to a distribution ratio and phase depending on the vertical pattern of the array antenna and fed to antenna elements 5a, 5b. Since the antenna elements 5a, 5b are directed so that the plane of the polarized wave radiating from the antenna elements 5a, 5b is directed in a direction different by 45 deg. with respect to the vertical direction, a deviation in the polarized wave plane by 90 deg. is caused between both the waves. Thus, the polarized wave is momentarily switched into a vertical, a horizontal and a circularly polarized wave by varying a phase difference between the adjacent array antenna elements as 0,pi, and pi/2.

Description

【発明の詳細な説明】[Detailed description of the invention]

【0001】0001

【産業上の利用分野】本発明はフェーズドアレイアンテ
ナに関し、特に偏波切替を行うレーダー用フェーズドア
レイアンテナの偏波切替装置に関する。
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a phased array antenna, and more particularly to a polarization switching device for a radar phased array antenna that performs polarization switching.

【0002】0002

【従来の技術】従来のフェーズドアレイアンテナとして
、水平方向にビームを走査するフェーズドアレイアンテ
ナを例にとると、図3に示すように入力端子1に入力さ
れる高周波信号の位相をビーム走査方向によって決まる
位相量変化させる移相器2と、移相器2の位相量を制御
する制御器3と、移相器2の出力高周波信号をアレイア
ンテナの垂直パターンによって決まる振幅、移相に分配
する垂直給電回路4と、垂直給電回路4の出力を空間に
輻射するアンテナ素子51 ,52 ,…5n を有す
る垂直アレイを複数個水平方向に並べて構成される。
2. Description of the Related Art Taking as an example a phased array antenna that scans a beam in the horizontal direction as a conventional phased array antenna, as shown in FIG. A phase shifter 2 that changes the determined phase amount, a controller 3 that controls the phase amount of the phase shifter 2, and a vertical controller that distributes the output high frequency signal of the phase shifter 2 into amplitudes and phases determined by the vertical pattern of the array antenna. It is configured by horizontally arranging a plurality of vertical arrays each having a feeder circuit 4 and antenna elements 51 , 52 , . . . 5n that radiate the output of the vertical feeder circuit 4 into space.

【0003】図4は、図3の垂直アレイを複数個円筒状
に並べたシリンドリカルフェーズドアレイアンテナの例
である。この構成では、移相器モジュール20a,20
b,…に入力された高周波信号は、ビーム方向において
同相となるように位相制御され、垂直給電回路21a,
21b,…に給電される。高周波信号は垂直給電回路2
1a,21b…において分配され、アンテナ素子22a
(22a1…22an),22b(22b1…22bn
),…に給電され、アンテナ素子22a,22b,…に
よって決まる固有の偏波で空間に輻射される。
FIG. 4 is an example of a cylindrical phased array antenna in which a plurality of vertical arrays of FIG. 3 are arranged in a cylindrical shape. In this configuration, phase shifter modules 20a, 20
The high frequency signals inputted to the vertical feed circuits 21a, 21b, .
21b, . . . High frequency signal is vertical feed circuit 2
1a, 21b..., antenna element 22a
(22a1...22an), 22b (22b1...22bn
), . . . and is radiated into space with a unique polarization determined by the antenna elements 22a, 22b, .

【0004】0004

【発明が解決しようとする課題】ところで、レーダーに
おいては偏波の違いによって電波伝播特性に違いが生ず
るため、偏波を天候等の状況に合わせて適宜選択するこ
とによりクラッタの抑圧が可能であることが知られてい
る。しかしながら、従来のフェーズドアレイアンテナは
アンテナ素子によって決まる偏波以外の偏波で高周波信
号を輻射することは不可能である。即ち、前記したフェ
ーズドアレイアンテナでは、輻射高周波信号の偏波はア
ンテナ素子22a,22bの偏波によって一義的に決定
され、アンテナ素子22a,22bの偏波が水平ならば
フェーズドアレイアンテナの輻射高周波信号の偏波は水
平、垂直ならば垂直、円ならば円である。このため、ク
ラックの抑圧が難しいという問題がある。本発明の目的
は偏波を任意に切替可能なフェーズドアレイアンテナの
偏波切替装置を提供することにある。
[Problem to be Solved by the Invention] Incidentally, in radar, differences in polarization cause differences in radio wave propagation characteristics, so clutter can be suppressed by appropriately selecting polarization according to weather and other conditions. It is known. However, conventional phased array antennas are unable to radiate high-frequency signals with polarizations other than those determined by the antenna elements. That is, in the phased array antenna described above, the polarization of the radiated high-frequency signal is uniquely determined by the polarization of the antenna elements 22a and 22b, and if the polarization of the antenna elements 22a and 22b is horizontal, the radiated high-frequency signal of the phased array antenna is determined by the polarization of the antenna elements 22a and 22b. If the polarization is horizontal, it is vertical if it is vertical, and it is circular if it is circular. Therefore, there is a problem in that it is difficult to suppress cracks. An object of the present invention is to provide a polarization switching device for a phased array antenna that can arbitrarily switch polarization.

【0005】[0005]

【課題を解決するための手段】本発明のフェーズドアレ
イアンテナの偏波切替装置は、ビーム走査方向に対して
交互に45°偏波面を傾けたアンテナ素子をアレイ状に
配列したアレイアンテナと、アンテナ素子に夫々接続さ
れて任意の値に高周波位相を変化可能な複数個の移相器
と、各移相器の制御を行う制御器を備えている。制御器
は、隣り合うアンテナ素子の位相差を、少なくとも0、
π、π/2に切替可能に構成する。
[Means for Solving the Problems] A polarization switching device for a phased array antenna according to the present invention comprises an array antenna in which antenna elements whose polarization planes are alternately inclined by 45 degrees with respect to the beam scanning direction are arranged in an array, and an antenna. The device includes a plurality of phase shifters connected to each element and capable of changing the high-frequency phase to an arbitrary value, and a controller that controls each phase shifter. The controller sets the phase difference between adjacent antenna elements to at least 0,
It is configured to be switchable between π and π/2.

【0006】[0006]

【作用】本発明によれば、制御器により各アレイアンテ
ナの移相器を制御し、隣り合うアンテナの位相を変化さ
せることで、フェーズドアレイアンテナの偏波を任意に
切替ることが可能となる。
[Operation] According to the present invention, the polarization of the phased array antenna can be arbitrarily switched by controlling the phase shifter of each array antenna using a controller and changing the phase of adjacent antennas. .

【0007】[0007]

【実施例】次に、本発明について図面を参照して説明す
る。図1は本発明を一定の垂直パターンビームを水平方
向に走査するフェーズドアレイアンテナに実施した一実
施例の垂直アレイ対の系統図である。入力端子1aに入
力される高周波信号の位相をビーム走査方向によって決
まる位相量変化させる移相器2aと、移相器2aの出力
高周波信号をアレイアンテナの垂直パターンによって決
まる振幅、移相に分配する垂直給電回路4aと、垂直給
電回路4aの出力を空間に輻射するアンテナ素子5a(
 5a1,5a2,…5an)とで垂直アレイを有する
。又、同様に入力端子1bに入力される高周波信号に対
しても、移相器2b、垂直給電回路4b、アンテナ素子
5b(5b1,5b2,…5bn)で垂直アレイを構成
する。そして、これら垂直アレイを交互に水平方向に並
べて配設し、各移相器2a,2bには移相器における位
相量を制御する制御器3を接続するとともに、隣り合う
垂直アレイの各アンテナ素子5aと5bはその偏波面が
夫々垂直方向に対して45°異なる方向に向けられるよ
うに夫々設定している。尚、水平方向の配列は、ビーム
走査範囲及び水平ビーム幅,サイドローブレベルで決定
される間隔及び数だけ配設することは言うまでもない。
DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, the present invention will be explained with reference to the drawings. FIG. 1 is a system diagram of a vertical array pair in one embodiment in which the present invention is implemented in a phased array antenna that scans a fixed vertical pattern beam in the horizontal direction. A phase shifter 2a changes the phase of the high frequency signal input to the input terminal 1a by a phase amount determined by the beam scanning direction, and divides the output high frequency signal of the phase shifter 2a into amplitudes and phase shifts determined by the vertical pattern of the array antenna. A vertical feeding circuit 4a and an antenna element 5a (which radiates the output of the vertical feeding circuit 4a into space)
5a1, 5a2,...5an) to form a vertical array. Similarly, for a high-frequency signal input to the input terminal 1b, a vertical array is configured by a phase shifter 2b, a vertical feeding circuit 4b, and an antenna element 5b (5b1, 5b2, . . . 5bn). These vertical arrays are arranged alternately in the horizontal direction, and a controller 3 for controlling the phase amount in the phase shifter is connected to each phase shifter 2a, 2b, and each antenna element of the adjacent vertical array is connected to each phase shifter 2a, 2b. 5a and 5b are set so that their planes of polarization are oriented in directions different from each other by 45 degrees with respect to the vertical direction. It goes without saying that the number of horizontal arrays is determined by the interval and number determined by the beam scanning range, horizontal beam width, and side lobe level.

【0008】この構成によれば、隣り合う垂直アレイ対
の入力端1a,1bに等振幅,等位相の高周波信号を入
力する。高周波信号は移相器2a,2bによりアレイ対
の位置とビーム走査方向によって決まる位相量だけの位
相変化を受け垂直給電回路4a,4bに出力される。ア
レイアンテナ全体の移相器位相量の制御は制御器3によ
って行われる。垂直給電回路4a,4bに入力された高
周波信号はアレイアンテナの垂直パターンによって決ま
る分配比、位相に分配されアンテナ素子5a,5bに給
電される。アンテナ素子5aとアンテナ素子5bは互い
に輻射する偏波面が垂直方向に対して45°異なる方向
に向けているため、両者の間には90°の偏波面のずれ
が生じていることになる。
According to this configuration, high frequency signals of equal amplitude and equal phase are input to the input ends 1a and 1b of the adjacent vertical array pair. The high frequency signals undergo phase changes by phase shifters 2a, 2b by a phase amount determined by the position of the array pair and the beam scanning direction, and are output to vertical feed circuits 4a, 4b. A controller 3 controls the phase shifter phase amount of the entire array antenna. The high frequency signals input to the vertical feed circuits 4a, 4b are distributed at a distribution ratio and phase determined by the vertical pattern of the array antenna, and then fed to the antenna elements 5a, 5b. Since the antenna element 5a and the antenna element 5b have their radiating polarization planes oriented in directions that differ by 45° from the vertical direction, a 90° deviation in polarization plane occurs between them.

【0009】したがって、アレイアンテナ水平方向をx
軸、垂直方向をy軸とするとアンテナ素子5aより輻射
される高周波信号は、 y=Ksin ωt x=Ksin ωt で表される。但し、K=A/√2であり、Aは高周波信
号の振幅、ωは角周波数である。同様にアンテナ素5b
より輻射される高周波信号は、 y=Ksin(ωt+θ) x=−Ksin(ωt+θ) で表される。但し、θはアンテナ素子5aとアンテナ素
子5bに給電される高周波信号の位相差である。位相差
θは移相器2a,2bにより与えられ、制御器3により
制御を行う。
Therefore, the array antenna horizontal direction is x
When the vertical direction is the y-axis, the high frequency signal radiated from the antenna element 5a is expressed as y=Ksin ωt x=Ksin ωt. However, K=A/√2, A is the amplitude of the high frequency signal, and ω is the angular frequency. Similarly, antenna element 5b
The high frequency signal that is radiated is expressed as follows: y=Ksin(ωt+θ) x=−Ksin(ωt+θ). However, θ is the phase difference between the high frequency signals fed to the antenna element 5a and the antenna element 5b. The phase difference θ is given by phase shifters 2a and 2b, and controlled by a controller 3.

【0010】これにより、位相差θが0の場合、アンテ
ナ素子5aとアンテナ素子5bによる合成輻射信号は充
分遠方において、 y=2Ksin ωt x=0 と表され、偏波は垂直となる。又、位相差θがπの場合
、アンテナ素子5aとアンテナ素子5bの合成輻射信号
は、充分遠方において、 y=Ksin ωt+Ksin(ωt+π)=Ksin
 ωt−Ksin ωt=0 x=Ksin ωt−Ksin(ωt+π)=Ksin
 ωt+Ksin ωt=2Ksin ωt と表され、偏波は水平となる。
[0010] Accordingly, when the phase difference θ is 0, the combined radiation signal from the antenna elements 5a and 5b is expressed as y=2Ksin ωt x=0 at a sufficiently far distance, and the polarization is vertical. Furthermore, when the phase difference θ is π, the combined radiation signal of the antenna elements 5a and 5b is expressed as follows at a sufficiently far distance: y=Ksin ωt+Ksin (ωt+π)=Ksin
ωt−Ksin ωt=0 x=Ksin ωt−Ksin(ωt+π)=Ksin
It is expressed as ωt+Ksin ωt=2Ksin ωt, and the polarization is horizontal.

【0011】更に、位相差θがπ/2の場合、アンテナ
素子5aとアンテナ素子5bの合成輻射信号は充分遠方
において、 y=Ksin ωt+Ksin(ωt+π/2)=Ks
in ωt−Kcos ωt x=Ksin ωt−Ksin(ωt+π/2)=Ks
in ωt+Kcos ωt y2 +x2 =K2 〔sin2ωt−2sin ω
t・cos ωt+cos2ωt+sin2ωt+2c
os ωt・sin ωt+cos2ωt〕=K2 〔
2(sin2ωt+cos2ωt)〕=2K2 =A2
  と表され、偏波は円となる。この場合、アンテナ素子5
aに給電される位相よりアンテナ素子5bに給電される
位相がπ/2進んでいる場合は右旋円偏波となり、π/
2遅れている場合は左旋円偏波となる。同様に、垂直ア
レイ対の輻射高周波の偏波についても移相器2a,2b
により垂直アレイ対間の位相差を与えることにより、機
械的動作を必要としないので瞬時に、電気的に垂直,水
平,右旋円,左旋円と変化させることができる。
Furthermore, when the phase difference θ is π/2, the combined radiation signal of the antenna elements 5a and 5b is expressed as follows at a sufficiently far distance: y=Ksin ωt+Ksin(ωt+π/2)=Ks
in ωt-Kcos ωt x=Ksin ωt-Ksin(ωt+π/2)=Ks
in ωt+Kcos ωt y2 +x2 =K2 [sin2ωt-2sin ω
t・cos ωt+cos2ωt+sin2ωt+2c
os ωt・sin ωt+cos2ωt]=K2 [
2(sin2ωt+cos2ωt)]=2K2=A2
It is expressed as , and the polarization is circular. In this case, antenna element 5
If the phase fed to antenna element 5b is π/2 ahead of the phase fed to antenna element a, it becomes a right-handed circularly polarized wave, and the phase fed to antenna element 5b is π/2.
If it is delayed by 2, it becomes left-handed circularly polarized wave. Similarly, for the polarization of the radiated high frequency waves of the vertical array pair, the phase shifters 2a and 2b
By providing a phase difference between a pair of vertical arrays, it is possible to instantly and electrically change from vertical to horizontal, right-handed circular, and left-handed circular because no mechanical operation is required.

【0012】図2は本発明を一定の垂直パターン放射特
性を有するシリンドリカルフェーズドアレイアンテナに
実施した実施例である。RFモジュール10a,10b
,…で所望振幅値まで増幅された高周波信号は、移相器
モジュール11a,11b,…で所望の位相量の変化を
受け、垂直給電回路11a,11b…で分配され、アン
テナ素子12a(12a1,12a2,…12an),
12b(12b1,12b2,…12bn),…に給電
される。アンテナ素子12a(12a1,12a2,…
12an),12b(12b1,12b2,…12bn
),…は垂直給電回路上に配列され、アンテナ素子12
aとアンテナ素子12bでは偏波面が90°異なりすべ
てのアンテナ素子の偏波面はアレイアンテナの軸線に対
して+45°又は−45°傾いている。隣り合う垂直ア
レイが垂直アレイ対を作るが、ビーム走査方向が垂直ア
レイ間隔に当たる角度だけ変化する毎に垂直アレイ対の
対も1垂直アレイ分シフトする。また、円偏波輻射にお
いては、対となる垂直アレイが変わる毎に、左右の位相
関係の極性を変えて、右旋または左旋の偏波の回転方向
を維持する。
FIG. 2 shows an embodiment in which the present invention is implemented in a cylindrical phased array antenna having a fixed vertical pattern radiation characteristic. RF module 10a, 10b
The high frequency signal amplified to a desired amplitude value by the phase shifter modules 11a, 11b, . 12a2,...12an),
12b (12b1, 12b2, . . . 12bn), . Antenna element 12a (12a1, 12a2,...
12an), 12b (12b1, 12b2,...12bn
), ... are arranged on the vertical feeding circuit, and the antenna elements 12
The polarization planes of antenna element a and antenna element 12b differ by 90°, and the polarization planes of all antenna elements are tilted by +45° or −45° with respect to the axis of the array antenna. Adjacent vertical arrays form a vertical array pair, and each time the beam scanning direction changes by an angle corresponding to the vertical array spacing, the pair of vertical arrays also shifts by one vertical array. In addition, in circularly polarized radiation, each time the pair of vertical arrays changes, the polarity of the left and right phase relationship is changed to maintain the right-handed or left-handed rotation direction of the polarized waves.

【0013】[0013]

【発明の効果】以上説明したように本発明は、アンテナ
素子をビーム走査方向に交互に45°傾斜させ、制御器
によって制御される移相器の位相変化量を、隣り合うア
ンテナ素子間で特定の位相差となるように変化させるこ
とで、フェーズドアレイアンテナの輻射高周波信号の偏
波を垂直、水平、右旋円、左旋円と瞬時に変化させるこ
とができ、レーダーに適用して好ましい結果を得ること
ができる効果がある。
As explained above, the present invention tilts the antenna elements alternately at 45 degrees in the beam scanning direction, and specifies the amount of phase change of the phase shifter controlled by the controller between adjacent antenna elements. By changing the phase difference, the polarization of the radiated high-frequency signal of the phased array antenna can be instantly changed from vertical to horizontal to right-handed circular to left-handed circular. There are effects that can be obtained.

【図面の簡単な説明】[Brief explanation of drawings]

【図1】本発明のフェーズドアレイアンテナにかかる垂
直アレイ対の系統図である。
FIG. 1 is a system diagram of a vertical array pair according to a phased array antenna of the present invention.

【図2】本発明をシリンドリカルフェーズドアレイアン
テナに適用した構成の外観図である。
FIG. 2 is an external view of a configuration in which the present invention is applied to a cylindrical phased array antenna.

【図3】従来のフェーズドアレイアンテナの垂直アレイ
の系統図である。
FIG. 3 is a diagram of a vertical array of a conventional phased array antenna.

【図4】従来のシンリドリカルフェーズドアレイアンテ
ナの外観図である。
FIG. 4 is an external view of a conventional cylindrical phased array antenna.

【符号の説明】[Explanation of symbols]

1,1a,1b  入力端 2,2a,2b  移相器 3  制御器 4,4a,4b  垂直給電回路 5a,5b  アンテナ素子 1, 1a, 1b Input end 2, 2a, 2b Phase shifter 3 Controller 4, 4a, 4b Vertical power supply circuit 5a, 5b Antenna element

Claims (2)

【特許請求の範囲】[Claims] 【請求項1】  ビーム走査方向に対して交互に45°
偏波面を傾けたアンテナ素子をアレイ状に配列したアレ
イアンテナと、前記アンテナ素子に夫々接続されて任意
の値に高周波位相を変化可能な複数個の移相器と、前記
各移相器の制御を行う制御器を備えることを特徴とする
フェーズドアレイアンテナの偏波切替装置。
Claim 1: Alternately 45° with respect to the beam scanning direction.
An array antenna in which antenna elements with tilted polarization planes are arranged in an array, a plurality of phase shifters connected to each of the antenna elements and capable of changing a high frequency phase to an arbitrary value, and control of each of the phase shifters. What is claimed is: 1. A polarization switching device for a phased array antenna, comprising a controller that performs the following.
【請求項2】  制御器は、隣り合うアレイアンテナの
位相差を0、π、π/2に設定できるように各移相器を
制御可能に構成してなる請求項1のフェーズドアレイア
ンテナの偏波切替装置。
2. The polarization of the phased array antenna according to claim 1, wherein the controller is configured to control each phase shifter so that the phase difference between adjacent array antennas can be set to 0, π, and π/2. Wave switching device.
JP3116957A 1991-04-20 1991-04-20 Polarized wave changeover device for phased array antenna Pending JPH04321304A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP3116957A JPH04321304A (en) 1991-04-20 1991-04-20 Polarized wave changeover device for phased array antenna

Applications Claiming Priority (1)

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JP3116957A JPH04321304A (en) 1991-04-20 1991-04-20 Polarized wave changeover device for phased array antenna

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JPH04321304A true JPH04321304A (en) 1992-11-11

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH06230109A (en) * 1993-02-03 1994-08-19 Mitsubishi Electric Corp Radar antenna system
CN109782285A (en) * 2019-03-15 2019-05-21 中国科学院电子学研究所 A kind of single channel full-polarization SAR implementation method based on frequency transformation

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS59110205A (en) * 1982-12-15 1984-06-26 Mitsubishi Electric Corp Array antenna device
JPS61112404A (en) * 1984-11-06 1986-05-30 Mitsubishi Electric Corp Phased array antenna system
JPH033505A (en) * 1989-05-31 1991-01-09 Nec Corp Planer slot array antenna

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS59110205A (en) * 1982-12-15 1984-06-26 Mitsubishi Electric Corp Array antenna device
JPS61112404A (en) * 1984-11-06 1986-05-30 Mitsubishi Electric Corp Phased array antenna system
JPH033505A (en) * 1989-05-31 1991-01-09 Nec Corp Planer slot array antenna

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH06230109A (en) * 1993-02-03 1994-08-19 Mitsubishi Electric Corp Radar antenna system
CN109782285A (en) * 2019-03-15 2019-05-21 中国科学院电子学研究所 A kind of single channel full-polarization SAR implementation method based on frequency transformation
CN109782285B (en) * 2019-03-15 2021-06-04 中国科学院电子学研究所 Single-channel full-polarization SAR realization method based on frequency transformation

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