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CN108051783A - Wide band net echo simulator emits multichannel delay compensation method and system - Google Patents

Wide band net echo simulator emits multichannel delay compensation method and system Download PDF

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CN108051783A
CN108051783A CN201711281434.3A CN201711281434A CN108051783A CN 108051783 A CN108051783 A CN 108051783A CN 201711281434 A CN201711281434 A CN 201711281434A CN 108051783 A CN108051783 A CN 108051783A
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舒汀
詹健
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Shanghai Jiao Tong University
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    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The present invention relates to a kind of wide band net echo simulator transmitting multichannel delay compensation method and systems, belong to electronic technology field.Employ the wide band net echo simulator transmitting multichannel delay compensation method and system of the present invention, due to its using based on the variable fraction filtering wave by prolonging time device that Taylor expansion obtains to broadband signal carry out time-domain filtering, realize the delay of high-precision fraction, it realizes that high-precision integer is delayed by shift register again, and then realizes the multichannel transmission channel compensation of delay of wide band net echo simulator.The program is based on FPGA accurately timing control, fast parallel processing capacity, combined digital signal treatment technology, can effectively reduce that system is relatively low for hardware requirement, and compensation precision is high, and especially suitable for the compensation of delay of bandwidth varying scene.

Description

宽带相控阵雷达回波模拟器发射多通道延时补偿方法及系统Multi-channel delay compensation method and system for wideband phased array radar echo simulator launch

技术领域technical field

本发明涉及电子技术领域,特别涉及雷达模拟仿真技术领域,具体是指一种宽带相控阵雷达回波模拟器发射多通道延时补偿方法及系统。The present invention relates to the field of electronic technology, in particular to the field of radar simulation technology, in particular to a multi-channel delay compensation method and system for wideband phased array radar echo simulator emission.

背景技术Background technique

采用宽带信号的相控阵雷达可获得很高的距离分辨率,将广泛用于下一代多功能雷达系统中。在宽带相控阵雷达系统和各分系统的研制和调试的过程中,传统的雷达模拟器无法满足宽带数字阵列雷达大带宽、多通道、多工作模式等测试要求,因此需要研制专用的宽带数字阵列雷达模拟器。宽带相控阵在做宽角扫描时,仅通过相位控制不能有效地形成波束,进行精确的波束指向控制,必须在阵元或子阵间使用精确的时延补偿。为此需要解决多路宽带信号高精度延时控制的问题。Phased array radar using broadband signals can obtain very high range resolution and will be widely used in the next generation of multifunctional radar systems. In the process of developing and debugging the broadband phased array radar system and each subsystem, the traditional radar simulator cannot meet the test requirements of wideband digital array radar such as large bandwidth, multi-channel, and multi-working mode, so it is necessary to develop a dedicated broadband digital array radar simulator. Array radar simulator. When the wide-band phased array is used for wide-angle scanning, the beam cannot be effectively formed only by phase control, and precise beam pointing control must use precise time delay compensation between array elements or sub-arrays. Therefore, it is necessary to solve the problem of high-precision delay control of multi-channel broadband signals.

传统的宽带相控阵雷达模拟器采用模拟延迟线的思路来控制单元间的信号延时,即采用M位状态的数字延迟线,最小的延时量为一个波长,最大的延时量为2M个波长,数字延时线的延时精度影响相位的一致性,若延时精度为Δτ,则中心频率相位误差为:The traditional broadband phased array radar simulator uses the idea of analog delay line to control the signal delay between units, that is, the digital delay line with M bit state, the minimum delay is one wavelength, and the maximum delay is 2 For M wavelengths, the delay accuracy of the digital delay line affects the consistency of the phase. If the delay accuracy is Δτ, the center frequency phase error is:

其中,T为信号周期,宽带信号工作时,按中心频率计算延时,边频相位误差Δp为Among them, T is the signal period. When the broadband signal is working, the delay is calculated according to the center frequency, and the side frequency phase error Δp is

Δp=360°×Δτ×ΔfΔp=360°×Δτ×Δf

式中,Δf为中心频率与变频之间的频率差,因此,数字延迟线的延时精度不仅影响中心频率的相位误差,更重要的是影响阵列中边频信号的相位误差,延时精度越高,相位误差越小。采用M位状态的数字延迟线的延时精度不能满足宽带相控阵雷达模拟器数字波束形成的相位精度要求。In the formula, Δf is the frequency difference between the center frequency and the variable frequency. Therefore, the delay accuracy of the digital delay line not only affects the phase error of the center frequency, but more importantly, affects the phase error of the side frequency signal in the array. The higher the value, the smaller the phase error. The delay accuracy of the digital delay line using the M-bit state cannot meet the phase accuracy requirements of the digital beamforming of the broadband phased array radar simulator.

传统的分数延时滤波器使用加窗法实现,但加窗法对不同的延时需要产生不同的滤波器系数,而波束形成所需的时延随着雷达方向图指向的改变而改变,使用加窗法则需要存储大规模的滤波器系数,这显然在硬件实现时是有很大难度的。The traditional fractional delay filter is realized by windowing method, but the windowing method needs to generate different filter coefficients for different delays, and the delay required for beamforming changes with the change of the radar pattern pointing, using The windowing method needs to store large-scale filter coefficients, which is obviously very difficult to implement in hardware.

进而采用基于Farrow结构实现的可变分数延时滤波器可有效规避该问题,但是Farrow结构随着滤波器阶数的增加需要大量的乘法器和加法器,且滤波器系数的计算量大,难度高。Furthermore, the variable fractional delay filter based on the Farrow structure can effectively avoid this problem, but the Farrow structure requires a large number of multipliers and adders as the order of the filter increases, and the calculation of the filter coefficients is large and difficult. high.

因此,如何提供一种对于硬件要求较低,补偿精度高,且适用于可变带宽场景的补偿方法成为本领域亟待解决的问题。Therefore, how to provide a compensation method that requires less hardware, has high compensation accuracy, and is applicable to variable bandwidth scenarios has become an urgent problem to be solved in this field.

发明内容Contents of the invention

本发明的目的是克服了上述现有技术中的缺点,提供对于硬件要求较低,补偿精度高,且适用于可变带宽场景的宽带相控阵雷达回波模拟器发射多通道延时补偿方法及系统。The purpose of the present invention is to overcome the above-mentioned shortcomings in the prior art, and provide a multi-channel delay compensation method for launching a broadband phased array radar echo simulator that has low hardware requirements, high compensation accuracy, and is suitable for variable bandwidth scenarios. and system.

为了实现上述的目的,本发明的宽带相控阵雷达回波模拟器发射多通道延时补偿方法包括以下步骤:In order to achieve the above-mentioned purpose, the broadband phased array radar echo simulator of the present invention launches multi-channel delay compensation method comprising the following steps:

(1)根据天线阵列的几何结构确定雷达每个单元相对于参考单元的延时量,并将该延时量分解为整数延时量和分数延时量;(1) Determine the delay of each unit of the radar relative to the reference unit according to the geometric structure of the antenna array, and decompose the delay into integer delay and fractional delay;

(2)利用一基于泰勒展开法获得的可变分数延时滤波器并根据所述的分数延时量对宽带信号进行时域滤波,实现信号的高精度分数延时;(2) Utilize a variable fractional delay filter obtained based on the Taylor expansion method and carry out time-domain filtering to the broadband signal according to the fractional delay amount, so as to realize the high-precision fractional delay of the signal;

(3)利用整数延时器并根据所述的整数延时量实现信号的高精度整数延时;(3) Utilize the integer delayer and realize the high-precision integer delay of the signal according to the integer delay amount;

(4)将所述的可变分数延时滤波器和所述的整数延时器级联,基于所述的高精度分数延时和所述的高精度整数延时实现多通道高精度数字延时。(4) Cascading the variable fractional delay filter and the integer delayer, realizing multi-channel high-precision digital delay based on the high-precision fractional delay and the high-precision integer delay Time.

该宽带相控阵雷达回波模拟器发射多通道延时补偿方法中,步骤(2)中所述的基于泰勒展开法获得的可变分数延时滤波器具体为:In this wideband phased array radar echo simulator launch multi-channel delay compensation method, the variable fractional delay filter obtained based on the Taylor expansion method described in step (2) is specifically:

所述可变分数延时滤波器的理想冲击响应为:The ideal impulse response of the variable fractional delay filter is:

h(n)=sinc(n-D)h(n)=sinc(n-D)

式中,D表示延时量;In the formula, D represents the amount of delay;

所述可变分数延时滤波器的频率响应及其泰勒展开式为:The frequency response of the variable fractional delay filter and its Taylor expansion are:

式中,D表示延时量,z-1表示延时单元,N表示滤波器的阶数,滤波器为奇数阶滤波器,d为所述的分数延时量。In the formula, D represents the amount of delay, z -1 represents the delay unit, N represents the order of the filter, and the filter is an odd-order filter, d is the fractional delay amount.

该宽带相控阵雷达回波模拟器发射多通道延时补偿方法中,所述的步骤(3)具体为:In this broadband phased array radar echo simulator launch multi-channel delay compensation method, described step (3) is specifically:

利用信号的采样时钟驱动一移位寄存器,将待延时信号作为该移位寄存器的数据输入,根据所述的整数延时量配置所述的移位寄存器的级数,该移位寄存器的输出信号为高精度整数延时后的信号。Utilize the sampling clock of the signal to drive a shift register, use the signal to be delayed as the data input of the shift register, configure the stages of the shift register according to the integer delay amount, and the output of the shift register The signal is a signal after a high-precision integer delay.

该宽带相控阵雷达回波模拟器发射多通道延时补偿方法中,所述的延迟量D位于理想脉冲响应的中间部分,且所述的滤波器的阶数N给定,用以通过实现理想分数滤波器的最佳逼近,实现最小误差的延时补偿。In this wideband phased array radar echo simulator launch multi-channel delay compensation method, the delay amount D is located in the middle part of the ideal impulse response, and the order N of the filter is given to achieve The best approximation of the ideal fractional filter to achieve delay compensation with minimal error.

该宽带相控阵雷达回波模拟器发射多通道延时补偿方法中,所述的滤波器的系数仅与该滤波器的阶数N及所述的延迟量D相关,该滤波器的阶数N给定时,通过改变所述的延迟量D实现不同的延时。In this wideband phased array radar echo simulator launching multi-channel delay compensation method, the coefficient of the filter is only related to the order N of the filter and the delay D, and the order of the filter When N is given, different delays can be realized by changing the delay amount D.

本发明还提供一种宽带相控阵雷达回波模拟器发射多通道延时补偿系统,该系统包括:延时量分解模块、可变分数延时滤波器、整数延时器和级联模块。The invention also provides a broadband phased array radar echo simulator launch multi-channel delay compensation system, the system includes: a delay amount decomposition module, a variable fractional delay filter, an integer delayer and a cascade module.

其中,延时量分解模块,用以根据天线阵列的几何结构确定雷达每个单元相对于参考单元的延时量,并将该延时量分解为整数延时量和分数延时量;Wherein, the delay amount decomposition module is used to determine the delay amount of each radar unit relative to the reference unit according to the geometric structure of the antenna array, and decompose the delay amount into an integer delay amount and a fractional delay amount;

可变分数延时滤波器,基于泰勒展开法获得,该可变分数延时滤波器根据所述的分数延时量对宽带信号进行时域滤波,实现信号的高精度分数延时;The variable fractional delay filter is obtained based on the Taylor expansion method, and the variable fractional delay filter performs time-domain filtering on the broadband signal according to the fractional delay amount to realize high-precision fractional delay of the signal;

整数延时器,用以根据所述的整数延时量实现信号的高精度整数延时;Integer delay device, in order to realize the high-precision integer delay of signal according to described integer delay amount;

级联模块,用以将所述的可变分数延时滤波器和所述的整数延时器级联,基于所述的高精度分数延时和所述的高精度整数延时实现多通道高精度数字延时。The cascading module is used to cascade the variable fractional delay filter and the integer delayer, and realize multi-channel high-speed delay based on the high-precision fractional delay and the high-precision integer delay Precision digital delay.

该宽带相控阵雷达回波模拟器发射多通道延时补偿系统中,所述的基于泰勒展开法获得的可变分数延时滤波器具体为:In the broadband phased array radar echo simulator launch multi-channel delay compensation system, the variable fractional delay filter obtained based on the Taylor expansion method is specifically:

所述可变分数延时滤波器的理想冲击响应为:The ideal impulse response of the variable fractional delay filter is:

h(n)=sinc(n-D)h(n)=sinc(n-D)

式中,D表示延时量;In the formula, D represents the amount of delay;

所述可变分数延时滤波器的频率响应及其泰勒展开式为:The frequency response of the variable fractional delay filter and its Taylor expansion are:

式中,D表示延时量,z-1表示延时单元,N表示滤波器的阶数,滤波器为奇数阶滤波器,d为所述的分数延时量。In the formula, D represents the amount of delay, z -1 represents the delay unit, N represents the order of the filter, and the filter is an odd-order filter, d is the fractional delay amount.

该宽带相控阵雷达回波模拟器发射多通道延时补偿系统中,所述的整数延时器具体为:利用信号的采样时钟驱动一移位寄存器,将待延时信号作为该移位寄存器的数据输入,根据所述的整数延时量配置所述的移位寄存器的级数,该移位寄存器的输出信号为高精度整数延时后的信号。In the broadband phased array radar echo simulator launching multi-channel delay compensation system, the integer delayer is specifically: using the sampling clock of the signal to drive a shift register, and using the signal to be delayed as the shift register The data input, the number of stages of the shift register is configured according to the integer delay amount, and the output signal of the shift register is a signal after a high-precision integer delay.

该宽带相控阵雷达回波模拟器发射多通道延时补偿系统中,所述的延迟量D位于理想脉冲响应的中间部分,且所述的滤波器的阶数N给定,用以通过实现理想分数滤波器的最佳逼近,实现最小误差的延时补偿。In the multi-channel delay compensation system launched by the broadband phased array radar echo simulator, the delay D is located in the middle part of the ideal impulse response, and the order N of the filter is given to achieve The best approximation of the ideal fractional filter to achieve delay compensation with minimal error.

该宽带相控阵雷达回波模拟器发射多通道延时补偿系统中,所述的滤波器的系数仅与该滤波器的阶数N及所述的延迟量D相关,该滤波器的阶数N给定时,通过改变所述的延迟量D实现不同的延时。In the multi-channel delay compensation system launched by the wideband phased array radar echo simulator, the coefficient of the filter is only related to the order N of the filter and the delay D, and the order of the filter When N is given, different delays can be realized by changing the delay amount D.

采用了该发明的宽带相控阵雷达回波模拟器发射多通道延时补偿方法及系统,由于其利用基于泰勒展开法获得的可变分数延时滤波器对宽带信号进行时域滤波,实现高精度分数延时,再通过移位寄存器实现高精度整数延时,进而实现宽带相控阵雷达回波模拟器的多路发射通道延时补偿。该方案基于FPGA精准的时序控制、快速并行处理能力,结合数字信号处理技术,可以有效降低系统对于硬件要求较低,补偿精度高,且特别适用于可变带宽场景的延时补偿。The method and system for transmitting multi-channel delay compensation of the wideband phased array radar echo simulator of the invention is adopted, because it uses the variable fractional delay filter obtained based on the Taylor expansion method to filter the wideband signal in the time domain, realizing high Accurate fractional delay, and then realize high-precision integer delay through the shift register, and then realize the multi-channel transmit channel delay compensation of the wideband phased array radar echo simulator. Based on FPGA's precise timing control and fast parallel processing capabilities, combined with digital signal processing technology, this solution can effectively reduce the system's low hardware requirements and high compensation accuracy, and is especially suitable for delay compensation in variable bandwidth scenarios.

附图说明Description of drawings

图1为本发明的宽带相控阵雷达回波模拟器发射多通道延时补偿方法的步骤流程图。Fig. 1 is a flow chart of the steps of the multi-channel delay compensation method for the broadband phased array radar echo simulator of the present invention.

图2为本发明的宽带相控阵雷达回波模拟器发射多通道延时补偿系统在模拟系统中的结构框图。Fig. 2 is a structural block diagram of the broadband phased array radar echo simulator launch multi-channel delay compensation system in the simulation system of the present invention.

图3为本发明仿真阵列几何模型原理图。Fig. 3 is a schematic diagram of the simulation array geometry model of the present invention.

图4为本发明的可变分数延时滤波器结构原理图。Fig. 4 is a structural principle diagram of the variable fractional delay filter of the present invention.

图5为本发明的可变分数延时滤波器幅度响应曲线图。Fig. 5 is a curve diagram of the magnitude response of the variable fractional delay filter of the present invention.

图6为本发明的可变分数延时滤波器相位延时响应曲线图。Fig. 6 is a graph showing the phase delay response curve of the variable fractional delay filter of the present invention.

图7为本发明的延时控制方法预设延时的延时信号示波器实测截图。Fig. 7 is the preset delay of the delay control method of the present invention Screenshots of actual time-delay signal oscilloscope measurements.

图8为本发明的延时控制方法预设延时的延时信号示波器实测截图。Fig. 8 is the preset delay of the delay control method of the present invention Screenshots of actual time-delay signal oscilloscope measurements.

图9为传统移相实现宽带信号发射波束形成仿真图。FIG. 9 is a simulation diagram of traditional phase shifting to realize broadband signal transmission beamforming.

图10为本发明中的宽带信号发射波束形成仿真图。FIG. 10 is a simulation diagram of broadband signal transmission beamforming in the present invention.

具体实施方式Detailed ways

为了能够更清楚地理解本发明的技术内容,特举以下实施例详细说明。In order to understand the technical content of the present invention more clearly, the following examples are given in detail.

请参阅图1所示,为本发明的宽带相控阵雷达回波模拟器发射多通道延时补偿方法的步骤流程图。Please refer to FIG. 1 , which is a flow chart of the steps of the multi-channel delay compensation method for the broadband phased array radar echo simulator of the present invention.

在一种实施方式中,该宽带相控阵雷达回波模拟器发射多通道延时补偿方法,如图1及图2所示,包括以下步骤:In one embodiment, the broadband phased array radar echo simulator transmits a multi-channel delay compensation method, as shown in Figure 1 and Figure 2, comprising the following steps:

(1)根据天线阵列的几何结构确定雷达每个单元相对于参考单元的延时量,并将该延时量分解为整数延时量和分数延时量;(1) Determine the delay of each unit of the radar relative to the reference unit according to the geometric structure of the antenna array, and decompose the delay into integer delay and fractional delay;

(2)利用一基于泰勒展开法获得的可变分数延时滤波器并根据所述的分数延时量对宽带信号进行时域滤波,实现信号的高精度分数延时;(2) Utilize a variable fractional delay filter obtained based on the Taylor expansion method and carry out time-domain filtering to the broadband signal according to the fractional delay amount, so as to realize the high-precision fractional delay of the signal;

(3)利用整数延时器并根据所述的整数延时量实现信号的高精度整数延时;(3) Utilize the integer delayer and realize the high-precision integer delay of the signal according to the integer delay amount;

(4)将所述的可变分数延时滤波器和所述的整数延时器级联,基于所述的高精度分数延时和所述的高精度整数延时实现多通道高精度数字延时。(4) Cascading the variable fractional delay filter and the integer delayer, realizing multi-channel high-precision digital delay based on the high-precision fractional delay and the high-precision integer delay Time.

实现上述实施方式所述方法的宽带相控阵雷达回波模拟器发射多通道延时补偿系统包括:延时量分解模块、可变分数延时滤波器、整数延时器和级联模块。The broadband phased array radar echo simulator launch multi-channel delay compensation system implementing the method described in the above embodiment includes: a delay amount decomposition module, a variable fractional delay filter, an integer delayer and a cascade module.

其中,延时量分解模块,用以根据天线阵列的几何结构确定雷达每个单元相对于参考单元的延时量,并将该延时量分解为整数延时量和分数延时量;Wherein, the delay amount decomposition module is used to determine the delay amount of each radar unit relative to the reference unit according to the geometric structure of the antenna array, and decompose the delay amount into an integer delay amount and a fractional delay amount;

可变分数延时滤波器,基于泰勒展开法获得,该可变分数延时滤波器根据所述的分数延时量对宽带信号进行时域滤波,实现信号的高精度分数延时;The variable fractional delay filter is obtained based on the Taylor expansion method, and the variable fractional delay filter performs time-domain filtering on the broadband signal according to the fractional delay amount to realize high-precision fractional delay of the signal;

整数延时器,用以根据所述的整数延时量实现信号的高精度整数延时;Integer delay device, in order to realize the high-precision integer delay of signal according to described integer delay amount;

级联模块,用以将所述的可变分数延时滤波器和所述的整数延时器级联,基于所述的高精度分数延时和所述的高精度整数延时实现多通道高精度数字延时。The cascading module is used to cascade the variable fractional delay filter and the integer delayer, and realize multi-channel high-speed delay based on the high-precision fractional delay and the high-precision integer delay Precision digital delay.

在优选的实施方式中,步骤(2)中所述的基于泰勒展开法获得的可变分数延时滤波器具体为:In a preferred embodiment, the variable fraction delay filter obtained based on the Taylor expansion method described in step (2) is specifically:

所述可变分数延时滤波器的理想冲击响应为:The ideal impulse response of the variable fractional delay filter is:

h(n)=sinc(n-D)h(n)=sinc(n-D)

式中,D表示延时量;In the formula, D represents the amount of delay;

所述可变分数延时滤波器的频率响应及其泰勒展开式为:The frequency response of the variable fractional delay filter and its Taylor expansion are:

式中,D表示延时量,z-1表示延时单元,N表示滤波器的阶数,滤波器为奇数阶滤波器,d为所述的分数延时量。In the formula, D represents the amount of delay, z -1 represents the delay unit, N represents the order of the filter, and the filter is an odd-order filter, d is the fractional delay amount.

且所述的步骤(3)具体为:And described step (3) is specifically:

利用信号的采样时钟驱动一移位寄存器,将待延时信号作为该移位寄存器的数据输入,根据所述的整数延时量配置所述的移位寄存器的级数,该移位寄存器的输出信号为高精度整数延时后的信号。Utilize the sampling clock of the signal to drive a shift register, use the signal to be delayed as the data input of the shift register, configure the stages of the shift register according to the integer delay amount, and the output of the shift register The signal is a signal after a high-precision integer delay.

在更优选的实施方式中,所述的延迟量D位于理想脉冲响应的中间部分,且所述的滤波器的阶数N给定,用以通过实现理想分数滤波器的最佳逼近,实现最小误差的延时补偿。所述的滤波器的系数仅与该滤波器的阶数N及所述的延迟量D相关,该滤波器的阶数N给定时,通过改变所述的延迟量D实现不同的延时。In a more preferred embodiment, the delay D is located in the middle of the ideal impulse response, and the order N of the filter is given to realize the minimum by realizing the best approximation of the ideal fractional filter Error delay compensation. The coefficients of the filter are only related to the order N of the filter and the delay D. When the order N of the filter is given, different delays can be realized by changing the delay D.

在实际应用中,本发明的宽带相控阵雷达回波模拟器发射多通道延时补偿方法可以包括以下步骤:In practical applications, the wideband phased array radar echo simulator of the present invention transmits a multi-channel delay compensation method may include the following steps:

步骤A、根据天线阵列的几何结构确定雷达每个单元相对于参考单元的延时量,并分解为整数延时量和分数延时量;Step A, determine the delay of each unit of the radar relative to the reference unit according to the geometric structure of the antenna array, and decompose it into an integer delay and a fractional delay;

参照图3所示,以0号阵元为参考阵元,阵列单元信号的导向矢量为:Referring to Figure 3, with array element 0 as the reference array element, the steering vector of the array unit signal is:

式中,L为阵元间距,θB为回波入射方向与阵面垂线间的夹角,阵元个数为N,λ为信号波长。In the formula, L is the distance between the array elements, θ B is the angle between the incident direction of the echo and the vertical line of the array, the number of array elements is N, and λ is the signal wavelength.

相邻阵元之间的延时差为:The delay difference between adjacent array elements is:

式中,L为阵元间距,θB为回波入射方向与阵面垂线间的夹角,c为光速。In the formula, L is the distance between the array elements, θ B is the angle between the incident direction of the echo and the vertical line of the array, and c is the speed of light.

第k号阵元相对于参考阵元的延时量τk为:The delay amount τ k of the kth array element relative to the reference array element is:

通过延时时间τk和宽带LFM信号采样间隔Ts,得到整数延时量和分数延时量式中表示取不大于的最大整数。Through the delay time τ k and the wideband LFM signal sampling interval T s , the integer delay amount is obtained and fractional delay In the formula Indicates that it is not greater than largest integer of .

步骤B、通过泰勒展开法得到一种可变分数延时滤波器的实现结构,即泰勒结构可变分数延时滤波器、对宽带信号进行时域滤波,实现信号的高精度分数延时,具体为:Step B. Obtain a variable fractional delay filter implementation structure through the Taylor expansion method, that is, a Taylor structure variable fractional delay filter, which performs time-domain filtering on broadband signals to achieve high-precision fractional delay of the signal, specifically for:

分数延时滤波器的理想冲击响应为:The ideal impulse response of a fractional delay filter is:

h(n)=sinc(n-D)h(n)=sinc(n-D)

式中,D表示延时量;In the formula, D represents the amount of delay;

可变分数延时滤波器的频率响应及其泰勒展开式为:The frequency response of the variable fractional delay filter and its Taylor expansion are:

式中,D表示延时量,z-1表示延时单元,N表示滤波器的阶数,滤波器通常为奇数阶滤波器,d是分数延时量;In the formula, D represents the amount of delay, z -1 represents the delay unit, N represents the order of the filter, and the filter is usually an odd-order filter, d is the fractional delay;

如果雷达信号带宽为200Mhz,采样率为250Mhz,则可变分数延时滤波器的通带带宽为0.8π,于是将滤波器的阶数设为81阶。If the radar signal bandwidth is 200Mhz and the sampling rate is 250Mhz, the passband bandwidth of the variable fractional delay filter is 0.8π, so the order of the filter is set to 81.

参考图4的可变分数延时滤波器的结构可得各级所需的系数;With reference to the structure of the variable fraction time-delay filter of Fig. 4, the required coefficients at each level can be obtained;

步骤C、通过移位寄存器实现信号的高精度整数延时,具体为:Step C, realize the high-precision integer delay of the signal through the shift register, specifically:

用信号的采样时钟驱动移位寄存器,待延时信号作数据输入,按所需整数延时量正确配置移位寄存器的级数,移位寄存器的输出即为延时后的信号。The shift register is driven by the sampling clock of the signal, the delayed signal is used as data input, the number of stages of the shift register is correctly configured according to the required integer delay amount, and the output of the shift register is the delayed signal.

整数延时滤波器的频率响应为The frequency response of the integer delay filter is

HI(z)=z-I H I (z) = z -I

如果整数延时量为8,则移位寄存器的级数为8,移位寄存器的驱动时钟为Ts为宽带LFM信号采样间隔。If the integer delay amount is 8, the number of stages of the shift register is 8, and the driving clock of the shift register is T s is the sampling interval of the broadband LFM signal.

步骤D、将上述步骤B设计的可变分数延时滤波器和步骤C设计的整数延时器级联,则数字延时滤波器的频率响应为:Step D, cascading the variable fractional time-delay filter designed in the above step B and the integer time-delay device designed in step C, then the frequency response of the digital time-delay filter is:

Hd(z)=HI(z)H(z)H d (z) = H I (z) H (z)

本发明的方法已经通过了验证,取得了满意的应用效果:Method of the present invention has passed verification, obtained satisfactory application effect:

(1)实验条件:宽带相控阵雷达模拟器对应的雷达工作的中心频率为1.375Ghz,阵列单元为64单元的均匀线性阵列,阵元间距为最大波长的一半,期望信号波束方向为θB=-60°,信号形式为线性调频信号,带宽为200Mhz,时宽为20us,采样率为250Mhz。(1) Experimental conditions: The center frequency of the radar working corresponding to the broadband phased array radar simulator is 1.375Ghz, the array unit is a uniform linear array of 64 units, the array element spacing is half of the maximum wavelength, and the desired signal beam direction is θ B =-60°, the signal form is linear frequency modulation signal, the bandwidth is 200Mhz, the time width is 20us, and the sampling rate is 250Mhz.

(2)仿真内容:(2) Simulation content:

仿真1:基于仿真参数:可变分数延时滤波器的阶数定为81阶,设计泰勒结构的可变分数延时滤波器,图5给出了分数延时滤波器的幅度特性,图6给出了分数延时滤波器的相位延迟特性,分数延时量分别为d=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9。图7给出了整数延时值为8,分数延时值为0.0时的实测波形图。图8给出了整数延时值为8,分数延时值为0.1时的实测波形图。Simulation 1: Based on the simulation parameters: the order of the variable fractional delay filter is set to 81, and the variable fractional delay filter of the Taylor structure is designed. Figure 5 shows the amplitude characteristics of the fractional delay filter, and Figure 6 The phase delay characteristics of the fractional delay filter are given, and the fractional delay values are d=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. Figure 7 shows the measured waveform diagram when the integer delay value is 8 and the fractional delay value is 0.0. Figure 8 shows the measured waveform diagram when the integer delay value is 8 and the fractional delay value is 0.1.

仿真2:基于上述设计的滤波器,进行宽带数字波束形成,图10给出了采用本发明所提方法形成的宽带信号发射波束图,图9给出了仅通过移相方法获得的宽带信号发射波束图。Simulation 2: Based on the filter designed above, broadband digital beamforming is performed. Figure 10 shows the broadband signal transmission beam pattern formed by the method proposed in the present invention. Figure 9 shows the broadband signal transmission beam obtained only by phase shifting method. Beam diagram.

(3)仿真结果分析:(3) Simulation result analysis:

从图5可以看出,本发明所设计的分数延时滤波器的幅度特性在[0,0.8π]范围内非常平坦。It can be seen from Fig. 5 that the amplitude characteristics of the fractional delay filter designed in the present invention are very flat in the range [0, 0.8π].

从图6可以看出,本发明所设计的分数延时滤波器的相位延迟特性在[0,0.8π]范围内非常平坦。It can be seen from FIG. 6 that the phase delay characteristic of the fractional delay filter designed in the present invention is very flat in the range of [0, 0.8π].

图7中整数延时值为8,分数延时值为0.0,FPGA工作频率为250MHz,理论延时值为32ns,实测为32.00ns,验证了整数延时控制的有效性。In Figure 7, the integer delay value is 8, the fractional delay value is 0.0, the FPGA operating frequency is 250MHz, the theoretical delay value is 32ns, and the actual measurement is 32.00ns, which verifies the effectiveness of the integer delay control.

图8中整数延时值为8,分数延时值为0.1,FPGA工作频率为250MHz,理论延时值为32.4ns,实测为32.40ns,验证了分数延时滤波器的有效性。In Figure 8, the integer delay value is 8, the fractional delay value is 0.1, the FPGA operating frequency is 250MHz, the theoretical delay value is 32.4ns, and the measured value is 32.40ns, which verifies the effectiveness of the fractional delay filter.

图9所示的传统移相实现宽带信号发射波束形成仿真图表明,仅移相方法形成的波束指向随着工作频率的改变而改变。而图10是本发明提出的基于延时补偿的方法形成的发射波束图,波束指向不随着工作频率的改变而改变,实现了宽带的宽角扫描。,说明本发明所提方法是正确的。Fig. 9 shows the traditional phase shifting to realize the beamforming simulation of wideband signal transmission, which shows that the beam direction formed by only the phase shifting method changes with the change of the operating frequency. However, FIG. 10 is a transmission beam diagram formed by the method based on delay compensation proposed by the present invention. The beam pointing does not change with the change of the operating frequency, and wide-band wide-angle scanning is realized. , indicating that the proposed method of the present invention is correct.

由此可以证实,本发明的以上技术方案与现有技术相比,具有以下技术效果:Can confirm thus, above technical scheme of the present invention compares with prior art, has following technical effect:

(1)利用FPGA的信号处理资源,寄存器资源,进行数字延时滤波器的设计,用实时数字延时替代模拟延时线,用泰勒结构的可变分数延时滤波器代替加窗法的延时滤波器和基于Farrow结构的可变分数延时滤波器,实现了宽带信号的高精度延时控制;(1) Utilize the signal processing resources and register resources of FPGA to design the digital delay filter, replace the analog delay line with real-time digital delay, and replace the delay of windowing method with the variable fractional delay filter of Taylor structure Time filter and variable fractional delay filter based on Farrow structure realize high-precision delay control of broadband signals;

(2)一般地,N阶可变分数延时滤波器,Farrow结构需要N2+N个乘法器和N2个加法器,而泰勒结构只需要3N-2个乘法器和3N-1个加法器。随着阶数的增加,泰勒结构相对于Farrow结构将节省大量的乘法器和加法器。(2) In general, the N-order variable fractional delay filter, the Farrow structure requires N 2 +N multipliers and N 2 adders, while the Taylor structure only requires 3N-2 multipliers and 3N-1 additions device. As the order increases, the Taylor structure will save a lot of multipliers and adders compared to the Farrow structure.

(3)随着带宽的改变,基于Farrow结构的可变分数延时滤波器的系数需要重新计算且计算流程主要是向量运算,难以在FPGA上实时实现,而基于泰勒结构的可变分数延时滤波器带宽的增大和滤波器阶数的增加有一致性,且滤波器系数和阶数的关系明显,适用于带宽实时可变的场景。(3) As the bandwidth changes, the coefficients of the variable fractional delay filter based on the Farrow structure need to be recalculated and the calculation process is mainly a vector operation, which is difficult to implement in real time on the FPGA, while the variable fractional delay based on the Taylor structure The increase of the filter bandwidth is consistent with the increase of the filter order, and the relationship between the filter coefficient and the order is obvious, which is suitable for the scene where the bandwidth is variable in real time.

采用了该发明的宽带相控阵雷达回波模拟器发射多通道延时补偿方法及系统,由于其利用基于泰勒展开法获得的可变分数延时滤波器对宽带信号进行时域滤波,实现高精度分数延时,再通过移位寄存器实现高精度整数延时,进而实现宽带相控阵雷达回波模拟器的多路发射通道延时补偿。该方案基于FPGA精准的时序控制、快速并行处理能力,结合数字信号处理技术,可以有效降低系统对于硬件要求较低,补偿精度高,且特别适用于可变带宽场景的延时补偿。The method and system for transmitting multi-channel delay compensation of the wideband phased array radar echo simulator of the invention is adopted, because it uses the variable fractional delay filter obtained based on the Taylor expansion method to filter the wideband signal in the time domain, realizing high Accurate fractional delay, and then realize high-precision integer delay through the shift register, and then realize the multi-channel transmit channel delay compensation of the wideband phased array radar echo simulator. Based on FPGA's precise timing control and fast parallel processing capabilities, combined with digital signal processing technology, this solution can effectively reduce the system's low hardware requirements and high compensation accuracy, and is especially suitable for delay compensation in variable bandwidth scenarios.

在此说明书中,本发明已参照其特定的实施例作了描述。但是,很显然仍可以作出各种修改和变换而不背离本发明的精神和范围。因此,说明书和附图应被认为是说明性的而非限制性的。In this specification, the invention has been described with reference to specific embodiments thereof. However, it is obvious that various modifications and changes can be made without departing from the spirit and scope of the invention. Accordingly, the specification and drawings are to be regarded as illustrative rather than restrictive.

Claims (10)

1.一种宽带相控阵雷达回波模拟器发射多通道延时补偿方法,其特征在于,该方法包括以下步骤:1. a kind of broadband phased array radar echo emulator launches multi-channel delay compensation method, it is characterized in that, the method comprises the following steps: (1)根据天线阵列的几何结构确定雷达每个单元相对于参考单元的延时量,并将该延时量分解为整数延时量和分数延时量;(1) Determine the delay of each unit of the radar relative to the reference unit according to the geometric structure of the antenna array, and decompose the delay into integer delay and fractional delay; (2)利用一基于泰勒展开法获得的可变分数延时滤波器并根据所述的分数延时量对宽带信号进行时域滤波,实现信号的高精度分数延时;(2) Utilize a variable fractional delay filter obtained based on the Taylor expansion method and carry out time-domain filtering to the broadband signal according to the fractional delay amount, so as to realize the high-precision fractional delay of the signal; (3)利用整数延时器并根据所述的整数延时量实现信号的高精度整数延时;(3) Utilize the integer delayer and realize the high-precision integer delay of the signal according to the integer delay amount; (4)将所述的可变分数延时滤波器和所述的整数延时器级联,基于所述的高精度分数延时和所述的高精度整数延时实现多通道高精度数字延时。(4) Cascading the variable fractional delay filter and the integer delayer, realizing multi-channel high-precision digital delay based on the high-precision fractional delay and the high-precision integer delay Time. 2.根据权利要求1所述的宽带相控阵雷达回波模拟器发射多通道延时补偿方法,其特征在于,步骤(2)中所述的基于泰勒展开法获得的可变分数延时滤波器具体为:2. broadband phased array radar echo simulator according to claim 1 launches multi-channel delay compensation method, it is characterized in that, the variable fractional delay filter obtained based on Taylor expansion method described in step (2) The device is specifically: 所述可变分数延时滤波器的理想冲击响应为:The ideal impulse response of the variable fractional delay filter is: h(n)=sinc(n-D)h(n)=sinc(n-D) 式中,D表示延时量;In the formula, D represents the amount of delay; 所述可变分数延时滤波器的频率响应及其泰勒展开式为:The frequency response of the variable fractional delay filter and its Taylor expansion are: <mrow> <mrow> <mo>(</mo> <mi>z</mi> <mo>,</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mi>D</mi> </mrow> </msup> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>n</mi> </msup> <mfrac> <mrow> <mi>D</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mrow> <mo>(</mo> <mi>D</mi> <mo>-</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>n</mi> <mo>!</mo> </mrow> </mfrac> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <mi>n</mi> </msup> </mrow> <mrow><mrow><mo>(</mo><mi>z</mi><mo>,</mo><mi>D</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>z</mi><mrow><mo>-</mo><mi>D</mi></mrow></msup><mo>=</mo><munderover><mi>&amp;Sigma;</mi><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mi>N</mi></munderover><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mi>n</mi></msup><mfrac><mrow><mi>D</mi><mrow><mo>(</mo><mi>D</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>.</mo><mo>.</mo><mo>.</mo><mrow><mo>(</mo><mi>D</mi><mo>-</mo><mi>N</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>!</mo></mrow></mfrac><msup><mrow><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>z</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mi>n</mi></msup></mrow> 式中,D表示延时量,z-1表示延时单元,N表示滤波器的阶数,滤波器为奇数阶滤波器,d为所述的分数延时量。In the formula, D represents the amount of delay, z -1 represents the delay unit, N represents the order of the filter, and the filter is an odd-order filter, d is the fractional delay amount. 3.根据权利要求1所述的宽带相控阵雷达回波模拟器发射多通道延时补偿方法,其特征在于,所述的步骤(3)具体为:3. broadband phased array radar echo emulator according to claim 1 launches multi-channel delay compensation method, it is characterized in that, described step (3) is specially: 利用信号的采样时钟驱动一移位寄存器,将待延时信号作为该移位寄存器的数据输入,根据所述的整数延时量配置所述的移位寄存器的级数,该移位寄存器的输出信号为高精度整数延时后的信号。Utilize the sampling clock of the signal to drive a shift register, use the signal to be delayed as the data input of the shift register, configure the stages of the shift register according to the integer delay amount, and the output of the shift register The signal is a signal after a high-precision integer delay. 4.根据权利要求2所述的宽带相控阵雷达回波模拟器发射多通道延时补偿方法,其特征在于,所述的延迟量D位于理想脉冲响应的中间部分,且所述的滤波器的阶数N给定,用以实现最小误差的延时补偿。4. wideband phased array radar echo simulator according to claim 2 launches multi-channel delay compensation method, is characterized in that, described delay amount D is positioned at the middle part of ideal impulse response, and described filter The order N of is given to realize the delay compensation of the minimum error. 5.根据权利要求2所述的宽带相控阵雷达回波模拟器发射多通道延时补偿方法,其特征在于,所述的滤波器的系数仅与该滤波器的阶数N及所述的延迟量D相关,该滤波器的阶数N给定时,通过改变所述的延迟量D实现不同的延时。5. broadband phased array radar echo emulator according to claim 2 launches multi-channel delay compensation method, it is characterized in that, the coefficient of described filter is only with the order N of this filter and described The delay amount D is related, and when the order number N of the filter is given, different delays can be realized by changing the delay amount D. 6.一种宽带相控阵雷达回波模拟器发射多通道延时补偿系统,其特征在于,该系统包括:6. A broadband phased array radar echo simulator launches a multi-channel delay compensation system, characterized in that the system includes: 延时量分解模块,用以根据天线阵列的几何结构确定雷达每个单元相对于参考单元的延时量,并将该延时量分解为整数延时量和分数延时量;The delay amount decomposition module is used to determine the delay amount of each radar unit relative to the reference unit according to the geometric structure of the antenna array, and decompose the delay amount into an integer delay amount and a fractional delay amount; 可变分数延时滤波器,基于泰勒展开法获得,该可变分数延时滤波器根据所述的分数延时量对宽带信号进行时域滤波,实现信号的高精度分数延时;The variable fractional delay filter is obtained based on the Taylor expansion method, and the variable fractional delay filter performs time-domain filtering on the broadband signal according to the fractional delay amount to realize high-precision fractional delay of the signal; 整数延时器,用以根据所述的整数延时量实现信号的高精度整数延时;Integer delay device, in order to realize the high-precision integer delay of signal according to described integer delay amount; 级联模块,用以将所述的可变分数延时滤波器和所述的整数延时器级联,基于所述的高精度分数延时和所述的高精度整数延时实现多通道高精度数字延时。The cascading module is used to cascade the variable fractional delay filter and the integer delayer, and realize multi-channel high-speed delay based on the high-precision fractional delay and the high-precision integer delay Precision digital delay. 7.根据权利要求6所述的宽带相控阵雷达回波模拟器发射多通道延时补偿系统,其特征在于,所述的基于泰勒展开法获得的可变分数延时滤波器具体为:7. broadband phased array radar echo emulator according to claim 6 launches multi-channel delay compensation system, it is characterized in that, the variable fractional delay filter that described based on Taylor expansion method is specifically: 所述可变分数延时滤波器的理想冲击响应为:The ideal impulse response of the variable fractional delay filter is: h(n)=sinc(n-D)h(n)=sinc(n-D) 式中,D表示延时量;In the formula, D represents the amount of delay; 所述可变分数延时滤波器的频率响应及其泰勒展开式为:The frequency response of the variable fractional delay filter and its Taylor expansion are: <mrow> <mi>H</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>,</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mi>D</mi> </mrow> </msup> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>(</mo> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>n</mi> </msup> <mfrac> <mrow> <mi>D</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>...</mn> <mrow> <mo>(</mo> <mi>D</mi> <mo>-</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>n</mi> <mo>!</mo> </mrow> </mfrac> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <mi>n</mi> </msup> </mrow> <mrow><mi>H</mi><mrow><mo>(</mo><mi>z</mi><mo>,</mo><mi>D</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>z</mi><mrow><mo>-</mo><mi>D</mi></mrow></msup><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mi>N</mi></munderover><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mi>n</mi></msup><mfrac><mrow><mi>D</mi><mrow><mo>(</mo><mi>D</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>...</mn><mrow><mo>(</mo><mi>D</mi><mo>-</mo><mi>N</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>!</mo></mrow></mfrac><msup><mrow><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>z</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mi>n</mi></msup></mrow> 式中,D表示延时量,z-1表示延时单元,N表示滤波器的阶数,滤波器为奇数阶滤波器,d为所述的分数延时量。In the formula, D represents the amount of delay, z -1 represents the delay unit, N represents the order of the filter, and the filter is an odd-order filter, d is the fractional delay amount. 8.根据权利要求6所述的宽带相控阵雷达回波模拟器发射多通道延时补偿系统,其特征在于,所述的整数延时器具体为:利用信号的采样时钟驱动一移位寄存器,将待延时信号作为该移位寄存器的数据输入,根据所述的整数延时量配置所述的移位寄存器的级数,该移位寄存器的输出信号为高精度整数延时后的信号。8. wideband phased array radar echo emulator according to claim 6 launches multi-channel delay compensation system, is characterized in that, described integer delay device is specifically: utilize the sampling clock of signal to drive a shift register , the signal to be delayed is used as the data input of the shift register, the number of stages of the shift register is configured according to the integer delay amount, and the output signal of the shift register is a high-precision integer delayed signal . 9.根据权利要求7所述的宽带相控阵雷达回波模拟器发射多通道延时补偿系统,其特征在于,所述的延迟量D位于理想脉冲响应的中间部分,且所述的滤波器的阶数N给定,用以实现最小误差的延时补偿。9. broadband phased array radar echo emulator according to claim 7 launches multi-channel delay compensation system, is characterized in that, described delay amount D is positioned at the middle part of ideal impulse response, and described filter The order N of is given to realize the delay compensation of the minimum error. 10.根据权利要求7所述的宽带相控阵雷达回波模拟器发射多通道延时补偿系统,其特征在于,所述的滤波器的系数仅与该滤波器的阶数N及所述的延迟量D相关,该滤波器的阶数N给定时,通过改变所述的延迟量D实现不同的延时。10. broadband phased array radar echo emulator according to claim 7 launches multi-channel delay compensation system, is characterized in that, the coefficient of described filter is only with the order N of this filter and described The delay amount D is related, and when the order number N of the filter is given, different delays can be realized by changing the delay amount D.
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CN115882882A (en) * 2023-02-13 2023-03-31 天津七一二通信广播股份有限公司 Decimal time delay predistortion self-blocking interference cancellation method and system
CN115842251A (en) * 2023-02-16 2023-03-24 成都天锐星通科技有限公司 Antenna sampling compensation method and device and phased array panel antenna

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