WO2022237218A1 - 一种用于ota仿真的复包络蛙跳隐式时域有限差分法 - Google Patents

一种用于ota仿真的复包络蛙跳隐式时域有限差分法 Download PDF

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WO2022237218A1
WO2022237218A1 PCT/CN2022/071654 CN2022071654W WO2022237218A1 WO 2022237218 A1 WO2022237218 A1 WO 2022237218A1 CN 2022071654 W CN2022071654 W CN 2022071654W WO 2022237218 A1 WO2022237218 A1 WO 2022237218A1
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simulation
space
time
leapfrog
ota
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周健义
董云扬
于志强
洪伟
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东南大学
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
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  • the invention belongs to the technical field of computational electromagnetics, and in particular relates to a complex envelope leapfrog implicit time-domain finite difference method for OTA simulation.
  • the finite difference time domain (FDTD) method is widely used in solving electromagnetic problems.
  • the traditional FDTD algorithm needs to calculate extremely long time steps, and the traditional FDTD method is limited by the stability condition and cannot increase the time step, which makes the overall calculation efficiency low.
  • the traditional FDTD algorithm is used, it is necessary to run millions of time steps.
  • people began to study the unconditionally stable FDTD algorithm and the alternating direction implicit scheme (ADI) FDTD algorithm and the leapfrog (leapfrog) ADI-FDTD algorithm also appeared.
  • ADI alternating direction implicit scheme
  • the leapfrog leapfrog
  • the purpose of the present invention is to provide a complex envelope leapfrog implicit time domain finite difference method for OTA simulation, to solve the problem that the time step of the traditional time domain finite difference method is too small, the calculation efficiency is low, the alternating direction implicit scheme algorithm and frog The technical problem of the low precision of the jump algorithm.
  • a complex envelope leapfrog implicit time domain finite difference method for OTA simulation comprising the following steps:
  • Step 1 Set the center frequency and bandwidth of the solution, and calculate the corresponding wavelength according to the relationship between frequency and wavelength;
  • Step 2 Set the corresponding solution area according to the simulation environment, determine the size of the space to be sought, determine the processing method of the space boundary, determine the location of the scattering object in the space and its electromagnetic constant, determine the excitation point and receiving point, and then according to Yee
  • the grid discretizes the space, determines the number of grids in the space, the grid position of the object, the grid where the excitation point and the receiving point are located, and finally calculates the corresponding time step according to the CFL stability condition. According to the simulation accuracy, the simulation Set the time step multiple;
  • Step 3 Specify the modulation method of the transmitted signal and generate the transmitted signal, and set the number of time steps of the simulation according to the signal length;
  • Step 4 According to the number of Yee grids, apply for and initialize the memory space for each electromagnetic field component, and then save and initialize the coefficients that need to be used in the update iterative equation;
  • Step 5 Update and iterate the electromagnetic field. First update the electric field value in the area. After the electric field calculation is completed, add the electric excitation source, then update the magnetic field value, add the magnetic excitation source, and finally save the signal at the receiving point as the output at this moment ;Through the continuous iteration of the electric field and magnetic field, the calculation stops after the total time step is set; finally, the received signal at the receiving point for the entire time can be obtained;
  • Step 6 Demodulate according to the modulation mode of the signal, and solve the parameter index.
  • step 4 the iteration coefficients are stored in an index manner, which saves memory space and improves memory utilization efficiency.
  • the invention performs electromagnetic simulation on the simulation space to obtain the response between the transceivers, is applicable to the simulation of the OTA test, and has the characteristics of high precision and unconditional stability.
  • Fig. 1 is the simulation calculation flowchart of the present invention
  • Fig. 2 is the image schematic diagram that method error of the present invention changes with normalization frequency
  • FIG. 3 is a constellation diagram of a signal at a transmitting end
  • Fig. 4 is the frequency spectrum diagram of transmitting end signal
  • FIG. 5 is a constellation diagram of a signal at the receiving end.
  • FIG. 1 it is a simulation calculation flow chart of the present invention.
  • the complex envelope leapfrog implicit time domain finite difference method used for OTA simulation in the present invention comprises the following steps:
  • Step 1 Set the center frequency and bandwidth of the solution, and calculate the corresponding wavelength according to the relationship between frequency and wavelength;
  • Step 2 Set the corresponding solution area according to the simulated environment, determine the size of the required space, determine the processing method of the space boundary, determine the position of the scattering object in the space and its electromagnetic constant, determine the excitation point and receiving point, and then according to Yee
  • the grid discretizes the space, determines the number of grids in the space, the grid position of the object, the grid where the excitation point and the receiving point are located, and finally calculates the corresponding time step according to the CFL stability condition. According to the simulation accuracy, the simulation Set the time step multiple;
  • Step 3 Specify the modulation method of the transmitted signal and generate the transmitted signal, and set the number of time steps of the simulation according to the signal length;
  • Step 4 According to the number of Yee grids, apply for and initialize the memory space for each electromagnetic field component, and then save and initialize the coefficients that need to be used in the update iteration equation.
  • the iteration coefficients are stored in index mode, which saves memory Space, improve the efficiency of memory utilization;
  • Step 5 Update and iterate the electromagnetic field. First update the electric field value in the area. After the electric field calculation is completed, add the electric excitation source, then update the magnetic field value, add the magnetic excitation source, and finally save the signal at the receiving point as the output at this moment ;Through the continuous iteration of the electric field and magnetic field, the calculation stops after the total time step is set; finally, the received signal at the receiving point for the entire time can be obtained;
  • Step 6 Demodulate according to the modulation mode of the signal, and solve the parameter index.
  • the OTA measurement environment of a millimeter-wave anechoic chamber is analyzed, and the error vector magnitude (Error Vector Magnitude, EVM) value of the signal at the receiving end is calculated, including the following steps:
  • Step 1 Set the solution frequency, bandwidth and calculate the response wavelength.
  • Step 2 Set the solution area, discretize the space and time, and determine the time step.
  • the small black box used for 28GHz measurement is 0.3m long, 0.3m wide, and 0.1m high, and the six sides are all equipped with gradually changing wave-absorbing media.
  • the excitation points are located at (0.15m, 0.15m, 0.02m), and the observation points are located at (0.15m, 0.15m, 0.04m).
  • the number of spatial grids is 375 ⁇ 375 ⁇ 125, the excitation points are located in grids (187, 187, 25), and the observation points are located in grids (187, 187, 50).
  • the CFL stability condition can be obtained
  • the corresponding time step ⁇ t CFL 1.5396 ⁇ 10 -12 s.
  • Step 3 Determine the total time steps of the transmitted signal and the simulation.
  • Step 4 Apply for memory space and initialize it.
  • the electromagnetic field space includes six components of Ex, Ey, Ez, Hx, Hy and Hz, and each component needs to use a complex double type memory space of 375 ⁇ 375 ⁇ 125 and initialized to 0+0i. Then, the coefficients needed in updating the iterative equation are saved and initialized in index mode.
  • Step 5 Deriving and updating the iteration formula, and iterating the electromagnetic field according to the formula.
  • j is the imaginary number unit
  • t n ⁇ t
  • n is the number of time steps
  • ⁇ t is the time step length.
  • I is the identity matrix
  • a and B are the discrete curl operator matrices
  • Equation (7) is an unknown item, and the right side is all known items.
  • the coefficients of the equation are all located on the main diagonal and the upper and lower two diagonals, which can be quickly solved by the pursuit method.
  • the other electric field components are the same.
  • This step is only performed on the Ez component of the specified electric field excitation location grid (187, 187, 25).
  • magnetic field excitation is not performed, so no processing is performed.
  • Step 6 demodulating the observation signal.
  • the eigenvalue of the growth matrix corresponding to the method of the present invention is always not greater than 1, so it is unconditionally stable under any step size.
  • the curve of the error of this method changing with the normalized frequency normalized by the center frequency
  • the accuracy is extremely high near the set center frequency.
  • the invention provides a complex envelope leapfrog implicit time-domain finite difference method for OTA simulation, which is applicable to one-dimensional, two-dimensional and three-dimensional environments.
  • This method can perform electromagnetic simulation on the simulation space to obtain the response between the transceiver and is especially suitable for the simulation of the OTA test, and has the characteristics of high precision and unconditional stability.

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Abstract

提供了一种用于OTA仿真的复包络蛙跳隐式时域有限差分法。方法采用复包络交替方向隐格式时域有限差分法对全空间进行电磁仿真来获取收发之间的响应，从而达到获取性能指标的目的。首先，在设置空间媒质分布、确定信号调制方式的基础上，通过复包络蛙跳隐式时域有限差分法的更新方程对电场和磁场进行不断迭代，直到达到预设的时间总步数后停止；然后根据调制方式对接收信号进行解调以获取参数指标。方法具有无条件稳定和高精度的特点，适用性广泛，可用于进行OTA测试的仿真计算，也可用于其他复杂介质下的电磁计算问题。

Description

一种用于OTA仿真的复包络蛙跳隐式时域有限差分法 技术领域
本发明属于计算电磁学技术领域，尤其涉及一种用于OTA仿真的复包络蛙跳隐式时域有限差分法。
背景技术
随着计算电磁学的发展，时域有限差分法(FDTD)被广泛的应用于电磁问题的求解。然而在一些计算问题中，传统的FDTD算法需要计算极长的时间步数，而传统的FDTD方法受到稳定性条件的限制，无法加大时间步长，从而使得整体计算效率低下。比如对收发机的OTA测试，为了获得较好的结果，要发送不少于一帧的数据，如果利用传统FDTD算法，则需要运行百万千万量级的时间步长。为了突破时间步长的限制，人们开始研究无条件稳定的FDTD算法，交替方向隐格式(ADI)FDTD算法和蛙跳式(leapfrog)ADI-FDTD算法也随之出现。但由于时间步长变大后，造成了精度的下降。因此需要提高长时间仿真下带限系统的仿真精度。
发明内容
本发明目的在于提供一种用于OTA仿真的复包络蛙跳隐式时域有限差分法,以解决传统时域有限差分法时间步长过小，计算效率低，交替方向隐格式算法和蛙跳式算法精度低的技术问题。
为解决上述技术问题，本发明的具体技术方案如下：
一种用于OTA仿真的复包络蛙跳隐式时域有限差分法，包括以下步骤：
步骤1、设定求解的中心频率和带宽，并根据频率与波长的关系计算相应的波长；
步骤2、根据仿真的环境设定相应的求解区域，确定所求空间的大小， 确定空间边界的处理方式，确定空间内的散射物体位置及其电磁常数，确定激励点和接收点，然后根据Yee网格对空间进行离散化，确定空间的网格数、物体的网格位置和激励点、接收点所在的网格，最后由CFL稳定性条件求对应的时间步长，根据仿真精度需要为仿真设定时间步长倍数；
步骤3、指定发射信号的调制方式并生成发射信号，根据信号长度设定仿真的时间步数；
步骤4、根据Yee网格数，为各个电磁场分量申请内存空间并进行初始化，然后对更新迭代方程中需要用到的系数进行保存和初始化；
步骤5、对电磁场进行更新迭代，首先更新区域内的电场值，电场计算完成后加入电激励源，然后更新磁场值，加入磁激励源，最后保存接收点位置上的信号，作为该时刻的输出；通过电场、磁场不停的迭代，计算到设定的时间总步长后停止；最终可以得到接收点处整个时间的接收信号；
步骤6、根据信号的调制方式进行解调，并求解参数指标。
进一步的，步骤4中迭代系数采用索引方式进行存储，节省了内存空间，提高了内存的利用效率。
本发明的一种用于OTA仿真的复包络蛙跳隐式时域有限差分法具有以下优点：
本发明对仿真空间进行电磁仿真来获取收发之间的响应，可适用于OTA测试的仿真，具有精度高和无条件稳定的特点。
附图说明
图1为本发明的仿真计算流程图；
图2为本发明的方法误差随归一化频率变化的图像示意图；
图3为发射端信号的星座图；
图4为发射端信号的频谱图；
图5为接收端信号的星座图。
具体实施方式
为了更好地了解本发明的目的、结构及功能，下面结合附图，对本发明一种用于OTA仿真的复包络蛙跳隐式时域有限差分法做进一步详细的描述。
如图1所示，是本发明的仿真计算流程图。
本发明用于OTA仿真的复包络蛙跳隐式时域有限差分法，包括以下步骤：
步骤1、设定求解的中心频率和带宽，并根据频率与波长的关系计算相应的波长；
步骤2、根据仿真的环境设定相应的求解区域，确定所求空间的大小，确定空间边界的处理方式，确定空间内的散射物体位置及其电磁常数，确定激励点和接收点，然后根据Yee网格对空间进行离散化，确定空间的网格数、物体的网格位置和激励点、接收点所在的网格，最后由CFL稳定性条件求对应的时间步长，根据仿真精度需要为仿真设定时间步长倍数；
步骤3、指定发射信号的调制方式并生成发射信号，根据信号长度设定仿真的时间步数；
步骤4、根据Yee网格数，为各个电磁场分量申请内存空间并进行初始化，然后对更新迭代方程中需要用到的系数进行保存和初始化，所述的迭代系数采用索引方式进行存储，节省了内存空间，提高了内存的利用效率；
步骤5、对电磁场进行更新迭代，首先更新区域内的电场值，电场计算完成后加入电激励源，然后更新磁场值，加入磁激励源，最后保存接收点位置上的信号，作为该时刻的输出；通过电场、磁场不停的迭代，计算到设定的时间总步长后停止；最终可以得到接收点处整个时间的接收信号；
步骤6、根据信号的调制方式进行解调，并求解参数指标。
在实施例中对一毫米波暗室的OTA测量环境进行分析，计算接收端信号的误差向量幅度(Error Vector Magnitude，EVM)值，包括以下步骤：
步骤一、设定求解频率、带宽并计算响应波长。
假设仿真中心频率f c为28GHz，带宽BW为1GHz。因此中心频率波长λ c＝C/f c为10.71mm，其中C为电磁波在真空中的波长。
步骤二、设定求解区域并进行空间和时间的离散化，确定时间步长。
假设用于28GHz测量的小型暗箱长0.3m，宽0.3m，高0.1m，六个面均布置有渐变的吸波介质。激励点位于点(0.15m，0.15m，0.02m)处，观测点分别位于(0.15m，0.15m，0.04m)处。取x，y，z方向空间离散步长为0.8mm，对求解区域按Yee网格进行离散。空间网格数为375×375×125，激励点位于网格(187，187，25)，观测点分别位于网格(187，187，50)，根据式(1)可得CFL稳定性条件中对应的时间步长Δt CFL＝1.5396×10 -12s。
Figure PCTCN2022071654-appb-000001
由于本发明所提出的算法无条件稳定，因此，为了提高精度，根据图2所示误差随归一化频率变化曲线，取离散时间步长Δt＝2Δt CFL＝3.0792×10 -12s。
步骤三、确定发射信号和仿真总时间步数。
取发射信号激励为z方向的电场激励
Figure PCTCN2022071654-appb-000002
其波形为随机序列对应的QAM64调制的OFDM信号。信号星座图和频谱分别如图3和图4所示。根据所生成的随机信号长度以及设定的时间步长，取迭代总时间步数N t＝2×10 6步。
步骤四、申请内存空间并进行初始化。
电磁场空间包括Ex，Ey，Ez，Hx，Hy和Hz六个分量，每个分量需要用 到375×375×125的复数double类型内存空间，并初始化为0+0i。然后对更新迭代方程中需要用到的系数以索引方式进行保存和初始化。
步骤五、推导更新迭代公式，并按照公式对电磁场进行迭代。
将电场和磁场写成如式(2)的复包络形式
Figure PCTCN2022071654-appb-000003
其中
Figure PCTCN2022071654-appb-000004
分别为电场，磁场的复包络信号，j为虚数单位，ω c＝2πf c为中心角频率或称载波角频率，t＝nΔt，n为时间步数，Δt为时间步长。
将式(2)带入FDTD的更新方程并结合ADI方法和leapfrog方法，可得迭代更新方程为
Figure PCTCN2022071654-appb-000005
Figure PCTCN2022071654-appb-000006
其中
Figure PCTCN2022071654-appb-000007
为相应媒质中的光速，I为单位阵，A和B为离散旋度算子矩阵，有
Figure PCTCN2022071654-appb-000008
算子
Figure PCTCN2022071654-appb-000009
为中心差分算子
Figure PCTCN2022071654-appb-000010
其作用在任意分量f上有
Figure PCTCN2022071654-appb-000011
Figure PCTCN2022071654-appb-000012
将式(3)和(4)写成分量形式为
Figure PCTCN2022071654-appb-000013
Figure PCTCN2022071654-appb-000014
Figure PCTCN2022071654-appb-000015
Figure PCTCN2022071654-appb-000016
Figure PCTCN2022071654-appb-000017
Figure PCTCN2022071654-appb-000018
于是，在每一个时间步中依次进行如下操作：
(一)电场计算
采用追赶法求解式(7)(8)(9)对应的三对角方程。
以x方向的电场为例，等式(7)左侧为未知项，右侧全部为已知项。对于j∈[1,N y-1]∩Z，相邻的三个电场即
Figure PCTCN2022071654-appb-000019
构成一个方程，共构成N y-1个方程，当j＝0和j＝N y时，由计算空间的截断边界条件分别构成一个方程，共2个方程，因此
Figure PCTCN2022071654-appb-000020
共N y+1个方程，又
Figure PCTCN2022071654-appb-000021
有N y+1个未知数，方程可解。并且，方程系数全部位于主对角线和上下两次对角线，可以由追赶法进行快速求解。其他电场分量同理。
(2)电场激励处理
Figure PCTCN2022071654-appb-000022
此步仅在指定的电场激励位置网格(187，187，25)的Ez分量上进行。
(3)磁场计算
采用追赶法求解式(10)(11)(12)对应的三对角方程.
(4)磁场激励处理
本实施例不进行磁场激励，故不做处理。
(5)保存当前时间下观测点的值。
以此法迭代N t＝2×10 6步，可得观测点随时间的信号情况。
步骤六、对观测信号进行解调。
对观测点的接收信号进行OFDM解调和QAM64解调，可得接收星座图如图5所示，通过计算可得均方根EVM＝0.2487％。
本发明方法所对应的增长矩阵的特征值始终不大于1，因此在任何步长下均无条件稳定。如图2所示，给出了本方法误差随归一化频率(以中心频率归一化)变化的曲线，可以看到在所设定的中心频率附近具有极高的精度。
本发明给出了一种用于OTA仿真的复包络蛙跳隐式时域有限差分法，可适用于一维、二维及三维的环境中。该方法可对仿真空间进行电磁仿真来获取收发之间的响应，尤其适用于OTA测试的仿真，具有精度高和无条件稳定的特点。
可以理解，本发明是通过一些实施例进行描述的，本领域技术人员知悉的，在不脱离本发明的精神和范围的情况下，可以对这些特征和实施例进行各种改变或等效替换。另外，在本发明的教导下，可以对这些特征和实施例进行修改以适应具体的情况及材料而不会脱离本发明的精神和范围。因此，本发明不受此处所公开的具体实施例的限制，所有落入本申请的权利要求范围内的实施例都属于本发明所保护的范围内。

Claims (2)

  1. 一种用于OTA仿真的复包络蛙跳隐式时域有限差分法，其特征在于，包括以下步骤：
    步骤1、设定求解的中心频率和带宽，根据频率与波长的关系计算中心频率的波长；
    步骤2、根据仿真的环境设定相应的求解区域，确定所求空间的大小，确定空间边界的处理方式，确定空间内的散射物体位置及其电磁常数，确定激励点和接收点，然后根据Yee网格对空间进行离散化，确定空间的网格数、物体的网格位置和激励点、接收点所在的网格，最后由CFL稳定性条件求对应的时间步长，根据仿真精度需要为仿真设定时间步长倍数；
    步骤3、指定发射信号的调制方式并生成发射信号，根据信号长度设定仿真的时间步数；
    步骤4、根据Yee网格数，为各个电磁场分量申请内存空间并进行初始化，然后对更新迭代方程中需要用到的系数进行保存和初始化；
    步骤5、对电磁场进行更新迭代，首先更新区域内的电场值，电场计算完成后加入电激励源，然后更新磁场值，加入磁激励源，最后保存接收点位置上的信号，作为该时刻的输出；通过电场、磁场不停的迭代，计算到设定的时间总步长后停止；最终可以得到接收点处整个时间的接收信号；
    步骤6、根据信号的调制方式进行解调，并求解参数指标。
  2. 根据权利要求1所述的用于OTA仿真的复包络蛙跳隐式时域有限差分法，其特征在于，步骤4中所述的迭代系数采用索引方式进行存储。
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