CN105005036A

CN105005036A - Transmission loss compensation method used for short-range MIMO imaging

Info

Publication number: CN105005036A
Application number: CN201510429847.6A
Authority: CN
Inventors: 胡大海; 常庆功; 杜刘革; 王亚海
Original assignee: CETC 41 Research Institute
Current assignee: CETC 41 Research Institute
Priority date: 2015-07-16
Filing date: 2015-07-16
Publication date: 2015-10-28

Abstract

The invention proposes a propagation loss compensation method for short-range MIMO imaging, and re-deduces the RMA formula for short-range MIMO dual-station imaging. The echo signal considers the near-field distance attenuation item, and the image function amplitude item is found after the formula is deduced There is a compensation factor, and the corresponding parameters are compensated during imaging processing. The propagation loss compensation method of the present invention is suitable for ultra-wideband near-field and far-field imaging; it can realize MIMO imaging amplitude accuracy compensation without increasing any hardware cost, and improve imaging quality; dimensional and 3D imaging.

Description

A Propagation Loss Compensation Method for Short Range MIMO Imaging

技术领域technical field

本发明涉及雷达成像技术领域，特别涉及一种用于近程MIMO成像的传播损耗补偿方法。The invention relates to the technical field of radar imaging, in particular to a propagation loss compensation method for short-range MIMO imaging.

背景技术Background technique

MIMO雷达成像技术是一种新型雷达成像技术，采用多发多收的体制，经过适当处理，可以等效为一个同时独立收发的虚拟阵列，因而所得通道远远多于实际物理阵元数目，大大节省了硬件成本，提高分辨能力，使实时成像成为可能。在近程成像的条件下，天线发射的电磁波为球面波，电磁波传播路径损耗显著影响目标近场成像的幅度精度。MIMO radar imaging technology is a new type of radar imaging technology. It adopts a multi-transmit and multi-receive system. After proper processing, it can be equivalent to a virtual array that transmits and receives independently at the same time. Therefore, the obtained channels are far more than the actual number of physical array elements, which greatly saves The hardware cost is reduced, the resolution ability is improved, and real-time imaging becomes possible. Under the condition of short-range imaging, the electromagnetic wave emitted by the antenna is a spherical wave, and the electromagnetic wave propagation path loss significantly affects the amplitude accuracy of the target near-field imaging.

近程MIMO成像常用算法为距离徙动算法(Range Migration Algorithm，RMA)，针对单站RMA近程传播路径损耗问题，国防科技大学雷文太等人提出了改进的三维成像算法，效果明显，但对MIMO成像来说，双站RMA算法更为适用，因为不会引入等效相位中心误差。The commonly used algorithm for short-range MIMO imaging is the Range Migration Algorithm (RMA). Aiming at the problem of single-station RMA short-range propagation path loss, Lei Wentai from the National University of Defense Technology and others proposed an improved three-dimensional imaging algorithm. For MIMO imaging, the bistatic RMA algorithm is more suitable because it will not introduce the equivalent phase center error.

探头阵列成像技术在成像方面潜力巨大，其由多个发射单元和接收单元构成，采用开关控制的工作形式，每次有且只有一对收发天线工作，能够有效的抑制天线之间的耦合，产生出远远多于实际天线数目的虚拟阵列单元，从而大大的节省阵列的硬件成本和建造难度。Probe array imaging technology has great potential in imaging. It is composed of multiple transmitting units and receiving units. It adopts the working form of switch control, and only one pair of transmitting and receiving antennas works at a time, which can effectively suppress the coupling between antennas and generate The number of virtual array units is far more than the number of actual antennas, thereby greatly saving the hardware cost and construction difficulty of the array.

但在近程条件下，信号接收形式为球面波，电磁波传播路径损耗随距离显著衰减，必然严重影响MIMO成像结果的幅度精度，具体表现为距离阵列平面越近幅度越大，导致较远的目标在成像结果上不明显。However, under short-range conditions, the signal receiving form is a spherical wave, and the electromagnetic wave propagation path loss significantly attenuates with distance, which will inevitably seriously affect the amplitude accuracy of MIMO imaging results. Specifically, the closer the distance to the array plane, the larger the amplitude, resulting in farther targets. Not apparent in imaging results.

下面将详细介绍与本发明最相近的现有技术中的方法。The method in the prior art closest to the present invention will be described in detail below.

如图1所示为单站RMA成像算法，单站即收发天线在同一位置(x_n，y_m，0)，设待测目标(x，y，z)反射率函数O(x，y，z)，则天线接收回波：As shown in Figure 1, the single-station RMA imaging algorithm is shown. The single-station, that is, the transceiver antenna is at the same position (x _n , y _m , 0), and the reflectivity function O(x, y, z), then the antenna receives the echo:

$s the s (({x x}_{n no},, {y the y}_{m m},, k k)) \underset{V V}{&Integral; &Integral; &Integral; &Integral; &Integral; &Integral;} H h \cdot \cdot O o ((x x,, y the y,, z z)) \cdot \cdot \frac{exp exp ((- - jkR ikB))}{{R R}^{22}} dV dV - - - - - - ((11))$

$R R = = \sqrt{{((x x - - {x x}_{n no}))}^{22} + + {((y the y - - {y the y}_{n no}))}^{22} + + {z z}^{22}} - - - - - - ((22))$

其中，k为波数，R表示目标到天线之间的距离，可见电磁波与R²成反比，传播Among them, ^k is the wave number, R represents the distance between the target and the antenna, it can be seen that the electromagnetic wave is inversely proportional to R2, and the propagation

损耗补偿即消除它对成像精度的影响。H为常数项幅度，可以忽略。于是，Loss compensation is to eliminate its impact on imaging accuracy. H is the magnitude of the constant term, which can be ignored. then,

$\begin{matrix} O o ((x x,, y the y,, z z)) = = \underset{k k}{&Integral; &Integral;} dk dk {\underset{Λ Λ}{&Integral; &Integral; &Integral; &Integral;}}_{exp exp ((jk jk \sqrt{{((x x - - {x x}_{n no}))}^{22} + + {((y the y - - {y the y}_{n no}))}^{22} + + {z z}^{22}}))}^{s the s (({x x}_{n no},, {y the y}_{m m},, k k)) \cdot \cdot {[[((x x - - {x x}_{n no}))}^{22} + + {((y the y - - {y the y}_{n no}))}^{22} + + {z z}^{22}]]} {dx dx}_{n no} {dy dy}_{n no} \\ = = \underset{k k}{&Integral; &Integral;} s the s (({x x}_{n no},, {y the y}_{m m},, k k)) &CircleTimes; &CircleTimes; (({x x}^{22} + + {y the y}^{22} + + {z z}^{22})) exp exp ((jk jk \sqrt{{x x}^{22} + + {y the y}^{22} + + {z z}^{22}})) dk dk \end{matrix} - - - - - - ((33))$

根据驻定相位法原理求解上式，可得驻相点坐标为其中，k_x，k_y分别表示与坐标(x，y)对应的波谱域坐标。式(3)最终可化为Solving the above formula according to the principle of the stationary phase method, the coordinates of the stationary phase point can be obtained as in, k _x , _ky represent spectral domain coordinates corresponding to coordinates (x, y), respectively. Formula (3) can finally be transformed into

$O o ((x x,, y the y,, z z)) = = \frac{11}{22 π π} \underset{k k}{&Integral; &Integral; &Integral; &Integral; &Integral; &Integral;} S S (({k k}_{x x},, {k k}_{y the y} . . k k)) \cdot &Center Dot; \frac{j j {k k}^{33} {z z}^{33}}{{k k}_{z z}^{44}} \cdot &Center Dot; exp exp [[j j (({k k}_{x x} x x + + {k k}_{y the y} y the y + + {k k}_{z z} z z))]] {dk dk}_{x x} {dk dk}_{y the y} {dk dk}_{z z} - - - - - - ((44))$

式中即为单站RMA的传播损耗补偿因子，乘以该补偿因子即可消除传播损耗对成像幅度的影响。In the formula That is, the propagation loss compensation factor of the single station RMA, multiplied by this compensation factor can eliminate the influence of the propagation loss on the imaging amplitude.

目前国内关于多探头阵列成像起步较晚，主要集中在仿真阶段，关于近程路径损耗补偿问题主要以国防科技大学为代表，主要缺点是补偿方法值针对单站或准单站RMA算法，即收发天线位于同一位置或相距很近。At present, the multi-probe array imaging in China started relatively late, mainly in the simulation stage. The short-range path loss compensation problem is mainly represented by the National University of Defense Technology. The main disadvantage is that the compensation method value is based on the single-station or quasi-single-station RMA algorithm, that is The antennas are co-located or very close together.

国外相关研究的文献则相对多一些，如针对基尔霍夫偏移算法的路径衰减补偿，但存在以下问题：There are relatively more foreign related research literatures, such as path attenuation compensation for Kirchhoff migration algorithm, but there are the following problems:

(1)基尔霍夫偏移算法成像处理时间较长，不利于实时成像，因此针对该算法的补偿具有局限性；(1) The imaging processing time of the Kirchhoff migration algorithm is long, which is not conducive to real-time imaging, so the compensation for this algorithm has limitations;

(2)补偿方法的推导原理是基于基尔霍夫偏移算法公式推导的，因此仅仅适用于该算法，不再适用于其他成像处理时间短的算法，适用范围狭窄。(2) The derivation principle of the compensation method is based on the Kirchhoff migration algorithm formula, so it is only applicable to this algorithm, and is no longer applicable to other algorithms with short imaging processing time, and the scope of application is narrow.

发明内容Contents of the invention

针对上述现有技术中的不足，本发明的目的在于提出一种用于近程MIMO成像的传播损耗补偿方法，可以有效的对目标进行三维成像。In view of the deficiencies in the above prior art, the purpose of the present invention is to propose a propagation loss compensation method for short-range MIMO imaging, which can effectively perform three-dimensional imaging on the target.

本发明的技术方案是这样实现的：Technical scheme of the present invention is realized like this:

一种用于近程MIMO成像的传播损耗补偿方法，包括以下步骤：A propagation loss compensation method for short-range MIMO imaging, comprising the following steps:

步骤(1)，首先根据MIMO阵列的布局情况，建立坐标系确定接收信号b(x_Tx，x_Rx，y_Tx，y_Rx，k)与收发天线坐标、频率对应关系；Step (1), first, according to the layout of the MIMO array, establish a coordinate system to determine the corresponding relationship between the received signal b(x _Tx , x _Rx , y _Tx , y _Rx , k) and the coordinates and frequencies of the transmitting and receiving antennas;

步骤(2)，对步骤(1)的结果关于坐标(x_Tx，x_Rx，y_Tx，y_Rx)作四维傅里叶变换得到b(k_{x_T}，k_{x_R}，k_{y_T}，k_{y_R}，k)；Step (2), perform four-dimensional Fourier transform on the result of step (1) with respect to coordinates (x _Tx , x _Rx , y _Tx , y _Rx ) to obtain b(k _{x_T} , k _{x_R} , _{ky_T} , _{ky_R} , k) ;

步骤(3)，对步骤(2)作式(11)所示的变量代换，得到其中，式(11)为：In step (3), the variable substitution shown in formula (11) is performed on step (2) to obtain Among them, formula (11) is:

$\{\begin{matrix} {k k}_{x x} = = {k k}_{x x__T T} + + {k k}_{x x__R R} \\ {k k}_{y the y} = = {k k}_{y the y__T T} + + {k k}_{y the y__R R} \\ {k k}_{z z} = = {k k}_{z z__T T} + + {k k}_{z z__R R} \end{matrix} - - - - - - ((1111))$

步骤(4)，对步骤(3)的结果乘以传播损耗补偿因子 Step (4), multiply the result of step (3) by the propagation loss compensation factor

步骤(5)，对步骤(4)的结果作三维逆傅里叶变换。In step (5), three-dimensional inverse Fourier transform is performed on the result of step (4).

上述用于近程MIMO成像的传播损耗补偿方法中，发射单元坐标(x_Tx，y_Tx，0)，接收单元坐标(x_Rx，y_Rx，0)，待测目标坐标位置(x，y，z)，其像函数为f(x，y，z)，考虑电磁波传输过程中的空间衰减，信号由发射单元发射经过目标散射后，接收单元信号为In the above propagation loss compensation method for short-range MIMO imaging, the coordinates of the transmitting unit (x _Tx , y _Tx , 0), the coordinates of the receiving unit (x _Rx , y _Rx , 0), the coordinate position of the target to be measured (x, y, z), its image function is f(x, y, z), considering the spatial attenuation in the process of electromagnetic wave transmission, after the signal is emitted by the transmitting unit and scattered by the target, the signal of the receiving unit is

$s the s (({x x}_{Tx Tx},, {x x}_{Rx Rx},, {y the y}_{Tx Tx},, {y the y}_{Rx Rx},, k k)) = = \frac{11}{44 π π {R R}_{Tx Tx} {R R}_{Rx Rx}} \cdot &Center Dot; f f ((x x,, y the y,, z z)) \cdot &Center Dot; {e e}^{- - jk jk {R R}_{Tx Tx}} \cdot &Center Dot; {e e}^{- - jk jk {R R}_{Rx Rx}} - - - - - - ((55))$

其中，k＝ω/c表示波数，ω表示工作角频率，c为电磁波在自由空间中传播速度；电磁波由发射单元传播到目标区域距离为R_Tx，经由目标散射后，由目标传播到接收单元距离为R_Rx，具体表示如下：Among them, k=ω/c represents the wave number, ω represents the operating angular frequency, c is the propagation speed of electromagnetic waves in free space; the distance of electromagnetic waves from the transmitting unit to the target area is R _Tx , and after being scattered by the target, the electromagnetic wave propagates from the target to the receiving unit The distance is R _Rx , which is expressed as follows:

$\begin{matrix} {R R}_{Tx Tx} = = \sqrt{{(({x x}_{Tx Tx} - - x x))}^{22} + + {(({y the y}_{Tx Tx} - - y the y))}^{22} + + {z z}^{22}} \\ {R R}_{Rx Rx} = = \sqrt{{(({x x}_{Rx Rx} - - x x))}^{22} + + {(({y the y}_{Rx Rx} - - y the y))}^{22} + + {z z}^{22}} \end{matrix} - - - - - - ((66))$

对式(5)关于距离坐标进行4D空间傅里叶变换，分成两个2D空间傅里叶变换的乘积，式(5)的4D空间傅里叶变换化为Carry out 4D space Fourier transform to formula (5) about distance coordinates, divide into the product of two 2D space Fourier transforms, the 4D space Fourier transform of formula (5) is transformed into

$\begin{matrix} S S (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) = = \frac{11}{44 π π} f f ((x x,, y the y,, z z)) \cdot &Center Dot; \\ {S S}_{T T} (({k k}_{x x__T T},, {k k}_{y the y__T T},, k k)) \cdot \cdot {S S}_{R R} (({k k}_{x x__R R},, {k k}_{y the y__R R},, k k)) \end{matrix} - - - - - - ((77))$

$\begin{matrix} {S S}_{T T} (({k k}_{x x__T T},, {k k}_{y the y__T T},, k k)) = = &Integral; &Integral; &Integral; &Integral; \frac{11}{\sqrt{{(({x x}_{Tx Tx} - - x x))}^{22} + + {(({y the y}_{Tx Tx} - - y the y))}^{22} + + {z z}^{22}}} \\ \cdot &Center Dot; {e e}^{- - jk jk \sqrt{{(({x x}_{Tx Tx} - - x x))}^{22} + + {(({y the y}_{Tx Tx} - - y the y))}^{22} + + {z z}^{22}}} \cdot &Center Dot; {e e}^{- - j j {k k}_{x x__T T} \cdot &Center Dot; {x x}_{Tx Tx}} \cdot \cdot {e e}^{- - j j {k k}_{y the y__T T} \cdot &Center Dot; {y the y}_{Tx Tx}} {dx dx}_{Tx Tx} {dy dy}_{Tx Tx} \end{matrix} - - - - - - ((88))$

$\begin{matrix} {S S}_{R R} (({k k}_{x x__R R},, {k k}_{y the y__R R},, k k)) = = \frac{11}{\sqrt{{(({x x}_{Rx Rx} - - x x))}^{22} + + {(({y the y}_{Rx Rx} - - y the y))}^{22} + + {z z}^{22}}} \\ \cdot &Center Dot; {e e}^{- - jk jk \sqrt{{(({x x}_{Rx Rx} - - x x))}^{22} + + {(({y the y}_{Rx Rx} - - y the y))}^{22} + + {z z}^{22}}} \cdot &Center Dot; {e e}^{- - j j {k k}_{x x__R R} \cdot &Center Dot; {x x}_{Rx Rx}} \cdot \cdot {e e}^{- - j j {k k}_{y the y__R R} \cdot \cdot {y the y}_{Rx Rx}} {dx dx}_{Rx Rx} {dy dy}_{Rx Rx} \end{matrix} - - - - - - ((99))$

根据驻定相位原理，求解式(7)，得According to the principle of stationary phase, solving formula (7), we get

$\begin{matrix} S S (({k k}_{x x__T T} . . {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) = = - - f f ((x x,, y the y,, z z)) \cdot \cdot \\ \frac{π π {k k}_{z z__T T}^{11 / / 22} \cdot \cdot {k k}_{z z__R R}^{11 / / 22}}{{k k}^{33} \cdot \cdot {z z}^{33}} \cdot \cdot exp exp [[- - j j (({k k}_{z z__T T} + + {k k}_{z z__R R})) \cdot &Center Dot; z z]] \\ \cdot &Center Dot; exp exp [[- - j j (({k k}_{x x__T T} + + {k k}_{x x__R R})) x x]] \cdot &Center Dot; exp exp [[- - j j (({k k}_{y the y__T T} + + {k k}_{y the y__R R})) y the y]] \end{matrix} - - - - - - ((1010))$

其中， in,

进行变量代换，令To perform variable substitution, let

则(10)式化为Then (10) can be transformed into

$\begin{matrix} S S (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R} . . k k)) = = - - f f ((x x,, y the y,, k k)) \cdot \cdot \\ \frac{π π {k k}_{z z__T T}^{11 / / 22} \cdot \cdot {k k}_{z z__R R}^{11 / / 22}}{{k k}^{33} \cdot \cdot {z z}^{33}} \cdot &Center Dot; exp exp [[- - j j {k k}_{x x} \cdot &Center Dot; x x - - j j {k k}_{y the y} \cdot &Center Dot; y the y - - j j {k k}_{y the y} \cdot &Center Dot; z z]] \end{matrix} - - - - - - ((1212))$

设目标区域函数为O(x，y，z)，则其回波函数表示为Let the target area function be O(x, y, z), then its echo function is expressed as

$\begin{matrix} b b (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) = = \underset{O o ((x x,, y the y,, z z))}{&Integral; &Integral; &Integral; &Integral; &Integral; &Integral;} S S (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) dxdydz dxdydz \\ = = - - \frac{π π {k k}_{z z__T T}^{11 / / 22} \cdot &Center Dot; {k k}_{z z__R R}^{11 / / 22}}{{k k}^{33} {z z}^{33}} \cdot &Center Dot; \underset{O o ((x x,, y the y,, z z))}{&Integral; &Integral; &Integral; &Integral; &Integral; &Integral;} f f ((x x,, y the y,, z z)) \cdot &Center Dot; exp exp ((- - j j {k k}_{x x} \cdot &Center Dot; x x - - j j {k k}_{y the y} \cdot \cdot y the y - - j j {k k}_{z z} \cdot \cdot z z)) dxdydz dxdydz \end{matrix} - - - - - - ((1313))$

于是，像函数Thus, functions like

$\begin{matrix} f f ((x x,, y the y,, z z)) = = - - &Integral; &Integral; &Integral; &Integral; &Integral; &Integral; \frac{{k k}^{33} {z z}^{33}}{π π {k k}_{z z__T T}^{11 / / 22} \cdot \cdot {k k}_{z z__R R}^{11 / / 22}} \cdot \cdot b b (({k k}_{x x__T T},, {k k}_{y the y__T T},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) {dk dk}_{x x} {dk dk}_{y the y} dk dk \\ = = - - &Integral; &Integral; &Integral; &Integral; &Integral; &Integral; \frac{{k k}^{33} {z z}^{33}}{π π {k k}_{z z__T T}^{11 / / 22} \cdot &Center Dot; {k k}_{z z__R R}^{11 / / 22}} \cdot &Center Dot; {((\frac{k k}{{k k}_{z z__T T}} + + \frac{k k}{{k k}_{z z__R R}}))}^{- - 11} \cdot &Center Dot; \overset{&OverBar; &OverBar;}{b b} (({k k}_{x x},, {k k}_{y the y},, {k k}_{z z})) {dk dk}_{x x} {dk dk}_{y the y} {dk dk}_{z z} \\ {= = FFF FFF}_{33 D D.}^{- - 11} [[- - \frac{{k k}^{22} {z z}^{33}}{π π} \cdot &Center Dot; \frac{{k k}_{z z__T T}^{11 / / 22} \cdot &Center Dot; {k k}_{z z__R R}^{11 / / 22}}{(({k k}_{z z__R R} + + {k k}_{z z__R R}))} \cdot &Center Dot; \overset{&OverBar; &OverBar;}{b b} (({k k}_{x x},, {k k}_{y the y},, {k k}_{z z}))]] \end{matrix} - - - - - - ((1414))$

式中，即为双站RMA传播损耗补偿因子。In the formula, That is, the two-site RMA propagation loss compensation factor.

本发明的有益效果是：The beneficial effects of the present invention are:

(1)适用于超宽带近场、远场成像；(1) Suitable for ultra-wideband near-field and far-field imaging;

(2)在不增加任何硬件成本的情况下实现MIMO成像幅度精度补偿，提高成像质量；(2) Realize the compensation of MIMO imaging amplitude accuracy without increasing any hardware cost, and improve the imaging quality;

(3)可适用于一维阵列、二维阵列的二维、三维成像。(3) It is applicable to two-dimensional and three-dimensional imaging of one-dimensional array and two-dimensional array.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

图1为现有技术中单站RMA成像原理示意图；FIG. 1 is a schematic diagram of the principle of single-station RMA imaging in the prior art;

图2为基于本发明补偿方法的双站RMA成像原理示意图；Fig. 2 is a schematic diagram of the dual-station RMA imaging principle based on the compensation method of the present invention;

图3为本发明的MIMO成像传播损耗补偿流程图；Fig. 3 is a flowchart of MIMO imaging propagation loss compensation of the present invention;

图4(a)为传播损耗补偿前仿真图；Figure 4(a) is a simulation diagram before propagation loss compensation;

图4(b)为传播损耗补偿后仿真图。Figure 4(b) is a simulation diagram after propagation loss compensation.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

本发明提出了一种用于近程MIMO成像的传播损耗补偿方法，重新推导用于近程MIMO双站成像的RMA公式，回波信号考虑近场距离衰减项，公式推导后发现像函数幅度项存在补偿因子，成像处理时补偿相应的参数。The present invention proposes a propagation loss compensation method for short-range MIMO imaging, and re-deduces the RMA formula for short-range MIMO dual-station imaging. The echo signal considers the near-field distance attenuation item, and the image function amplitude item is found after the formula is deduced There is a compensation factor, and the corresponding parameters are compensated during imaging processing.

下面结合附图对本发明的用于近程MIMO成像的传播损耗补偿方法进行详细说明。The propagation loss compensation method for short-range MIMO imaging of the present invention will be described in detail below with reference to the accompanying drawings.

设二维阵列分布如图2所示，发射单元坐标(x_Tx，y_Tx，0)，接收单元坐标(x_Rx，y_Rx，0)，目标位置(x，y，z)，假设待测目标为一理想散射点，坐标位置(x，y，z)，其像函数为f(x，y，z)，考虑电磁波传输过程中的空间衰减，信号由发射单元发射经过目标散射后，接收单元信号为Assuming that the two-dimensional array distribution is shown in Figure 2, the coordinates of the transmitting unit (x _Tx , y _Tx , 0), the coordinates of the receiving unit (x _Rx , y _Rx , 0), and the target position (x, y, z), assuming that the measured The target is an ideal scattering point, the coordinate position is (x, y, z), and its image function is f(x, y, z). Considering the spatial attenuation in the process of electromagnetic wave transmission, the signal is emitted by the transmitting unit and scattered by the target, and then received The unit signal is

$s the s (({x x}_{Tx Tx},, {x x}_{Rx Rx},, {y the y}_{Tx Tx},, {y the y}_{Rx Rx},, k k)) = = \frac{11}{44 π π {R R}_{Tx Tx} {R R}_{Rx Rx}} \cdot \cdot f f ((x x,, y the y,, z z)) \cdot &Center Dot; {e e}^{- - jk jk {R R}_{Tx Tx}} \cdot \cdot {e e}^{- - jk jk {R R}_{Rx Rx}} - - - - - - ((55))$

其中，k＝ω/c表示波数，ω表示工作角频率，c为电磁波在自由空间中传播速度。电磁波由发射单元传播到目标区域距离为R_Tx，经由目标散射后，由目标传播到接收单元距离为R_Rx，具体表示如下Among them, k=ω/c represents the wave number, ω represents the operating angular frequency, and c represents the propagation speed of electromagnetic waves in free space. The electromagnetic wave propagates from the transmitting unit to the target area at a distance of R _Tx , and after being scattered by the target, the distance from the target to the receiving unit is R _Rx , specifically expressed as follows

对式(5)关于距离坐标进行4D空间傅里叶变换，可以分成两个2D空间傅里叶变换的乘积，式(5)的4D空间傅里叶变换可化为Carrying out the 4D space Fourier transform of formula (5) with respect to the distance coordinates can be divided into the product of two 2D space Fourier transforms, and the 4D space Fourier transform of formula (5) can be transformed into

$\begin{matrix} S S (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) = = \frac{11}{44 π π} f f ((x x,, y the y,, z z)) \cdot &Center Dot; \\ {S S}_{T T} (({k k}_{x x__T T},, {k k}_{y the y__T T},, k k)) \cdot &Center Dot; {S S}_{R R} (({k k}_{x x__R R},, {k k}_{y the y__R R},, k k)) \end{matrix} - - - - - - ((77))$

$\begin{matrix} {S S}_{T T} (({k k}_{x x__T T},, {k k}_{y the y__T T},, k k)) = = &Integral; &Integral; &Integral; &Integral; \frac{11}{\sqrt{{(({x x}_{Tx Tx} - - x x))}^{22} + + {(({y the y}_{Tx Tx} - - y the y))}^{22} + + {z z}^{22}}} \\ \cdot \cdot {e e}^{- - jk jk \sqrt{{(({x x}_{Tx Tx} - - x x))}^{22} + + {(({y the y}_{Tx Tx} - - y the y))}^{22} + + {z z}^{22}}} \cdot \cdot {e e}^{- - j j {k k}_{x x__T T} \cdot \cdot {x x}_{Tx Tx}} \cdot \cdot {e e}^{- - j j {k k}_{y the y__T T} \cdot \cdot {y the y}_{Tx Tx}} {dx dx}_{Tx Tx} {dy dy}_{Tx Tx} \end{matrix} - - - - - - ((88))$

$\begin{matrix} {S S}_{R R} (({k k}_{x x__R R},, {k k}_{y the y__R R},, k k)) = = \frac{11}{\sqrt{{(({x x}_{Rx Rx} - - x x))}^{22} + + {(({y the y}_{Rx Rx} - - y the y))}^{22} + + {z z}^{22}}} \\ \cdot \cdot {e e}^{- - jk jk \sqrt{{(({x x}_{Rx Rx} - - x x))}^{22} + + {(({y the y}_{Rx Rx} - - y the y))}^{22} + + {z z}^{22}}} \cdot &Center Dot; {e e}^{- - j j {k k}_{x x__R R} \cdot &Center Dot; {x x}_{Rx Rx}} \cdot &Center Dot; {e e}^{- - j j {k k}_{y the y__R R} \cdot &Center Dot; {y the y}_{Rx Rx}} {dx dx}_{Rx Rx} {dy dy}_{Rx Rx} \end{matrix} - - - - - - ((99))$

根据驻定相位原理，求解式(7)，得According to the principle of stationary phase, solving equation (7), we get

$\begin{matrix} S S (({k k}_{x x__T T} . . {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) = = - - f f ((x x,, y the y,, z z)) \cdot &Center Dot; \\ \frac{π π {k k}_{z z__T T}^{11 / / 22} \cdot \cdot {k k}_{z z__R R}^{11 / / 22}}{{k k}^{33} \cdot \cdot {z z}^{33}} \cdot \cdot exp exp [[- - j j (({k k}_{z z__T T} + + {k k}_{z z__R R})) \cdot \cdot z z]] \\ \cdot &Center Dot; exp exp [[- - j j (({k k}_{x x__T T} + + {k k}_{x x__R R})) x x]] \cdot &Center Dot; exp exp [[- - j j (({k k}_{y the y__T T} + + {k k}_{y the y__R R})) y the y]] \end{matrix} - - - - - - ((1010))$

其中， $k_{z_T} = \sqrt{k^{2} - k_{x_T}^{2} - k_{y_T}^{2}}, k_{z_R} = \sqrt{k^{2} - k_{x_R}^{2} - k_{y_R}^{2}} .$ in, $k_{z_T} = \sqrt{k^{2} - k_{x_T}^{2} - k_{the y_T}^{2}}, k_{z_R} = \sqrt{k^{2} - k_{x_R}^{2} - k_{the y_R}^{2}} .$

进行变量代换，令To perform variable substitution, let

则(10)式可以化为Then (10) can be transformed into

$\begin{matrix} S S (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R} . . k k)) = = - - f f ((x x,, y the y,, k k)) \cdot &Center Dot; \\ \frac{π π {k k}_{z z__T T}^{11 / / 22} \cdot \cdot {k k}_{z z__R R}^{11 / / 22}}{{k k}^{33} \cdot \cdot {z z}^{33}} \cdot \cdot exp exp [[- - j j {k k}_{x x} \cdot \cdot x x - - j j {k k}_{y the y} \cdot \cdot y the y - - j j {k k}_{y the y} \cdot \cdot z z]] \end{matrix} - - - - - - ((1212))$

实际应用中目标总是为一片区域，设目标区域函数为O(x，y，z)，则其回波函数可表示为In practical applications, the target is always an area, and if the target area function is O(x, y, z), then its echo function can be expressed as

$\begin{matrix} b b (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) = = \underset{O o ((x x,, y the y,, z z))}{&Integral; &Integral; &Integral; &Integral; &Integral; &Integral;} S S (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) dxdydz dxdydz \\ = = - - \frac{π π {k k}_{z z__T T}^{11 / / 22} \cdot \cdot {k k}_{z z__R R}^{11 / / 22}}{{k k}^{33} {z z}^{33}} \cdot \cdot \underset{O o ((x x,, y the y,, z z))}{&Integral; &Integral; &Integral; &Integral; &Integral; &Integral;} f f ((x x,, y the y,, z z)) \cdot &Center Dot; exp exp ((- - j j {k k}_{x x} \cdot \cdot x x - - j j {k k}_{y the y} \cdot &Center Dot; y the y - - j j {k k}_{z z} \cdot &Center Dot; z z)) dxdydz dxdydz \end{matrix} - - - - - - ((1313))$

于是，像函数Thus, functions like

$\begin{matrix} f f ((x x,, y the y,, z z)) = = - - &Integral; &Integral; &Integral; &Integral; &Integral; &Integral; \frac{{k k}^{33} {z z}^{33}}{π π {k k}_{z z__T T}^{11 / / 22} \cdot &Center Dot; {k k}_{z z__R R}^{11 / / 22}} \cdot &Center Dot; b b (({k k}_{x x__T T},, {k k}_{y the y__T T},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) {dk dk}_{x x} {dk dk}_{y the y} dk dk \\ = = - - &Integral; &Integral; &Integral; &Integral; &Integral; &Integral; \frac{{k k}^{33} {z z}^{33}}{π π {k k}_{z z__T T}^{11 / / 22} \cdot \cdot {k k}_{z z__R R}^{11 / / 22}} \cdot \cdot {((\frac{k k}{{k k}_{z z__T T}} + + \frac{k k}{{k k}_{z z__R R}}))}^{- - 11} \cdot \cdot \overset{&OverBar; &OverBar;}{b b} (({k k}_{x x},, {k k}_{y the y},, {k k}_{z z})) {dk dk}_{x x} {dk dk}_{y the y} {dk dk}_{z z} \\ {= = FFF FFF}_{33 D D.}^{- - 11} [[- - \frac{{k k}^{22} {z z}^{33}}{π π} \cdot &Center Dot; \frac{{k k}_{z z__T T}^{11 / / 22} \cdot &Center Dot; {k k}_{z z__R R}^{11 / / 22}}{(({k k}_{z z__R R} + + {k k}_{z z__R R}))} \cdot &Center Dot; \overset{&OverBar; &OverBar;}{b b} (({k k}_{x x},, {k k}_{y the y},, {k k}_{z z}))]] \end{matrix} - - - - - - ((1414))$

如图3所示，利用本发明的方法对近程MIMO成像的传播损耗补偿的过程包括以下步骤：As shown in Figure 3, the process of using the method of the present invention to compensate for the propagation loss of short-range MIMO imaging includes the following steps:

步骤(3)，对步骤(2)作式(11)所示的变量代换，得到 In step (3), the variable substitution shown in formula (11) is performed on step (2) to obtain

根据本发明的补偿方法对多探头阵列进行幅度补偿效果进行对比仿真，图4(a)所示为传播损耗补偿前仿真图，图4(b)所示为传播损耗补偿后仿真图，对比图4的成像结果可以看出，采用本发明的补偿方法，能够有效的提高成像的幅度精度，提高成像质量。According to the compensation method of the present invention, the amplitude compensation effect of the multi-probe array is compared and simulated, and Fig. 4 (a) shows the simulation diagram before the propagation loss compensation, and Fig. 4 (b) shows the simulation diagram after the propagation loss compensation, and the comparison diagram 4, it can be seen that the compensation method of the present invention can effectively improve the amplitude accuracy of imaging and improve the imaging quality.

本发明的传播损耗补偿方法适用于超宽带近场、远场成像；在不增加任何硬件成本的情况下实现MIMO成像幅度精度补偿，提高成像质量；可适用于一维阵列、二维阵列的二维、三维成像。The propagation loss compensation method of the present invention is suitable for ultra-wideband near-field and far-field imaging; it can realize MIMO imaging amplitude accuracy compensation without increasing any hardware cost, and improve imaging quality; dimensional and 3D imaging.

以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of the present invention. within the scope of protection.

Claims

1. A propagation loss compensation method for short-range MIMO imaging, characterized in that, comprising the following steps:

Step (1), first, according to the layout of the MIMO array, establish a coordinate system to determine the corresponding relationship between the received signal b(x _Tx , x _Rx , y _Tx , y _Rx , k) and the coordinates and frequencies of the transmitting and receiving antennas;

Step (2), perform four-dimensional Fourier transform on the result of step (1) with respect to coordinates (x _Tx , x _Rx , y _Tx , y _Rx ) to obtain b(k _{x_T} , k _{x_R} , _{ky_T} , _{ky_R} , k) ;

In step (3), the variable substitution shown in formula (11) is performed on step (2) to obtain Among them, formula (11) is:

\{\begin{matrix} {k k}_{x x} = = {k k}_{x x__T T} + + {k k}_{x x__R R} \\ {k k}_{y the y} = = {k k}_{y the y__T T} + + {k k}_{y the y__R R} \\ {k k}_{z z} = = {k k}_{z z__T T} + + {k k}_{z z__R R} \end{matrix} - - - - - - ((1111))

Step (4), multiply the result of step (3) by the propagation loss compensation factor

In step (5), three-dimensional inverse Fourier transform is performed on the result of step (4).

2. the propagation loss compensation method for short-range MIMO imaging as claimed in claim 1, is characterized in that, transmitting unit coordinates (x _Tx , y _Tx , 0), receiving unit coordinates (x _Rx , y _Rx , 0) , the coordinate position (x, y, z) of the target to be measured, its image function is f(x, y, z), considering the spatial attenuation in the process of electromagnetic wave transmission, the signal is emitted by the transmitting unit and scattered by the target, the signal of the receiving unit is

s the s (({x x}_{Tx Tx},, {x x}_{Rx Rx},, {y the y}_{Tx Tx},, {y the y}_{Rx Rx},, k k)) = = \frac{11}{44 π π {R R}_{Tx Tx} {R R}_{Rx Rx}} \cdot &Center Dot; f f ((x x,, y the y,, z z)) \cdot &Center Dot; {e e}^{- - jk jk {R R}_{Tx Tx}} \cdot &Center Dot; {e e}^{- - jk jk {R R}_{Rx Rx}} - - - - - - ((55))

Among them, k=ω/c represents the wave number, ω represents the operating angular frequency, c is the propagation speed of electromagnetic waves in free space; the distance of electromagnetic waves from the transmitting unit to the target area is R _Tx , and after being scattered by the target, the electromagnetic wave propagates from the target to the receiving unit The distance is R _Rx , which is expressed as follows:

\begin{matrix} {R R}_{Tx Tx} = = \sqrt{{(({x x}_{Tx Tx} - - x x))}^{22} + + {(({y the y}_{Tx Tx} - - y the y))}^{22} + + {z z}^{22}} \\ {R R}_{Rx Rx} = = \sqrt{{(({x x}_{Rx Rx} - - x x))}^{22} + + {(({y the y}_{Rx Rx} - - y the y))}^{22} + + {z z}^{22}} \end{matrix} - - - - - - ((66))

Carry out 4D space Fourier transform to formula (5) about distance coordinates, divide into the product of two 2D space Fourier transforms, the 4D space Fourier transform of formula (5) is transformed into

\begin{matrix} S S (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T,, {k k}_{y the y__R R},, k k})) = = \frac{11}{44 π π} f f ((x x,, y the y,, z z)) \cdot \cdot \\ {S S}_{T T} (({k k}_{x x__T T},, {k k}_{y the y__T T} . . k k)) \cdot \cdot {S S}_{R R} (({k k}_{x x__R R},, {k k}_{y the y__R R},, k k)) \end{matrix} - - - - - - ((77))

\begin{matrix} {S S}_{T T} (({k k}_{x x__T T,,} {k k}_{y the y__T T},, k k)) = = &Integral; &Integral; &Integral; &Integral; \frac{11}{\sqrt{{(({x x}_{Tx Tx} - - x x))}^{22} + + {(({y the y}_{Tx Tx} - - y the y))}^{22} + + {z z}^{22}}} \\ \cdot \cdot {e e}^{- - jk jk \sqrt{{(({x x}_{Tx Tx} - - x x))}^{22} + + {(({y the y}_{Tx Tx} - - y the y))}^{22} + + {z z}^{22}}} \cdot &Center Dot; {e e}^{- - j j {k k}_{x x__T T} \cdot &Center Dot; {x x}_{Tx Tx}} \cdot &Center Dot; {e e}^{- - j j {k k}_{y the y__T T} \cdot &Center Dot; {y the y}_{Tx Tx}} d d {x x}_{Tx Tx} {dy dy}_{Tx Tx} \end{matrix} - - - - - - ((88))

\begin{matrix} {S S}_{R R} (({k k}_{x x__R R,,} {k k}_{y the y__R R},, k k)) = = &Integral; &Integral; &Integral; &Integral; \frac{11}{\sqrt{{(({x x}_{Rx Rx} - - x x))}^{22} + + {(({y the y}_{Rx Rx} - - y the y))}^{22} + + {z z}^{22}}} \\ \cdot &Center Dot; {e e}^{- - jk jk \sqrt{{(({x x}_{Rx Rx} - - x x))}^{22} + + {(({y the y}_{Rx Rx} - - y the y))}^{22} + + {z z}^{22}}} \cdot \cdot {e e}^{- - j j {k k}_{x x__R R} \cdot &Center Dot; {x x}_{Rx Rx}} \cdot \cdot {e e}^{- - j j {k k}_{y the y__R R} \cdot &Center Dot; {y the y}_{Rx Rx}} d d {x x}_{Rx Rx} {dy dy}_{Rx Rx} \end{matrix} - - - - - - ((99))

According to the principle of stationary phase, solving formula (7), we get

\begin{matrix} S S (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) = = - - f f ((x x,, y the y,, z z)) \cdot \cdot \\ \frac{{π π {k k}_{z z__T T}}^{11 / / 22} \cdot &Center Dot; {k k}_{z z__R R}^{11 / / 22}}{{k k}^{33} \cdot &Center Dot; {z z}^{33}} \cdot &Center Dot; exp exp [[- - j j (({k k}_{z z__T T} + + {k k}_{z z__R R})) \cdot &Center Dot; z z]] \\ \cdot \cdot exp exp [[- - j j (({k k}_{x x__T T} + + {k k}_{x x__R R})) x x]] \cdot \cdot exp exp [[- - j j (({k k}_{y the y__T T} + + {k k}_{y the y__R R})) y the y]] \end{matrix} - - - - - - ((1010))

in,

k_{z_T} = \sqrt{k^{2} - k_{x_T}^{2} - k_{the y_T}^{2}},

k_{z_R} = \sqrt{k^{2} - k_{x_R}^{2} - k_{the y_R}^{2}} .

To perform variable substitution, let

\{\begin{matrix} {k k}_{x x} = = {k k}_{x x__T T} + + {k k}_{x x__R R} \\ {k k}_{y the y} = = {k k}_{y the y__T T} + + {k k}_{y the y__R R} \\ {k k}_{z z} = = {k k}_{z z__T T} + + {k k}_{z z__R R} \end{matrix} - - - - - - ((1111))

Then (10) can be transformed into

\begin{matrix} S S (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) = = - - f f ((x x,, y the y,, z z)) \cdot &Center Dot; \\ \frac{{πk πk}_{z z__T T}^{11 / / 22} \cdot &Center Dot; {k k}_{z z__R R}^{11 / / 22}}{{k k}^{33} \cdot &Center Dot; {z z}^{33}} \cdot &Center Dot; exp exp [[- - j j {k k}_{x x} \cdot &Center Dot; x x - - {jk jk}_{y the y} \cdot &Center Dot; y the y - - {jk jk}_{y the y} \cdot &Center Dot; z z]] \end{matrix} - - - - - - ((1212))

Let the target area function be O(x, y, z), then its echo function is expressed as

\begin{matrix} b b (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) = = \underset{O o ((x x,, y the y,, z z))}{&Integral; &Integral; &Integral; &Integral; &Integral; &Integral;} S S (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) dxdydz dxdydz \\ = = - - \frac{π π {k k}_{z z__T T}^{11 / / 22} \cdot &Center Dot; {k k}_{z z__R R}^{11 / / 22}}{{k k}^{33} {z z}^{33}} \cdot &Center Dot; \underset{O o ((x x,, y the y,, z z))}{&Integral; &Integral; &Integral; &Integral; &Integral; &Integral;} f f ((x x,, y the y,, z z)) \cdot \cdot exp exp ((- - {jk jk}_{x x} \cdot \cdot x x - - {jk jk}_{y the y} \cdot \cdot y the y - - {jk jk}_{z z} \cdot &Center Dot; z z)) dxdydz dxdydz \end{matrix} - - - - - - ((1313))

Thus, functions like

\begin{matrix} f f ((x x,, y the y,, z z)) = = - - &Integral; &Integral; &Integral; &Integral; &Integral; &Integral; \frac{{k k}^{33} {z z}^{33}}{{πk πk}_{z z__T T}^{11 / / 22} \cdot &Center Dot; {k k}_{z z__R R}^{11 / / 22}} \cdot &Center Dot; b b (({k k}_{x x__T T},, {k k}_{x x__R R},, {k k}_{y the y__T T},, {k k}_{y the y__R R},, k k)) {dk dk}_{x x} {dk dk}_{y the y} dk dk \\ = = - - &Integral; &Integral; &Integral; &Integral; &Integral; &Integral; \frac{{k k}^{33} {z z}^{33}}{{πk πk}_{z z__T T}^{11 / / 22} \cdot &Center Dot; {k k}_{z z__R R}^{11 / / 22}} \cdot \cdot {((\frac{k k}{{k k}_{z z__T T}} + + \frac{k k}{{k k}_{z z__R R}}))}^{- - 11} \cdot \cdot \overset{&OverBar; &OverBar;}{b b} (({k k}_{x x},, {k k}_{y the y},, {k k}_{z z})) {dx dx}_{x x} {dk dk}_{y the y} {dk dk}_{z z} \\ = = FF FF {T T}_{33 D D.}^{- - 11} [[- - \frac{{k k}^{22} {z z}^{33}}{π π} \cdot \cdot \frac{{k k}_{z z__T T}^{11 / / 22} \cdot \cdot {k k}_{z z__R R}^{11 / / 22}}{(({k k}_{z z__T T} + + {k k}_{z z__R R}))} \cdot \cdot \overset{&OverBar; &OverBar;}{b b} (({k k}_{x x},, {k k}_{y the y},, {k k}_{z z}))]] \end{matrix} - - - - - - ((1414))

In the formula, That is, the two-site RMA propagation loss compensation factor.