MIMO Radar

Abstract

We show the concept of multiple-input multiple-output (MIMO) radar and introduce practical applications, which include ground based synthetic aperture radar (GB-SAR) and ground penetrating radar (GPR). As an example, a 17 GHz MIMO GB-SAR system to be used for landslide monitoring and infrastructure measurement is described. We also show that a MIMO GPR system “Yakumo” can achieve dense three-dimensional (3D) subsurface imaging compared to conventional GPR. We also explain that MIMO GPR can be used for common midpoint (CMP) measurement, which can be used for the estimation of the vertical profile of EM velocity, which is related to soil moisture.

1. Introduction

Ground based synthetic aperture radar (GB-SAR) has been used for the observation of the displacement of ground surface and can be applied, for example, to remote landslide monitoring. GPR is a useful method for shallow subsurface imaging and widely used for the detection of buried pipes. Conventional GB-SAR systems and GPR systems are equipped with a pair of a transmitting antenna and receiving antenna, and synthetic aperture radar (SAR) processing is applied to the data sets acquired by moving the pair of antennas.

Instead of moving antennas for radar imaging, we introduce MIMO technique, where we use fixed multiple antennas for equivalent SAR imaging. In both GB-SAR and GPR systems, we use multiple transmitting and receiving antennas equivalent to multiple-input and multiple-output (MIMO). This radar configuration is referred as multi-static radar. However, we acquire all the combination of transmitting and receiving antennas, which is not common in the conventional multi-static radar. This is the reason why we call it MIMO radar, and we show that it expands the potential of radar drastically. The targets of MIMO GB-SAR and MIMO GPR such as land slope and buried pipes are stational, and we can acquire radar signal from these targets by switching all the transmitting and receiving antenna combinations. We do not need orthogonal signal transmission for the identification of the transmitted signal by receiver, because signals can be separated by the time sequence.

2. GB-SAR

Differential interferometric synthetic aperture radar (DInSAR) by GB-SAR is used to measure the displacement of the target surface [1]. This method has been used for monitoring landslide slopes [2, 3, 4], volcanic lava domes [4, 5], and inspection of large-scale infrastructure facilities such as dams and bridges [6, 7]. However, by conventional GB-SAR, the data for SAR processing is acquired by physically moving a radar unit equipped with a pair of transmitting and receiving antennas on a rail. The size of the rail determines the synthetic aperture length, which is typically about 2 m for 17 GHz GB-SAR. The data acquisition takes several tens of seconds to several minutes for one SAR image. Recently, MIMO radar [8, 9, 10, 11], which does not have to move a radar unit, has been proposed to use for GB-SAR applications.

MIMO radar is a multi-static array type radar that has multiple transmitting and receiving antennas. However, MIMO radar transmits electromagnetic wave from one of the transmitting antennas, and the reflected signal is received by all the receiving antennas. Consequently, for a radar system with M transmitting and N receiving antennas, M × N independent radar signals can be measured. This is equivalent to acquire radar signal by using M × N independent antenna pairs. This concept is called virtual array.

Compared to conventional GB-SAR, MIMO radar can acquire data in a short time by using electronic switches for multiple transmitting and receiving antennas. Since MIMO radar has no mechanical moving parts, it can improve the reliability of long-term operation.

3. MIMO GB-SAR

MIMO radar uses multiple transmitting and receiving antennas independently to form a single SAR image, and a virtual array replaces the physical transmitting and receiving array which is equivalent to an array composed of monostatic radar capable of transmitting and receiving.

Figure 1 shows the relationship between a physical bistatic radar consisting of a pair of transmitting and receiving antennas and a monostatic radar with a virtual array. Here, $O$ is the coordinate origin, $P$ is the target position, Tx and Rx are the transmitting and receiving antenna positions, ${\overrightarrow{a}}_n$ and ${\overrightarrow{b}}_m$ are the position vectors of the transmitting and receiving antennas, and $\overrightarrow{r}$ is the target position vector. The path length $R_{n,m}$ is that of the EM wave propagating from the n-th Tx antenna to the target and to the m-th Rx antenna is given as:

Figure 1.

The relationship between a physical bistatic radar consisting of a pair of transmitting and receiving antennas and a monostatic radar with a virtual array.

$$R_{n,m}=\left|\overrightarrow{r}-{\overrightarrow{a}}_n\right|+\left|\overrightarrow{r}-{\overrightarrow{b}}_m\right|$$E1

When the target is far enough from the origin compared to the wavelength, it can be approximated by

$$R_{n,m}=2\left|\overrightarrow{r}-\frac{{\overrightarrow{a}}_n+{\overrightarrow{b}}_m}{2}\right|$$E2

The condition for this approximation [11] is determined by the total length of the transmitting and receiving array $L_{\mathrm{Tx}}$, $L_{\mathrm{Rx}}$ as shown in (3). If (3) is satisfied, the array factor generated by the virtual array will be given by the product of the physical transmitting array factor (4) and the receiving array factor (5), where $\lambda$ is the wavelength, $k$ is the wavenumber, and $\overrightarrow{l}$ is the directional $\overrightarrow{r}$ vector given by (6).

$$\mid \overrightarrow{r}\mid \ge 1.24\sqrt{\frac{L_{\mathrm{Tx}}^3+L_{\mathrm{Rx}}^3}{\lambda }}$$E3

$$F_{\mathrm{Tx}}\left(\theta ,\varphi \right)=\frac{1}{N}{\mathrm{e}}^{-\mathit{jk}\mid \overrightarrow{r}\mid }\sum _{n=1}^N{\mathrm{e}}^{-\mathit{jk}{\overrightarrow{a}}_n\cdot \overrightarrow{l}}$$E4

$$F_{\mathrm{Rx}}\left(\theta ,\varphi \right)=\frac{1}{M}{\mathrm{e}}^{-\mathit{jk}\left|\overrightarrow{r}\right|}\sum _{n=1}^M{\mathrm{e}}^{-\mathit{jk}{\overrightarrow{b}}_m\cdot \overrightarrow{l}}$$E5

$$\overrightarrow{l}=\left(\begin{array}{c}sin\theta cos\varphi \\ sin\theta sin\varphi \\ cos\theta \end{array}\right)$$E6

To prevent the generation of grating lobes in a basic concept for designing array antenna, and the antenna spacing d must satisfy the condition $d<\lambda /2$. In MIMO radar, we consider this condition for the virtual array, but not for the physical antenna positions.

Back-projection algorithm is used to reconstruct the SAR image from data acquired by MIMO GB-SAR. The SAR image $I\left(\overrightarrow{r}\right)$ is obtained by (7), where, $s_{n,m}$ is the radar waveform (range profile) measured by the combination of the n-th transmit antenna and the m-th receive antenna.

$$I\left(\overrightarrow{r}\right)=\sum _{m=1}^M\sum _{n=1}^N{s}_{n,m}\left(t\right)e^{j4\pi R_{n,m}/c}$$E7

To estimate the surface displacement of the imaged objects, DInSAR is performed using the phase difference of a pair of SAR images acquired at different times. Assuming two SAR images acquired at different time as master and slave images, the phase difference $\mathrm{\Delta }\varphi$ between the master image I M and the slave image I S is given by (8).

$$\mathrm{\Delta }\varphi \left(\overrightarrow{r}\right)=arctan\left(\frac{Im\left(I_M\left(\overrightarrow{r}\right)I_S^{\ast }\left(\overrightarrow{r}\right)\right)}{Re\left(I_M\left(\overrightarrow{r}\right)I_S^{\ast }\left(\overrightarrow{r}\right)\right)}\right)$$E8

The actual displacement $\mathrm{\Delta }d$ is obtained by (9), where ${\lambda }_{\mathrm{c}}$ is the wavelength at the center frequency.

$$\mathrm{\Delta }d\left(\overrightarrow{r}\right)=\frac{{\lambda }_{\mathrm{c}}}{4\pi }\mathrm{\Delta }\varphi \left(\overrightarrow{r}\right)$$E9

4. 17 GHz MIMO radar design

By the recommendation of ITU, 17 GHz is one of the standard frequencies used for GB-SAR all over the world, and it is suitable for the measurement of bare soil ground surface. We use 17 GHz for our system, and the specifications of the MIMO radar that we designed are shown in Table 1. The designed antenna arrangement is shown in Figure 2. By using these technical specifications, the antenna array factors are simulated and shown in Figure 3. Figure 3 shows the array factors of the transmitting antenna array and the receiving antenna array and the virtual array. The separation of adjacent transmitting antennas is 17.5 mm, which is one wavelength at 17 GHz, and the separation of the adjacent receiving antennas is 131.3 mm, which corresponds to 7.5 wavelengths, and the separation of the adjacent virtual antennas is 4.4 mm, which is the 1/4 wavelength. The transmitting and receiving equidistant arrays are separated by 150 mm vertically.

Center frequency	fc	17.1 GHz
Frequency bandwidth	B	200 MHz
FM-CW sweep time	T	100 μs
Number of transmitting antennas	N	15
Number of receiving antennas	M	15

Table 1.

The technical specification of the 17 GHz MIMO radar.

Figure 2.

The antenna arrangement of the 17 GHz MIMO radar. 15Tx, 16Rx and 240 virtual antennas.

Figure 3.

The antenna factor of the 15 × 16 17 GHz MIMO radar.

In Figure 3, we find that the grating lobes are generated in the physical receiving antenna array. However, since the null points of the transmitting antenna array overlap it and cancel in the virtual array and the radar system has no grating lobes. We should note that the number of physical antennas can drastically be reduced from M × N to M + N by MIMO GB-SAR.

5. Evaluation of 17 GHz MIMO radar

A prototype MIMO radar based on the above design was built and evaluated. We used a patch antenna for the array antenna element [12], which has a wide beam in the horizontal direction and sharp beam in the vertical direction, to avoid the ground surface clutter. We adopt FMCW radar system, and the antennas were connected with coaxial cables through a 16ch semiconductor switch.

Experiments were conducted to evaluate the MIMO radar system. Figure 4 shows the MIMO radar facing the targets. A 15 cm trihedral square metal corner reflector is placed at 5 m from the center of the radar. In addition to the corner reflectors, there are also some targets. Figure 5 shows the reconstructed SAR intensity image. In Figure 5, we can find the image of the corner reflector at $\left[X,Z\right]=\left[0,5\right]$. The images of other targets are also formed accurately; we think the system works properly.

Figure 4.

The 17 GHz MIMO radar and targets.

Figure 5.

The reconstructed SAR intensity image of the 17 GHz MIMO radar.

We will use the prototype MIMO GB-SAR for ground surface displacement measurement. In order to evaluate the capability of DInSAR, we made a wooden wall having 10 m width and 2 m height, with 20 cm × 20 patches, which will be displaced from the flat surface. This wall has five displacement patches at 2.5 m intervals. The wall has a rough surface to suppress the specular reflection. In this experiment, the distance from the radar to the wall was 10 m. Figure 6 shows SAR interferograms when the displacement of all five patches is –4 mm. At this time, pixels below −35 dB were masked in the SAR intensity image in order to extract the displacement on the wall surface. Also, the squares in Figure 6 indicate the position of each displacement plane.

Figure 6.

SAR interferograms when the displacement of all five patches is –4 mm. The positions of the displacement are also shown.

We can confirm that the displacement was detected at the position of each displacement plane in Figure 6; Figure 7 shows a comparison of displacement and estimated displacement in each displacement plan, and we can see that the displacement is correctly estimated.

Figure 7.

A comparison of displacement and estimated displacement in each displacement plane.

6. GPR

Ground penetrating radar (GPR) is a useful method for shallow geophysical exploration and is widely used for the detection of buried objects such as pipes and cables and voids under pavement. GPR basically has a pair of transmit and receive antennas. By scanning the GPR unit, GPR profiles along the survey line can be obtained. In order to extend the swath width in the direction perpendicular to the survey line, we can set multiple radar units and measure simultaneously. If the multiple radar devices are synchronized, it is a multi-static radar and can greatly improve the quality of radar data. And if we use all the combinations of the transmit and receive antennas, we can configurate MIMO GPR.

7. MIMO-GPR “Yakumo”

We developed a MIMO GPR system “Yakumo” shown in Figure 8, for scanning a large area [13, 14, 15]. Yakumo was developed for surveying 1–2 m in depth, which is relatively deep compared to the similar multi-static GPR systems. Yakumo is a SF-CW radar that uses 50 MHz–1.5 GHz, which is a relatively low frequency compared to MIMO-GPR for pavement inspection. Since this device operates in a wide frequency bandwidth, it can select optimal frequency.

Figure 8.

MIMO GPR system “Yakumo”.

Figure 9 shows the antenna arrangement of this system, which is equipped with eight transmitting and receiving antennas, and Table 2 shows the technical specifications. Antenna feeding point separation in the same row is 240 mm but a minimum of 120 mm in the transverse direction between transmit and receive antenna by the staggered position.

Figure 9.

The antenna arrangement of the MIMO GPR system “Yakumo”.

Frequency	50 MHz–1.5 GHz
Radar system	SF-CW
Antenna element	Bowtie antenna
Number of antenna element	Tx 8, Rx 8
Data acquisition interval	1 cm
Data acquisition speed	7 km/h (1 cm interval)

Table 2.

The technical specifications of the MIMO GPR.

Yakumo is a multi-static radar, but by measuring the radio waves transmitted from one transmitting antenna with all receiving antennas, it is possible to acquire complete three-dimensional (3D) subsurface information by looking at the target from different angles. This leads to advanced 3D imaging.

8. Measurement example

An example of C-scan imaging by Yakumo is shown in Figure 10, which was acquired in a rice paddy field in winter time [14]. The radar was scanned in the horizontal direction of the figure, and six images of 2 m swarth width are superimposed vertically. The two white lines that can be seen in the C-scan image are agricultural drainage. Due to the high accuracy of the position control, the water pipes for drainage are correctly visualized in a straight line.

Figure 10.

C-scan imaging by Yakumo. The two white lines are agricultural drainage.

9. CMP measurement

Common midpoint (CMP) technique is used for estimating vertical profile of the velocity of electromagnetic wave in subsurface geological layers. In order to acquire the CMP data by using a conventional GPR system, we move the transmit and receive antenna simultaneously to the opposite direction so that the reflection from the CMP point stays at one position. We fit theoretical arrival time of the reflected wave from the target at the midpoint position and estimate the velocity and the depth of the reflecting layer simultaneously by the use of a velocity spectrum. MIMO GPR can achieve CMP measurement by selecting a combination of antennas so that the center of the array is the midpoint (midpoint) of the transmitting and receiving antennas, as shown in Figure 11. CMP measurement can be performed without moving antennas by MIMO GPR [15, 16].

Figure 11.

Combinations of the transmitting and receiving antennas to acquire CMP data sets.

We show an example of simultaneous CMP and profile measurements performed by Yakumo near Sendai Airport, which was damaged by the tsunami of the Great East Japan Earthquake in 2011. This site was a rice paddy field, but the tsunami invaded, and then, the surface soil was releveled. Figure 12 is the CMP data, and Figure 13 is the velocity spectrum obtained by the CMP analysis. Spectral peaks are seen at four different depths, detecting four stratified geological boundaries. Figure 14 shows a continuous display of the velocity obtained by the CMP analysis along the survey line. Under the assumption that homogeneous soil moisture is almost uniform, the distribution of geological boundaries can be detected. These are considered to contain information from geological deposited by the Great East Japan Earthquake in 2011 to past tsunami deposits from more than 1000 years ago.

Figure 12.

CMP profile measured by Yakumo near Sendai Airport.

Figure 13.

The velocity spectrum of the CMP profile in Figure 12a.

Figure 14.

Continuous display of the velocity obtained by the CMP analysis along the survey line.

10. Conclusion

The design and prototype MIMO GB-SAR was shown in this chapter. Higher pulse repetition frequency (PRF) of MIMO GB-SAR can easily be achieved, and it can be used for vibration measurement. Compared to the conventional GB-SAR, MIMO GB-SAR has advantage in maintenance, because there is no mechanical moving component.

By using MIMO-GPR, it is possible to measure a wide area with a wide swarth width for one scan. However, MIMO-GPR is not limited to wide-area measurement, but it can be used for simultaneous measurement of the wave velocity by CMP and common offset profiling [17, 18].

Acknowledgments

MIMO GB-SAR and MINO GPR have been conducted by graduate students of Tohoku University. I acknowledge the contribution especially by Yuya Akiyama and Amarsaikhan Tsogtbaatar. Part of this work was supported by JSPS KAKENHI Grant Number 20K20990.