# Design and Analysis of a UWB MIMO Radar System with Miniaturized Vivaldi Antenna for Through-Wall Imaging

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## Abstract

**:**

## 1. Introduction

## 2. UWB MIMO Radar System

#### 2.1. SFCW Signal Model and Conventional BP Algorithm

_{m},0) and (x

_{n},0), where $m=1,2,\dots ,M$ and $n=1,2,\dots ,N.$ Given a point target located at (x

_{0},y

_{0}), the average distance between the target and the l-th pair of transmitter and receiver (l-th sampling point) is given by

_{q}= 2πf

_{q}/c is the wavenumber, R

_{l}(x

_{i},y

_{i}) is the average distance between the grid at (x

_{i},y

_{j}) and the l-th sampling point; f

_{0}is the start frequency, ∆f is the frequency step, α(x

_{i},y

_{j}) is the reflection coefficient of target, c is the velocity of light, and n(l,q) is the noise.

_{i},y

_{j}) is estimated by

#### 2.2. MIMO Array Topology Design

_{m}-th position and the n-th receiver at x

_{n}-th position are switched on, while all the other paths are switched off. This is equivalent (in far field) to transmitting and receiving with one single ‘virtual’ antenna in the median position (x

_{m}+ x

_{n})/2 of the axis. The midpoints of each transmit and receive element are regarded as virtual elements for a linear equivalent monostatic array. Hence, for each combination of the m-th and n-th antennas, a specific pattern along the median axis is defined. As a result, we can first obtain an equivalent uniform array with MN (MN = M×N) monostatic transceivers, which has expected resolution and low-level grating/side lobes. Then, corresponding to the reverse thinking process mentioned above, the MIMO sparse array can be designed by factorization. In this case, a synthetic aperture imaging algorithm, such as the BP-based imaging algorithm, can be directly used to image the targets.

#### 2.3. Low-Frequency UWB Miniaturized Vivaldi Antenna

#### 2.4. Radar Prototyping Result

## 3. Through-Wall Imaging Method with the Improved BP-Based Algorithm

_{2}. The distance from the equivalent phase center of MIMO antenna array to the surface of the wall is d

_{3}. The distance from the point p to the wall is d

_{1}. According to Snell’s law, we can obtain

_{x}

_{1}is T

_{t}

_{1}and the receiver R

_{x}

_{1}is T

_{r}

_{1}. For a pair of transmitting and receiving antennas, T

_{x}

_{1}and R

_{x}

_{1}, the whole travel time behind the wall can be obtained by ${T}_{1}={T}_{r1}+{T}_{t1}$. According to the designed sparse MIMO array, we can obtain the whole travel time from all transmitters and receivers (at the pair of T

_{x}

_{1}-R

_{x}

_{2}, R

_{x}

_{3}, … R

_{x}

_{8}to T

_{x}

_{8}− R

_{x}

_{8}) to the imaging area behind the wall (Figure 13, Part II).

## 4. Experiment Results

#### 4.1. Preliminary Experimental Tests

#### 4.2. Through-Wall Experiment Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Block diagram of the designed ultra-wideband multi-input multi-output (UWB MIMO) radar system.

**Figure 6.**Simulations for the MIMO sparse array by: (

**a**) the time domain back projection (TDBP) algorithm; (

**b**) the cross-correlation-based time domain back projection (CC-TDBP) algorithm.

**Figure 7.**(

**a**) Configurations of the designed Vivaldi antenna; (

**b**) Top and bottom view of the manufactured Vivaldi antenna.

**Figure 8.**Simulated E-plane and H-plane radiation patterns of the designed Vivaldi antenna. (

**a**) 0.5 GHz, (

**b**) 1.5 GHz, and (

**c**) 2.5 GHz.

**Figure 9.**(

**a**) The measured S11 of designed Vivaldi antenna with shorting slots and the simulated S11 of the proposed Vivaldi antenna with and without shorting slots; (

**b**) The measured result of S12 in time domain of the designed Vivaldi antenna with slots.

**Figure 13.**Flow chart of the improved TDBP algorithm. Part I: One-way travel time calculation based on the parallel algorithm; Part II: the whole travel time for the MIMO sparse array; Part III: TDBP imaging.

**Figure 15.**Imaging results of two corner reflectors by: (

**a**) the TDBP algorithm with direct coupling removal; (

**b**) the CC-TDBP algorithm with direct coupling removal; (

**c**) the TDBP algorithm with background removal; (

**d**) the CC-TDBP algorithm with background removal.

**Figure 17.**Imaging results obtained by the CC-TDBP algorithm with: (

**a**) direct coupling removal; (

**b**) background removal.

**Figure 19.**2D through-wall imaging results for two humans behind a wall: (

**a**) Imaging directly by the CC-TDBP algorithm with background removal; (

**b**) Imaging by improved the CC-TDBP algorithm considering the presence of the wall.

Parameters | Value |
---|---|

Start frequency | 0.4 GHz |

Stop frequency | 2.6 GHz |

Number of frequencies | 256 |

Number of transmitters/receivers | 8/8 |

Range resolution | 0.068 m |

Azimuth resolution | 5.8 rad |

Maximum range | 17.4 m |

Length of aperture | 1.1 m |

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## Share and Cite

**MDPI and ACS Style**

Hu, Z.; Zeng, Z.; Wang, K.; Feng, W.; Zhang, J.; Lu, Q.; Kang, X.
Design and Analysis of a UWB MIMO Radar System with Miniaturized Vivaldi Antenna for Through-Wall Imaging. *Remote Sens.* **2019**, *11*, 1867.
https://doi.org/10.3390/rs11161867

**AMA Style**

Hu Z, Zeng Z, Wang K, Feng W, Zhang J, Lu Q, Kang X.
Design and Analysis of a UWB MIMO Radar System with Miniaturized Vivaldi Antenna for Through-Wall Imaging. *Remote Sensing*. 2019; 11(16):1867.
https://doi.org/10.3390/rs11161867

**Chicago/Turabian Style**

Hu, Zhipeng, Zhaofa Zeng, Kun Wang, Weike Feng, Jianmin Zhang, Qi Lu, and Xiaoqian Kang.
2019. "Design and Analysis of a UWB MIMO Radar System with Miniaturized Vivaldi Antenna for Through-Wall Imaging" *Remote Sensing* 11, no. 16: 1867.
https://doi.org/10.3390/rs11161867