# Terahertz active imaging radar: preprocessing and experiment results

- Gang Yao
^{1}Email author and - Yiming Pi
^{1}

**2014**:10

https://doi.org/10.1186/1687-1499-2014-10

© Yao and Pi; licensee Springer. 2014

**Received: **29 July 2013

**Accepted: **14 November 2013

**Published: **17 January 2014

## Abstract

A terahertz (THz) radar provides the possibility of higher precision imaging due to the wider bandwidth. A summary of a THz imaging radar system is presented with emphasis on THz radar component design, system design, and detective imaging. In this article, we introduce a linear frequency-modulated continuous wave (LFMCW) radar system with a 4.8-GHz bandwidth and theoretical resolution of 3.125 cm. The heterodyne RF receiver structure is applied to the system to reduce the sampling rate. A non-linear correction method is applied to compensate the range backscatter signal. With the presented LFMCW radar system, high-resolution images (3.5 cm × 3.5 cm) are achieved using the ISAR imaging technique. The experiments performed on the real LFMCW radar data have shown the capability of high-resolution imaging.

## Keywords

## 1. Introduction

A terahertz frequency band is a very important research and valuable undeveloped frequency resource, which especially has a great potential for the development of a high-resolution imaging radar. Compared to the traditional microwave radar, the advantages of a terahertz radar system are as follows: Firstly, the shorter wavelength is favorable toward providing a wider bandwidth, which could benefit the higher precision of imaging. Secondly, the narrow antenna beam in the terahertz band could not only obtain higher antenna gain in radar LOS, improving the ability of multi-target discrimination and recognition, but also reduce the opportunity of main lobe jamming [1–3]. The terahertz radar detection system is an important direction of terahertz technology domestic and overseas [4].

A linear frequency-modulated continuous wave (LFMCW) radar has advantages of high range resolution, low transmit power, high receiver sensitivity, simple structure, etc. [5, 6]. There is no distance blind area, better anti-stealth ability than a pulse radar, anti-background clutter, and anti-jamming characteristics, and it is particularly suitable for near-range applications [7]. A terahertz wave has great bandwidth itself, so making use of the LFMCW radar structure can obtain a very high range resolution; the emission power of the terahertz wave is still very low at present, and the LFMCW radar has lower emission power than the pulse radar, so using a LFMCW radar system can reduce the transmitter power requirements. In consideration of the great bandwidth of terahertz waves and the high range resolution of the LFMCW radar, the terahertz LFMCW radar can obtain high range resolution [8, 9].

Currently, the international research institutions with terahertz radar experimental systems are the Jet Propulsion Laboratory (JPL) (0.6 THz radar imaging system) [10] and the German Institute of Applied Science (Forschungsgesellschaft für Angewandte Naturwissenschaften, FGAN) High Frequency Physics and Radar Techniques (FHR) Laboratory (0.22 THz COBRA inverse synthetic aperture radar (ISAR) imaging system) [11]. In 2006, RJ Dengler and KB Cooper et al. of JPL have successfully developed the first high-resolution terahertz imaging system with a 2-cm range resolution; this system introduced FMCW radar technology into the imaging system, processed the waveform distortion compensation by software, and obtained a 2-cm range resolution (internal 4 m) [12]. In 2008, KB Cooper et al. who came up with a 0.6 THz radar imaging system have successfully developed a 0.58 THz high-resolution three-dimensional imaging radar system based on the 0.6 THz radar imaging system [13]. The imaging system used in ISAR imaging can obtain subcentimeter resolution. In 2007, Essen and Wahlen et al. of the German Institute of Applied Science (FGAN) High Frequency Physics and Radar Technology (FHR) Laboratory have successfully developed a 220-GHz terahertz imaging radar system COBRA-220 [14]. The system is also based on a LFMCW radar system, in which the FM bandwidth is 8 GHz, successfully achieving the 1.8-cm range resolution in a 200-m distance.

In this paper, we present an overview of the THz imaging radar technology. The radar is currently a portable laboratory prototype system operating in a LFMCW mode over a 4.8-GHz bandwidth in the University of Electronic Science and Technology of China (UESTC). The remainder of this paper is organized as follows. Section 2 describes the LFMCW signal model. In Section 3, a dual-source structure model for an intermediate frequency receiver in the THz radar is developed. This is followed by Section 4 in which a detailed analysis of the signal and the correcting method are presented. In Section 5, the experiment results for the LMFCW THz radar are shown. We conclude the paper in Section 6.

## 2. LFMCW signal analysis

*f*

_{0}is the carrier frequency,

*t*is the time variable,

*K*is the frequency modulation slope,

*T*is the duration of the signal, and

*θ*

_{0}is the initial phase.

*τ*is the time delay of a stationary target at the range

*R*, then the received signal can be expressed as

where *τ* = 2*R*/*c*, and *c* is the speed of light.

So the frequency of the beat signal is the identification to the target range. After sampling was carried out on the beat signal of the LFMCW radar, the beat frequency signal's frequency spectrum can be obtained by discrete Fourier transform (DFT). In the spectrum, the peak lines are corresponding to the beat frequency and static target's range.

## 3. Intermediate frequency receiver

*S*

_{1}and

*S*

_{2}, two low-frequency linear frequency modulation signals, are used to produce the transmitting signal and the local oscillator (LO) signal, respectively. They can be respectively represented as

where *f*_{c 1} and *f*_{c 2} are the carrier frequency, *t* is the time variable, *K*_{s 1} and *K*_{s 2} are the frequency modulation slope, and *ϕ*_{1} and *ϕ*_{2} are the initial phase.

*S*

_{1}by means of × 12 frequency multiplication (×2 twice and × 3 once), band-pass filtering, and amplification. Then, it can be represented as

*A*

_{ T }is the signal amplitude. It is supposed that

*R*(

*t*) is the range of target and

*τ*(

*t*) = 2

*R*(

*t*)/

*c*is the echo signal time delay. The received echo signal can be expressed as

*S*

_{2}by the same procedure as the transmitting signal. It can be expressed as

*A*

_{LO1}is the amplitude of the LO signal. The first mixing is realized between the received echo signal (

*S*

_{ R }(

*t*)) and the LO signal (

*S*

_{LO1}(

*t*)). So the obtained intermediate signal is

where *A*_{IF} is the amplitude of the intermediate frequency signal, *μ* = 12 *K*_{0} is the frequency modulation slope, and *Δϕ* = *ϕ*_{2} - *ϕ*_{1} is the difference of initial phases.

*S*

_{1}and

*S*

_{2}, ×12 frequency multiplication, amplifying, and filtering. It can be represented as

*S*

_{IF}(

*t*) and LO signal

*S*

_{LO}(

*t*) is

The results show that the initial phase difference is offset through taking advantage of the dual-source system structure. The results are consistent with the traditional single-source LFMCW radar system structure. Thereby, the problem about the dual-source's non-sync can be solved effectively.

## 4. Error analysis and correction

In the FMCW radar, the range information of the target can be obtained from the spectral content of the final signal. The range resolution of a FMCW radar depends only on the bandwidth of the transmitting signal. The range resolution is the minimum distance that two targets can be separated along the radar's line of sight before they are indistinguishable.

*t*, the Fourier-limited single-target spectral width will be

*δf*

_{b min}= 1/

*Δt*. In according to formula (5), the minimum range resolution can become

It means that the range resolution only depends on the total swept bandwidth. The inverse relationship between the range resolution and bandwidth is similar to the ordinary pulsed radar. With a bandwidth of 4.8 GHz, the theoretical range resolution of our THz radar is 3.1 cm; however, this theoretical value is only achieved if unwanted modulation in the LFM waveform is compensated for.

*φ*(

*t*) and

*A*(

*t*) in the transmitted and LO signals which are not flat in the total bandwidth. Besides, a direct current or low-frequency component

*S*

_{L}(

*t*) will result owing to the sampling in our practical THz radar system. Thus, formula (12) becomes

where *A*(*t*) = *A*_{LO}(*t*) · *A*_{
T
}(*t* - *τ*) and Δφ(*t*) = *φ*_{LO}(*t*) - *φ*_{
T
}(*t* - *τ*).

In order to compensate for this degradation, some steps are taken in signal processing.

Firstly, a smoothing low-pass filter is applied to remove the low-frequency component *S*_{L}(*t*).

*R*0 in the radar's operating range, and the referent IF signal is recorded.

The signal spectrum will also be shifted by a known amount *Δf* = *μτ*_{0} = 2*μR*_{0}/*c* which can be added back easily. The resolution can improve significantly as long as the compensated amplitude approaches unity and the phase approaches zero.

From the above formula derivation, we know that this method can perfectly compensate the range spectrum of the target which is located in the same distance with the reference target. Practically, calibrating using the target at *R* = *R*_{0} results in excellent non-linearity compensation over the entire range of *R*_{0} ± 1, and a high resolution can also be obtained.

## 5. Experimental results

## 6. Conclusions

It is feasible to use the LMFCW radar in THz waveband to obtain high range resolution and high-quality images. Some measures taken for correcting the signal error are valid in the intermediate frequency receiver to optimize the radar's range resolution. The radar's system structure low-noise LMF source can do the trick. In short, the THz LFMCW radar is an effective tool for range detection and imaging.

## Declarations

## Authors’ Affiliations

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This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.