An effective method to compensate the nonlinearity of terahertz FMCW radar

Transcription

1 An effective method to compensate the nonlinearity of terahertz FMCW radar More info about this article: Weidong HU, Weikang SI,Yade LI, Xin ZHANG, Leo LIGTHART Beijing Institute of Technology, Beijing, China Corresponding author: Weidong Hu, Abstract Terahertz FMCW radar with wide bandwidth is often used to achieve high resolution range profiles, but the practicability is usually hampered by the nonlinearity of LFM(Linear Frequency Modulation) signal which leads to the spectrum s distortion. In this paper, an effective nonlinear compensation method which based on the time distribution is proposed to compensate for the signal distortion caused by the radar waveform nonlinearities. The method can eliminate the range profiles blur caused by the nonlinearity of LFM signal. Furthermore, the experiment data of a 220GHz terahertz FMCW radar with 15GHz bandwidth is used to validate the proposed compensation method. Keywords: THz, Non-destructive technique, Frequency modulated continuous wave, Nonlinear compensation 1. Introduction Non-destructive testing technology is designed to detect internal defects without destroying the material. Terahertz waves(0.1~10thz) can penetrate non-metallic and non-polar materials such as ceramics, graphite, polymer composites, plastics, foams, etc. In recent years, with the emergence of high-power, large-bandwidth terahertz devices, high-resolution terahertz wave imaging has become possible[1][2]. Considering the system implementation difficulty, the broadband modulated continuous wave (FMCW) is transmitted in most THz radar systems and the de-chirp technique is used to receive the signal scattered by the target. Due to the time delay, there is a beat between referenced signal and received signal. This signal s is proportional to the depth of the object. However, the presence of nonlinearities in the transmitted signal is limiting the use of FMCW systems to short range applications. Nonlinearities deteriorate the range resolution when de-chirp techniques are used because they spread the target energy through different frequencies [3]. The traditional correction method is hardware approach. By observing the operating characteristic curve of VCO, we could compensate the signal s phase. However, this correction approach is severely limited by external factors. Another correction approach is using Direct Digital Synthesizer (DDS) to offer compensated signal, but DDS often limits the sweep rate of the system[4]. Consequently, we propose a software correction method based on time- (TF) distribution. This method eliminates the need for measuring the system s hardware operating curve point by point. In order to verify the effect of the algorithm, the real date of 220GHz FMCW radar is used and the corrective result is good. 2. Algorithm Description In general, the compensation method mentioned in this paper can only be used to images which contain a dominate scatters. However the range profile is blurred because of the nonlinearity of the LFM(Linear Frequency Modulation) signal[5]. As shown in Fig.1, the beat between the referenced signal and received signal of a single target is distort by the nonlinear signal, which leads to the low precision of the range profile. 1

2 referenced near range far range f 0 t=0 time spectrum de-chirped t=0 time Figure 1 De-chirp signal Therefore, we proposed a method based on time-(tf) plane to compensate the distortion. The diagram of the compensation method is shown in fig.2, and the specific procedures of the method are provided as follows: Nonlinear dechirped signal STFT Reference extraction Frequency compensation Phase compensation Linear signal Figure 2 The process diagram of the compensation algorithm. 1. Reference Extraction: The short-time Fourier transform(stft) is firstly performed on the de-chirp signal to get the TF distribution on each time point. Then the maximum value should be searched column by column to extract the beat line, and the maximum value is set as the reference. Finally, compare the beat line at every time point with the reference and lower the weight of the time window if there is a big difference between the two. 2

3 2. Frequency Compensation: Since the fluctuate of the beat line leads to the blur of the range profile, compensation is carried out in the time domain at every time point. Calculate the phase to compensate through the deviation between the reference and the beat line. Hence, we can get a straight beat line. 3. Phase Compensation: After compensation, calculate the phase of reference at each column. Then compensate the phase at each column to a unified value. Thus, we can eliminate the range profiles blur caused by the nonlinearity of LFM signal. 3. Processing Result In this paper, the real data of a THz radar system is used to demonstrate the validity of the compensation method. The system is created in our lab to perform Non-destructive testing. The bandwidth of the 220GHz FMCW radar is 15GHz, and the output power is more than 80mW. Firstly, the range profile is achieved by performing FFT to the de-chirp data and the TP plane is achieved by performing STFT to the de-chirp data, shown in fig.3. In fig.3(a) the defocusing phenomena of the radar range profile is obvious. Fig.3(b) is the original time- diagram, we can observe that the energy distribution of the signal is really scattered. Figure 3(a)Original range profile Figure 3(b)Original TF diagram The processing result of the compensation method is shown in fig.4. The range profile is achieved by performing FFT to the compensation de-chirp data and the TP plane is achieved by performing STFT to the compensation de-chirp data. Fig.4(a) shows the range profile after the compensation, we can easily find the position of the target. In fig.4(b), the spectrum lines are more straightened and focused than fig.3(b). 3

4 Figure 4(a)Range profile after phase compensation Figure 4(b)TF diagram after phase compensation Finally, we compared the beat before and after the correction in fig.5. While eliminating the non-linearity of the LFM, the method can retain the true small signal spectrum. The correction time of the algorithm is less than 0.5 second on a normal laptop computer, which can realize the real-time processing of the data. In conclusion, the proposed method can achieve a good performance in the nonlinear phase compensation. 4. Conclusion Figure 5 comparison of beat The paper has proposed a new compensation method, which aims at solving the range profiles blur caused by non - linearity. It can eliminate the blurs in a short time, avoid repeating measurements for the complex hardware system. And the proposed method has been demonstrated by the real data of a 220GHz FMCW radar which is very helpful for the next THz 3D imaging work. 4

5 References 1. H. Quast and T. Loffler, "3D-terahertz-tomography for material inspection and security," th International Conference on Infrared, Millimeter, and Terahertz Waves, Busan, 2009, pp C. am Weg et al., "Fast active THz camera with range detection by modulation," rd International Conference on Infrared, Millimeter and Terahertz Waves, Pasadena, CA, 2008, pp Y. Jiang, B. Deng, H. Wang, Y. Qin and K. Liu, "An Effective Nonlinear Phase Compensation Method for FMCW Terahertz Radar," in IEEE Photonics Technology Letters, vol. 28, no. 15, pp , Aug.1, A.Meta, P. Hoogeboom and L. Ligthart, "Range Non-linearities Correction in FMCW SAR," 2006 IEEE International Symposium on Geoscience and Remote Sensing, Denver, CO, 2006, pp A. Frischen, J. Hasch and C. Waldschmidt, "FMCW ramp non-linearity effects and measurement technique for cooperative radar,"2015 European Radar Conference (EuRAD), Paris, 2015, pp