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Abstract
A conventional millimeter-wave stepped frequency continuous wave (SFCW) synthetic aperture radar (SAR) imaging system generally utilizes IQ modulation technique to acquire the amplitude and phase of the waves scattered from a target object. Due to measure both in-phase signal and quadrature signal, the transceiver of the conventional system is complicate and costly, and the IQ imbalance problem makes the system difficult to calibrate. To reduce hardware complexity and enhance efficiency-cost ratio, a novel SFCW SAR imaging system only measuring in-phase signal is proposed and demonstrated. For lack of quadrature signal measurement, an algorithm based on Fourier transform is proposed to estimate the amplitude and phase. The ultimate images are obtained through an image-reconstruction algorithm, which uses the estimated amplitude and phase as input parameters. The proposed system is verified by both simulation and experiment, where the frequencies are set from 24GHz to 30GHz. The imaging results with high resolution and low noise are demonstrated. Compared to the conventional system, the image quality of the proposed system is almost identical, but the transceiver of the proposed system is greatly simplified.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Millimeter waves are high-frequency (30GHz-300GHz) electromagnetic waves with wavelengths between 1mm and 1cm, furthermore, millimeter waves are nonionizing and can easily penetrate solid isolators such as clothing, papers, plastics, glasses, ceramics and so on [1,2], these natures make millimeter waves suitable for high-resolution radar imaging systems for non-contact and non-destructive detection [3,4]. SFCW SAR is a mainstream technique for millimeter-wave radar imaging, and it is widely applied on numbers of radar imaging systems, such as concealed weapon detection system [5-7], medical imaging system [8], foreign objects debris (FOD) detection system [9], through-the-wall radar imaging system [10], et al.
A SFCW SAR imaging system transmits stepped-frequency millimeter waves, and samples the waves scattered from a target object, ultimately utilizes a computer image-reconstruction algorithm to obtain the image of the target object [11]. The synthetic aperture mainly includes uniform planar synthetic aperture [5,11,12], sparse planar synthetic aperture [13,14], cylindrical synthetic aperture [15,16], et al. The image-reconstruction algorithm includes range migration algorithm [5,17], range stacking algorithm [7], back projection algorithm [18], compressed sensing algorithm [19,20], et al. Whichever synthetic aperture or image-reconstruction algorithm is selected, the imaging system generally requires the amplitude and phase of the scattering waves as input parameters. A conventional SFCW SAR imaging system uses IQ-modulation technique to obtain the amplitude and phase directly, it measures both in-phase signal and quadrature signal, and the scattering waves can be expressed as a complex $I + jQ = A\exp ({j\varphi } )$, where I is the in-phase signal, Q is the quadrature signal, A is the amplitude and $\varphi $ is the phase [5,21]. To acquire the quadrature signal, 90-degree or 45-degree phase shift of the transmitting millimeter waves is required. However, for wide transmission bandwidth, the phase shift is difficult and the measuring circuit of the transceiver is much complicate. At the same time, the IQ imbalance problem makes the system hard to calibrate [22,23].
To solve the problem, one approach is that, only incomplete data are sampled with simplified acquisition hardware, and then the amplitude and phase are retrieved through estimation algorithms. There are numerous methods to recover the amplitude and phase, such as Gerchberg-Saxton (GS) method, Flenup method, et al [24-26]. The aforementioned methods are based on amplitude measurement, and the phase is retrieved through various estimation algorithms. Different to these methods, a new technique is explored, that is, the in-phase signal is measured with hardware, and the amplitude and phase are retrieved through an estimation algorithm. The described in-phase signal measurement is based on homodyne detection technique, which is widely applied in microwave band, terahertz band, visible band, et al, therefore, the proposed technique including the in-phase signal measurement and the retrieval algorithm can be applied not only in millimeter-wave band, theoretically, but also in whole electromagnetic-wave band.
Based on this technique, a novel SFCW SAR imaging system only measuring in-phase signal is proposed. Compared to the conventional system utilizing IQ-modulation technique, the proposed system spares the phase shift operation and the quadrature signal measurement, the transceiver is greatly simplified, and the proposed system is easier to implement and has lower hardware cost.
Because only the in-phase signal is measured, an estimating algorithm is required to retrieve the amplitude and phase. At the same time, there generally exist amplitude amplification and phase delay caused by hardware, this will lead to measurement error [27,28], so it needs to be considered in this algorithm. The proposed algorithm is based on Fourier transform, and it is demonstrated. A method measuring the amplitude amplification and phase delay is proposed and demonstrated, too. A simulation compares the imaging results between the proposed system and the conventional system, and an experiment is presented. Finally, we give our conclusions.
2. Operation principle
2.1 SFCW SAR imaging model
Figure 1 shows the measurement configuration of this SFCW SAR imaging system, where the transceiver is scanned over a rectilinear planar aperture, the measure plane is at $z = L$, the transceiver position is expressed as $({x^{\prime},y^{\prime},L} )$. At each position, the transceiver transmits and receives millimeter waves with stepped frequency, and this system samples the in-phase signal of the waves scattered from the target at each transceiver position and frequency, which is recorded as $I({x^{\prime},y^{\prime},\omega } )$, where $\omega $ is the temporal angular frequency. The in-phase signal $I({x^{\prime},y^{\prime},\omega } )$ is the real part of $S({x^{\prime},y^{\prime},\omega } )$, where $S({x^{\prime},y^{\prime},\omega } )$ is the complex expression of the amplitude and phase of the receiving millimeter waves, that is
Assume the position of a target point is $({x,y,z} )$, and the target image is characterized by a reflective function $\sigma ({x,y,z} )$, the relationship between ${S_{\textrm{theo}}}({x^{\prime},y^{\prime},\omega } )$ and $\sigma ({x,y,z} )$ is
According to [5], the spatial cross-range resolution and the range resolution based on this image-reconstruction algorithm are estimated by
Combining above relationships, the whole imaging procedure is as follows
Step 1. Measure error multiplier ${S_{\textrm{err}}}({x^{\prime},y^{\prime},\omega } )$.
Step 2. Measure in-phase signal $I({x^{\prime},y^{\prime},\omega } )$.
Step 3. Estimate ${S_{\textrm{theo}}}({x^{\prime},y^{\prime},\omega } )$ by using ${S_{\textrm{err}}}({x^{\prime},y^{\prime},\omega } )$ and $I({x^{\prime},y^{\prime},\omega } )$ as input parameters.
Step 4. Obtain $\sigma ({x,y,z} )$ by using the image-reconstruction algorithm as shown in Eq. (4).
2.2 Measurement of scattering waves
Figure 2(a) shows the schematic of the transceiver used in the proposed SFCW SAR imaging system, and it only measures in-phase signal of the scattering waves. It is obvious that the transceiver is very simple, and it has only one voltage controlled oscillator (VCO) source, one coupler and one mixer. Assume the transmitting millimeter-wave signal is ${A_{\textrm{trans}}}\cos ({\omega t + {\varphi_0}} )$, and the receiving millimeter-wave signal is ${A_{\textrm{recv}}}\cos ({\omega t + {\varphi_0} + \varphi } )$, where ${A_{\textrm{trans}}}$ is the amplitude of the transmitting signal, it is a constant, $\omega $ is the temporal angular frequency, t is the time, ${\varphi _0}$ is the initial phase of the transmitting signal, ${A_{\textrm{recv}}}$ is the amplitude of the receiving signal, $\varphi $ is the round-trip phase between the transceiver and the target. After mix the transmitting signal and the receiving signal and filter the high-frequency signal, the output zero-frequency signal is $\frac{1}{2}{A_{\textrm{trans}}}{A_{\textrm{recv}}}\cos ({0 \times t + \varphi } )= A\cos (\varphi )$, and this is the in-phase signal of the scattering waves [30].
Fig. 2. Schematics of the transceivers. (a) is used in the proposed system only measuring in-phase signal; (b) and (c) are used in the conventional system measuring both in-phase signal and quadrature signal, (b) has two VCOs; (c) has one VCO and a tunable BPF.
As a comparison, Figs. 2(b) and 2(c) show two typical schematics of the transceivers used in the conventional system, and they measure both in-phase signal and quadrature phase signal. A frequency down-conversion technique is applied in these transceivers. This technique firstly down converts the radio frequency (RF) signal with changing and high frequency to the intermediate frequency (IF) signal with constant and low frequency, then use an electrical phase shifter to realize 90-degree phase shift of the IF signal [31]. The transceiver shown in Fig. 2(b) was applied in [5], it has two VCOs as swept sources, one VCO is as RF source, and the other is as local oscillator (LO) source, these two VCOs have fixed frequency difference which is equal to the frequency of the IF signal. Compared to the transceiver shown in Fig. 2(a), one more VCO enhances the cost of hardware, and the structure is complicate. Figure 2(c) shows another transceiver, the LO signal is generated by mixing the RF signal and the IF reference signal, and this method will cause image signal which effects the measure result. To eliminate the image signal, a tunable band pass filter (BPF) is introduced. The tunable BPF need to adapt the variation of the frequencies of the RF signal, if the bandwidth is quite wide, the design and fabrication of the tunable BPF will be very difficult even impossible. Hence, it is obvious that the transceiver used in the proposed system is much simpler, cheaper and easier to implement.
2.3 Estimation of amplitude and phase
According to Eqs. (1) and (2), the in-phase signal $I({x^{\prime},y^{\prime},\omega } )$ can be expressed as
According to Eq. (7), the inverse Fourier transform of $P({x^{\prime},y^{\prime},\omega } )$ along the dimension $\omega $ is the sum of the inverse Fourier transform of ${P_1}({x^{\prime},y^{\prime},\omega } )$ and ${P_2}({x^{\prime},y^{\prime},\omega } )$,
As mentioned above, the values of ${\mathop{\rm FT}\nolimits} _{(\omega )}^{ - 1}[{{P_2}({x^{\prime},y^{\prime},\omega } )} ]$ are precisely estimated on the range $[0,{r_{\min }}) \cup ({r_{\max }},R]$, where R is the maximum range value which is equal to $c/({2{f_\textrm{s}}} )$, where${f_\textrm{s}}$ is the frequency step. However, on the range from ${r_{\min }}$ to ${r_{\max }}$, the values of ${\mathop{\rm FT}\nolimits} _{(\omega )}^{ - 1}[{{P_2}({x^{\prime},y^{\prime},\omega } )} ]$ are unknown, because both the magnitudes of ${\mathop{\rm FT}\nolimits} _{(\omega )}^{ - 1}[{{P_1}({x^{\prime},y^{\prime},\omega } )} ]$ and ${\mathop{\rm FT}\nolimits} _{(\omega )}^{ - 1}[{{P_2}({x^{\prime},y^{\prime},\omega } )} ]$ which are far greater than zero are existent on this range. To get the estimated values of ${\mathop{\rm FT}\nolimits} _{(\omega )}^{ - 1}[{{P_2}({x^{\prime},y^{\prime},\omega } )} ]$ on the whole range, a simple and feasible method is to set the values to zero on the range from ${r_{\min }}$ to ${r_{\max }}$, if the value of ${\eta _{\textrm{loss}}}$ is small enough, where ${\eta _{\textrm{loss}}}$ is defined as
After Fourier transform of the proximate ${\mathop{\rm FT}\nolimits} _{(\omega )}^{ - 1}[{{P_2}({x^{\prime},y^{\prime},\omega } )} ]$, the proximate ${P_2}({x^{\prime},y^{\prime},\omega } )$ is obtained as shown in Eq. (12). According to Eq. (8), the proximate ${S_{\textrm{theo}}}({x^{\prime},y^{\prime},\omega } )$ is obtained as shown in Eq. (13).
2.4 Measurement of error multiplier
The error multiplier is the amplitude amplification and phase delay caused by hardware. If the number of channels is M and the number of frequencies is N, there are $MN$ error multipliers need to be measured. A channel is composed of a transmitting antenna and a receiving antenna, the channel position is assumed to be the position of the midpoint of these two antennas, and the channel position is deemed as the transceiver position. The error multiplier is recorded as ${S_\textrm{e}}({h,\omega } )= {A_\textrm{e}}({h,\omega } )\exp [{j{\varphi_\textrm{e}}({h,\omega } )} ]$, where h is the serial number of a channel, ${A_\textrm{e}}({h,\omega } )$ is the amplitude amplification, ${\varphi _\textrm{e}}({h,\omega } )$ is the phase delay, and the values of ${S_{\textrm{err}}}({x^{\prime},y^{\prime},\omega } )$ are obtained by mapping${S_\textrm{e}}({h,\omega } )$ according to the actual layout of the channels.
Figure 5 shows the geometry of error multiplier measurement, the transmitting antennas and receiving antennas are on plane $z = 0$, the target is a metal plate which is on plane $z = D$, that is, the distance between antenna plane and target plane is D, the stepping motor is used to move the metal plate along z direction, and the in-phase signals are sampled at each distance. As shown in Fig. 6, the in-phase signals are in cosine distribution along z direction, the period is a half of the wavelength, so the moving distance should be at least a half of the wavelength for getting the in-phase signals in a whole period [32,33]. The amplitude decay is not in consideration, since the moving range is short and it has very little impact.
${I_{\textrm{max}}}({h,\omega } )$ is the maximum value of the sampled in-phase signals, and ${D_{\textrm{ref}}}({h,\omega } )$ is the reference position where the in-phase signal is equal to ${I_{\textrm{max}}}({h,\omega } )$. When the metal plate is at the reference position ${D_{\textrm{ref}}}({h,\omega } )$, the amplitude of the receiving waves is ${I_{\textrm{max}}}({h,\omega } )$, the phase of the receiving waves is $2n\pi $, n is an integer, the theoretical amplitude is assumed to be 1, the theoretical phase is $- 2\omega {D_{\textrm{ref}}}({h,\omega } )/c$, and ${S_\textrm{e}}({h,\omega } )$ can be computed by
3. System simulation
The imaging performances of the proposed system and the conventional system are compared, and the imaging performances with different ${\eta _{\textrm{loss}}}$are compared, too.
In this simulation, the RF frequencies are set from 24GHz to 30GHz, the image target is composed of nine points in a 20cm×20cm×20cm space, the space sampling intervals in x and y directions are both set to 0.5cm, the amplitude amplification and phase delay are set to large random numbers. For getting the different values of ${\eta _{\textrm{loss}}}$, the frequency steps ${f_\textrm{s}}$ are set to 100MHz and 20MHz.
Figure 7 shows the simulation results of the estimation of the scattering waves where ${f_\textrm{s}} = 100\textrm{MHz}$ and ${f_\textrm{s}} = 20\textrm{MHz}$ respectively, the red line corresponds to the theoretical values, the blue line corresponds to the estimated values, and it is obvious that the estimation results where ${f_\textrm{s}} = 20\textrm{MHz}$ have higher precision.
Fig. 7. Simulation of estimation of the scattering waves. (a) estimation of the in-phase signal, ${f_\textrm{s}} = 100\textrm{MHz}$; (b) estimation of the quadrature signal, ${f_\textrm{s}} = 100\textrm{MHz}$; (c) estimation of the in-phase signal, ${f_\textrm{s}} = 20\textrm{MHz}$; (d) estimation of the quadrature signal, ${f_\textrm{s}} = 20\textrm{MHz}$.
Figure 8 shows the simulation results of the SFCW SAR imaging, the images of the proposed system and the conventional system are nearly identical wherever the frequency step is set to 100MHz or 20MHz.
Fig. 8. Simulation of SFCW SAR imaging. The upper images are from the proposed system, and the lower images are from the conventional system, (a) ${f_\textrm{s}} = 100\textrm{MHz}$; (b) ${f_\textrm{s}} = 20\textrm{MHz}$.
The correlation coefficient is used to measure the similarity of the images from different systems [34,35]. The correlation coefficient is defined as
Table 1. Correlation coefficients of images of two systems with different frequency steps
Table 1 shows that all correlation coefficients are close to 1, and the correlation coefficients with 20MHz frequency step are slightly higher, it means that the images obtained by the proposed system and the conventional system are very similar, and the similarity with lower frequency step is higher.
Though low frequency step brings high accuracy, it also brings large sampling and computing burden. Therefore, the frequency step should be corresponding to the actual demand.
4. Experiment
4.1 Facilities
The experiment system for SFCW SAR imaging is established as Fig. 9 shows. The PC is used to control hardware and execute image-reconstruction algorithm, and the data acquisition card (DAQ) is placed in the computer case, it is used to sample in-phase signal, the channel switch is used to select working channel, the stepping motor is used to move the target. The transceiver generates millimeter waves with stepped frequency, transmit and receive waves, and measure in-phase signal.
For save sampling time, the antenna array is utilized for electric scanning along y direction, and the stepping motor is utilized to move the target along x direction, it is equivalent to move antennas along x direction. Figure 10 shows the layout of the antennas and channels, and the antenna array is composed of 16 transmitting antennas and 16 receiving antennas. To acquire 0.5cm sampling interval in y direction, each transmitting antenna and receiving antenna are used twice except T1 and R16, hence there are 31 channels in the system, and the mapping relationship between ${S_{\textrm{err}}}({x^{\prime},y^{\prime},\omega } )$ and ${S_\textrm{e}}({h,\omega } )$ is
4.2 Imaging results
In this experiment, the RF VCO is swept from 24GHz to 30GHz, and the frequency step is 100MHz, so the number of frequencies is 61. The full beamwidths of the antenna in x and y direction are both approximately ${60^ \circ }$, according to Eq. (5), the cross-range resolution and range resolution are ${\Delta _{x,y}} \approx 0.55\textrm{cm}$ and ${\Delta _z} \approx 2.5\textrm{cm}$, the space sampling intervals in x and y direction are both set to 0.5cm, and the scanning range in x direction is 20cm, the scanning range in y direction is 15cm.
The photograph of the targets and the imaging results are shown in Fig. 11. Target 1 is a metal frame, and target 2 is a paper box with two aluminum letters ‘N’ and ‘T’ stuck on each side. Both two targets are clearly displayed in the imaging results with low noise. The images of plane $xy$ demonstrate cross-range resolution, and the images of plane $xz$ and $yz$ demonstrate cross-range and range resolutions, from the imaging results, it is obvious that both cross-range resolution and range resolution can reach theoretical value.
Fig. 11. (a) and (c) are photograph of target 1 and target 2; (b) and (d) are 3d imaging results of target 1 and target 2.
5. Conclusion
This paper has demonstrated the novel technique only measuring in-phase signal of back scattering waves for millimeter-wave SFCW SAR imaging. Compared to the conventional technique measuring both in-phase signal and quadrature signal, the proposed technique has much simpler transceiver configuration, which make the SAR imaging system easier to be implemented and cheaper.
For lack of the measurement of the quadrature signal, the proposed algorithm estimating the amplitude and phase has been applied and demonstrated. This algorithm is under the condition that there exist amplitude amplification and phase delay caused by hardware, and the measurement method of the amplitude amplification and phase delay has been demonstrated, too.
The simulation has compared the imaging results between the proposed system and the conventional system, the results have very small differences which can be ignored, and the experiment has also certificated that high quality 3D SAR images can be acquired through the proposed system with simplified transceiver.
Funding
National Natural Science Foundation of China (11574105); Fundamental Research Funds for the Central Universities (2017KFYXJJ029).
Disclosures
The authors declare no conflicts of interest.
References
1. M. Kazemi, Z. Kavehvash, and M. Shabany, “K-space aware multi-static millimeter-wave imaging,” IEEE Trans. on Image Process. 28(7), 3613–3623 (2019). [CrossRef]
2. V. M. Patel, J. N. Mait, D. W. Prather, and A. S. Hedden, “Computational millimeter wave imaging: problems, progress, and prospects,” IEEE Signal Process. Mag. 33(5), 109–118 (2016). [CrossRef]
3. C. Viegas, B. Alderman, P. G. Huggard, J. Powell, K. Parow-Souchon, M. Firdaus, H. Liu, C. I. Duff, and R. Sloan, “"Active millimeter-wave radiometry for nondestructive testing/evaluation of composites-glass fiber reinforced polymer,” IEEE Trans. Microwave Theory Tech. 65(2), 641–650 (2017). [CrossRef]
4. M. T. Ghasr, B. Carroll, S. Kharkovsky, R. Austin, and R. Zoughi, “Millimeter-wave differential probe for nondestructive detection of corrosion precursor pitting,” IEEE Trans. Instrum. Meas. 55(5), 1620–1627 (2006). [CrossRef]
5. D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter-wave imaging for concealed weapon detection,” IEEE Trans. Microwave Theory Tech. 49(9), 1581–1592 (2001). [CrossRef]
6. X. Zhuge and A. G. Yarovoy, “A sparse aperture MIMO-SAR-based UWB imaging system for concealed weapon detection,” IEEE Trans. Geosci. Remote Sensing 49(1), 509–518 (2011). [CrossRef]
7. W. Tan, P. Huang, Z. Huang, Y. Qi, and W. Wang, “Three-dimensional microwave imaging for concealed weapon detection using range stacking technique,” Int. J. Antenn. Propag. 2017, 1–11 (2017). [CrossRef]
8. A. Mirbeik-Sabzevari, S. Li, E. Garay, H. Nguyen, H. Wang, and N. Tavassolian, “Synthetic ultra-high-resolution millimeter-wave imaging for skin cancer detection,” IEEE Trans. Biomed. Eng. 66(1), 61–71 (2019). [CrossRef]
9. E. Yigit, S. Demirci, A. Unal, C. Ozdemir, and A. Vertiy, “Millimeter-wave ground-based synthetic aperture radar imaging for foreign object debris detection: experimental studies at short ranges,” J. Infrared, Millimeter, Terahertz Waves 33(12), 1227–1238 (2012). [CrossRef]
10. U. Alkus, A. B. Sahin, and H. Altan, “Stand-off through-the-wall W-band millimeter-wave imaging using compressive sensing,” IEEE Geosci. Remote Sensing Lett. 15(7), 1025–1029 (2018). [CrossRef]
11. Y. Zhang, B. Deng, Q. Yang, J. Gao, Y. Qin, and H. Wang, “Near-field three-dimensional planar millimeter-wave holographic imaging by using frequency scaling algorithm,” Sensors 17(10), 2438 (2017). [CrossRef]
12. L. Qiao, Y. Wang, Z. Zhao, and Z. Chen, “Exact reconstruction for near-field three-dimensional planar millimeter-wave holographic imaging,” J. Infrared, Millimeter, Terahertz Waves 36(12), 1221–1236 (2015). [CrossRef]
13. X. Hu, N. Tong, J. Wang, S. Ding, and X. Zhao, “Matrix completion-based MIMO radar imaging with sparse planar array,” Signal Process. 131, 49–57 (2017). [CrossRef]
14. M. E. Yanik and M. Torlak, “Near-field MIMO-SAR millimeter-wave imaging with sparsely sampled aperture data,” IEEE Access 7, 31801–31819 (2019). [CrossRef]
15. J. Gao, B. Deng, Y. Qin, H. Wang, and X. Li, “An efficient algorithm for MIMO cylindrical millimeter-wave holographic 3-D imaging,” IEEE Trans. Microwave Theory Tech. 66(11), 1–10 (2018). [CrossRef]
16. G. Zhao, S. Li, B. Ren, Q. Qiu, and H. Sun, “Cylindrical three-dimensional millimeter-wave imaging via compressive sensing,” Int. J. Antenn. Propag. 2015, 1–6 (2015). [CrossRef]
17. R. Zhu, J. Zhou, G. Jiang, and Q. Fu, “Range migration algorithm for near-field MIMO-SAR imaging,” IEEE Geosci. Remote Sensing Lett. 14(12), 2280–2284 (2017). [CrossRef]
18. Y. Cho, H. Jung, C. Cheon, and Y. Chung, “Adaptive back-projection algorithm based on climb method for microwave imaging,” IEEE Trans. Magn. 52(3), 1–4 (2016). [CrossRef]
19. S. Jung, Y. Cho, R. Park, J. Kim, H. Jung, and Y. Chung, “High-resolution millimeter-wave ground-based SAR imaging via compressed sensing,” IEEE Trans. Magn. 54(3), 1–4 (2018). [CrossRef]
20. D. Bi, Y. Xie, L. Ma, X. Li, X. Yang, and Y. R. Zheng, “Multifrequency compressed sensing for 2-D near-field synthetic aperture radar image reconstruction,” IEEE Trans. Instrum. Meas. 66(4), 777–791 (2017). [CrossRef]
21. A. A. Farsaei, F. Mokhtari-Koushyar, S. M. Javad Seyed-Talebi, Z. Kavehvash, and M. Shabany, “Improved two-dimensional millimeter-wave imaging for concealed weapon detection through partial fourier sampling,” J. Infrared, Millimeter, Terahertz Waves 37(3), 267–280 (2016). [CrossRef]
22. H. Alsuraisry, M. Wu, W. Lin, J. Tsai, and T. Huang, “Millimeter-wave ultra-broadband IQ transceiver design - current status and future outlook,” in Proceedings of IEEE Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems (IEEE, 2017), pp. 19–22.
23. K. Lin, J. Deng, and K. Feng, “Time–frequency multiplex transceiver design with RX IQ imbalance, CFO, and multipath channel estimation and compensation for multicarrier systems,” Wireless Pers. Commun. 87(1), 107–123 (2016). [CrossRef]
24. A. Capozzoli, C. Curcio, G. D’Elia, and A. Liseno, “Millimeter-wave phaseless antenna characterization,” IEEE Trans. Instrum. Meas. 57(7), 1330–1337 (2008). [CrossRef]
25. E. J. R. Pauwels, A. Beck, Y. C. Eldar, and S. Sabach, “On Fienup methods for sparse phase retrieval,” IEEE Trans. Signal Process. 66(4), 982–991 (2018). [CrossRef]
26. P. Netrapalli, P. Jain, and S. Sanghavi, “Phase retrieval using alternating minimization,” IEEE Trans. Signal Process. 63(18), 4814–4826 (2015). [CrossRef]
27. G. Jing, G. Sun, X. Xia, M. Xing, and Z. Bao, “A novel two-step approach of error estimation for stepped-frequency MIMO-SAR,” IEEE Geosci. Remote Sensing Lett. 14(12), 2290–2294 (2017). [CrossRef]
28. S. Zhang, M. Xing, X. Xia, Y. Liu, R. Guo, and Z. Bao, “A robust channel-calibration algorithm for multi-channel in azimuth HRWS SAR imaging based on local maximum-likelihood weighted minimum entropy,” IEEE Trans. on Image Process. 22(12), 5294–5305 (2013). [CrossRef]
29. M. Soumekh, “A system model and inversion for synthetic aperture radar imaging,” IEEE Trans. on Image Process. 1(1), 64–76 (1992). [CrossRef]
30. J. Tsai and T. Huang, “35-65-GHz CMOS broadband modulator and demodulator with sub-harmonic pumping for MMW wireless gigabit applications,” IEEE Trans. Microwave Theory Tech. 55(10), 2075–2085 (2007). [CrossRef]
31. F. Zhu, W. Hong, J. Chen, X. Jiang, K. Wu, P. Yan, and C. Han, “A broadband low-power millimeter-wave CMOS down-conversion mixer with improved linearity,” IEEE Trans. Circuits Syst. II 61(3), 138–142 (2014). [CrossRef]
32. D. M. Sheen and T. E. Hall, “Calibration, reconstruction, and rendering of cylindrical millimeter-wave image data,” Proc. SPIE 8022, 80220H (2011). [CrossRef]
33. J. T. Logan, D. S. Reinhard, and K. E. Hauck, “Phased array calibration and diagnostics utilizing a student-built planar near-field system,” in Proceedings of IEEE International Symposium on Phased Array Systems and Technology (IEEE, 2010), pp. 279–286.
34. S. Mohapatra and J. Weisshaar, “Modified Pearson correlation coefficient for two-color imaging in spherocylindrical cells,” BMC Bioinformatics 19(1), 428 (2018). [CrossRef]
35. Y. Liu, Q. Meng, R. Chen, J. Wang, S. Jiang, and Y. Hu, “A new method to evaluate the similarity of chromatographic fingerprints: weighted Pearson product-moment correlation coefficient,” J. Chromatogr. Sci. 42(10), 545–550 (2004). [CrossRef]
