Time-Range Adaptive Focusing Method Based on APC and Iterative Adaptive Radon-Fourier Transform

Round 1

Reviewer 1 Report

An adaptive pulse compression (APC) and an iterative adaptive Radon-Fourier transform (IARFT)-based time-range adaptive focusing method is proposed in this paper. The APC-IARFT is a combination of two processes: pulse compression in the range dimension and long-time focusing in the velocity dimension. Despite the interesting method presented in the paper and presenting well the theory behind the study, I have some comments to improve it. 

1)The English writing should be checked.

2)It is better to present Fig.5, Fig.8, Fig.11, and Fig.14 in a more visually appealing manner. A bit of difficulty is involved in recognizing the peak.

3) Presenting scenario 3 subsection should be highlighted in the same manner as other subsections. I would like scenario 3 to be highlighted.

 

Author Response

Response to Reviewer 1 Comments

 

Point 1: The English writing should be checked.

 

Response 1:

Thank you very much for this suggestion. This point was accepted and made.

It is very kind of you to give me (the corrsponding author) another chance to check the English writing and correct the grammatical mistakes in the paper. It is really a challenge for me to write this paper in English. I have entirely read the manuscript to find the mistakes and corrected them one by one. We (all authors) hope to present a better manuscript to you.

 

Point 2: It is better to present Fig.5, Fig.8, Fig.11, and Fig.14 in a more visually appealing manner. A bit of difficulty is involved in recognizing the peak.

 

Response 2:

Thank you very much for this suggestion. This point was accepted and made.

It is very kind of you to give me this suggestion to help improve the quality of the manuscript. In fact, in the process of writing, we also worried about the visibility of the stereogram in Fig.5, Fig.8, Fig.11, and Fig.14.

However, at that time, I (the corrsponding author) considered the consistency with the colormap of the plan view in Fig.6, Fig.9, Fig.12, and Fig.15, and chose to set the colormap of Fig.5, Fig.8, Fig.11, Fig.14 and Fig.6, Fig.9, Fig.12,Fig.15 to “jet” type.

Based on your point, I choose to set the colormap in Fig.5, Fig.8, Fig.11, Fig.14 to “HSV” type this time. In this way, the positions of the targets’ peaks in Fig.5, Fig.8, Fig.11, Fig.14 will be dark tone, which can be better identified. The colormap of Fig.6, Fig.9, Fig.12,Fig.15 remains “jet” type.

 

Point 3: Presenting scenario 3 subsection should be highlighted in the same manner as other subsections. I would like scenario 3 to be highlighted.

 

Response 3:

Thank you very much for this suggestion. This point was accepted and made.

It is very kind of you to give me this suggestion to help improve the quality of the manuscript and reorganize Scenario 3 in Section 6. To better highlight Scenario 3, two fast-moving point targets is set, and their initial position is located at 100km. The radial velocity, Doppler frequency and initial SNR of each moving target are shown in Table 5.

Table 5. Basic information of the targets set in Scenario 3.

Target No.	Initial Position	Radial Velocity		Doppler Frequency	SNR
1	100 km	480 m/s		3200 Hz	0 dB
2	100 km	510 m/s		3400 Hz	0 dB
(a)			(b)
(c)			(d)

Figure 11. Stereogram output of four methods in Scenario 3: (a) Output of RFT; (b) Output of ARFT; (c) Output of IARFT; (d) Output of APC-IARFT.

Figure 11 shows the two-dimensional stereogram of range-velocity output. In Figure 11(a), we can distinguish the main lobe and BSSL of the point targets. In Figure 11(b), the output of ARFT method is similar to that of RFT method, but veloci-ty-dimension sidelobes are more serious than that in in Figure 11(a) due to the processing of covariance matrix in ARFT method. It can be seen that for point targets with low SNR, the output of IARFT method is consistent with that of RFT method. However, the output of APC-IARFT method is intuitively better than that of IARFT method. The range-velocity two-dimensional plan output of RFT, ARFT, IARFT and APC-IARFT methods is shown in Figure 12. The relative position relationship between the main lobes and BSSL in the output of different methods can be more clearly seen in Figure 12. Due to the small number of coherent pulses in the scene, it can be seen from the output of ARFT method that the clutter’s covariance matrix makes more obvious velocity sidelobes appear in the velocity dimension.

Figure 12. Plan output of four methods in Scenario 3.

Figure 13. Velocity-dimension output of four methods in Scenario 3.

Figure 13 shows the comparison of velocity-dimension output at the range cell where the targets are located. The velocity-dimension output of IARFT method and RFT method is basically the same, so their curves overlap with each other. In ARFT method, there are more obvious sidelobes in the velocity dimension. APC-IARFT method further suppress the velocity sidelobes on the basis of IARFT method. The cal-culated APSL2D and APSLv of the targets set in Scenario 4 are listed in Table 6. According to the data comparison in Table 6, APC-IARFT method is still the best among the four methods.

Table 6. APSL_2D and APSL_v of the targets set in Scenario 3.

	RFT	ARFT	IARFT	APC-IARFT
APSL2D of Target 1	30.99 dB	25.08 dB	30.99 dB	37.34 dB
APSL2D of Target 2	31.23 dB	27.95 dB	31.23 dB	37.14 dB
APSLv of Target 1	19.84 dB	13.37 dB	19.85 dB	28.98 dB
APSLv of Target 2	19.08 dB	15.84 dB	19.09 dB	28.41 dB

Please refer to the attachment for details, thank you.

Author Response File: Author Response.docx

Reviewer 2 Report

The main problem of the paper by Jian Guan et al. is the total lack of context.

What is the reason of this study? What are the real-world applications? How is the method presented in this paper addressing shortcomings of previous methods? 

The abstract as well as the conclusion are totally cryptic even for a reader versed in radar technology.

I urge the authors to provide context, perspective and discussion with respect to previous methods, and to describe the underlying physics. As presented, the paper is a technical report for happy fews.

Author Response

Response to Reviewer 2 Comments

 

Point 1: The main problem of the paper by Jian Guan et al. is the total lack of context.

 

Response 1:

Thank you very much for this suggestion. This point was accepted and made.

We are sorry to make you have some unpleasant reading experience. It is very kind of you to give me (the corresponding author) this suggestion to help improve the quality of the manuscript. We will make good use of this opportunity.

Please allow me to explain the context of the paper. The context of this study basiacally derives form the research of Jia Xu’s paper about Radon-Fourier transform (RFT) method [1-3]. It is known that pulse integration is an effective method to improve radar target detection performance in a noisy background, while the coherent integration may obtain better performance than the incoherent integration by compensating phase fluctuation among different sampling pulses [4-11]. For example, the well-known moving target detection (MTD) [4,5] method has been widely applied by modern coherent radar, where Doppler filter bank processing is used for the effective suppression of strong background clutter, as well as for the coherent integration of a moving target with unknown Doppler frequency. Besides, the MTD may be efficiently implemented via fast Fourier transform (FFT). Unfortunately, the MTD input vectors are the pulse samplings distributed along range cells one-by-one and the performance gain is limited by the target’s resident time in a single range cell. As a result, it is difficult to further improve the performance via MTD for the low signal-to-noise (SNR) target or the high-speed target [6-7]. For the low SNR target, e.g., far-range or low radar cross section (RCS) target, the integration time should be adequately enlarged and the range walk, i.e., the linearly varied distance between target and radar, of even a slowly moving target will exceed several range cells. For a high-speed target, this kind of across range cells (ARC) effect may also be drawn even in a very short integration time. Furthermore, with the remarkably refined range resolution of modern radar, it becomes necessary to deal with the ARC effect of moving targets.

In this regard, Perry, et al. [12,13] and Zhang, et al. [14] have introduced the Keystone transform (KT) for synthetic aperture radar (SAR) ground moving targets imaging and weak radar target detection via long-time coherent integration. KT may blindly compensate the ARU effect and not destroy the pulse phase modulation. So MTD may be used for the successive coherent integration after KT. However, the existing radar, especially the searching radar, normally adopts the low pulse repetition frequency (PRF) to guarantee the far-range target detection. Therefore, most air targets may be Doppler ambiguous, for which KT may be invalidated without ambiguity correction. Yang, et al. [15] have proposed a modified KT method via simultaneous searching of the Doppler ambiguous integers and frequency, but it needs repeated implementations of high-complexity KT operators. Another more natural method is to realize the successive Doppler matching after compensation of the target’s unknown range walk. Reed, et al. [16] have proposed a coherent integration method for MTD of optical image sequence. However, this method needs a 3-dimensional matched filtering, which is not realistic for radar target detection. Wang, et al. [17] have proposed an envelope compensation method based on range stretching and time-frequency analysis, which is applicable to the time-varied Doppler case but is also computational complicated. Chen, et al. [18, 19] proposed a method to realize the echo envelopes’ shifting compensation by searching the target speed and accomplish the coherent integration by using the FFT-based Doppler filter bank. However, the coupling relationship between velocity and Doppler of moving target is not exploited and its FFT-based Doppler filter bank processing seems to be abundant.

Also, there are other researchers who have proposed to adopt the incoherent integration, or the hybrid coherent-incoherent method to improve the weak target detection performance. Along this direction, the typical works may be the Hough transform (HT) based method proposed by Carlson, et al. [20-25]. The HT is used to inherently integrate the target slots exceeding the first low decision threshold, which may remarkably suppress false alarms and improve the ultimate detection performance. Furthermore, Mo, et al. [25] have also proposed an HT-based long-time integration method, which transforms the radar raw data into range-Doppler-time space and realizes the high-performance detection for targets with constant velocity or acceleration. However, without compensation of the phase fluctuation, the integration loss of the HT-based method may be large compared with a coherent integration method and it thus may not be applied when the SNR is extremely low.

Based on the signal model of a rectilinearly moving target in a long-time integration, Jia Xu proposes a novel Radon-Fourier transform (RFT) to realize the long-time coherent integration for the moving targets with ARC range walk. Different from the existing Radon or Fourier transform methods [29, 30], RFT can effectively overcome the coupling between the range walk and phase modulations by jointly searching along range and velocity directions of moving targets. Furthermore, the Doppler filtering is also used for the successive long-time coherent integration. With different searching parameters, four equivalent continuous RFT forms are obtained. Then, the parameter space of RFTs is analyzed and discrete RFTs are also derived. Furthermore, a generalized form of RFT, called generalized RFT (GRFT), is defined for radar target detection with arbitrarily parameterized motions. MTD is a special case of RFT method, and the RFT method is a generalized Doppler filter bank processing. Finally, some numerical experiments are provided to show that the RFT may obtain the coherent integration gain in the different SNR background and the blind speed may also be effectively suppressed. In the meantime, both the weak target detection performance and the radar coverage of high-speed target may be significantly improved via RFT without change of the radar hardware system.

Since RFT can be regarded as the expansion of Fourier transform, it is non-adaptive. Xu and Yan extend the RFT to the field of adaptive clutter suppression [31], and propose sub-aperture adaptive RFT (SA-ARFT) method to reduce the requirements for the amount of independent and identically distributed data and reduce the computational cost. However, the adaptive method in [31] is aimed at clutter suppression, and does not have the ability of adaptive suppression for the jamming targets in the training samples. Pengjie You et al. also consider the adaptive GRFT under the clutter background, and derives the Cramer-Rao lower bound of parameter estimation [32]. Its essence is the same as that in [31], so it is also limited by the independent and identically distributed training samples, and does not have the ability to adaptively suppress jamming targets. Zegang Ding utilizes adaptive RFT (ARFT) method after dividing the parameter space into subspaces, and balances the computational cost and detection performance by increasing the length of sub-aperture [33]. ARFT method uses the inverse of clutter covariance matrix to form clutter notch and suppress clutter, which is helpful to focus the target energy in the time-range plane under the clutter background. However, when the target’s velocity is too high, which causes the fluctuation of amplitude between pulses and makes the number of effective pulses available for long-time coherent integration few, which decreases the velocity resolution of ARFT method and weakens the performance of focusing.

On the other hand, because the mathematical model of Doppler estimation is similar to that of direction of arrival (DOA) estimation, the research related to DOA estimation can also be used to solve the problems of Doppler sidelobes suppression. Conventional DOA estimation methods such as MUSIC [34], root-MUSIC [35] and ESPRIT [36] use the spatial snapshots to calculate the sample covariance matrix (SCM) to estimate the unknown spatial covariance matrix, and use SCM to estimate the number and direction of signal sources. Professor Blunt studies a reiterative super-resolution (RISR) method, which was originally used for DOA estimation in array signal processing [37,38]. RISR method is based on the minimum mean square error (MMSE) criterion and is implemented with a recursive structure. The method does not need the prior knowledge of the number of signal sources, and can automatically determine the number, direction and power of signal sources. Given the information about the spatial covariance of noise and one snapshot, RISR updates the structured MMSE filter bank by iteratively using the previous estimation of spatial power distribution, and applies the filter bank to update the estimation of spatial power distribution. Based on the same theoretical basis, Professor Blunt applies RISR method to time dimension for high-resolution frequency estimation [38], proposes adaptive pulse compression (APC) method in the range dimension [39], and proposes space-time adaptive processing [40], time-range adaptive processing [41] which are adaptive methods combining different dimensions. Almost at the same time, professor Li proposes a nonparametric iterative adaptive approach (IAA) [42]. IAA method comprehensively considers the joint estimation of Doppler and range, and its essential idea is the same as that of APC method [43]. Although IAA method iterates over the whole data and has a large amount of computational cost, it does effectively improve the resolution and estimation accuracy in active sensing such as range-Doppler imaging and passive sensing such as underwater acoustic measurements.

From the above analysis, it can be seen that IAA method has the ability of range-Doppler sidelobes suppression. However, the existing relevant methods of IAA also imply the assumption that the target is only in one range cell within the processing time, and IAA method considering the problems of ARC has not been carried out. In order to solve the sidelobes masking problem in range-velocity domain, this paper proposes a time-range adaptive focusing method (which is named APC-IARFT for short) based on APC and iterative adaptive Radon-Fourier transform (IARFT).

 

1. Xu, J.; Yu, J.; Peng, Y.; Xia, X. Radon-Fourier Transform for Radar Target Detection, I: Generalized Doppler filter bank. IEEE Transactions on Aerospace and Electronic Systems, 2011, 47, 1186-1202. DOI: 10.1109/TAES.2011.5751251.
2. Xu, J.; Yu, J.; Peng, Y.; Xia, X. Radon-Fourier Transform for Radar Target Detection (II): Blind speed sidelobe suppression. IEEE Transactions on Aerospace and Electronic Systems. 2011, 47, 2473-2489. DOI: 10.1109/TAES.2011.6034645.
3. Xu, J.; Yu, J.; Peng, Y.; Xia, X. Radon-Fourier Transform for Radar Target Detection (III): Optimality and fast implementations. IEEE Transactions on Aerospace and Electronic Systems. 2012, 48, 991-1004. DOI: 10.1109/TAES.2012.6178044.
4. Barton, D. K. Radar System Analysis and Modeling. Beijing, China: Publishing House of Electronics Industry. 2004.
5. Skolnik, M. I. Introduction to Radar System (3rd ed.). Columbus, OH: McGraw-Hill. 2002.
6. Skolnik, M. I., Linde, G., and Meads, K. Senrad: An advanced wideband air-surveillance. IEEE Transactions on Aerospace and Electronic Systems. 2001, 37, 1163-1175.
7. Loomis, J. M. Army radar requirements for the 21st century. In Proceedings of IEEE Radar Conference, 2007, 1-6.
8. Wirth, W. D. Radar Techniques Using Array Antennas. London: IEE, 2001.
9. Richards, M. A. Coherent integration loss due to white Gaussian phase noise. IEEE Signal Processing Letters. 2003, 10, 208-210.
10. Yu, J., Xu, J., and Peng, Y-N. Upper bound of coherent integration loss for symmetrically distributed phase noise. IEEE Signal Processing Letters. 2008, 15, 661-664.
11. Allen, M. R. Long term integration for radar detection of small targets in clutter. Ph.D. dissertation, University of Pennsylvania, PA, 1988.
12. Perry, R. P., Dipietro, R. C., and Fante, R. L. SAR imaging of moving targets. IEEE Transaction on Aerospace and Electronic Systems. 1999, 35, 188-200.
13. Perry, R. P., Dipietro, R. C., and Fante, R. L. Coherent integration with range migration using Keystone formatting. In Proceedings of IEEE Radar Conference, 2007.
14. Zhang, S. S. and Zeng, T. Dim target detection based on Keystone transform. In Proceedings of IEEE International Radar Conference, May 2005, 889—894.
15. Li, Y., Zeng, T., and Long, T. Range migration compensation and Doppler ambiguity resolution by Keystone transform. In Proceedings of International Conference on Radar, Shanghai, China, 2006.
16. Reed, I., Gagliardi, R., and Stotts, L. Optical moving target detection with 3-D matched filtering. IEEE Transactions on Aerospace and Electronic Systems. 1998, 24, 327-335.
17. Wang, J. and Zhang, S. H. Weak target integration detection and envelope shifting compensation method. Acta Electronica Sinica. 2000, 28, 56-59.
18. Chen, Y. Z., Zhu, Y. F., Zhao, H. Z., and Fu, Q. High-speed target integration detection algorithms based on the envelope shifting and compensation. Journal of Signal Processing (in Chinese). 2004, 20, 380-390.
19. Wang, Y. M., Ma, J. G., Fu, Q., and Zhuang, Z. W. Research on integration detection of high-speed moving target. Modern Radar (in Chinese). 2006, 28, , 24-27.
20. Orlenko, V. M. and Shirman, Y. D. Non-coherent integration losses of wideband target detection. In Proceedings of the European Radar Conference, 2004, 225-228.
21. Satzoda, R. K., Suchitra, S., and Srikanthan, T. Parallelizing the Hough transform computation. IEEE Signal Processing Letters. 2008, 15, 297-300.
22. Carlson, B. D., Evans, E. D., and Wilson, S. L. Search radar detection and track with the Hough transform Part I: System concept. IEEE Transactions on Aerospace and Electronic Systems. 1994, 30, 102-108.
23. Carlson, B. D., Evans, E. D., and Wilson, S. L. Search radar detection and track with the Hough transform Part II: Detection statistics. IEEE Transactions on Aerospace and Electronic Systems. 1994, 30, 109-115.
24. Carlson, B. D., Evans, E. D., and Wilson, S. L. Search radar detection and track with the Hough transform Part III: Detection performance with binary integration. IEEE Transactions on Aerospace and Electronic Systems. 1994, 30, 116-125.
25. Mo, L., Wu, S. L., and Li, H. Radar detection of range migrated weak target through long-term integration. Chinese Journal of Electronics. 2003, 12, 539-544.
26. Hough, P. V. C. Method and means for recognizing complex patterns. U.S. Patent 3069654, 1962.
27. Deans, S. R. Hough transform from the Radon transform. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1998, PAMI-3, 185-188.
28. Skolnik, M. I. Opportunities in radar–2002. Electronics & Communication Engineering Journal. 2002, 14, 263-27.
29. Easton, Jr., R. L., Ticknor, A. J., and Barrett, H. H. Two-dimensional complex Fourier transform via the Radon transform. Applied Optics. 1985, 24, 3817-3824.
30. Leavers, V. F. Statistical properties of the hybrid Radon Fourier transform. In Proceedings of British Machine Vision Conference (BMVC2000), 2000.
31. Xu, J.; Yan, L.; Zhou, X.; Long, T.; Xia, X.; Wang, Y.; Farina, A. Adaptive Radon–Fourier transform for weak radar target detection. IEEE Transactions on Aerospace and Electronic Systems. 2018, 54, 1641-1663. DOI: 10.1109/TAES.2018.2798358.
32. You, P.; Ding, Z.; Qian, L.; Li, M.; Zhou, X.; Liu, W.; Liu, S. A motion parameter estimation method for radar maneuvering target in gaussian clutter. IEEE Transactions on Signal Processing. 2019, 67, 5433-5446. DOI: 10.1109/TSP.2019.2939082.
33. Ding, D.; You, P.; Qian, L.; Zhou, X.; Liu, S.; Long, T. A subspace hybrid integration method for High-Speed and maneuvering target detection. IEEE Transactions on Aerospace and Electronic Systems. 2020, 56, 630-644. DOI: 10.1109/TAES.2019.2919478.
34. Schmidt, R. Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation. 1986, 34, 276-280. DOI: 10.1109/TAP.1986.1143830.
35. Barabell, A. Improving the resolution performance of eigenstructure-based direction-finding algorithms. ICASSP '83. IEEE International Conference on Acoustics, Speech, and Signal Processing. Boston, MA, USA, 14-16 April 1983. DOI: 10.1109/ICASSP.1983.1172124.
36. Paulraj, A.; Roy, R.; Kailath, T. A subspace rotation approach to signal parameter estimation. Proceedings of the IEEE. 1986, 74, 1044-1046. DOI: 10.1109/PROC.1986.13583.
37. Blunt, S. D.; Chan, T.; Gerlach, K. A new framework for direction-of-arrival estimation. 2008 5th IEEE Sensor Array and Multichannel Signal Processing Workshop. Darmstadt, Germany, 21-23 July 2008. DOI: 10.1109/SAM.2008.4606829.
38. Blunt, S. D.; Chan, T.; Gerlach, K. Robust DOA estimation: the reiterative superresolution (RISR) algorithm. IEEE Transactions on Aerospace and Electronic Systems. 2011, 47, 332–346. DOI: 10.1109/TAES.2011.5705679.
39. Blunt, S. D.; Gerlach, K. Adaptive pulse compression via MMSE estimation. IEEE transactions on aerospace and electronic systems. 2006, 42, 572-584. DOI: 10.1109/TAES.2006.1642573.
40. Higgins, T.; Blunt, S. D.; Shackelford, A. K. Space-Range Adaptive Processing for Waveform-Diverse Radar Imaging. 2010 IEEE Radar Conference. Arlington, VA, USA, 10-14 May 2010. DOI: 10.1109/RADAR.2010.5494604.
41. Higgins, T.; Blunt, S. D.; Shackelford, A. K. Time-Range Adaptive Processing for pulse agile radar. 2010 International Waveform Diversity and Design Conference. Niagara Falls, ON, Canada, 08-13 August 2010. DOI: 10.1109/WDD.2010.5592394.
42. Yardibi, T.; Li, J.; Stoica, P.; Xue, M.; Baggeroer, A. B. Source localization and sensing: A nonparametric iterative adaptive approach based on weighted least squares. IEEE Transactions on Aerospace and Electronic Systems. 2010, 46, 425-443. DOI: 10.1109/TAES.2010.5417172.
43. Chen, B.; Huang, Y.; Chen, X.; Guan, J. Space-Time-Range Adaptive Processing for MIMO Radar Imaging. International Conference on Radar. 2018, 1-6, Brisbane, QLD, Australia, 27-31 August 2018. DOI: 10.1109/RADAR.2018.8557230

 

Point 2: What is the reason of this study? What are the real-world applications? How is the method presented in this paper addressing shortcomings of previous methods?

 

Response 2:

Thank you very much for this suggestion. This point was accepted and made.

It is very kind of you to give me this suggestion to help improve the quality of the manuscript.

(1) The reason of this study

First of all, please allow me to answer the first question. Based on the context of this study, the reasons for this study can be summarized as follows:

1)The well-known moving target detection (MTD) [4,5] method has been widely applied by modern coherent radar, where Doppler filter bank processing is used for the effective suppression of strong background clutter, as well as for the coherent integration of a moving target with unknown Doppler frequency. Besides, the MTD may be efficiently implemented via fast Fourier transform (FFT). Unfortunately, the MTD input vectors are the pulse samplings distributed along range cells one-by-one and the performance gain is limited by the target’s resident time in a single range cell. As a result, it is difficult to further improve the performance via MTD for the low signal-to-noise (SNR) target or the high-speed target [6-7]. For the low SNR target, e.g., far-range or low radar cross section (RCS) target, the integration time should be adequately enlarged and the range walk, i.e., the linearly varied distance between target and radar, of even a slowly moving target will exceed several range cells. For a high-speed target, this kind of across range cell (ARC) effect may also be drawn even in a very short integration time. Furthermore, with the remarkably refined range resolution of modern radar, it becomes necessary to deal with the ARC effect of moving targets.

2)Based on the signal model of a rectilinearly moving target in a long-time integration, Jia Xu proposes a novel Radon-Fourier transform (RFT) to realize the long-time coherent integration for the moving targets with ARC range walk. In the conventional signal processing flow, matched filter and RFT are often cascaded to complete time-range focusing. However, RFT still belong to standard time-domain matched filter, which will cause range-velocity sidelobes of strong targets. The range-velocity sidelobes result from matched filter and RFT will mask other weak targets, which will and affect the subsequent signal processing processes such as target detection and tracking.

3)On the other hand, because the mathematical model of Doppler estimation is similar to that of direction of arrival (DOA) estimation, the research related to DOA estimation can also be used to solve the problems of Doppler sidelobes suppression. Conventional DOA estimation methods such as MUSIC [34], root-MUSIC [35] and ESPRIT [36] use the spatial snapshots to calculate the sample covariance matrix (SCM) to estimate the unknown spatial covariance matrix, and use SCM to estimate the number and direction of signal sources. Professor Blunt studies a reiterative super-resolution (RISR) method, which was originally used for DOA estimation in array signal processing [37,38]. RISR method is based on the minimum mean square error (MMSE) criterion and is implemented with a recursive structure. The method does not need the prior knowledge of the number of signal sources, and can automatically determine the number, direction and power of signal sources. Given the information about the spatial covariance of noise and one snapshot, RISR updates the structured MMSE filter bank by iteratively using the previous estimation of spatial power distribution, and applies the filter bank to update the estimation of spatial power distribution. Based on the same theoretical basis, Professor Blunt applies RISR method to time dimension for high-resolution frequency estimation [38], proposes adaptive pulse compression (APC) method in the range dimension [39], and proposes space-time adaptive processing [40], time-range adaptive processing [41] which are adaptive methods combining different dimensions. Almost at the same time, professor Li proposes a nonparametric iterative adaptive approach (IAA) [42]. IAA method comprehensively considers the joint estimation of Doppler and range, and its essential idea is the same as that of APC method [43]. Although IAA method iterates over the whole data and has a large amount of computational cost, it does effectively improve the resolution and estimation accuracy in active sensing such as range-Doppler imaging and passive sensing such as underwater acoustic measurements.

4) At the beginning, we only expect that the idea of IAA may be applied to pulse compression and long-time coherent integration to achieve better a sidelobes suppression. To suppress range-velocity sidelobes synthetically, this study puts theory into simulation. Appling IAA to pulse compression,we can get APC method. Appling IAA to RFT is never proposed before, so we propose IARFT which applies IAA to RFT as the basis. Later, we combine APC and IARFT together to get APC-IARFT method which can achieve range-velocity sidelobes suppression and time-range adaptive focusing.

(2) Real-world applications

For the RFT methods, the target to be detected is assumed to be a nonfluctuating target in this article, i.e., the Swerling 0 target. In real applications with a long coherent processing interval (CPI), the target's fluctuation, however, cannot be neglected with the increase of the illumination time and the change of the radar line-of-sight (LOS). Therefore, the backscattering responses should be analyzed and measured quantitatively for targets to be detected on the backscattering amplitude, shifted envelopes, and phase modulation via real experiments versus different factors, e.g., high-order motion, carrier frequency, radar LOS, and CPI. Furthermore, the coherence loss caused by radar hardware should be studied like the dynamic range and stability of the receivers, which are mainly decided by the phase noise of the oscillators. Accordingly, the bounds of coherent integration on LOS, CPI and carrier frequency difference need to be determined for RFT methods on different kinds of targets. In order to simplify the above considerations on fluctuating of target’s backscattering responses, the CPI we set is not very long, but it is sufficient for long-time coherent integration.

As for the real-world applications, we have envisaged the following scenarios:

1)Airborne radar detection of bombers and missiles. Bomber can be a slow and strong target for moving airborne radar. Missiles launched by bombers are high-speed targets for airborne radar. When a bomber launches a missile, if traditional methods are used, the range-velocity sidelobes of the bomber may cover the main lobe of the missile.

2)High resolution is always desired for dense target scenarios, such as the well-known multiple aircraft formation (MAF). The resolution on the spatial and motion parameters should be discussed for the RFT method in depth.

3)In the transformed parameter space some unwanted responses like blind speed sidelobes (BSSL) will be generated by RFT method, which should be effectively suppressed.

4)The performance of RFT methods in the complicated environment with strong clutter and jamming should be discussed. In particular, ARFT only has the ability of adaptive clutter suppression. When there are jamming targets in secondary data, the performance of ARFT will degrade.

(3) How to addresses shortcomings of previous methods

As for how the method presented in this paper addresses shortcomings of previous methods, please allow me to use some simulation scenarios in the paper to explain.

1)It is known that The traditional pulse compression technology is based on matched filter (MF). Under the assumption of the solitary point target and Gaussian white noise, MF is an optimal linear filter aiming at maximizing the signal-to-noise ratio (SNR) of a target. Its essence is autocorrelation of the reference signal. However, in practical application, the MF has the problems, such as the range sidelobes of large targets which mask the nearby small targets, susceptible to sampling mismatch and intrapulse Doppler mismatch, and so on.

Like MTD, RFT belongs to standard time-domain matched filter. RFT will cause velocity sidelobes of strong targets. The range-velocity sidelobes result from matched filter and RFT will mask other weak targets, which will and affect the subsequent signal processing processes such as target detection and tracking.

Take Scenario 1 in Section 6 of the paper as an example. In Figure 5(a), the main lobe and the BSSL of Target 1 can be clearly seen. The sidelobes of target 1 completely cover the main lobe of Target 2.

2) Since RFT can be regarded as the expansion of Fourier transform, it is non-adaptive. Xu and Yan extend the RFT to the field of adaptive clutter suppression [31], and propose sub-aperture adaptive RFT (SA-ARFT) method to reduce the requirements for the amount of independent and identically distributed data and reduce the computational cost. However, the adaptive method in [19] is aimed at clutter suppression, and does not have the ability of adaptive suppression for the jamming targets in the training samples. ARFT method uses the inverse of clutter covariance matrix to form clutter notch and suppress clutter, which is helpful to the target energy’ focusing in the time-range plane under clutter background. However, when the target’s velocity is too high, which causes the fluctuation of amplitude between pulses and makes the number of effective pulses available for long-time coherent integration few, which decreases the velocity resolution of ARFT method and weakens the performance of focusing.

Take Scenario 1 in Section 6 of the paper as an example. the limited number of coherent pulses affects the output of ARFT method. At the same time, due to the processing of clutter’s covariance matrix, the energy at the velocity of Target 1 is excavated to form a notch.

3)As described at the beginning of Section 4 in the paper, the iterative adaptive idea of IARFT method is originally used for signal source localization in array signal processing. At present, it has been extended to Doppler-domain processing, pulse compression processing, and other fields such as multi-dimensional signal processing. As a nonparametric method derived based on the weighted least squares criterion, iterative adaptation approach aims to solve the estimation problem of coefficients in the following linear models:

where  is the steering vector and  is the noise vector. For the process of proof, please refer to the papers and works of Jian Li [42,44]and S. D. Blunt [37-41,45], which will not be repeated here. To realize the IARFT method, we need to build a linear model which is in the same form as the equation above. This linear model needs to be related to the two-dimensional parameters of range and velocity. So we form the data model in Section 4.1 to implement IARFT method.

Take Scenario 1 in Section 6 of the paper as an example. The output of IARFT method in Figure 5(c) is better comparing with those of RFT and ARFT. IARFT suppresses the velocity sidelobes of Target 1, so we can distinguish the main lobe of Target 2 (the position marked by the red ellipse in Figure 5(c)). However, the BSSL of Target 1 in Figure 5(c) is still too obvious.

4) Because APC can better suppress the range sidelobes and IARFT can better suppress the velocity sidelobes. To better suppress range-velocity sidelobes, we can replace the conventional signal processing flow based on matched filter and RFT with a new kind of flow based on APC and IARFT.

Take Scenario 1 in Section 6 of the paper as an example. APC-IARFT method is the best among the four methods. The velocity sidelobes and BSSL of Target 1 are suppressed simultaneously in Figure 5(d).

44. Tan, X.; Roberts, W.; Li, J.; Stoica, P. Range-Doppler Imaging Via a Train of Probing Pulses. IEEE Transactions on Signal Processing. 2009, 57, 1084-1097. DOI: 10.1109/TSP.2008.2010010
45. Higgins, T.; Blunt, S. D.; Gerlach, K. Gain-constrained adaptive pulse compression via an MVDR framework. 2009 IEEE Radar Conference. Pasadena, CA, USA, 04-08 May 2009. DOI: 10.1109/RADAR.2009.4977011.

 

 

Point 3: The abstract as well as the conclusion are totally cryptic even for a reader versed in radar technology.

 

Response 3: Please provide your response for Point 3. (in red)

Thank you very much for this suggestion. This point was accepted and made.

We are sorry to make you have some unpleasant reading experience. It is very kind of you to give me (the corresponding author) this suggestion to help improve the quality of the manuscript. We will make good use of this opportunity.

Due to the English writing of the corresponding author, the abstract and conclusion may be kind of confusing. Although English writing is a bit difficult for me (the corresponding author), please believe that I can revise it well.

After considering the context of the paper and the reason of this study, I have already known how to revise the abstract, introduction and conclusion of the paper. I think the revised abstract, introduction and conclusion can better express our authoes’ thoughts.

The revised abstract is “In the conventional radar signal processing, the cascade of pulse compression (i.e., matched filter) and Radon-Fourier transform (RFT) can extract the estimated scattering coefficient of the target in the range-velocity dimension through long-time coherent integration (i.e., long-time focusing) in noise background. However, matched filter has the problems such as range sidelobes. RFT belongs to standard time-dimension matched filter, which will cause velocity sidelobes of strong targets. The range-velocity sidelobes caused by matched filter and RFT will mask other weak targets and affect the subsequent signal processing processes such as target detection and tracking. To suppress range-velocity sidelobes and achieve better range-velocity focusing, this paper proposes a time-range adaptive focusing method named APC-IARFT for short, which is based on adaptive pulse compression (APC) and newly proposed iterative adaptive Radon-Fourier transform (IARFT). In APC-IARFT method, the radar time-range focusing process consists of two steps: range-dimension focusing and long-time focusing in velocity dimension. APC method can realize range-dimension focusing and suppress range sidelobes of strong targets. Then, based on the minimum variance distortionless response (MVDR) formulation, the proposed IARFT method iteratively designs time-dimension adaptive filter of each range-velocity grid according to the received signal processed by APC to suppress velocity sidelobes of strong targets and achieve long-time focusing. Compared with conventional cascade of matched filter and RFT, the cascade of matched filter and adaptive Radon-Fourier transform (ARFT), the results show that the proposed time-range adaptive focusing method (i.e., APC-IARFT) is competent for a variety of scenarios.”.

The revised conclusion is “By considering the coherent integration as focusing, we consider pulse compression as range-dimensional focusing and long-time coherent integration as long-time focusing. However, matched filter has the problems such as range sidelobes. RFT belongs to standard time-dimension matched filter, which will cause velocity sidelobes of strong targets. The range-velocity sidelobes caused by matched filter and RFT will mask other weak targets and affect the energy focusing and the subsequent signal processing processes such as target detection and tracking. To achieve better focusing, this paper studies the adaptive focusing of two dimensions of time and range. Firstly, the idea of iterative adaptive approach is applied to long-time focusing and a long-time adaptive focusing method based on iterative adaptive RFT (IARFT) is designed. Further, in order to solve the problem of two-dimensional sidelobes masking, this paper proposes a time-range adaptive focusing method (APC-IARFT for short) based on APC and IARFT. By cascading APC method and IARFT method, the range-velocity sidelobes can be adaptively suppressed under the range-velocity grid without additional prior information.

In addition, the computational cost of IARFT method is high, and the research on its fast implementation will be an important part of the future research.

It should be noted that, IARFT method suppress the velocity sidelobes, but it does not completely suppress the clutter. In order to suppress the clutter, we think that the feasible method is to estimate the clutter’s covariance matrix , and whiten the echo data before IARFT method. Another method is to add the estimation of clutter’s covariance matrix, i.e., add the clutter’s covariance matrix to the covariance matrix calculation of IARFT method (i.e., equation in Section 5.2).

Furthermore, we also found that there are still some problems if IARFT method is carried out after APC method in the clutter background through Section 6.4. We think that APC method may affect the statistical characteristics of clutter in the cascaded processing. The next research content is to integrate APC method and IARFT method into the multi-dimensional joint processing to realize the joint processing of the two methods, which can further expand the dimensions and manners of processing, and achieve the optimal processing in coherent integration of high-speed weak targets.”.

 

 

Point 4: I urge the authors to provide context, perspective and discussion with respect to previous methods, and to describe the underlying physics. As presented, the paper is a technical report for happy fews.

 

Response 4: Please provide your response for Point 4. (in red)

Thank you very much for this suggestion. This point was accepted and made.

We are sorry to make you have some unpleasant reading experience. It is very kind of you to give me (the corresponding author) this suggestion to help improve the quality of the manuscript. We will make good use of this opportunity.

(1) To answer your all questions in detail, I (the corresponding author) sum up your question as the above 4 points. For the Point 1 (i.e, the context of the paper), I have revised the introduction of this paper. In the introduction, we explain the drawback of MTD method when dealing with the echo of high-speed moving targets and introduce the advantage of RFT method. But RFT method is not a perfect method. RFT method is a generalized form of Fourier transform and it is still a time-dimensional matched filter. Because the interval of velocity considered in RFT method is much bigger than the range of maximun unambiguous velocity considered in MTD method, velocity sidelobes of slow and strong tragets can mask the high-speed weak targets in RFT method. So how to suppress velocity sidelobes of slow and strong tragets is an important problem in RFT method. what's more, cascade of matched filter and RFT method is widely applied to focus the energy of high-speed targets. However, matched filter has the problems such as range sidelobes. RFT belongs to standard time-dimension matched filter, which will cause velocity sidelobes of strong targets. The range-velocity sidelobes caused by matched filter and RFT will mask other weak targets and affect the subsequent signal processing processes such as target detection and tracking. To suppress range-velocity sidelobes and achieve better range-velocity focusing, this paper proposes a time-range adaptive focusing method named APC-IARFT for short, which is based on adaptive pulse compression (APC) and newly proposed iterative adaptive Radon-Fourier transform (IARFT). I believe the revised introduction can better explain the research context of this paper.

(2)As for the perspective and discussion with respect to previous methods, please allow me to explain as follows.

1)The focus of this paper is to analyze the defects of RFT method and improve RFT method. Therefore, the comparison between MTD and RFT is only described in the introduction, not proved by physical analysis. For detailed analysis between MTD and RFT, please refer to Jia Xu's literature [1-3].

2)In order to save the space of the paper, although the flow of APC-IARFT method and the derivation process of IARFT method are directly proposed in this paper, the expression of RFT is mentioned in Section 4. Because IARFT method is based on RFT method, we believe that the derivation in Section 4 can make readers intuitively understand the difference and relationship between the RFT method and the IARFT method.

3)The mathematical expression and physical meaning of the ARFT method are not explained in detail in this paper, because this method is also not the focus of this paper. For the specific derivation of the ARFT method, please refer to the literature [31]. Therefore, this paper only explains the principle of ARFT method in the introduction, and illustrates the difference between the adaptive processing of ARFT method and the adaptive processing of IARFT method through simulation experiments.

(3)As for the underlying physics, Please allow me to use the answer to Point 2 to explain:

1)It is known that The traditional pulse compression technology is based on matched filter (MF). Under the assumption of the solitary point target and Gaussian white noise, MF is an optimal linear filter aiming at maximizing the signal-to-noise ratio (SNR) of a target. Its essence is autocorrelation of the reference signal. However, in practical application, the MF has the problems, such as the range sidelobes of large targets which mask the nearby small targets, susceptible to sampling mismatch and intrapulse Doppler mismatch, and so on.

Like MTD, RFT belongs to standard time-domain matched filter. RFT will cause velocity sidelobes of strong targets. The range-velocity sidelobes result from matched filter and RFT will mask other weak targets, which will and affect the subsequent signal processing processes such as target detection and tracking.

Take Scenario 1 in Section 6 of the paper as an example. In Figure 5(a), the main lobe and the BSSL of Target 1 can be clearly seen. The sidelobes of target 1 completely cover the main lobe of Target 2.

2) Since RFT can be regarded as the expansion of Fourier transform, it is non-adaptive. Xu and Yan extend the RFT to the field of adaptive clutter suppression [19], and propose sub-aperture adaptive RFT (SA-ARFT) method to reduce the requirements for the amount of independent and identically distributed data and reduce the computational cost. However, the adaptive method in [19] is aimed at clutter suppression, and does not have the ability of adaptive suppression for the jamming targets in the training samples. ARFT method uses the inverse of clutter covariance matrix to form clutter notch and suppress clutter, which is helpful to the target energy’ focusing in the time-range plane under clutter background. However, when the target’s velocity is too high, which causes the fluctuation of amplitude between pulses and makes the number of effective pulses available for long-time coherent integration few, which decreases the velocity resolution of ARFT method and weakens the performance of focusing.

Take Scenario 1 in Section 6 of the paper as an example. the limited number of coherent pulses affects the output of ARFT method. At the same time, due to the processing of clutter’s covariance matrix, the energy at the velocity of Target 1 is excavated to form a notch.

3)As described at the beginning of Section 4 in the paper, the iterative adaptive idea of IARFT method is originally used for signal source localization in array signal processing. At present, it has been extended to Doppler-domain processing, pulse compression processing, and other fields such as multi-dimensional signal processing. As a nonparametric method derived based on the weighted least squares criterion, iterative adaptation approach aims to solve the estimation problem of coefficients in the following linear models:

where  is the steering vector and  is the noise vector. For the process of proof, please refer to the papers and works of Jian Li [42,44]and S. D. Blunt [37-41,45], which will not be repeated here. To realize the IARFT method, we need to build a linear model which is in the same form as the equation above. This linear model needs to be related to the two-dimensional parameters of range and velocity. So we form the data model in Section 4.1 to implement IARFT method.

Take Scenario 1 in Section 6 of the paper as an example. The output of IARFT method in Figure 5(c) is better comparing with those of RFT and ARFT. IARFT suppresses the velocity sidelobes of Target 1, so we can distinguish the main lobe of Target 2 (the position marked by the red ellipse in Figure 5(c)). However, the BSSL of Target 1 in Figure 5(c) is still too obvious.

4) Because APC can better suppress the range sidelobes and IARFT can better suppress the velocity sidelobes. To better suppress range-velocity sidelobes, we can replace the conventional signal processing flow based on matched filter and RFT with a new kind of flow based on APC and IARFT.

(4) As you said, long-time coherent integration (or long time focusing) based on RFT is indeed a relatively small research field of radar signal processing proposed in the past decade. However, we believe that this research field has a very broad application prospect.

The modern radar target and detection environment are becoming increasingly challenging. For down-looking radars mounted in flying platforms, strong ground or sea clutter is always a difficult problem for detecting weak slow-moving targets. Furthermore, with the fast development of electronic countermeasure (ECM) technologies, strong active jamming may affect effective target detection. Apart from the quickly changed background, more high-speed, highly maneuvering, and weak targets, like aerospace vehicles, satellites, ballistic missiles, and unmanned aerial vehicles (UAVs), are emerging in air, in space, and on the ground, which will inevitably cause challenges to target detection, estimation, and tracking. The main challenges of target characteristics, as well as the environment, can be summarized for modern radar as follows:

High speed: The velocities of some ultra-high-speed aerospace vehicles can approach Mach 5-25, which can pass through a radar beam or range cell in a very short instant. Therefore, the number of integrated pulses is limited in a single range-Doppler-beam cell. However, the scale effect caused by the ultra-high speed of an air or airspace target may cause significant SNR integration loss.

Low radar cross section (RCS): Aircraft, missiles, and warships with an extremely low RCS have been widely used in modern battlefields. Compared to conventional radar targets, the detection coverage will be reduced dramatically for these low observable targets because of the RCS reduction.

Strong maneuver: The accelerations of aerospace vehicles in near space may approach 2-4 g. Besides, they can use corkscrew spin, sinusoid motion, large leap, and big-corner turns to realize orbital transfer and collision avoidance. These strong maneuverings may inevitably cause difficulties on target detection, parameter estimation, continuous tracking, and target recognition.

Far range: Space targets of modern radar may move in low orbit, middle orbit, and geostationary high orbit and even near space, which implies that target detection should be accomplished in the far range. Furthermore, more efficient and effective RSP methods are needed for an extremely low-SNR far-range application.

Strong clutter: There are three typical challenges related to clutter environment for modern radar. First, for downlooking radars mounted on airborne, airboat, and spaceborne platforms, strong ground clutter caused by platform motion is always a difficult problem. Second, strong sea clutter requires effective clutter-suppressing methods for weak marine target detection. Third, the time–space varied ionosphere clutter may shelter radar targets when they fly through the atmosphere layers.

Jamming: With the quick development of wideband, high-power, and intelligent active jammers, strong active and/or passive jamming can affect the radar detection performance in all dimensions, like time, space, frequency, and polarization, which causes difficulties for real-time detection, accurate estimation, and effective recognition of a radar target.

To overcome the above problems, the conventional solutions are to optimize the radar carrier frequencies, to increase the antenna transmitting power, to enlarge the antenna aperture, etc. That is, a radar with a large power aperture product is preferred. Nevertheless, these methods may cause problems of ECM and even the radar's survivability, which is also related to the high cost, high probability of interception, and high vulnerability. Therefore, it is attractive to ask whether we can improve radar ability in a troublesome environment by changing its RSP without changing system parameters.

Radar equations of different types and application scenarios have told us that the radar's maximum coverage range will be proportional to the fourth root of the integration time with the given system parameters. Therefore, it is possible to use more illumination time to improve radar detection performance. Unfortunately, it is easy to find many limitations that affect the effective implementation of the cascaded RSP flow. Among these, the target's echoes should be limited in a single range-Doppler-beam cell as much as possible. Otherwise, in a long CPI, the received energy and detection performance are reduced because of the effects of across-range cells (ARCs), across-Doppler cells (ADCs), and across-beam widths (ABWs). ARC, across Doppler cells (ADC), and across-beam widths (ABW) in a long CPI will bring about integration difficulties, as well as SNR loss. Fortunately, it is obvious that the target's time-varied range migration (RM) causes ARC, ADC, and ABW effects, the first two of which have been discussed in high-resolution SAR/ISAR target imaging. If a parametric time-variant function can be introduced for modeling the RM of a target, its echoes with the ARC, ADC, and ABW effects can be compensated according to the parametric motion parameters. Besides, the number of the unknown parameters is finite in many scenarios. For example, only two parameters, e.g., the initial range and the radial velocity, are needed for modeling a uniformly moving target. Therefore, RFT can be introduced from the range-compressed radar echoes into the low-dimensional parameter space, in which all preceding effects (both envelope and phase) can be compensated for in accordance with the correct parameters. That is why RFT is the basis of Focus-before-detect (FBD).

Multidimensional FBD propoed by Jia Xu is a kind of advanced RSP method. The methods proposed in the paper is inspired by the thought of FBD to suppress the sidelobes in FBD and help energy’s focusing. In the future research, we believe IAA can be applied to more dimensions in FBD and makes the result of focusing better. So IARFT method and APC-IARFT method proposed in the paper are just the beginning of applying IAA to multidimensional FBD.

Please refer to the attachment for details, thank you.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Guan et al. took great care to answer all the points raised by the reviewers, The paper is still highly technical, but at least a lot clearer, with some context. I appreciated the new conclusion, abstract and the extensive reply.