Enhancing Calibration Precision in MIMO Radar with Initial Parameter Optimization

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The author's review and summary of relevant methods are too limited. Many related methods have been published in IEEE TGRS in recent years, and it is recommended to supplement them.

2. What is the difference between the MIMO architecture and existing methods?

3. How does MIMO echo separation ensure high accuracy?

4. Table 1: Many parameters are incomplete.

 

Author Response

Author’s Reply to the Reviewers' Comments and Recommendations

 

*Title of the Manuscript:

Enhancing Calibration Precision in MIMO Radar with Initial Parameter Optimization

 

Reviewer #1:

We sincerely appreciate the insightful questions and comments from the reviewers, which have greatly enhanced the quality and completeness of this paper. Your detailed feedback has helped us address areas we had previously overlooked, and we have made every effort to improve the manuscript accordingly. We are deeply grateful for your thoughtful input and have provided our best possible responses to each point. We earnestly hope that this revised paper will be considered for publication in ‘Remote Sensing’.

 

Furthermore, the revised sections in the manuscript are highlighted in red text.

 

Point 1:

The author’s review and summary of relevant methods are too limited. Many related methods have been published in IEEE TGRS in recent years, and it is recommended to supplement them.

 

Response:

We fully agree your comments and sincerely thank the reviewer for highlighting this important aspect. Your advice provided an opportunity to further explore research on calibration using covariance matrices.

As the reviewer noted, the Journal of IEEE Geoscience and Remote Sensing has published results on a number of calibration studies.

Among them, we looked for results related to the content of our study and found that the following three papers could be referenced.

 

• Zhang, Y. Gao and X. Liu, "Robust Channel Phase Error Calibration Algorithm for Multichannel High-Resolution and Wide-Swath SAR Imaging," in IEEE Geoscience and Remote Sensing Letters, vol. 14, no. 5, pp. 649-653, May 2017, doi: 10.1109/LGRS.2017.2668390.
• Baffelli, O. Frey, C. Werner and I. Hajnsek, "Polarimetric Calibration of the Ku-Band Advanced Polarimetric Radar Interferometer," in IEEE Transactions on Geoscience and Remote Sensing, vol. 56, no. 4, pp. 2295-2311, April 2018, doi: 10.1109/TGRS.2017.2778049.
• Guo, Y. Gao, K. Wang and X. Liu, "Improved Channel Error Calibration Algorithm for Azimuth Multichannel SAR Systems," in IEEE Geoscience and Remote Sensing Letters, vol. 13, no. 7, pp. 1022-1026, July 2016, doi: 10.1109/LGRS.2016.2561961.

 

As a result of analyzing the reference papers, all of them were analysis papers on multiple channels (MIMO-channel or V/H pol.-channel), and they proposed their own calibration method to minimize the error in the initial variables between channels.

We think these are very improved methods, but this is a calibration method for synthetic aperture radar. It is a method of signal processing the data received during the SAR synthetic aperture time, and the calibration method proposed in the reference paper is a post-processing method that processes the data received after a certain period of time.

Additional research is needed to apply it to mass-produced vehicle radars used for real-time processing. Acquiring SAR data requires significant time for transmitting and receiving numerous pulses. Even with fast signal processing, the time required to acquire data makes real-time SAR implementation a highly challenging and complex task.

Therefore, we have cited the relevant references and provided additional explanations to help readers understand and clarify our goals.

[Please see Section I]

‘…In the mass production of the small radar industry (automotive, UAV/UAM, cube-SAT, etc.), cost competitiveness necessitates achieving optimal performance at minimal expense. Consequently, RF chips and memory capacity are often limited, making it challenging to execute the calibration process for every chirp signal. Additionally, due to memory constraints, the calibration parameters calculated during initial manufacturing at the factory are conventionally stored in EEPROM. These initial parameters are then used to compensate all MIMO signals for radar detection throughout the radar's lifespan. As close to an ideal environment with low interference, we can compensate for the unexpected phase and magnitude difference between each MIMO channel using the initial parameters. However, we cannot always measure the expected reference signal with a stable and low-noise environment. And also, the reference signal can be changed according to various environmental conditions. In a situation with unexpected interference during the operation of radar, it becomes difficult to secure the reliability of the calibration and causes inaccurate results such as errors in target detection and target classification, etc. In recent research, there are various calibration methods to compensate for the unexpected interference [3]-[8], using the saved parameters. A method of obtaining high-resolution quality radar images by adjusting the calibration values of the received MIMO structure has also been studied [9]-[10]. However, it is optimized for Synthetic Aperture Radar (SAR) image extraction, and research on applying it to real-time vehicle radar has not yet been conducted…’

 

Point 2:

What is the difference between the MIMO architecture and existing methods?

 

Response:

In radar systems, the arrangement of antennas can be classified into SISO, SIMO, MISO, and MIMO architectures. Research on beamforming methods using single output structures has been actively conducted, driven by efforts to perform DoA estimation with a minimal number of antennas. However, multiple outputs are now widely utilized due to their advantages in easily implementing high resolution radar systems.

In this study, we propose a method to reduce errors caused by not only mutual coupling but also thermal conditions and circuit errors between multiple channels in MIMO architecture.

For single output systems, there is no need to consider or compensate for coupling errors between echoes. However, calibration for environmental factors, such as thermal conditions, remains necessary. In this case, since the calibration points of a multiple output system are absent in a single output system, the lack of reference points for calibration can lead to challenges in compensating for the aforementioned errors.

 

Point 3:

How does MIMO echo separation ensure high accuracy?

 

Response:

We sincerely apologize for not providing sufficient explanation in the initial submission. We acknowledge that our explanation was lacking and appreciate the opportunity to address this.

First, in a single-channel radar, detection relies on the antenna gain, which is measured as being higher in the direction of the target's signal. However, since antenna gain is highly susceptible to changes in the surrounding environment, its accuracy is often limited.

To address this limitation, utilizing multiple channels allows the reflected signal from a target at a specific location to be received with varying phase angles across channels (please see the figure below).

[Angle estimation using MIMO radar system]

By leveraging the differences in phase angles between channels, accurate location information can be extracted regardless of the variability in antenna gain, which is particularly vulnerable to environmental changes.

In this context, we focused on the concept that "signals received across multiple channels must preserve accurate phase information" to enable precise target localization. This approach underpins high-precision target detection.

Therefore, in this paper, we propose a calibration method designed to preserve accurate phase information, specifically targeting real-time MIMO FMCW radar systems used in automotive applications.

Since the accurate separation of MIMO echo signals based on the principle described above directly impacts detection accuracy, the proposed calibration method represents a critical technology.

To facilitate the reader's understanding, we have provided the following detailed supplementary explanation in this paper.

[Please see Section I]

'…In this paper, we introduce the improved calibration technique, used to increase the accuracy of radar detection. Not only in the automotive field but also in small radar system field, radar calibration is the essential process to generate the high performance of not only target detection but also target classification for MIMO radar [3]-[8]. Signals received across multiple channels must preserve accurate phase information to enable precise target localization. This approach underpins high-precision target detection...’

'…In this paper, comparing other calibration studies, we propose the easy and simple calibration method with a covariance matrix of MIMO channels and design to preserve accurate phase information, specifically targeting real-time MIMO FMCW radar systems such as automotive applications. The proposed technique can compensate for every signal with initial calibration parameters, even though the received signal is not matched with initial calibration parameters due to unexpected environmental conditions...’

 

Point 4:

Table 1: Many parameters incomplete.

 

Response:

During the course of our study, we utilized the raw data from HYUNDAI-MOBIS’s automotive radar, which is currently used for commercial vehicle. To share the detailed specifications of the radar publicly, prior approval from HYUNDAI-MOBIS would be required.

In order to increase the reliability of our paper's verification process, we requested HYUNDAI-MOBIS to disclose the detailed specifications of the radar. However, unfortunately, we received a response that HYUNDAI-MOBIS, as a commercial company, operates under strict security policies and therefore cannot disclose the detailed specifications.

We kindly request your understanding regarding this matter. Therefore, we strongly agree with the reviewer's comments and have tried to modify them in a different way to overcome our shortcomings.

The core of our proposed method is to present a 'easy and simple calibration method for radars with MIMO channels'. We have modified a table of radar specification ranges to which our proposed technology is applied, and mentioned to the readers that 'our technology can be applied to various radars with MIMO channels'.

 

[Please see Section II]

‘…To verify the proposed calibration method, we designed the FMCW MIMO radar system, which is conventionally used for the front radar and corner radar of automobiles. The experiment was done with a corner reflector in an anechoic chamber. And also, we operate the designed radar, combined with a 360-degree rotator to monitor the signals in all angle directions. In table 1, the specifications of the FMCW MIMO radar system are introduced within the following system specification range. In other words, our proposed method is applicable to various radars with multi-channels…’

Table 1. FMCW MIMO radar system specification

System Parameter	Value
Center Frequency Range	70-80GHz
Chirp signal Bandwidth	200-500MHz
PRF	3000-10000 Hz
Chirp Duration	100us-0.5ms
Sampling rate	< 10 Mbps
Total Channel	3 Tx / 4 Rx (12 channels)

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposed the calibration method with a covariance matrix of MIMO channels. The paper needs to be well revised based on the following detailed comments for publication in this journal.

 

Point 1: The authors proposed the calibration method with a covariance matrix of MIMO channels. However, the authors did not sufficiently mention for the novel aspect of the proposed calibration method compared with the previous studies in the introduction. Therefore, the authors should clearly explain the novel aspect and contributions in this field.

 

Point 2: In the introduction, the authors explain the problems and limitations of the camera, LiDAR, and radar systems. However, the explanation for these problems is not sufficient, so the detailed explanation and various references about these problem are added to the introduction.

 

Point 3: In Figs. 1 and 3, the authors should correct the notations, such as "TX” and "RX”, to appropriate notation.

 

Point 4: In Table 1, the authors present the FMCW MIMO radar specification used to test the proposed calibration process. However, the detailed specification of this radar system is not sufficiently explained. Specifically, the detailed values for parameters, such as the PRF, chirp duration, and sampling rate, should be added to this table.

 

Point 5: In Fig. 7, the authors should revise the legend formats of the graph to clearly present the results of the proposed process.

 

Point 6: In Table 2, the detailed values of the noise level and channel difference should be added.

 

Point 7: The authors should recheck the format of this paper, including the reference section.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

The authors should recheck the English grammer of this paper.

Author Response

Author’s Reply to the Reviewers' Comments and Recommendations

 

*Title of the Manuscript:

Enhancing Calibration Precision in MIMO Radar with Initial Parameter Optimization

 

Reviewer #2:

This paper proposed the calibration method with a covariance matrix of MIMO channels. The paper needs to be well revised based on the following detailed comments for publication in this journal.

We sincerely appreciate the insightful questions and comments from the reviewers, which have greatly enhanced the quality and completeness of this paper. Your detailed feedback has helped us address areas we had previously overlooked, and we have made every effort to improve the manuscript accordingly. We are deeply grateful for your thoughtful input and have provided our best possible responses to each point. We earnestly hope that this revised paper will be considered for publication in ‘Remote Sensing’.

 

Furthermore, the revised sections in the manuscript are highlighted in red text.

 

Point 1:

The authors proposed the calibration method with a covariance matrix of MIMO channels. However, the authors did not sufficiently mention for the novel aspect of the proposed calibration method compared with the previous studies in the introduction. Therefore, the authors should clearly explain the novel aspect and contributions in this field.

 

Response:

To clearly highlight the novelty and contributions of our research, we have refined and elaborated on the Introduction section. The unique aspects and contributions of the technology presented in this paper can be more importantly emphasized from the perspective of mass production. First, additional references have been supplemented to introduce previous studies.

[Please see Section I]

‘…In recent research, there are various calibration methods to compensate for the unexpected interference [3]-[8], using the saved parameters…’

*Description of the papers being compared

-Reference paper [3]: This paper proposes a calibration method for FMCW MIMO radar that enables calibration without requiring distance information to the target.

-Reference paper [4]: This paper discusses the impact of impedance matching on radar system performance. The proposed impedance matching network demonstrates significant reductions in detection angle errors and sidelobe levels, with particularly pronounced effectiveness in compact-sized system.

-Reference paper [5]: This letter demonstrates that radar sensors with non-uniform antenna arrays achieve superior resolution. In this process, the two-way radiation pattern and the ambiguity function (AF) were used as evaluation metrics.

-Reference paper [6]: This paper evaluates calibration parameters using signals reflected from dominant targets. Unlike other calibration methods, it does not require prior knowledge of the target angles.

-Reference paper [7]: This paper discusses methods for obtaining high-quality images with accurate RCS in MIMO radar systems. To achieve high-performance imaging, the authors employ an adaptive weighting technique to calibrate amplitude and phase errors and reduce sidelobe levels. In addition, precise images are derived by compensating for phase distortions caused by propagating path-loss, and antenna pattern tapering.

-Reference paper [8]: This paper addresses phase error compensation caused by delays along the propagation path. In this context, it compensates for hard to measure delays caused by waveguides or feed lines through phase shifts, enabling the extraction of higher-quality images without the need for reference targets.

 

Radars that produce noise due to temperature variations or diverse environmental changes require calibration parameters tailored to specific conditions. However, from a mass production perspective, where cost-performance is a critical consideration, defining unique calibration parameters for each scenario poses a significant challenge. This process entails repeating the steps below for each chirp pulse, significantly increasing complexity and effort. It emphasizes the difficulties in generating distinct calibration parameters for every chirp pulse.

 

[Please see Section II]

1) Measurement for ideal signals: measuring each signal of each channel in an un-echoic chamber.

2) Averaging: applying the averaging technique with the stacked all data.

3) Estimating fractional term: estimating the fractional term of magnitude and phase to compensate for raw data.

4) Extracting final calibration function: Define the final calibration function of each channel with the estimated magnitude and phase results

 

Therefore, in actual mass production, the initially set calibration parameter values ​​are stored in the radar memory room and used until the end of the lifespan. The initial parameter values often fail to adapt effectively due to variations in diverse environmental conditions. To address the resulting errors, we propose a calibration technique designed to compensate for these discrepancies.

[Please see Section I]

‘…In the mass production of the small radar industry (automotive, UAV/UAM, cube-SAT, etc.), cost competitiveness necessitates achieving optimal performance at minimal expense. Consequently, RF chips and memory capacity are often limited, making it challenging to execute the calibration process for every chirp signal. Additionally, due to memory constraints, the calibration parameters calculated during initial manufacturing at the factory are conventionally stored in EEPROM. These initial parameters are then used to compensate all MIMO signals for radar detection throughout the radar's lifespan…’

‘…In this paper, comparing other calibration studies, we propose the easy and simple calibration method with a covariance matrix of MIMO channels and design to preserve accurate phase information, specifically targeting real-time MIMO FMCW radar systems such as automotive applications. The proposed technique can compensate for every signal with initial calibration parameters, even though the received signal is not matched with initial calibration parameters due to unexpected environmental conditions. It leads to the least disturbance and derives accurate calibration results even in adverse conditions outside the radar. In other words, the proposed process diversifies the matching point of calibration for the MIMO radar, based on the coupling matrix method…’

We addressed the changes in calibration points caused by environmental factors by applying a covariance matrix to the ideal calibrated signal and the actual calibrated signal. This method rearranges the calibrated points using the covariance matrices of the ideal environment and the unexpected environment, ensuring consistently improved results for all chirp pulses, even under changing environmental conditions.

  Figure 5 demonstrates that the proposed method can correct phase errors caused by environmental variations. Figure 6 shows that the influence of the surrounding side lobes is reduced compared to when the parameter values ​​stored at the time of mass production were
applied to the radar. Figure 7 shows that the gain error between channels is significantly reduced. Additionally in table 2, the proposed method reduces noise levels and inter-channel differences by minimizing coupling between uncorrelated channels, a characteristic feature of the covariance matrix.

[Please see Section III]

Table 2. Processing performance comparison

		Noise Level		Channel Difference		Processing Complexity
		Front Radar	Corner Radar	Front Radar	Corner Radar
The conventional method		-	-			Low
The proposed method						Low

 

In addition, a potential concern arises from the computational complexity associated with covariance matrices. However, this concern can be addressed in the context of compact automotive radar systems, as the method is applied to a single snapshot across only 12 channels, resulting in significantly lower dimensionality.

In summary, we apply a covariance matrix to the existing ideal calibrated signal and the non-ideal calibrated signal. This approach enables us to obtain more accurate calibrated signals for all chirp pulses compared to previous methods (currently employed in the industry). It provides greater resilience to environmental factors, such as climate changes, while simultaneously reducing channel differences and noise levels. This simple, intuitive, and computationally efficient method ultimately offers enhanced reliability in radar results.

 

Point 2:

In the introduction, the authors explain the problems and limitations of the camera, LiDAR, and radar systems. However, the explanation for these problems is not sufficient, so the detailed explanation and various references about these problems are added to the introduction.

Response:

We agree with the author's opinion that the description of the three major sensors, camera, lidar, and radar, should be supplemented sufficiently. Therefore, we have incorporated detailed explanations and examples, supported by relevant references, in the introduction section.

[Please see Section I]

‘…In other words, since the camera and LiDAR are based on ‘light’, it becomes difficult to distinguish and recognize the interested targets according to snow/rain, night/day, unexpected weather conditions, and various blockages. It has been previously studied that adverse weather conditions, such as rain and fog, significantly increase light attenuation [1]. This phenomenon critically affects the performance degradation of camera and LiDAR, particularly for Lane Departure Warning Systems, which are designed to prevent accidents caused by driver carelessness [2]. Consequently, many automotive manufacturers are actively striving to enhance sensing accuracy by integrating the advantages of multiple sensors, ensuring reliable performance even under adverse weather conditions. Due to the characteristics of electromagnetic waves, the radar can have more strong detection performance even under the interference of these unexpected environmental factors…’

 

*Reference paper [1]: This paper discusses the impact of additional water particles in adverse weather conditions on electromagnetic wave systems. By analyzing the attenuation effects across different frequency bands of electromagnetic waves, it highlights in Sections 4 and 5 how rain and for-induced attenuation lead to performance degradation in cameras and LiDAR systems.

Section 4. Rain and Fog Attenuation

Regarding fog influence, it can be seen that radar sensors are much more robust. For lidar sensors, as well as camera sensors, the specific attenuation reaches values over 100db/km. Therefore, surround sensors operating at optical and near infrared wavelengths are not recommendable for environment detection and vehicle control under foggy conditions. It can lead to a total failure of the sensor. Longer wavelengths, such as millimeter waves, show lower attenuation.

Section 5. Conclusion. (The second paragraph)

This paper gives an overview about the interaction of electromagnetic waves and hydrometeors. Automotive surround sensors such as camera, lidar, and radar operate at different frequency ranges. Based on Rayleigh scattering, Mie theory, and geometric optics the extinction efficiency can be determined in visible, infrared, and millimeter frequency range. Using the extinction efficiency, the specific attenuation can be calculated with known physical characteristics of rain and fog. It is shown that the rain and fog attenuation, calculated by using the equations in this paper, correspond to literature. Radar sensor radiation penetrate more effective through suspended water in the air, especially under foggy conditions. Camera and lidar sensors are strongly influenced by fog. However, due to the advantages of lidar and camera sensors regarding object classification and tracking, the sensors are essential for automated safety systems. Therefore, it is advisable to detect degraded sensor performance depending on the outdoor condition. Vehicles should use the most reliable sensor data by reducing the weighting of sensors with degraded performance. This work can help to get a quick introduction to the field of rain and fog attenuation on automotive sensor systems.

 

*Reference paper [2]: This paper examines the limitations of ADAS sensors by evaluating the view range performance under varying rainfall intensities. In this process, the Lane Departure Warning System (LDWS), which is used to prevent accidents caused by driver carelessness, was utilized as an evaluation metric.

 

Both [1] and [2] highlight the performance degradation of sensors in situations where the view range decreases. Also, they emphasize the importance of combining appropriate (highly reliable) sensors based on each specific condition.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Point 3:

In Figs. 1 and 3, the authors should correct the notations, such as “TX” and “RX”, to appropriate notation.

 

Response:

We have corrected mislabeled expressions such as “TX” and “RX” in Figure 1 and 3, to align with the context mentioned in the main manuscript.

 

[Please see Section II]

Point 4:

In Table 1, the authors present the FMCW MIMO radar specification used to test the proposed calibration process. However, the detailed specification of this radar system is not sufficiently explained. Specifically, the detailed values for parameters, such as the PRF, chirp duration, and sampling rate, should be added to this table.

 

Response:

During the course of our study, we utilized the raw data from HYUNDAI-MOBIS’s automotive radar, which is currently used for commercial vehicle. To share the detailed specifications of the radar publicly, prior approval from HYUNDAI-MOBIS would be required.

In order to increase the reliability of our paper's verification process, we requested HYUNDAI-MOBIS to disclose the detailed specifications of the radar. However, unfortunately, we received a response that HYUNDAI-MOBIS, as a commercial company, operates under strict security policies and therefore cannot disclose the detailed specifications.

We kindly request your understanding regarding this matter. Therefore, we strongly agree with the reviewer's comments and have tried to modify them in a different way to overcome our shortcomings.

The core of our proposed method is to present a 'easy and simple calibration method for radars with MIMO channels'. We have modified a table of radar specification ranges to which our proposed technology is applied, and mentioned to the readers that 'our technology can be applied to various radars with MIMO channels'.

[Please see Section II]

‘…To verify the proposed calibration method, we designed the FMCW MIMO radar system, which is conventionally used for the front radar and corner radar of automobiles. The experiment was done with a corner reflector in an anechoic chamber. And also, we operate the designed radar, combined with a 360-degree rotator to monitor the signals in all angle directions. In table 1, the specifications of the FMCW MIMO radar system are introduced within the following system specification range. In other words, our proposed method is applicable to various radars with multi-channels…’

Table 1. FMCW MIMO radar system specification

System Parameter	Value
Center Frequency Range	70-80GHz
Chirp signal Bandwidth	200-500MHz
PRF	3000-10000 Hz
Chirp Duration	100us-0.5ms
Sampling rate	< 10 Mbps
Total Channel	3 Tx / 4 Rx (12 channels)

 

 

Point 5:

In Fig. 7, the authors should revise the legend formats of the graph to clearly present the results of the proposed process.

 

Response:

We have also revised the legend in Figure 7 to avoid any confusion in interpreting the results.

[Please see page 12]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Point 6:

In Table 2, the detailed values of the noise level and channel difference should be added.

 

Response:

We have revised Table 2 to categorize the exact noise reduction levels and channel differences by radar objectives. The reduced noise level values are specified in the proposed method. Additionally, for the channel differences, the maximum magnitude difference for each method is indicated.

 

[Please see page 11]

Table 2. Processing performance comparison

	Noise Level		Channel Difference		Processing Complexity
	Front Radar	Corner Radar	Front Radar	Corner Radar
The conventional method	-	-			Low
The proposed method					Low

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Point 7:

The authors should recheck the format of this paper, including the reference section.

Response:

We have carefully reviewed and refined the formatting of the entire manuscript, including the reference section, in accordance with your valuable feedback.

*Formatting of the References & Re-ordering the reference’s numbers: We have rewritten it taking into account the journal's 'official referencing article format'.

[Please see the Section of ‘Reference’]

1. Hasirlioglu, S; Riener, A. Introduction to Rain and Fog Attenuation on Automotive Surround Sensors. In Proceedings of the 2017 IEEE 20th International Conference on Intelligent Transportation Systems, Yokohama, Japan, 16-19 October 2017, 1-7. 10.1109/ITSC.2017.8317823.
2. Roh, C.-G.; Kim, J.; Im, I.-J. Analysis of Impact of Rain Conditions on ADAS. Sensors2020, 20, 6720.3390/s20236720.
3. Schmid, M.; Pfeffer, C.; Feger R.; Stelzer A. An FMCW MIMO radar calibration and mutual coupling compensation approach. In Proceedings of the 2013 European Radar Conference, Nuremberg, Germany, 9-11 October 2013, 13-16.
4. Arnold, T.; Jensen, M. A. The Effect of Antenna Mutual Coupling on MIMO Radar System Performance. IEEE Trans. Antennas Propag. 2019, 67(3), 1410-1416. 10.1109/TAP.2018.2888702.
5. Vasanelli,; Batra, R.; Serio, A. D.; Boegelsack, F.; Waldschmidt C. Assessment of a Millimeter-Wave Antenna System for MIMO Radar Applications. IEEE Antennas Wirel. Propag. Lett. 2017, 16, 1261-1264. 10.1109/LAWP.2016.2631889.
6. Belfiori,; van Rossum, W.; Hoogeboom, P. Array calibration technique for a coherent MIMO radar. In Proceedings of the 2012 13th International Radar Symposium, Warsaw, Poland, 23-25 May 2012, 122-125. 10.1109/IRS.2012.6233301.
7. Liu, Y.; Xu,; Xu, G. MIMO Radar Calibration and Imagery for Near-Field Scattering Diagnosis. IEEE Trans. Aerosp. Electron. Syst. 2018. 54(1). 442-452. 10.1109/TAES.2017.2760758.
8. Tian,; Guo, Q.; Wang, Z.; Chang, T.; Cui, H. -L. Pragmatic Approach to Phase Self-Calibration for Planar Array Millimeter-Wave MIMO Imaging. IEEE Trans. Instrum. Meas. 2021, 70, 1-11. 10.1109/TIM.2020.3031167.
9. Zhang, Y. Gao and X. Liu, "Robust Channel Phase Error Calibration Algorithm for Multichannel High-Resolution and Wide-Swath SAR Imaging," in IEEE Geoscience and Remote Sensing Letters, vol. 14, no. 5, pp. 649-653, May 2017, doi: 10.1109/LGRS.2017.2668390.
10. Guo, Y. Gao, K. Wang and X. Liu, "Improved Channel Error Calibration Algorithm for Azimuth Multichannel SAR Systems," in IEEE Geoscience and Remote Sensing Letters, vol. 13, no. 7, pp. 1022-1026, July 2016, doi: 10.1109/LGRS.2016.2561961.
11. Pozar, D.M.; Microwave Engineering, 4th ; John Wiley & Sons Inc.: Hoboken, NJ, USA, 2012.
12. Gogineni,; Nehorai, A. Monopulse MIMO Radar for Target Tracking. IEEE Trans. Aerosp. Electron. Syst. 2011, 47(1), 755-768. 10.1109/TAES.2011.5705707.

 

* Figure and Table preparation method: To help the prospective readers understand, we have modified it to fit the format the author indicated. In other words, we have modified the picture to make it more clear and intuitive.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

No further comments.