Geostationary Orbital Targets Imaging Based on Ground-Based Multiple-Input Multiple-Output Radar

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a method for three-dimensional imaging of geosynchronous orbit satellites using ground-based MIMO radar. Its main contribution lies in analyzing the system's resolution performance through spatial spectrum and investigating applicable imaging methods. The topic of this work is of considerable importance. My detailed comments and suggestions are as follows:

1. It is recommended that the authors supplement the analysis of the system's spatial coverage. As the method requires deploying multiple ground observation stations, cost-effectiveness is a critical factor to consider.
2. In lines 100–102, the authors state that existing hardware schemes are used for synchronization. However, to my knowledge, such schemes still leave certain residual phase errors. Given that the resolution in this paper reaches 0.1 m, I think these errors are non-negligible. It is suggested to include an analysis of the impact of synchronization errors in the results.
3. Due to the scarcity of geosynchronous orbital resources, satellites are typically densely distributed. As noted by the authors in lines 131–139, grating lobe suppression is a key concern for such systems. However, in the simulations in Section 4, only a single-target scenario is considered, and the weighting process in Figure 12 primarily demonstrates sidelobe suppression. Further analysis of the impact and suppression of grating lobes in multi-target scenarios is recommended.
4. As shown in Figure 2, the ground-based MIMO radar has a long baseline. How have the authors accounted for the effects of baseline decorrelation? While the CST simulation in Section 4.3 may partially address this, there is a lack of explanation regarding specific parameters, especially the relative positional relationship between the radar and the target.
5. As illustrated in Figure 5, the proposed MIMO system has a large baseline span, which makes ionospheric effects and their compensation more complex. Unlike the slow-varying nature of ionospheric errors in SAR or ISAR, the two-way ionospheric paths in a long-baseline MIMO system are independent for transmission and reception. A discussion or clarification on this point is advised.

 

Additionally, there are several minor writing and formatting issues that should be addressed:

1. In the title, "Multipe-Input" should be corrected to "Multiple-Input."
2. Punctuation is missing at some figure captions. The authors are advised to consult the MDPI submission guidelines to standardize the formatting throughout the manuscript.
3. Some references are formatted incorrectly, such as the repetitive placeholders "Author 1, A.; Author 2, B" in References 1–3.

Author Response

Comment 1. It is recommended that the authors supplement the analysis of the system's spatial coverage. As the method requires deploying multiple ground observation stations, cost-effectiveness is a critical factor to consider."

 

Response 1: Thank you for this important suggestion. As requested, we have supplemented the manuscript with an analysis of the system's spatial coverage, which has been added at the end of Section 2.

This analysis examines the observational coverage of ground-based radar arrays for geostationary orbit (GEO) targets using a geometric model. We first establish a coverage calculation model in the equatorial plane (as shown in Figure ), deriving a maximum observable angle of 162.608° for a single radar station. The combined coverage of a linear array deployed along the equator is further analyzed, yielding a coverage angle of 149.1793° for a baseline length of 1500 km. Additionally, we extend the model to evaluate the coverage capability of radars at non-equatorial locations (different latitudes), as illustrated in Figure . Results show that even at high latitudes (e.g., φ = 60°), a single radar can still maintain an effective coverage of 144.5123°, and a multi-station array can achieve continuous observation of GEO targets through coverage intersection.

Comment 2. In lines 100–102, the authors state that existing hardware schemes are used for synchronization. However, to my knowledge, such schemes still leave certain residual phase errors. Given that the resolution in this paper reaches 0.1 m, I think these errors are non-negligible. It is suggested to include an analysis of the impact of synchronization errors in the results.

 

Response 2: Thank you for this important reminder. Your suggestion regarding the analysis of synchronization error impact on imaging is indeed crucial. Following your advice, we have supplemented the manuscript with simulation experiments on the influence of time synchronization errors. This content has been added as a new Section 4.1.5 “Analysis of the Impact of Synchronization Errors”. The main work is summarized as follows:

Based on conclusions from references [33-35]regarding synchronization performance in distributed MIMO radar—particularly the fiber-based time synchronization achieving TDEV < 32 ps/10 s and combined uncertainty < 89.6 ps over 13,134 km—we systematically investigated the effect of different time synchronization errors (standard deviations of 0.01–0.05 ns) on imaging quality across the Ka, Ku, and X frequency bands.

In the simulations, random time synchronization errors were added to the received signals. Point targets were imaged, and the Peak Sidelobe Ratio (PSLR) in azimuth was extracted. Results show that the Ka band exhibits noticeable defocusing when errors exceed 0.01 ns; the Ku band tolerates up to 0.02 ns. Imaging results and PSLR curves are presented in Figures 18 and 19, respectively.

 

Comment 3. Due to the scarcity of geosynchronous orbital resources, satellites are typically densely distributed. As noted by the authors in lines 131–139, grating lobe suppression is a key concern for such systems. However, in the simulations in Section 4, only a single-target scenario is considered, and the weighting process in Figure 12 primarily demonstrates sidelobe suppression. Further analysis of the impact and suppression of grating lobes in multi-target scenarios is recommended.

 

Response 3:Thank you for this important suggestion. Your comment regarding the analysis of grating lobe impact on imaging is indeed crucial. Following your advice, we have supplemented the manuscript with simulation experiments on the influence and suppression of grating lobes. This content has been added as a new Section 4.1.6 “Analysis of the Impact and Suppression of Grating Lobes”. The main work is summarized as follows:

We investigated the effect of the number and distribution of antenna elements on grating lobes in ground-based MIMO radar imaging. In the simulation, with a baseline length of 1500 km, imaging was conducted for uniform arrays with 100, 50, 40, 30, 20, and 10 antennas, respectively. The imaging area was extended to 30 × 30 m to accommodate typical satellite dimensions. Results show that as the number of antennas decreases, grating lobes gradually emerge in the azimuth dimension and move closer to the main lobe, confirming that sparse arrays may cause false targets in practical imaging.

Furthermore, we explored grating lobe suppression through antenna layout optimization. We compared the imaging results of equally spaced arrays and arrays distributed according to the Fibonacci sequence under identical imaging conditions. Simulations show that non-uniform layouts (e.g., Fibonacci distribution) can effectively reduce grating lobe levels. This provides a practical direction for balancing resolution and grating lobe suppression through array optimization.

 

Comment 4. As shown in Figure 2, the ground-based MIMO radar has a long baseline. How have the authors accounted for the effects of baseline decorrelation? While the CST simulation in Section 4.3 may partially address this, there is a lack of explanation regarding specific parameters, especially the relative positional relationship between the radar and the target.

 

Response 4: Thank you for your careful review. We apologize for the previously unclear description of the CST simulation parameters, which may have raised questions regarding the consideration of baseline decorrelation effects. The clarification is provided below:

In the CST simulation, the parameters are consistent with those described in Section 4.1: the target is centered relative to the array, the transmit antenna array length is 1500 km, and the corresponding Earth observation angle is 13.43°. According to Equation (3), the angular span of the ground-based array relative to the GEO target is only 2.38°. Although the system employs a long baseline of 1500 km, the angular extent of the array as viewed from the GEO target does not exceed 3°. This small angular span indicates that baseline decorrelation effects are negligible in this configuration.

 

Comment 5. As illustrated in Figure 5, the proposed MIMO system has a large baseline span, which makes ionospheric effects and their compensation more complex. Unlike the slow-varying nature of ionospheric errors in SAR or ISAR, the two-way ionospheric paths in a long-baseline MIMO system are independent for transmission and reception. A discussion or clarification on this point is advised.

 

Response 5: Thank you for this important suggestion. The distinctive impact of ionospheric effects in long-baseline MIMO systems that you pointed out is indeed crucial. We have supplemented the manuscript with simulation content on the analysis of ionospheric phase errors, which has been added as a new Section 4.1.7 “Analysis of Ionospheric Error Impact”.

Based on the International Reference Ionosphere (IRI) model , this section introduces ionospheric phase errors into the echo signals and evaluates the impact of different TEC residuals (0–10 TECU) on imaging quality. Simulations were conducted with a center frequency of 35 GHz, a baseline length of 3000 km, and a one-transmit-multiple-receive array configuration. Results show that as the TEC error increases from 0 to 10 TECU, the Peak Sidelobe Ratio (PSLR) in azimuth degrades by approximately 6 dB.We also note that existing compensation methods can control TEC residuals within 2 TECU, thereby effectively mitigating the loss in imaging performance.

 

 

Comment 6. Additionally, there are several minor writing and formatting issues that should be addressed:

1.In the title, "Multipe-Input" should be corrected to "Multiple-Input."

2.Punctuation is missing at some figure captions. The authors are advised to consult the MDPI submission guidelines to standardize the formatting throughout the manuscript.

3.Some references are formatted incorrectly, such as the repetitive placeholders "Author 1, A.; Author 2, B" in References 1–3.

 

Response 6:Thank you for your careful review and detailed corrections. We have corrected the title to “Multiple-Input.” All figure captions have been reviewed and punctuated according to MDPI guidelines. The reference list has been thoroughly revised, and placeholder entries have been replaced with complete citation information.

 

 

 

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes an imaging method for GEO targets based on ground-based Multiple-Input Multiple-Output (MIMO) radar, which combines multiple ground-based radars distributed across the Earth's surface to image GEO targets. Firstly, the ground-Based MIMO radar imaging scenario for GEO targets is introduced and azimuth resolution is analyzed, then a TDTO coordinate system is established, and Back projection imaging algorithm is used to image the target. Finally, the simulation results show that when the center frequency is 35GHz, and the baseline length is 1500km, azimuth resolution of the imaging is better than 0.1m. 

There are some comments as following.

1) There is no essential difference between the long-distance imaging scenario considered in this paper and the traditional MIMO short-distance imaging scenario. What is the essential difference in the consideration of imaging resolution under the two conditions? It is suggested that the paper should further emphasize and clarify this point in the abstract and introduction sections to highlight the research contributions of this paper.

2) In Sections 4.1.2 and 4.1.3, it is recommended to add target imaging results under different conditions, so as to more intuitively demonstrate the impact of varying conditions on imaging quality. For instance, an increase in antenna spacing may introduce the effect of grating lobes.

3) The simulation scenario setup for point targets is overly simplistic. What changes will occur in the imaging resolution when the point target is not aligned in the same azimuth as the array center?

4) It is recommended to supplement the distribution images of scattering points from different perspectives in Figure 15, as the currently provided single-perspective image makes it difficult to discern the detailed distribution of the scattering points.

5) Can the CST simulation in Section 4.3 and the numerical simulation in Section 4.2 be configured with the same target shape and radar parameters? In this way, the feasibility of the imaging algorithm can be verified simultaneously from two levels.

6) The simulation results presented in this paper correspond to only a single set of scenario parameters. To better verify the conclusions of the theoretical analysis, it is recommended to supplement the imaging results under different scenario parameters.

7) If convenient, could you supplement the comparison of imaging results obtained by different imaging algorithms?

Author Response

Comment 1. There is no essential difference between the long-distance imaging scenario considered in this paper and the traditional MIMO short-distance imaging scenario. What is the essential difference in the consideration of imaging resolution under the two conditions? It is suggested that the paper should further emphasize and clarify this point in the abstract and introduction sections to highlight the research contributions of this paper."

 

Response 1: Thank you for the suggestion. We agree with the reviewer that the imaging principle employed in this paper originates from conventional MIMO technology, and there is no fundamental difference in this regard.

The core contribution of this work lies in proposing and systematically investigating a novel imaging scenario: namely, how to achieve three-dimensional imaging of stationary Geostationary Orbit (GEO) targets by utilizing distributed radar resources on the Earth's surface. To address this unique scenario, we have accomplished the following pioneering work:

Established an imaging model constrained by Earth's geometry: Following valuable suggestions from another reviewer, we have, for the first time in this context, systematically incorporated Earth's curvature as a core physical constraint and explicitly derived the observable angular range for GEO targets, thereby clearly defining the theoretical performance bounds of the system.

Proposed a complete imaging processing framework: To handle the complex geometric relationships arising from global station deployment, we established a Three-Dimensional Target-Oriented (TDTO) coordinate system and provided a complete processing chain from echo modeling to image reconstruction.

Demonstrated the theoretical feasibility of this scenario for the first time: Through systematic simulation experiments (from point targets to full-wave electromagnetic simulation), we have provided the first proof that high-resolution 3D imaging of GEO targets using ground-based distributed MIMO radar is theoretically feasible under these constraints.

We will follow your advice to further emphasize the above points in the abstract and introduction of the manuscript, in order to more clearly highlight the paper's contribution in "defining a new scenario and verifying its feasibility".

 

Comment 2. In Sections 4.1.2 and 4.1.3, it is recommended to add target imaging results under different conditions, so as to more intuitively demonstrate the impact of varying conditions on imaging quality. For instance, an increase in antenna spacing may introduce the effect of grating lobes.

 

Response 2: Thank you very much for your suggestion to expand the simulations. We have added some target imaging results under different conditions, including resolution variation with azimuth angle in Section 4.1.2, Analysis of the Impact of Synchronization Errors in Section 4.1.5, analysis of the impact and suppression of grating lobes in Section 4.1.6, and analysis of the impact and ionospheric errors in Section 4.1.7.

In 4.1.6, we investigated the effect of the number and distribution of antenna elements on grating lobes in ground-based MIMO radar imaging. In the simulation, with a baseline length of 1500 km, imaging was conducted for uniform arrays with 100, 50, 40, 30, 20, and 10 antennas, respectively. The imaging area was extended to 30 × 30 m to accommodate typical satellite dimensions. Results show that as the number of antennas decreases, grating lobes gradually emerge in the azimuth dimension and move closer to the main lobe, confirming that sparse arrays may cause false targets in practical imaging.

Furthermore, we explored grating lobe suppression through antenna layout optimization. We compared the imaging results of equally spaced arrays and arrays distributed according to the Fibonacci sequence under identical imaging conditions. Simulations show that non-uniform layouts (e.g., Fibonacci distribution) can effectively reduce grating lobe levels. This provides a practical direction for balancing resolution and grating lobe suppression through array optimization.

 

Comment 3. The simulation scenario setup for point targets is overly simplistic. What changes will occur in the imaging resolution when the point target is not aligned in the same azimuth as the array center?

 

Response 3: Thank you for your suggestion, which helps enhance the comprehensiveness of the simulations. We have added some point target imaging results under different azimuth angles in Section 4.1.2.The main additions are summarized as follows:

The antenna array configuration is the same as in Section 4.1.1, with the latitudes of array centers being 0°, 10°, 20°, 30°, 40° and 50° respectively. Resolutions at different azimuth angles were simulated, and the range resolution and azimuth resolutions are depicted in Figure 15 .

Note that the X-axis of TDTO coordinate system is always pointing towards the center of the target. When the target is directly aligned with the center of the array, the azimuth and range directions generated by the array are perpendicular. However, when the target deviates from the center of the array, the azimuth and range directions are no longer perpendicular. At this time, the range direction remains pointing from the geocenter towards the target, while the azimuth direction is perpendicular to the range direction, but not necessarily perpendicular to the distribution of the antenna array. Therefore, as shown in Figure 15, when the deviation angle is not large, the resolution in the range direction does not differ significantly from that when directly aligned, while the azimuth direction exhibits periodic changes with changes in angle, but the value of azimuth resolution changes slightly. Simulation results show that when the point target is not aligned in the same azimuth as the array center, it can still be imaged while maintaining good azimuth and range resolutions.

Comment 4. It is recommended to supplement the distribution images of scattering points from different perspectives in Figure 15, as the currently provided single-perspective image makes it difficult to discern the detailed distribution of the scattering points.

 

Response 4: Thank you for your suggestion on image presentation. We have supplemented its optical image to emphasize this point. As depicted in Figure Based on this optical image, we can imagine its images from different perspectives.

 

Comment 5. Can the CST simulation in Section 4.3 and the numerical simulation in Section 4.2 be configured with the same target shape and radar parameters? In this way, the feasibility of the imaging algorithm can be verified simultaneously from two levels.

 

Response 5: Thank you for your constructive suggestion. We have unified the target model and radar parameters between Sections 4.2 and 4.3. Both now use the GOES satellite model with identical imaging parameters, enabling direct comparison between ideal scatter-point simulation and CST-based electromagnetic simulation.

 

Comment 6. The simulation results presented in this paper correspond to only a single set of scenario parameters. To better verify the conclusions of the theoretical analysis, it is recommended to supplement the imaging results under different scenario parameters.

 

Response 6: Thank you very much for your suggestion, which helps strengthen the persuasiveness of the research. We have supplemented some imaging results under different scenario parameters, besides different scenario in section 4.2. CST simulation with different azimuth angle, and different transmitting signal frequency was performed.

Comment 7. If convenient, could you supplement the comparison of imaging results obtained by different imaging algorithms?

 

Response 7: Thank you for suggesting the algorithm comparison.

Traditional SAR and MIMO imaging algorithms can be divided into time-domain algorithms and frequency-domain algorithms. Time-domain algorithms, such as the Back Projection Algorithm (BPA), are applicable to arrays of any configuration. Range Migration Algorithm (RMA), Chirp Scaling Algorithm (CSA) and Range-Doppler Algorithm (RDA) are frequency-domain algorithms.

The premise for the application of frequency-domain methods is that the target is uniformly sampled in the spatial domain. In this paper, the arrays are not uniformly sampled, which does not meet the application conditions of frequency-domain methods. Therefore, the comparison of imaging results obtained by different imaging algorithms is not easy to accomplish. However, to compare the frequency domain imaging algorithm and the time domain algorithm used in this paper, we designed a MIMO antenna as shown in the figure below, where the transmitting antennas are vertically distributed and the receiving antennas are horizontally distributed.

Author Response File: Author Response.pdf